Finite Group Databasebeta

← #33300225

Subgroups — #33300225

Order 18688.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618322C211yesmaximal, characteristic, complemented
2#22618314C211yesmaximal, characteristic, complemented
3#22617845C211yesmaximal, characteristic, complemented
4#22617833C211yesmaximal, characteristic, complemented
5#22617536C211yesmaximal, characteristic, complemented
6#22617452C211yesmaximal, characteristic, complemented
7#22617384C211yesmaximal, characteristic, complemented
8#22617372C211yesmaximal, characteristic, complemented
9#22617320C211yesmaximal, characteristic, complemented
10#22617178C211yesmaximal, characteristic, complemented
11#22617178C211yesmaximal, characteristic, complemented
12#22617156C211yesmaximal, characteristic
13#22617012C211yesmaximal, characteristic, complemented
14#22616990C211yesmaximal, characteristic, complemented
15#22616910C211yesmaximal, characteristic, complemented
16#22616753C211yesmaximal, characteristic, complemented
17#22616346C211yesmaximal, characteristic, complemented
18#22615989C211yesmaximal, characteristic, complemented
19#22615982C211yesmaximal, characteristic, complemented
20#22615536C211yesmaximal, characteristic
21#22615365C211yesmaximal, characteristic, complemented
22#22615277C211yesmaximal, characteristic, complemented
23#22615221C211yesmaximal, characteristic, complemented
24#22614143C211yesmaximal, characteristic, complemented
25#22614133C211yesmaximal, characteristic, complemented
26#22613617C211yesmaximal, characteristic, complemented
27#22613334C211yesmaximal, characteristic, complemented
28#22612718C211yesmaximal, characteristic, complemented
29#22612533C211yesmaximal, characteristic, complemented
30#22612393C211yesmaximal, characteristic, complemented
31C73×#2705C211yesmaximal, characteristic
32C2×#14556590C2211yescharacteristic
33C2×#14556572C2211yescharacteristic
34C2×#14556568C2211yescharacteristic
35C2×D4×Dic73C2211yescharacteristic
36C2×#14556547C2211yescharacteristic
37C2×#14556547C2211yescharacteristic
38C22×#11924007C2211yescharacteristic
39C73⋊#401C2211yescharacteristic
40#17988529C2211yescharacteristic
41#17988529C2211yescharacteristic
42#17988528C2211yescharacteristic
43#17988526C2211yescharacteristic
44#17988526C2211yescharacteristic
45#17988526C2211yescharacteristic
46#17988525C2211yescharacteristic
47#17988525C2211yescharacteristic
48#17988521C2211yescharacteristic
49#17988521C2211yescharacteristic
50#17988520C2211yescharacteristic
51#17988520C2211yescharacteristic
52#17988519C2211yescharacteristic
53#17988518C2211yescharacteristic
54#17988518C2211yescharacteristic
55#17988518C2211yescharacteristic
56#17988518C2211yescharacteristic
57#17988515C2211yescharacteristic
58#17988515C2211yescharacteristic
59#17988515C2211yescharacteristic
60#17988515C2211yescharacteristic
61#17988515C2211yescharacteristic
62#17988512C2211yescharacteristic
63#17988512C2211yescharacteristic
64#17988512C2211yescharacteristic
65#17988512C2211yescharacteristic
66#17988512C2211yescharacteristic
67#17988510C2211yescharacteristic
68#17988510C2211yescharacteristic
69#17988510C2211yescharacteristic
70#17988510C2211yescharacteristic
71#17988510C2211yescharacteristic
72#17988508C2211yescharacteristic
73#17988501C2211yescharacteristic
74#17988501C2211yescharacteristic
75#17988501C2211yescharacteristic
76#17988499C2211yescharacteristic
77#17988499C2211yescharacteristic
78#17988499C2211yescharacteristic
79#17988499C2211yescharacteristic
80#17988499C2211yescharacteristic
81#17988493C2211yescharacteristic
82#17988493C2211yescharacteristic
83#17988492C2211yescharacteristic
84#17988492C2211yescharacteristic
85#17988491C2211yescharacteristic
86#17988490C2211yescharacteristic
87#17988490C2211yescharacteristic
88#17988486C2211yescharacteristic
89#17988485C2211yescharacteristic
90#17988484C2211yescharacteristic
91#17988483C2211yescharacteristic
92#17988483C2211yescharacteristic
93#17988483C2211yescharacteristic
94#17988482C2211yescharacteristic
95#17988482C2211yescharacteristic
96#17988482C2211yescharacteristic
97#17988482C2211yescharacteristic
98#17988481C2211yescharacteristic
99#17988481C2211yescharacteristic
100#17988481C2211yescharacteristic
101#17988481C2211yescharacteristic
102#17988480C2211yescharacteristic
103#17988480C2211yescharacteristic
104#17988480C2211yescharacteristic
105#17988480C2211yescharacteristic
106#17988480C2211yescharacteristic
107#17988475C2211yescharacteristic
108#17988475C2211yescharacteristic
109#17988475C2211yescharacteristic
110#17988475C2211yescharacteristic
111#17988475C2211yescharacteristic
112#17988475C2211yescharacteristic
113#17988475C2211yescharacteristic
114#17988475C2211yescharacteristic
115#17988475C2211yescharacteristic
116#17988474C2211yescharacteristic
117#17988474C2211yescharacteristic
118#17988474C2211yescharacteristic
119#17988474C2211yescharacteristic
120#17988474C2211yescharacteristic
121#17988474C2211yescharacteristic
122#17988473C2211yescharacteristic
123#17988473C2211yescharacteristic
124#17988473C2211yescharacteristic
125#17988473C2211yescharacteristic
126#17988473C2211yescharacteristic
127#17988472C2211yescharacteristic
128#17988471C2211yescharacteristic
129#17988471C2211yescharacteristic
130#17988471C2211yescharacteristic
131#17988470C2211yescharacteristic
132#17988470C2211yescharacteristic
133#17988470C2211yescharacteristic
134#17988469C2211yescharacteristic
135#17988468C2211yescharacteristic
136#17988468C2211yescharacteristic
137#17988468C2211yescharacteristic
138#17988468C2211yescharacteristic
139#17988468C2211yescharacteristic
140#17988468C2211yescharacteristic
141#17988468C2211yescharacteristic
142#17988467C2211yescharacteristic
143#17988467C2211yescharacteristic
144#17988467C2211yescharacteristic
145#17988467C2211yescharacteristic
146#17988467C2211yescharacteristic
147#17988462C2211yescharacteristic
148#17988462C2211yescharacteristic
149#17988462C2211yescharacteristic
150#17988460C2211yescharacteristic
151#17988459C2211yescharacteristic
152#17988459C2211yescharacteristic
153#17988459C2211yescharacteristic
154#17988459C2211yescharacteristic
155#17988454C2211yescharacteristic
156#17988454C2211yescharacteristic
157#17988452C2211yescharacteristic
158#17988451C2211yescharacteristic
159#17988450C2211yescharacteristic
160#17988448C2211yescharacteristic
161#17988448C2211yescharacteristic
162#17988448C2211yescharacteristic
163#17988447C2211yescharacteristic
164#17988445C2211yescharacteristic
165C4⋊C4×Dic73C2211yescharacteristic
166C4×#11924007C2211yescharacteristic
167C22⋊C4×Dic73C2211yescharacteristic
168C22⋊C4×Dic73C2211yescharacteristic
169C22⋊C4×Dic73C2211yescharacteristic
170C22⋊C4×Dic73C2211yescharacteristic
171C42×Dic73C2211yescharacteristic
172C2×#126×C73C2211yescharacteristic
173C2×#123×C73C2211yescharacteristic
174#399×C73C2211yescharacteristic
175#396×C73C2211yescharacteristic
176#396×C73C2211yescharacteristic
177#394×C73C2211yescharacteristic
178#394×C73C2211yescharacteristic
179#392×C73C2211yescharacteristic
180#390×C73C2211yescharacteristic
181#390×C73C2211yescharacteristic
182#389×C73C2211yescharacteristic
183#388×C73C2211yescharacteristic
184#387×C73C2211yescharacteristic
185#386×C73C2211yescharacteristic
186#380×C73C2211yescharacteristic
187C22×Dic146C2311yescharacteristic
188C22×Dic146C2311yescharacteristic
189C23×Dic73C2311yescharacteristic
190C23×Dic73C2311yescharacteristic
191C23×Dic73C2311yescharacteristic
192C23×Dic73C2311yescharacteristic
193#14556590—42no—
194#14556572—24no—
195#14556568—42no—
196D4×Dic73—24no—
197#14556547—42no—
198#14556547—42no—
199C2×C4⋊Dic73C2311yescharacteristic
200C2×C4⋊Dic73C2311yescharacteristic
201C2×C4⋊Dic73C2311yescharacteristic
202C2×C4⋊Dic73C2311yescharacteristic
203C2×C4⋊Dic73C2311yescharacteristic
204C2×C4⋊Dic73C2311yescharacteristic
205C2×C4⋊Dic73C2311yescharacteristic
206C2×C4⋊Dic73C2311yescharacteristic
207C2×C4⋊Dic73C2311yescharacteristic
208C2×C4⋊Dic73C2311yescharacteristic
209C2×#11924007—24no—
210C2×#11924007C2311yescharacteristic
211C2×#11924007C2311yescharacteristic
212C2×#11924007C2311yescharacteristic
213C2×#11924007C2311yescharacteristic
214C2×#11924007C2311yescharacteristic
215C2×#11924007C2311yescharacteristic
216C2×#11924007C2311yescharacteristic
217C2×#11924007C2311yescharacteristic
218C2×#11924007C2311yescharacteristic
219C2×#11924007C2311yescharacteristic
220C2×#11924007C2311yescharacteristic
221C2×#11924007C2311yescharacteristic
222C2×#11924007C2311yescharacteristic
223C2×#11924007C2311yescharacteristic
224C2×#11924007C2311yescharacteristic
225C2×#11924007C2311yescharacteristic
226C2×#11924007C2311yescharacteristic
227C2×#11924007C2311yescharacteristic
228C2×#11924007C2311yescharacteristic
229C2×#11924007C2311yescharacteristic
230C2×C22⋊Dic73C2311yescharacteristic
231C2×C22⋊Dic73C2311yescharacteristic
232C2×C22⋊Dic73C2311yescharacteristic
233C2×C22⋊Dic73C2311yescharacteristic
234C2×C22⋊Dic73C2311yescharacteristic
235C2×C22⋊Dic73C2311yescharacteristic
236C2×C22⋊Dic73C2311yescharacteristic
237C2×C22⋊Dic73C2311yescharacteristic
238C2×C22⋊Dic73C2311yescharacteristic
239C2×C22⋊Dic73C2311yescharacteristic
240C2×C22⋊Dic73C2311yescharacteristic
241C2×C22⋊Dic73C2311yescharacteristic
242C2×C22⋊Dic73C2311yescharacteristic
243C2×C22⋊Dic73C2311yescharacteristic
244C2×C22⋊Dic73C2311yescharacteristic
245C2×C22⋊Dic73C2311yescharacteristic
246C2×C22⋊Dic73C2311yescharacteristic
247C2×C22⋊Dic73C2311yescharacteristic
248C2×C22⋊Dic73C2311yescharacteristic
249C2×C22⋊Dic73C2311yescharacteristic
250C2×C4×Dic73C2311yescharacteristic
251C2×C4×Dic73C2311yescharacteristic
252C2×C4×Dic73C2311yescharacteristic
253C2×C4×Dic73C2311yescharacteristic
254C2×C4×Dic73C2311yescharacteristic
255C2×C4×Dic73C2311yescharacteristic
256C2×C4×Dic73C2311yescharacteristic
257C2×C4×Dic73C2311yescharacteristic
258C2×C4×Dic73C2311yescharacteristic
259C2×C4×Dic73C2311yescharacteristic
260C2×C4×Dic73C2311yescharacteristic
261C2×C4×Dic73C2311yescharacteristic
262#14556498C2311yescharacteristic
263#14556498C2311yescharacteristic
264#14556498C2311yescharacteristic
265#14556498C2311yescharacteristic
266#14556498C2311yescharacteristic
267#14556498C2311yescharacteristic
268#14556498C2311yescharacteristic
269#14556498C2311yescharacteristic
270#14556498C2311yescharacteristic
271#14556498C2311yescharacteristic
272#14556498C2311yescharacteristic
273#14556498C2311yescharacteristic
274#14556498C2311yescharacteristic
275#14556498C2311yescharacteristic
276#14556498C2311yescharacteristic
277#14556498C2311yescharacteristic
278#14556498C2311yescharacteristic
279#14556498C2311yescharacteristic
280#14556498C2311yescharacteristic
281#14556498C2311yescharacteristic
282#14556498C2311yescharacteristic
283#14556498C2311yescharacteristic
284#14556498C2311yescharacteristic
285#14556498C2311yescharacteristic
286#14556498C2311yescharacteristic
287#14556498C2311yescharacteristic
288#14556498C2311yescharacteristic
289#14556498C2311yescharacteristic
290#14556498C2311yescharacteristic
291#14556498C2311yescharacteristic
292#14556498C2311yescharacteristic
293#14556498C2311yescharacteristic
294#14556498C2311yescharacteristic
295#14556498C2311yescharacteristic
296#14556498C2311yescharacteristic
297#14556498C2311yescharacteristic
298#14556498C2311yescharacteristic
299#14556498C2311yescharacteristic
300#14556498C2311yescharacteristic
301#14556498C2311yescharacteristic
302#14556498C2311yescharacteristic
303#14556498C2311yescharacteristic
304#14556498C2311yescharacteristic
305#14556498C2311yescharacteristic
306#14556498C2311yescharacteristic
307#14556498C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314C22×D4×C73C2311yescharacteristic
315C22×D4×C73C2311yescharacteristic
316C22×D4×C73C2311yescharacteristic
317C23×C4×C73C2311yescharacteristic
318#126×C73—42no—
319#123×C73—42no—
320C2×C4⋊C4×C73C2311yescharacteristic
321C2×C4⋊C4×C73C2311yescharacteristic
322C2×C4⋊C4×C73C2311yescharacteristic
323C2×C4⋊C4×C73C2311yescharacteristic
324C2×C4⋊C4×C73C2311yescharacteristic
325C2×C4⋊C4×C73C2311yescharacteristic
326C2×C4⋊C4×C73C2311yescharacteristic
327C2×C4⋊C4×C73C2311yescharacteristic
328C2×C4⋊C4×C73C2311yescharacteristic
329C2×C22⋊C4×C73C2311yescharacteristic
330C2×C22⋊C4×C73C2311yescharacteristic
331C2×C22⋊C4×C73C2311yescharacteristic
332C2×C22⋊C4×C73C2311yescharacteristic
333C2×C22⋊C4×C73C2311yescharacteristic
334C2×C22⋊C4×C73C2311yescharacteristic
335C2×C22⋊C4×C73C2311yescharacteristic
336C2×C22⋊C4×C73C2311yescharacteristic
337C2×C22⋊C4×C73C2311yescharacteristic
338C2×C22⋊C4×C73C2311yescharacteristic
339C2×C22⋊C4×C73C2311yescharacteristic
340C2×C22⋊C4×C73C2311yescharacteristic
341C2×C22⋊C4×C73C2311yescharacteristic
342C2×C22⋊C4×C73C2311yescharacteristic
343C2×C42×C73C2311yescharacteristic
344C2×C42×C73C2311yescharacteristic
345#95×C73C2311yescharacteristic
346#95×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×C73C2311yescharacteristic
351C2×Dic146—22no—
352C2×Dic146—41no—
353C2×Dic146—41no—
354C2×Dic146—41no—
355C2×Dic146—41no—
356C2×Dic146—41no—
357C22×Dic73—22no—
358C22×Dic73—22no—
359C22×Dic73—41no—
360C22×Dic73—41no—
361C22×Dic73—41no—
362C22×Dic73—41no—
363C22×Dic73—41no—
364C22×Dic73—41no—
365C22×Dic73—41no—
366C22×Dic73—41no—
367C22×Dic73—41no—
368C22×Dic73#4114yes—
369C22×Dic73C2411yescharacteristic
370C22×Dic73C2411yescharacteristic
371C22×Dic73C2411yescharacteristic
372C22×Dic73C2411yescharacteristic
373C22×Dic73C2411yescharacteristic
374C22×Dic73C2411yescharacteristic
375C22×Dic73C2411yescharacteristic
376C22×Dic73C2411yescharacteristic
377C22×Dic73C2411yescharacteristic
378C22×Dic73C2411yescharacteristic
379C22×Dic73C2411yescharacteristic
380C22×Dic73C2411yescharacteristic
381C22×Dic73C2411yescharacteristic
382C22×Dic73C2411yescharacteristic
383C22×Dic73C2411yescharacteristic
384C22×Dic73C2411yescharacteristic
385C4⋊Dic73—22no—
386C4⋊Dic73—41no—
387C4⋊Dic73—41no—
388C4⋊Dic73—41no—
389C4⋊Dic73—41no—
390C4⋊Dic73—41no—
391C4⋊Dic73—41no—
392C4⋊Dic73—41no—
393C4⋊Dic73—41no—
394C4⋊Dic73—41no—
395#11924007—22no—
396#11924007—22no—
397#11924007—22no—
398#11924007—22no—
399#11924007—22no—
400#11924007—22no—
401#11924007—22no—
402#11924007—22no—
403#11924007—22no—
404#11924007—41no—
405#11924007—41no—
406#11924007—41no—
407#11924007—41no—
408#11924007—41no—
409#11924007—41no—
410#11924007—41no—
411#11924007—41no—
412#11924007—41no—
413#11924007—41no—
414#11924007—41no—
415C22⋊Dic73—22no—
416C22⋊Dic73—22no—
417C22⋊Dic73—22no—
418C22⋊Dic73—22no—
419C22⋊Dic73—22no—
420C22⋊Dic73—41no—
421C22⋊Dic73—41no—
422C22⋊Dic73—41no—
423C22⋊Dic73—41no—
424C22⋊Dic73—41no—
425C22⋊Dic73—41no—
426C22⋊Dic73—41no—
427C22⋊Dic73—41no—
428C22⋊Dic73—41no—
429C22⋊Dic73—41no—
430C22⋊Dic73—41no—
431C22⋊Dic73—41no—
432C22⋊Dic73—41no—
433C22⋊Dic73—41no—
434C22⋊Dic73—41no—
435C4×Dic73—22no—
436C4×Dic73—22no—
437C4×Dic73—22no—
438C4×Dic73—41no—
439C4×Dic73—41no—
440C4×Dic73—41no—
441C4×Dic73—41no—
442C4×Dic73—41no—
443C4×Dic73—41no—
444C4×Dic73—41no—
445C4×Dic73—41no—
446C4×Dic73—41no—
447C24×C73C2411yescharacteristic
448C24×C73C2411yescharacteristic
449C24×C73C2411yescharacteristic
450C2×D4×C73—22no—
451C2×D4×C73—22no—
452C2×D4×C73—22no—
453C2×D4×C73—41no—
454C2×D4×C73—41no—
455C2×D4×C73—41no—
456C2×D4×C73—41no—
457C2×D4×C73—41no—
458C2×D4×C73—41no—
459C22×C4×C73—22no—
460C22×C4×C73—41no—
461C22×C4×C73—41no—
462C22×C4×C73C2411yescharacteristic
463C22×C4×C73C2411yescharacteristic
464C22×C4×C73C2411yescharacteristic
465C22×C4×C73C2411yescharacteristic
466C22×C4×C73C2411yescharacteristic
467C22×C4×C73C2411yescharacteristic
468C22×C4×C73C2411yescharacteristic
469C22×C4×C73C2411yescharacteristic
470C22×C4×C73C2411yescharacteristic
471C22×C4×C73C2411yescharacteristic
472C22×C4×C73C2411yescharacteristic
473C22×C4×C73C2411yescharacteristic
474C4⋊C4×C73—22no—
475C4⋊C4×C73—22no—
476C4⋊C4×C73—22no—
477C4⋊C4×C73—41no—
478C4⋊C4×C73—41no—
479C4⋊C4×C73—41no—
480C4⋊C4×C73—41no—
481C4⋊C4×C73—41no—
482C4⋊C4×C73—41no—
483C22⋊C4×C73—22no—
484C22⋊C4×C73—22no—
485C22⋊C4×C73—22no—
486C22⋊C4×C73—22no—
487C22⋊C4×C73—41no—
488C22⋊C4×C73—41no—
489C22⋊C4×C73—41no—
490C22⋊C4×C73—41no—
491C22⋊C4×C73—41no—
492C22⋊C4×C73—41no—
493C22⋊C4×C73—41no—
494C22⋊C4×C73—41no—
495C22⋊C4×C73—41no—
496C22⋊C4×C73—41no—
497C42×C73—41no—
498C42×C73—41no—
499C23×C73—21no—
500C23×C73—21no—
501C23×C73—21no—
502C23×C73—21no—
503C23×C73—21no—
504C23×C73—21no—
505C23×C73—21no—
506C23×C73—21no—
507C23×C73—21no—
508C23×C73—21no—
509C23×C73—21no—
510C23×C73—21no—
511C23×C73—21no—
512C23×C73—21no—
513C23×C73—21no—
514C23×C73—21no—
515C23×C73—21no—
516C23×C73—21no—
517C23×C73—21no—
518C23×C73—21no—
519C23×C73C2×#4112yes—
520C23×C73C2511yescharacteristic
521D4×C73—44no—
522D4×C73—82no—
523D4×C73—82no—
524C2×C4×C73—21no—
525C2×C4×C73—21no—
526C2×C4×C73—21no—
527C2×C4×C73—21no—
528C2×C4×C73—21no—
529C2×C4×C73—21no—
530C2×C4×C73—21no—
531C2×C4×C73—21no—
532C2×C4×C73—21no—
533C2×C4×C73—21no—
534C2×C4×C73—21no—
535C2×C4×C73—21no—
536C2×C4×C73—21no—
537C2×C4×C73—21no—
538C2×C4×C73—21no—
539C2×C4×C73—21no—
540C2×C4×C73—21no—
541C2×C4×C73—21no—
542C2×C4×C73—21no—
543C2×C4×C73—21no—
544C2×C4×C73—21no—
545C2×C4×C73—21no—
546C2×C4×C73—21no—
547C2×C4×C73—21no—
548C2×C4×C73—21no—
549C2×C4×C73—21no—
550C2×C4×C73—21no—
551C2×C4×C73—21no—
552C2×C4×C73—21no—
553C2×C4×C73—21no—
554C2×C4×C73—21no—
555C2×C4×C73—21no—
556C2×C4×C73—21no—
557C2×C4×C73—21no—
558C2×C4×C73—82no—
559C2×C4×C73H(5,𝔽2)12yes—
560C2×C4×C732−1+412yes—
561C2×Dic73—21no—
562C2×Dic73—21no—
563C2×Dic73—21no—
564C2×Dic73—21no—
565C2×Dic73—21no—
566C2×Dic73—21no—
567C2×Dic73—21no—
568C2×Dic73—21no—
569C2×Dic73—21no—
570C2×Dic73—21no—
571C2×Dic73—21no—
572C2×Dic73—21no—
573C2×Dic73—21no—
574C2×Dic73—21no—
575C2×Dic73—21no—
576C2×Dic73—21no—
577C2×Dic73—21no—
578C2×Dic73—21no—
579C2×Dic73—21no—
580C2×Dic73—21no—
581C2×Dic73—21no—
582C2×Dic73—21no—
583C2×Dic73—21no—
584C2×Dic73—21no—
585C2×Dic73—21no—
586C2×Dic73—21no—
587C2×Dic73—21no—
588C2×Dic73—21no—
589C2×Dic73—21no—
590C2×Dic73—21no—
591C2×Dic73—21no—
592C2×Dic73—21no—
593C2×Dic73—21no—
594C2×Dic73—21no—
595C2×Dic73—21no—
596C2×Dic73—21no—
597C2×Dic73—21no—
598C2×Dic73—21no—
599C2×Dic73—21no—
600C2×Dic73—21no—
601C2×Dic73—21no—
602C2×Dic73—21no—
603C2×Dic73—21no—
604C2×Dic73—21no—
605C2×Dic73—21no—
606C2×Dic73—21no—
607C2×Dic73—44no—
608C2×Dic73—44no—
609C2×Dic73—44no—
610C2×Dic73—82no—
611C2×Dic73C2×#4112yes—
612C2×Dic73C2×#4112yes—
613Dic146—82no—
614Dic146—82no—
615C22×C73—22no—
616C22×C73—22no—
617C22×C73—22no—
618C22×C73—41no—
619C22×C73—41no—
620C22×C73—41no—
621C22×C73—41no—
622C22×C73—41no—
623C22×C73—41no—
624C22×C73—41no—
625C22×C73—41no—
626C22×C73—41no—
627C22×C73—41no—
628C22×C73—41no—
629C22×C73—41no—
630C22×C73—41no—
631C22×C73—41no—
632C22×C73—41no—
633C22×C73—41no—
634C22×C73—41no—
635C22×C73—41no—
636C22×C73C22×#4111yescharacteristic
637C22×C73C2×H(5,𝔽2)11yescharacteristic
638C22×C73C2×2−1+411yescharacteristic
639C22×C73#58511yescharacteristic
640C22×C73#58511yescharacteristic
641C22×C73#58511yescharacteristic
642C22×C73#58511yescharacteristic
643C4×C73—22no—
644C4×C73—22no—
645C4×C73—41no—
646C4×C73—41no—
647C4×C73—41no—
648C4×C73—41no—
649C4×C73—41no—
650C4×C73—41no—
651C4×C73—41no—
652C4×C73—41no—
653C4×C73—41no—
654C4×C73—41no—
655Dic73—22no—
656Dic73—22no—
657Dic73—41no—
658Dic73—41no—
659Dic73—41no—
660Dic73—41no—
661Dic73—41no—
662Dic73—41no—
663Dic73—41no—
664Dic73—41no—
665Dic73—41no—
666Dic73—41no—
667Dic73—41no—
668Dic73—41no—
669Dic73—41no—
670Dic73—41no—
671#36989—731nomaximal, Sylow
672C2×C73—42no—
673C2×C73—81no—
674C2×C73—81no—
675C2×C73#345511yescharacteristic
676C2×C73#349511yescharacteristic
677C2×C73#350511yescharacteristic
678C2×C73#355411yescharacteristic
679C2×C73#356011yescharacteristic
680C2×C73#356511yescharacteristic
681C2×C73#356611yescharacteristic
682#2866—731no—
683#2863—731no—
684#2802—731no—
685#2800—731no—
686#2777—731no—
687#2772—731no—
688#2766—731no—
689#2765—731no—
690#2761—731no—
691#2751—731no—
692#2751—731no—
693#2749—731no—
694#2739—731no—
695#2737—731no—
696#2729—731no—
697#2716—731no—
698#2705D7311yescharacteristic
699#2687—731no—
700#2653—731no—
701#2652—731no—
702#2602—731no—
703#2588—731no—
704#2579—731no—
705#2575—731no—
706#2478—731no—
707#2477—731no—
708#2439—731no—
709#2413—731no—
710#2335—731no—
711#2313—731no—
712#2293—731no—
713C73#3698911yescharacteristic, complemented, Sylow
714C2×C4⋊Q8—731no—
715C2×#126C2×D7311yescharacteristic
716C2×#123—731no—
717C2×#123C2×D7311yescharacteristic
718C2×C22⋊Q8—731no—
719C2×C4×D4—731no—
720C2×#117—731no—
721C2×#117—731no—
722C22×C4⋊C4—731no—
723#401—731no—
724#400—731no—
725#400—731no—
726#400—731no—
727#400—731no—
728#400—731no—
729#400—731no—
730#400—731no—
731#400—731no—
732#399C2×D7311yescharacteristic
733#398—731no—
734#398—731no—
735#398—731no—
736#398—731no—
737#398—731no—
738#398—731no—
739#398—731no—
740#398—731no—
741#398—731no—
742#397—731no—
743#397—731no—
744#397—731no—
745#397—731no—
746#397—731no—
747#397—731no—
748#397—731no—
749#397—731no—
750#397—731no—
751#397—731no—
752#396—731no—
753#396—731no—
754#396—731no—
755#396—731no—
756#396—731no—
757#396C2×D7311yescharacteristic
758#396C2×D7311yescharacteristic
759#395—731no—
760#394—731no—
761#394—731no—
762#394—731no—
763#394C2×D7311yescharacteristic
764#394C2×D7311yescharacteristic
765#393—731no—
766#393—731no—
767#393—731no—
768#393—731no—
769#393—731no—
770#392C2×D7311yescharacteristic
771#391—731no—
772#391—731no—
773#391—731no—
774#391—731no—
775#391—731no—
776#390—731no—
777#390—731no—
778#390C2×D7311yescharacteristic
779#390C2×D7311yescharacteristic
780#389—731no—
781#389—731no—
782#389—731no—
783#389—731no—
784#389—731no—
785#389—731no—
786#389—731no—
787#389—731no—
788#389—731no—
789#389—731no—
790#389C2×D7311yescharacteristic
791#388—731no—
792#388—731no—
793#388—731no—
794#388—731no—
795#388—731no—
796#388—731no—
797#388—731no—
798#388—731no—
799#388—731no—
800#388—731no—
801#388—731no—
802#388—731no—
803#388—731no—
804#388—731no—
805#388—731no—
806#388—731no—
807#388—731no—
808#388—731no—
809#388C2×D7311yescharacteristic
810#387—731no—
811#387—731no—
812#387—731no—
813#387—731no—
814#387—731no—
815#387—731no—
816#387—731no—
817#387—731no—
818#387—731no—
819#387—731no—
820#387—731no—
821#387—731no—
822#387—731no—
823#387—731no—
824#387—731no—
825#387—731no—
826#387—731no—
827#387—731no—
828#387—731no—
829#387—731no—
830#387—731no—
831#387—731no—
832#387—731no—
833#387—731no—
834#387—731no—
835#387—731no—
836#387C2×D7311yescharacteristic
837#386—731no—
838#386—731no—
839#386—731no—
840#386—731no—
841#386—731no—
842#386C2×D7311yescharacteristic
843#385—731no—
844#385—731no—
845#385—731no—
846#385—731no—
847#385—731no—
848#385—731no—
849#385—731no—
850#385—731no—
851#383—731no—
852#383—731no—
853#382—731no—
854#382—731no—
855#381—731no—
856#381—731no—
857#381—731no—
858#381—731no—
859#380—731no—
860#380—731no—
861#380C2×D7311yescharacteristic
862C4×C4⋊C4—731no—
863C4×C4⋊C4—731no—
864C4×C22⋊C4—731no—
865C4×C22⋊C4—731no—
866C4×C22⋊C4—731no—
867C4×C22⋊C4—731no—
868C43—731no—
869C22×Q8—731no—
870C22×Q8—731no—
871C22×D4C22×D7311yescharacteristic
872C22×D4C22×D7311yescharacteristic
873C22×D4C22×D7311yescharacteristic
874C23×C4—731no—
875C23×C4—731no—
876C23×C4—731no—
877C23×C4—731no—
878C23×C4C22×D7311yescharacteristic
879C4⋊Q8—2922no—
880#126—42no—
881#123—42no—
882#123—1464no—
883C22⋊Q8—2922no—
884C4×D4—1464no—
885#117—2922no—
886#117—2922no—
887C2×C4⋊C4—731no—
888C2×C4⋊C4—731no—
889C2×C4⋊C4—731no—
890C2×C4⋊C4—731no—
891C2×C4⋊C4—731no—
892C2×C4⋊C4—731no—
893C2×C4⋊C4—731no—
894C2×C4⋊C4—731no—
895C2×C4⋊C4—731no—
896C2×C4⋊C4—731no—
897C2×C4⋊C4—731no—
898C2×C4⋊C4—731no—
899C2×C4⋊C4—731no—
900C2×C4⋊C4—731no—
901C2×C4⋊C4—731no—
902C2×C4⋊C4—731no—
903C2×C4⋊C4—731no—
904C2×C4⋊C4—731no—
905C2×C4⋊C4—731no—
906C2×C4⋊C4—731no—
907C2×C4⋊C4—731no—
908C2×C4⋊C4—731no—
909C2×C4⋊C4—731no—
910C2×C4⋊C4—731no—
911C2×C4⋊C4—731no—
912C2×C4⋊C4—731no—
913C2×C4⋊C4—731no—
914C2×C4⋊C4—731no—
915C2×C4⋊C4—731no—
916C2×C4⋊C4—731no—
917C2×C4⋊C4—1464no—
918C2×C4⋊C4C22×D7311yescharacteristic
919C2×C4⋊C4C22×D7311yescharacteristic
920C2×C4⋊C4C22×D7311yescharacteristic
921C2×C4⋊C4C22×D7311yescharacteristic
922C2×C4⋊C4C22×D7311yescharacteristic
923C2×C4⋊C4C22×D7311yescharacteristic
924C2×C4⋊C4C22×D7311yescharacteristic
925C2×C4⋊C4C22×D7311yescharacteristic
926C2×C4⋊C4C22×D7311yescharacteristic
927C2×C22⋊C4—731no—
928C2×C22⋊C4—731no—
929C2×C22⋊C4—731no—
930C2×C22⋊C4—731no—
931C2×C22⋊C4—731no—
932C2×C22⋊C4—731no—
933C2×C22⋊C4—731no—
934C2×C22⋊C4—731no—
935C2×C22⋊C4—731no—
936C2×C22⋊C4—731no—
937C2×C22⋊C4—731no—
938C2×C22⋊C4—731no—
939C2×C22⋊C4—731no—
940C2×C22⋊C4—731no—
941C2×C22⋊C4—731no—
942C2×C22⋊C4—731no—
943C2×C22⋊C4—731no—
944C2×C22⋊C4—731no—
945C2×C22⋊C4—731no—
946C2×C22⋊C4—731no—
947C2×C22⋊C4C22×D7311yescharacteristic
948C2×C22⋊C4C22×D7311yescharacteristic
949C2×C22⋊C4C22×D7311yescharacteristic
950C2×C22⋊C4C22×D7311yescharacteristic
951C2×C22⋊C4C22×D7311yescharacteristic
952C2×C22⋊C4C22×D7311yescharacteristic
953C2×C22⋊C4C22×D7311yescharacteristic
954C2×C22⋊C4C22×D7311yescharacteristic
955C2×C22⋊C4C22×D7311yescharacteristic
956C2×C22⋊C4C22×D7311yescharacteristic
957C2×C22⋊C4C22×D7311yescharacteristic
958C2×C22⋊C4C22×D7311yescharacteristic
959C2×C22⋊C4C22×D7311yescharacteristic
960C2×C22⋊C4C22×D7311yescharacteristic
961C2×C42—731no—
962C2×C42—731no—
963C2×C42—731no—
964C2×C42—731no—
965C2×C42—731no—
966C2×C42—731no—
967C2×C42—731no—
968C2×C42—731no—
969C2×C42—731no—
970C2×C42—731no—
971C2×C42—731no—
972C2×C42—731no—
973C2×C42C22×D7311yescharacteristic
974C2×C42C22×D7311yescharacteristic
975#95—731no—
976#95—731no—
977#95—731no—
978#95—731no—
979#95—731no—
980#95—731no—
981#95—731no—
982#95—731no—
983#95—731no—
984#95—731no—
985#95—731no—
986#95—731no—
987#95—731no—
988#95—731no—
989#95—731no—
990#95—731no—
991#95—731no—
992#95—731no—
993#95—731no—
994#95—731no—
995#95—731no—
996#95—731no—
997#95—731no—
998#95—731no—
999#95—731no—
1000#95—731no—
1001#95—731no—
1002#95—731no—
1003#95—731no—
1004#95—731no—
1005#95—731no—
1006#95—731no—
1007#95—731no—
1008#95—731no—
1009#95—731no—
1010#95—731no—
1011#95—731no—
1012#95—731no—
1013#95—731no—
1014#95—731no—
1015#95—731no—
1016#95—731no—
1017#95—731no—
1018#95—731no—
1019#95—731no—
1020#95—731no—
1021#95—731no—
1022#95—731no—
1023#95—731no—
1024#95—731no—
1025#95—731no—
1026#95—731no—
1027#95C22×D7311yescharacteristic
1028#95C22×D7311yescharacteristic
1029#95C22×D7311yescharacteristic
1030#95C22×D7311yescharacteristic
1031#95C22×D7311yescharacteristic
1032#95C22×D7311yescharacteristic
1033C24C23×D7311yescharacteristic
1034C24C23×D7311yescharacteristic
1035C24C23×D7311yescharacteristic
1036C2×Q8—2921no—
1037C2×Q8—2921no—
1038C2×Q8—2921no—
1039C2×Q8—2921no—
1040C2×Q8—2921no—
1041C2×Q8—1462no—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—22no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C2×D4—41no—
1048C2×D4—41no—
1049C2×D4—41no—
1050C2×D4—41no—
1051C22×C4—22no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—2921no—
1055C22×C4—2921no—
1056C22×C4—2921no—
1057C22×C4—2921no—
1058C22×C4—2921no—
1059C22×C4—2921no—
1060C22×C4—2921no—
1061C22×C4—2921no—
1062C22×C4—2921no—
1063C22×C4—734no—
1064C22×C4—731no—
1065C22×C4—731no—
1066C22×C4—731no—
1067C22×C4—731no—
1068C22×C4—731no—
1069C22×C4—731no—
1070C22×C4—731no—
1071C22×C4—731no—
1072C22×C4—731no—
1073C22×C4—731no—
1074C22×C4—731no—
1075C22×C4—731no—
1076C22×C4—731no—
1077C22×C4—731no—
1078C22×C4—731no—
1079C22×C4—731no—
1080C22×C4—1462no—
1081C22×C4—1462no—
1082C22×C4C23×D7311yescharacteristic
1083C22×C4C23×D7311yescharacteristic
1084C22×C4C23×D7311yescharacteristic
1085C22×C4C23×D7311yescharacteristic
1086C22×C4C23×D7311yescharacteristic
1087C22×C4C23×D7311yescharacteristic
1088C22×C4C23×D7311yescharacteristic
1089C22×C4C23×D7311yescharacteristic
1090C22×C4C23×D7311yescharacteristic
1091C22×C4C23×D7311yescharacteristic
1092C22×C4C23×D7311yescharacteristic
1093C22×C4C23×D7311yescharacteristic
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—41no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—41no—
1101C4⋊C4—41no—
1102C4⋊C4—41no—
1103C4⋊C4—2921no—
1104C4⋊C4—2921no—
1105C4⋊C4—2921no—
1106C4⋊C4—2921no—
1107C4⋊C4—2921no—
1108C4⋊C4—2921no—
1109C4⋊C4—2921no—
1110C4⋊C4—2921no—
1111C4⋊C4—2921no—
1112C4⋊C4—2921no—
1113C4⋊C4—2921no—
1114C4⋊C4—2921no—
1115C4⋊C4—2921no—
1116C4⋊C4—2921no—
1117C4⋊C4—2921no—
1118C4⋊C4—2921no—
1119C4⋊C4—2921no—
1120C4⋊C4—2921no—
1121C4⋊C4—2921no—
1122C4⋊C4—2921no—
1123C4⋊C4—1462no—
1124C4⋊C4—1462no—
1125C4⋊C4—1462no—
1126C4⋊C4—1462no—
1127C4⋊C4—1462no—
1128C4⋊C4—1462no—
1129C4⋊C4—1462no—
1130C4⋊C4—1462no—
1131C4⋊C4—1462no—
1132C4⋊C4—1462no—
1133C22⋊C4—22no—
1134C22⋊C4—22no—
1135C22⋊C4—22no—
1136C22⋊C4—22no—
1137C22⋊C4—41no—
1138C22⋊C4—41no—
1139C22⋊C4—41no—
1140C22⋊C4—41no—
1141C22⋊C4—41no—
1142C22⋊C4—41no—
1143C22⋊C4—41no—
1144C22⋊C4—41no—
1145C22⋊C4—41no—
1146C22⋊C4—41no—
1147C22⋊C4—2921no—
1148C22⋊C4—2921no—
1149C22⋊C4—2921no—
1150C22⋊C4—2921no—
1151C22⋊C4—2921no—
1152C22⋊C4—2921no—
1153C22⋊C4—2921no—
1154C22⋊C4—2921no—
1155C22⋊C4—2921no—
1156C22⋊C4—2921no—
1157C22⋊C4—2921no—
1158C22⋊C4—2921no—
1159C22⋊C4—2921no—
1160C22⋊C4—2921no—
1161C22⋊C4—2921no—
1162C22⋊C4—1462no—
1163C22⋊C4—1462no—
1164C22⋊C4—1462no—
1165C22⋊C4—1462no—
1166C22⋊C4—1462no—
1167C42—41no—
1168C42—41no—
1169C42—2921no—
1170C42—2921no—
1171C42—2921no—
1172C42—2921no—
1173C42—2921no—
1174C42—2921no—
1175C42—2921no—
1176C42—2921no—
1177C42—2921no—
1178C42—1462no—
1179C42—1462no—
1180C42—1462no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23#41×D7312yes—
1202C23C24×D7311yescharacteristic
1203Q8—5842no—
1204Q8—5842no—
1205D4—44no—
1206D4—82no—
1207D4—82no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—82no—
1243C2×C4—2924no—
1244C2×C4—2924no—
1245C2×C4—2924no—
1246C2×C4—5842no—
1247C2×C4—732no—
1248C2×C4—732no—
1249C2×C4—1461no—
1250C2×C4—1461no—
1251C2×C4—1461no—
1252C2×C4—1461no—
1253C2×C4—1461no—
1254C2×C4—1461no—
1255C2×C4—1461no—
1256C2×C4—1461no—
1257C2×C4—1461no—
1258C2×C4—1461no—
1259C2×C4—1461no—
1260C2×C4—1461no—
1261C2×C4—1461no—
1262C2×C4—1461no—
1263C2×C4—1461no—
1264C2×C4—1461no—
1265C2×C4—1461no—
1266C2×C4—1461no—
1267C2×C4—1461no—
1268C2×C4—1461no—
1269C2×C4—1461no—
1270C2×C4—1461no—
1271C2×C4—1461no—
1272C2×C4—1461no—
1273C2×C4—1461no—
1274C2×C4—1461no—
1275C2×C4—1461no—
1276C2×C4—1461no—
1277C2×C4—1461no—
1278C2×C4—1461no—
1279C2×C4—1461no—
1280C2×C4—1461no—
1281C2×C4—1461no—
1282C2×C4—1461no—
1283C2×C4—1461no—
1284C2×C4—1461no—
1285C2×C4—1461no—
1286C2×C4—1461no—
1287C2×C4—1461no—
1288C2×C4—1461no—
1289C2×C4—1461no—
1290C2×C4—1461no—
1291C2×C4—1461no—
1292C2×C4—1461no—
1293C2×C4—1461no—
1294C2×C4—1461no—
1295C2×C4#1455663612yes—
1296C2×C4#1455663812yes—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22C2×#41×D7311yescharacteristic
1319C22C2×#1455663611yescharacteristic
1320C22C2×#1455663811yescharacteristic
1321C22#1798942211yescharacteristic
1322C22#1798942211yescharacteristic
1323C22#1798942211yescharacteristic
1324C22#1798942411yescharacteristic
1325C4—22no—
1326C4—22no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—2921no—
1338C4—2921no—
1339C4—2921no—
1340C4—2921no—
1341C4—2921no—
1342C4—2921no—
1343C4—2921no—
1344C4—2921no—
1345C4—2921no—
1346C4—2921no—
1347C4—2921no—
1348C4—2921no—
1349C4—2921no—
1350C4—2921no—
1351C4—1462no—
1352C4—1462no—
1353C2—42no—
1354C2—81no—
1355C2—81no—
1356C2#2262331711yescharacteristic
1357C2#2262367011yescharacteristic
1358C2#2262375811yescharacteristic
1359C2#2262439811yescharacteristic
1360C2#2262448011yescharacteristic
1361C2#2262457811yescharacteristic
1362C2#2262458811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2705C2
prime radical#392×C73C22
hypercenter#2705D73
hypocenterC73#36989
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2705

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22618322C2semidirect
2. #22618314C2semidirect
3. #22617845C2semidirect
4. #22617833C2semidirect
5. #22617536C2semidirect
6. #22617452C2semidirect
7. #22617384C2semidirect
8. #22617372C2semidirect
9. #22617320C2semidirect
10. #22617178C2semidirect
11. #22617178C2semidirect
13. #22617012C2semidirect
14. #22616990C2semidirect
15. #22616910C2semidirect
16. #22616753C2semidirect
17. #22616346C2semidirect
18. #22615989C2semidirect
19. #22615982C2semidirect
21. #22615365C2semidirect
22. #22615277C2semidirect
23. #22615221C2semidirect
24. #22614143C2semidirect
25. #22614133C2semidirect
26. #22613617C2semidirect
27. #22613334C2semidirect
28. #22612718C2semidirect
29. #22612533C2semidirect
30. #22612393C2semidirect
713. C73#36989semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226183222
#226183142
#226178452
#226178332
#226175362
#226174522
#226173842
#226173722
#226173202
#226171782
#226171562
#226170122
#226169902
#226169102
#226167532
#226163462
#226159892
#226159822
#226155362
#226153652
#226152772
#226152212
#226141432
#226141332
#226136172
#226133342
#226127182
#226125332
#226123932
C73×#27052
#3698973