Finite Group Databasebeta

← #33949280

Subgroups — #33949280

Order 18688.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22617754C211yesmaximal, characteristic, complemented
2#22616907C211yesmaximal, characteristic, complemented
3#22616269C211yesmaximal, characteristic
4#22615586C211yesmaximal, characteristic, complemented
5#22615582C211yesmaximal, characteristic, complemented
6#22615503C211yesmaximal, characteristic, complemented
7#22615501C211yesmaximal, characteristic, complemented
8#22615338C211yesmaximal, characteristic, complemented
9#22615295C211yesmaximal, characteristic, complemented
10#22615176C211yesmaximal, characteristic
11#22614838C211yesmaximal, characteristic
12#22614767C211yesmaximal, characteristic, complemented
13#22614758C211yesmaximal, characteristic, complemented
14#22614676C211yesmaximal, characteristic, complemented
15#22614674C211yesmaximal, characteristic, complemented
16#22614553C211yesmaximal, characteristic, complemented
17#22614551C211yesmaximal, characteristic, complemented
18#22614028C211yesmaximal, characteristic
19#22614025C211yesmaximal, characteristic
20#22613608C211yesmaximal, characteristic, complemented
21#22613605C211yesmaximal, characteristic, complemented
22#22613016C211yesmaximal, characteristic, complemented
23#22613010C211yesmaximal, characteristic, complemented
24#22612961C211yesmaximal, characteristic, complemented
25#22612957C211yesmaximal, characteristic, complemented
26#22612926C211yesmaximal, characteristic
27#22612921C211yesmaximal, characteristic
28C4⋊Q8×Dic73C211yesmaximal, characteristic, complemented
29#22612425C211yesmaximal, characteristic, complemented
30#22612423C211yesmaximal, characteristic, complemented
31C73×#2729C211yesmaximal, characteristic, complemented
32C2×#14556575C2211yescharacteristic
33C2×#14556573C2211yescharacteristic
34C2×#14556571C2211yescharacteristic
35C2×#14556568C2211yescharacteristic
36C2×#14556567C2211yescharacteristic
37C2×Q8×Dic73C2211yescharacteristic
38C2×Q8×Dic73C2211yescharacteristic
39C2×C4×Dic146C2211yescharacteristic
40C2×C4×C22⋊D73C2211yescharacteristic
41C2×#14556549C2211yescharacteristic
42C2×#14556549C2211yescharacteristic
43C2×#14556547C2211yescharacteristic
44C2×#14556547C2211yescharacteristic
45#17988529C2211yescharacteristic
46#17988529C2211yescharacteristic
47#17988527C2211yescharacteristic
48#17988527C2211yescharacteristic
49#17988526C2211yescharacteristic
50#17988526C2211yescharacteristic
51#17988526C2211yescharacteristic
52#17988520C2211yescharacteristic
53#17988520C2211yescharacteristic
54#17988520C2211yescharacteristic
55#17988519C2211yescharacteristic
56#17988519C2211yescharacteristic
57#17988517C2211yescharacteristic
58#17988517C2211yescharacteristic
59#17988517C2211yescharacteristic
60#17988514C2211yescharacteristic
61#17988514C2211yescharacteristic
62#17988512C2211yescharacteristic
63#17988512C2211yescharacteristic
64#17988509C2211yescharacteristic
65#17988508C2211yescharacteristic
66#17988508C2211yescharacteristic
67#17988506C2211yescharacteristic
68#17988503C2211yescharacteristic
69#17988503C2211yescharacteristic
70#17988498C2211yescharacteristic
71#17988494C2211yescharacteristic
72#17988494C2211yescharacteristic
73#17988494C2211yescharacteristic
74#17988492C2211yescharacteristic
75#17988491C2211yescharacteristic
76#17988486C2211yescharacteristic
77#17988486C2211yescharacteristic
78#17988486C2211yescharacteristic
79#17988486C2211yescharacteristic
80#17988486C2211yescharacteristic
81#17988485C2211yescharacteristic
82#17988483C2211yescharacteristic
83#17988482C2211yescharacteristic
84#17988482C2211yescharacteristic
85#17988481C2211yescharacteristic
86#17988481C2211yescharacteristic
87#17988481C2211yescharacteristic
88#17988481C2211yescharacteristic
89#17988480C2211yescharacteristic
90#17988479C2211yescharacteristic
91#17988478C2211yescharacteristic
92#17988477C2211yescharacteristic
93#17988477C2211yescharacteristic
94#17988477C2211yescharacteristic
95#17988477C2211yescharacteristic
96#17988476C2211yescharacteristic
97#17988476C2211yescharacteristic
98#17988475C2211yescharacteristic
99#17988474C2211yescharacteristic
100#17988474C2211yescharacteristic
101#17988474C2211yescharacteristic
102#17988474C2211yescharacteristic
103#17988474C2211yescharacteristic
104#17988474C2211yescharacteristic
105#17988473C2211yescharacteristic
106#17988473C2211yescharacteristic
107#17988473C2211yescharacteristic
108#17988473C2211yescharacteristic
109#17988473C2211yescharacteristic
110#17988473C2211yescharacteristic
111#17988472C2211yescharacteristic
112#17988472C2211yescharacteristic
113#17988472C2211yescharacteristic
114#17988472C2211yescharacteristic
115#17988472C2211yescharacteristic
116#17988471C2211yescharacteristic
117#17988470C2211yescharacteristic
118#17988470C2211yescharacteristic
119#17988470C2211yescharacteristic
120#17988470C2211yescharacteristic
121#17988470C2211yescharacteristic
122#17988470C2211yescharacteristic
123#17988470C2211yescharacteristic
124#17988469C2211yescharacteristic
125#17988468C2211yescharacteristic
126#17988468C2211yescharacteristic
127#17988468C2211yescharacteristic
128#17988464C2211yescharacteristic
129#17988463C2211yescharacteristic
130#17988462C2211yescharacteristic
131#17988462C2211yescharacteristic
132#17988462C2211yescharacteristic
133#17988461C2211yescharacteristic
134#17988461C2211yescharacteristic
135#17988458C2211yescharacteristic
136#17988458C2211yescharacteristic
137#17988458C2211yescharacteristic
138#17988457C2211yescharacteristic
139#17988454C2211yescharacteristic
140#17988454C2211yescharacteristic
141#17988454C2211yescharacteristic
142#17988454C2211yescharacteristic
143#17988452C2211yescharacteristic
144#17988452C2211yescharacteristic
145#17988449C2211yescharacteristic
146#17988448C2211yescharacteristic
147#17988447C2211yescharacteristic
148#17988444C2211yescharacteristic
149C4⋊C4×Dic73C2211yescharacteristic
150C4⋊C4×Dic73C2211yescharacteristic
151C4⋊C4×Dic73C2211yescharacteristic
152C4⋊C4×Dic73C2211yescharacteristic
153C4⋊C4×Dic73C2211yescharacteristic
154C4⋊C4×Dic73C2211yescharacteristic
155C4⋊C4×Dic73C2211yescharacteristic
156C4×#11924007C2211yescharacteristic
157#17988438C2211yescharacteristic
158#17988438C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic
161C22⋊C4×Dic73C2211yescharacteristic
162C4×#11924005C2211yescharacteristic
163C4×C22⋊Dic73C2211yescharacteristic
164#17988434C2211yescharacteristic
165#17988434C2211yescharacteristic
166#17988434C2211yescharacteristic
167#17988432C2211yescharacteristic
168#17988432C2211yescharacteristic
169C2×#14556498C2211yescharacteristic
170#95×D73C2211yescharacteristic
171C42×Dic73C2211yescharacteristic
172C2×C4⋊Q8×C73C2211yescharacteristic
173C2×C22⋊Q8×C73C2211yescharacteristic
174#400×C73C2211yescharacteristic
175#398×C73C2211yescharacteristic
176#398×C73C2211yescharacteristic
177#396×C73C2211yescharacteristic
178#395×C73C2211yescharacteristic
179#393×C73C2211yescharacteristic
180#391×C73C2211yescharacteristic
181#389×C73C2211yescharacteristic
182#388×C73C2211yescharacteristic
183#388×C73C2211yescharacteristic
184#387×C73C2211yescharacteristic
185#385×C73C2211yescharacteristic
186#385×C73C2211yescharacteristic
187C22×Dic146C2311yescharacteristic
188C22×C22⋊D73C2311yescharacteristic
189C23×Dic73C2311yescharacteristic
190C23×Dic73C2311yescharacteristic
191C22×C4×D73C2311yescharacteristic
192C22×C4×D73C2311yescharacteristic
193C22×C4×D73C2311yescharacteristic
194#14556575—24no—
195#14556573—24no—
196#14556571—24no—
197#14556568—24no—
198#14556567—24no—
199Q8×Dic73—42no—
200Q8×Dic73—42no—
201C4×Dic146—42no—
202C4×C22⋊D73—42no—
203#14556549—24no—
204#14556549—42no—
205#14556547—24no—
206#14556547—42no—
207C2×C4⋊Dic73C2311yescharacteristic
208C2×C4⋊Dic73C2311yescharacteristic
209C2×C4⋊Dic73C2311yescharacteristic
210C2×C4⋊Dic73C2311yescharacteristic
211C2×C4⋊Dic73C2311yescharacteristic
212C2×C4⋊Dic73C2311yescharacteristic
213C2×C4⋊Dic73C2311yescharacteristic
214C2×C4⋊Dic73C2311yescharacteristic
215C2×C4⋊Dic73C2311yescharacteristic
216C2×C4⋊Dic73C2311yescharacteristic
217C2×C4⋊Dic73C2311yescharacteristic
218C2×C4⋊Dic73C2311yescharacteristic
219C2×C4⋊Dic73C2311yescharacteristic
220C2×C4⋊Dic73C2311yescharacteristic
221C2×C4⋊Dic73C2311yescharacteristic
222C2×C4⋊Dic73C2311yescharacteristic
223C2×C4⋊Dic73C2311yescharacteristic
224C2×#11924007C2311yescharacteristic
225C2×#11924007C2311yescharacteristic
226C2×#11924007C2311yescharacteristic
227C2×#11924007C2311yescharacteristic
228C2×#11924007C2311yescharacteristic
229C2×#11924007C2311yescharacteristic
230C2×#11924007C2311yescharacteristic
231C2×#11924007C2311yescharacteristic
232C2×#11924007C2311yescharacteristic
233C2×#11924007C2311yescharacteristic
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×C22⋊Dic73C2311yescharacteristic
238C2×C22⋊Dic73C2311yescharacteristic
239C2×C22⋊Dic73C2311yescharacteristic
240C2×C22⋊Dic73C2311yescharacteristic
241C2×C22⋊Dic73C2311yescharacteristic
242C2×#11924005C2311yescharacteristic
243C2×#11924005C2311yescharacteristic
244C2×#11924005C2311yescharacteristic
245C2×#11924005C2311yescharacteristic
246C2×#11924005C2311yescharacteristic
247C2×#11924005C2311yescharacteristic
248C2×#11924005C2311yescharacteristic
249C2×#11924005C2311yescharacteristic
250C2×#11924005C2311yescharacteristic
251C2×#11924005C2311yescharacteristic
252C2×#11924005C2311yescharacteristic
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
262C2×C4×Dic73C2311yescharacteristic
263C2×C4×Dic73C2311yescharacteristic
264C2×C4×Dic73C2311yescharacteristic
265C2×C4×Dic73C2311yescharacteristic
266C2×C4×Dic73C2311yescharacteristic
267C2×C4×Dic73C2311yescharacteristic
268C2×C4×Dic73C2311yescharacteristic
269C2×C4×Dic73C2311yescharacteristic
270C2×C4×Dic73C2311yescharacteristic
271C2×C4×Dic73C2311yescharacteristic
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
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320C22×Q8×C73C2311yescharacteristic
321C22×Q8×C73C2311yescharacteristic
322C23×C4×C73C2311yescharacteristic
323C4⋊Q8×C73—24no—
324C22⋊Q8×C73—24no—
325C2×C4⋊C4×C73C2311yescharacteristic
326C2×C4⋊C4×C73C2311yescharacteristic
327C2×C4⋊C4×C73C2311yescharacteristic
328C2×C4⋊C4×C73C2311yescharacteristic
329C2×C4⋊C4×C73C2311yescharacteristic
330C2×C4⋊C4×C73C2311yescharacteristic
331C2×C4⋊C4×C73C2311yescharacteristic
332C2×C4⋊C4×C73C2311yescharacteristic
333C2×C4⋊C4×C73C2311yescharacteristic
334C2×C4⋊C4×C73C2311yescharacteristic
335C2×C4⋊C4×C73C2311yescharacteristic
336C2×C4⋊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
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357C23×D73C2411yescharacteristic
358C2×Dic146—22no—
359C2×Dic146—22no—
360C2×Dic146—41no—
361C2×C22⋊D73—22no—
362C2×C22⋊D73—22no—
363C2×C22⋊D73—41no—
364C22×Dic73—22no—
365C22×Dic73—22no—
366C22×Dic73—22no—
367C22×Dic73—22no—
368C22×Dic73—41no—
369C22×Dic73—41no—
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
385C2×C4×D73—22no—
386C2×C4×D73—22no—
387C2×C4×D73—22no—
388C2×C4×D73—22no—
389C2×C4×D73—22no—
390C2×C4×D73—41no—
391C2×C4×D73—41no—
392C2×C4×D73—41no—
393C2×C4×D73—41no—
394C4⋊Dic73—22no—
395C4⋊Dic73—22no—
396C4⋊Dic73—22no—
397C4⋊Dic73—22no—
398C4⋊Dic73—22no—
399C4⋊Dic73—22no—
400C4⋊Dic73—22no—
401C4⋊Dic73—22no—
402C4⋊Dic73—22no—
403C4⋊Dic73—22no—
404C4⋊Dic73—41no—
405C4⋊Dic73—41no—
406C4⋊Dic73—41no—
407C4⋊Dic73—41no—
408C4⋊Dic73—41no—
409C4⋊Dic73—41no—
410C4⋊Dic73—41no—
411#11924007—22no—
412#11924007—22no—
413#11924007—22no—
414#11924007—22no—
415#11924007—22no—
416#11924007—22no—
417#11924007—22no—
418#11924007—22no—
419#11924007—22no—
420#11924007—41no—
421#11924007—41no—
422#11924007—41no—
423#11924007—41no—
424C22⋊Dic73—22no—
425C22⋊Dic73—22no—
426C22⋊Dic73—22no—
427C22⋊Dic73—22no—
428C22⋊Dic73—22no—
429#11924005—22no—
430#11924005—22no—
431#11924005—22no—
432#11924005—22no—
433#11924005—22no—
434#11924005—22no—
435#11924005—22no—
436#11924005—22no—
437#11924005—41no—
438#11924005—41no—
439#11924005#4114yes—
440C4×Dic73—22no—
441C4×Dic73—22no—
442C4×Dic73—22no—
443C4×Dic73—22no—
444C4×Dic73—22no—
445C4×Dic73—22no—
446C4×Dic73—22no—
447C4×Dic73—22no—
448C4×Dic73—22no—
449C4×Dic73—22no—
450C4×Dic73—22no—
451C4×Dic73—22no—
452C4×Dic73—22no—
453C4×Dic73—41no—
454C4×Dic73—41no—
455C4×Dic73—41no—
456C4×Dic73—41no—
457C4×Dic73—41no—
458C4×Dic73—41no—
459C24×C73C2411yescharacteristic
460C2×Q8×C73—22no—
461C2×Q8×C73—41no—
462C2×Q8×C73—41no—
463C2×Q8×C73—41no—
464C2×Q8×C73—41no—
465C2×Q8×C73#4114yes—
466C22×C4×C73—22no—
467C22×C4×C73—41no—
468C22×C4×C73—41no—
469C22×C4×C73C2411yescharacteristic
470C22×C4×C73C2411yescharacteristic
471C22×C4×C73C2411yescharacteristic
472C22×C4×C73C2411yescharacteristic
473C22×C4×C73C2411yescharacteristic
474C22×C4×C73C2411yescharacteristic
475C22×C4×C73C2411yescharacteristic
476C22×C4×C73C2411yescharacteristic
477C22×C4×C73C2411yescharacteristic
478C22×C4×C73C2411yescharacteristic
479C22×C4×C73C2411yescharacteristic
480C22×C4×C73C2411yescharacteristic
481C22×C4×C73C2411yescharacteristic
482C22×C4×C73C2411yescharacteristic
483C4⋊C4×C73—22no—
484C4⋊C4×C73—22no—
485C4⋊C4×C73—22no—
486C4⋊C4×C73—22no—
487C4⋊C4×C73—22no—
488C4⋊C4×C73—22no—
489C4⋊C4×C73—22no—
490C4⋊C4×C73—22no—
491C4⋊C4×C73—22no—
492C4⋊C4×C73—41no—
493C4⋊C4×C73—41no—
494C4⋊C4×C73—41no—
495C22⋊C4×C73—22no—
496C22⋊C4×C73—22no—
497C22⋊C4×C73—22no—
498C22⋊C4×C73—41no—
499C22⋊C4×C73—41no—
500C22⋊C4×C73#4114yes—
501C42×C73—22no—
502C42×C73—41no—
503C23×C73—21no—
504C23×C73—21no—
505C23×C73—21no—
506C23×C73—21no—
507C23×C73—21no—
508C23×C73—21no—
509C23×C73C2×#4112yes—
510C23×C73C2511yescharacteristic
511C22×D73—21no—
512C22×D73—21no—
513C22×D73—21no—
514C22×D73—21no—
515C22×D73—21no—
516C22×D73—21no—
517C22×D73C2×#4112yes—
518Q8×C73—44no—
519Q8×C73—44no—
520C2×C4×C73—21no—
521C2×C4×C73—21no—
522C2×C4×C73—21no—
523C2×C4×C73—21no—
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—82no—
557C2×C4×C73C2×#4112yes—
558C2×C4×C73C2×#4112yes—
559C2×C4×C73C2×#4112yes—
560C2×C4×C73C2×#4112yes—
561C2×C4×C73C2×#4112yes—
562C2×C4×C73C2×#4112yes—
563C22⋊D73—44no—
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—44no—
606C2×Dic73—44no—
607C2×Dic73C2×#4112yes—
608C2×Dic73H(5,𝔽2)12yes—
609C2×Dic732−1+412yes—
610C2×Dic732−1+412yes—
611C4×D73—44no—
612C4×D73—44no—
613C4×D73—82no—
614Dic146—44no—
615C22×C73—22no—
616C22×C73—22no—
617C22×C73—22no—
618C22×C73—41no—
619C22×C73—41no—
620C22×C73—41no—
621C22×C73—41no—
622C22×C73C22×#4111yescharacteristic
623C22×C73C22×#4111yescharacteristic
624C22×C73C22×#4111yescharacteristic
625C22×C73C2×H(5,𝔽2)11yescharacteristic
626C22×C73C2×2−1+411yescharacteristic
627C22×C73C2×2−1+411yescharacteristic
628C22×C73#58511yescharacteristic
629C2×D73—22no—
630C2×D73—22no—
631C2×D73—22no—
632C2×D73—41no—
633C2×D73—41no—
634C2×D73—41no—
635C2×D73—41no—
636C4×C73—22no—
637C4×C73—22no—
638C4×C73—22no—
639C4×C73—22no—
640C4×C73—22no—
641C4×C73—22no—
642C4×C73—41no—
643C4×C73—41no—
644C4×C73—41no—
645C4×C73—41no—
646C4×C73—41no—
647C4×C73—41no—
648C4×C73—41no—
649C4×C73—41no—
650Dic73—22no—
651Dic73—22no—
652Dic73—22no—
653Dic73—22no—
654Dic73—41no—
655Dic73—41no—
656Dic73—41no—
657Dic73—41no—
658Dic73—41no—
659Dic73—41no—
660Dic73—41no—
661Dic73—41no—
662Dic73—41no—
663Dic73—41no—
664Dic73—41no—
665#60043—731nomaximal, Sylow
666C2×C73—42no—
667C2×C73#348111yescharacteristic
668C2×C73#348211yescharacteristic
669C2×C73#348211yescharacteristic
670C2×C73#349511yescharacteristic
671C2×C73#349511yescharacteristic
672C2×C73#350511yescharacteristic
673C2×C73#354411yescharacteristic
674D73—42no—
675#2794—731no—
676#2729—731no—
677#2729D7311yescharacteristic, complemented
678#2680—731no—
679#2606—731no—
680#2606—731no—
681#2599—731no—
682#2599—731no—
683#2586—731no—
684#2581—731no—
685#2572—731no—
686#2536—731no—
687#2530—731no—
688#2530—731no—
689#2524—731no—
690#2524—731no—
691#2515—731no—
692#2515—731no—
693#2470—731no—
694#2470—731no—
695#2438—731no—
696#2438—731no—
697#2368—731no—
698#2368—731no—
699#2362—731no—
700#2362—731no—
701#2359—731no—
702#2359—731no—
703C4×C4⋊Q8—731no—
704#2298—731no—
705#2298—731no—
706C73#6004311yescharacteristic, complemented, Sylow
707C2×C4⋊Q8C2×D7311yescharacteristic
708C2×#123—731no—
709C2×#123—731no—
710C2×C22⋊Q8—731no—
711C2×C22⋊Q8—731no—
712C2×C22⋊Q8—731no—
713C2×C22⋊Q8C2×D7311yescharacteristic
714C2×C4×Q8—731no—
715C2×C4×Q8—731no—
716C2×C4×Q8—731no—
717C2×C4×D4—731no—
718C2×#117—731no—
719C2×#117—731no—
720C2×#117—731no—
721C2×#117—731no—
722#400—731no—
723#400—731no—
724#400—731no—
725#400—731no—
726#400—731no—
727#400—731no—
728#400—731no—
729#400C2×D7311yescharacteristic
730#398—731no—
731#398—731no—
732#398—731no—
733#398—731no—
734#398—731no—
735#398—731no—
736#398—731no—
737#398—731no—
738#398C2×D7311yescharacteristic
739#398C2×D7311yescharacteristic
740#397—731no—
741#397—731no—
742#397—731no—
743#397—731no—
744#396—731no—
745#396C2×D7311yescharacteristic
746#395—731no—
747#395—731no—
748#395—731no—
749#395C2×D7311yescharacteristic
750#394—731no—
751#394—731no—
752#393—731no—
753#393C2×D7311yescharacteristic
754#391—731no—
755#391—731no—
756#391—731no—
757#391—731no—
758#391—731no—
759#391C2×D7311yescharacteristic
760#389—731no—
761#389—731no—
762#389—731no—
763#389—731no—
764#389—731no—
765#389—731no—
766#389—731no—
767#389—731no—
768#389—731no—
769#389C2×D7311yescharacteristic
770#388—731no—
771#388—731no—
772#388—731no—
773#388—731no—
774#388—731no—
775#388—731no—
776#388—731no—
777#388—731no—
778#388—731no—
779#388—731no—
780#388—731no—
781#388—731no—
782#388—731no—
783#388—731no—
784#388C2×D7311yescharacteristic
785#388C2×D7311yescharacteristic
786#387—731no—
787#387—731no—
788#387—731no—
789#387—731no—
790#387—731no—
791#387—731no—
792#387—731no—
793#387—731no—
794#387—731no—
795#387—731no—
796#387—731no—
797#387—731no—
798#387—731no—
799#387—731no—
800#387—731no—
801#387—731no—
802#387—731no—
803#387—731no—
804#387—731no—
805#387—731no—
806#387—731no—
807#387—731no—
808#387—731no—
809#387—731no—
810#387—731no—
811#387—731no—
812#387—731no—
813#387—731no—
814#387—731no—
815#387C2×D7311yescharacteristic
816#386—731no—
817#386—731no—
818#385—731no—
819#385—731no—
820#385—731no—
821#385—731no—
822#385—731no—
823#385—731no—
824#385—731no—
825#385—731no—
826#385C2×D7311yescharacteristic
827#385C2×D7311yescharacteristic
828#384—731no—
829#383—731no—
830#383—731no—
831#383—731no—
832#383—731no—
833#382—731no—
834#382—731no—
835#381—731no—
836#381—731no—
837#380—731no—
838#380—731no—
839C4×C4⋊C4—731no—
840C4×C4⋊C4—731no—
841C4×C4⋊C4—731no—
842C4×C4⋊C4—731no—
843C4×C4⋊C4—731no—
844C4×C4⋊C4—731no—
845C4×C4⋊C4—731no—
846C4×C4⋊C4—731no—
847C4×C4⋊C4—731no—
848C4×C4⋊C4—731no—
849C4×C22⋊C4—731no—
850C4×C22⋊C4—731no—
851C4×C22⋊C4—731no—
852C4×C22⋊C4—731no—
853C4×C22⋊C4—731no—
854C4×C22⋊C4—731no—
855C4×C22⋊C4—731no—
856C4×C22⋊C4—731no—
857#376—731no—
858#376—731no—
859C2×#95—731no—
860C2×#95—731no—
861C43—731no—
862C22×Q8—731no—
863C22×Q8C22×D7311yescharacteristic
864C22×Q8C22×D7311yescharacteristic
865C22×D4—731no—
866C23×C4—731no—
867C23×C4—731no—
868C23×C4—731no—
869C23×C4—731no—
870C23×C4—731no—
871C23×C4C22×D7311yescharacteristic
872C4⋊Q8—24no—
873#123—1464no—
874#123—1464no—
875C22⋊Q8—24no—
876C22⋊Q8—1464no—
877C22⋊Q8—1464no—
878C22⋊Q8—1464no—
879C4×Q8—2922no—
880C4×Q8—2922no—
881C4×Q8—2922no—
882C4×D4—2922no—
883#117—2922no—
884#117—2922no—
885#117—1464no—
886#117—1464no—
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⋊C4C22×D7311yescharacteristic
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×C4⋊C4C22×D7311yescharacteristic
928C2×C4⋊C4C22×D7311yescharacteristic
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⋊C4C22×D7311yescharacteristic
946C2×C22⋊C4C22×D7311yescharacteristic
947C2×C22⋊C4C22×D7311yescharacteristic
948C2×C22⋊C4C22×D7311yescharacteristic
949C2×C22⋊C4C22×D7311yescharacteristic
950C2×C22⋊C4C22×D7311yescharacteristic
951C2×C42—731no—
952C2×C42—731no—
953C2×C42—731no—
954C2×C42—731no—
955C2×C42—731no—
956C2×C42—731no—
957C2×C42—731no—
958C2×C42—731no—
959C2×C42—731no—
960C2×C42—731no—
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×C42C22×D7311yescharacteristic
971C2×C42C22×D7311yescharacteristic
972#95—731no—
973#95—731no—
974#95—731no—
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#95C22×D7311yescharacteristic
1021#95C22×D7311yescharacteristic
1022#95C22×D7311yescharacteristic
1023#95C22×D7311yescharacteristic
1024#95C22×D7311yescharacteristic
1025#95C22×D7311yescharacteristic
1026#95C22×D7311yescharacteristic
1027#95C22×D7311yescharacteristic
1028#95C22×D7311yescharacteristic
1029#95C22×D7311yescharacteristic
1030#95C22×D7311yescharacteristic
1031#95C22×D7311yescharacteristic
1032C24—731no—
1033C24C23×D7311yescharacteristic
1034C2×Q8—22no—
1035C2×Q8—41no—
1036C2×Q8—41no—
1037C2×Q8—41no—
1038C2×Q8—41no—
1039C2×Q8—2921no—
1040C2×Q8—1462no—
1041C2×Q8—1462no—
1042C2×Q8#1192402714yes—
1043C2×D4—2921no—
1044C2×D4—1462no—
1045C2×D4—1462no—
1046C22×C4—22no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4—2921no—
1050C22×C4—2921no—
1051C22×C4—2921no—
1052C22×C4—2921no—
1053C22×C4—2921no—
1054C22×C4—2921no—
1055C22×C4—731no—
1056C22×C4—731no—
1057C22×C4—731no—
1058C22×C4—731no—
1059C22×C4—731no—
1060C22×C4—731no—
1061C22×C4—731no—
1062C22×C4—731no—
1063C22×C4—731no—
1064C22×C4—731no—
1065C22×C4—731no—
1066C22×C4—731no—
1067C22×C4—731no—
1068C22×C4—731no—
1069C22×C4—731no—
1070C22×C4—1462no—
1071C22×C4—1462no—
1072C22×C4—1462no—
1073C22×C4—1462no—
1074C22×C4—1462no—
1075C22×C4—1462no—
1076C22×C4—1462no—
1077C22×C4—1462no—
1078C22×C4—1462no—
1079C22×C4C23×D7311yescharacteristic
1080C22×C4C23×D7311yescharacteristic
1081C22×C4C23×D7311yescharacteristic
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
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—22no—
1099C4⋊C4—22no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—41no—
1103C4⋊C4—41no—
1104C4⋊C4—41no—
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—1462no—
1117C4⋊C4—1462no—
1118C4⋊C4—1462no—
1119C4⋊C4—1462no—
1120C4⋊C4—1462no—
1121C4⋊C4—1462no—
1122C4⋊C4—1462no—
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—
1133C4⋊C4—1462no—
1134C4⋊C4—1462no—
1135C22⋊C4—22no—
1136C22⋊C4—22no—
1137C22⋊C4—22no—
1138C22⋊C4—41no—
1139C22⋊C4—41no—
1140C22⋊C4—2921no—
1141C22⋊C4—2921no—
1142C22⋊C4—734no—
1143C22⋊C4—1462no—
1144C22⋊C4—1462no—
1145C22⋊C4—1462no—
1146C22⋊C4—1462no—
1147C22⋊C4—1462no—
1148C22⋊C4—1462no—
1149C22⋊C4—1462no—
1150C22⋊C4—1462no—
1151C22⋊C4—1462no—
1152C22⋊C4—1462no—
1153C22⋊C4—1462no—
1154C22⋊C4—1462no—
1155C22⋊C4—1462no—
1156C22⋊C4#1192402914yes—
1157C42—22no—
1158C42—41no—
1159C42—2921no—
1160C42—2921no—
1161C42—2921no—
1162C42—2921no—
1163C42—2921no—
1164C42—2921no—
1165C42—1462no—
1166C42—1462no—
1167C42—1462no—
1168C42—1462no—
1169C42—1462no—
1170C42—1462no—
1171C42—1462no—
1172C42—1462no—
1173C42—1462no—
1174C42—1462no—
1175C42—1462no—
1176C42—1462no—
1177C42—1462no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—732no—
1185C23—1461no—
1186C23—1461no—
1187C23—1461no—
1188C23—1461no—
1189C23—1461no—
1190C23—1461no—
1191C23C2×#1192402912yes—
1192C23C24×D7311yescharacteristic
1193Q8—44no—
1194Q8—44no—
1195Q8—2924no—
1196D4—2924no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
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—82no—
1234C2×C4—2924no—
1235C2×C4—2924no—
1236C2×C4—2924no—
1237C2×C4—2924no—
1238C2×C4—5842no—
1239C2×C4—732no—
1240C2×C4—732no—
1241C2×C4—732no—
1242C2×C4—732no—
1243C2×C4—1461no—
1244C2×C4—1461no—
1245C2×C4—1461no—
1246C2×C4—1461no—
1247C2×C4—1461no—
1248C2×C4—1461no—
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#41×D7312yes—
1285C2×C4C2×#1192402712yes—
1286C2×C4C2×#1192402712yes—
1287C2×C4C2×#1192402712yes—
1288C2×C4C2×#1192402912yes—
1289C2×C4C2×#1192402912yes—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—2921no—
1298C22—2921no—
1299C22—2921no—
1300C22—2921no—
1301C22—1462no—
1302C22—1462no—
1303C22—1462no—
1304C22C2×#41×D7311yescharacteristic
1305C22C22×#1192402711yescharacteristic
1306C22C22×#1192402911yescharacteristic
1307C22H(5,𝔽2)×D7311yescharacteristic
1308C222−1+4×D7311yescharacteristic
1309C222−1+4×D7311yescharacteristic
1310C22#1798942211yescharacteristic
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—2921no—
1326C4—2921no—
1327C4—2921no—
1328C4—2921no—
1329C4—2921no—
1330C4—2921no—
1331C4—2921no—
1332C4—2921no—
1333C4—2921no—
1334C4—2921no—
1335C4—2921no—
1336C4—1462no—
1337C4—1462no—
1338C4—1462no—
1339C4—1462no—
1340C2—42no—
1341C2—2922no—
1342C2#2262354211yescharacteristic
1343C2#2262354711yescharacteristic
1344C2#2262355211yescharacteristic
1345C2#2262368111yescharacteristic
1346C2#2262368611yescharacteristic
1347C2#2262376811yescharacteristic
1348C2#2262427011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2729C2
prime radicalC22×C22⋊D73C23
hypercenter#2729D73
hypocenterC73#60043
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2729

Complements

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

NH ≅ G/Ntype
1. #22617754C2semidirect
2. #22616907C2semidirect
4. #22615586C2semidirect
5. #22615582C2semidirect
6. #22615503C2semidirect
7. #22615501C2semidirect
8. #22615338C2semidirect
9. #22615295C2semidirect
12. #22614767C2semidirect
13. #22614758C2semidirect
14. #22614676C2semidirect
15. #22614674C2semidirect
16. #22614553C2semidirect
17. #22614551C2semidirect
20. #22613608C2semidirect
21. #22613605C2semidirect
22. #22613016C2semidirect
23. #22613010C2semidirect
24. #22612961C2semidirect
25. #22612957C2semidirect
28. C4⋊Q8×Dic73C2semidirect
29. #22612425C2semidirect
30. #22612423C2semidirect
31. C73×#2729C2semidirect
677. #2729D73semidirect
706. C73#60043semidirect

Maximal subgroups

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

subgroupindex
#226177542
#226169072
#226162692
#226155862
#226155822
#226155032
#226155012
#226153382
#226152952
#226151762
#226148382
#226147672
#226147582
#226146762
#226146742
#226145532
#226145512
#226140282
#226140252
#226136082
#226136052
#226130162
#226130102
#226129612
#226129572
#226129262
#226129212
C4⋊Q8×Dic732
#226124252
#226124232
C73×#27292
#6004373