Finite Group Databasebeta

← #33299990

Subgroups — #33299990

Order 18688.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618270C211yesmaximal, characteristic, complemented
2#22618253C211yesmaximal, characteristic
3#22617530C211yesmaximal, characteristic, complemented
4#22617446C211yesmaximal, characteristic, complemented
5#22617407C211yesmaximal, characteristic, complemented
6#22617392C211yesmaximal, characteristic, complemented
7#22617376C211yesmaximal, characteristic, complemented
8#22617362C211yesmaximal, characteristic, complemented
9#22617353C211yesmaximal, characteristic, complemented
10#22617336C211yesmaximal, characteristic, complemented
11#22617314C211yesmaximal, characteristic
12#22617234C211yesmaximal, characteristic, complemented
13#22617219C211yesmaximal, characteristic, complemented
14#22617111C211yesmaximal, characteristic
15#22617081C211yesmaximal, characteristic, complemented
16#22617067C211yesmaximal, characteristic
17#22617027C211yesmaximal, characteristic
18#22616997C211yesmaximal, characteristic, complemented
19#22616125C211yesmaximal, characteristic, complemented
20#22616079C211yesmaximal, characteristic
21#22615431C211yesmaximal, characteristic, complemented
22#22615391C211yesmaximal, characteristic, complemented
23#22615391C211yesmaximal, characteristic, complemented
24#22615214C211yesmaximal, characteristic, complemented
25#22614802C211yesmaximal, characteristic, complemented
26#22614757C211yesmaximal, characteristic, complemented
27#22614742C211yesmaximal, characteristic, complemented
28#22614727C211yesmaximal, characteristic, complemented
29#22612721C211yesmaximal, characteristic
30#22612687C211yesmaximal, characteristic, complemented
31C73×#2283C211yesmaximal, characteristic, complemented
32C2×#14556574C2211yescharacteristic
33C2×#14556570C2211yescharacteristic
34C73⋊#401C2211yescharacteristic
35C73⋊#401C2211yescharacteristic
36#17988529C2211yescharacteristic
37#17988529C2211yescharacteristic
38#17988529C2211yescharacteristic
39#17988529C2211yescharacteristic
40#17988528C2211yescharacteristic
41#17988528C2211yescharacteristic
42#17988528C2211yescharacteristic
43#17988528C2211yescharacteristic
44#17988528C2211yescharacteristic
45#17988528C2211yescharacteristic
46#17988527C2211yescharacteristic
47#17988527C2211yescharacteristic
48#17988527C2211yescharacteristic
49#17988525C2211yescharacteristic
50#17988524C2211yescharacteristic
51#17988523C2211yescharacteristic
52#17988523C2211yescharacteristic
53#17988522C2211yescharacteristic
54#17988521C2211yescharacteristic
55#17988521C2211yescharacteristic
56#17988521C2211yescharacteristic
57#17988521C2211yescharacteristic
58#17988521C2211yescharacteristic
59#17988521C2211yescharacteristic
60#17988520C2211yescharacteristic
61#17988520C2211yescharacteristic
62#17988520C2211yescharacteristic
63#17988520C2211yescharacteristic
64#17988519C2211yescharacteristic
65#17988519C2211yescharacteristic
66#17988518C2211yescharacteristic
67#17988516C2211yescharacteristic
68#17988516C2211yescharacteristic
69#17988514C2211yescharacteristic
70#17988514C2211yescharacteristic
71#17988513C2211yescharacteristic
72#17988512C2211yescharacteristic
73#17988512C2211yescharacteristic
74#17988511C2211yescharacteristic
75#17988511C2211yescharacteristic
76#17988510C2211yescharacteristic
77#17988510C2211yescharacteristic
78#17988508C2211yescharacteristic
79#17988503C2211yescharacteristic
80#17988503C2211yescharacteristic
81#17988500C2211yescharacteristic
82#17988493C2211yescharacteristic
83#17988493C2211yescharacteristic
84#17988491C2211yescharacteristic
85#17988491C2211yescharacteristic
86#17988487C2211yescharacteristic
87#17988485C2211yescharacteristic
88#17988485C2211yescharacteristic
89#17988485C2211yescharacteristic
90#17988485C2211yescharacteristic
91#17988485C2211yescharacteristic
92#17988485C2211yescharacteristic
93#17988484C2211yescharacteristic
94#17988484C2211yescharacteristic
95#17988484C2211yescharacteristic
96#17988484C2211yescharacteristic
97#17988482C2211yescharacteristic
98#17988481C2211yescharacteristic
99#17988481C2211yescharacteristic
100#17988481C2211yescharacteristic
101#17988479C2211yescharacteristic
102#17988479C2211yescharacteristic
103#17988478C2211yescharacteristic
104#17988478C2211yescharacteristic
105#17988478C2211yescharacteristic
106#17988478C2211yescharacteristic
107#17988478C2211yescharacteristic
108#17988478C2211yescharacteristic
109#17988478C2211yescharacteristic
110#17988477C2211yescharacteristic
111#17988476C2211yescharacteristic
112#17988476C2211yescharacteristic
113#17988475C2211yescharacteristic
114#17988475C2211yescharacteristic
115#17988475C2211yescharacteristic
116#17988474C2211yescharacteristic
117#17988474C2211yescharacteristic
118#17988474C2211yescharacteristic
119#17988474C2211yescharacteristic
120#17988473C2211yescharacteristic
121#17988473C2211yescharacteristic
122#17988473C2211yescharacteristic
123#17988473C2211yescharacteristic
124#17988472C2211yescharacteristic
125#17988472C2211yescharacteristic
126#17988472C2211yescharacteristic
127#17988472C2211yescharacteristic
128#17988471C2211yescharacteristic
129#17988471C2211yescharacteristic
130#17988471C2211yescharacteristic
131#17988471C2211yescharacteristic
132#17988471C2211yescharacteristic
133#17988471C2211yescharacteristic
134#17988471C2211yescharacteristic
135#17988471C2211yescharacteristic
136#17988471C2211yescharacteristic
137#17988471C2211yescharacteristic
138#17988471C2211yescharacteristic
139#17988471C2211yescharacteristic
140#17988471C2211yescharacteristic
141#17988470C2211yescharacteristic
142#17988470C2211yescharacteristic
143#17988469C2211yescharacteristic
144#17988469C2211yescharacteristic
145#17988469C2211yescharacteristic
146#17988469C2211yescharacteristic
147#17988468C2211yescharacteristic
148#17988466C2211yescharacteristic
149#17988466C2211yescharacteristic
150#17988463C2211yescharacteristic
151#17988461C2211yescharacteristic
152#17988461C2211yescharacteristic
153#17988460C2211yescharacteristic
154#17988460C2211yescharacteristic
155#17988460C2211yescharacteristic
156#17988460C2211yescharacteristic
157#17988458C2211yescharacteristic
158#17988454C2211yescharacteristic
159#17988451C2211yescharacteristic
160#17988451C2211yescharacteristic
161#17988451C2211yescharacteristic
162#17988450C2211yescharacteristic
163#17988450C2211yescharacteristic
164#17988450C2211yescharacteristic
165#17988449C2211yescharacteristic
166#17988447C2211yescharacteristic
167#17988446C2211yescharacteristic
168C4×#11924007C2211yescharacteristic
169C4×#11924007C2211yescharacteristic
170C4×#11924007C2211yescharacteristic
171C4×#11924005C2211yescharacteristic
172C22×C42×C73C2211yescharacteristic
173#383×C73C2211yescharacteristic
174#383×C73C2211yescharacteristic
175#382×C73C2211yescharacteristic
176#382×C73C2211yescharacteristic
177#381×C73C2211yescharacteristic
178#381×C73C2211yescharacteristic
179#380×C73C2211yescharacteristic
180#380×C73C2211yescharacteristic
181C4×C4⋊C4×C73C2211yescharacteristic
182C4×C4⋊C4×C73C2211yescharacteristic
183C4×C22⋊C4×C73C2211yescharacteristic
184C4×C22⋊C4×C73C2211yescharacteristic
185#376×C73C2211yescharacteristic
186#376×C73C2211yescharacteristic
187C22×Dic146C2311yescharacteristic
188C22×C22⋊D73C2311yescharacteristic
189C22×C4×D73C2311yescharacteristic
190#14556574—24no—
191#14556570—24no—
192C2×C4⋊Dic73C2311yescharacteristic
193C2×C4⋊Dic73C2311yescharacteristic
194C2×C4⋊Dic73C2311yescharacteristic
195C2×C4⋊Dic73C2311yescharacteristic
196C2×C4⋊Dic73C2311yescharacteristic
197C2×C4⋊Dic73C2311yescharacteristic
198C2×C4⋊Dic73C2311yescharacteristic
199C2×C4⋊Dic73C2311yescharacteristic
200C2×C4⋊Dic73C2311yescharacteristic
201C2×C4⋊Dic73C2311yescharacteristic
202C2×C4⋊Dic73C2311yescharacteristic
203C2×#11924007C2311yescharacteristic
204C2×#11924007C2311yescharacteristic
205C2×#11924007C2311yescharacteristic
206C2×#11924007C2311yescharacteristic
207C2×#11924007C2311yescharacteristic
208C2×#11924007C2311yescharacteristic
209C2×#11924007C2311yescharacteristic
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×#11924005C2311yescharacteristic
238C2×#11924005C2311yescharacteristic
239C2×#11924005C2311yescharacteristic
240C2×#11924005C2311yescharacteristic
241C2×#11924005C2311yescharacteristic
242C2×#11924005C2311yescharacteristic
243C2×#11924005C2311yescharacteristic
244C2×#11924005C2311yescharacteristic
245C2×#11924005C2311yescharacteristic
246C2×#11924005C2311yescharacteristic
247C2×#11924005C2311yescharacteristic
248C2×#11924005C2311yescharacteristic
249C2×#11924005C2311yescharacteristic
250C2×C4×Dic73C2311yescharacteristic
251C2×C4×Dic73C2311yescharacteristic
252C2×C4×Dic73C2311yescharacteristic
253C2×C4×Dic73C2311yescharacteristic
254C2×C4×Dic73C2311yescharacteristic
255C2×C4×Dic73C2311yescharacteristic
256C2×C4×Dic73C2311yescharacteristic
257#14556498C2311yescharacteristic
258#14556498C2311yescharacteristic
259#14556498C2311yescharacteristic
260#14556498C2311yescharacteristic
261#14556498C2311yescharacteristic
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
309C23×C4×C73C2311yescharacteristic
310C23×C4×C73C2311yescharacteristic
311C23×C4×C73C2311yescharacteristic
312C2×C4⋊C4×C73C2311yescharacteristic
313C2×C4⋊C4×C73C2311yescharacteristic
314C2×C4⋊C4×C73C2311yescharacteristic
315C2×C4⋊C4×C73C2311yescharacteristic
316C2×C22⋊C4×C73C2311yescharacteristic
317C2×C22⋊C4×C73C2311yescharacteristic
318C2×C22⋊C4×C73C2311yescharacteristic
319C2×C22⋊C4×C73C2311yescharacteristic
320C2×C42×C73—24no—
321C2×C42×C73C2311yescharacteristic
322C2×C42×C73C2311yescharacteristic
323C2×C42×C73C2311yescharacteristic
324C2×C42×C73C2311yescharacteristic
325C2×C42×C73C2311yescharacteristic
326C2×C42×C73C2311yescharacteristic
327C2×C42×C73C2311yescharacteristic
328C2×C42×C73C2311yescharacteristic
329#95×C73C2311yescharacteristic
330#95×C73C2311yescharacteristic
331#95×C73C2311yescharacteristic
332#95×C73C2311yescharacteristic
333#95×C73C2311yescharacteristic
334#95×C73C2311yescharacteristic
335#95×C73C2311yescharacteristic
336#95×C73C2311yescharacteristic
337#95×C73C2311yescharacteristic
338#95×C73C2311yescharacteristic
339#95×C73C2311yescharacteristic
340#95×C73C2311yescharacteristic
341#95×C73C2311yescharacteristic
342#95×C73C2311yescharacteristic
343#95×C73C2311yescharacteristic
344#95×C73C2311yescharacteristic
345C23×D73C2411yescharacteristic
346C2×Dic146—22no—
347C2×Dic146—41no—
348C2×Dic146—41no—
349C2×C22⋊D73—22no—
350C2×C22⋊D73—41no—
351C2×C22⋊D73—41no—
352C22×Dic73C2411yescharacteristic
353C22×Dic73C2411yescharacteristic
354C22×Dic73C2411yescharacteristic
355C22×Dic73C2411yescharacteristic
356C22×Dic73C2411yescharacteristic
357C22×Dic73C2411yescharacteristic
358C22×Dic73C2411yescharacteristic
359C22×Dic73C2411yescharacteristic
360C22×Dic73C2411yescharacteristic
361C22×Dic73C2411yescharacteristic
362C22×Dic73C2411yescharacteristic
363C22×Dic73C2411yescharacteristic
364C22×Dic73C2411yescharacteristic
365C22×Dic73C2411yescharacteristic
366C22×Dic73C2411yescharacteristic
367C2×C4×D73—41no—
368C2×C4×D73—41no—
369C2×C4×D73—41no—
370C4⋊Dic73—22no—
371C4⋊Dic73—41no—
372C4⋊Dic73—41no—
373C4⋊Dic73—41no—
374C4⋊Dic73—41no—
375C4⋊Dic73—41no—
376C4⋊Dic73—41no—
377C4⋊Dic73—41no—
378C4⋊Dic73—41no—
379C4⋊Dic73—41no—
380C4⋊Dic73—41no—
381#11924007—22no—
382#11924007—22no—
383#11924007—22no—
384#11924007—22no—
385#11924007—22no—
386#11924007—41no—
387#11924007—41no—
388#11924007—41no—
389#11924007—41no—
390#11924007—41no—
391#11924007—41no—
392#11924007—41no—
393#11924007—41no—
394#11924007—41no—
395#11924007—41no—
396#11924007—41no—
397#11924007—41no—
398#11924007—41no—
399#11924007—41no—
400#11924007—41no—
401#11924007—41no—
402#11924007—41no—
403#11924007—41no—
404#11924007—41no—
405#11924007—41no—
406#11924007—41no—
407#11924007—41no—
408C22⋊Dic73—22no—
409C22⋊Dic73—22no—
410C22⋊Dic73—22no—
411C22⋊Dic73—41no—
412C22⋊Dic73—41no—
413C22⋊Dic73—41no—
414C22⋊Dic73—41no—
415#11924005—22no—
416#11924005—22no—
417#11924005—22no—
418#11924005—41no—
419#11924005—41no—
420#11924005—41no—
421#11924005—41no—
422#11924005—41no—
423#11924005—41no—
424#11924005—41no—
425#11924005—41no—
426#11924005—41no—
427#11924005—41no—
428C4×Dic73—41no—
429C4×Dic73—41no—
430C4×Dic73—41no—
431C4×Dic73—41no—
432C4×Dic73—41no—
433C4×Dic73—41no—
434C4×Dic73—41no—
435C24×C73C2411yescharacteristic
436C22×C4×C73—22no—
437C22×C4×C73—22no—
438C22×C4×C73—22no—
439C22×C4×C73—41no—
440C22×C4×C73—41no—
441C22×C4×C73—41no—
442C22×C4×C73—41no—
443C22×C4×C73—41no—
444C22×C4×C73#4114yes—
445C22×C4×C73C2411yescharacteristic
446C22×C4×C73C2411yescharacteristic
447C22×C4×C73C2411yescharacteristic
448C22×C4×C73C2411yescharacteristic
449C22×C4×C73C2411yescharacteristic
450C22×C4×C73C2411yescharacteristic
451C22×C4×C73C2411yescharacteristic
452C22×C4×C73C2411yescharacteristic
453C22×C4×C73C2411yescharacteristic
454C22×C4×C73C2411yescharacteristic
455C22×C4×C73C2411yescharacteristic
456C22×C4×C73C2411yescharacteristic
457C22×C4×C73C2411yescharacteristic
458C22×C4×C73C2411yescharacteristic
459C4⋊C4×C73—22no—
460C4⋊C4×C73—22no—
461C4⋊C4×C73—41no—
462C4⋊C4×C73—41no—
463C22⋊C4×C73—41no—
464C22⋊C4×C73—41no—
465C22⋊C4×C73—41no—
466C22⋊C4×C73—41no—
467C42×C73—22no—
468C42×C73—22no—
469C42×C73—22no—
470C42×C73—22no—
471C42×C73—41no—
472C42×C73—41no—
473C42×C73—41no—
474C42×C73—41no—
475C23×C73—21no—
476C23×C73—21no—
477C23×C73—21no—
478C23×C73—21no—
479C23×C73—21no—
480C23×C73—21no—
481C23×C73C2×#4112yes—
482C23×C73C2511yescharacteristic
483C22×D73—21no—
484C22×D73—21no—
485C22×D73—21no—
486C22×D73—21no—
487C22×D73—21no—
488C22×D73—21no—
489C22×D73—21no—
490C2×C4×C73—21no—
491C2×C4×C73—21no—
492C2×C4×C73—21no—
493C2×C4×C73—21no—
494C2×C4×C73—21no—
495C2×C4×C73—21no—
496C2×C4×C73—21no—
497C2×C4×C73—21no—
498C2×C4×C73—21no—
499C2×C4×C73—21no—
500C2×C4×C73—21no—
501C2×C4×C73—21no—
502C2×C4×C73—21no—
503C2×C4×C73—21no—
504C2×C4×C73—21no—
505C2×C4×C73—21no—
506C2×C4×C73—21no—
507C2×C4×C73—21no—
508C2×C4×C73—21no—
509C2×C4×C73—21no—
510C2×C4×C73—21no—
511C2×C4×C73—21no—
512C2×C4×C73—21no—
513C2×C4×C73—21no—
514C2×C4×C73—21no—
515C2×C4×C73—21no—
516C2×C4×C73—21no—
517C2×C4×C73—21no—
518C2×C4×C73—21no—
519C2×C4×C73—21no—
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—44no—
530C2×C4×C73—44no—
531C2×C4×C73—44no—
532C2×C4×C73C2×#4112yes—
533C2×C4×C73C2×#4112yes—
534C2×C4×C732−1+412yes—
535C22⋊D73—82no—
536C2×Dic73—21no—
537C2×Dic73—21no—
538C2×Dic73—21no—
539C2×Dic73—21no—
540C2×Dic73—21no—
541C2×Dic73—21no—
542C2×Dic73—21no—
543C2×Dic73—21no—
544C2×Dic73—21no—
545C2×Dic73—21no—
546C2×Dic73—21no—
547C2×Dic73—21no—
548C2×Dic73—21no—
549C2×Dic73—21no—
550C2×Dic73—21no—
551C2×Dic73—21no—
552C2×Dic73—21no—
553C2×Dic73—21no—
554C2×Dic73—21no—
555C2×Dic73—21no—
556C2×Dic73—21no—
557C2×Dic73—21no—
558C2×Dic73—21no—
559C2×Dic73—21no—
560C2×Dic73—21no—
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—
581C4×D73—82no—
582Dic146—82no—
583C22×C73—22no—
584C22×C73—22no—
585C22×C73—22no—
586C22×C73—41no—
587C22×C73—41no—
588C22×C73—41no—
589C22×C73—41no—
590C22×C73C22×#4111yescharacteristic
591C22×C73C2×2−1+411yescharacteristic
592C22×C73#58511yescharacteristic
593C22×C73#58511yescharacteristic
594C22×C73#58511yescharacteristic
595C22×C73#58511yescharacteristic
596C22×C73#58511yescharacteristic
597C2×D73—41no—
598C2×D73—41no—
599C2×D73—41no—
600C2×D73—41no—
601C2×D73—41no—
602C2×D73—41no—
603C2×D73—41no—
604C4×C73—22no—
605C4×C73—22no—
606C4×C73—22no—
607C4×C73—41no—
608C4×C73—41no—
609C4×C73—41no—
610C4×C73—41no—
611C4×C73—41no—
612C4×C73—41no—
613C4×C73—41no—
614C4×C73—41no—
615C4×C73—41no—
616C4×C73—41no—
617C4×C73—41no—
618Dic73—41no—
619Dic73—41no—
620Dic73—41no—
621Dic73—41no—
622Dic73—41no—
623Dic73—41no—
624Dic73—41no—
625Dic73—41no—
626Dic73—41no—
627Dic73—41no—
628Dic73—41no—
629Dic73—41no—
630Dic73—41no—
631Dic73—41no—
632Dic73—41no—
633#36981—731nomaximal, Sylow
634C2×C73—42no—
635C2×C73#345511yescharacteristic
636C2×C73#349111yescharacteristic
637C2×C73#349511yescharacteristic
638C2×C73#355711yescharacteristic
639C2×C73#356511yescharacteristic
640C2×C73#356611yescharacteristic
641C2×C73#356711yescharacteristic
642D73—81no—
643#2855—731no—
644#2853—731no—
645#2777—731no—
646#2771—731no—
647#2768—731no—
648#2767—731no—
649#2766—731no—
650#2765—731no—
651#2764—731no—
652#2762—731no—
653#2761—731no—
654#2755—731no—
655#2754—731no—
656#2746—731no—
657#2744—731no—
658#2743—731no—
659#2740—731no—
660#2738—731no—
661#2667—731no—
662#2663—731no—
663#2594—731no—
664#2590—731no—
665#2590—731no—
666#2575—731no—
667#2533—731no—
668#2530—731no—
669#2529—731no—
670#2528—731no—
671#2335—731no—
672#2332—731no—
673#2283D7311yescharacteristic, complemented
674C73#3698111yescharacteristic, complemented, Sylow
675C2×#123—731no—
676C2×C22⋊Q8—731no—
677C22×C42C2×D7311yescharacteristic
678#401—731no—
679#401—731no—
680#400—731no—
681#400—731no—
682#400—731no—
683#400—731no—
684#400—731no—
685#400—731no—
686#400—731no—
687#400—731no—
688#400—731no—
689#400—731no—
690#400—731no—
691#400—731no—
692#400—731no—
693#400—731no—
694#399—731no—
695#399—731no—
696#399—731no—
697#399—731no—
698#398—731no—
699#398—731no—
700#398—731no—
701#398—731no—
702#398—731no—
703#398—731no—
704#398—731no—
705#398—731no—
706#398—731no—
707#398—731no—
708#398—731no—
709#398—731no—
710#398—731no—
711#397—731no—
712#397—731no—
713#397—731no—
714#397—731no—
715#397—731no—
716#397—731no—
717#397—731no—
718#396—731no—
719#396—731no—
720#396—731no—
721#396—731no—
722#395—731no—
723#394—731no—
724#394—731no—
725#393—731no—
726#391—731no—
727#391—731no—
728#391—731no—
729#391—731no—
730#390—731no—
731#389—731no—
732#389—731no—
733#389—731no—
734#389—731no—
735#389—731no—
736#389—731no—
737#389—731no—
738#389—731no—
739#389—731no—
740#389—731no—
741#389—731no—
742#388—731no—
743#388—731no—
744#388—731no—
745#388—731no—
746#388—731no—
747#388—731no—
748#388—731no—
749#388—731no—
750#388—731no—
751#388—731no—
752#388—731no—
753#388—731no—
754#388—731no—
755#388—731no—
756#388—731no—
757#388—731no—
758#388—731no—
759#388—731no—
760#387—731no—
761#387—731no—
762#387—731no—
763#387—731no—
764#387—731no—
765#387—731no—
766#387—731no—
767#387—731no—
768#387—731no—
769#387—731no—
770#387—731no—
771#387—731no—
772#387—731no—
773#387—731no—
774#387—731no—
775#387—731no—
776#387—731no—
777#387—731no—
778#387—731no—
779#387—731no—
780#387—731no—
781#387—731no—
782#387—731no—
783#387—731no—
784#387—731no—
785#387—731no—
786#387—731no—
787#387—731no—
788#387—731no—
789#387—731no—
790#387—731no—
791#387—731no—
792#386—731no—
793#386—731no—
794#386—731no—
795#385—731no—
796#385—731no—
797#385—731no—
798#385—731no—
799#385—731no—
800#385—731no—
801#385—731no—
802#383—731no—
803#383C2×D7311yescharacteristic
804#383C2×D7311yescharacteristic
805#382—731no—
806#382—731no—
807#382—731no—
808#382C2×D7311yescharacteristic
809#382C2×D7311yescharacteristic
810#381—731no—
811#381—731no—
812#381—731no—
813#381—731no—
814#381C2×D7311yescharacteristic
815#381C2×D7311yescharacteristic
816#380—731no—
817#380—731no—
818#380C2×D7311yescharacteristic
819#380C2×D7311yescharacteristic
820C4×C4⋊C4—731no—
821C4×C4⋊C4—731no—
822C4×C4⋊C4—731no—
823C4×C4⋊C4C2×D7311yescharacteristic
824C4×C4⋊C4C2×D7311yescharacteristic
825C4×C22⋊C4—731no—
826C4×C22⋊C4C2×D7311yescharacteristic
827C4×C22⋊C4C2×D7311yescharacteristic
828#376C2×D7311yescharacteristic
829#376C2×D7311yescharacteristic
830C22×Q8—731no—
831C22×D4—731no—
832C23×C4—731no—
833C23×C4C22×D7311yescharacteristic
834C23×C4C22×D7311yescharacteristic
835C23×C4C22×D7311yescharacteristic
836#123—1464no—
837C22⋊Q8—1464no—
838C2×C4⋊C4—731no—
839C2×C4⋊C4—731no—
840C2×C4⋊C4—731no—
841C2×C4⋊C4—731no—
842C2×C4⋊C4—731no—
843C2×C4⋊C4—731no—
844C2×C4⋊C4—731no—
845C2×C4⋊C4—731no—
846C2×C4⋊C4—731no—
847C2×C4⋊C4—731no—
848C2×C4⋊C4—731no—
849C2×C4⋊C4—731no—
850C2×C4⋊C4—731no—
851C2×C4⋊C4—731no—
852C2×C4⋊C4—731no—
853C2×C4⋊C4—731no—
854C2×C4⋊C4—731no—
855C2×C4⋊C4—731no—
856C2×C4⋊C4—731no—
857C2×C4⋊C4—731no—
858C2×C4⋊C4—731no—
859C2×C4⋊C4—731no—
860C2×C4⋊C4—731no—
861C2×C4⋊C4—731no—
862C2×C4⋊C4—731no—
863C2×C4⋊C4—731no—
864C2×C4⋊C4—731no—
865C2×C4⋊C4—731no—
866C2×C4⋊C4—731no—
867C2×C4⋊C4—731no—
868C2×C4⋊C4—731no—
869C2×C4⋊C4—731no—
870C2×C4⋊C4—731no—
871C2×C4⋊C4—731no—
872C2×C4⋊C4—731no—
873C2×C4⋊C4—731no—
874C2×C4⋊C4—731no—
875C2×C4⋊C4—731no—
876C2×C4⋊C4C22×D7311yescharacteristic
877C2×C4⋊C4C22×D7311yescharacteristic
878C2×C4⋊C4C22×D7311yescharacteristic
879C2×C4⋊C4C22×D7311yescharacteristic
880C2×C22⋊C4—731no—
881C2×C22⋊C4—731no—
882C2×C22⋊C4—731no—
883C2×C22⋊C4—731no—
884C2×C22⋊C4—731no—
885C2×C22⋊C4—731no—
886C2×C22⋊C4—731no—
887C2×C22⋊C4—731no—
888C2×C22⋊C4—731no—
889C2×C22⋊C4—731no—
890C2×C22⋊C4—731no—
891C2×C22⋊C4—731no—
892C2×C22⋊C4—731no—
893C2×C22⋊C4—731no—
894C2×C22⋊C4—731no—
895C2×C22⋊C4—731no—
896C2×C22⋊C4—731no—
897C2×C22⋊C4—731no—
898C2×C22⋊C4—731no—
899C2×C22⋊C4—731no—
900C2×C22⋊C4C22×D7311yescharacteristic
901C2×C22⋊C4C22×D7311yescharacteristic
902C2×C22⋊C4C22×D7311yescharacteristic
903C2×C22⋊C4C22×D7311yescharacteristic
904C2×C42—24no—
905C2×C42—731no—
906C2×C42—731no—
907C2×C42—731no—
908C2×C42—731no—
909C2×C42—731no—
910C2×C42—731no—
911C2×C42—731no—
912C2×C42C22×D7311yescharacteristic
913C2×C42C22×D7311yescharacteristic
914C2×C42C22×D7311yescharacteristic
915C2×C42C22×D7311yescharacteristic
916C2×C42C22×D7311yescharacteristic
917C2×C42C22×D7311yescharacteristic
918C2×C42C22×D7311yescharacteristic
919C2×C42C22×D7311yescharacteristic
920#95—731no—
921#95—731no—
922#95—731no—
923#95—731no—
924#95—731no—
925#95—731no—
926#95—731no—
927#95—731no—
928#95—731no—
929#95—731no—
930#95—731no—
931#95—731no—
932#95—731no—
933#95—731no—
934#95—731no—
935#95—731no—
936#95—731no—
937#95—731no—
938#95—731no—
939#95—731no—
940#95—731no—
941#95—731no—
942#95—731no—
943#95—731no—
944#95—731no—
945#95—731no—
946#95—731no—
947#95—731no—
948#95—731no—
949#95—731no—
950#95—731no—
951#95—731no—
952#95—731no—
953#95—731no—
954#95—731no—
955#95—731no—
956#95—731no—
957#95—731no—
958#95—731no—
959#95—731no—
960#95—731no—
961#95—731no—
962#95—731no—
963#95—731no—
964#95—731no—
965#95—731no—
966#95—731no—
967#95—731no—
968#95—731no—
969#95—731no—
970#95—731no—
971#95—731no—
972#95C22×D7311yescharacteristic
973#95C22×D7311yescharacteristic
974#95C22×D7311yescharacteristic
975#95C22×D7311yescharacteristic
976#95C22×D7311yescharacteristic
977#95C22×D7311yescharacteristic
978#95C22×D7311yescharacteristic
979#95C22×D7311yescharacteristic
980#95C22×D7311yescharacteristic
981#95C22×D7311yescharacteristic
982#95C22×D7311yescharacteristic
983#95C22×D7311yescharacteristic
984#95C22×D7311yescharacteristic
985#95C22×D7311yescharacteristic
986#95C22×D7311yescharacteristic
987#95C22×D7311yescharacteristic
988C24—731no—
989C24C23×D7311yescharacteristic
990C2×Q8—2921no—
991C2×Q8—2921no—
992C2×Q8—1462no—
993C2×D4—2921no—
994C2×D4—2921no—
995C2×D4—1462no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—41no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—2921no—
1005C22×C4—2921no—
1006C22×C4—2921no—
1007C22×C4—731no—
1008C22×C4—731no—
1009C22×C4—731no—
1010C22×C4—731no—
1011C22×C4—731no—
1012C22×C4—731no—
1013C22×C4—731no—
1014C22×C4—731no—
1015C22×C4—731no—
1016C22×C4—731no—
1017C22×C4—731no—
1018C22×C4—731no—
1019C22×C4—731no—
1020C22×C4—731no—
1021C22×C4—731no—
1022C22×C4#1192402814yes—
1023C22×C4C23×D7311yescharacteristic
1024C22×C4C23×D7311yescharacteristic
1025C22×C4C23×D7311yescharacteristic
1026C22×C4C23×D7311yescharacteristic
1027C22×C4C23×D7311yescharacteristic
1028C22×C4C23×D7311yescharacteristic
1029C22×C4C23×D7311yescharacteristic
1030C22×C4C23×D7311yescharacteristic
1031C22×C4C23×D7311yescharacteristic
1032C22×C4C23×D7311yescharacteristic
1033C22×C4C23×D7311yescharacteristic
1034C22×C4C23×D7311yescharacteristic
1035C22×C4C23×D7311yescharacteristic
1036C22×C4C23×D7311yescharacteristic
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—2921no—
1042C4⋊C4—2921no—
1043C4⋊C4—2921no—
1044C4⋊C4—2921no—
1045C4⋊C4—2921no—
1046C4⋊C4—2921no—
1047C4⋊C4—2921no—
1048C4⋊C4—2921no—
1049C4⋊C4—2921no—
1050C4⋊C4—2921no—
1051C4⋊C4—2921no—
1052C4⋊C4—2921no—
1053C4⋊C4—2921no—
1054C4⋊C4—2921no—
1055C4⋊C4—2921no—
1056C4⋊C4—2921no—
1057C4⋊C4—2921no—
1058C4⋊C4—2921no—
1059C4⋊C4—2921no—
1060C4⋊C4—2921no—
1061C4⋊C4—2921no—
1062C4⋊C4—2921no—
1063C4⋊C4—2921no—
1064C4⋊C4—2921no—
1065C4⋊C4—2921no—
1066C4⋊C4—2921no—
1067C4⋊C4—2921no—
1068C4⋊C4—2921no—
1069C4⋊C4—2921no—
1070C4⋊C4—2921no—
1071C4⋊C4—2921no—
1072C4⋊C4—2921no—
1073C4⋊C4—1462no—
1074C4⋊C4—1462no—
1075C4⋊C4—1462no—
1076C4⋊C4—1462no—
1077C4⋊C4—1462no—
1078C4⋊C4—1462no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—2921no—
1084C22⋊C4—2921no—
1085C22⋊C4—2921no—
1086C22⋊C4—2921no—
1087C22⋊C4—2921no—
1088C22⋊C4—2921no—
1089C22⋊C4—2921no—
1090C22⋊C4—2921no—
1091C22⋊C4—2921no—
1092C22⋊C4—2921no—
1093C22⋊C4—2921no—
1094C22⋊C4—2921no—
1095C22⋊C4—2921no—
1096C22⋊C4—2921no—
1097C22⋊C4—1462no—
1098C22⋊C4—1462no—
1099C22⋊C4—1462no—
1100C22⋊C4—1462no—
1101C22⋊C4—1462no—
1102C22⋊C4—1462no—
1103C42—22no—
1104C42—22no—
1105C42—22no—
1106C42—22no—
1107C42—41no—
1108C42—41no—
1109C42—41no—
1110C42—41no—
1111C42—2921no—
1112C42—2921no—
1113C42—2921no—
1114C42—2921no—
1115C42—2921no—
1116C42—2921no—
1117C42—2921no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—1461no—
1125C23—1461no—
1126C23—1461no—
1127C23—1461no—
1128C23—1461no—
1129C23—1461no—
1130C23—1461no—
1131C23C2×#1192402812yes—
1132C23C24×D7311yescharacteristic
1133Q8—5842no—
1134D4—5842no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—44no—
1175C2×C4—44no—
1176C2×C4—44no—
1177C2×C4—5842no—
1178C2×C4—1461no—
1179C2×C4—1461no—
1180C2×C4—1461no—
1181C2×C4—1461no—
1182C2×C4—1461no—
1183C2×C4—1461no—
1184C2×C4—1461no—
1185C2×C4—1461no—
1186C2×C4—1461no—
1187C2×C4—1461no—
1188C2×C4—1461no—
1189C2×C4—1461no—
1190C2×C4—1461no—
1191C2×C4—1461no—
1192C2×C4—1461no—
1193C2×C4—1461no—
1194C2×C4—1461no—
1195C2×C4—1461no—
1196C2×C4—1461no—
1197C2×C4—1461no—
1198C2×C4—1461no—
1199C2×C4—1461no—
1200C2×C4—1461no—
1201C2×C4—1461no—
1202C2×C4—1461no—
1203C2×C4—1461no—
1204C2×C4—1461no—
1205C2×C4—1461no—
1206C2×C4—1461no—
1207C2×C4—1461no—
1208C2×C4—1461no—
1209C2×C4—1461no—
1210C2×C4—1461no—
1211C2×C4—1461no—
1212C2×C4—1461no—
1213C2×C4—1461no—
1214C2×C4—1461no—
1215C2×C4—1461no—
1216C2×C4—1461no—
1217C2×C4—1461no—
1218C2×C4—1461no—
1219C2×C4—1461no—
1220C2×C4—1461no—
1221C2×C4—1461no—
1222C2×C4—1461no—
1223C2×C4C2×#1192402812yes—
1224C2×C4C2×#1192402812yes—
1225C2×C4#1455663812yes—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—2921no—
1234C22—2921no—
1235C22—2921no—
1236C22—2921no—
1237C22—2921no—
1238C22—2921no—
1239C22—2921no—
1240C22C22×#1192402811yescharacteristic
1241C22C2×#1455663811yescharacteristic
1242C22#1798942311yescharacteristic
1243C22#1798942311yescharacteristic
1244C22#1798942311yescharacteristic
1245C22#1798942311yescharacteristic
1246C22#1798942311yescharacteristic
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—2921no—
1262C4—2921no—
1263C4—2921no—
1264C4—2921no—
1265C4—2921no—
1266C4—2921no—
1267C4—2921no—
1268C4—2921no—
1269C4—2921no—
1270C4—2921no—
1271C4—2921no—
1272C4—2921no—
1273C4—2921no—
1274C4—2921no—
1275C4—2921no—
1276C2—42no—
1277C2—5841no—
1278C2#2262332111yescharacteristic
1279C2#2262362911yescharacteristic
1280C2#2262368311yescharacteristic
1281C2#2262443311yescharacteristic
1282C2#2262456811yescharacteristic
1283C2#2262459911yescharacteristic
1284C2#2262461911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2283C2
prime radicalC22×C22⋊D73C23
hypercenter#2283D73
hypocenterC73#36981
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2283

Complements

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

NH ≅ G/Ntype
1. #22618270C2semidirect
3. #22617530C2semidirect
4. #22617446C2semidirect
5. #22617407C2semidirect
6. #22617392C2semidirect
7. #22617376C2semidirect
8. #22617362C2semidirect
9. #22617353C2semidirect
10. #22617336C2semidirect
12. #22617234C2semidirect
13. #22617219C2semidirect
15. #22617081C2semidirect
18. #22616997C2semidirect
19. #22616125C2semidirect
21. #22615431C2semidirect
22. #22615391C2semidirect
23. #22615391C2semidirect
24. #22615214C2semidirect
25. #22614802C2semidirect
26. #22614757C2semidirect
27. #22614742C2semidirect
28. #22614727C2semidirect
30. #22612687C2semidirect
31. C73×#2283C2semidirect
673. #2283D73semidirect
674. C73#36981semidirect

Maximal subgroups

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

subgroupindex
#226182702
#226182532
#226175302
#226174462
#226174072
#226173922
#226173762
#226173622
#226173532
#226173362
#226173142
#226172342
#226172192
#226171112
#226170812
#226170672
#226170272
#226169972
#226161252
#226160792
#226154312
#226153912
#226152142
#226148022
#226147572
#226147422
#226147272
#226127212
#226126872
C73×#22832
#3698173