Finite Group Databasebeta

← #13524661

Subgroups — #13524661

Order 1792.

2040 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2388C211yesmaximal, characteristic
2#11741531C212yesmaximal, complemented
3#11739791C211yesmaximal, characteristic, complemented
4C4×#6499C211yesmaximal, characteristic, complemented
5C4×#6498C212yesmaximal, complemented
6#11739764C212yesmaximal, complemented
7#11734645C211yesmaximal, characteristic, complemented
8#11734639C211yesmaximal, characteristic, complemented
9#11734413C211yesmaximal, characteristic, complemented
10#11734401C211yesmaximal, characteristic, complemented
11#11734386C212yesmaximal, complemented
12#11734377C212yesmaximal, complemented
13#11734241C212yesmaximal, complemented
14#11734141C212yesmaximal, complemented
15#11734134C212yesmaximal, complemented
16#11734130C212yesmaximal, complemented
17#11730925C212yesmaximal, complemented
18C4×#6442C212yesmaximal, complemented
19C4×#6440C212yesmaximal, complemented
20C22×C7×#41C2211yescharacteristic
21C2×C4×C7×D4C2212yes—
22C2×C4×C7×D4C2211yescharacteristic
23C2×#6499C2211yescharacteristic
24C2×#6498C2212yes—
25C2×#6489C2212yes—
26C2×#6489C2211yescharacteristic
27C22×C4×Dic7C2212yes—
28C2×#6442C2212yes—
29C2×#6440C2212yes—
30C2×#6440C2212yes—
31C2×C4×Dic14C2211yescharacteristic
32C7×#395C2211yescharacteristic
33C7×#394C2212yes—
34C7×#394C2211yescharacteristic
35C7×#393C2211yescharacteristic
36C7×#392C2211yescharacteristic
37C7×#392C2212yes—
38C4×C7×C22⋊C4C2212yes—
39C4×C7×C22⋊C4C2211yescharacteristic
40#90002C2212yes—
41#90002C2212yes—
42#89994C2212yes—
43#89993C2212yes—
44#89993C2212yes—
45#89993C2212yes—
46#89993C2212yes—
47#89993C2211yescharacteristic
48#89992C2212yes—
49#89992C2212yes—
50#89992C2212yes—
51#89992C2212yes—
52#89992C2212yes—
53C4×C22⋊Dic7C2212yes—
54C4×C22⋊Dic7C2212yes—
55C4×C22⋊Dic7C2212yes—
56C4×C22⋊Dic7C2212yes—
57C4×C22⋊Dic7C2212yes—
58C4×C22⋊Dic7C2211yescharacteristic
59#89758C2211yescharacteristic
60#89757C2212yes—
61#89757C2212yes—
62#89755C2211yescharacteristic
63#89750C2212yes—
64#89750C2212yes—
65#89749C2211yescharacteristic
66#89746C2211yescharacteristic
67#89725C2211yescharacteristic
68#89724C2212yes—
69#89723C2212yes—
70#89723C2212yes—
71#89723C2212yes—
72#89723C2212yes—
73#89723C2212yes—
74#89721C2211yescharacteristic
75#89721C2212yes—
76#89720C2212yes—
77#89720C2212yes—
78#89719C2212yes—
79#89718C2212yes—
80#89717C2212yes—
81#89717C2212yes—
82#89717C2212yes—
83#89716C2212yes—
84#89716C2212yes—
85#89716C2212yes—
86#89715C2212yes—
87C22⋊C4×Dic7C2212yes—
88C22⋊C4×Dic7C2212yes—
89C4×C4⋊Dic7C2212yes—
90C4×Dic7⋊C4C2212yes—
91C4×Dic7⋊C4C2212yes—
92C4×Dic7⋊C4C2212yes—
93C42×Dic7C2212yes—
94C42×Dic7C2211yescharacteristic
95#89433C2212yes—
96#89432C2212yes—
97#89429C2212yes—
98#89428C2212yes—
99#89427C2212yes—
100#89425C2212yes—
101#89424C2212yes—
102#89423C2212yes—
103#89421C2212yes—
104#89421C2212yes—
105#89420C2212yes—
106#89420C2212yes—
107#34871—71nomaximal, Sylow
108C2×C7×#41—28no—
109C2×C7×#41—42no—
110C22×C7×Q8C2311yescharacteristic
111C22×C7×D4C2311yescharacteristic
112C22×C7×D4C2312yes—
113C22×C7×D4C2312yes—
114C22×C7×D4C2311yescharacteristic
115C23×C4×C7C2311yescharacteristic
116C23×C4×C7C2311yescharacteristic
117C23×C4×C7C2312yes—
118C23×Dic7C2312yes—
119C23×Dic7C2312yes—
120C22×Dic14C2311yescharacteristic
121C4×C7×D4—28no—
122C4×C7×D4—42no—
123C2×C7×C4⋊C4C2312yes—
124C2×C7×C4⋊C4C2311yescharacteristic
125C2×C7×C22⋊C4C2312yes—
126C2×C7×C22⋊C4C2312yes—
127C2×C7×C22⋊C4C2312yes—
128C2×C7×C22⋊C4C2312yes—
129C2×C7×C22⋊C4C2312yes—
130C2×C7×C22⋊C4C2311yescharacteristic
131C2×C7×C22⋊C4C2311yescharacteristic
132C2×C42×C7C2311yescharacteristic
133C2×C42×C7C2312yes—
134C2×C22⋊Dic7C2312yes—
135C2×C22⋊Dic7C2312yes—
136C2×C22⋊Dic7C2312yes—
137C2×C22⋊Dic7C2312yes—
138C2×C22⋊Dic7C2312yes—
139C2×C22⋊Dic7C2312yes—
140C2×C22⋊Dic7C2312yes—
141C2×C22⋊Dic7C2312yes—
142C2×C22⋊Dic7C2312yes—
143C2×C22⋊Dic7C2312yes—
144C2×C22⋊Dic7C2312yes—
145C2×C22⋊Dic7C2312yes—
146C2×C22⋊Dic7C2312yes—
147C2×C22⋊Dic7C2312yes—
148#6499—24no—
149#6498—28no—
150#6489—44no—
151#6489—42no—
152C2×C4⋊Dic7C2312yes—
153C2×C4⋊Dic7C2311yescharacteristic
154C2×C4⋊Dic7C2312yes—
155C2×C4⋊Dic7C2312yes—
156C2×C4⋊Dic7C2312yes—
157C2×C4⋊Dic7C2311yescharacteristic
158C2×C4⋊Dic7C2311yescharacteristic
159C2×Dic7⋊C4C2312yes—
160C2×Dic7⋊C4C2312yes—
161C2×Dic7⋊C4C2312yes—
162C2×Dic7⋊C4C2312yes—
163C2×Dic7⋊C4C2312yes—
164C2×Dic7⋊C4C2312yes—
165C2×Dic7⋊C4C2312yes—
166C2×C4×Dic7—28no—
167C2×C4×Dic7C2312yes—
168C2×C4×Dic7C2312yes—
169C2×C4×Dic7C2312yes—
170C2×C4×Dic7C2312yes—
171C2×C4×Dic7C2312yes—
172C2×C4×Dic7C2312yes—
173C2×C4×Dic7C2312yes—
174C2×C4×Dic7C2312yes—
175C2×C4×Dic7C2312yes—
176C2×C4×Dic7C2312yes—
177C2×C4×Dic7C2311yescharacteristic
178C2×C4×Dic7C2312yes—
179C2×C4×Dic7C2311yescharacteristic
180#6442—28no—
181#6440—28no—
182#6440—28no—
183C4×Dic14—42no—
184C7×#95C2312yes—
185C7×#95C2312yes—
186C7×#95C2311yescharacteristic
187C7×#95C2311yescharacteristic
188C7⋊#95C2312yes—
189C7⋊#95C2312yes—
190C7⋊#95C2312yes—
191C7⋊#95C2312yes—
192C7⋊#95C2312yes—
193C7⋊#95C2312yes—
194C7⋊#95C2312yes—
195C7⋊#95C2312yes—
196C7⋊#95C2312yes—
197C7⋊#95C2312yes—
198C7⋊#95C2312yes—
199C7⋊#95C2312yes—
200C7⋊#95C2312yes—
201C7⋊#95C2312yes—
202C7⋊#95C2312yes—
203C7⋊#95C2312yes—
204C7⋊#95C2311yescharacteristic
205C7⋊#95C2312yes—
206C7⋊#95C2312yes—
207C7⋊#95C2311yescharacteristic
208#2612—71no—
209#2610—72no—
210#2609—71no—
211#2586—71no—
212#2572—71no—
213#2554—72no—
214#2532—72no—
215#2526—72no—
216#2479—72no—
217#2471—72no—
218#2396—72no—
219#2395—71no—
220#2388D711yescharacteristic
221C4×#126—72no—
222C4×#124—71no—
223C4×#123—72no—
224#2297—72no—
225#2293—72no—
226C4×#117—72no—
227C24×C7C2411yescharacteristic
228C24×C7C2411yescharacteristic
229C24×C7C2412yes—
230C7×#41—416no—
231C2×C7×Q8—24no—
232C2×C7×Q8—41no—
233C2×C7×D4—24no—
234C2×C7×D4—24no—
235C2×C7×D4—24no—
236C2×C7×D4—24no—
237C2×C7×D4—22no—
238C2×C7×D4—24no—
239C2×C7×D4—41no—
240C2×C7×D4—42no—
241C2×C7×D4—41no—
242C2×C7×D4—42no—
243C2×C7×D4—41no—
244C22×C4×C7—24no—
245C22×C4×C7—24no—
246C22×C4×C7—24no—
247C22×C4×C7—24no—
248C22×C4×C7—22no—
249C22×C4×C7—22no—
250C22×C4×C7#4118yes—
251C22×C4×C7C2411yescharacteristic
252C22×C4×C7C2411yescharacteristic
253C22×C4×C7C2412yes—
254C22×C4×C7C2411yescharacteristic
255C22×C4×C7C2412yes—
256C22×C4×C7C2412yes—
257C22×C4×C7C2411yescharacteristic
258C22×C4×C7C2411yescharacteristic
259C22×Dic7—24no—
260C22×Dic7—24no—
261C22×Dic7—24no—
262C22×Dic7—24no—
263C22×Dic7—24no—
264C22×Dic7—42no—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C2×Dic14—22no—
274C2×Dic14—41no—
275C2×Dic14—41no—
276C7×C4⋊C4—24no—
277C7×C4⋊C4—41no—
278C7×C22⋊C4—24no—
279C7×C22⋊C4—24no—
280C7×C22⋊C4—24no—
281C7×C22⋊C4—24no—
282C7×C22⋊C4—24no—
283C7×C22⋊C4—41no—
284C7×C22⋊C4—41no—
285C42×C7—24no—
286C42×C7—22no—
287C22⋊Dic7—24no—
288C22⋊Dic7—24no—
289C22⋊Dic7—24no—
290C22⋊Dic7—24no—
291C22⋊Dic7—24no—
292C22⋊Dic7—24no—
293C22⋊Dic7—24no—
294C22⋊Dic7—24no—
295C22⋊Dic7—24no—
296C22⋊Dic7—42no—
297C22⋊Dic7—42no—
298C22⋊Dic7—42no—
299C22⋊Dic7—42no—
300C22⋊Dic7—42no—
301C4⋊Dic7—24no—
302C4⋊Dic7—41no—
303C4⋊Dic7—42no—
304C4⋊Dic7—42no—
305C4⋊Dic7—42no—
306C4⋊Dic7—41no—
307C4⋊Dic7—41no—
308Dic7⋊C4—24no—
309Dic7⋊C4—24no—
310Dic7⋊C4—24no—
311Dic7⋊C4—24no—
312Dic7⋊C4—24no—
313Dic7⋊C4—42no—
314Dic7⋊C4#4118yescomplemented
315C4×Dic7—24no—
316C4×Dic7—24no—
317C4×Dic7—24no—
318C4×Dic7—24no—
319C4×Dic7—24no—
320C4×Dic7—24no—
321C4×Dic7—24no—
322C4×Dic7—24no—
323C4×Dic7—24no—
324C4×Dic7—24no—
325C4×Dic7—41no—
326C4×Dic7—42no—
327C4×Dic7#4114yescomplemented
328C22×#41C2×D711yescharacteristic
329C2×#126—72no—
330C2×#124—71no—
331C2×#123—72no—
332C2×C4×Q8—71no—
333C2×C4×D4C2×D712yes—
334C2×C4×D4C2×D711yescharacteristic
335C2×#117—71no—
336C2×#117—72no—
337C2×#117—72no—
338C2×#117—72no—
339C22×C42—72no—
340#400—71no—
341#400—72no—
342#399—71no—
343#399—72no—
344#398—71no—
345#398—72no—
346#398—72no—
347#397—72no—
348#397—71no—
349#396—72no—
350#396—72no—
351#395—72no—
352#395C2×D711yescharacteristic
353#394—72no—
354#394C2×D711yescharacteristic
355#394C2×D712yes—
356#393—72no—
357#393C2×D711yescharacteristic
358#392C2×D712yes—
359#392C2×D711yescharacteristic
360#391—72no—
361#391—72no—
362#391—71no—
363#390—72no—
364#390—72no—
365#390—72no—
366#390—72no—
367#390—71no—
368#389—72no—
369#389—72no—
370#388—72no—
371#388—72no—
372#388—72no—
373#388—72no—
374#388—72no—
375#388—72no—
376#388—72no—
377#388—72no—
378#388—72no—
379#388—72no—
380#388—72no—
381#387—72no—
382#387—72no—
383#387—72no—
384#387—72no—
385#387—72no—
386#386—72no—
387#386—72no—
388#386—72no—
389#386—72no—
390#386—72no—
391#385—72no—
392#383—72no—
393#382—71no—
394#381—72no—
395C4×C4⋊C4—72no—
396C4×C4⋊C4—72no—
397C4×C4⋊C4—72no—
398C4×C4⋊C4—72no—
399C4×C4⋊C4—72no—
400C4×C4⋊C4—72no—
401C4×C22⋊C4—72no—
402C4×C22⋊C4—72no—
403C4×C22⋊C4—71no—
404C4×C22⋊C4—72no—
405C4×C22⋊C4—72no—
406C4×C22⋊C4—72no—
407C4×C22⋊C4—72no—
408C4×C22⋊C4—72no—
409C4×C22⋊C4C2×D711yescharacteristic
410C4×C22⋊C4C2×D712yes—
411#376—72no—
412#376—72no—
413C43—72no—
414C43—71no—
415C23×C7—22no—
416C23×C7—22no—
417C23×C7—22no—
418C23×C7—22no—
419C23×C7—22no—
420C23×C7—22no—
421C23×C7—22no—
422C23×C7—21no—
423C23×C7—21no—
424C23×C7—22no—
425C23×C7—22no—
426C23×C7—22no—
427C23×C7—21no—
428C23×C7—21no—
429C23×C7—21no—
430C23×C7—21no—
431C23×C7C2×#4114yes—
432C23×C7C2511yescharacteristic
433C7×Q8—44no—
434C7×D4—48no—
435C7×D4—48no—
436C7×D4—44no—
437C7×D4—44no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—21no—
442C2×C4×C7—22no—
443C2×C4×C7—21no—
444C2×C4×C7—216no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—22no—
450C2×C4×C7—22no—
451C2×C4×C7—21no—
452C2×C4×C7—21no—
453C2×C4×C7—21no—
454C2×C4×C7—44no—
455C2×C4×C7—44no—
456C2×C4×C7C2×#4114yes—
457C2×C4×C7C2×#4114yes—
458C2×C4×C7C2×#4114yes—
459C2×C4×C7C2×#4112yes—
460C2×C4×C7H(5,𝔽2)12yes—
461C2×Dic7—216no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—22no—
483C2×Dic7—48no—
484C2×Dic7C2×#4114yes—
485C2×Dic7C2×#4114yes—
486C2×Dic7C2×#4114yes—
487Dic14—44no—
488C2×#41—28no—
489C2×#41—42no—
490C22×Q8—71no—
491C22×Q8C22×D711yescharacteristic
492C22×D4C22×D712yes—
493C22×D4C22×D711yescharacteristic
494C22×D4C22×D712yes—
495C22×D4C22×D711yescharacteristic
496C23×C4—72no—
497C23×C4—72no—
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500C23×C4C22×D712yes—
501#126—148no—
502#124—144no—
503#123—148no—
504C4×Q8—282no—
505C4×D4—28no—
506C4×D4—42no—
507#117—148no—
508#117—148no—
509#117—282no—
510#117—284no—
511C2×C4⋊C4—72no—
512C2×C4⋊C4—72no—
513C2×C4⋊C4—72no—
514C2×C4⋊C4—72no—
515C2×C4⋊C4—72no—
516C2×C4⋊C4—72no—
517C2×C4⋊C4—72no—
518C2×C4⋊C4—71no—
519C2×C4⋊C4—71no—
520C2×C4⋊C4—72no—
521C2×C4⋊C4—72no—
522C2×C4⋊C4—72no—
523C2×C4⋊C4—71no—
524C2×C4⋊C4—72no—
525C2×C4⋊C4C22×D712yes—
526C2×C4⋊C4C22×D711yescharacteristic
527C2×C22⋊C4—72no—
528C2×C22⋊C4—72no—
529C2×C22⋊C4—72no—
530C2×C22⋊C4—72no—
531C2×C22⋊C4—72no—
532C2×C22⋊C4—72no—
533C2×C22⋊C4—72no—
534C2×C22⋊C4—72no—
535C2×C22⋊C4—72no—
536C2×C22⋊C4—72no—
537C2×C22⋊C4—72no—
538C2×C22⋊C4—72no—
539C2×C22⋊C4—72no—
540C2×C22⋊C4—72no—
541C2×C22⋊C4C22×D712yes—
542C2×C22⋊C4C22×D712yes—
543C2×C22⋊C4C22×D712yes—
544C2×C22⋊C4C22×D712yes—
545C2×C22⋊C4C22×D712yes—
546C2×C22⋊C4C22×D711yescharacteristic
547C2×C22⋊C4C22×D711yescharacteristic
548C2×C42—71no—
549C2×C42—72no—
550C2×C42—72no—
551C2×C42—72no—
552C2×C42—72no—
553C2×C42—72no—
554C2×C42—72no—
555C2×C42—72no—
556C2×C42—72no—
557C2×C42—72no—
558C2×C42—72no—
559C2×C42—71no—
560C2×C42—72no—
561C2×C42—148no—
562C2×C42C22×D711yescharacteristic
563C2×C42C22×D712yes—
564#95—72no—
565#95—72no—
566#95—72no—
567#95—72no—
568#95—72no—
569#95—72no—
570#95—71no—
571#95—72no—
572#95—72no—
573#95—72no—
574#95—72no—
575#95—72no—
576#95—71no—
577#95—72no—
578#95—72no—
579#95—72no—
580#95—72no—
581#95—72no—
582#95—72no—
583#95—72no—
584#95C22×D712yes—
585#95C22×D712yes—
586#95C22×D711yescharacteristic
587#95C22×D711yescharacteristic
588C22×C7—24no—
589C22×C7—24no—
590C22×C7—24no—
591C22×C7—42no—
592C22×C7—42no—
593C22×C7—42no—
594C22×C7—42no—
595C22×C7—42no—
596C22×C7—42no—
597C22×C7—41no—
598C22×C7—41no—
599C22×C7—41no—
600C22×C7—41no—
601C22×C7—42no—
602C22×C7—42no—
603C22×C7—41no—
604C22×C7—41no—
605C22×C7C22×#4112yes—
606C22×C7C22×#4111yescharacteristic
607C22×C7C22×#4112yes—
608C22×C7C2×H(5,𝔽2)11yescharacteristic
609C22×C7#58511yescharacteristic
610C4×C7—22no—
611C4×C7—24no—
612C4×C7—24no—
613C4×C7—42no—
614C4×C7—41no—
615C4×C7—41no—
616C4×C7—41no—
617C4×C7#55114yes—
618Dic7—24no—
619Dic7—24no—
620Dic7—24no—
621Dic7—42no—
622Dic7—42no—
623Dic7—42no—
624Dic7—42no—
625Dic7—42no—
626C24C23×D711yescharacteristic
627C24C23×D711yescharacteristic
628C24C23×D712yes—
629#41—416no—
630C2×Q8—24no—
631C2×Q8—41no—
632C2×Q8—142no—
633C2×Q8—281no—
634C2×Q8—281no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—22no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—41no—
644C2×D4—42no—
645C2×D4—41no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—72no—
653C22×C4—72no—
654C22×C4—72no—
655C22×C4—72no—
656C22×C4—72no—
657C22×C4—72no—
658C22×C4—72no—
659C22×C4—72no—
660C22×C4—144no—
661C22×C4—144no—
662C22×C4—144no—
663C22×C4—144no—
664C22×C4—144no—
665C22×C4—282no—
666C22×C4#115918yes—
667C22×C4C23×D711yescharacteristic
668C22×C4C23×D711yescharacteristic
669C22×C4C23×D712yes—
670C22×C4C23×D711yescharacteristic
671C22×C4C23×D712yes—
672C22×C4C23×D712yes—
673C22×C4C23×D711yescharacteristic
674C22×C4C23×D711yescharacteristic
675C4⋊C4—24no—
676C4⋊C4—41no—
677C4⋊C4—78no—
678C4⋊C4—144no—
679C4⋊C4—144no—
680C4⋊C4—144no—
681C4⋊C4—144no—
682C4⋊C4—144no—
683C4⋊C4—144no—
684C4⋊C4—282no—
685C4⋊C4—282no—
686C4⋊C4—282no—
687C4⋊C4—282no—
688C4⋊C4—281no—
689C4⋊C4—281no—
690C4⋊C4—281no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—144no—
699C22⋊C4—144no—
700C22⋊C4—144no—
701C22⋊C4—144no—
702C22⋊C4—144no—
703C22⋊C4—144no—
704C22⋊C4—144no—
705C22⋊C4—144no—
706C22⋊C4—144no—
707C22⋊C4—282no—
708C22⋊C4—282no—
709C22⋊C4—282no—
710C22⋊C4—282no—
711C22⋊C4—282no—
712C42—24no—
713C42—22no—
714C42—74no—
715C42—144no—
716C42—144no—
717C42—144no—
718C42—144no—
719C42—144no—
720C42—144no—
721C42—144no—
722C42—144no—
723C42—144no—
724C42—144no—
725C42—282no—
726C42—281no—
727C2×C7—44no—
728C2×C7—81no—
729C2×C7—81no—
730C2×C7#344412yes—
731C2×C7#346011yescharacteristic
732C2×C7C2×#55111yescharacteristic
733C2×C7#347512yes—
734C2×C7#348311yescharacteristic
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—21no—
750C23—21no—
751C23C2×#115914yes—
752C23C24×D711yescharacteristic
753Q8—44no—
754Q8—284no—
755D4—48no—
756D4—48no—
757D4—44no—
758D4—44no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—216no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—74no—
778C2×C4—74no—
779C2×C4—74no—
780C2×C4—1416no—
781C2×C4—142no—
782C2×C4—142no—
783C2×C4—142no—
784C2×C4—142no—
785C2×C4—142no—
786C2×C4—142no—
787C2×C4—142no—
788C2×C4—142no—
789C2×C4—142no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—142no—
794C2×C4—142no—
795C2×C4—142no—
796C2×C4—142no—
797C2×C4—142no—
798C2×C4—142no—
799C2×C4—142no—
800C2×C4—142no—
801C2×C4—142no—
802C2×C4—288no—
803C2×C4C2×#115914yes—
804C2×C4C2×#115914yes—
805C2×C4#654812yes—
806C2×C4D7×#4112yes—
807C2×C4D7×#4114yes—
808C7#3487111yescharacteristic, complemented, Sylow
809C22—24no—
810C22—24no—
811C22—24no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—42no—
826C22C22×#115912yes—
827C22C2×#654811yescharacteristic
828C22C2×D7×#4111yescharacteristic
829C22C2×D7×#4112yes—
830C22#9061611yescharacteristic
831C4—24no—
832C4—22no—
833C4—24no—
834C4—41no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—144no—
839C4—144no—
840C4—144no—
841C4—282no—
842C4—282no—
843C4—282no—
844C4—282no—
845C4—282no—
846C4#9027814yes—
847C2—44no—
848C2—81no—
849C2—81no—
850C2C2×#9027811yescharacteristic
851C2#1174308811yescharacteristic
852C2#1174308912yes—
853C2#1174328712yes—
854C2#1174328911yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutator, socle, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC7×#2388C2
hypercenter#2388D7
hypocenterC7#34871
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
2. #11741531C2semidirect
3. #11739791C2semidirect
4. C4×#6499C2semidirect
5. C4×#6498C2semidirect
6. #11739764C2semidirect
7. #11734645C2semidirect
8. #11734639C2semidirect
9. #11734413C2semidirect
10. #11734401C2semidirect
11. #11734386C2semidirect
12. #11734377C2semidirect
13. #11734241C2semidirect
14. #11734141C2semidirect
15. #11734134C2semidirect
16. #11734130C2semidirect
17. #11730925C2semidirect
18. C4×#6442C2semidirect
19. C4×#6440C2semidirect
314. Dic7⋊C4#41semidirect
327. C4×Dic7#41semidirect
808. C7#34871semidirect

Maximal subgroups

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

subgroupindex
C7×#23882
#117415312
#117397912
C4×#64992
C4×#64982
#117397642
#117346452
#117346392
#117344132
#117344012
#117343862
#117343772
#117342412
#117341412
#117341342
#117341302
#117309252
C4×#64422
C4×#64402
#348717