Finite Group Databasebeta

← #13525513

Subgroups — #13525513

Order 1792.

2014 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×#2397C211yesmaximal, characteristic
2#11739793C212yesmaximal, complemented
3#11739791C211yesmaximal, characteristic, complemented
4C4×#6499C212yesmaximal, complemented
5C4×#6498C211yesmaximal, characteristic, complemented
6C4×#6498C212yesmaximal, complemented
7#11739763C212yesmaximal, complemented
8C4×D4×Dic7C212yesmaximal, complemented
9#11735491C211yesmaximal, characteristic, complemented
10#11735488C212yesmaximal, complemented
11#11735487C212yesmaximal, complemented
12#11735485C212yesmaximal, complemented
13#11735477C211yesmaximal, characteristic, complemented
14#11734139C212yesmaximal, complemented
15#11734138C211yesmaximal, characteristic, complemented
16#11734136C212yesmaximal, complemented
17#11734124C212yesmaximal, complemented
18#11734119C211yesmaximal, characteristic, complemented
19#11730829C212yesmaximal, complemented
20C2×C4×C7×D4C2212yes—
21C2×C4×C7×D4C2212yes—
22C2×C4×C7×D4C2211yescharacteristic
23C2×C4×C7×D4C2211yescharacteristic
24C2×#6499C2212yes—
25C2×#6498C2212yes—
26C2×#6498C2211yescharacteristic
27C2×D4×Dic7C2212yes—
28C2×D4×Dic7C2212yes—
29C2×#6489C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2212yes—
32C2×C4×Dic14C2212yes—
33C7×#399C2211yescharacteristic
34C7×#399C2212yes—
35C7×#399C2211yescharacteristic
36C7×#392C2211yescharacteristic
37C7×#392C2212yes—
38C7×#392C2211yescharacteristic
39C7×#376C2211yescharacteristic
40#89994C2212yes—
41#89994C2212yes—
42#89994C2212yes—
43#89993C2212yes—
44#89992C2211yescharacteristic
45#89992C2212yes—
46#89992C2212yes—
47#89992C2212yes—
48C4×C22⋊Dic7C2212yes—
49C4×C22⋊Dic7C2212yes—
50C4×C22⋊Dic7C2212yes—
51C4×C22⋊Dic7C2212yes—
52C4×C22⋊Dic7C2212yes—
53C4×C22⋊Dic7C2211yescharacteristic
54C4×C22⋊Dic7C2211yescharacteristic
55#89758C2211yescharacteristic
56#89755C2211yescharacteristic
57#89754C2212yes—
58#89754C2212yes—
59#89753C2212yes—
60#89753C2212yes—
61#89750C2212yes—
62#89750C2212yes—
63#89750C2212yes—
64#89749C2212yes—
65C4⋊C4×Dic7C2212yes—
66C4⋊C4×Dic7C2212yes—
67#89746C2212yes—
68#89725C2212yes—
69#89725C2211yescharacteristic
70#89725C2212yes—
71#89724C2212yes—
72#89723C2212yes—
73#89723C2212yes—
74#89722C2212yes—
75#89722C2212yes—
76#89721C2211yescharacteristic
77#89719C2212yes—
78#89719C2212yes—
79#89718C2211yescharacteristic
80#89718C2212yes—
81#89717C2212yes—
82#89717C2212yes—
83#89717C2212yes—
84#89717C2212yes—
85#89716C2212yes—
86#89716C2212yes—
87#89716C2212yes—
88#89715C2212yes—
89#89715C2211yescharacteristic
90C22⋊C4×Dic7C2212yes—
91C22⋊C4×Dic7C2212yes—
92C22⋊C4×Dic7C2212yes—
93C22⋊C4×Dic7C2212yes—
94C4×C4⋊Dic7C2212yes—
95#89704C2212yes—
96C4×Dic7⋊C4C2212yes—
97C4×Dic7⋊C4C2212yes—
98C42×Dic7C2212yes—
99#89427C2212yes—
100#89427C2212yes—
101#89426C2212yes—
102#89426C2212yes—
103#89419C2212yes—
104#89419C2212yes—
105#89418C2212yes—
106#89418C2212yes—
107#34921—71nomaximal, Sylow
108C22×C7×D4C2312yes—
109C22×C7×D4C2311yescharacteristic
110C22×C7×D4C2312yes—
111C22×C7×D4C2311yescharacteristic
112C23×C4×C7C2311yescharacteristic
113C23×C4×C7C2312yes—
114C23×C4×C7C2311yescharacteristic
115C23×Dic7C2311yescharacteristic
116C23×Dic7C2312yes—
117C23×Dic7C2312yes—
118C23×Dic7C2311yescharacteristic
119C22×Dic14C2312yes—
120C4×C7×D4—28no—
121C4×C7×D4—28no—
122C4×C7×D4—42no—
123C4×C7×D4—42no—
124C2×C7×C4⋊C4C2312yes—
125C2×C7×C4⋊C4C2312yes—
126C2×C7×C4⋊C4C2311yescharacteristic
127C2×C7×C4⋊C4C2311yescharacteristic
128C2×C7×C22⋊C4C2312yes—
129C2×C7×C22⋊C4C2312yes—
130C2×C7×C22⋊C4C2312yes—
131C2×C7×C22⋊C4C2312yes—
132C2×C7×C22⋊C4C2312yes—
133C2×C7×C22⋊C4C2311yescharacteristic
134C2×C7×C22⋊C4C2311yescharacteristic
135C2×C42×C7C2311yescharacteristic
136C2×C42×C7C2312yes—
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⋊Dic7C2311yescharacteristic
147C2×C22⋊Dic7C2312yes—
148C2×C22⋊Dic7C2311yescharacteristic
149C2×C22⋊Dic7C2312yes—
150C2×C22⋊Dic7C2312yes—
151#6499—28no—
152#6498—24no—
153#6498—28no—
154D4×Dic7—28no—
155D4×Dic7—28no—
156#6489—42no—
157C2×C4⋊Dic7C2312yes—
158C2×C4⋊Dic7C2312yes—
159C2×C4⋊Dic7C2312yes—
160C2×C4⋊Dic7C2311yescharacteristic
161C2×C4⋊Dic7C2311yescharacteristic
162C2×Dic7⋊C4C2312yes—
163C2×Dic7⋊C4C2312yes—
164C2×Dic7⋊C4C2312yes—
165C2×Dic7⋊C4C2312yes—
166C2×Dic7⋊C4C2312yes—
167C2×Dic7⋊C4C2312yes—
168C2×C4×Dic7—42no—
169C2×C4×Dic7—44no—
170C2×C4×Dic7C2312yes—
171C2×C4×Dic7C2312yes—
172C2×C4×Dic7C2312yes—
173C2×C4×Dic7C2312yes—
174C2×C4×Dic7C2312yes—
175C2×C4×Dic7C2312yes—
176C2×C4×Dic7C2312yes—
177C2×C4×Dic7C2312yes—
178C2×C4×Dic7C2312yes—
179C2×C4×Dic7C2312yes—
180C2×C4×Dic7C2312yes—
181C4×Dic14—28no—
182C7×#95C2311yescharacteristic
183C7×#95C2312yes—
184C7×#95C2311yescharacteristic
185C7⋊#95C2312yes—
186C7⋊#95C2312yes—
187C7⋊#95C2312yes—
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⋊#95C2311yescharacteristic
206C7⋊#95C2312yes—
207C7⋊#95C2312yes—
208#2607—71no—
209#2602—72no—
210#2600—71no—
211#2596—72no—
212#2589—72no—
213#2575—72no—
214#2557—72no—
215#2517—71no—
216#2459—72no—
217#2455—71no—
218#2398—72no—
219#2397D711yescharacteristic
220#2395—71no—
221C4×#124—72no—
222C4×#123—71no—
223C4×#123—72no—
224#2295—72no—
225#2290—72no—
226C42×D4—72no—
227C24×C7C2411yescharacteristic
228C24×C7C2411yescharacteristic
229C24×C7C2412yes—
230C2×C7×D4—24no—
231C2×C7×D4—24no—
232C2×C7×D4—24no—
233C2×C7×D4—22no—
234C2×C7×D4—24no—
235C2×C7×D4—24no—
236C2×C7×D4—24no—
237C2×C7×D4—41no—
238C2×C7×D4—41no—
239C2×C7×D4—42no—
240C2×C7×D4—41no—
241C22×C4×C7—24no—
242C22×C4×C7—24no—
243C22×C4×C7—24no—
244C22×C4×C7—24no—
245C22×C4×C7—22no—
246C22×C4×C7—24no—
247C22×C4×C7—22no—
248C22×C4×C7C2412yes—
249C22×C4×C7C2411yescharacteristic
250C22×C4×C7C2411yescharacteristic
251C22×C4×C7C2411yescharacteristic
252C22×C4×C7C2411yescharacteristic
253C22×C4×C7C2412yes—
254C22×C4×C7C2412yes—
255C22×C4×C7C2411yescharacteristic
256C22×Dic7—24no—
257C22×Dic7—24no—
258C22×Dic7—24no—
259C22×Dic7—24no—
260C22×Dic7—41no—
261C22×Dic7—41no—
262C22×Dic7—42no—
263C22×Dic7—42no—
264C22×Dic7—41no—
265C22×Dic7—42no—
266C22×Dic7#4114yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C22×Dic7C2412yes—
275C2×Dic14—24no—
276C2×Dic14—24no—
277C2×Dic14—42no—
278C7×C4⋊C4—24no—
279C7×C4⋊C4—24no—
280C7×C4⋊C4—41no—
281C7×C4⋊C4—41no—
282C7×C22⋊C4—24no—
283C7×C22⋊C4—24no—
284C7×C22⋊C4—24no—
285C7×C22⋊C4—24no—
286C7×C22⋊C4—42no—
287C7×C22⋊C4—41no—
288C7×C22⋊C4—41no—
289C42×C7—22no—
290C42×C7#4118yes—
291C22⋊Dic7—24no—
292C22⋊Dic7—22no—
293C22⋊Dic7—24no—
294C22⋊Dic7—24no—
295C22⋊Dic7—24no—
296C22⋊Dic7—24no—
297C22⋊Dic7—24no—
298C22⋊Dic7—24no—
299C22⋊Dic7—24no—
300C22⋊Dic7—24no—
301C22⋊Dic7—42no—
302C22⋊Dic7—42no—
303C22⋊Dic7—41no—
304C22⋊Dic7#4118yes—
305C4⋊Dic7—24no—
306C4⋊Dic7—24no—
307C4⋊Dic7—24no—
308C4⋊Dic7—41no—
309C4⋊Dic7—41no—
310Dic7⋊C4—24no—
311Dic7⋊C4—24no—
312Dic7⋊C4—24no—
313Dic7⋊C4—24no—
314Dic7⋊C4—24no—
315Dic7⋊C4—42no—
316C4×Dic7—24no—
317C4×Dic7—24no—
318C4×Dic7—24no—
319C4×Dic7—24no—
320C4×Dic7—24no—
321C4×Dic7—24no—
322C4×Dic7—24no—
323C4×Dic7—42no—
324C4×Dic7—42no—
325C4×Dic7—42no—
326C4×Dic7—42no—
327C2×#124—72no—
328C2×#123—71no—
329C2×#123—72no—
330C2×C4×Q8—72no—
331C2×C4×D4—72no—
332C2×C4×D4—72no—
333C2×C4×D4C2×D712yes—
334C2×C4×D4C2×D712yes—
335C2×C4×D4C2×D711yescharacteristic
336C2×C4×D4C2×D711yescharacteristic
337C2×#117—71no—
338C22×C42—71no—
339C22×C42—72no—
340#400—71no—
341#400—72no—
342#400—72no—
343#399—71no—
344#399C2×D712yes—
345#399C2×D711yescharacteristic
346#399C2×D711yescharacteristic
347#398—71no—
348#397—72no—
349#397—72no—
350#397—71no—
351#397—72no—
352#394—72no—
353#394—72no—
354#394—72no—
355#393—72no—
356#393—72no—
357#392C2×D711yescharacteristic
358#392C2×D712yes—
359#392C2×D711yescharacteristic
360#391—72no—
361#391—72no—
362#391—72no—
363#390—72no—
364#389—72no—
365#389—72no—
366#388—72no—
367#388—72no—
368#388—72no—
369#388—72no—
370#388—72no—
371#388—72no—
372#388—72no—
373#388—72no—
374#388—72no—
375#387—72no—
376#387—72no—
377#387—72no—
378#387—72no—
379#387—72no—
380#387—72no—
381#387—72no—
382#387—72no—
383#387—72no—
384#386—72no—
385#386—72no—
386#386—71no—
387#386—72no—
388#385—72no—
389#385—72no—
390#385—72no—
391#385—71no—
392#382—72no—
393#381—72no—
394#381—71no—
395C4×C4⋊C4—72no—
396C4×C4⋊C4—72no—
397C4×C4⋊C4—72no—
398C4×C4⋊C4—72no—
399C4×C4⋊C4—72no—
400C4×C22⋊C4—72no—
401C4×C22⋊C4—71no—
402C4×C22⋊C4—71no—
403C4×C22⋊C4—72no—
404C4×C22⋊C4—72no—
405C4×C22⋊C4—72no—
406C4×C22⋊C4—72no—
407C4×C22⋊C4—72no—
408C4×C22⋊C4—72no—
409C4×C22⋊C4—72no—
410C4×C22⋊C4—72no—
411#376—72no—
412#376C2×D711yescharacteristic
413C43—72no—
414C23×C7—22no—
415C23×C7—22no—
416C23×C7—22no—
417C23×C7—22no—
418C23×C7—22no—
419C23×C7—22no—
420C23×C7—21no—
421C23×C7—22no—
422C23×C7—21no—
423C23×C7—22no—
424C23×C7—21no—
425C23×C7—22no—
426C23×C7—22no—
427C23×C7—21no—
428C23×C7—21no—
429C23×C7C2×#4112yes—
430C23×C7C2×#4114yes—
431C23×C7C2511yescharacteristic
432C7×D4—216no—
433C7×D4—48no—
434C7×D4—44no—
435C7×D4—44no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—21no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—21no—
447C2×C4×C7—22no—
448C2×C4×C7—21no—
449C2×C4×C7—21no—
450C2×C4×C7—21no—
451C2×C4×C7—21no—
452C2×C4×C7—44no—
453C2×C4×C7—48no—
454C2×C4×C7—44no—
455C2×C4×C7C2×#4114yes—
456C2×C4×C7C2×#4114yes—
457C2×C4×C7C2×#4114yes—
458C2×C4×C7H(5,𝔽2)12yes—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
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—44no—
481C2×Dic7—44no—
482C2×Dic7—48no—
483C2×Dic7—48no—
484C2×Dic7C2×#4114yes—
485C2×Dic7C2×#4114yes—
486C2×Dic7C2×#4114yes—
487Dic14—48no—
488C22×Q8—72no—
489C22×D4C22×D712yes—
490C22×D4C22×D711yescharacteristic
491C22×D4C22×D712yes—
492C22×D4C22×D711yescharacteristic
493C23×C4—71no—
494C23×C4—71no—
495C23×C4—72no—
496C23×C4—72no—
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D712yes—
500#124—148no—
501#123—148no—
502#123—144no—
503C4×Q8—148no—
504C4×D4—28no—
505C4×D4—28no—
506C4×D4—42no—
507C4×D4—42no—
508C4×D4—148no—
509C4×D4—148no—
510#117—282no—
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—72no—
519C2×C4⋊C4—71no—
520C2×C4⋊C4—71no—
521C2×C4⋊C4—72no—
522C2×C4⋊C4C22×D712yes—
523C2×C4⋊C4C22×D712yes—
524C2×C4⋊C4C22×D711yescharacteristic
525C2×C4⋊C4C22×D711yescharacteristic
526C2×C22⋊C4—72no—
527C2×C22⋊C4—72no—
528C2×C22⋊C4—72no—
529C2×C22⋊C4—72no—
530C2×C22⋊C4—72no—
531C2×C22⋊C4—72no—
532C2×C22⋊C4—71no—
533C2×C22⋊C4—72no—
534C2×C22⋊C4—72no—
535C2×C22⋊C4—72no—
536C2×C22⋊C4—72no—
537C2×C22⋊C4—72no—
538C2×C22⋊C4—71no—
539C2×C22⋊C4—72no—
540C2×C22⋊C4C22×D712yes—
541C2×C22⋊C4C22×D712yes—
542C2×C22⋊C4C22×D712yes—
543C2×C22⋊C4C22×D712yes—
544C2×C22⋊C4C22×D712yes—
545C2×C22⋊C4C22×D711yescharacteristic
546C2×C22⋊C4C22×D711yescharacteristic
547C2×C42—72no—
548C2×C42—72no—
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—282no—
559C2×C42—284no—
560C2×C42C22×D711yescharacteristic
561C2×C42C22×D712yes—
562#95—72no—
563#95—72no—
564#95—72no—
565#95—72no—
566#95—72no—
567#95—72no—
568#95—72no—
569#95—72no—
570#95—72no—
571#95—72no—
572#95—72no—
573#95—72no—
574#95—71no—
575#95—72no—
576#95—72no—
577#95—72no—
578#95—72no—
579#95—72no—
580#95—71no—
581#95—72no—
582#95—72no—
583#95—72no—
584#95—72no—
585#95C22×D711yescharacteristic
586#95C22×D712yes—
587#95C22×D711yescharacteristic
588C22×C7—24no—
589C22×C7—24no—
590C22×C7—22no—
591C22×C7—24no—
592C22×C7—24no—
593C22×C7—42no—
594C22×C7—42no—
595C22×C7—42no—
596C22×C7—42no—
597C22×C7—41no—
598C22×C7—42no—
599C22×C7—41no—
600C22×C7—42no—
601C22×C7—41no—
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—24no—
611C4×C7—24no—
612C4×C7—41no—
613C4×C7—42no—
614C4×C7—41no—
615C4×C7—41no—
616C4×C7—41no—
617C4×C7#55914yes—
618Dic7—24no—
619Dic7—24no—
620Dic7—24no—
621Dic7—42no—
622Dic7—42no—
623Dic7—42no—
624Dic7—42no—
625Dic7—42no—
626C24C23×D711yescharacteristic
627C24C23×D712yes—
628C24C23×D711yescharacteristic
629C2×Q8—144no—
630C2×Q8—144no—
631C2×Q8—282no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—22no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—41no—
640C2×D4—41no—
641C2×D4—42no—
642C2×D4—41no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—22no—
648C22×C4—24no—
649C22×C4—22no—
650C22×C4—72no—
651C22×C4—72no—
652C22×C4—72no—
653C22×C4—74no—
654C22×C4—72no—
655C22×C4—72no—
656C22×C4—72no—
657C22×C4—72no—
658C22×C4—72no—
659C22×C4—144no—
660C22×C4—144no—
661C22×C4—144no—
662C22×C4—144no—
663C22×C4—281no—
664C22×C4—281no—
665C22×C4—282no—
666C22×C4—282no—
667C22×C4—281no—
668C22×C4—282no—
669C22×C4C23×D712yes—
670C22×C4C23×D711yescharacteristic
671C22×C4C23×D711yescharacteristic
672C22×C4C23×D711yescharacteristic
673C22×C4C23×D711yescharacteristic
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D711yescharacteristic
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—144no—
682C4⋊C4—144no—
683C4⋊C4—144no—
684C4⋊C4—144no—
685C4⋊C4—144no—
686C4⋊C4—144no—
687C4⋊C4—144no—
688C4⋊C4—144no—
689C4⋊C4—282no—
690C4⋊C4—281no—
691C4⋊C4—281no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—42no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—78no—
700C22⋊C4—144no—
701C22⋊C4—144no—
702C22⋊C4—144no—
703C22⋊C4—144no—
704C22⋊C4—144no—
705C22⋊C4—144no—
706C22⋊C4—144no—
707C22⋊C4—142no—
708C22⋊C4—144no—
709C22⋊C4—144no—
710C22⋊C4—282no—
711C22⋊C4—281no—
712C22⋊C4—282no—
713C42—22no—
714C42—144no—
715C42—144no—
716C42—144no—
717C42—144no—
718C42—144no—
719C42—144no—
720C42—144no—
721C42—282no—
722C42—282no—
723C42—282no—
724C42—282no—
725C42#115918yes—
726C2×C7—42no—
727C2×C7—44no—
728C2×C7—81no—
729C2×C7#344412yes—
730C2×C7#345911yescharacteristic
731C2×C7#347512yes—
732C2×C7C2×#55911yescharacteristic
733C2×C7#348111yescharacteristic
734C23—22no—
735C23—22no—
736C23—22no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—21no—
747C23—22no—
748C23—21no—
749C23D7×#4114yes—
750C23D7×#4112yes—
751C23C24×D711yescharacteristic
752Q8—288no—
753D4—216no—
754D4—48no—
755D4—44no—
756D4—44no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—44no—
774C2×C4—48no—
775C2×C4—44no—
776C2×C4—74no—
777C2×C4—74no—
778C2×C4—74no—
779C2×C4—142no—
780C2×C4—142no—
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—284no—
801C2×C4—284no—
802C2×C4—288no—
803C2×C4—288no—
804C2×C4C2×#115914yes—
805C2×C4C2×#115914yes—
806C2×C4C2×#115914yes—
807C2×C4#654812yes—
808C7#3492111yescharacteristic, complemented, Sylow
809C22—24no—
810C22—24no—
811C22—24no—
812C22—22no—
813C22—24no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—41no—
822C22—42no—
823C22—42no—
824C22—41no—
825C22—41no—
826C22C22×#115912yes—
827C22C2×#654811yescharacteristic
828C22C2×D7×#4111yescharacteristic
829C22C2×D7×#4112yes—
830C22#9061611yescharacteristic
831C4—24no—
832C4—24no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—144no—
839C4—144no—
840C4—144no—
841C4—282no—
842C4—282no—
843C4—282no—
844C4—282no—
845C4—282no—
846C4#9040414yes—
847C2—42no—
848C2—44no—
849C2—81no—
850C2#1174308612yes—
851C2#1174308912yes—
852C2#1174310411yescharacteristic
853C2#1174310611yescharacteristic
854C2C2×#9040411yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutator, socle, cosocleC23×C7C25
FrattiniC23C24×D7
Fitting, prime radicalC7×#2397C2
hypercenter#2397D7
hypocenterC7#34921
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #2397

Complements

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

NH ≅ G/Ntype
2. #11739793C2semidirect
3. #11739791C2semidirect
4. C4×#6499C2semidirect
5. C4×#6498C2semidirect
6. C4×#6498C2semidirect
7. #11739763C2semidirect
8. C4×D4×Dic7C2semidirect
9. #11735491C2semidirect
10. #11735488C2semidirect
11. #11735487C2semidirect
12. #11735485C2semidirect
13. #11735477C2semidirect
14. #11734139C2semidirect
15. #11734138C2semidirect
16. #11734136C2semidirect
17. #11734124C2semidirect
18. #11734119C2semidirect
19. #11730829C2semidirect
808. C7#34921semidirect

Maximal subgroups

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

subgroupindex
C7×#23972
#117397932
#117397912
C4×#64992
C4×#64982
#117397632
C4×D4×Dic72
#117354912
#117354882
#117354872
#117354852
#117354772
#117341392
#117341382
#117341362
#117341242
#117341192
#117308292
#349217