Finite Group Databasebeta

← #13560728

Subgroups — #13560728

Order 1792.

3034 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90495C211yesmaximal, characteristic, complemented
2C22×#6502C211yesmaximal, characteristic, complemented
3C7×#2309C211yesmaximal, characteristic, complemented
4#11739720C212yesmaximal, complemented
5#11739691C212yesmaximal, complemented
6#11733908C214yesmaximal, complemented
7#11733831C214yesmaximal, complemented
8#11733830C214yesmaximal, complemented
9#11733824C214yesmaximal, complemented
10#11731300C212yesmaximal, complemented
11#11731297C211yesmaximal, characteristic, complemented
12#11731292C212yesmaximal, complemented
13#11731278C211yesmaximal, characteristic, complemented
14#11731268C211yesmaximal, characteristic, complemented
15#11731268C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C23×C22⋊D7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic, complemented
20C24×Dic7C2211yescharacteristic, complemented
21C2×C7×#117C2212yescomplemented
22C2×#6516C2212yes—
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25#90495—28no—
26C2×#6502—28no—
27C2×#6502C2214yes—
28C2×#6502C2214yescomplemented
29C2×#6502C2212yescomplemented
30C2×#6502C2212yescomplemented
31C2×#6500C2212yescomplemented
32C2×#6498C2212yescomplemented
33C2×#6492C2212yes—
34C22×(C2×D7)⋊C4C2211yescharacteristic, complemented
35C22×Dic7⋊C4C2211yescharacteristic, complemented
36C2×#6449C2212yes—
37C2×#6449C2212yescomplemented
38C2×#6449C2214yescomplemented
39C2×#6445C2212yes—
40C2×#6445C2212yescomplemented
41C7×#390C2214yescomplemented
42C7×#390C2214yescomplemented
43C7×#379C2211yescharacteristic
44C7×#379C2211yescharacteristic
45C7×#379C2212yescomplemented
46#89766C2214yescomplemented
47#89766C2214yescomplemented
48#89763C2214yescomplemented
49#89755C2214yescomplemented
50#89733C2214yescomplemented
51#89733C2214yescomplemented
52#89733C2214yescomplemented
53#89733C2214yescomplemented
54#89732C2214yescomplemented
55#89732C2214yescomplemented
56#89732C2214yescomplemented
57#89730C2212yes—
58#89730C2212yes—
59#89730C2212yescomplemented
60#89730C2214yescomplemented
61#89730C2212yescomplemented
62#89727C2212yescomplemented
63#89727C2212yescomplemented
64#89725C2214yescomplemented
65#89722C2212yescomplemented
66#89722C2212yescomplemented
67#89722C2214yescomplemented
68#89722C2212yescomplemented
69#89722C2212yescomplemented
70#89715C2212yescomplemented
71#89715C2212yescomplemented
72#89715C2214yescomplemented
73#89712C2214yescomplemented
74#89712C2214yescomplemented
75#89711C2214yescomplemented
76#89700C2214yescomplemented
77#36715—71nomaximal, Sylow
78C25×C7C2311yescharacteristic
79C25×C7C2311yescharacteristic
80C24×D7C2311yescharacteristic
81C24×D7C2311yescharacteristic
82C22×C7×D4—44no—
83C22×C7×D4D418yescomplemented
84C22×C7×D4C2312yes—
85C22×C7×D4C2312yes—
86C23×C4×C7C2311yescharacteristic
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7—44no—
91C22×C22⋊D7—44no—
92C22×C22⋊D7—44no—
93C22×C22⋊D7C2312yes—
94C22×C22⋊D7C2312yes—
95C22×C22⋊D7C2312yes—
96C22×C22⋊D7C2312yes—
97C22×C22⋊D7C2312yes—
98C22×C22⋊D7C2314yes—
99C22×C22⋊D7C2312yes—
100C23×Dic7—24no—
101C23×Dic7—44no—
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2314yes—
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C23×Dic7C2311yescharacteristic
108C23×Dic7C2311yescharacteristic
109C22×D28C2314yes—
110C7×#117—44no—
111C2×C7×C4⋊C4C2314yes—
112C2×C7×C22⋊C4C2312yes—
113C2×C7×C22⋊C4C2312yes—
114C2×C7×C22⋊C4C2312yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C7×C22⋊C4C2312yes—
117C2×C7×C22⋊C4C2312yes—
118C2×C7×C22⋊C4C2312yes—
119C2×C7×C22⋊C4C2314yes—
120C2×C42×C7C2314yes—
121#6516—28no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7C2312yes—
125C2×C22⋊Dic7C2312yes—
126C2×C22⋊Dic7C2312yes—
127C2×C22⋊Dic7C2312yes—
128C2×C22⋊Dic7C2312yes—
129C2×C22⋊Dic7C2312yes—
130#6502—216no—
131#6502—216no—
132#6502—28no—
133#6502—28no—
134#6500—28no—
135#6498—28no—
136#6492—28no—
137C2×(C2×D7)⋊C4—24no—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2312yes—
141C2×(C2×D7)⋊C4C2312yes—
142C2×(C2×D7)⋊C4C2314yes—
143C2×(C2×D7)⋊C4C2314yes—
144C2×(C2×D7)⋊C4C2314yes—
145C2×(C2×D7)⋊C4C2314yes—
146C2×(C2×D7)⋊C4C2314yes—
147C2×C4⋊Dic7C2314yes—
148C2×C4⋊Dic7C2314yes—
149C2×C4⋊Dic7C2314yes—
150C2×Dic7⋊C4—24no—
151C2×Dic7⋊C4C2312yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2312yes—
154#6449—44no—
155#6449—48no—
156#6449—44no—
157#6445—44no—
158#6445—44no—
159C7⋊#95C2314yes—
160C7⋊#95C2314yes—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C2×#534—71no—
166C22×#121—71no—
167#2849—72no—
168#2701—74no—
169#2699—74no—
170#2682—74no—
171#2678—74no—
172#2613—72no—
173#2483—71no—
174#2413—72no—
175#2411—72no—
176#2405—71no—
177#2405—71no—
178#2403—71no—
179#2309D711yescharacteristic, complemented
180C24×C7—24no—
181C24×C7—24no—
182C24×C7—42no—
183C24×C7—42no—
184C24×C7—42no—
185C24×C7—42no—
186C24×C7C2×D414yes—
187C24×C7C2×D414yes—
188C24×C7C2411yescharacteristic
189C24×C7C2412yes—
190C24×C7C2411yescharacteristic
191C24×C7C2411yescharacteristic
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—24no—
195C23×D7—42no—
196C23×D7—42no—
197C23×D7—42no—
198C23×D7—42no—
199C23×D7—42no—
200C23×D7C2412yes—
201C23×D7C2412yes—
202C2×C7×D4—416no—
203C2×C7×D4—42no—
204C2×C7×D4—42no—
205C2×C7×D4—42no—
206C2×C7×D4—42no—
207C2×C7×D4C2×D418yes—
208C2×C7×D4C2×D418yes—
209C22×C4×C7—24no—
210C22×C4×C7C2×D414yes—
211C22×C4×C7C2414yes—
212C22×C4×C7C2414yes—
213C22×C4×C7C2412yes—
214C2×C22⋊D7—24no—
215C2×C22⋊D7—24no—
216C2×C22⋊D7—24no—
217C2×C22⋊D7—28no—
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—42no—
226C2×C22⋊D7—42no—
227C2×C22⋊D7—42no—
228C2×C22⋊D7—44no—
229C2×C22⋊D7—44no—
230C2×C22⋊D7—42no—
231C2×C22⋊D7—416no—
232C2×C22⋊D7—44no—
233C2×C22⋊D7—44no—
234C2×C22⋊D7—416no—
235C2×C22⋊D7—416no—
236C22×Dic7—22no—
237C22×Dic7—24no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—28no—
242C22×Dic7—24no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—28no—
246C22×Dic7—44no—
247C22×Dic7—42no—
248C22×Dic7—42no—
249C22×Dic7—42no—
250C22×Dic7—42no—
251C22×Dic7—416no—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2412yes—
257C22×Dic7C2412yes—
258C2×D28—44no—
259C2×D28—44no—
260C2×D28—44no—
261C7×C4⋊C4—44no—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C7×C22⋊C4—42no—
265C7×C22⋊C4—42no—
266C7×C22⋊C4—44no—
267C7×C22⋊C4—42no—
268C7×C22⋊C4—44no—
269C7×C22⋊C4—42no—
270C42×C7—44no—
271C22⋊Dic7—24no—
272C22⋊Dic7—24no—
273C22⋊Dic7—24no—
274C22⋊Dic7—24no—
275C22⋊Dic7—24no—
276C22⋊Dic7—24no—
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—28no—
281(C2×D7)⋊C4—44no—
282(C2×D7)⋊C4—44no—
283(C2×D7)⋊C4—44no—
284(C2×D7)⋊C4—44no—
285(C2×D7)⋊C4—44no—
286C4⋊Dic7—28no—
287C4⋊Dic7—44no—
288C4⋊Dic7—44no—
289Dic7⋊C4—28no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292C23×D4—71no—
293C23×D4—71no—
294C23×D4—71no—
295C23×D4C2×D711yescharacteristic
296C24×C4—71no—
297#534—148no—
298C2×#123—72no—
299C2×#123—72no—
300C2×#123—74no—
301C2×#123—72no—
302C2×#123—72no—
303C2×#121—74no—
304C2×#121—74no—
305C2×#121—72no—
306C2×#121—72no—
307C2×#121—148no—
308C2×#120—72no—
309C2×#120—72no—
310C2×#120—72no—
311C2×#120—72no—
312C2×#117C2×D712yescomplemented
313C22×C4⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317#398—74no—
318#397—74no—
319#396—74no—
320#396—74no—
321#394—74no—
322#394—74no—
323#394—74no—
324#394—74no—
325#394—74no—
326#392—74no—
327#392—74no—
328#392—74no—
329#390—74no—
330#390C2×D714yescomplemented
331#390C2×D714yescomplemented
332#389—74no—
333#388—74no—
334#388—74no—
335#386—72no—
336#386—72no—
337#386—74no—
338#386—72no—
339#386—72no—
340#385—72no—
341#385—72no—
342#385—74no—
343#385—72no—
344#385—72no—
345#381—74no—
346#381—72no—
347#381—72no—
348#379—72no—
349#379—72no—
350#379C2×D711yescharacteristic
351#379C2×D711yescharacteristic
352#379C2×D712yescomplemented
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—28no—
356C23×C7—24no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—24no—
365C23×C7—22no—
366C23×C7—28no—
367C23×C7—44no—
368C23×C7—44no—
369C23×C7—44no—
370C23×C7—44no—
371C23×C7—416no—
372C23×C7—88no—
373C23×C7C22×D412yes—
374C23×C7C22×D414yes—
375C23×C7C22×D412yes—
376C23×C7C22×D412yes—
377C23×C7H(5,𝔽2)14yes—
378C23×C7C2511yescharacteristic
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—24no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—24no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—24no—
388C22×D7—24no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7—44no—
392C22×D7—44no—
393C22×D7—82no—
394C22×D7—82no—
395C22×D7—88no—
396C22×D7—88no—
397C7×D4—48no—
398C7×D4—48no—
399C2×C4×C7—28no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—24no—
403C2×C4×C7—24no—
404C2×C4×C7—24no—
405C2×C4×C7—24no—
406C2×C4×C7—24no—
407C2×C4×C7—24no—
408C2×C4×C7C22×D414yes—
409C22⋊D7—48no—
410C22⋊D7—48no—
411C22⋊D7—48no—
412C22⋊D7—416no—
413C22⋊D7—48no—
414C22⋊D7—84no—
415C22⋊D7—84no—
416C2×Dic7—28no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—24no—
425C2×Dic7—22no—
426C2×Dic7—24no—
427C2×Dic7—24no—
428C2×Dic7—22no—
429C2×Dic7—24no—
430C2×Dic7—416no—
431C2×Dic7—44no—
432C2×Dic7—44no—
433C2×Dic7—44no—
434C2×Dic7—82no—
435C2×Dic7—82no—
436C2×Dic7H(5,𝔽2)14yes—
437D28—88no—
438C25—71no—
439C25—71no—
440C25C22×D711yescharacteristic
441C25C22×D711yescharacteristic
442C22×D4—44no—
443C22×D4—72no—
444C22×D4—72no—
445C22×D4—72no—
446C22×D4—72no—
447C22×D4—72no—
448C22×D4—74no—
449C22×D4—72no—
450C22×D4—74no—
451C22×D4—144no—
452C22×D4—144no—
453C22×D4—144no—
454C22×D4—284no—
455C22×D4—284no—
456C22×D4—284no—
457C22×D4D2818yescomplemented
458C22×D4C22×D712yes—
459C22×D4C22×D712yes—
460C23×C4—71no—
461C23×C4—71no—
462C23×C4—74no—
463C23×C4—71no—
464C23×C4—71no—
465C23×C4—71no—
466C23×C4—71no—
467C23×C4—144no—
468C23×C4—284no—
469C23×C4C22×D711yescharacteristic
470#123—148no—
471#123—148no—
472#123—284no—
473#123—288no—
474#123—284no—
475#121—1416no—
476#121—1416no—
477#121—148no—
478#121—148no—
479#120—148no—
480#120—148no—
481#120—284no—
482#120—284no—
483#117—44no—
484C2×C4⋊C4—74no—
485C2×C4⋊C4—72no—
486C2×C4⋊C4—72no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—144no—
491C2×C4⋊C4C22×D714yes—
492C2×C22⋊C4—72no—
493C2×C22⋊C4—72no—
494C2×C22⋊C4—72no—
495C2×C22⋊C4—72no—
496C2×C22⋊C4—72no—
497C2×C22⋊C4—72no—
498C2×C22⋊C4—74no—
499C2×C22⋊C4—72no—
500C2×C22⋊C4—72no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—74no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—74no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—144no—
508C2×C22⋊C4—144no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4C22×D712yes—
511C2×C22⋊C4C22×D712yes—
512C2×C22⋊C4C22×D712yes—
513C2×C22⋊C4C22×D712yes—
514C2×C22⋊C4C22×D714yes—
515C2×C22⋊C4C22×D712yes—
516C2×C22⋊C4C22×D712yes—
517C2×C22⋊C4C22×D714yes—
518C2×C42C22×D714yes—
519#95—74no—
520#95—74no—
521#95—74no—
522#95—74no—
523#95—74no—
524#95—74no—
525C22×C7—22no—
526C22×C7—22no—
527C22×C7—28no—
528C22×C7—22no—
529C22×C7—24no—
530C22×C7—22no—
531C22×C7—24no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—22no—
535C22×C7—24no—
536C22×C7—22no—
537C22×C7—416no—
538C22×C7—44no—
539C22×C7—44no—
540C22×C7—44no—
541C22×C7—44no—
542C22×C7—88no—
543C22×C7#53414yes—
544C22×C7C23×D411yescharacteristic
545C22×C7C2×H(5,𝔽2)12yes—
546C22×C7C2×H(5,𝔽2)12yes—
547C22×C7#58512yes—
548C2×D7—42no—
549C2×D7—42no—
550C2×D7—42no—
551C2×D7—42no—
552C2×D7—42no—
553C2×D7—42no—
554C2×D7—44no—
555C2×D7—44no—
556C2×D7—44no—
557C2×D7—44no—
558C2×D7—88no—
559C2×D7—88no—
560C4×C7—24no—
561C4×C7—44no—
562C4×C7—44no—
563Dic7—24no—
564Dic7—42no—
565Dic7—42no—
566Dic7—42no—
567Dic7—42no—
568Dic7—42no—
569C24—24no—
570C24—24no—
571C24—42no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24—72no—
576C24—72no—
577C24—142no—
578C24—142no—
579C24—144no—
580C24—282no—
581C24—282no—
582C24—282no—
583C24—282no—
584C24—282no—
585C24C2×D2814yes—
586C24C2×D2814yes—
587C24C23×D711yescharacteristic
588C24C23×D712yes—
589C24C23×D711yescharacteristic
590C24C23×D711yescharacteristic
591C2×D4—416no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—144no—
597C2×D4—144no—
598C2×D4—144no—
599C2×D4—144no—
600C2×D4—144no—
601C2×D4—148no—
602C2×D4—144no—
603C2×D4—144no—
604C2×D4—144no—
605C2×D4—144no—
606C2×D4—144no—
607C2×D4—284no—
608C2×D4—284no—
609C2×D4—284no—
610C2×D4—282no—
611C2×D4—282no—
612C2×D4—282no—
613C2×D4—284no—
614C2×D4—284no—
615C2×D4—282no—
616C2×D4—2816no—
617C2×D4—284no—
618C2×D4—284no—
619C2×D4—2816no—
620C2×D4—2816no—
621C2×D4C2×D2818yes—
622C2×D4C2×D2818yes—
623C22×C4—24no—
624C22×C4—72no—
625C22×C4—72no—
626C22×C4—72no—
627C22×C4—72no—
628C22×C4—72no—
629C22×C4—72no—
630C22×C4—144no—
631C22×C4—148no—
632C22×C4—142no—
633C22×C4—142no—
634C22×C4—142no—
635C22×C4—148no—
636C22×C4—142no—
637C22×C4—144no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4—284no—
641C22×C4—282no—
642C22×C4—282no—
643C22×C4—282no—
644C22×C4—282no—
645C22×C4—2816no—
646C22×C4C2×D2814yes—
647C22×C4C23×D714yes—
648C22×C4C23×D714yes—
649C22×C4C23×D712yes—
650C4⋊C4—44no—
651C4⋊C4—148no—
652C4⋊C4—148no—
653C4⋊C4—144no—
654C4⋊C4—144no—
655C4⋊C4—284no—
656C4⋊C4—284no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—42no—
660C22⋊C4—44no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—44no—
664C22⋊C4—42no—
665C22⋊C4—148no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C22⋊C4—144no—
669C22⋊C4—144no—
670C22⋊C4—144no—
671C22⋊C4—144no—
672C22⋊C4—148no—
673C22⋊C4—144no—
674C22⋊C4—144no—
675C22⋊C4—284no—
676C22⋊C4—284no—
677C22⋊C4—284no—
678C22⋊C4—284no—
679C22⋊C4—284no—
680C42—44no—
681C2×C7—24no—
682C2×C7—42no—
683C2×C7—44no—
684C2×C7—42no—
685C2×C7C2×#53411yescharacteristic
686C2×C7#348411yescharacteristic
687C2×C7#348511yescharacteristic
688C2×C7#354214yes—
689D7—82no—
690D7—82no—
691C23—22no—
692C23—22no—
693C23—28no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—24no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—22no—
704C23—28no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—416no—
710C23—88no—
711C23—142no—
712C23—142no—
713C23—142no—
714C23—144no—
715C23—142no—
716C23—144no—
717C23—142no—
718C23—142no—
719C23—144no—
720C23—144no—
721C23—284no—
722C23—284no—
723C23—284no—
724C23—284no—
725C23—568no—
726C23—562no—
727C23—562no—
728C23—568no—
729C23C22×D2812yes—
730C23C22×D2812yes—
731C23C22×D2814yes—
732C23C22×D2812yes—
733C23#654814yes—
734C23C24×D711yescharacteristic
735D4—48no—
736D4—48no—
737D4—288no—
738D4—288no—
739D4—288no—
740D4—2816no—
741D4—288no—
742D4—568no—
743D4—564no—
744D4—564no—
745C2×C4—28no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—74no—
755C2×C4—148no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—144no—
765C2×C4—142no—
766C2×C4—144no—
767C2×C4—144no—
768C2×C4—144no—
769C2×C4—2816no—
770C2×C4—284no—
771C2×C4—284no—
772C2×C4—284no—
773C2×C4—562no—
774C2×C4—562no—
775C2×C4C22×D2814yes—
776C7#3671511yescharacteristic, complemented, Sylow
777C22—28no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—24no—
782C22—22no—
783C22—22no—
784C22—24no—
785C22—22no—
786C22—24no—
787C22—22no—
788C22—22no—
789C22—416no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—88no—
795C22—282no—
796C22—282no—
797C22—284no—
798C22—284no—
799C22—284no—
800C22—284no—
801C22—282no—
802C22—282no—
803C22—282no—
804C22—282no—
805C22—568no—
806C22—568no—
807C22#9018414yes—
808C22C23×D2811yescharacteristic
809C22C2×#654812yes—
810C22D7×H(5,𝔽2)12yes—
811C22#9061812yes—
812C4—24no—
813C4—44no—
814C4—44no—
815C4—144no—
816C4—282no—
817C4—282no—
818C4—282no—
819C4—282no—
820C4—282no—
821C2—24no—
822C2—44no—
823C2—42no—
824C2—42no—
825C2—562no—
826C2—562no—
827C2C2×#9018411yescharacteristic
828C2#1174292611yescharacteristic
829C2#1174293511yescharacteristic
830C2#1174339114yes—
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2309C2
hypercenter#2309D7
hypocenterC7#36715
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2309

Complements

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

NH ≅ G/Ntype
1. C2×#90495C2semidirect
2. C22×#6502C2semidirect
3. C7×#2309C2semidirect
4. #11739720C2semidirect
5. #11739691C2semidirect
6. #11733908C2semidirect
7. #11733831C2semidirect
8. #11733830C2semidirect
9. #11733824C2semidirect
10. #11731300C2semidirect
11. #11731297C2semidirect
12. #11731292C2semidirect
13. #11731278C2semidirect
14. #11731268C2semidirect
15. #11731268C2semidirect
19. C23×C22⋊D7C22semidirect
20. C24×Dic7C22semidirect
21. C2×C7×#117C22semidirect
28. C2×#6502C22semidirect
29. C2×#6502C22semidirect
30. C2×#6502C22semidirect
31. C2×#6500C22semidirect
32. C2×#6498C22semidirect
34. C22×(C2×D7)⋊C4C22semidirect
35. C22×Dic7⋊C4C22semidirect
37. C2×#6449C22semidirect
38. C2×#6449C22semidirect
40. C2×#6445C22semidirect
41. C7×#390C22semidirect
42. C7×#390C22semidirect
45. C7×#379C22semidirect
46. #89766C22semidirect
47. #89766C22semidirect
48. #89763C22semidirect
49. #89755C22semidirect
50. #89733C22semidirect
51. #89733C22semidirect
52. #89733C22semidirect
53. #89733C22semidirect
54. #89732C22semidirect
55. #89732C22semidirect
56. #89732C22semidirect
59. #89730C22semidirect
60. #89730C22semidirect
61. #89730C22semidirect
62. #89727C22semidirect
63. #89727C22semidirect
64. #89725C22semidirect
65. #89722C22semidirect
66. #89722C22semidirect
67. #89722C22semidirect
68. #89722C22semidirect
69. #89722C22semidirect
70. #89715C22semidirect
71. #89715C22semidirect
72. #89715C22semidirect
73. #89712C22semidirect
74. #89712C22semidirect
75. #89711C22semidirect
76. #89700C22semidirect
83. C22×C7×D4D4semidirect
179. #2309D7semidirect
312. C2×#117C2×D7semidirect
330. #390C2×D7semidirect
331. #390C2×D7semidirect
352. #379C2×D7semidirect
457. C22×D4D28semidirect
776. C7#36715semidirect

Maximal subgroups

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

subgroupindex
C2×#904952
C22×#65022
C7×#23092
#117397202
#117396912
#117339082
#117338312
#117338302
#117338242
#117313002
#117312972
#117312922
#117312782
#117312682
#367157