Finite Group Databasebeta

← #13560739

Subgroups — #13560739

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
1C22×#6501C211yesmaximal, characteristic, complemented
2C2×#90184C211yesmaximal, characteristic, complemented
3C7×#2405C211yesmaximal, characteristic, complemented
4#11741497C211yesmaximal, characteristic, complemented
5#11740318C214yesmaximal, complemented
6#11739559C211yesmaximal, characteristic, complemented
7#11734593C214yesmaximal, complemented
8#11734582C214yesmaximal, complemented
9#11732255C214yesmaximal, complemented
10#11732101C212yesmaximal, complemented
11#11731852C212yesmaximal, complemented
12#11731300C212yesmaximal, complemented
13#11731270C212yesmaximal, complemented
14#11731268C211yesmaximal, characteristic, complemented
15#11731264C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C23×C22⋊D7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic, complemented
20C23×C4×D7C2211yescharacteristic, complemented
21C2×C7×#123C2212yescomplemented
22C22×C7×C22⋊C4C2211yescharacteristic
23C2×#6516C2212yes—
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic, complemented
26C2×#6501—28no—
27C2×#6501C2214yes—
28C2×#6501C2214yescomplemented
29C2×#6500C2212yescomplemented
30C2×#6493C2212yescomplemented
31C2×#6493C2212yescomplemented
32C22×C4⋊Dic7C2211yescharacteristic, complemented
33C2×#6457C2214yescomplemented
34#90184—28no—
35C2×#6449C2212yes—
36C2×#6449C2212yes—
37C2×#6449C2212yescomplemented
38C2×#6445C2212yes—
39C2×#6445C2212yescomplemented
40C2×#6440C2212yescomplemented
41C7×#394C2214yescomplemented
42C7×#386C2212yescomplemented
43C7×#385C2212yescomplemented
44C7×#379C2211yescharacteristic
45C7×#379C2212yescomplemented
46#90019C2211yescharacteristic
47#89995C2214yescomplemented
48#89992C2212yescomplemented
49#89985C2212yes—
50#89983C2212yescomplemented
51#89982C2212yescomplemented
52#89766C2214yescomplemented
53#89761C2214yescomplemented
54#89757C2214yescomplemented
55#89733C2214yescomplemented
56#89733C2214yescomplemented
57#89733C2214yescomplemented
58#89732C2214yescomplemented
59#89732C2214yescomplemented
60#89731C2214yescomplemented
61#89730C2212yes—
62#89729C2214yescomplemented
63#89729C2214yescomplemented
64#89729C2214yescomplemented
65#89727C2212yescomplemented
66#89727C2212yescomplemented
67#89724C2214yescomplemented
68#89723C2214yescomplemented
69#89722C2212yescomplemented
70#89720C2214yescomplemented
71#89718C2212yescomplemented
72#89715C2212yescomplemented
73#89442C2214yescomplemented
74#89437C2214yescomplemented
75#89436C2214yescomplemented
76#89433C2214yescomplemented
77#36715—71nomaximal, Sylow
78C25×C7C2311yescharacteristic
79C25×C7C2311yescharacteristic
80C24×D7C2311yescharacteristic
81C24×D7C2311yescharacteristic
82C22×C7×D4—24no—
83C22×C7×D4—44no—
84C22×C7×D4C2312yes—
85C22×C7×D4C2312yes—
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C22×C22⋊D7—24no—
90C22×C22⋊D7—24no—
91C22×C22⋊D7—44no—
92C22×C22⋊D7—44no—
93C22×C22⋊D7—44no—
94C22×C22⋊D7D418yescomplemented
95C22×C22⋊D7C2312yes—
96C22×C22⋊D7C2312yes—
97C22×C22⋊D7C2314yes—
98C22×C22⋊D7C2314yes—
99C22×C22⋊D7C2312yes—
100C22×C22⋊D7C2312yes—
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C22×D28C2312yes—
106C22×D28C2312yes—
107C22×C4×D7—24no—
108C22×C4×D7—44no—
109C22×C4×D7C2314yes—
110C7×#123—44no—
111C2×C7×C4⋊C4C2314yes—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4C2312yes—
114C2×C7×C22⋊C4C2312yes—
115C2×C7×C22⋊C4C2312yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2312yes—
118C2×C7×C22⋊C4C2314yes—
119C2×C7×C22⋊C4C2312yes—
120#6516—44no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7C2312yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2312yes—
126C2×C22⋊Dic7C2312yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2312yes—
129C2×C22⋊Dic7C2312yes—
130#6501—216no—
131#6501—216no—
132#6500—44no—
133#6493—28no—
134#6493—28no—
135C2×(C2×D7)⋊C4C2312yes—
136C2×(C2×D7)⋊C4C2312yes—
137C2×(C2×D7)⋊C4C2312yes—
138C2×(C2×D7)⋊C4C2312yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×(C2×D7)⋊C4C2314yes—
142C2×(C2×D7)⋊C4C2314yes—
143C2×(C2×D7)⋊C4C2314yes—
144C2×C4⋊Dic7—24no—
145C2×C4⋊Dic7C2312yes—
146C2×C4⋊Dic7C2312yes—
147C2×C4⋊Dic7C2314yes—
148C2×C4⋊Dic7C2314yes—
149C2×Dic7⋊C4C2314yes—
150C2×Dic7⋊C4C2314yes—
151C2×C4×Dic7C2314yes—
152#6457—48no—
153#6449—28no—
154#6449—28no—
155#6449—44no—
156#6445—28no—
157#6445—28no—
158#6440—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#2405D711yescharacteristic, complemented
178#2403—71no—
179#2309—71no—
180C24×C7—24no—
181C24×C7—22no—
182C24×C7—24no—
183C24×C7—42no—
184C24×C7—42no—
185C24×C7—42no—
186C24×C7—42no—
187C24×C7C2×D414yes—
188C24×C7C2412yes—
189C24×C7C2411yescharacteristic
190C24×C7C2411yescharacteristic
191C24×C7C2411yescharacteristic
192C23×D7—24no—
193C23×D7—22no—
194C23×D7—42no—
195C23×D7—42no—
196C23×D7—42no—
197C23×D7—42no—
198C23×D7—42no—
199C23×D7C2×D414yes—
200C23×D7C2412yes—
201C23×D7C2412yes—
202C2×C7×D4—24no—
203C2×C7×D4—24no—
204C2×C7×D4—24no—
205C2×C7×D4—24no—
206C2×C7×D4—42no—
207C2×C7×D4—42no—
208C2×C7×D4—416no—
209C22×C4×C7—22no—
210C22×C4×C7—24no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—42no—
214C22×C4×C7—42no—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2414yes—
218C22×C4×C7C2412yes—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—24no—
223C2×C22⋊D7—28no—
224C2×C22⋊D7—416no—
225C2×C22⋊D7—42no—
226C2×C22⋊D7—42no—
227C2×C22⋊D7—42no—
228C2×C22⋊D7—42no—
229C2×C22⋊D7—42no—
230C2×C22⋊D7—44no—
231C2×C22⋊D7—44no—
232C2×C22⋊D7—42no—
233C2×C22⋊D7—44no—
234C2×C22⋊D7—44no—
235C2×C22⋊D7—44no—
236C2×C22⋊D7—416no—
237C2×C22⋊D7—416no—
238C2×C22⋊D7C2×D418yes—
239C2×C22⋊D7C2×D418yes—
240C22×Dic7—24no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—24no—
245C22×Dic7—42no—
246C22×Dic7—42no—
247C22×Dic7C2×D414yes—
248C22×Dic7C2414yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C2×D28—24no—
254C2×D28—24no—
255C2×D28—44no—
256C2×D28—44no—
257C2×C4×D7—28no—
258C2×C4×D7—28no—
259C2×C4×D7—44no—
260C2×C4×D7—416no—
261C7×C4⋊C4—28no—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C7×C22⋊C4—24no—
265C7×C22⋊C4—42no—
266C7×C22⋊C4—44no—
267C7×C22⋊C4—44no—
268C7×C22⋊C4—42no—
269C22⋊Dic7—24no—
270C22⋊Dic7—24no—
271C22⋊Dic7—24no—
272C22⋊Dic7—28no—
273C22⋊Dic7—42no—
274C22⋊Dic7—42no—
275C22⋊Dic7—44no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4—44no—
282(C2×D7)⋊C4—44no—
283(C2×D7)⋊C4—44no—
284(C2×D7)⋊C4—44no—
285C4⋊Dic7—24no—
286C4⋊Dic7—24no—
287C4⋊Dic7—28no—
288C4⋊Dic7—44no—
289Dic7⋊C4—44no—
290Dic7⋊C4—44no—
291C4×Dic7—44no—
292C23×D4—71no—
293C23×D4—71no—
294C23×D4—71no—
295C23×D4C2×D711yescharacteristic
296C24×C4—71no—
297#534—148no—
298C2×#123—74no—
299C2×#123—72no—
300C2×#123—72no—
301C2×#123—72no—
302C2×#123C2×D712yescomplemented
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×#117—72no—
313C22×C4⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4C2×D711yescharacteristic
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#394C2×D714yescomplemented
326#392—74no—
327#392—74no—
328#392—74no—
329#390—74no—
330#390—74no—
331#390—74no—
332#389—74no—
333#388—74no—
334#388—74no—
335#386—72no—
336#386—72no—
337#386—72no—
338#386—74no—
339#386C2×D712yescomplemented
340#385—72no—
341#385—74no—
342#385—72no—
343#385—72no—
344#385C2×D712yescomplemented
345#381—72no—
346#381—72no—
347#381—74no—
348#379—71no—
349#379—72no—
350#379—72no—
351#379C2×D711yescharacteristic
352#379C2×D712yescomplemented
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—28no—
362C23×C7—22no—
363C23×C7—24no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—24no—
367C23×C7—44no—
368C23×C7—44no—
369C23×C7—44no—
370C23×C7—44no—
371C23×C7—44no—
372C23×C7—88no—
373C23×C7—88no—
374C23×C7C22×D412yes—
375C23×C7C22×D412yes—
376C23×C7C22×D412yes—
377C23×C7H(5,𝔽2)14yes—
378C23×C7C2511yescharacteristic
379C22×D7—28no—
380C22×D7—24no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—24no—
384C22×D7—22no—
385C22×D7—24no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—24no—
389C22×D7—44no—
390C22×D7—44no—
391C22×D7—416no—
392C22×D7—44no—
393C22×D7—82no—
394C22×D7—82no—
395C22×D7—88no—
396C22×D7C22×D414yes—
397C7×D4—48no—
398C7×D4—48no—
399C2×C4×C7—28no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—24no—
405C2×C4×C7—24no—
406C2×C4×C7—24no—
407C2×C4×C7—24no—
408C2×C4×C7—24no—
409C2×C4×C7—82no—
410C2×C4×C7—82no—
411C2×C4×C7H(5,𝔽2)14yes—
412C22⋊D7—48no—
413C22⋊D7—48no—
414C22⋊D7—416no—
415C22⋊D7—48no—
416C22⋊D7—48no—
417C22⋊D7—88no—
418C2×Dic7—28no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—24no—
425C2×Dic7—24no—
426C2×Dic7—24no—
427C2×Dic7—22no—
428C2×Dic7—24no—
429C2×Dic7—22no—
430C2×Dic7—24no—
431C2×Dic7—44no—
432C2×Dic7—44no—
433C2×Dic7—44no—
434C2×Dic7C22×D414yes—
435D28—84no—
436D28—84no—
437C4×D7—416no—
438C25—71no—
439C25—71no—
440C25C22×D711yescharacteristic
441C25C22×D711yescharacteristic
442C22×D4—24no—
443C22×D4—44no—
444C22×D4—78no—
445C22×D4—72no—
446C22×D4—72no—
447C22×D4—72no—
448C22×D4—74no—
449C22×D4—72no—
450C22×D4—74no—
451C22×D4—72no—
452C22×D4—72no—
453C22×D4—144no—
454C22×D4—144no—
455C22×D4—284no—
456C22×D4—284no—
457C22×D4—284no—
458C22×D4C22×D712yes—
459C22×D4C22×D712yes—
460C23×C4—71no—
461C23×C4—71no—
462C23×C4—71no—
463C23×C4—71no—
464C23×C4—74no—
465C23×C4—144no—
466C23×C4—284no—
467C23×C4C22×D711yescharacteristic
468C23×C4C22×D711yescharacteristic
469C23×C4C22×D711yescharacteristic
470#123—44no—
471#123—148no—
472#123—148no—
473#123—284no—
474#123—288no—
475#121—148no—
476#121—148no—
477#121—1416no—
478#121—1416no—
479#120—148no—
480#120—148no—
481#120—284no—
482#120—284no—
483#117—284no—
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—24no—
493C2×C22⋊C4—72no—
494C2×C22⋊C4—72no—
495C2×C22⋊C4—74no—
496C2×C22⋊C4—72no—
497C2×C22⋊C4—72no—
498C2×C22⋊C4—72no—
499C2×C22⋊C4—72no—
500C2×C22⋊C4—72no—
501C2×C22⋊C4—74no—
502C2×C22⋊C4—72no—
503C2×C22⋊C4—74no—
504C2×C22⋊C4—72no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—74no—
507C2×C22⋊C4—74no—
508C2×C22⋊C4—74no—
509C2×C22⋊C4—144no—
510C2×C22⋊C4—144no—
511C2×C22⋊C4C22×D712yes—
512C2×C22⋊C4C22×D712yes—
513C2×C22⋊C4C22×D712yes—
514C2×C22⋊C4C22×D712yes—
515C2×C22⋊C4C22×D714yes—
516C2×C22⋊C4C22×D712yes—
517C2×C22⋊C4C22×D714yes—
518C2×C42—74no—
519#95—74no—
520#95—74no—
521#95—74no—
522#95—74no—
523#95—74no—
524#95C22×D714yes—
525C22×C7—22no—
526C22×C7—22no—
527C22×C7—28no—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—22no—
531C22×C7—22no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—44no—
535C22×C7—44no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—44no—
540C22×C7—44no—
541C22×C7—88no—
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—24no—
549C2×D7—24no—
550C2×D7—24no—
551C2×D7—416no—
552C2×D7—44no—
553C2×D7—44no—
554C2×D7—42no—
555C2×D7—42no—
556C2×D7—42no—
557C2×D7—44no—
558C2×D7—44no—
559C2×D7—88no—
560C4×C7—24no—
561C4×C7—42no—
562C4×C7—42no—
563C4×C7—44no—
564Dic7—24no—
565Dic7—42no—
566Dic7—42no—
567Dic7—42no—
568Dic7—44no—
569C24—24no—
570C24—22no—
571C24—24no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24—42no—
576C24—72no—
577C24—74no—
578C24—72no—
579C24—144no—
580C24—142no—
581C24—282no—
582C24—282no—
583C24—282no—
584C24—282no—
585C24—282no—
586C24D4×D714yes—
587C24C23×D712yes—
588C24C23×D711yescharacteristic
589C24C23×D711yescharacteristic
590C24C23×D711yescharacteristic
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—24no—
594C2×D4—24no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—416no—
598C2×D4—78no—
599C2×D4—78no—
600C2×D4—144no—
601C2×D4—144no—
602C2×D4—148no—
603C2×D4—144no—
604C2×D4—144no—
605C2×D4—144no—
606C2×D4—144no—
607C2×D4—284no—
608C2×D4—284no—
609C2×D4—2816no—
610C2×D4—282no—
611C2×D4—282no—
612C2×D4—282no—
613C2×D4—282no—
614C2×D4—282no—
615C2×D4—284no—
616C2×D4—284no—
617C2×D4—282no—
618C2×D4—284no—
619C2×D4—284no—
620C2×D4—284no—
621C2×D4—2816no—
622C2×D4—2816no—
623C22×C4—22no—
624C22×C4—24no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—74no—
630C22×C4—72no—
631C22×C4—74no—
632C22×C4—72no—
633C22×C4—72no—
634C22×C4—72no—
635C22×C4—148no—
636C22×C4—144no—
637C22×C4—142no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4—144no—
641C22×C4—148no—
642C22×C4—284no—
643C22×C4—2816no—
644C22×C4—282no—
645C22×C4—282no—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C22×C4C23×D714yes—
649C22×C4C23×D712yes—
650C4⋊C4—28no—
651C4⋊C4—148no—
652C4⋊C4—144no—
653C4⋊C4—144no—
654C4⋊C4—284no—
655C4⋊C4—284no—
656C4⋊C4—284no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—42no—
661C22⋊C4—44no—
662C22⋊C4—42no—
663C22⋊C4—44no—
664C22⋊C4—144no—
665C22⋊C4—144no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C22⋊C4—148no—
669C22⋊C4—144no—
670C22⋊C4—144no—
671C22⋊C4—144no—
672C22⋊C4—148no—
673C22⋊C4—284no—
674C22⋊C4—284no—
675C22⋊C4—284no—
676C22⋊C4—284no—
677C22⋊C4—282no—
678C22⋊C4—284no—
679C22⋊C4—282no—
680C42—284no—
681C2×C7—24no—
682C2×C7—42no—
683C2×C7—42no—
684C2×C7—82no—
685C2×C7C2×#53411yescharacteristic
686C2×C7#348411yescharacteristic
687C2×C7#348511yescharacteristic
688C2×C7#354214yes—
689D7—44no—
690D7—82no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—28no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—24no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—74no—
711C23—88no—
712C23—88no—
713C23—148no—
714C23—144no—
715C23—142no—
716C23—142no—
717C23—144no—
718C23—142no—
719C23—144no—
720C23—142no—
721C23—142no—
722C23—144no—
723C23—284no—
724C23—284no—
725C23—2816no—
726C23—284no—
727C23—562no—
728C23—562no—
729C23—568no—
730C23C2×D4×D712yes—
731C23C2×D4×D712yes—
732C23C2×D4×D712yes—
733C23#655314yes—
734C23C24×D711yescharacteristic
735D4—48no—
736D4—48no—
737D4—288no—
738D4—288no—
739D4—288no—
740D4—2816no—
741D4—288no—
742D4—564no—
743D4—564no—
744D4—568no—
745C2×C4—28no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—74no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—148no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—144no—
765C2×C4—144no—
766C2×C4—144no—
767C2×C4—142no—
768C2×C4—144no—
769C2×C4—142no—
770C2×C4—144no—
771C2×C4—2816no—
772C2×C4—284no—
773C2×C4—284no—
774C2×C4—284no—
775C2×C4#654814yes—
776C7#3671511yescharacteristic, complemented, Sylow
777C22—22no—
778C22—22no—
779C22—28no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—44no—
787C22—44no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—44no—
792C22—44no—
793C22—88no—
794C22—88no—
795C22—144no—
796C22—144no—
797C22—144no—
798C22—2816no—
799C22—284no—
800C22—284no—
801C22—282no—
802C22—282no—
803C22—282no—
804C22—284no—
805C22—284no—
806C22—568no—
807C22#9034414yes—
808C22C22×D4×D711yescharacteristic
809C22C2×#654812yes—
810C22C2×#655312yes—
811C22#9061812yes—
812C4—24no—
813C4—42no—
814C4—42no—
815C4—44no—
816C4—144no—
817C4—282no—
818C4—282no—
819C4—282no—
820C4—284no—
821C2—24no—
822C2—42no—
823C2—42no—
824C2—82no—
825C2—284no—
826C2—562no—
827C2#1174298711yescharacteristic
828C2C2×#9034411yescharacteristic
829C2#1174336411yescharacteristic
830C2#1174371614yes—
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2405C2
hypercenter#2405D7
hypocenterC7#36715
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2405

Complements

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

NH ≅ G/Ntype
1. C22×#6501C2semidirect
2. C2×#90184C2semidirect
3. C7×#2405C2semidirect
4. #11741497C2semidirect
5. #11740318C2semidirect
6. #11739559C2semidirect
7. #11734593C2semidirect
8. #11734582C2semidirect
9. #11732255C2semidirect
10. #11732101C2semidirect
11. #11731852C2semidirect
12. #11731300C2semidirect
13. #11731270C2semidirect
14. #11731268C2semidirect
15. #11731264C2semidirect
19. C23×C22⋊D7C22semidirect
20. C23×C4×D7C22semidirect
21. C2×C7×#123C22semidirect
25. C22×C22⋊Dic7C22semidirect
28. C2×#6501C22semidirect
29. C2×#6500C22semidirect
30. C2×#6493C22semidirect
31. C2×#6493C22semidirect
32. C22×C4⋊Dic7C22semidirect
33. C2×#6457C22semidirect
37. C2×#6449C22semidirect
39. C2×#6445C22semidirect
40. C2×#6440C22semidirect
41. C7×#394C22semidirect
42. C7×#386C22semidirect
43. C7×#385C22semidirect
45. C7×#379C22semidirect
47. #89995C22semidirect
48. #89992C22semidirect
50. #89983C22semidirect
51. #89982C22semidirect
52. #89766C22semidirect
53. #89761C22semidirect
54. #89757C22semidirect
55. #89733C22semidirect
56. #89733C22semidirect
57. #89733C22semidirect
58. #89732C22semidirect
59. #89732C22semidirect
60. #89731C22semidirect
62. #89729C22semidirect
63. #89729C22semidirect
64. #89729C22semidirect
65. #89727C22semidirect
66. #89727C22semidirect
67. #89724C22semidirect
68. #89723C22semidirect
69. #89722C22semidirect
70. #89720C22semidirect
71. #89718C22semidirect
72. #89715C22semidirect
73. #89442C22semidirect
74. #89437C22semidirect
75. #89436C22semidirect
76. #89433C22semidirect
94. C22×C22⋊D7D4semidirect
177. #2405D7semidirect
302. C2×#123C2×D7semidirect
325. #394C2×D7semidirect
339. #386C2×D7semidirect
344. #385C2×D7semidirect
352. #379C2×D7semidirect
776. C7#36715semidirect

Maximal subgroups

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

subgroupindex
C22×#65012
C2×#901842
C7×#24052
#117414972
#117403182
#117395592
#117345932
#117345822
#117322552
#117321012
#117318522
#117313002
#117312702
#117312682
#117312642
#367157