Finite Group Databasebeta

← #13514743

Subgroups — #13514743

Order 1792.

3106 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90214C211yesmaximal, characteristic
2C2×#90213C211yesmaximal, characteristic
3C2×#90195C211yesmaximal, characteristic
4C7×#2317C211yesmaximal, characteristic, complemented
5#11739677C211yesmaximal, characteristic, complemented
6#11739672C211yesmaximal, characteristic, complemented
7C2×#89745C211yesmaximal, characteristic, complemented
8#11733640C212yesmaximal, complemented
9D7×#389C212yesmaximal, complemented
10#11733413C212yesmaximal, complemented
11#11733408C212yesmaximal, complemented
12#11731839C214yesmaximal, complemented
13#11731838C214yesmaximal, complemented
14#11731805C212yesmaximal, complemented
15#11731768C212yesmaximal, complemented
16#11731673C212yesmaximal, complemented
17#11731602C212yesmaximal, complemented
18C22×#1157C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C2×C4×C22⋊D7C2214yes—
23C2×#6489C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2212yes—
26C22×C4×Dic7C2211yescharacteristic
27#90214C4116yescomplemented
28#90213—28no—
29#90195—28no—
30C2×#6456C2212yes—
31C2×#6456C2211yescharacteristic
32C2×#6456C2211yescharacteristic
33C2×#6455C2212yes—
34C2×#6455C2212yes—
35C2×D7×C4⋊C4C2212yes—
36C2×D7×C4⋊C4C2214yes—
37C2×D7×C4⋊C4C2212yes—
38C2×#6450C2211yescharacteristic
39C2×#6450C2212yes—
40C2×#6450C2211yescharacteristic
41C2×(C22⋊D7)⋊C4C2212yes—
42C2×(C22⋊D7)⋊C4C2212yes—
43C2×(C22⋊D7)⋊C4C2214yes—
44C2×C4×D28C2212yes—
45C2×#6435C2212yes—
46C2×C42×D7C2212yes—
47C2×C4×Dic14C2212yes—
48C7×#389C2212yes—
49C7×#389C2212yes—
50C7×#385C2214yes—
51C7×#384C2212yes—
52C7×#382C2212yes—
53C2×C7⋊#95C2212yes—
54#89761C2214yes—
55#89761C2214yes—
56#89759C2214yes—
57#89757C2211yescharacteristic
58#89757C2211yescharacteristic
59#89757C2211yescharacteristic
60#89757C2211yescharacteristic
61#89748C2214yes—
62C4⋊C4×Dic7C2214yes—
63#89745C2212yes—
64#89745C2212yes—
65#89745C2212yes—
66#89745C2212yes—
67#89745C2212yes—
68#89745C2212yes—
69#89744C2214yes—
70#89744C2214yes—
71#89722C2212yes—
72#89722C2212yes—
73#89714C2214yes—
74C4×C4⋊Dic7C2212yes—
75C4×C4⋊Dic7C2212yes—
76#89700C2212yes—
77#89700C2212yes—
78#89440C2214yes—
79#89440C2214yes—
80#89439C2214yes—
81D7×#95C2214yes—
82#89422C2214yes—
83#89421C2214yes—
84#89419C2214yes—
85#89419C2214yes—
86#34250—71nomaximal, Sylow
87C23×C4×C7C2312yes—
88C23×C4×C7C2311yescharacteristic
89C22×C22⋊D7C2312yes—
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2312yes—
93C2×#1157C2×C418yes—
94C2×#1157D418yes—
95C2×#1157Q818yes—
96C22×D28C2311yescharacteristic
97C22×C4×D7C2312yes—
98C22×C4×D7C2312yes—
99C22×C4×D7C2314yes—
100C22×C4×D7C2314yes—
101C22×C4×D7C2312yes—
102C22×Dic14C2311yescharacteristic
103C7×#117—24no—
104C7×#117C2×C418yescomplemented
105C2×C7×C4⋊C4—24no—
106C2×C7×C4⋊C4C2312yes—
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2312yes—
110C2×C7×C4⋊C4C2314yes—
111C2×C7×C4⋊C4C2314yes—
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C22⋊C4C2312yes—
115C2×C7×C22⋊C4C2312yes—
116C2×C42×C7C2312yes—
117C2×C42×C7C2312yes—
118C2×C22⋊Dic7C2312yes—
119C4×C22⋊D7—216no—
120C2×(C2×D7)⋊C4C2312yes—
121C2×(C2×D7)⋊C4C2312yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124#6489—24no—
125C2×C4⋊Dic7C2×C418yescomplemented
126C2×C4⋊Dic7C2312yes—
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2312yes—
130C2×C4⋊Dic7C2312yes—
131C2×C4⋊Dic7C2312yes—
132C2×C4⋊Dic7C2312yes—
133C2×C4⋊Dic7C2312yes—
134C2×Dic7⋊C4—44no—
135C2×Dic7⋊C4C2312yes—
136C2×Dic7⋊C4C2312yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C2×C4×Dic7—24no—
144C2×C4×Dic7C2311yescharacteristic
145C2×C4×Dic7C2312yes—
146C2×C4×Dic7C2312yes—
147C2×C4×Dic7C2311yescharacteristic
148C2×C4×Dic7C2314yes—
149C2×C4×Dic7C2311yescharacteristic
150C2×C4×Dic7C2311yescharacteristic
151C2×C4×Dic7C2312yes—
152C2×C4×Dic7C2314yes—
153#6456—28no—
154#6456—24no—
155#6456—24no—
156#6455—28no—
157#6455C2×C4116yescomplemented
158D7×C4⋊C4—28no—
159D7×C4⋊C4—48no—
160D7×C4⋊C4C2×C4116yescomplemented
161#6450—28no—
162#6450—24no—
163#6450—24no—
164(C22⋊D7)⋊C4—28no—
165(C22⋊D7)⋊C4—28no—
166(C22⋊D7)⋊C4C2×C4132yescomplemented
167C4×D28C2×C4116yescomplemented
168#6435—28no—
169C42×D7—28no—
170C4×Dic14C2×C4116yescomplemented
171C7×#95C2314yes—
172C7×#95C2314yes—
173C7⋊#95C2314yes—
174C7⋊#95C2314yes—
175C7⋊#95C2312yes—
176C7⋊#95C2312yes—
177C7⋊#95C2312yes—
178C7⋊#95C2314yes—
179C7⋊#95C2312yes—
180C7⋊#95C2314yes—
181C2×#520—71no—
182C2×#520—71no—
183C2×C4×#41—71no—
184#2351—72no—
185Q8×C4⋊C4—72no—
186#2349—74no—
187#2349—72no—
188D4×C4⋊C4—74no—
189D4×C4⋊C4—72no—
190#2317—72no—
191#2317D711yescharacteristic, complemented
192#2316—72no—
193#2316—71no—
194#2296—72no—
195#2296—71no—
196C2×#389—72no—
197C2×#389—71no—
198C24×C7C2411yescharacteristic
199C23×D7C2412yes—
200C22×C4×C7—24no—
201C22×C4×C7—42no—
202C22×C4×C7—42no—
203C22×C4×C7C22×C414yes—
204C22×C4×C7C2×D414yes—
205C22×C4×C7C2×Q814yes—
206C22×C4×C7C2412yes—
207C22×C4×C7C2414yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2411yescharacteristic
212C22×C4×C7C2411yescharacteristic
213C2×C22⋊D7C22×C418yes—
214C2×C22⋊D7C2×D418yes—
215C2×C22⋊D7C2×Q818yes—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—42no—
221C22×Dic7—42no—
222C22×Dic7—41no—
223C22×Dic7—41no—
224C22×Dic7C22×C418yes—
225C22×Dic7C2411yescharacteristic
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2411yescharacteristic
229C22×Dic7C2414yes—
230C22×Dic7C2411yescharacteristic
231C22×Dic7C2411yescharacteristic
232C22×Dic7C2412yes—
233#1157C4⋊C4164yescomplemented
234C2×D28C22×C414yes—
235C2×D28C2×D414yes—
236C2×D28C2×Q814yes—
237C2×C4×D7—24no—
238C2×C4×D7—24no—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—28no—
242C2×C4×D7—44no—
243C2×C4×D7—44no—
244C2×C4×D7—42no—
245C2×C4×D7—42no—
246C2×C4×D7—44no—
247C2×C4×D7—44no—
248C2×C4×D7C22×C4116yes—
249C2×C4×D7C22×C418yes—
250C2×C4×D7C2×D418yes—
251C2×C4×D7C2×Q818yes—
252C2×Dic14C22×C414yes—
253C2×Dic14C2×D414yes—
254C2×Dic14C2×Q814yes—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—22no—
257C7×C4⋊C4—22no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4—44no—
260C7×C4⋊C4—44no—
261C7×C4⋊C4C22×C414yes—
262C7×C4⋊C4C22×C414yes—
263C7×C22⋊C4—24no—
264C7×C22⋊C4C22×C418yes—
265C42×C7—24no—
266C42×C7C22×C418yes—
267C22⋊Dic7—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—28no—
271(C2×D7)⋊C4C22×C4116yes—
272C4⋊Dic7—22no—
273C4⋊Dic7—22no—
274C4⋊Dic7—24no—
275C4⋊Dic7—24no—
276C4⋊Dic7—42no—
277C4⋊Dic7—42no—
278C4⋊Dic7C22×C418yes—
279C4⋊Dic7C22×C418yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—28no—
283Dic7⋊C4—28no—
284Dic7⋊C4—44no—
285Dic7⋊C4—44no—
286Dic7⋊C4—44no—
287Dic7⋊C4C22×C4116yes—
288C4×Dic7—22no—
289C4×Dic7—22no—
290C4×Dic7—22no—
291C4×Dic7—22no—
292C4×Dic7—24no—
293C4×Dic7—24no—
294C4×Dic7—24no—
295C4×Dic7—28no—
296C4×Dic7C22×C4116yes—
297C22×#41—71no—
298#520—716no—
299#520—148no—
300C4×#41—148no—
301C2×C4×Q8—71no—
302C2×C4×Q8—72no—
303C2×C4×Q8—71no—
304C2×C4×Q8—72no—
305C2×C4×D4—74no—
306C2×C4×D4—71no—
307C2×C4×D4—72no—
308C2×C4×D4—71no—
309C2×C4×D4—74no—
310C2×C4×D4—72no—
311C2×C4×D4—72no—
312C2×C4×D4—72no—
313C2×#117—71no—
314C2×#117—72no—
315C2×#117—72no—
316C2×#117—72no—
317C2×#117C2×D711yescharacteristic
318C2×#117C2×D711yescharacteristic
319C22×C4⋊C4—71no—
320C22×C4⋊C4—72no—
321C22×C4⋊C4—72no—
322C22×C4⋊C4—72no—
323C22×C4⋊C4—74no—
324C22×C4⋊C4C2×D711yescharacteristic
325C22×C42—71no—
326C22×C42—72no—
327#389—71no—
328#389—72no—
329#389—74no—
330#389—72no—
331#389—72no—
332#389—71no—
333#389—72no—
334#389—74no—
335#389—72no—
336#389—72no—
337#389—71no—
338#389—71no—
339#389—72no—
340#389—72no—
341#389—74no—
342#389—74no—
343#389C2×D712yes—
344#389C2×D712yes—
345#385—74no—
346#385—74no—
347#385—72no—
348#385—72no—
349#385—74no—
350#385—74no—
351#385C2×D714yes—
352#384—74no—
353#384C2×D712yes—
354#382—74no—
355#382C2×D712yes—
356#380—74no—
357#380—74no—
358#380—74no—
359C4×C4⋊C4—74no—
360C4×C4⋊C4—72no—
361C4×C4⋊C4—72no—
362C4×C4⋊C4—74no—
363C2×#95—72no—
364C2×#95—74no—
365C23×C7—21no—
366C23×C7—21no—
367C23×C7—21no—
368C23×C7—21no—
369C23×C7C23×C412yes—
370C23×C7C22×D412yes—
371C23×C7C22×Q812yes—
372C23×C7C2511yescharacteristic
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7C23×C414yes—
378C22×D7C22×D414yes—
379C22×D7C22×Q814yes—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—24no—
387C2×C4×C7—24no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—24no—
393C2×C4×C7—84no—
394C2×C4×C7C2×C4⋊C4116yescomplemented
395C2×C4×C7C23×C414yes—
396C2×C4×C7C23×C414yes—
397C2×C4×C7C23×C412yes—
398C2×C4×C7C23×C412yes—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D412yes—
401C2×C4×C7C22×Q812yes—
402C2×C4×C7C22×Q812yes—
403C22⋊D7C2×C4⋊C4132yescomplemented
404C2×Dic7—21no—
405C2×Dic7—21no—
406C2×Dic7—24no—
407C2×Dic7—24no—
408C2×Dic7—21no—
409C2×Dic7—21no—
410C2×Dic7—22no—
411C2×Dic7—21no—
412C2×Dic7—21no—
413C2×Dic7—22no—
414C2×Dic7—21no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—21no—
418C2×Dic7—22no—
419C2×Dic7—21no—
420C2×Dic7—21no—
421C2×Dic7—22no—
422C2×Dic7—48no—
423C2×Dic7—44no—
424C2×Dic7—44no—
425C2×Dic7C23×C418yes—
426C2×Dic7C23×C414yes—
427C2×Dic7C22×D414yes—
428C2×Dic7C22×Q814yes—
429C2×Dic7H(5,𝔽2)12yes—
430C2×Dic72−1+412yes—
431D28C2×C4⋊C4116yescomplemented
432C4×D7—416no—
433C4×D7—48no—
434C4×D7—48no—
435C4×D7—88no—
436C4×D7C2×C4⋊C4132yescomplemented
437Dic14C2×C4⋊C4116yescomplemented
438C2×#41—78no—
439C2×#41—78no—
440C2×#41—78no—
441C22×Q8—71no—
442C22×D4—72no—
443C22×D4—71no—
444C23×C4—72no—
445C23×C4—72no—
446C23×C4—74no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—72no—
450C23×C4—72no—
451C23×C4—74no—
452C23×C4C22×D712yes—
453C23×C4C22×D711yescharacteristic
454C4×Q8—716no—
455C4×Q8—144no—
456C4×Q8—144no—
457C4×Q8—148no—
458C4×D4—732no—
459C4×D4—716no—
460C4×D4—148no—
461C4×D4—148no—
462C4×D4—144no—
463C4×D4—144no—
464C4×D4—148no—
465C4×D4—1416no—
466#117—24no—
467#117—716no—
468#117—148no—
469#117—148no—
470#117—144no—
471#117C4×D718yescomplemented
472C2×C4⋊C4—24no—
473C2×C4⋊C4—78no—
474C2×C4⋊C4—72no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—72no—
477C2×C4⋊C4—716no—
478C2×C4⋊C4—71no—
479C2×C4⋊C4—74no—
480C2×C4⋊C4—72no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—72no—
484C2×C4⋊C4—72no—
485C2×C4⋊C4—72no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—72no—
490C2×C4⋊C4—72no—
491C2×C4⋊C4—148no—
492C2×C4⋊C4—288no—
493C2×C4⋊C4—284no—
494C2×C4⋊C4C22×D712yes—
495C2×C4⋊C4C22×D712yes—
496C2×C4⋊C4C22×D711yescharacteristic
497C2×C4⋊C4C22×D711yescharacteristic
498C2×C4⋊C4C22×D714yes—
499C2×C4⋊C4C22×D714yes—
500C2×C4⋊C4C22×D711yescharacteristic
501C2×C4⋊C4C22×D711yescharacteristic
502C2×C22⋊C4—74no—
503C2×C22⋊C4—72no—
504C2×C22⋊C4—72no—
505C2×C22⋊C4—74no—
506C2×C22⋊C4—72no—
507C2×C22⋊C4C22×D712yes—
508C2×C22⋊C4C22×D712yes—
509C2×C42—74no—
510C2×C42—71no—
511C2×C42—74no—
512C2×C42—72no—
513C2×C42—72no—
514C2×C42—72no—
515C2×C42—71no—
516C2×C42—71no—
517C2×C42—71no—
518C2×C42—148no—
519C2×C42—144no—
520C2×C42C22×D712yes—
521C2×C42C22×D712yes—
522#95—74no—
523#95—72no—
524#95—74no—
525#95—74no—
526#95—72no—
527#95—74no—
528#95—72no—
529#95—72no—
530#95C22×D714yes—
531#95C22×D714yes—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—22no—
535C22×C7—22no—
536C22×C7—22no—
537C22×C7—22no—
538C22×C7C22×C4⋊C414yes—
539C22×C7C24×C411yescharacteristic
540C22×C7C23×D411yescharacteristic
541C22×C7C23×Q811yescharacteristic
542C22×C7C2×H(5,𝔽2)11yescharacteristic
543C22×C7C2×2−1+411yescharacteristic
544C22×C7#58511yescharacteristic
545C22×C7#58511yescharacteristic
546C2×D7—24no—
547C2×D7—24no—
548C2×D7—24no—
549C2×D7—24no—
550C2×D7—24no—
551C2×D7—24no—
552C2×D7C22×C4⋊C418yes—
553C4×C7—24no—
554C4×C7—24no—
555C4×C7—42no—
556C4×C7—44no—
557C4×C7—42no—
558C4×C7C22×C4⋊C414yes—
559C4×C7C22×C4⋊C414yes—
560Dic7—28no—
561Dic7—22no—
562Dic7—22no—
563Dic7—42no—
564Dic7—41no—
565Dic7—42no—
566Dic7—41no—
567Dic7C22×C4⋊C418yes—
568C24—72no—
569C24C23×D711yescharacteristic
570#41—764no—
571C2×Q8—74no—
572C2×Q8—74no—
573C2×Q8—74no—
574C2×D4—78no—
575C2×D4—78no—
576C2×D4—78no—
577C2×D4—74no—
578C2×D4—74no—
579C2×D4—74no—
580C22×C4—24no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—72no—
584C22×C4—78no—
585C22×C4—78no—
586C22×C4—78no—
587C22×C4—71no—
588C22×C4—74no—
589C22×C4—71no—
590C22×C4—78no—
591C22×C4—716no—
592C22×C4—71no—
593C22×C4—72no—
594C22×C4—72no—
595C22×C4—71no—
596C22×C4—144no—
597C22×C4—144no—
598C22×C4—144no—
599C22×C4—144no—
600C22×C4—148no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—284no—
606C22×C4—284no—
607C22×C4—282no—
608C22×C4—282no—
609C22×C4—284no—
610C22×C4—284no—
611C22×C4—282no—
612C22×C4—281no—
613C22×C4—282no—
614C22×C4—281no—
615C22×C4C2×C4×D714yes—
616C22×C4D4×D714yes—
617C22×C4Q8×D714yes—
618C22×C4C23×D712yes—
619C22×C4C23×D714yes—
620C22×C4C23×D712yes—
621C22×C4C23×D712yes—
622C22×C4C23×D712yes—
623C22×C4C23×D711yescharacteristic
624C22×C4C23×D711yescharacteristic
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—716no—
632C4⋊C4—78no—
633C4⋊C4—78no—
634C4⋊C4—148no—
635C4⋊C4—148no—
636C4⋊C4—144no—
637C4⋊C4—144no—
638C4⋊C4—144no—
639C4⋊C4—144no—
640C4⋊C4—142no—
641C4⋊C4—142no—
642C4⋊C4—284no—
643C4⋊C4—284no—
644C4⋊C4—284no—
645C4⋊C4—282no—
646C4⋊C4—282no—
647C4⋊C4C2×C4×D714yes—
648C4⋊C4C2×C4×D714yes—
649C22⋊C4—24no—
650C22⋊C4—716no—
651C22⋊C4—144no—
652C22⋊C4—144no—
653C22⋊C4—148no—
654C22⋊C4—144no—
655C22⋊C4C2×C4×D718yes—
656C42—24no—
657C42—716no—
658C42—144no—
659C42—144no—
660C42—148no—
661C42—142no—
662C42—142no—
663C42—142no—
664C42—142no—
665C42—144no—
666C42C2×C4×D718yes—
667C2×C7—24no—
668C2×C7C23×C4⋊C411yescharacteristic
669C2×C7C4×H(5,𝔽2)11yescharacteristic
670C2×C7C4×2−1+411yescharacteristic
671C2×C7#348811yescharacteristic
672C2×C7#348911yescharacteristic
673C2×C7#350311yescharacteristic
674C2×C7#350411yescharacteristic
675D7—28no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—74no—
681C23—74no—
682C23—74no—
683C23—142no—
684C23—142no—
685C23—142no—
686C23—142no—
687C23C22×C4×D712yes—
688C23C2×D4×D712yes—
689C23C2×Q8×D712yes—
690C23C24×D711yescharacteristic
691Q8—716no—
692D4—732no—
693D4—716no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—74no—
708C2×C4—74no—
709C2×C4—74no—
710C2×C4—732no—
711C2×C4—78no—
712C2×C4—72no—
713C2×C4—72no—
714C2×C4—84no—
715C2×C4—141no—
716C2×C4—141no—
717C2×C4—144no—
718C2×C4—141no—
719C2×C4—144no—
720C2×C4—141no—
721C2×C4—142no—
722C2×C4—141no—
723C2×C4—141no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—141no—
727C2×C4—141no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—141no—
731C2×C4—142no—
732C2×C4—141no—
733C2×C4—2816no—
734C2×C4—288no—
735C2×C4—288no—
736C2×C4—288no—
737C2×C4—284no—
738C2×C4—284no—
739C2×C4—568no—
740C2×C4D7×C4⋊C4116yescomplemented
741C2×C4C22×C4×D714yes—
742C2×C4C22×C4×D714yes—
743C2×C4C22×C4×D712yes—
744C2×C4C22×C4×D712yes—
745C2×C4C2×D4×D712yes—
746C2×C4C2×D4×D712yes—
747C2×C4C2×Q8×D712yes—
748C2×C4C2×Q8×D712yes—
749C7#3425011yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—78no—
757C22—144no—
758C22—144no—
759C22—144no—
760C22—144no—
761C22—144no—
762C22—144no—
763C22C2×D7×C4⋊C414yes—
764C22C23×C4×D711yescharacteristic
765C22C22×D4×D711yescharacteristic
766C22C22×Q8×D711yescharacteristic
767C22D7×H(5,𝔽2)11yescharacteristic
768C22#9061811yescharacteristic
769C22D7×2−1+411yescharacteristic
770C22#9062011yescharacteristic
771C4—24no—
772C4—24no—
773C4—44no—
774C4—42no—
775C4—42no—
776C4—78no—
777C4—142no—
778C4—142no—
779C4—148no—
780C4—281no—
781C4—282no—
782C4—281no—
783C4—282no—
784C4C2×D7×C4⋊C414yes—
785C4C2×D7×C4⋊C414yes—
786C2—24no—
787C2—148no—
788C2C22×D7×C4⋊C411yescharacteristic
789C2#1174295411yescharacteristic
790C2#1174295511yescharacteristic
791C2#1174339911yescharacteristic
792C2#1174342411yescharacteristic
793C2#1174365411yescharacteristic
794C2#1174365511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D7
commutatorC22×C7C24×C4
FittingC7×#2317C2
socle, cosocleC23×C7C25
prime radicalC22×#1157C22
hypercenter#2317D7
hypocenterC7#34250
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
4. C7×#2317C2semidirect
5. #11739677C2semidirect
6. #11739672C2semidirect
7. C2×#89745C2semidirect
8. #11733640C2semidirect
9. D7×#389C2semidirect
10. #11733413C2semidirect
11. #11733408C2semidirect
12. #11731839C2semidirect
13. #11731838C2semidirect
14. #11731805C2semidirect
15. #11731768C2semidirect
16. #11731673C2semidirect
17. #11731602C2semidirect
27. #90214C4semidirect
104. C7×#117C2×C4semidirect
125. C2×C4⋊Dic7C2×C4semidirect
157. #6455C2×C4semidirect
160. D7×C4⋊C4C2×C4semidirect
166. (C22⋊D7)⋊C4C2×C4semidirect
167. C4×D28C2×C4semidirect
170. C4×Dic14C2×C4semidirect
191. #2317D7semidirect
233. #1157C4⋊C4semidirect
394. C2×C4×C7C2×C4⋊C4semidirect
403. C22⋊D7C2×C4⋊C4semidirect
431. D28C2×C4⋊C4semidirect
436. C4×D7C2×C4⋊C4semidirect
437. Dic14C2×C4⋊C4semidirect
471. #117C4×D7semidirect
740. C2×C4D7×C4⋊C4semidirect
749. C7#34250semidirect

Maximal subgroups

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

subgroupindex
C2×#902142
C2×#902132
C2×#901952
C7×#23172
#117396772
#117396722
C2×#897452
#117336402
D7×#3892
#117334132
#117334082
#117318392
#117318382
#117318052
#117317682
#117316732
#117316022
#342507