Finite Group Databasebeta

← C2×#11743038 #14262216

Subgroups — C2×#11743038 #14262216

Order 1792.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#90507C211yesmaximal, characteristic, complemented
3C2×#90503C211yesmaximal, characteristic, complemented
4C2×#90482C211yesmaximal, characteristic
5C22×#6489C211yesmaximal, characteristic, complemented
6C2×#90330C212yesmaximal, complemented
7#11743038C2132yesmaximal, direct product factor
8C2×#90332C212yesmaximal, complemented
9C2×#90326C212yesmaximal, complemented
10C2×#90333C212yesmaximal, complemented
11C2×#90334C212yesmaximal, complemented
12C2×#90316C212yesmaximal, complemented
13C2×#90313C212yesmaximal, complemented
14C2×#90315C212yesmaximal, complemented
15C2×#90195C211yesmaximal, characteristic, complemented
16C2×#90204C214yesmaximal, complemented
17C2×#90191C211yesmaximal, characteristic, complemented
18C2×#90186C214yesmaximal, complemented
19C23×C7×Q8C2211yescharacteristic
20C24×C4×C7C2211yescharacteristic
21C22×#1157C2211yescharacteristic
22C2×C7×C22⋊Q8C2212yes—
23C2×C7×C22⋊Q8C2212yes—
24C2×C7×C22⋊Q8C2212yes—
25C2×C7×C22⋊Q8C2212yes—
26C2×C7×C22⋊Q8C22116yescomplemented
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C4⋊C4C2212yes—
29C22×C7×C22⋊C4C2212yes—
30C2×#6516C2212yes—
31C22×C22⋊Dic7C2212yes—
32#90507C22116yescomplemented
33C2×#6510C2212yescomplemented
34C2×#6509C2212yescomplemented
35C2×#6509C2212yescomplemented
36#90503C22116yescomplemented
37C2×Q8×Dic7C2212yescomplemented
38C2×Q8×Dic7C2212yescomplemented
39C2×Q8×Dic7C2212yescomplemented
40C2×Q8×Dic7C2212yescomplemented
41C2×#6507C2212yescomplemented
42#90482C22116yes—
43C2×#6493C2211yescharacteristic
44C2×#6493C2211yescharacteristic
45C2×#6492C2212yes—
46C2×#6492C2214yes—
47C2×C4×C22⋊D7C2212yes—
48C2×C4×C22⋊D7C2212yes—
49C2×C4×C22⋊D7C2214yes—
50C2×#6489C2211yescharacteristic
51C2×#6489C2212yes—
52C2×#6489C2212yes—
53C2×#6489C2211yescharacteristic
54C2×#6489C2211yescharacteristic
55C2×#6489C2211yescharacteristic
56C2×#6489C2211yescharacteristic
57C2×#6489C2214yes—
58C2×#6489C22116yescomplemented
59C22×C4⋊Dic7C2211yescharacteristic
60C22×C4⋊Dic7C2211yescharacteristic
61C2×#6487C2211yescharacteristic
62C2×#6487C2211yescharacteristic
63C2×#6487C2214yes—
64C22×C4×Dic7C2212yes—
65#90334C22132yescomplemented
66#90333C22132yescomplemented
67#90332C22132yescomplemented
68#90330C22132yescomplemented
69#90326C22132yescomplemented
70#90316C22132yescomplemented
71#90315C22132yescomplemented
72#90313C22132yescomplemented
73#90204C22164yescomplemented
74C2×#6461C2214yescomplemented
75C2×#6461C2214yescomplemented
76C2×#6460C2214yescomplemented
77#90195C22116yescomplemented
78C2×#6456C2212yescomplemented
79C2×#6455C2214yescomplemented
80C2×#6455C2212yescomplemented
81C2×D7×C4⋊C4C2212yescomplemented
82#90191C22116yescomplemented
83C2×#6453C2212yescomplemented
84C2×#6453C2212yescomplemented
85C2×#6453C2214yescomplemented
86C2×#6452C2214yescomplemented
87C2×#6452C2214yescomplemented
88C2×#6451C2212yescomplemented
89C2×#6451C2212yescomplemented
90C2×#6450C2212yescomplemented
91C2×#6450C2214yescomplemented
92#90186C22164yescomplemented
93C2×#6449C2214yes—
94C2×#6448C2214yes—
95C2×#6446C2214yes—
96C2×(C22⋊D7)⋊C4C2214yes—
97C2×#6442C2214yes—
98C2×#6442C2214yes—
99C2×#6441C2214yes—
100C2×#6440C2214yes—
101C2×#3495—71nomaximal, Sylow
102C25×C7C2311yescharacteristic
103C22×C7×Q8—28no—
104C22×C7×Q8C2312yes—
105C22×C7×Q8C2312yes—
106C22×C7×Q8C2318yes—
107C23×C4×C7—28no—
108C23×C4×C7C2312yes—
109C23×C4×C7C2311yescharacteristic
110C23×C4×C7C2311yescharacteristic
111C23×C4×C7C2311yescharacteristic
112C23×C4×C7C2311yescharacteristic
113C23×C4×C7C2311yescharacteristic
114C23×C4×C7C2318yes—
115C23×C4×C7C2312yes—
116C23×C4×C7C2311yescharacteristic
117C22×C22⋊D7C2312yes—
118C22×C22⋊D7C2312yes—
119C22×C22⋊D7C2312yes—
120C23×Dic7C2312yes—
121C23×Dic7C2312yes—
122C2×#1157—28no—
123C2×#1157C2318yes—
124C22×D28C2311yescharacteristic
125C22×C4×D7C2312yes—
126C22×C4×D7C2314yes—
127C22×Dic14C2311yescharacteristic
128C22×Dic14C2314yes—
129C7×C22⋊Q8C23116yes—
130C7×C22⋊Q8C23116yes—
131C7×C22⋊Q8C23116yes—
132C7×C22⋊Q8C23116yes—
133C2×C7×C4⋊C4C2312yes—
134C2×C7×C4⋊C4C2314yes—
135C2×C7×C4⋊C4C2312yes—
136C2×C7×C4⋊C4C2314yes—
137C2×C7×C4⋊C4C2318yes—
138C2×C7×C4⋊C4C23116yes—
139C2×C7×C22⋊C4C2314yes—
140C2×C7×C22⋊C4C2314yes—
141C2×C7×C22⋊C4C23116yes—
142#6516C23116yes—
143C2×C22⋊Dic7C2312yes—
144C2×C22⋊Dic7C2312yes—
145C2×C22⋊Dic7C2312yes—
146C2×C22⋊Dic7C2312yes—
147C2×C22⋊Dic7C23116yes—
148C2×C22⋊Dic7C2312yes—
149C2×C22⋊Dic7C2312yes—
150C2×C22⋊Dic7C2312yes—
151#6510C23116yescomplemented
152#6509C23116yescomplemented
153#6509C23116yescomplemented
154Q8×Dic7C23116yescomplemented
155Q8×Dic7C23116yescomplemented
156Q8×Dic7C23116yescomplemented
157Q8×Dic7C23116yescomplemented
158#6507C23116yescomplemented
159#6493C2318yes—
160#6493C2318yes—
161#6492C23132yes—
162#6492C23116yes—
163C4×C22⋊D7C23132yes—
164C4×C22⋊D7C23116yes—
165C4×C22⋊D7C23116yes—
166C2×(C2×D7)⋊C4C2314yes—
167C2×(C2×D7)⋊C4C2314yes—
168C2×(C2×D7)⋊C4C2314yes—
169C2×(C2×D7)⋊C4C2312yes—
170C2×(C2×D7)⋊C4C2312yes—
171#6489C23132yes—
172#6489C2318yes—
173#6489C2318yes—
174#6489C2318yes—
175#6489C23116yes—
176#6489C23116yes—
177#6489C2318yes—
178#6489C2318yes—
179C2×C4⋊Dic7C2314yes—
180C2×C4⋊Dic7C2314yes—
181C2×C4⋊Dic7C2314yes—
182C2×C4⋊Dic7C2311yescharacteristic
183C2×C4⋊Dic7C2311yescharacteristic
184C2×C4⋊Dic7C2312yes—
185C2×C4⋊Dic7C2312yes—
186C2×C4⋊Dic7C2311yescharacteristic
187C2×C4⋊Dic7C2311yescharacteristic
188C2×C4⋊Dic7C2311yescharacteristic
189C2×C4⋊Dic7C2311yescharacteristic
190C2×C4⋊Dic7C2318yes—
191C2×C4⋊Dic7C2318yes—
192#6487C23132yes—
193#6487C2318yes—
194#6487C2318yes—
195C2×Dic7⋊C4C2314yes—
196C2×Dic7⋊C4C2314yes—
197C2×Dic7⋊C4C2314yes—
198C2×Dic7⋊C4C2314yes—
199C2×Dic7⋊C4C2314yes—
200C2×Dic7⋊C4C2312yes—
201C2×Dic7⋊C4C2312yes—
202C2×C4×Dic7C2314yes—
203C2×C4×Dic7C2314yes—
204C2×C4×Dic7C2314yes—
205C2×C4×Dic7C2312yes—
206C2×C4×Dic7C2312yes—
207C2×C4×Dic7C2312yes—
208C2×C4×Dic7C2312yes—
209C2×C4×Dic7C2312yes—
210C2×C4×Dic7C23116yes—
211#6461C23132yescomplemented
212#6461C23132yescomplemented
213#6460C23132yescomplemented
214#6456C23116yescomplemented
215#6455C23116yescomplemented
216#6455C23132yescomplemented
217D7×C4⋊C4C23116yescomplemented
218#6453C23116yescomplemented
219#6453C23116yescomplemented
220#6453C23132yescomplemented
221#6452C23132yescomplemented
222#6452C23132yescomplemented
223#6451C23116yescomplemented
224#6451C23116yescomplemented
225#6450C23116yescomplemented
226#6450C23132yescomplemented
227#6449C23132yes—
228#6448C23132yes—
229#6446C23132yes—
230(C22⋊D7)⋊C4C23132yes—
231#6442C23132yes—
232#6442C23132yes—
233#6441C23132yes—
234#6440C23132yes—
235#3495—732no—
236C2×#556—72no—
237C2×#554—72no—
238C2×#552—72no—
239C2×#552—72no—
240C2×#552—74no—
241C2×#551—74no—
242C2×#544—71no—
243C2×#542—72no—
244C2×#541—72no—
245C2×#536—71no—
246C2×#533—72no—
247C2×#529—72no—
248C2×#525—71no—
249C22×C22⋊Q8D711yescharacteristic, complemented
250C2×#520—71no—
251C2×#519—71no—
252C22×#117—71no—
253C24×C7—24no—
254C24×C7—24no—
255C24×C7—42no—
256C24×C7C2411yescharacteristic
257C24×C7C2414yes—
258C24×C7C2411yescharacteristic
259C24×C7C2411yescharacteristic
260C23×D7C2412yes—
261C2×C7×Q8—28no—
262C2×C7×Q8—28no—
263C2×C7×Q8—232no—
264C2×C7×Q8C2418yes—
265C2×C7×Q8C2418yes—
266C22×C4×C7—24no—
267C22×C4×C7—28no—
268C22×C4×C7—24no—
269C22×C4×C7—24no—
270C22×C4×C7—24no—
271C22×C4×C7—24no—
272C22×C4×C7—232no—
273C22×C4×C7—44no—
274C22×C4×C7#4118yes—
275C22×C4×C7C2411yescharacteristic
276C22×C4×C7C2414yes—
277C22×C4×C7C2414yes—
278C22×C4×C7C2414yes—
279C22×C4×C7C2411yescharacteristic
280C22×C4×C7C2414yes—
281C22×C4×C7C2414yes—
282C22×C4×C7C2414yes—
283C22×C4×C7C2418yes—
284C22×C4×C7C2414yes—
285C22×C4×C7C2418yes—
286C22×C4×C7C2411yescharacteristic
287C22×C4×C7C2411yescharacteristic
288C22×C4×C7C2414yes—
289C2×C22⋊D7—28no—
290C2×C22⋊D7—28no—
291C2×C22⋊D7—44no—
292C2×C22⋊D7C2418yes—
293C2×C22⋊D7C2418yes—
294C2×C22⋊D7C2418yes—
295C22×Dic7—28no—
296C22×Dic7—44no—
297C22×Dic7C2418yes—
298C22×Dic7C2412yes—
299C22×Dic7C2412yes—
300C22×Dic7C2412yes—
301C22×Dic7C2412yes—
302C22×Dic7C2412yes—
303C22×Dic7C2412yes—
304C22×Dic7C2412yes—
305C22×Dic7C2418yes—
306#1157—232no—
307C2×D28—24no—
308C2×D28C2414yes—
309C2×C4×D7—28no—
310C2×C4×D7—48no—
311C2×C4×D7C2418yes—
312C2×C4×D7C24116yes—
313C2×Dic14—24no—
314C2×Dic14—48no—
315C2×Dic14C2414yes—
316C2×Dic14C24116yes—
317C7×C4⋊C4C2418yes—
318C7×C4⋊C4C24116yes—
319C7×C4⋊C4C2418yes—
320C7×C4⋊C4C24116yes—
321C7×C22⋊C4C24116yes—
322C7×C22⋊C4C24116yes—
323C22⋊Dic7C2418yes—
324C22⋊Dic7C2418yes—
325C22⋊Dic7C2418yes—
326C22⋊Dic7C2418yes—
327C22⋊Dic7C2418yes—
328C22⋊Dic7C2418yes—
329C22⋊Dic7C2418yes—
330(C2×D7)⋊C4C24116yes—
331(C2×D7)⋊C4C24116yes—
332(C2×D7)⋊C4C24116yes—
333(C2×D7)⋊C4C2418yes—
334(C2×D7)⋊C4C2418yes—
335C4⋊Dic7C24116yes—
336C4⋊Dic7C24116yes—
337C4⋊Dic7C24116yes—
338C4⋊Dic7C2414yes—
339C4⋊Dic7C2414yes—
340C4⋊Dic7C2418yes—
341C4⋊Dic7C2418yes—
342C4⋊Dic7C2414yes—
343C4⋊Dic7C2414yes—
344C4⋊Dic7C2414yes—
345C4⋊Dic7C2414yes—
346Dic7⋊C4C24116yes—
347Dic7⋊C4C24116yes—
348Dic7⋊C4C24116yes—
349Dic7⋊C4C24116yes—
350Dic7⋊C4C24116yes—
351Dic7⋊C4C2418yes—
352Dic7⋊C4C2418yes—
353C4×Dic7C24116yes—
354C4×Dic7C24116yes—
355C4×Dic7C24116yes—
356C4×Dic7C2418yes—
357C4×Dic7C2418yes—
358C4×Dic7C2418yes—
359C4×Dic7C2418yes—
360C4×Dic7C2418yes—
361C22×#41—71no—
362C23×Q8C2×D711yescharacteristic
363C24×C4C2×D711yescharacteristic
364#556—732no—
365#554—732no—
366#552—732no—
367#552—732no—
368#552—764no—
369#551—764no—
370#544—716no—
371#542—732no—
372#541—732no—
373#536—716no—
374#533—732no—
375C2×C4⋊Q8—72no—
376C2×C4⋊Q8—72no—
377C2×C4⋊Q8—72no—
378#529—732no—
379C2×#126—74no—
380C2×#126—74no—
381C2×#126—74no—
382C2×#126—74no—
383C2×#125—74no—
384C2×#125—74no—
385C2×#125—72no—
386C2×#125—74no—
387C2×#125—72no—
388C2×#124—72no—
389C2×#124—74no—
390#525—716no—
391C2×#123—72no—
392C2×#123—74no—
393C2×#123—74no—
394C2×#123—74no—
395C2×C22⋊Q8—72no—
396C2×C22⋊Q8—72no—
397C2×C22⋊Q8—71no—
398C2×C22⋊Q8—71no—
399C2×C22⋊Q8—74no—
400C2×C22⋊Q8—74no—
401C2×C22⋊Q8—74no—
402C2×C22⋊Q8C2×D712yes—
403C2×C22⋊Q8C2×D712yes—
404C2×C22⋊Q8C2×D712yes—
405C2×C22⋊Q8C2×D712yes—
406C2×C22⋊Q8C2×D7116yescomplemented
407C2×#121—71no—
408C2×#121—71no—
409C2×#120—72no—
410#520—716no—
411#519—716no—
412C2×C4×Q8—72no—
413C2×C4×Q8—72no—
414C2×C4×Q8—72no—
415C2×C4×Q8—72no—
416C2×C4×Q8—72no—
417C2×C4×Q8—74no—
418C2×C4×D4—74no—
419C2×C4×D4—72no—
420C2×C4×D4—72no—
421C2×C4×D4—72no—
422C2×C4×D4—74no—
423C2×#117—71no—
424C2×#117—71no—
425C2×#117—72no—
426C2×#117—71no—
427C2×#117—72no—
428C2×#117—71no—
429C2×#117—716no—
430C2×#117—71no—
431C2×#117—74no—
432C2×#117—72no—
433C2×#117—74no—
434C2×#117—74no—
435C22×C4⋊C4—71no—
436C22×C4⋊C4—71no—
437C22×C4⋊C4—72no—
438C22×C4⋊C4C2×D711yescharacteristic
439C22×C4⋊C4C2×D712yes—
440C22×C22⋊C4—72no—
441C22×C22⋊C4C2×D712yes—
442C22×C42—72no—
443C23×C7—22no—
444C23×C7—22no—
445C23×C7—22no—
446C23×C7—22no—
447C23×C7—28no—
448C23×C7—22no—
449C23×C7—28no—
450C23×C7—22no—
451C23×C7—22no—
452C23×C7—44no—
453C23×C7—416no—
454C23×C7C2×#4114yes—
455C23×C72−1+414yes—
456C23×C7C2512yes—
457C23×C7C2512yes—
458C23×C7C2512yes—
459C23×C7C2511yescharacteristic
460C22×D7—24no—
461C22×D7—24no—
462C22×D7—24no—
463C22×D7C2514yes—
464C7×Q8—216no—
465C7×Q8—216no—
466C2×C4×C7—28no—
467C2×C4×C7—22no—
468C2×C4×C7—22no—
469C2×C4×C7—216no—
470C2×C4×C7—28no—
471C2×C4×C7—28no—
472C2×C4×C7—28no—
473C2×C4×C7—28no—
474C2×C4×C7—28no—
475C2×C4×C7—28no—
476C2×C4×C7—48no—
477C2×C4×C7C2×#4114yes—
478C2×C4×C7C2×#4114yes—
479C2×C4×C7C2×#41116yes—
480C2×C4×C7C2512yes—
481C2×C4×C7C2518yes—
482C2×C4×C7C2518yes—
483C2×C4×C7C2512yes—
484C2×C4×C7C2512yes—
485C2×C4×C7C2512yes—
486C22⋊D7—216no—
487C22⋊D7—216no—
488C22⋊D7—48no—
489C2×Dic7—24no—
490C2×Dic7—216no—
491C2×Dic7—24no—
492C2×Dic7—24no—
493C2×Dic7—24no—
494C2×Dic7—24no—
495C2×Dic7—24no—
496C2×Dic7—24no—
497C2×Dic7—48no—
498C2×Dic7C2514yes—
499C2×Dic7C2514yes—
500C2×Dic7C2514yes—
501C2×Dic7C2514yes—
502C2×Dic7C2514yes—
503C2×Dic7C2514yes—
504C2×Dic7C2514yes—
505D28—28no—
506C4×D7—216no—
507C4×D7—416no—
508Dic14—28no—
509Dic14—416no—
510C25C22×D711yescharacteristic
511C2×#41—78no—
512C2×#41—148no—
513C22×Q8—28no—
514C22×Q8—71no—
515C22×Q8—74no—
516C22×Q8C22×D712yes—
517C22×Q8C22×D712yes—
518C22×Q8C22×D718yes—
519C22×D4—72no—
520C22×D4—72no—
521C22×D4—72no—
522C22×D4—71no—
523C23×C4—28no—
524C23×C4—72no—
525C23×C4—72no—
526C23×C4—72no—
527C23×C4—74no—
528C23×C4C22×D712yes—
529C23×C4C22×D711yescharacteristic
530C23×C4C22×D711yescharacteristic
531C23×C4C22×D711yescharacteristic
532C23×C4C22×D711yescharacteristic
533C23×C4C22×D718yes—
534C23×C4C22×D711yescharacteristic
535C23×C4C22×D712yes—
536C23×C4C22×D711yescharacteristic
537C4⋊Q8—716no—
538C4⋊Q8—716no—
539C4⋊Q8—716no—
540#126—732no—
541#126—732no—
542#126—732no—
543#126—732no—
544#125—716no—
545#125—732no—
546#125—732no—
547#125—732no—
548#125—716no—
549#124—716no—
550#124—732no—
551#123—716no—
552#123—732no—
553#123—732no—
554#123—732no—
555C22⋊Q8—716no—
556C22⋊Q8—716no—
557C22⋊Q8—78no—
558C22⋊Q8—78no—
559C22⋊Q8—732no—
560C22⋊Q8—732no—
561C22⋊Q8—732no—
562C22⋊Q8C22×D7116yes—
563C22⋊Q8C22×D7116yes—
564C22⋊Q8C22×D7116yes—
565C22⋊Q8C22×D7116yes—
566#121—78no—
567#121—78no—
568#120—716no—
569C4×Q8—716no—
570C4×Q8—716no—
571C4×Q8—716no—
572C4×Q8—716no—
573C4×Q8—716no—
574C4×Q8—732no—
575C4×D4—732no—
576C4×D4—716no—
577C4×D4—716no—
578C4×D4—716no—
579C4×D4—732no—
580#117—78no—
581#117—78no—
582#117—716no—
583#117—78no—
584#117—716no—
585#117—78no—
586#117—78no—
587#117—732no—
588#117—716no—
589#117—732no—
590#117—732no—
591C2×C4⋊C4—71no—
592C2×C4⋊C4—71no—
593C2×C4⋊C4—72no—
594C2×C4⋊C4—71no—
595C2×C4⋊C4—71no—
596C2×C4⋊C4—72no—
597C2×C4⋊C4—78no—
598C2×C4⋊C4—78no—
599C2×C4⋊C4—74no—
600C2×C4⋊C4—71no—
601C2×C4⋊C4—71no—
602C2×C4⋊C4—74no—
603C2×C4⋊C4—74no—
604C2×C4⋊C4—74no—
605C2×C4⋊C4—74no—
606C2×C4⋊C4—74no—
607C2×C4⋊C4—72no—
608C2×C4⋊C4—72no—
609C2×C4⋊C4—74no—
610C2×C4⋊C4—74no—
611C2×C4⋊C4—716no—
612C2×C4⋊C4C22×D712yes—
613C2×C4⋊C4C22×D714yes—
614C2×C4⋊C4C22×D712yes—
615C2×C4⋊C4C22×D718yes—
616C2×C4⋊C4C22×D714yes—
617C2×C4⋊C4C22×D7116yes—
618C2×C22⋊C4—72no—
619C2×C22⋊C4—72no—
620C2×C22⋊C4—72no—
621C2×C22⋊C4—72no—
622C2×C22⋊C4—716no—
623C2×C22⋊C4—72no—
624C2×C22⋊C4—72no—
625C2×C22⋊C4—72no—
626C2×C22⋊C4—72no—
627C2×C22⋊C4—74no—
628C2×C22⋊C4—74no—
629C2×C22⋊C4—72no—
630C2×C22⋊C4—74no—
631C2×C22⋊C4C22×D714yes—
632C2×C22⋊C4C22×D714yes—
633C2×C22⋊C4C22×D7116yes—
634C2×C42—72no—
635C2×C42—72no—
636C2×C42—74no—
637C2×C42—74no—
638C2×C42—74no—
639C2×C42—72no—
640C2×C42—72no—
641C2×C42—716no—
642C2×C42—72no—
643C22×C7—22no—
644C22×C7—22no—
645C22×C7—22no—
646C22×C7—22no—
647C22×C7—28no—
648C22×C7—28no—
649C22×C7—22no—
650C22×C7—22no—
651C22×C7—22no—
652C22×C7—416no—
653C22×C7—44no—
654C22×C7C22×#4114yes—
655C22×C7C22×#4112yes—
656C22×C7C2×2−1+414yes—
657C22×C7C2×2−1+412yes—
658C22×C7#58512yes—
659C22×C7C2611yescharacteristic
660C2×D7—24no—
661C2×D7—24no—
662C2×D7—24no—
663C2×D7—48no—
664C4×C7—22no—
665C4×C7—22no—
666C4×C7—28no—
667C4×C7—28no—
668C4×C7C22×#4114yes—
669C4×C7C22×#4114yes—
670Dic7—24no—
671Dic7—24no—
672Dic7—24no—
673Dic7—24no—
674Dic7—24no—
675Dic7—24no—
676Dic7—24no—
677C24—24no—
678C24—24no—
679C24—42no—
680C24—72no—
681C24C23×D711yescharacteristic
682C24C23×D714yes—
683C24C23×D711yescharacteristic
684C24C23×D711yescharacteristic
685#41—1432no—
686C2×Q8—28no—
687C2×Q8—28no—
688C2×Q8—232no—
689C2×Q8—74no—
690C2×Q8—716no—
691C2×Q8—144no—
692C2×Q8—288no—
693C2×Q8C23×D718yes—
694C2×Q8C23×D718yes—
695C2×D4—78no—
696C2×D4—78no—
697C2×D4—78no—
698C2×D4—74no—
699C2×D4—148no—
700C2×D4—148no—
701C2×D4—144no—
702C2×D4—284no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—232no—
710C22×C4—44no—
711C22×C4—78no—
712C22×C4—72no—
713C22×C4—72no—
714C22×C4—72no—
715C22×C4—72no—
716C22×C4—72no—
717C22×C4—72no—
718C22×C4—72no—
719C22×C4—78no—
720C22×C4—78no—
721C22×C4—716no—
722C22×C4—148no—
723C22×C4—148no—
724C22×C4—288no—
725C22×C4—284no—
726C22×C4#115918yes—
727C22×C4C23×D714yes—
728C22×C4C23×D718yes—
729C22×C4C23×D714yes—
730C22×C4C23×D714yes—
731C22×C4C23×D714yes—
732C22×C4C23×D714yes—
733C22×C4C23×D711yescharacteristic
734C22×C4C23×D714yes—
735C22×C4C23×D714yes—
736C22×C4C23×D711yescharacteristic
737C22×C4C23×D718yes—
738C22×C4C23×D714yes—
739C22×C4C23×D711yescharacteristic
740C22×C4C23×D711yescharacteristic
741C4⋊C4—716no—
742C4⋊C4—716no—
743C4⋊C4—716no—
744C4⋊C4—78no—
745C4⋊C4—78no—
746C4⋊C4—716no—
747C4⋊C4—716no—
748C4⋊C4—74no—
749C4⋊C4—74no—
750C4⋊C4—78no—
751C4⋊C4—74no—
752C4⋊C4—74no—
753C4⋊C4—78no—
754C4⋊C4—74no—
755C4⋊C4—74no—
756C4⋊C4—716no—
757C4⋊C4—716no—
758C4⋊C4—716no—
759C4⋊C4C23×D718yes—
760C4⋊C4C23×D7116yes—
761C4⋊C4C23×D718yes—
762C4⋊C4C23×D7116yes—
763C22⋊C4—78no—
764C22⋊C4—78no—
765C22⋊C4—78no—
766C22⋊C4—78no—
767C22⋊C4—78no—
768C22⋊C4—78no—
769C22⋊C4—78no—
770C22⋊C4—78no—
771C22⋊C4—716no—
772C22⋊C4—716no—
773C22⋊C4—78no—
774C22⋊C4—716no—
775C22⋊C4C23×D7116yes—
776C22⋊C4C23×D7116yes—
777C42—78no—
778C42—78no—
779C42—78no—
780C42—78no—
781C42—716no—
782C42—716no—
783C42—716no—
784C42—78no—
785C2×C7—24no—
786C2×C7—24no—
787C2×C7—42no—
788C2×C7#349514yescomplemented
789C2×C7C23×#4111yescharacteristic
790C2×C7C22×2−1+411yescharacteristic
791C2×C7C2×#58511yescharacteristic
792D7—44no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—28no—
798C23—22no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—44no—
803C23—416no—
804C23—74no—
805C23—144no—
806C23—144no—
807C23—144no—
808C23C2×#115914yes—
809C23#655114yes—
810C23C24×D712yes—
811C23C24×D712yes—
812C23C24×D712yes—
813C23C24×D711yescharacteristic
814Q8—216no—
815Q8—216no—
816Q8—148no—
817Q8—2816no—
818D4—1416no—
819D4—1416no—
820D4—148no—
821D4—288no—
822C2×C4—28no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—216no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—48no—
833C2×C4—74no—
834C2×C4—74no—
835C2×C4—74no—
836C2×C4—74no—
837C2×C4—74no—
838C2×C4—74no—
839C2×C4—74no—
840C2×C4—144no—
841C2×C4—1416no—
842C2×C4—144no—
843C2×C4—144no—
844C2×C4—144no—
845C2×C4—144no—
846C2×C4—144no—
847C2×C4—144no—
848C2×C4—1416no—
849C2×C4—2816no—
850C2×C4—288no—
851C2×C4C2×#115914yes—
852C2×C4C2×#115914yes—
853C2×C4C2×#1159116yes—
854C2×C4C24×D712yes—
855C2×C4C24×D718yes—
856C2×C4C24×D718yes—
857C2×C4C24×D712yes—
858C2×C4C24×D712yes—
859C2×C4C24×D712yes—
860C7C2×#349511yescharacteristic, complemented, Sylow
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—28no—
866C22—28no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—416no—
871C22—44no—
872C22—144no—
873C22—144no—
874C22—144no—
875C22—288no—
876C22C22×#115914yes—
877C22C22×#115912yes—
878C22C2×#655114yes—
879C22C2×#655112yes—
880C22#9061612yes—
881C22C25×D711yescharacteristic
882C4—22no—
883C4—22no—
884C4—28no—
885C4—28no—
886C4—144no—
887C4—144no—
888C4—144no—
889C4—144no—
890C4—144no—
891C4—144no—
892C4—144no—
893C4C22×#115914yes—
894C4C22×#115914yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—284no—
899C2#1174303814yesdirect product factor
900C2C23×#115911yescharacteristic
901C2C22×#655111yescharacteristic
902C2C2×#9061611yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC22×C7×C22⋊Q8C2
socleC23×C7C25
prime radicalC2×#90482C2
hypercenterC22×C22⋊Q8D7
hypocenterC7C2×#3495
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C7×C22⋊Q8C2semidirect
2. C2×#90507C2semidirect
3. C2×#90503C2semidirect
5. C22×#6489C2semidirect
6. C2×#90330C2semidirect
7. #11743038C2direct (N × H)
8. C2×#90332C2semidirect
9. C2×#90326C2semidirect
10. C2×#90333C2semidirect
11. C2×#90334C2semidirect
12. C2×#90316C2semidirect
13. C2×#90313C2semidirect
14. C2×#90315C2semidirect
15. C2×#90195C2semidirect
16. C2×#90204C2semidirect
17. C2×#90191C2semidirect
18. C2×#90186C2semidirect
26. C2×C7×C22⋊Q8C22semidirect
32. #90507C22semidirect
33. C2×#6510C22semidirect
34. C2×#6509C22semidirect
35. C2×#6509C22semidirect
36. #90503C22semidirect
37. C2×Q8×Dic7C22semidirect
38. C2×Q8×Dic7C22semidirect
39. C2×Q8×Dic7C22semidirect
40. C2×Q8×Dic7C22semidirect
41. C2×#6507C22semidirect
58. C2×#6489C22semidirect
65. #90334C22semidirect
66. #90333C22semidirect
67. #90332C22semidirect
68. #90330C22semidirect
69. #90326C22semidirect
70. #90316C22semidirect
71. #90315C22semidirect
72. #90313C22semidirect
73. #90204C22semidirect
74. C2×#6461C22semidirect
75. C2×#6461C22semidirect
76. C2×#6460C22semidirect
77. #90195C22semidirect
78. C2×#6456C22semidirect
79. C2×#6455C22semidirect
80. C2×#6455C22semidirect
81. C2×D7×C4⋊C4C22semidirect
82. #90191C22semidirect
83. C2×#6453C22semidirect
84. C2×#6453C22semidirect
85. C2×#6453C22semidirect
86. C2×#6452C22semidirect
87. C2×#6452C22semidirect
88. C2×#6451C22semidirect
89. C2×#6451C22semidirect
90. C2×#6450C22semidirect
91. C2×#6450C22semidirect
92. #90186C22semidirect
151. #6510C23semidirect
152. #6509C23semidirect
153. #6509C23semidirect
154. Q8×Dic7C23semidirect
155. Q8×Dic7C23semidirect
156. Q8×Dic7C23semidirect
157. Q8×Dic7C23semidirect
158. #6507C23semidirect
211. #6461C23semidirect
212. #6461C23semidirect
213. #6460C23semidirect
214. #6456C23semidirect
215. #6455C23semidirect
216. #6455C23semidirect
217. D7×C4⋊C4C23semidirect
218. #6453C23semidirect
219. #6453C23semidirect
220. #6453C23semidirect
221. #6452C23semidirect
222. #6452C23semidirect
223. #6451C23semidirect
224. #6451C23semidirect
225. #6450C23semidirect
226. #6450C23semidirect
249. C22×C22⋊Q8D7semidirect
406. C2×C22⋊Q8C2×D7semidirect
788. C2×C7#3495semidirect
860. C7C2×#3495semidirect
899. C2#11743038direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C2×#905072
C2×#905032
C2×#904822
C22×#64892
C2×#903302
#117430382
C2×#903322
C2×#903262
C2×#903332
C2×#903342
C2×#903162
C2×#903132
C2×#903152
C2×#901952
C2×#902042
C2×#901912
C2×#901862
C2×#34957