Finite Group Databasebeta

← C2×#11742899 #14261910

Subgroups — C2×#11742899 #14261910

Order 1792.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×#41C211yesmaximal, characteristic, complemented
2C2×#90515C212yesmaximal, complemented
3#11742899C2132yesmaximal, direct product factor
4C2×#90270C211yesmaximal, characteristic, complemented
5C2×#90274C212yesmaximal, complemented
6C2×#90258C211yesmaximal, characteristic, complemented
7C2×#90234C211yesmaximal, characteristic, complemented
8C2×#90256C212yesmaximal, complemented
9C2×#90232C212yesmaximal, complemented
10C2×#90246C211yesmaximal, characteristic, complemented
11C2×#90255C214yesmaximal, complemented
12C2×#90237C212yesmaximal, complemented
13C2×#90220C212yesmaximal, complemented
14C2×#90222C214yesmaximal, complemented
15C2×#90170C212yesmaximal, complemented
16C2×#90170C211yesmaximal, characteristic, complemented
17C2×#90161C211yesmaximal, characteristic, complemented
18C22×#6433C212yesmaximal, complemented
19C22×C7×#41C2211yescharacteristic
20C22×#1159C2212yes—
21C4×C7×#41C22116yescomplemented
22C2×C4×C7×Q8C2211yescharacteristic
23C2×C4×C7×Q8C2211yescharacteristic
24C2×C4×C7×D4C2211yescharacteristic
25C2×C4×C7×D4C2212yes—
26C2×C4×C7×D4C2211yescharacteristic
27C2×C4×C7×D4C2212yes—
28C2×C7×#117C2212yes—
29C2×C7×#117C2211yescharacteristic
30C22×C42×C7C2212yes—
31C22×C42×C7C2211yescharacteristic
32#90515C22132yescomplemented
33C2×#6509C2212yes—
34C2×#6507C2212yes—
35C2×#6502C2214yes—
36C2×#6498C2214yes—
37C2×D4×Dic7C2212yes—
38C2×#6493C2212yes—
39C2×#6493C2211yescharacteristic
40C2×#6492C2214yes—
41C2×#6492C2212yes—
42C2×C4×C22⋊D7C2212yes—
43C2×C4×C22⋊D7C2214yes—
44C2×#6489C2212yes—
45C22×C4⋊Dic7C2212yes—
46C22×C4⋊Dic7C2212yes—
47C2×#6487C2212yes—
48C2×#6487C2212yes—
49C2×#6487C2211yescharacteristic
50C2×#6487C2212yes—
51C22×Dic7⋊C4C2214yes—
52C22×Dic7⋊C4C2214yes—
53#90274C22132yescomplemented
54#90270C22116yescomplemented
55#90258C22116yescomplemented
56#90256C22132yescomplemented
57#90255C22164yescomplemented
58#90246C22116yescomplemented
59#90237C22132yescomplemented
60#90234C22116yescomplemented
61#90232C22132yescomplemented
62#90222C22164yescomplemented
63#90220C22132yescomplemented
64C2×#6461C2214yes—
65C2×#6460C2212yes—
66C2×#6459C2214yes—
67C2×D7×C4⋊C4C2212yes—
68C2×#6453C2212yes—
69C2×#6452C2214yes—
70C2×#6452C2214yes—
71C2×#6450C2212yes—
72C2×#6449C2214yes—
73C2×#6446C2214yes—
74C2×(C22⋊D7)⋊C4C2214yes—
75C2×#6442C2214yes—
76C2×#6441C2214yes—
77C2×#6440C2214yes—
78#90170C22132yescomplemented
79#90170C22116yescomplemented
80C2×#6439C2212yes—
81C2×#6439C2214yes—
82C2×#6438C2211yescharacteristic
83C2×C4×D28C2211yescharacteristic
84C2×C4×D28C2212yes—
85C2×#6435C2214yes—
86C2×#6435C2212yes—
87#90161C22116yescomplemented
88C2×#6433C2211yescharacteristic
89C2×#6433C2212yes—
90C2×#6433C2214yes—
91C2×#6433C2214yes—
92C2×#6433C2212yes—
93C2×#6433C2212yes—
94C2×#6433C22132yescomplemented
95C2×#6432C2211yescharacteristic
96C2×#6432C2211yescharacteristic
97C2×C4×Dic14C2212yes—
98C2×C4×Dic14C2212yes—
99C2×C4×Dic14C2212yes—
100C2×C4×Dic14C2211yescharacteristic
101C2×#3515—71nomaximal, Sylow
102C2×C7×#41—28no—
103C2×C7×#41C2318yes—
104C22×C7×Q8C2311yescharacteristic
105C22×C7×D4C2312yes—
106C22×C7×D4C2311yescharacteristic
107C23×C4×C7C2312yes—
108C23×C4×C7C2311yescharacteristic
109C23×C4×C7C2312yes—
110C23×C4×C7C2311yescharacteristic
111C23×C4×C7C2312yes—
112C23×C4×C7C2311yescharacteristic
113C22×C22⋊D7C2314yes—
114C22×C22⋊D7C2312yes—
115C23×Dic7C2314yes—
116C23×Dic7C2314yes—
117C2×#1159—216no—
118C2×#1159C23116yes—
119C22×D28C2311yescharacteristic
120C22×C4×D7C2312yes—
121C22×C4×D7C2314yes—
122C22×Dic14C2311yescharacteristic
123C22×Dic14C2312yes—
124C22×Dic14C2312yes—
125C4×C7×Q8C2318yes—
126C4×C7×Q8C2318yes—
127C4×C7×D4C23116yes—
128C4×C7×D4C2318yes—
129C4×C7×D4C2318yes—
130C4×C7×D4C23116yes—
131C7×#117C2318yes—
132C7×#117C23116yes—
133C2×C7×C4⋊C4C2311yescharacteristic
134C2×C7×C4⋊C4C2312yes—
135C2×C7×C4⋊C4C2312yes—
136C2×C7×C4⋊C4C2311yescharacteristic
137C2×C7×C22⋊C4C2312yes—
138C2×C7×C22⋊C4C2312yes—
139C2×C7×C22⋊C4C2312yes—
140C2×C42×C7C2311yescharacteristic
141C2×C42×C7C2311yescharacteristic
142C2×C42×C7C2311yescharacteristic
143C2×C42×C7C2312yes—
144C2×C42×C7C2311yescharacteristic
145C2×C42×C7C2312yes—
146C2×C42×C7C2312yes—
147C2×C42×C7C23116yes—
148C2×C42×C7C2318yes—
149C2×C22⋊Dic7C2314yes—
150C2×C22⋊Dic7C2312yes—
151C2×C22⋊Dic7C2314yes—
152#6509C23116yes—
153#6507C23116yes—
154#6502C23132yes—
155#6498C23132yes—
156D4×Dic7C23116yes—
157#6493C23116yes—
158#6493C2318yes—
159#6492C23132yes—
160#6492C23116yes—
161C4×C22⋊D7C23116yes—
162C4×C22⋊D7C23132yes—
163C2×(C2×D7)⋊C4C2312yes—
164C2×(C2×D7)⋊C4C2312yes—
165C2×(C2×D7)⋊C4C2312yes—
166C2×(C2×D7)⋊C4C2314yes—
167C2×(C2×D7)⋊C4C2312yes—
168C2×(C2×D7)⋊C4C2314yes—
169#6489C23116yes—
170C2×C4⋊Dic7C2312yes—
171C2×C4⋊Dic7C2312yes—
172C2×C4⋊Dic7C2312yes—
173C2×C4⋊Dic7C2311yescharacteristic
174C2×C4⋊Dic7C2312yes—
175C2×C4⋊Dic7C2311yescharacteristic
176C2×C4⋊Dic7C2314yes—
177C2×C4⋊Dic7C2314yes—
178C2×C4⋊Dic7C23116yes—
179C2×C4⋊Dic7C23116yes—
180#6487C23116yes—
181#6487C23116yes—
182#6487C2318yes—
183#6487C23116yes—
184C2×Dic7⋊C4C2314yes—
185C2×Dic7⋊C4C2314yes—
186C2×Dic7⋊C4C2312yes—
187C2×Dic7⋊C4C2314yes—
188C2×Dic7⋊C4C2312yes—
189C2×Dic7⋊C4C2312yes—
190C2×Dic7⋊C4C2314yes—
191C2×Dic7⋊C4C2314yes—
192C2×Dic7⋊C4C2314yes—
193C2×Dic7⋊C4C2314yes—
194C2×Dic7⋊C4C23132yes—
195C2×Dic7⋊C4C23132yes—
196C2×Dic7⋊C4C2312yes—
197C2×Dic7⋊C4C2314yes—
198C2×C4×Dic7C2314yes—
199C2×C4×Dic7C2314yes—
200C2×C4×Dic7C2312yes—
201#6461C23132yes—
202#6460C23116yes—
203#6459C23132yes—
204D7×C4⋊C4C23116yes—
205#6453C23116yes—
206#6452C23132yes—
207#6452C23132yes—
208#6450C23116yes—
209#6449C23132yes—
210#6446C23132yes—
211(C22⋊D7)⋊C4C23132yes—
212#6442C23132yes—
213#6441C23132yes—
214#6440C23132yes—
215#6439C23116yes—
216#6439C23132yes—
217#6438C2318yes—
218C4×D28C2318yes—
219C4×D28C23116yes—
220#6435C23132yes—
221#6435C23116yes—
222#6433C2318yes—
223#6433C23116yes—
224#6433C23132yes—
225#6433C23116yes—
226#6433C23132yes—
227#6433C23116yes—
228#6432C2318yes—
229#6432C2318yes—
230C4×Dic14C23116yes—
231C4×Dic14C23116yes—
232C4×Dic14C23116yes—
233C4×Dic14C2318yes—
234#3515—732no—
235C2×#557—71no—
236C2×#554—71no—
237C2×#554—71no—
238C2×#553—72no—
239C2×#552—72no—
240C2×#552—74no—
241C2×#552—72no—
242C2×#547—72no—
243C2×#547—71no—
244C2×#541—72no—
245C2×#539—74no—
246C2×#533—71no—
247C2×#529—71no—
248C2×#529—72no—
249C22×#125—72no—
250C2×#520—72no—
251C2×C4×#41D711yescharacteristic, complemented
252C24×C7C2411yescharacteristic
253C24×C7C2412yes—
254C23×D7C2412yes—
255C7×#41—232no—
256C2×C7×Q8—24no—
257C2×C7×Q8C2414yes—
258C2×C7×D4—28no—
259C2×C7×D4#4118yes—
260C2×C7×D4C2418yes—
261C2×C7×D4C2414yes—
262C22×C4×C7—28no—
263C22×C4×C7—24no—
264C22×C4×C7—28no—
265C22×C4×C7—24no—
266C22×C4×C7—42no—
267C22×C4×C7—44no—
268C22×C4×C7C2411yescharacteristic
269C22×C4×C7C2412yes—
270C22×C4×C7C2411yescharacteristic
271C22×C4×C7C2411yescharacteristic
272C22×C4×C7C2412yes—
273C22×C4×C7C2418yes—
274C22×C4×C7C2412yes—
275C22×C4×C7C2411yescharacteristic
276C22×C4×C7C2414yes—
277C22×C4×C7C2418yes—
278C22×C4×C7C2414yes—
279C22×C4×C7C2418yes—
280C22×C4×C7C2414yes—
281C22×C4×C7C2411yescharacteristic
282C22×C4×C7C2411yescharacteristic
283C2×C22⋊D7—216no—
284C2×C22⋊D7—44no—
285C2×C22⋊D7C24116yes—
286C2×C22⋊D7C2418yes—
287C22×Dic7—216no—
288C22×Dic7—48no—
289C22×Dic7C24116yes—
290C22×Dic7C2412yes—
291C22×Dic7C2414yes—
292C22×Dic7C2412yes—
293C22×Dic7C2414yes—
294C22×Dic7C2412yes—
295C22×Dic7C24116yes—
296#1159—264no—
297C2×D28—24no—
298C2×D28C2414yes—
299C2×C4×D7—28no—
300C2×C4×D7—48no—
301C2×C4×D7C2418yes—
302C2×C4×D7C24116yes—
303C2×Dic14—28no—
304C2×Dic14—24no—
305C2×Dic14—44no—
306C2×Dic14C2414yes—
307C2×Dic14C2418yes—
308C2×Dic14C2418yes—
309C7×C4⋊C4C2414yes—
310C7×C4⋊C4C2418yes—
311C7×C4⋊C4C2418yes—
312C7×C4⋊C4C2414yes—
313C7×C22⋊C4C2418yes—
314C7×C22⋊C4C2418yes—
315C7×C22⋊C4C2418yes—
316C42×C7C2414yes—
317C42×C7C2414yes—
318C42×C7C2414yes—
319C42×C7C2418yes—
320C42×C7C2414yes—
321C42×C7C2418yes—
322C42×C7C2418yes—
323C22⋊Dic7C24116yes—
324C22⋊Dic7C2418yes—
325C22⋊Dic7C24116yes—
326(C2×D7)⋊C4C2418yes—
327(C2×D7)⋊C4C2418yes—
328(C2×D7)⋊C4C2418yes—
329(C2×D7)⋊C4C24116yes—
330(C2×D7)⋊C4C2418yes—
331(C2×D7)⋊C4C24116yes—
332C4⋊Dic7C2418yes—
333C4⋊Dic7C2418yes—
334C4⋊Dic7C2418yes—
335C4⋊Dic7C2414yes—
336C4⋊Dic7C2418yes—
337C4⋊Dic7C2414yes—
338C4⋊Dic7C24116yes—
339C4⋊Dic7C24116yes—
340Dic7⋊C4C24116yes—
341Dic7⋊C4C24116yes—
342Dic7⋊C4C2418yes—
343Dic7⋊C4C24116yes—
344Dic7⋊C4C2418yes—
345Dic7⋊C4C2418yes—
346Dic7⋊C4C24116yes—
347Dic7⋊C4C24116yes—
348Dic7⋊C4C24116yes—
349Dic7⋊C4C24116yes—
350Dic7⋊C4C2418yes—
351Dic7⋊C4C24116yes—
352C4×Dic7C24116yes—
353C4×Dic7C24116yes—
354C4×Dic7C2418yes—
355C22×#41—72no—
356C22×#41C2×D711yescharacteristic
357#557—716no—
358#554—716no—
359#554—716no—
360#553—732no—
361#552—732no—
362#552—732no—
363#552—764no—
364#547—732no—
365#547—716no—
366#541—732no—
367#539—764no—
368#533—716no—
369C2×C4⋊Q8—72no—
370C2×C4⋊Q8—71no—
371C2×C4⋊Q8—71no—
372#529—732no—
373#529—716no—
374C2×#126—74no—
375C2×#126—74no—
376C2×#126—74no—
377C2×#126—72no—
378C2×#125—74no—
379C2×#125—74no—
380C2×#125—72no—
381C2×#125—71no—
382C2×#125—72no—
383C2×#125—74no—
384C2×#125—74no—
385C2×#125—72no—
386C2×#125—72no—
387C2×#125—732no—
388C2×#124—71no—
389C2×#123—74no—
390C2×#123—72no—
391C2×#123—74no—
392C2×#123—74no—
393C2×#123—74no—
394C2×C22⋊Q8—72no—
395C2×C22⋊Q8—71no—
396C2×C22⋊Q8—72no—
397C2×C22⋊Q8—72no—
398C2×C22⋊Q8—72no—
399C2×C22⋊Q8—74no—
400C2×C22⋊Q8—72no—
401C2×C22⋊Q8—74no—
402C2×#121—74no—
403C2×#121—72no—
404C2×#121—71no—
405#520—732no—
406C4×#41C2×D7116yescomplemented
407C2×C4×Q8—72no—
408C2×C4×Q8—72no—
409C2×C4×Q8—72no—
410C2×C4×Q8—71no—
411C2×C4×Q8—72no—
412C2×C4×Q8C2×D711yescharacteristic
413C2×C4×Q8C2×D711yescharacteristic
414C2×C4×D4—72no—
415C2×C4×D4—74no—
416C2×C4×D4—72no—
417C2×C4×D4—74no—
418C2×C4×D4—71no—
419C2×C4×D4—72no—
420C2×C4×D4C2×D711yescharacteristic
421C2×C4×D4C2×D712yes—
422C2×C4×D4C2×D711yescharacteristic
423C2×C4×D4C2×D712yes—
424C2×#117—72no—
425C2×#117—74no—
426C2×#117—72no—
427C2×#117—74no—
428C2×#117C2×D711yescharacteristic
429C2×#117C2×D712yes—
430C22×C4⋊C4—74no—
431C22×C4⋊C4—74no—
432C22×C4⋊C4—72no—
433C22×C4⋊C4—72no—
434C22×C4⋊C4—72no—
435C22×C42C2×D712yes—
436C22×C42C2×D711yescharacteristic
437C23×C7—24no—
438C23×C7—24no—
439C23×C7—22no—
440C23×C7—22no—
441C23×C7—22no—
442C23×C7C2×#4118yes—
443C23×C7C2512yes—
444C23×C7C2514yes—
445C23×C7C2511yescharacteristic
446C22×D7—24no—
447C22×D7—24no—
448C22×D7—24no—
449C22×D7C2514yes—
450C7×Q8—28no—
451C7×D4—216no—
452C7×D4C2×#41116yes—
453C2×C4×C7—22no—
454C2×C4×C7—24no—
455C2×C4×C7—216no—
456C2×C4×C7—22no—
457C2×C4×C7—24no—
458C2×C4×C7—22no—
459C2×C4×C7—24no—
460C2×C4×C7—22no—
461C2×C4×C7—28no—
462C2×C4×C7—216no—
463C2×C4×C7—28no—
464C2×C4×C7—44no—
465C2×C4×C7—48no—
466C2×C4×C7C2×#4114yes—
467C2×C4×C72−1+414yes—
468C2×C4×C7C2512yes—
469C2×C4×C7C2514yes—
470C2×C4×C7C2512yes—
471C2×C4×C7C2512yes—
472C2×C4×C7C2514yes—
473C2×C4×C7C2514yes—
474C2×C4×C7C2512yes—
475C2×C4×C7C2512yes—
476C2×C4×C7C2512yes—
477C22⋊D7—232no—
478C22⋊D7—48no—
479C2×Dic7—28no—
480C2×Dic7—24no—
481C2×Dic7—232no—
482C2×Dic7—24no—
483C2×Dic7—28no—
484C2×Dic7—24no—
485C2×Dic7—416no—
486C2×Dic7C2514yes—
487C2×Dic7C2518yes—
488C2×Dic7C2514yes—
489C2×Dic7C2518yes—
490C2×Dic7C2514yes—
491D28—28no—
492C4×D7—216no—
493C4×D7—416no—
494Dic14—216no—
495Dic14—28no—
496Dic14—48no—
497C2×#41—28no—
498C2×#41—716no—
499C2×#41—1416no—
500C2×#41C22×D718yes—
501C22×Q8—71no—
502C22×Q8—72no—
503C22×Q8—72no—
504C22×Q8C22×D711yescharacteristic
505C22×D4—74no—
506C22×D4—72no—
507C22×D4—71no—
508C22×D4C22×D712yes—
509C22×D4C22×D711yescharacteristic
510C23×C4—74no—
511C23×C4—74no—
512C23×C4—72no—
513C23×C4—74no—
514C23×C4C22×D712yes—
515C23×C4C22×D712yes—
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C23×C4C22×D712yes—
519C23×C4C22×D711yescharacteristic
520C4⋊Q8—716no—
521C4⋊Q8—78no—
522C4⋊Q8—78no—
523#126—732no—
524#126—732no—
525#126—732no—
526#126—716no—
527#125—732no—
528#125—732no—
529#125—716no—
530#125—78no—
531#125—716no—
532#125—732no—
533#125—732no—
534#125—716no—
535#125—716no—
536#124—78no—
537#123—732no—
538#123—716no—
539#123—732no—
540#123—732no—
541#123—732no—
542C22⋊Q8—716no—
543C22⋊Q8—78no—
544C22⋊Q8—716no—
545C22⋊Q8—716no—
546C22⋊Q8—716no—
547C22⋊Q8—732no—
548C22⋊Q8—716no—
549C22⋊Q8—732no—
550#121—732no—
551#121—716no—
552#121—78no—
553C4×Q8—716no—
554C4×Q8—716no—
555C4×Q8—716no—
556C4×Q8—78no—
557C4×Q8—716no—
558C4×Q8C22×D718yes—
559C4×Q8C22×D718yes—
560C4×D4—716no—
561C4×D4—732no—
562C4×D4—716no—
563C4×D4—732no—
564C4×D4—78no—
565C4×D4—716no—
566C4×D4C22×D718yes—
567C4×D4C22×D7116yes—
568C4×D4C22×D718yes—
569C4×D4C22×D7116yes—
570#117—716no—
571#117—732no—
572#117—716no—
573#117—732no—
574#117C22×D718yes—
575#117C22×D7116yes—
576C2×C4⋊C4—74no—
577C2×C4⋊C4—72no—
578C2×C4⋊C4—71no—
579C2×C4⋊C4—72no—
580C2×C4⋊C4—71no—
581C2×C4⋊C4—72no—
582C2×C4⋊C4—72no—
583C2×C4⋊C4—74no—
584C2×C4⋊C4—72no—
585C2×C4⋊C4—74no—
586C2×C4⋊C4—74no—
587C2×C4⋊C4—732no—
588C2×C4⋊C4—74no—
589C2×C4⋊C4—74no—
590C2×C4⋊C4—74no—
591C2×C4⋊C4—74no—
592C2×C4⋊C4—732no—
593C2×C4⋊C4—716no—
594C2×C4⋊C4—716no—
595C2×C4⋊C4—72no—
596C2×C4⋊C4—74no—
597C2×C4⋊C4—72no—
598C2×C4⋊C4—72no—
599C2×C4⋊C4—74no—
600C2×C4⋊C4—716no—
601C2×C4⋊C4C22×D711yescharacteristic
602C2×C4⋊C4C22×D712yes—
603C2×C4⋊C4C22×D711yescharacteristic
604C2×C4⋊C4C22×D712yes—
605C2×C22⋊C4—74no—
606C2×C22⋊C4—74no—
607C2×C22⋊C4—72no—
608C2×C22⋊C4—72no—
609C2×C22⋊C4—72no—
610C2×C22⋊C4—72no—
611C2×C22⋊C4—74no—
612C2×C22⋊C4—74no—
613C2×C22⋊C4—72no—
614C2×C22⋊C4C22×D712yes—
615C2×C22⋊C4C22×D712yes—
616C2×C22⋊C4C22×D712yes—
617C2×C42—74no—
618C2×C42—74no—
619C2×C42—72no—
620C2×C42C22×D712yes—
621C2×C42C22×D711yescharacteristic
622C2×C42C22×D711yescharacteristic
623C2×C42C22×D712yes—
624C2×C42C22×D711yescharacteristic
625C2×C42C22×D712yes—
626C2×C42C22×D7116yes—
627C2×C42C22×D718yes—
628C2×C42C22×D711yescharacteristic
629C22×C7—24no—
630C22×C7—24no—
631C22×C7—216no—
632C22×C7—22no—
633C22×C7—22no—
634C22×C7—22no—
635C22×C7—44no—
636C22×C7C22×#4118yes—
637C22×C7C22×#4112yes—
638C22×C7C2×2−1+412yes—
639C22×C7#58512yes—
640C22×C7C2611yescharacteristic
641C2×D7—24no—
642C2×D7—24no—
643C2×D7—24no—
644C2×D7—48no—
645C4×C7—22no—
646C4×C7—24no—
647C4×C7—22no—
648C4×C7—24no—
649C4×C7—22no—
650C4×C7—24no—
651C4×C7—22no—
652C4×C7C22×#4114yes—
653C4×C7C2×2−1+414yes—
654Dic7—28no—
655Dic7—24no—
656Dic7—24no—
657Dic7—28no—
658Dic7—24no—
659C24—72no—
660C24C23×D711yescharacteristic
661C24C23×D712yes—
662#41—232no—
663#41—1464no—
664C2×Q8—24no—
665C2×Q8—74no—
666C2×Q8—78no—
667C2×Q8—78no—
668C2×Q8—148no—
669C2×Q8—144no—
670C2×Q8—284no—
671C2×Q8C23×D714yes—
672C2×D4—28no—
673C2×D4—716no—
674C2×D4—78no—
675C2×D4—74no—
676C2×D4—1416no—
677C2×D4—144no—
678C2×D4—284no—
679C2×D4#115718yes—
680C2×D4C23×D718yes—
681C2×D4C23×D714yes—
682C22×C4—28no—
683C22×C4—24no—
684C22×C4—28no—
685C22×C4—24no—
686C22×C4—44no—
687C22×C4—42no—
688C22×C4—716no—
689C22×C4—72no—
690C22×C4—74no—
691C22×C4—74no—
692C22×C4—72no—
693C22×C4—72no—
694C22×C4—716no—
695C22×C4—78no—
696C22×C4—716no—
697C22×C4—1416no—
698C22×C4—148no—
699C22×C4—288no—
700C22×C4—288no—
701C22×C4C23×D718yes—
702C22×C4C23×D718yes—
703C22×C4C23×D714yes—
704C22×C4C23×D714yes—
705C22×C4C23×D711yescharacteristic
706C22×C4C23×D712yes—
707C22×C4C23×D711yescharacteristic
708C22×C4C23×D711yescharacteristic
709C22×C4C23×D712yes—
710C22×C4C23×D711yescharacteristic
711C22×C4C23×D712yes—
712C22×C4C23×D718yes—
713C22×C4C23×D714yes—
714C22×C4C23×D711yescharacteristic
715C22×C4C23×D711yescharacteristic
716C4⋊C4—716no—
717C4⋊C4—78no—
718C4⋊C4—78no—
719C4⋊C4—716no—
720C4⋊C4—716no—
721C4⋊C4—716no—
722C4⋊C4—716no—
723C4⋊C4—716no—
724C4⋊C4—78no—
725C4⋊C4—716no—
726C4⋊C4—78no—
727C4⋊C4—716no—
728C4⋊C4—74no—
729C4⋊C4—74no—
730C4⋊C4—78no—
731C4⋊C4—78no—
732C4⋊C4—78no—
733C4⋊C4—716no—
734C4⋊C4—716no—
735C4⋊C4—78no—
736C4⋊C4C23×D714yes—
737C4⋊C4C23×D718yes—
738C4⋊C4C23×D714yes—
739C4⋊C4C23×D718yes—
740C22⋊C4—716no—
741C22⋊C4—716no—
742C22⋊C4—78no—
743C22⋊C4—78no—
744C22⋊C4—78no—
745C22⋊C4—78no—
746C22⋊C4—716no—
747C22⋊C4—716no—
748C22⋊C4—78no—
749C22⋊C4C23×D718yes—
750C22⋊C4C23×D718yes—
751C22⋊C4C23×D718yes—
752C42—716no—
753C42—716no—
754C42—78no—
755C42C23×D714yes—
756C42C23×D718yes—
757C42C23×D714yes—
758C42C23×D714yes—
759C42C23×D718yes—
760C42C23×D714yes—
761C42C23×D718yes—
762C2×C7—28no—
763C2×C7—42no—
764C2×C7#351514yescomplemented
765C2×C7C23×#4111yescharacteristic
766C2×C7C22×2−1+411yescharacteristic
767C2×C7C2×#58511yescharacteristic
768D7—44no—
769C23—24no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—74no—
775C23—144no—
776C23—144no—
777C23—144no—
778C23C2×#115718yes—
779C23C24×D712yes—
780C23C24×D714yes—
781C23C24×D711yescharacteristic
782Q8—28no—
783Q8—1416no—
784Q8—148no—
785Q8—288no—
786D4—216no—
787D4—1432no—
788D4—148no—
789D4—288no—
790D4C2×#1157116yes—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—216no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—216no—
801C2×C4—28no—
802C2×C4—48no—
803C2×C4—44no—
804C2×C4—74no—
805C2×C4—78no—
806C2×C4—78no—
807C2×C4—74no—
808C2×C4—74no—
809C2×C4—144no—
810C2×C4—148no—
811C2×C4—1432no—
812C2×C4—144no—
813C2×C4—144no—
814C2×C4—148no—
815C2×C4—1416no—
816C2×C4—2816no—
817C2×C4—2816no—
818C2×C4C2×#115714yes—
819C2×C4#655414yes—
820C2×C4C24×D712yes—
821C2×C4C24×D714yes—
822C2×C4C24×D712yes—
823C2×C4C24×D712yes—
824C2×C4C24×D714yes—
825C2×C4C24×D712yes—
826C2×C4C24×D714yes—
827C2×C4C24×D712yes—
828C2×C4C24×D712yes—
829C7C2×#351511yescharacteristic, complemented, Sylow
830C22—24no—
831C22—24no—
832C22—216no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—144no—
838C22—144no—
839C22—144no—
840C22—288no—
841C22C22×#115718yes—
842C22C22×#115712yes—
843C22C2×#655412yes—
844C22#9061612yes—
845C22C25×D711yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—144no—
854C4—148no—
855C4—144no—
856C4—144no—
857C4—148no—
858C4C22×#115714yes—
859C4C2×#655414yes—
860C2—28no—
861C2—42no—
862C2—284no—
863C2#1174289914yesdirect product factor
864C2C23×#115711yescharacteristic
865C2C22×#655411yescharacteristic
866C2C2×#9061611yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C4×C7×#41C2
socleC23×C7C25
hypercenterC2×C4×#41D7
hypocenterC7C2×#3515
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×#41C2semidirect
2. C2×#90515C2semidirect
3. #11742899C2direct (N × H)
4. C2×#90270C2semidirect
5. C2×#90274C2semidirect
6. C2×#90258C2semidirect
7. C2×#90234C2semidirect
8. C2×#90256C2semidirect
9. C2×#90232C2semidirect
10. C2×#90246C2semidirect
11. C2×#90255C2semidirect
12. C2×#90237C2semidirect
13. C2×#90220C2semidirect
14. C2×#90222C2semidirect
15. C2×#90170C2semidirect
16. C2×#90170C2semidirect
17. C2×#90161C2semidirect
18. C22×#6433C2semidirect
21. C4×C7×#41C22semidirect
32. #90515C22semidirect
53. #90274C22semidirect
54. #90270C22semidirect
55. #90258C22semidirect
56. #90256C22semidirect
57. #90255C22semidirect
58. #90246C22semidirect
59. #90237C22semidirect
60. #90234C22semidirect
61. #90232C22semidirect
62. #90222C22semidirect
63. #90220C22semidirect
78. #90170C22semidirect
79. #90170C22semidirect
87. #90161C22semidirect
94. C2×#6433C22semidirect
251. C2×C4×#41D7semidirect
406. C4×#41C2×D7semidirect
764. C2×C7#3515semidirect
829. C7C2×#3515semidirect
863. C2#11742899direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×#412
C2×#905152
#117428992
C2×#902702
C2×#902742
C2×#902582
C2×#902342
C2×#902562
C2×#902322
C2×#902462
C2×#902552
C2×#902372
C2×#902202
C2×#902222
C2×#901702
C2×#901612
C22×#64332
C2×#35157