Finite Group Databasebeta

← C2×#11743096 #14262227

Subgroups — C2×#11743096 #14262227

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
1C2×C7×#525C211yesmaximal, characteristic
2C2×#90516C211yesmaximal, characteristic, complemented
3C2×#90518C211yesmaximal, characteristic, complemented
4C22×#6487C211yesmaximal, characteristic, complemented
5C22×#6489C211yesmaximal, characteristic, complemented
6#11743096C2132yesmaximal, direct product factor
7C2×#90341C214yesmaximal, complemented
8C2×#90316C212yesmaximal, complemented
9C2×#90313C212yesmaximal, complemented
10C2×#90294C212yesmaximal, complemented
11C2×#90291C212yesmaximal, complemented
12C2×#90278C214yesmaximal, complemented
13C2×#90233C212yesmaximal, complemented
14C2×#90234C212yesmaximal, complemented
15C2×#90232C212yesmaximal, complemented
16C2×#90232C212yesmaximal, complemented
17C2×#90210C211yesmaximal, characteristic, complemented
18C2×#90207C211yesmaximal, characteristic, complemented
19C22×C7×#41C2211yescharacteristic
20C24×C4×C7C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C7×#525C22116yes—
23C2×C7×#123C2212yes—
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C7×#121C2211yescharacteristic
28C2×C7×#120C2212yes—
29C2×C4×C7×D4C2212yes—
30C2×C4×C7×D4C2212yes—
31C2×C7×#117C2211yescharacteristic
32C22×C22⋊Dic7C2212yes—
33C22×C22⋊Dic7C2212yes—
34#90518C22116yescomplemented
35#90516C22116yescomplemented
36C2×Q8×Dic7C2212yescomplemented
37C2×#6507C2212yescomplemented
38C2×#6499C2214yes—
39C2×#6499C2212yescomplemented
40C2×#6498C2214yes—
41C2×#6498C2214yes—
42C2×#6498C2214yes—
43C2×D4×Dic7C2214yes—
44C2×D4×Dic7C2214yes—
45C2×D4×Dic7C2212yescomplemented
46C2×#6489C2212yes—
47C2×#6489C2211yescharacteristic
48C2×#6489C2211yescharacteristic
49C2×#6489C2212yes—
50C2×#6489C2211yescharacteristic
51C2×#6489C2211yescharacteristic
52C2×#6489C22116yescomplemented
53C2×#6489C2212yescomplemented
54C22×C4⋊Dic7C2211yescharacteristic
55C22×C4⋊Dic7C2211yescharacteristic
56C22×C4⋊Dic7C2211yescharacteristic
57C22×C4⋊Dic7C2212yescomplemented
58C2×#6487C2212yes—
59C2×#6487C2212yes—
60C2×#6487C2212yes—
61C2×#6487C2212yes—
62C2×#6487C22116yescomplemented
63C2×#6487C2212yescomplemented
64C2×#6487C2212yescomplemented
65C22×Dic7⋊C4C2212yes—
66C22×C4×Dic7C2212yes—
67#90341C22164yescomplemented
68#90316C22132yescomplemented
69#90313C22132yescomplemented
70#90294C22132yescomplemented
71#90291C22132yescomplemented
72#90278C22164yescomplemented
73#90234C22132yescomplemented
74#90233C22132yescomplemented
75#90232C22132yescomplemented
76#90232C22132yescomplemented
77#90210C22116yescomplemented
78#90207C22116yescomplemented
79C2×#6453C2212yescomplemented
80C2×#6453C2214yescomplemented
81C2×#6452C2214yescomplemented
82C2×#6452C2214yescomplemented
83C2×#6451C2212yescomplemented
84C2×#6450C2212yescomplemented
85C2×#6450C2212yescomplemented
86C2×#6450C2214yescomplemented
87C2×#6442C2214yes—
88C2×#6442C2214yes—
89C2×#6442C2214yescomplemented
90C2×#6442C2214yescomplemented
91C2×#6441C2214yes—
92C2×#6441C2214yes—
93C2×#6441C2214yescomplemented
94C2×#6440C2214yes—
95C2×#6440C2214yes—
96C2×#6440C2214yescomplemented
97C2×#6433C2212yescomplemented
98C2×#6432C2212yescomplemented
99C2×C4×Dic14C2212yescomplemented
100C2×C4×Dic14C2212yescomplemented
101C2×#3495—71nomaximal, Sylow
102C25×C7C2311yescharacteristic
103C2×C7×#41—28no—
104C2×C7×#41C2318yes—
105C22×C7×Q8C2311yescharacteristic
106C22×C7×D4C2312yes—
107C22×C7×D4C2311yescharacteristic
108C22×C7×D4C2312yes—
109C22×C7×D4C2312yes—
110C23×C4×C7—28no—
111C23×C4×C7C2312yes—
112C23×C4×C7C2311yescharacteristic
113C23×C4×C7C2311yescharacteristic
114C23×C4×C7C2311yescharacteristic
115C23×C4×C7C2311yescharacteristic
116C23×C4×C7C2311yescharacteristic
117C23×C4×C7C2318yes—
118C23×C4×C7C2311yescharacteristic
119C23×Dic7C2312yes—
120C23×Dic7C2312yes—
121C23×Dic7C2314yes—
122C23×Dic7C2312yes—
123C23×Dic7C2312yes—
124C22×Dic14—28no—
125C22×Dic14C2312yes—
126C22×Dic14C2312yes—
127C22×Dic14C2318yes—
128C22×Dic14C2314yes—
129C7×#123C23116yes—
130C7×C22⋊Q8C2318yes—
131C7×C22⋊Q8C2318yes—
132C7×#121C2318yes—
133C7×#121C2318yes—
134C7×#120C23116yes—
135C4×C7×D4C23116yes—
136C4×C7×D4C23116yes—
137C7×#117C2318yes—
138C2×C7×C4⋊C4C2311yescharacteristic
139C2×C7×C4⋊C4C2312yes—
140C2×C7×C4⋊C4C2311yescharacteristic
141C2×C7×C4⋊C4C2312yes—
142C2×C7×C22⋊C4C2312yes—
143C2×C7×C22⋊C4C2312yes—
144C2×C7×C22⋊C4C2312yes—
145C2×C7×C22⋊C4C2312yes—
146C2×C7×C22⋊C4C2312yes—
147C2×C42×C7C2312yes—
148C2×C22⋊Dic7C2312yes—
149C2×C22⋊Dic7C2314yes—
150C2×C22⋊Dic7C2314yes—
151C2×C22⋊Dic7C2312yes—
152C2×C22⋊Dic7C2314yes—
153C2×C22⋊Dic7C2314yes—
154C2×C22⋊Dic7C2312yes—
155C2×C22⋊Dic7C2312yes—
156C2×C22⋊Dic7C2314yes—
157C2×C22⋊Dic7C23116yes—
158C2×C22⋊Dic7C23116yes—
159Q8×Dic7C23116yescomplemented
160#6507C23116yescomplemented
161#6499C23132yes—
162#6499C23116yescomplemented
163#6498C23132yes—
164#6498C23132yes—
165#6498C23132yes—
166D4×Dic7C23132yes—
167D4×Dic7C23132yes—
168D4×Dic7C23116yescomplemented
169#6489C2318yes—
170#6489C2318yes—
171#6489C2318yes—
172#6489C2318yes—
173#6489C23116yes—
174#6489C23116yes—
175#6489C23116yescomplemented
176C2×C4⋊Dic7C2311yescharacteristic
177C2×C4⋊Dic7C2311yescharacteristic
178C2×C4⋊Dic7C2311yescharacteristic
179C2×C4⋊Dic7C2312yes—
180C2×C4⋊Dic7C2314yes—
181C2×C4⋊Dic7C2311yescharacteristic
182C2×C4⋊Dic7C2314yes—
183C2×C4⋊Dic7C2312yes—
184C2×C4⋊Dic7C2312yes—
185C2×C4⋊Dic7C2312yes—
186C2×C4⋊Dic7C2318yes—
187C2×C4⋊Dic7C2318yes—
188C2×C4⋊Dic7C2318yes—
189C2×C4⋊Dic7C23116yescomplemented
190#6487C23116yes—
191#6487C23116yes—
192#6487C23116yes—
193#6487C23116yes—
194#6487C23116yescomplemented
195#6487C23116yescomplemented
196C2×Dic7⋊C4C2314yes—
197C2×Dic7⋊C4C2314yes—
198C2×Dic7⋊C4C2314yes—
199C2×Dic7⋊C4C2314yes—
200C2×Dic7⋊C4C2314yes—
201C2×Dic7⋊C4C2314yes—
202C2×Dic7⋊C4C2314yes—
203C2×Dic7⋊C4C2314yes—
204C2×Dic7⋊C4C23116yes—
205C2×C4×Dic7C2314yes—
206C2×C4×Dic7C2314yes—
207C2×C4×Dic7C2314yes—
208C2×C4×Dic7C2312yes—
209C2×C4×Dic7C2312yes—
210C2×C4×Dic7C2312yes—
211C2×C4×Dic7C2312yes—
212C2×C4×Dic7C23116yes—
213#6453C23116yescomplemented
214#6453C23132yescomplemented
215#6452C23132yescomplemented
216#6452C23132yescomplemented
217#6451C23116yescomplemented
218#6450C23116yescomplemented
219#6450C23116yescomplemented
220#6450C23132yescomplemented
221#6442C23132yes—
222#6442C23132yes—
223#6442C23132yescomplemented
224#6442C23132yescomplemented
225#6441C23132yes—
226#6441C23132yes—
227#6441C23132yescomplemented
228#6440C23132yes—
229#6440C23132yes—
230#6440C23132yescomplemented
231#6433C23116yescomplemented
232#6432C23116yescomplemented
233C4×Dic14C23116yescomplemented
234C4×Dic14C23116yescomplemented
235#3495—732no—
236C2×#556—72no—
237C2×#554—72no—
238C2×#552—74no—
239C2×#552—72no—
240C2×#552—72no—
241C2×#551—74no—
242C2×#544—71no—
243C2×#542—72no—
244C2×#541—72no—
245C2×#536—71no—
246C2×#533—72no—
247C2×#529—72no—
248C2×#525D711yescharacteristic
249C22×C22⋊Q8—71no—
250C2×#520—71no—
251C2×#519—71no—
252C22×#117—71no—
253C24×C7—24no—
254C24×C7—24no—
255C24×C7—42no—
256C24×C7C2411yescharacteristic
257C24×C7C2412yes—
258C24×C7C2414yes—
259C24×C7C2411yescharacteristic
260C24×C7C2411yescharacteristic
261C7×#41—232no—
262C2×C7×Q8—24no—
263C2×C7×Q8C2414yes—
264C2×C7×D4—28no—
265C2×C7×D4—28no—
266C2×C7×D4—24no—
267C2×C7×D4—44no—
268C2×C7×D4C2418yes—
269C2×C7×D4C2418yes—
270C2×C7×D4C2414yes—
271C2×C7×D4C2418yes—
272C22×C4×C7—24no—
273C22×C4×C7—24no—
274C22×C4×C7—24no—
275C22×C4×C7—24no—
276C22×C4×C7—24no—
277C22×C4×C7—232no—
278C22×C4×C7—28no—
279C22×C4×C7#4118yes—
280C22×C4×C7C2411yescharacteristic
281C22×C4×C7C2414yes—
282C22×C4×C7C2412yes—
283C22×C4×C7C2412yes—
284C22×C4×C7C2412yes—
285C22×C4×C7C2411yescharacteristic
286C22×C4×C7C2414yes—
287C22×C4×C7C2414yes—
288C22×C4×C7C2414yes—
289C22×C4×C7C2414yes—
290C22×C4×C7C2418yes—
291C22×C4×C7C2411yescharacteristic
292C22×C4×C7C2411yescharacteristic
293C22×C4×C7C2414yes—
294C22×Dic7—28no—
295C22×Dic7—28no—
296C22×Dic7—44no—
297C22×Dic7—44no—
298C22×Dic7—48no—
299C22×Dic7C2418yes—
300C22×Dic7C2418yes—
301C22×Dic7C2412yes—
302C22×Dic7C2412yes—
303C22×Dic7C2412yes—
304C22×Dic7C2414yes—
305C22×Dic7C2412yes—
306C22×Dic7C2414yes—
307C22×Dic7C24116yes—
308C22×Dic7C2418yes—
309C22×Dic7C2418yes—
310C2×Dic14—28no—
311C2×Dic14—28no—
312C2×Dic14—232no—
313C2×Dic14—48no—
314C2×Dic14C2418yes—
315C2×Dic14C2418yes—
316C2×Dic14C24116yes—
317C7×C4⋊C4C2414yes—
318C7×C4⋊C4C2418yes—
319C7×C4⋊C4C2414yes—
320C7×C4⋊C4C2418yes—
321C7×C22⋊C4C2418yes—
322C7×C22⋊C4C2418yes—
323C7×C22⋊C4C2418yes—
324C7×C22⋊C4C2418yes—
325C7×C22⋊C4C2418yes—
326C42×C7C2418yes—
327C22⋊Dic7C2418yes—
328C22⋊Dic7C24116yes—
329C22⋊Dic7C24116yes—
330C22⋊Dic7C2418yes—
331C22⋊Dic7C24116yes—
332C22⋊Dic7C24116yes—
333C22⋊Dic7C2418yes—
334C22⋊Dic7C2418yes—
335C22⋊Dic7C24116yes—
336C4⋊Dic7C2414yes—
337C4⋊Dic7C2414yes—
338C4⋊Dic7C2414yes—
339C4⋊Dic7C2418yes—
340C4⋊Dic7C24116yes—
341C4⋊Dic7C2414yes—
342C4⋊Dic7C24116yes—
343C4⋊Dic7C2418yes—
344C4⋊Dic7C2418yes—
345C4⋊Dic7C2418yes—
346Dic7⋊C4C24116yes—
347Dic7⋊C4C24116yes—
348Dic7⋊C4C24116yes—
349Dic7⋊C4C24116yes—
350Dic7⋊C4C24116yes—
351Dic7⋊C4C24116yes—
352Dic7⋊C4C24116yes—
353Dic7⋊C4C24116yes—
354C4×Dic7C24116yes—
355C4×Dic7C24116yes—
356C4×Dic7C24116yes—
357C4×Dic7C2418yes—
358C4×Dic7C2418yes—
359C4×Dic7C2418yes—
360C4×Dic7C2418yes—
361C22×#41C2×D711yescharacteristic
362C23×Q8—71no—
363C24×C4C2×D711yescharacteristic
364#556—732no—
365#554—732no—
366#552—764no—
367#552—732no—
368#552—732no—
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#525C2×D7116yes—
391C2×#123—74no—
392C2×#123—74no—
393C2×#123—74no—
394C2×#123C2×D712yes—
395C2×C22⋊Q8—72no—
396C2×C22⋊Q8—72no—
397C2×C22⋊Q8—72no—
398C2×C22⋊Q8—72no—
399C2×C22⋊Q8—716no—
400C2×C22⋊Q8—72no—
401C2×C22⋊Q8—72no—
402C2×C22⋊Q8—74no—
403C2×C22⋊Q8—74no—
404C2×C22⋊Q8—74no—
405C2×C22⋊Q8C2×D711yescharacteristic
406C2×C22⋊Q8C2×D711yescharacteristic
407C2×#121C2×D711yescharacteristic
408C2×#121C2×D711yescharacteristic
409C2×#120C2×D712yes—
410#520—716no—
411#519—716no—
412C2×C4×Q8—72no—
413C2×C4×Q8—72no—
414C2×C4×Q8—72no—
415C2×C4×Q8—74no—
416C2×C4×Q8—72no—
417C2×C4×Q8—72no—
418C2×C4×D4—72no—
419C2×C4×D4—74no—
420C2×C4×D4—74no—
421C2×C4×D4C2×D712yes—
422C2×C4×D4C2×D712yes—
423C2×#117—71no—
424C2×#117—71no—
425C2×#117—72no—
426C2×#117—71no—
427C2×#117—72no—
428C2×#117—71no—
429C2×#117—716no—
430C2×#117—72no—
431C2×#117—74no—
432C2×#117—74no—
433C2×#117—74no—
434C2×#117C2×D711yescharacteristic
435C22×C4⋊C4—71no—
436C22×C4⋊C4—71no—
437C22×C4⋊C4—71no—
438C22×C4⋊C4—72no—
439C22×C4⋊C4—72no—
440C22×C22⋊C4—72no—
441C22×C22⋊C4—72no—
442C22×C42—72no—
443C23×C7—22no—
444C23×C7—22no—
445C23×C7—22no—
446C23×C7—22no—
447C23×C7—28no—
448C23×C7—22no—
449C23×C7—24no—
450C23×C7—24no—
451C23×C7—28no—
452C23×C7—22no—
453C23×C7—24no—
454C23×C7—22no—
455C23×C7—44no—
456C23×C7—416no—
457C23×C7C2×#4114yes—
458C23×C72−1+414yes—
459C23×C7C2512yes—
460C23×C7C2514yes—
461C23×C7C2512yes—
462C23×C7C2512yes—
463C23×C7C2511yescharacteristic
464C7×Q8—28no—
465C7×D4—216no—
466C7×D4—216no—
467C7×D4—28no—
468C7×D4—48no—
469C2×C4×C7—28no—
470C2×C4×C7—22no—
471C2×C4×C7—22no—
472C2×C4×C7—24no—
473C2×C4×C7—24no—
474C2×C4×C7—24no—
475C2×C4×C7—28no—
476C2×C4×C7—28no—
477C2×C4×C7—28no—
478C2×C4×C7—28no—
479C2×C4×C7—216no—
480C2×C4×C7C2×#4114yes—
481C2×C4×C7C2×#4114yes—
482C2×C4×C7C2×#41116yes—
483C2×C4×C7C2512yes—
484C2×C4×C7C2514yes—
485C2×C4×C7C2514yes—
486C2×C4×C7C2514yes—
487C2×C4×C7C2512yes—
488C2×C4×C7C2512yes—
489C2×C4×C7C2512yes—
490C2×Dic7—216no—
491C2×Dic7—28no—
492C2×Dic7—216no—
493C2×Dic7—24no—
494C2×Dic7—24no—
495C2×Dic7—24no—
496C2×Dic7—28no—
497C2×Dic7—24no—
498C2×Dic7—48no—
499C2×Dic7—48no—
500C2×Dic7—416no—
501C2×Dic7C2514yes—
502C2×Dic7C2514yes—
503C2×Dic7C2514yes—
504C2×Dic7C2518yes—
505C2×Dic7C2514yes—
506C2×Dic7C2518yes—
507Dic14—216no—
508Dic14—216no—
509Dic14—416no—
510C25C22×D711yescharacteristic
511C2×#41—28no—
512C2×#41C22×D718yes—
513C22×Q8—72no—
514C22×Q8—72no—
515C22×Q8—78no—
516C22×Q8—74no—
517C22×Q8—148no—
518C22×Q8C22×D711yescharacteristic
519C22×D4C22×D712yes—
520C22×D4C22×D712yes—
521C22×D4C22×D711yescharacteristic
522C22×D4C22×D712yes—
523C23×C4—28no—
524C23×C4—72no—
525C23×C4—72no—
526C23×C4—72no—
527C23×C4—72no—
528C23×C4—74no—
529C23×C4C22×D711yescharacteristic
530C23×C4C22×D711yescharacteristic
531C23×C4C22×D712yes—
532C23×C4C22×D711yescharacteristic
533C23×C4C22×D711yescharacteristic
534C23×C4C22×D718yes—
535C23×C4C22×D711yescharacteristic
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—732no—
552#123—732no—
553#123—732no—
554#123C22×D7116yes—
555C22⋊Q8—716no—
556C22⋊Q8—716no—
557C22⋊Q8—716no—
558C22⋊Q8—716no—
559C22⋊Q8—716no—
560C22⋊Q8—716no—
561C22⋊Q8—732no—
562C22⋊Q8—732no—
563C22⋊Q8—732no—
564C22⋊Q8C22×D718yes—
565C22⋊Q8C22×D718yes—
566#121C22×D718yes—
567#121C22×D718yes—
568#120C22×D7116yes—
569C4×Q8—716no—
570C4×Q8—716no—
571C4×Q8—716no—
572C4×Q8—732no—
573C4×Q8—716no—
574C4×Q8—716no—
575C4×D4—716no—
576C4×D4—732no—
577C4×D4—732no—
578C4×D4C22×D7116yes—
579C4×D4C22×D7116yes—
580#117—78no—
581#117—78no—
582#117—716no—
583#117—78no—
584#117—716no—
585#117—78no—
586#117—716no—
587#117—732no—
588#117—732no—
589#117—732no—
590#117C22×D718yes—
591C2×C4⋊C4—71no—
592C2×C4⋊C4—72no—
593C2×C4⋊C4—71no—
594C2×C4⋊C4—72no—
595C2×C4⋊C4—71no—
596C2×C4⋊C4—71no—
597C2×C4⋊C4—72no—
598C2×C4⋊C4—78no—
599C2×C4⋊C4—78no—
600C2×C4⋊C4—74no—
601C2×C4⋊C4—72no—
602C2×C4⋊C4—74no—
603C2×C4⋊C4—78no—
604C2×C4⋊C4—716no—
605C2×C4⋊C4—74no—
606C2×C4⋊C4—716no—
607C2×C4⋊C4—74no—
608C2×C4⋊C4—74no—
609C2×C4⋊C4—74no—
610C2×C4⋊C4—74no—
611C2×C4⋊C4—74no—
612C2×C4⋊C4—74no—
613C2×C4⋊C4—74no—
614C2×C4⋊C4C22×D711yescharacteristic
615C2×C4⋊C4C22×D711yescharacteristic
616C2×C4⋊C4C22×D712yes—
617C2×C4⋊C4C22×D712yes—
618C2×C22⋊C4—72no—
619C2×C22⋊C4—72no—
620C2×C22⋊C4—72no—
621C2×C22⋊C4—72no—
622C2×C22⋊C4—716no—
623C2×C22⋊C4—74no—
624C2×C22⋊C4—74no—
625C2×C22⋊C4—716no—
626C2×C22⋊C4—74no—
627C2×C22⋊C4—74no—
628C2×C22⋊C4—74no—
629C2×C22⋊C4C22×D712yes—
630C2×C22⋊C4C22×D712yes—
631C2×C22⋊C4C22×D712yes—
632C2×C22⋊C4C22×D712yes—
633C2×C22⋊C4C22×D712yes—
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×C42C22×D712yes—
643C22×C7—22no—
644C22×C7—22no—
645C22×C7—22no—
646C22×C7—22no—
647C22×C7—28no—
648C22×C7—28no—
649C22×C7—22no—
650C22×C7—24no—
651C22×C7—24no—
652C22×C7—22no—
653C22×C7—24no—
654C22×C7—22no—
655C22×C7—416no—
656C22×C7—48no—
657C22×C7—44no—
658C22×C7C22×#4114yes—
659C22×C7C22×#4112yes—
660C22×C7C2×2−1+414yes—
661C22×C7C2×2−1+412yes—
662C22×C7#58512yes—
663C22×C7C2611yescharacteristic
664C4×C7—22no—
665C4×C7—22no—
666C4×C7—24no—
667C4×C7—24no—
668C4×C7—24no—
669C4×C7C22×#4114yes—
670C4×C7C22×#4114yes—
671Dic7—28no—
672Dic7—24no—
673Dic7—24no—
674Dic7—24no—
675Dic7—28no—
676Dic7—24no—
677C24—24no—
678C24—24no—
679C24—42no—
680C24C23×D711yescharacteristic
681C24C23×D712yes—
682C24C23×D714yes—
683C24C23×D711yescharacteristic
684C24C23×D711yescharacteristic
685#41—232no—
686C2×Q8—24no—
687C2×Q8—78no—
688C2×Q8—78no—
689C2×Q8—716no—
690C2×Q8—148no—
691C2×Q8—148no—
692C2×Q8—1432no—
693C2×Q8—288no—
694C2×Q8C23×D714yes—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—24no—
698C2×D4—44no—
699C2×D4C23×D718yes—
700C2×D4C23×D718yes—
701C2×D4C23×D714yes—
702C2×D4C23×D718yes—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—232no—
709C22×C4—28no—
710C22×C4—78no—
711C22×C4—78no—
712C22×C4—72no—
713C22×C4—72no—
714C22×C4—72no—
715C22×C4—74no—
716C22×C4—72no—
717C22×C4—74no—
718C22×C4—78no—
719C22×C4—78no—
720C22×C4—716no—
721C22×C4—148no—
722C22×C4—148no—
723C22×C4—288no—
724C22×C4—284no—
725C22×C4—284no—
726C22×C4#115918yes—
727C22×C4C23×D714yes—
728C22×C4C23×D714yes—
729C22×C4C23×D714yes—
730C22×C4C23×D718yes—
731C22×C4C23×D714yes—
732C22×C4C23×D714yes—
733C22×C4C23×D711yescharacteristic
734C22×C4C23×D712yes—
735C22×C4C23×D712yes—
736C22×C4C23×D712yes—
737C22×C4C23×D711yescharacteristic
738C22×C4C23×D714yes—
739C22×C4C23×D711yescharacteristic
740C22×C4C23×D711yescharacteristic
741C4⋊C4—716no—
742C4⋊C4—716no—
743C4⋊C4—716no—
744C4⋊C4—716no—
745C4⋊C4—716no—
746C4⋊C4—716no—
747C4⋊C4—716no—
748C4⋊C4—716no—
749C4⋊C4—74no—
750C4⋊C4—78no—
751C4⋊C4—74no—
752C4⋊C4—78no—
753C4⋊C4—74no—
754C4⋊C4—74no—
755C4⋊C4—78no—
756C4⋊C4—78no—
757C4⋊C4—716no—
758C4⋊C4—716no—
759C4⋊C4C23×D714yes—
760C4⋊C4C23×D714yes—
761C4⋊C4C23×D718yes—
762C4⋊C4C23×D718yes—
763C22⋊C4—78no—
764C22⋊C4—78no—
765C22⋊C4—78no—
766C22⋊C4—78no—
767C22⋊C4—716no—
768C22⋊C4—716no—
769C22⋊C4—716no—
770C22⋊C4—716no—
771C22⋊C4—716no—
772C22⋊C4C23×D718yes—
773C22⋊C4C23×D718yes—
774C22⋊C4C23×D718yes—
775C22⋊C4C23×D718yes—
776C22⋊C4C23×D718yes—
777C42—78no—
778C42—78no—
779C42—78no—
780C42—78no—
781C42—716no—
782C42—716no—
783C42—716no—
784C42C23×D718yes—
785C2×C7—24no—
786C2×C7—24no—
787C2×C7—44no—
788C2×C7—42no—
789C2×C7#349514yescomplemented
790C2×C7C23×#4111yescharacteristic
791C2×C7C22×2−1+411yescharacteristic
792C2×C7C2×#58511yescharacteristic
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—28no—
798C23—22no—
799C23—24no—
800C23—24no—
801C23—28no—
802C23—22no—
803C23—24no—
804C23—22no—
805C23—44no—
806C23—416no—
807C23C2×#115914yes—
808C23#655414yes—
809C23C24×D712yes—
810C23C24×D714yes—
811C23C24×D712yes—
812C23C24×D712yes—
813C23C24×D711yescharacteristic
814Q8—28no—
815Q8—1416no—
816Q8—1416no—
817Q8—2816no—
818D4—216no—
819D4—216no—
820D4—28no—
821D4—48no—
822C2×C4—28no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—216no—
833C2×C4—74no—
834C2×C4—74no—
835C2×C4—74no—
836C2×C4—78no—
837C2×C4—74no—
838C2×C4—78no—
839C2×C4—1416no—
840C2×C4—148no—
841C2×C4—1416no—
842C2×C4—144no—
843C2×C4—144no—
844C2×C4—144no—
845C2×C4—148no—
846C2×C4—144no—
847C2×C4—2816no—
848C2×C4—288no—
849C2×C4—288no—
850C2×C4C2×#115914yes—
851C2×C4C2×#115914yes—
852C2×C4C2×#1159116yes—
853C2×C4C24×D712yes—
854C2×C4C24×D714yes—
855C2×C4C24×D714yes—
856C2×C4C24×D714yes—
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—24no—
869C22—24no—
870C22—22no—
871C22—24no—
872C22—22no—
873C22—416no—
874C22—44no—
875C22—48no—
876C22C22×#115914yes—
877C22C22×#115912yes—
878C22C2×#655414yes—
879C22C2×#655412yes—
880C22#9061612yes—
881C22C25×D711yescharacteristic
882C4—22no—
883C4—22no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—148no—
888C4—144no—
889C4—144no—
890C4—144no—
891C4—148no—
892C4—144no—
893C4C22×#115914yes—
894C4C22×#115914yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—44no—
899C2#1174309614yesdirect product factor
900C2C23×#115911yescharacteristic
901C2C22×#655411yescharacteristic
902C2C2×#9061611yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
Fitting, prime radicalC2×C7×#525C2
socleC23×C7C25
hypercenterC2×#525D7
hypocenterC7C2×#3495
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
2. C2×#90516C2semidirect
3. C2×#90518C2semidirect
4. C22×#6487C2semidirect
5. C22×#6489C2semidirect
6. #11743096C2direct (N × H)
7. C2×#90341C2semidirect
8. C2×#90316C2semidirect
9. C2×#90313C2semidirect
10. C2×#90294C2semidirect
11. C2×#90291C2semidirect
12. C2×#90278C2semidirect
13. C2×#90233C2semidirect
14. C2×#90234C2semidirect
15. C2×#90232C2semidirect
16. C2×#90232C2semidirect
17. C2×#90210C2semidirect
18. C2×#90207C2semidirect
34. #90518C22semidirect
35. #90516C22semidirect
36. C2×Q8×Dic7C22semidirect
37. C2×#6507C22semidirect
39. C2×#6499C22semidirect
45. C2×D4×Dic7C22semidirect
52. C2×#6489C22semidirect
53. C2×#6489C22semidirect
57. C22×C4⋊Dic7C22semidirect
62. C2×#6487C22semidirect
63. C2×#6487C22semidirect
64. C2×#6487C22semidirect
67. #90341C22semidirect
68. #90316C22semidirect
69. #90313C22semidirect
70. #90294C22semidirect
71. #90291C22semidirect
72. #90278C22semidirect
73. #90234C22semidirect
74. #90233C22semidirect
75. #90232C22semidirect
76. #90232C22semidirect
77. #90210C22semidirect
78. #90207C22semidirect
79. C2×#6453C22semidirect
80. C2×#6453C22semidirect
81. C2×#6452C22semidirect
82. C2×#6452C22semidirect
83. C2×#6451C22semidirect
84. C2×#6450C22semidirect
85. C2×#6450C22semidirect
86. C2×#6450C22semidirect
89. C2×#6442C22semidirect
90. C2×#6442C22semidirect
93. C2×#6441C22semidirect
96. C2×#6440C22semidirect
97. C2×#6433C22semidirect
98. C2×#6432C22semidirect
99. C2×C4×Dic14C22semidirect
100. C2×C4×Dic14C22semidirect
159. Q8×Dic7C23semidirect
160. #6507C23semidirect
162. #6499C23semidirect
168. D4×Dic7C23semidirect
175. #6489C23semidirect
189. C2×C4⋊Dic7C23semidirect
194. #6487C23semidirect
195. #6487C23semidirect
213. #6453C23semidirect
214. #6453C23semidirect
215. #6452C23semidirect
216. #6452C23semidirect
217. #6451C23semidirect
218. #6450C23semidirect
219. #6450C23semidirect
220. #6450C23semidirect
223. #6442C23semidirect
224. #6442C23semidirect
227. #6441C23semidirect
230. #6440C23semidirect
231. #6433C23semidirect
232. #6432C23semidirect
233. C4×Dic14C23semidirect
234. C4×Dic14C23semidirect
789. C2×C7#3495semidirect
860. C7C2×#3495semidirect
899. C2#11743096direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5252
C2×#905162
C2×#905182
C22×#64872
C22×#64892
#117430962
C2×#903412
C2×#903162
C2×#903132
C2×#902942
C2×#902912
C2×#902782
C2×#902332
C2×#902342
C2×#902322
C2×#902102
C2×#902072
C2×#34957