Finite Group Databasebeta

← C2×#11743336 #14261516

Subgroups — C2×#11743336 #14261516

Order 1792.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic, complemented
2#11743336C2132yesmaximal, direct product factor
3C2×#90420C212yesmaximal, complemented
4C2×#90422C212yesmaximal, complemented
5C2×#90387C214yesmaximal, complemented
6C2×#90330C212yesmaximal, complemented
7C2×#90337C214yesmaximal, complemented
8C2×#90332C212yesmaximal, complemented
9C2×#90270C211yesmaximal, characteristic, complemented
10C2×Q8×Dic14C211yesmaximal, characteristic, complemented
11C2×#90258C212yesmaximal, complemented
12C2×#90261C211yesmaximal, characteristic, complemented
13C2×#90275C212yesmaximal, complemented
14C2×#90275C211yesmaximal, characteristic, complemented
15C2×#90225C212yesmaximal
16C2×#90209C212yesmaximal, complemented
17C2×#90170C211yesmaximal, characteristic
18C2×#90161C211yesmaximal, characteristic, complemented
19C7×#533C22116yescomplemented
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×C4⋊Q8C2211yescharacteristic
22C2×C7×#125C2212yes—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×C22⋊Q8C2212yes—
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C4×C7×Q8C2212yes—
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×Q8C2211yescharacteristic
29C2×C7×#117C2212yes—
30C22×C42×C7C2211yescharacteristic
31C2×#6509C2212yes—
32C2×#6509C2212yes—
33C2×#6509C2214yes—
34C2×Q8×Dic7C2212yes—
35C2×Q8×Dic7C2212yes—
36C2×#6507C2214yes—
37C2×#6493C2211yescharacteristic
38C2×#6492C2212yes—
39C2×C4×C22⋊D7C2212yes—
40C2×#6489C2212yes—
41C2×#6487C2212yes—
42C2×#6487C2212yes—
43C2×#6487C2211yescharacteristic
44#90422C22132yescomplemented
45#90420C22132yescomplemented
46#90387C22164yescomplemented
47#90337C22164yescomplemented
48#90332C22132yescomplemented
49#90330C22132yescomplemented
50#90275C22132yescomplemented
51#90275C22116yescomplemented
52#90270C22116yescomplemented
53#90261C22116yescomplemented
54#90258C22132yescomplemented
55Q8×Dic14C22116yescomplemented
56#90225C22132yes—
57#90209C22132yescomplemented
58C2×#6461C2214yes—
59C2×#6461C2214yes—
60C2×#6461C2214yes—
61C2×#6461C2214yes—
62C2×#6459C2214yes—
63C2×#6459C2214yes—
64C2×#6455C2212yes—
65C2×#6455C2214yes—
66C2×D7×C4⋊C4C2212yes—
67C2×#6453C2212yes—
68C2×#6453C2214yes—
69C2×#6452C2214yes—
70C2×#6452C2214yes—
71C2×#6452C2214yes—
72C2×#6452C2214yes—
73C2×#6451C2212yes—
74C2×#6451C2214yes—
75C2×#6450C2214yes—
76C2×#6448C2214yes—
77C2×#6446C2214yes—
78C2×#6442C2214yes—
79C2×#6442C2214yes—
80#90170C22116yes—
81C2×#6439C2212yes—
82C2×#6438C2211yescharacteristic
83C2×#6438C2212yes—
84C2×C4×D28C2211yescharacteristic
85C2×C4×D28C2212yes—
86C2×#6435C2212yes—
87#90161C22116yescomplemented
88C2×#6433C2212yes—
89C2×#6433C2211yescharacteristic
90C2×#6433C2212yes—
91C2×#6432C2211yescharacteristic
92C2×#6432C2211yescharacteristic
93C2×#6432C2212yes—
94C2×#6432C2212yes—
95C2×C4×Dic14C2212yes—
96C2×C4×Dic14C2212yes—
97C2×C4×Dic14C2211yescharacteristic
98C2×C4×Dic14C2212yes—
99C2×C4×Dic14C2212yes—
100C2×C4×Dic14C2212yes—
101C2×#3555—71nomaximal, Sylow
102C22×C7×Q8C2311yescharacteristic
103C22×C7×Q8C2311yescharacteristic
104C22×C7×Q8C2312yes—
105C23×C4×C7C2311yescharacteristic
106C23×C4×C7C2311yescharacteristic
107C23×C4×C7C2311yescharacteristic
108C22×C22⋊D7C2312yes—
109C22×D28C2311yescharacteristic
110C22×C4×D7C2312yes—
111C22×C4×D7C2314yes—
112C22×Dic14C2312yes—
113C22×Dic14C2311yescharacteristic
114C22×Dic14C2312yes—
115C22×Dic14C2314yes—
116C7×C4⋊Q8C2318yes—
117C7×C4⋊Q8C2318yes—
118C7×#125C23116yes—
119C7×C22⋊Q8C2318yes—
120C7×C22⋊Q8C2318yes—
121C7×C22⋊Q8C23116yes—
122C4×C7×Q8C2318yes—
123C4×C7×Q8C23116yes—
124C4×C7×Q8C2318yes—
125C7×#117C23116yes—
126C2×C7×C4⋊C4C2312yes—
127C2×C7×C4⋊C4C2311yescharacteristic
128C2×C7×C4⋊C4C2312yes—
129C2×C7×C4⋊C4C2312yes—
130C2×C7×C4⋊C4C2312yes—
131C2×C7×C4⋊C4C2312yes—
132C2×C7×C4⋊C4C2312yes—
133C2×C7×C4⋊C4C2311yescharacteristic
134C2×C7×C4⋊C4C2312yes—
135C2×C7×C22⋊C4C2312yes—
136C2×C7×C22⋊C4C2312yes—
137C2×C42×C7C2312yes—
138C2×C42×C7C2311yescharacteristic
139C2×C42×C7C2311yescharacteristic
140C2×C42×C7C2311yescharacteristic
141C2×C42×C7C2312yes—
142C2×C42×C7C2311yescharacteristic
143C2×C42×C7C2318yes—
144C2×C22⋊Dic7C2312yes—
145C2×C22⋊Dic7C2314yes—
146#6509C23132yes—
147#6509C23116yes—
148#6509C23116yes—
149Q8×Dic7C23116yes—
150Q8×Dic7C23116yes—
151#6507C23132yes—
152#6493C2318yes—
153#6492C23116yes—
154C4×C22⋊D7C23116yes—
155C2×(C2×D7)⋊C4C2312yes—
156C2×(C2×D7)⋊C4C2312yes—
157C2×(C2×D7)⋊C4C2312yes—
158C2×(C2×D7)⋊C4C2314yes—
159C2×(C2×D7)⋊C4C2312yes—
160C2×(C2×D7)⋊C4C2314yes—
161C2×(C2×D7)⋊C4C2314yes—
162#6489C23116yes—
163C2×C4⋊Dic7C2311yescharacteristic
164C2×C4⋊Dic7C2312yes—
165C2×C4⋊Dic7C2311yescharacteristic
166C2×C4⋊Dic7C2312yes—
167C2×C4⋊Dic7C2312yes—
168C2×C4⋊Dic7C2312yes—
169C2×C4⋊Dic7C2314yes—
170C2×C4⋊Dic7C2314yes—
171C2×C4⋊Dic7C2314yes—
172#6487C23116yes—
173#6487C23116yes—
174#6487C2318yes—
175C2×Dic7⋊C4C2314yes—
176C2×Dic7⋊C4C2314yes—
177C2×Dic7⋊C4C2312yes—
178C2×Dic7⋊C4C2314yes—
179C2×Dic7⋊C4C2314yes—
180C2×Dic7⋊C4C2314yes—
181C2×Dic7⋊C4C2312yes—
182C2×Dic7⋊C4C2312yes—
183C2×Dic7⋊C4C2314yes—
184C2×Dic7⋊C4C2314yes—
185C2×Dic7⋊C4C2312yes—
186C2×C4×Dic7C2314yes—
187C2×C4×Dic7C2312yes—
188C2×C4×Dic7C2314yes—
189C2×C4×Dic7C2314yes—
190C2×C4×Dic7C2314yes—
191#6461C23132yes—
192#6461C23132yes—
193#6461C23132yes—
194#6461C23132yes—
195#6459C23132yes—
196#6459C23132yes—
197#6455C23132yes—
198#6455C23116yes—
199D7×C4⋊C4C23116yes—
200#6453C23132yes—
201#6453C23116yes—
202#6452C23132yes—
203#6452C23132yes—
204#6452C23132yes—
205#6452C23132yes—
206#6451C23132yes—
207#6451C23116yes—
208#6450C23132yes—
209#6448C23132yes—
210#6446C23132yes—
211#6442C23132yes—
212#6442C23132yes—
213#6439C23116yes—
214#6438C2318yes—
215#6438C23116yes—
216C4×D28C2318yes—
217C4×D28C23116yes—
218#6435C23116yes—
219#6433C23116yes—
220#6433C2318yes—
221#6433C23116yes—
222#6432C2318yes—
223#6432C2318yes—
224#6432C23116yes—
225#6432C23116yes—
226C4×Dic14C23116yes—
227C4×Dic14C23116yes—
228C4×Dic14C2318yes—
229C4×Dic14C23116yes—
230C4×Dic14C23116yes—
231C4×Dic14C23116yes—
232#3555—732no—
233C2×#563—74no—
234C2×Q82—71no—
235C2×#557—71no—
236C2×#557—72no—
237C2×#556—72no—
238C2×#556—72no—
239C2×#556—71no—
240C2×#554—71no—
241C2×#552—72no—
242C2×#544—72no—
243C2×#542—72no—
244C2×#541—72no—
245C2×#541—74no—
246C2×#541—72no—
247C2×#533—71no—
248C2×#533D711yescharacteristic, complemented
249C2×#529—71no—
250C24×C7C2411yescharacteristic
251C23×D7C2412yes—
252C2×C7×Q8—24no—
253C2×C7×Q8—24no—
254C2×C7×Q8—44no—
255C2×C7×Q8C2414yes—
256C2×C7×Q8C2414yes—
257C2×C7×Q8C2418yes—
258C22×C4×C7—24no—
259C22×C4×C7—24no—
260C22×C4×C7—42no—
261C22×C4×C7C2411yescharacteristic
262C22×C4×C7C2412yes—
263C22×C4×C7C2412yes—
264C22×C4×C7C2412yes—
265C22×C4×C7C2411yescharacteristic
266C22×C4×C7C2411yescharacteristic
267C22×C4×C7C2412yes—
268C22×C4×C7C2411yescharacteristic
269C22×C4×C7C2414yes—
270C22×C4×C7C2414yes—
271C22×C4×C7C2414yes—
272C22×C4×C7C2411yescharacteristic
273C22×C4×C7C2411yescharacteristic
274C2×C22⋊D7—44no—
275C2×C22⋊D7C2418yes—
276C22×Dic7C2412yes—
277C22×Dic7C2414yes—
278C22×Dic7C2412yes—
279C22×Dic7C2412yes—
280C22×Dic7C2414yes—
281C2×D28—24no—
282C2×D28C2414yes—
283C2×C4×D7—28no—
284C2×C4×D7—48no—
285C2×C4×D7C2418yes—
286C2×C4×D7C24116yes—
287C2×Dic14—28no—
288C2×Dic14—24no—
289C2×Dic14—44no—
290C2×Dic14—48no—
291C2×Dic14C2418yes—
292C2×Dic14C2414yes—
293C2×Dic14C2418yes—
294C2×Dic14C24116yes—
295C7×C4⋊C4C2418yes—
296C7×C4⋊C4C2414yes—
297C7×C4⋊C4C2418yes—
298C7×C4⋊C4C2418yes—
299C7×C4⋊C4C2418yes—
300C7×C4⋊C4C2418yes—
301C7×C4⋊C4C2418yes—
302C7×C4⋊C4C2414yes—
303C7×C4⋊C4C2418yes—
304C7×C22⋊C4C2418yes—
305C7×C22⋊C4C2418yes—
306C42×C7C2418yes—
307C42×C7C2414yes—
308C42×C7C2414yes—
309C42×C7C2414yes—
310C42×C7C2418yes—
311C42×C7C2414yes—
312C22⋊Dic7C2418yes—
313C22⋊Dic7C24116yes—
314(C2×D7)⋊C4C2418yes—
315(C2×D7)⋊C4C2418yes—
316(C2×D7)⋊C4C2418yes—
317(C2×D7)⋊C4C24116yes—
318(C2×D7)⋊C4C2418yes—
319(C2×D7)⋊C4C24116yes—
320(C2×D7)⋊C4C24116yes—
321C4⋊Dic7C2414yes—
322C4⋊Dic7C2418yes—
323C4⋊Dic7C2414yes—
324C4⋊Dic7C2418yes—
325C4⋊Dic7C2418yes—
326C4⋊Dic7C2418yes—
327C4⋊Dic7C24116yes—
328C4⋊Dic7C24116yes—
329C4⋊Dic7C24116yes—
330Dic7⋊C4C24116yes—
331Dic7⋊C4C24116yes—
332Dic7⋊C4C2418yes—
333Dic7⋊C4C24116yes—
334Dic7⋊C4C24116yes—
335Dic7⋊C4C24116yes—
336Dic7⋊C4C2418yes—
337Dic7⋊C4C2418yes—
338Dic7⋊C4C24116yes—
339Dic7⋊C4C24116yes—
340Dic7⋊C4C2418yes—
341C4×Dic7C24116yes—
342C4×Dic7C2418yes—
343C4×Dic7C24116yes—
344C4×Dic7C24116yes—
345C4×Dic7C24116yes—
346#563—764no—
347Q82—716no—
348#557—732no—
349#557—716no—
350#556—732no—
351#556—732no—
352#556—716no—
353#554—716no—
354#552—732no—
355#544—732no—
356#542—732no—
357#541—732no—
358#541—764no—
359#541—732no—
360#533—716no—
361#533C2×D7116yescomplemented
362C2×C4⋊Q8—74no—
363C2×C4⋊Q8—74no—
364C2×C4⋊Q8—72no—
365C2×C4⋊Q8—71no—
366C2×C4⋊Q8—71no—
367C2×C4⋊Q8—72no—
368C2×C4⋊Q8—72no—
369C2×C4⋊Q8C2×D711yescharacteristic
370C2×C4⋊Q8C2×D711yescharacteristic
371#529—716no—
372C2×#126—74no—
373C2×#126—74no—
374C2×#126—74no—
375C2×#126—74no—
376C2×#126—74no—
377C2×#126—74no—
378C2×#126—72no—
379C2×#125—74no—
380C2×#125—74no—
381C2×#125—74no—
382C2×#125—74no—
383C2×#125—74no—
384C2×#125—72no—
385C2×#125—71no—
386C2×#125—72no—
387C2×#125—72no—
388C2×#125C2×D712yes—
389C2×#124—74no—
390C2×#124—71no—
391C2×#124—72no—
392C2×#123—72no—
393C2×#123—74no—
394C2×C22⋊Q8—72no—
395C2×C22⋊Q8—72no—
396C2×C22⋊Q8—74no—
397C2×C22⋊Q8—71no—
398C2×C22⋊Q8—72no—
399C2×C22⋊Q8—72no—
400C2×C22⋊Q8—74no—
401C2×C22⋊Q8—74no—
402C2×C22⋊Q8C2×D711yescharacteristic
403C2×C22⋊Q8C2×D711yescharacteristic
404C2×C22⋊Q8C2×D712yes—
405C2×#121—71no—
406C2×C4×Q8—72no—
407C2×C4×Q8—72no—
408C2×C4×Q8—74no—
409C2×C4×Q8—71no—
410C2×C4×Q8—72no—
411C2×C4×Q8—72no—
412C2×C4×Q8—72no—
413C2×C4×Q8—72no—
414C2×C4×Q8—72no—
415C2×C4×Q8C2×D711yescharacteristic
416C2×C4×Q8C2×D712yes—
417C2×C4×Q8C2×D711yescharacteristic
418C2×C4×D4—72no—
419C2×C4×D4—71no—
420C2×C4×D4—72no—
421C2×#117—72no—
422C2×#117—74no—
423C2×#117—72no—
424C2×#117—72no—
425C2×#117C2×D712yes—
426C22×C4⋊C4—72no—
427C22×C42C2×D711yescharacteristic
428C23×C7—22no—
429C23×C7—22no—
430C23×C7—22no—
431C23×C7C2512yes—
432C23×C7C2511yescharacteristic
433C22×D7—24no—
434C22×D7—24no—
435C22×D7—24no—
436C22×D7C2514yes—
437C7×Q8—28no—
438C7×Q8—28no—
439C7×Q8—48no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—24no—
443C2×C4×C7—24no—
444C2×C4×C7—22no—
445C2×C4×C7—24no—
446C2×C4×C7—24no—
447C2×C4×C7—22no—
448C2×C4×C7—28no—
449C2×C4×C7—28no—
450C2×C4×C7—44no—
451C2×C4×C72−1+414yes—
452C2×C4×C72−1+414yes—
453C2×C4×C7C2512yes—
454C2×C4×C7C2514yes—
455C2×C4×C7C2514yes—
456C2×C4×C7C2514yes—
457C2×C4×C7C2512yes—
458C2×C4×C7C2512yes—
459C2×C4×C7C2514yes—
460C2×C4×C7C2512yes—
461C2×C4×C7C2512yes—
462C2×C4×C7C2512yes—
463C22⋊D7—48no—
464C2×Dic7—28no—
465C2×Dic7—24no—
466C2×Dic7—24no—
467C2×Dic7—28no—
468C2×Dic7—24no—
469C2×Dic7C2514yes—
470C2×Dic7C2518yes—
471C2×Dic7C2514yes—
472C2×Dic7C2514yes—
473C2×Dic7C2518yes—
474D28—28no—
475C4×D7—216no—
476C4×D7—416no—
477Dic14—216no—
478Dic14—28no—
479Dic14—48no—
480Dic14—416no—
481C22×Q8—71no—
482C22×Q8—72no—
483C22×Q8—72no—
484C22×Q8—74no—
485C22×Q8C22×D711yescharacteristic
486C22×Q8C22×D711yescharacteristic
487C22×Q8C22×D712yes—
488C22×D4—72no—
489C22×D4—71no—
490C23×C4—72no—
491C23×C4—74no—
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C4⋊Q8—732no—
496C4⋊Q8—732no—
497C4⋊Q8—716no—
498C4⋊Q8—78no—
499C4⋊Q8—78no—
500C4⋊Q8—716no—
501C4⋊Q8—716no—
502C4⋊Q8C22×D718yes—
503C4⋊Q8C22×D718yes—
504#126—732no—
505#126—732no—
506#126—732no—
507#126—732no—
508#126—732no—
509#126—732no—
510#126—716no—
511#125—732no—
512#125—732no—
513#125—732no—
514#125—732no—
515#125—732no—
516#125—716no—
517#125—78no—
518#125—716no—
519#125—716no—
520#125C22×D7116yes—
521#124—732no—
522#124—78no—
523#124—716no—
524#123—716no—
525#123—732no—
526C22⋊Q8—716no—
527C22⋊Q8—716no—
528C22⋊Q8—732no—
529C22⋊Q8—78no—
530C22⋊Q8—716no—
531C22⋊Q8—716no—
532C22⋊Q8—732no—
533C22⋊Q8—732no—
534C22⋊Q8C22×D718yes—
535C22⋊Q8C22×D718yes—
536C22⋊Q8C22×D7116yes—
537#121—78no—
538C4×Q8—716no—
539C4×Q8—716no—
540C4×Q8—732no—
541C4×Q8—78no—
542C4×Q8—716no—
543C4×Q8—716no—
544C4×Q8—716no—
545C4×Q8—716no—
546C4×Q8—716no—
547C4×Q8C22×D718yes—
548C4×Q8C22×D7116yes—
549C4×Q8C22×D718yes—
550C4×D4—716no—
551C4×D4—78no—
552C4×D4—716no—
553#117—716no—
554#117—732no—
555#117—716no—
556#117—716no—
557#117C22×D7116yes—
558C2×C4⋊C4—72no—
559C2×C4⋊C4—74no—
560C2×C4⋊C4—72no—
561C2×C4⋊C4—72no—
562C2×C4⋊C4—74no—
563C2×C4⋊C4—72no—
564C2×C4⋊C4—71no—
565C2×C4⋊C4—72no—
566C2×C4⋊C4—72no—
567C2×C4⋊C4—71no—
568C2×C4⋊C4—74no—
569C2×C4⋊C4—74no—
570C2×C4⋊C4—74no—
571C2×C4⋊C4—74no—
572C2×C4⋊C4—74no—
573C2×C4⋊C4—72no—
574C2×C4⋊C4—74no—
575C2×C4⋊C4—72no—
576C2×C4⋊C4—74no—
577C2×C4⋊C4—74no—
578C2×C4⋊C4—716no—
579C2×C4⋊C4C22×D711yescharacteristic
580C2×C4⋊C4C22×D712yes—
581C2×C4⋊C4C22×D711yescharacteristic
582C2×C4⋊C4C22×D712yes—
583C2×C4⋊C4C22×D712yes—
584C2×C4⋊C4C22×D712yes—
585C2×C4⋊C4C22×D712yes—
586C2×C4⋊C4C22×D712yes—
587C2×C4⋊C4C22×D712yes—
588C2×C22⋊C4—74no—
589C2×C22⋊C4—72no—
590C2×C22⋊C4—72no—
591C2×C22⋊C4—72no—
592C2×C22⋊C4—72no—
593C2×C22⋊C4—74no—
594C2×C22⋊C4—74no—
595C2×C22⋊C4—72no—
596C2×C22⋊C4—74no—
597C2×C22⋊C4C22×D712yes—
598C2×C22⋊C4C22×D712yes—
599C2×C42—74no—
600C2×C42—72no—
601C2×C42—74no—
602C2×C42—74no—
603C2×C42—74no—
604C2×C42C22×D711yescharacteristic
605C2×C42C22×D712yes—
606C2×C42C22×D712yes—
607C2×C42C22×D711yescharacteristic
608C2×C42C22×D711yescharacteristic
609C2×C42C22×D711yescharacteristic
610C2×C42C22×D718yes—
611C22×C7—22no—
612C22×C7—22no—
613C22×C7—22no—
614C22×C7—44no—
615C22×C7C2×2−1+412yes—
616C22×C7C2×2−1+412yes—
617C22×C7#58512yes—
618C22×C7C2611yescharacteristic
619C2×D7—24no—
620C2×D7—24no—
621C2×D7—24no—
622C2×D7—48no—
623C4×C7—22no—
624C4×C7—22no—
625C4×C7—24no—
626C4×C7—24no—
627C4×C7—22no—
628C4×C7—24no—
629C4×C7—24no—
630C4×C7—22no—
631C4×C7C2×2−1+414yes—
632C4×C7C2×2−1+414yes—
633Dic7—28no—
634Dic7—24no—
635Dic7—24no—
636Dic7—28no—
637Dic7—24no—
638C24—72no—
639C24C23×D711yescharacteristic
640C2×Q8—24no—
641C2×Q8—24no—
642C2×Q8—44no—
643C2×Q8—74no—
644C2×Q8—78no—
645C2×Q8—78no—
646C2×Q8—716no—
647C2×Q8—144no—
648C2×Q8—148no—
649C2×Q8—284no—
650C2×Q8—288no—
651C2×Q8C23×D714yes—
652C2×Q8C23×D714yes—
653C2×Q8C23×D718yes—
654C2×D4—78no—
655C2×D4—74no—
656C2×D4—144no—
657C2×D4—284no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—42no—
661C22×C4—74no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—74no—
666C22×C4—78no—
667C22×C4—716no—
668C22×C4—148no—
669C22×C4—288no—
670C22×C4C23×D714yes—
671C22×C4C23×D714yes—
672C22×C4C23×D711yescharacteristic
673C22×C4C23×D712yes—
674C22×C4C23×D712yes—
675C22×C4C23×D712yes—
676C22×C4C23×D711yescharacteristic
677C22×C4C23×D711yescharacteristic
678C22×C4C23×D711yescharacteristic
679C22×C4C23×D712yes—
680C22×C4C23×D714yes—
681C22×C4C23×D711yescharacteristic
682C22×C4C23×D711yescharacteristic
683C4⋊C4—716no—
684C4⋊C4—78no—
685C4⋊C4—78no—
686C4⋊C4—78no—
687C4⋊C4—716no—
688C4⋊C4—716no—
689C4⋊C4—716no—
690C4⋊C4—716no—
691C4⋊C4—716no—
692C4⋊C4—716no—
693C4⋊C4—78no—
694C4⋊C4—78no—
695C4⋊C4—78no—
696C4⋊C4—716no—
697C4⋊C4—74no—
698C4⋊C4—78no—
699C4⋊C4—74no—
700C4⋊C4—78no—
701C4⋊C4—716no—
702C4⋊C4—716no—
703C4⋊C4C23×D714yes—
704C4⋊C4C23×D718yes—
705C4⋊C4C23×D714yes—
706C4⋊C4C23×D718yes—
707C4⋊C4C23×D718yes—
708C4⋊C4C23×D718yes—
709C4⋊C4C23×D718yes—
710C4⋊C4C23×D718yes—
711C4⋊C4C23×D718yes—
712C22⋊C4—716no—
713C22⋊C4—78no—
714C22⋊C4—78no—
715C22⋊C4—78no—
716C22⋊C4—78no—
717C22⋊C4—716no—
718C22⋊C4—716no—
719C22⋊C4—78no—
720C22⋊C4—716no—
721C22⋊C4C23×D718yes—
722C22⋊C4C23×D718yes—
723C42—716no—
724C42—78no—
725C42—716no—
726C42—716no—
727C42—716no—
728C42C23×D714yes—
729C42C23×D714yes—
730C42C23×D714yes—
731C42C23×D714yes—
732C42C23×D718yes—
733C42C23×D718yes—
734C2×C7—42no—
735C2×C7#355514yescomplemented
736C2×C7C22×2−1+411yescharacteristic
737C2×C7C22×2−1+411yescharacteristic
738C2×C7C2×#58511yescharacteristic
739D7—44no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—74no—
744C23—144no—
745C23—144no—
746C23—144no—
747C23C24×D712yes—
748C23C24×D711yescharacteristic
749Q8—28no—
750Q8—28no—
751Q8—48no—
752Q8—148no—
753Q8—1416no—
754Q8—288no—
755Q8—2816no—
756D4—148no—
757D4—288no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—44no—
769C2×C4—78no—
770C2×C4—74no—
771C2×C4—74no—
772C2×C4—74no—
773C2×C4—78no—
774C2×C4—148no—
775C2×C4—144no—
776C2×C4—144no—
777C2×C4—148no—
778C2×C4—144no—
779C2×C4—1416no—
780C2×C4—2816no—
781C2×C4#655114yes—
782C2×C4#655414yes—
783C2×C4C24×D712yes—
784C2×C4C24×D714yes—
785C2×C4C24×D714yes—
786C2×C4C24×D714yes—
787C2×C4C24×D712yes—
788C2×C4C24×D712yes—
789C2×C4C24×D712yes—
790C2×C4C24×D714yes—
791C2×C4C24×D712yes—
792C2×C4C24×D712yes—
793C7C2×#355511yescharacteristic, complemented, Sylow
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—144no—
799C22—144no—
800C22—144no—
801C22—288no—
802C22C2×#655112yes—
803C22C2×#655412yes—
804C22#9061612yes—
805C22C25×D711yescharacteristic
806C4—22no—
807C4—22no—
808C4—24no—
809C4—24no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—24no—
814C4—148no—
815C4—144no—
816C4—144no—
817C4—148no—
818C4—144no—
819C4C2×#655114yes—
820C4C2×#655414yes—
821C2—42no—
822C2—284no—
823C2#1174333614yesdirect product factor
824C2C22×#655111yescharacteristic
825C2C22×#655411yescharacteristic
826C2C2×#9061611yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#533C2
socleC23×C7C25
prime radicalC2×#6493C22
hypercenterC2×#533D7
hypocenterC7C2×#3555
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C7×#533C2semidirect
2. #11743336C2direct (N × H)
3. C2×#90420C2semidirect
4. C2×#90422C2semidirect
5. C2×#90387C2semidirect
6. C2×#90330C2semidirect
7. C2×#90337C2semidirect
8. C2×#90332C2semidirect
9. C2×#90270C2semidirect
10. C2×Q8×Dic14C2semidirect
11. C2×#90258C2semidirect
12. C2×#90261C2semidirect
13. C2×#90275C2semidirect
14. C2×#90275C2semidirect
16. C2×#90209C2semidirect
18. C2×#90161C2semidirect
19. C7×#533C22semidirect
44. #90422C22semidirect
45. #90420C22semidirect
46. #90387C22semidirect
47. #90337C22semidirect
48. #90332C22semidirect
49. #90330C22semidirect
50. #90275C22semidirect
51. #90275C22semidirect
52. #90270C22semidirect
53. #90261C22semidirect
54. #90258C22semidirect
55. Q8×Dic14C22semidirect
57. #90209C22semidirect
87. #90161C22semidirect
248. C2×#533D7semidirect
361. #533C2×D7semidirect
735. C2×C7#3555semidirect
793. C7C2×#3555semidirect
823. C2#11743336direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5332
#117433362
C2×#904202
C2×#904222
C2×#903872
C2×#903302
C2×#903372
C2×#903322
C2×#902702
C2×Q8×Dic142
C2×#902582
C2×#902612
C2×#902752
C2×#902252
C2×#902092
C2×#901702
C2×#901612
C2×#35557