Finite Group Databasebeta

← C2×#11744095 #14261631

Subgroups — C2×#11744095 #14261631

Order 1792.

6338 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#557C211yesmaximal, characteristic, complemented
2#11744095C2132yesmaximal, direct product factor
3C2×#90422C212yesmaximal
4C2×#90412C211yesmaximal, characteristic, complemented
5C2×#90412C212yesmaximal, complemented
6C2×#90419C211yesmaximal, characteristic
7C2×#90388C212yesmaximal
8C2×C7⋊#564C214yesmaximal, complemented
9C2×#90376C212yesmaximal, complemented
10C2×#90387C214yesmaximal
11C2×#90274C212yesmaximal
12C2×#90274C212yesmaximal
13C2×#90269C211yesmaximal, characteristic
14C2×#90269C211yesmaximal, characteristic
15C2×#90260C212yesmaximal, complemented
16C2×#90258C211yesmaximal, characteristic, complemented
17C2×#90258C212yesmaximal, complemented
18C2×#90261C211yesmaximal, characteristic, complemented
19C7×#557C22116yescomplemented
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×C4⋊Q8C2212yes—
22C2×C7×#125C2214yes—
23C2×C7×#125C2212yes—
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×Q8C2212yes—
27C2×C4×C7×Q8C2212yes—
28C2×#6509C2212yes—
29C2×#6509C2211yescharacteristic
30C2×#6509C2211yescharacteristic
31C2×Q8×Dic7C2212yes—
32C2×Q8×Dic7C2212yes—
33C2×Q8×Dic7C2212yes—
34C2×#6507C2211yescharacteristic
35C2×#6507C2212yes—
36C2×#6507C2211yescharacteristic
37C2×#6507C2212yes—
38#90422C22132yes—
39#90419C22116yes—
40#90412C22116yescomplemented
41#90412C22132yescomplemented
42#90388C22132yes—
43#90387C22164yes—
44C7⋊#564C22164yescomplemented
45#90376C22132yescomplemented
46#90274C22132yes—
47#90274C22132yes—
48#90269C22116yes—
49#90269C22116yes—
50#90261C22116yescomplemented
51#90260C22132yescomplemented
52#90258C22132yescomplemented
53#90258C22116yescomplemented
54C2×#6461C2214yes—
55C2×#6461C2214yes—
56C2×#6461C2214yes—
57C2×#6460C2212yes—
58C2×#6460C2211yescharacteristic
59C2×#6460C2211yescharacteristic
60C2×#6459C2212yes—
61C2×#6459C2212yes—
62C2×#6455C2212yes—
63C2×#6453C2212yes—
64C2×#6453C2212yes—
65C2×#6453C2214yes—
66C2×#6453C2212yes—
67C2×#6453C2214yes—
68C2×#6453C2214yes—
69C2×#6452C2214yes—
70C2×#6452C2214yes—
71C2×#6452C2214yes—
72C2×#6452C2214yes—
73C2×#6452C2214yes—
74C2×#6452C2214yes—
75C2×#6452C2212yes—
76C2×#6452C2212yes—
77C2×#6452C2214yes—
78C2×#6451C2211yescharacteristic
79C2×#6451C2214yes—
80C2×#6451C2211yescharacteristic
81C2×#6450C2212yes—
82C2×#6450C2212yes—
83C2×#6450C2214yes—
84C2×#6450C2212yes—
85C2×#6439C2214yes—
86C2×#6435C2212yes—
87C2×#6435C2212yes—
88C2×C42×D7C2211yescharacteristic
89C2×#6433C2212yes—
90C2×#6433C2214yes—
91C2×#6433C2214yes—
92C2×#6432C2211yescharacteristic
93C2×#6432C2212yes—
94C2×C4×Dic14C2211yescharacteristic
95C2×C4×Dic14C2211yescharacteristic
96C2×C4×Dic14C2212yes—
97C2×C4×Dic14C2212yes—
98C2×C4×Dic14C2212yes—
99C2×C4×Dic14C2214yes—
100C2×C4×Dic14C2212yes—
101C2×#3556—71nomaximal, Sylow
102C22×C7×Q8C2311yescharacteristic
103C22×C7×Q8C2311yescharacteristic
104C22×C7×Q8C2312yes—
105C22×C4×D7C2311yescharacteristic
106C22×C4×D7C2311yescharacteristic
107C22×C4×D7C2311yescharacteristic
108C22×Dic14C2312yes—
109C22×Dic14C2311yescharacteristic
110C22×Dic14C2311yescharacteristic
111C22×Dic14C2312yes—
112C22×Dic14C2312yes—
113C7×C4⋊Q8C2318yes—
114C7×C4⋊Q8C23116yes—
115C7×#125C23116yes—
116C7×#125C23132yes—
117C4×C7×Q8C2318yes—
118C4×C7×Q8C23116yes—
119C4×C7×Q8C23116yes—
120C4×C7×Q8C2318yes—
121C2×C7×C4⋊C4C2311yescharacteristic
122C2×C7×C4⋊C4C2312yes—
123C2×C7×C4⋊C4C2314yes—
124C2×C7×C4⋊C4C2314yes—
125C2×C7×C4⋊C4C2311yescharacteristic
126C2×C7×C4⋊C4C2312yes—
127C2×C7×C4⋊C4C2314yes—
128C2×C7×C4⋊C4C2312yes—
129C2×C7×C4⋊C4C2312yes—
130C2×C42×C7C2311yescharacteristic
131C2×C42×C7C2312yes—
132C2×C42×C7C2312yes—
133C2×C42×C7C2314yes—
134#6509C23116yes—
135#6509C2318yes—
136#6509C2318yes—
137Q8×Dic7C23116yes—
138Q8×Dic7C23116yes—
139Q8×Dic7C23116yes—
140#6507C2318yes—
141#6507C23116yes—
142#6507C2318yes—
143#6507C23116yes—
144C2×(C2×D7)⋊C4C2312yes—
145C2×(C2×D7)⋊C4C2312yes—
146C2×(C2×D7)⋊C4C2312yes—
147C2×(C2×D7)⋊C4C2312yes—
148C2×(C2×D7)⋊C4C2314yes—
149C2×C4⋊Dic7C2311yescharacteristic
150C2×C4⋊Dic7C2314yes—
151C2×C4⋊Dic7C2312yes—
152C2×C4⋊Dic7C2311yescharacteristic
153C2×C4⋊Dic7C2312yes—
154C2×C4⋊Dic7C2312yes—
155C2×C4⋊Dic7C2312yes—
156C2×C4⋊Dic7C2314yes—
157C2×C4⋊Dic7C2314yes—
158C2×C4⋊Dic7C2314yes—
159C2×Dic7⋊C4C2312yes—
160C2×Dic7⋊C4C2312yes—
161C2×Dic7⋊C4C2314yes—
162C2×Dic7⋊C4C2314yes—
163C2×Dic7⋊C4C2314yes—
164C2×Dic7⋊C4C2312yes—
165C2×Dic7⋊C4C2312yes—
166C2×Dic7⋊C4C2312yes—
167C2×Dic7⋊C4C2312yes—
168C2×Dic7⋊C4C2312yes—
169C2×Dic7⋊C4C2312yes—
170C2×Dic7⋊C4C2314yes—
171C2×Dic7⋊C4C2314yes—
172C2×Dic7⋊C4C2314yes—
173C2×Dic7⋊C4C2312yes—
174C2×Dic7⋊C4C2312yes—
175C2×Dic7⋊C4C2314yes—
176C2×C4×Dic7C2311yescharacteristic
177C2×C4×Dic7C2311yescharacteristic
178C2×C4×Dic7C2312yes—
179C2×C4×Dic7C2312yes—
180C2×C4×Dic7C2314yes—
181C2×C4×Dic7C2314yes—
182C2×C4×Dic7C2314yes—
183C2×C4×Dic7C2314yes—
184C2×C4×Dic7C2311yescharacteristic
185#6461C23132yes—
186#6461C23132yes—
187#6461C23132yes—
188#6460C2318yes—
189#6460C23116yes—
190#6460C2318yes—
191#6459C23116yes—
192#6459C23116yes—
193#6455C23116yes—
194#6453C23116yes—
195#6453C23116yes—
196#6453C23132yes—
197#6453C23132yes—
198#6453C23132yes—
199#6453C23116yes—
200#6452C23132yes—
201#6452C23132yes—
202#6452C23116yes—
203#6452C23116yes—
204#6452C23132yes—
205#6452C23132yes—
206#6452C23132yes—
207#6452C23132yes—
208#6452C23132yes—
209#6451C2318yes—
210#6451C23132yes—
211#6451C2318yes—
212#6450C23132yes—
213#6450C23116yes—
214#6450C23116yes—
215#6450C23116yes—
216#6439C23132yes—
217#6435C23116yes—
218#6435C23116yes—
219C42×D7C2318yes—
220#6433C23132yes—
221#6433C23132yes—
222#6433C23116yes—
223#6432C23116yes—
224#6432C2318yes—
225C4×Dic14C23116yes—
226C4×Dic14C23116yes—
227C4×Dic14C23132yes—
228C4×Dic14C2318yes—
229C4×Dic14C23116yes—
230C4×Dic14C23116yes—
231C4×Dic14C2318yes—
232#3556—732no—
233C2×#564—74no—
234C2×#557—72no—
235C2×#557—71no—
236C2×#557—72no—
237C2×#557—71no—
238C2×#557—72no—
239C2×#557—71no—
240C2×#557—72no—
241C2×#557D711yescharacteristic, complemented
242C2×#541—72no—
243C2×#541—74no—
244C2×#541—72no—
245C2×#541—72no—
246C2×#541—72no—
247C2×#533—71no—
248C2×#533—71no—
249C2×#533—71no—
250C23×D7C2411yescharacteristic
251C2×C7×Q8—24no—
252C2×C7×Q8—24no—
253C2×C7×Q8—28no—
254C2×C7×Q8C2414yes—
255C2×C7×Q8C2414yes—
256C2×C7×Q8C2418yes—
257C22×C4×C7C2414yes—
258C22×C4×C7C2412yes—
259C22×C4×C7C2412yes—
260C22×C4×C7C2411yescharacteristic
261C22×C4×C7C2412yes—
262C22×C4×C7C2412yes—
263C22×C4×C7C2411yescharacteristic
264C22×C4×C7C2411yescharacteristic
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2414yes—
270C22×Dic7C2411yescharacteristic
271C22×Dic7C2411yescharacteristic
272C22×Dic7C2411yescharacteristic
273C2×C4×D7—24no—
274C2×C4×D7—24no—
275C2×C4×D7—24no—
276C2×C4×D7C2414yes—
277C2×C4×D7C2414yes—
278C2×C4×D7C2414yes—
279C2×Dic14—24no—
280C2×Dic14—28no—
281C2×Dic14—24no—
282C2×Dic14—28no—
283C2×Dic14—28no—
284C2×Dic14C2418yes—
285C2×Dic14C2414yes—
286C2×Dic14C2418yes—
287C2×Dic14C2414yes—
288C2×Dic14C2418yes—
289C7×C4⋊C4C2414yes—
290C7×C4⋊C4C2418yes—
291C7×C4⋊C4C24116yes—
292C7×C4⋊C4C24116yes—
293C7×C4⋊C4C2414yes—
294C7×C4⋊C4C2418yes—
295C7×C4⋊C4C24116yes—
296C7×C4⋊C4C2418yes—
297C7×C4⋊C4C2418yes—
298C42×C7C2414yes—
299C42×C7C2418yes—
300C42×C7C2418yes—
301C42×C7C24116yes—
302(C2×D7)⋊C4C2418yes—
303(C2×D7)⋊C4C2418yes—
304(C2×D7)⋊C4C2418yes—
305(C2×D7)⋊C4C2418yes—
306(C2×D7)⋊C4C24116yes—
307C4⋊Dic7C2414yes—
308C4⋊Dic7C24116yes—
309C4⋊Dic7C2418yes—
310C4⋊Dic7C2414yes—
311C4⋊Dic7C2418yes—
312C4⋊Dic7C2418yes—
313C4⋊Dic7C2418yes—
314C4⋊Dic7C24116yes—
315C4⋊Dic7C24116yes—
316C4⋊Dic7C24116yes—
317Dic7⋊C4C2418yes—
318Dic7⋊C4C2418yes—
319Dic7⋊C4C24116yes—
320Dic7⋊C4C24116yes—
321Dic7⋊C4C24116yes—
322Dic7⋊C4C2418yes—
323Dic7⋊C4C2418yes—
324Dic7⋊C4C2418yes—
325Dic7⋊C4C2418yes—
326Dic7⋊C4C2418yes—
327Dic7⋊C4C2418yes—
328Dic7⋊C4C24116yes—
329Dic7⋊C4C24116yes—
330Dic7⋊C4C24116yes—
331Dic7⋊C4C2418yes—
332Dic7⋊C4C2418yes—
333Dic7⋊C4C24116yes—
334C4×Dic7C2414yes—
335C4×Dic7C2414yes—
336C4×Dic7C2418yes—
337C4×Dic7C2418yes—
338C4×Dic7C24116yes—
339C4×Dic7C24116yes—
340C4×Dic7C24116yes—
341C4×Dic7C24116yes—
342C4×Dic7C2414yes—
343#564—764no—
344#557—732no—
345#557—716no—
346#557—732no—
347#557—732no—
348#557—716no—
349#557—732no—
350#557—716no—
351#557C2×D7116yescomplemented
352#541—732no—
353#541—764no—
354#541—732no—
355#541—732no—
356#541—732no—
357#533—716no—
358#533—716no—
359#533—716no—
360C2×C4⋊Q8—71no—
361C2×C4⋊Q8—71no—
362C2×C4⋊Q8—72no—
363C2×C4⋊Q8—72no—
364C2×C4⋊Q8—71no—
365C2×C4⋊Q8—71no—
366C2×C4⋊Q8—74no—
367C2×C4⋊Q8—71no—
368C2×C4⋊Q8—72no—
369C2×C4⋊Q8C2×D711yescharacteristic
370C2×C4⋊Q8C2×D712yes—
371C2×#126—74no—
372C2×#126—74no—
373C2×#126—74no—
374C2×#126—74no—
375C2×#125—72no—
376C2×#125—72no—
377C2×#125—74no—
378C2×#125—74no—
379C2×#125—74no—
380C2×#125—74no—
381C2×#125—74no—
382C2×#125—74no—
383C2×#125—74no—
384C2×#125—72no—
385C2×#125—72no—
386C2×#125—72no—
387C2×#125—74no—
388C2×#125—74no—
389C2×#125—74no—
390C2×#125—72no—
391C2×#125—74no—
392C2×#125—74no—
393C2×#125C2×D712yes—
394C2×#125C2×D714yes—
395C2×C22⋊Q8—72no—
396C2×C22⋊Q8—71no—
397C2×C22⋊Q8—71no—
398C2×C22⋊Q8—72no—
399C2×C22⋊Q8—72no—
400C2×C22⋊Q8—72no—
401C2×C22⋊Q8—71no—
402C2×C22⋊Q8—71no—
403C2×C4×Q8—72no—
404C2×C4×Q8—72no—
405C2×C4×Q8—72no—
406C2×C4×Q8—72no—
407C2×C4×Q8—74no—
408C2×C4×Q8—72no—
409C2×C4×Q8—72no—
410C2×C4×Q8—71no—
411C2×C4×Q8—71no—
412C2×C4×Q8—72no—
413C2×C4×Q8—72no—
414C2×C4×Q8—74no—
415C2×C4×Q8—72no—
416C2×C4×Q8—72no—
417C2×C4×Q8C2×D711yescharacteristic
418C2×C4×Q8C2×D711yescharacteristic
419C2×C4×Q8C2×D712yes—
420C2×C4×Q8C2×D712yes—
421C2×#117—72no—
422C2×#117—72no—
423C2×#117—72no—
424C22×C42—71no—
425C23×C7C2511yescharacteristic
426C22×D7—22no—
427C22×D7—22no—
428C22×D7—22no—
429C22×D7C2512yes—
430C7×Q8—28no—
431C7×Q8—28no—
432C7×Q8—216no—
433C2×C4×C7—24no—
434C2×C4×C7—24no—
435C2×C4×C7—22no—
436C2×C4×C7—24no—
437C2×C4×C7—28no—
438C2×C4×C7—24no—
439C2×C4×C72−1+414yes—
440C2×C4×C72−1+414yes—
441C2×C4×C7C2518yes—
442C2×C4×C7C2514yes—
443C2×C4×C7C2514yes—
444C2×C4×C7C2512yes—
445C2×C4×C7C2514yes—
446C2×C4×C7C2514yes—
447C2×C4×C7C2512yes—
448C2×C4×C7C2512yes—
449C2×Dic7—24no—
450C2×Dic7—28no—
451C2×Dic7—24no—
452C2×Dic7—24no—
453C2×Dic7—24no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic72−1+414yes—
457C2×Dic7C2514yes—
458C2×Dic7C2514yes—
459C2×Dic7C2514yes—
460C2×Dic7C2514yes—
461C2×Dic7C2518yes—
462C2×Dic7C2512yes—
463C2×Dic7C2512yes—
464C2×Dic7C2512yes—
465C4×D7—28no—
466C4×D7—28no—
467C4×D7—28no—
468Dic14—216no—
469Dic14—28no—
470Dic14—28no—
471Dic14—216no—
472Dic14—216no—
473C22×Q8—72no—
474C22×Q8—72no—
475C22×Q8—72no—
476C22×Q8—71no—
477C22×Q8—71no—
478C22×Q8C22×D712yes—
479C22×Q8C22×D711yescharacteristic
480C22×Q8C22×D711yescharacteristic
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—71no—
484C4⋊Q8—78no—
485C4⋊Q8—78no—
486C4⋊Q8—716no—
487C4⋊Q8—716no—
488C4⋊Q8—78no—
489C4⋊Q8—78no—
490C4⋊Q8—732no—
491C4⋊Q8—78no—
492C4⋊Q8—716no—
493C4⋊Q8C22×D718yes—
494C4⋊Q8C22×D7116yes—
495#126—732no—
496#126—732no—
497#126—732no—
498#126—732no—
499#125—716no—
500#125—716no—
501#125—716no—
502#125—732no—
503#125—716no—
504#125—716no—
505#125—732no—
506#125—732no—
507#125—732no—
508#125—732no—
509#125—732no—
510#125—732no—
511#125—732no—
512#125—732no—
513#125—732no—
514#125—716no—
515#125—732no—
516#125—732no—
517#125C22×D7116yes—
518#125C22×D7132yes—
519C22⋊Q8—716no—
520C22⋊Q8—78no—
521C22⋊Q8—78no—
522C22⋊Q8—716no—
523C22⋊Q8—716no—
524C22⋊Q8—716no—
525C22⋊Q8—78no—
526C22⋊Q8—78no—
527C4×Q8—716no—
528C4×Q8—716no—
529C4×Q8—716no—
530C4×Q8—716no—
531C4×Q8—732no—
532C4×Q8—716no—
533C4×Q8—716no—
534C4×Q8—716no—
535C4×Q8—716no—
536C4×Q8—78no—
537C4×Q8—78no—
538C4×Q8—732no—
539C4×Q8—716no—
540C4×Q8—716no—
541C4×Q8C22×D718yes—
542C4×Q8C22×D718yes—
543C4×Q8C22×D7116yes—
544C4×Q8C22×D7116yes—
545#117—716no—
546#117—716no—
547#117—716no—
548C2×C4⋊C4—72no—
549C2×C4⋊C4—72no—
550C2×C4⋊C4—72no—
551C2×C4⋊C4—72no—
552C2×C4⋊C4—72no—
553C2×C4⋊C4—72no—
554C2×C4⋊C4—72no—
555C2×C4⋊C4—71no—
556C2×C4⋊C4—72no—
557C2×C4⋊C4—71no—
558C2×C4⋊C4—72no—
559C2×C4⋊C4—72no—
560C2×C4⋊C4—74no—
561C2×C4⋊C4—72no—
562C2×C4⋊C4—72no—
563C2×C4⋊C4—74no—
564C2×C4⋊C4—72no—
565C2×C4⋊C4—72no—
566C2×C4⋊C4—74no—
567C2×C4⋊C4—74no—
568C2×C4⋊C4—74no—
569C2×C4⋊C4—74no—
570C2×C4⋊C4—74no—
571C2×C4⋊C4—74no—
572C2×C4⋊C4—74no—
573C2×C4⋊C4—74no—
574C2×C4⋊C4—74no—
575C2×C4⋊C4C22×D712yes—
576C2×C4⋊C4C22×D712yes—
577C2×C4⋊C4C22×D711yescharacteristic
578C2×C4⋊C4C22×D714yes—
579C2×C4⋊C4C22×D711yescharacteristic
580C2×C4⋊C4C22×D712yes—
581C2×C4⋊C4C22×D712yes—
582C2×C4⋊C4C22×D714yes—
583C2×C4⋊C4C22×D714yes—
584C2×C22⋊C4—74no—
585C2×C22⋊C4—72no—
586C2×C22⋊C4—72no—
587C2×C22⋊C4—72no—
588C2×C22⋊C4—72no—
589C2×C42—74no—
590C2×C42—72no—
591C2×C42—72no—
592C2×C42—71no—
593C2×C42—71no—
594C2×C42—74no—
595C2×C42—74no—
596C2×C42—74no—
597C2×C42—71no—
598C2×C42—78no—
599C2×C42C22×D712yes—
600C2×C42C22×D712yes—
601C2×C42C22×D711yescharacteristic
602C2×C42C22×D714yes—
603C22×C7C2×2−1+412yes—
604C22×C7C2×2−1+412yes—
605C22×C7C2×2−1+412yes—
606C22×C7C2611yescharacteristic
607C2×D7—22no—
608C2×D7—22no—
609C2×D7—22no—
610C2×D7—44no—
611C4×C7—24no—
612C4×C7—24no—
613C4×C7—22no—
614C4×C7—24no—
615C4×C7—28no—
616C4×C7—24no—
617C4×C7C2×2−1+414yes—
618C4×C7C2×2−1+414yes—
619Dic7—24no—
620Dic7—28no—
621Dic7—24no—
622Dic7—24no—
623Dic7—24no—
624Dic7—22no—
625Dic7—22no—
626Dic7C2×2−1+414yes—
627C24—71no—
628C2×Q8—24no—
629C2×Q8—28no—
630C2×Q8—24no—
631C2×Q8—78no—
632C2×Q8—78no—
633C2×Q8—78no—
634C2×Q8—74no—
635C2×Q8—74no—
636C2×Q8—148no—
637C2×Q8—148no—
638C2×Q8—148no—
639C2×Q8—144no—
640C2×Q8—144no—
641C2×Q8C23×D718yes—
642C2×Q8C23×D714yes—
643C2×Q8C23×D714yes—
644C22×C4—71no—
645C22×C4—72no—
646C22×C4—74no—
647C22×C4—72no—
648C22×C4—72no—
649C22×C4—72no—
650C22×C4—71no—
651C22×C4—71no—
652C22×C4—74no—
653C22×C4—74no—
654C22×C4—74no—
655C22×C4—144no—
656C22×C4—144no—
657C22×C4—144no—
658C22×C4C23×D714yes—
659C22×C4C23×D712yes—
660C22×C4C23×D712yes—
661C22×C4C23×D711yescharacteristic
662C22×C4C23×D712yes—
663C22×C4C23×D712yes—
664C22×C4C23×D711yescharacteristic
665C22×C4C23×D711yescharacteristic
666C4⋊C4—78no—
667C4⋊C4—78no—
668C4⋊C4—78no—
669C4⋊C4—78no—
670C4⋊C4—78no—
671C4⋊C4—78no—
672C4⋊C4—78no—
673C4⋊C4—78no—
674C4⋊C4—78no—
675C4⋊C4—716no—
676C4⋊C4—78no—
677C4⋊C4—716no—
678C4⋊C4—716no—
679C4⋊C4—716no—
680C4⋊C4—716no—
681C4⋊C4—716no—
682C4⋊C4—716no—
683C4⋊C4—78no—
684C4⋊C4—74no—
685C4⋊C4—78no—
686C4⋊C4—74no—
687C4⋊C4—716no—
688C4⋊C4—78no—
689C4⋊C4—78no—
690C4⋊C4—716no—
691C4⋊C4—716no—
692C4⋊C4—716no—
693C4⋊C4C23×D718yes—
694C4⋊C4C23×D718yes—
695C4⋊C4C23×D714yes—
696C4⋊C4C23×D7116yes—
697C4⋊C4C23×D714yes—
698C4⋊C4C23×D718yes—
699C4⋊C4C23×D718yes—
700C4⋊C4C23×D7116yes—
701C4⋊C4C23×D7116yes—
702C22⋊C4—78no—
703C22⋊C4—716no—
704C22⋊C4—78no—
705C22⋊C4—78no—
706C22⋊C4—78no—
707C42—74no—
708C42—74no—
709C42—74no—
710C42—716no—
711C42—78no—
712C42—78no—
713C42—716no—
714C42—716no—
715C42—716no—
716C42C23×D714yes—
717C42C23×D718yes—
718C42C23×D718yes—
719C42C23×D7116yes—
720C2×C7#355614yescomplemented
721C2×C7C22×2−1+411yescharacteristic
722C2×C7C22×2−1+411yescharacteristic
723C2×C7C22×2−1+411yescharacteristic
724D7—42no—
725C23—72no—
726C23—142no—
727C23—142no—
728C23—142no—
729C23C24×D711yescharacteristic
730Q8—28no—
731Q8—216no—
732Q8—28no—
733Q8—1416no—
734Q8—1416no—
735Q8—1416no—
736Q8—148no—
737Q8—148no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—72no—
745C2×C4—74no—
746C2×C4—74no—
747C2×C4—78no—
748C2×C4—74no—
749C2×C4—74no—
750C2×C4—74no—
751C2×C4—72no—
752C2×C4—72no—
753C2×C4—148no—
754C2×C4—142no—
755C2×C4—144no—
756C2×C4—148no—
757C2×C4—142no—
758C2×C4—144no—
759C2×C4—144no—
760C2×C4—144no—
761C2×C4—148no—
762C2×C4—148no—
763C2×C4#655114yes—
764C2×C4#655414yes—
765C2×C4C24×D718yes—
766C2×C4C24×D714yes—
767C2×C4C24×D714yes—
768C2×C4C24×D712yes—
769C2×C4C24×D714yes—
770C2×C4C24×D714yes—
771C2×C4C24×D712yes—
772C2×C4C24×D712yes—
773C7C2×#355611yescharacteristic, complemented, Sylow
774C22—142no—
775C22—142no—
776C22—142no—
777C22—284no—
778C22C2×#655112yes—
779C22C2×#655412yes—
780C22D7×2−1+412yes—
781C22C25×D711yescharacteristic
782C4—24no—
783C4—28no—
784C4—24no—
785C4—22no—
786C4—24no—
787C4—24no—
788C4—74no—
789C4—142no—
790C4—144no—
791C4—148no—
792C4—142no—
793C4—144no—
794C4—144no—
795C4—144no—
796C4C2×#655114yes—
797C4C2×#655414yes—
798C2—282no—
799C2#1174409514yesdirect product factor
800C2C22×#655111yescharacteristic
801C2C22×#655411yescharacteristic
802C2C2×D7×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#557C2
socleC23×C7C25
prime radicalC23×D7C24
hypercenterC2×#557D7
hypocenterC7C2×#3556
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C7×#557C2semidirect
2. #11744095C2direct (N × H)
4. C2×#90412C2semidirect
5. C2×#90412C2semidirect
8. C2×C7⋊#564C2semidirect
9. C2×#90376C2semidirect
15. C2×#90260C2semidirect
16. C2×#90258C2semidirect
17. C2×#90258C2semidirect
18. C2×#90261C2semidirect
19. C7×#557C22semidirect
40. #90412C22semidirect
41. #90412C22semidirect
44. C7⋊#564C22semidirect
45. #90376C22semidirect
50. #90261C22semidirect
51. #90260C22semidirect
52. #90258C22semidirect
53. #90258C22semidirect
241. C2×#557D7semidirect
351. #557C2×D7semidirect
720. C2×C7#3556semidirect
773. C7C2×#3556semidirect
799. C2#11744095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
#117440952
C2×#904222
C2×#904122
C2×#904192
C2×#903882
C2×C7⋊#5642
C2×#903762
C2×#903872
C2×#902742
C2×#902692
C2×#902602
C2×#902582
C2×#902612
C2×#35567