Finite Group Databasebeta

← C2×#11743337 #14261512

Subgroups — C2×#11743337 #14261512

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#11743337C2132yesmaximal, direct product factor
3C2×#90421C211yesmaximal, characteristic, complemented
4C2×#90413C211yesmaximal, characteristic, complemented
5C2×#90412C211yesmaximal, characteristic, complemented
6C2×#90423C211yesmaximal, characteristic, complemented
7C2×#90380C212yesmaximal, complemented
8C2×#90388C212yesmaximal, complemented
9C2×#90337C214yesmaximal, complemented
10C2×#90334C212yesmaximal
11C2×#90316C212yesmaximal, complemented
12C2×#90274C214yesmaximal, complemented
13C2×#90260C212yesmaximal, complemented
14C2×#90259C212yesmaximal, complemented
15C2×#90224C212yesmaximal, complemented
16C2×#90220C212yesmaximal, complemented
17C2×#90170C211yesmaximal, characteristic
18C2×#90161C211yesmaximal, characteristic, complemented
19C7×#533C22116yescomplemented
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×C4⋊Q8C2211yescharacteristic
22C2×C7×#125C2212yes—
23C2×C7×C22⋊Q8C2212yes—
24C2×C7×C22⋊Q8C2212yes—
25C2×C4×C7×Q8C2212yes—
26C2×C4×C7×Q8C2212yes—
27C2×C7×#117C2212yes—
28C22×C42×C7C2211yescharacteristic
29C2×#6510C2212yes—
30C2×#6509C2214yes—
31C2×Q8×Dic7C2212yes—
32C2×Q8×Dic7C2212yes—
33C2×#6507C2212yes—
34C2×#6507C2214yes—
35C2×#6493C2211yescharacteristic
36C2×#6492C2212yes—
37C2×C4×C22⋊D7C2212yes—
38C2×#6489C2212yes—
39C2×#6487C2212yes—
40C2×#6487C2211yescharacteristic
41C2×#6487C2211yescharacteristic
42C2×#6487C2211yescharacteristic
43#90423C22116yescomplemented
44#90421C22116yescomplemented
45#90413C22116yescomplemented
46#90412C22116yescomplemented
47#90388C22132yescomplemented
48#90380C22132yescomplemented
49#90337C22164yescomplemented
50#90334C22132yes—
51#90316C22132yescomplemented
52#90274C22164yescomplemented
53#90260C22132yescomplemented
54#90259C22132yescomplemented
55#90224C22132yescomplemented
56#90220C22132yescomplemented
57C2×#6461C2214yes—
58C2×#6461C2214yes—
59C2×#6461C2214yes—
60C2×#6460C2212yes—
61C2×#6460C2212yes—
62C2×#6460C2214yes—
63C2×#6459C2214yes—
64C2×#6456C2212yes—
65C2×#6455C2212yes—
66C2×D7×C4⋊C4C2212yes—
67C2×#6453C2212yes—
68C2×#6453C2212yes—
69C2×#6453C2214yes—
70C2×#6453C2214yes—
71C2×#6452C2214yes—
72C2×#6452C2214yes—
73C2×#6451C2212yes—
74C2×#6451C2212yes—
75C2×#6451C2214yes—
76C2×#6450C2212yes—
77C2×#6450C2212yes—
78C2×#6450C2212yes—
79C2×#6448C2214yes—
80C2×#6446C2214yes—
81C2×#6442C2214yes—
82C2×#6442C2214yes—
83#90170C22116yes—
84C2×#6439C2212yes—
85C2×#6439C2214yes—
86C2×#6438C2211yescharacteristic
87C2×C4×D28C2211yescharacteristic
88C2×#6435C2212yes—
89C2×#6435C2214yes—
90#90161C22116yescomplemented
91C2×#6433C2212yes—
92C2×#6433C2211yescharacteristic
93C2×#6433C2214yes—
94C2×#6432C2211yescharacteristic
95C2×#6432C2211yescharacteristic
96C2×C4×Dic14C2211yescharacteristic
97C2×C4×Dic14C2211yescharacteristic
98C2×C4×Dic14C2212yes—
99C2×C4×Dic14C2211yescharacteristic
100C2×C4×Dic14C2214yes—
101C2×#3555—71nomaximal, Sylow
102C22×C7×Q8C2312yes—
103C22×C7×Q8C2312yes—
104C23×C4×C7C2311yescharacteristic
105C23×C4×C7C2311yescharacteristic
106C23×C4×C7C2311yescharacteristic
107C22×C22⋊D7C2312yes—
108C22×D28C2311yescharacteristic
109C22×C4×D7C2312yes—
110C22×C4×D7C2314yes—
111C22×Dic14C2311yescharacteristic
112C22×Dic14C2311yescharacteristic
113C22×Dic14C2311yescharacteristic
114C22×Dic14C2312yes—
115C22×Dic14C2314yes—
116C7×C4⋊Q8C2318yes—
117C7×C4⋊Q8C2318yes—
118C7×#125C23116yes—
119C7×C22⋊Q8C23116yes—
120C7×C22⋊Q8C23116yes—
121C4×C7×Q8C23116yes—
122C4×C7×Q8C23116yes—
123C7×#117C23116yes—
124C2×C7×C4⋊C4C2312yes—
125C2×C7×C4⋊C4C2312yes—
126C2×C7×C4⋊C4C2312yes—
127C2×C7×C4⋊C4C2314yes—
128C2×C7×C4⋊C4C2312yes—
129C2×C7×C4⋊C4C2314yes—
130C2×C7×C22⋊C4C2314yes—
131C2×C42×C7C2311yescharacteristic
132C2×C42×C7C2311yescharacteristic
133C2×C42×C7C2314yes—
134C2×C42×C7C2311yescharacteristic
135C2×C42×C7C2311yescharacteristic
136C2×C42×C7C2318yes—
137C2×C22⋊Dic7C2312yes—
138C2×C22⋊Dic7C2312yes—
139C2×C22⋊Dic7C2312yes—
140#6510C23116yes—
141#6509C23132yes—
142Q8×Dic7C23116yes—
143Q8×Dic7C23116yes—
144#6507C23116yes—
145#6507C23132yes—
146#6493C2318yes—
147#6492C23116yes—
148C4×C22⋊D7C23116yes—
149C2×(C2×D7)⋊C4C2312yes—
150C2×(C2×D7)⋊C4C2312yes—
151C2×(C2×D7)⋊C4C2312yes—
152C2×(C2×D7)⋊C4C2314yes—
153C2×(C2×D7)⋊C4C2312yes—
154C2×(C2×D7)⋊C4C2314yes—
155C2×(C2×D7)⋊C4C2314yes—
156#6489C23116yes—
157C2×C4⋊Dic7C2311yescharacteristic
158C2×C4⋊Dic7C2311yescharacteristic
159C2×C4⋊Dic7C2312yes—
160C2×C4⋊Dic7C2311yescharacteristic
161C2×C4⋊Dic7C2314yes—
162C2×C4⋊Dic7C2312yes—
163C2×C4⋊Dic7C2312yes—
164C2×C4⋊Dic7C2311yescharacteristic
165C2×C4⋊Dic7C2314yes—
166C2×C4⋊Dic7C2314yes—
167#6487C2318yes—
168#6487C2318yes—
169#6487C23116yes—
170#6487C2318yes—
171C2×Dic7⋊C4C2312yes—
172C2×Dic7⋊C4C2312yes—
173C2×Dic7⋊C4C2312yes—
174C2×Dic7⋊C4C2312yes—
175C2×Dic7⋊C4C2312yes—
176C2×Dic7⋊C4C2312yes—
177C2×Dic7⋊C4C2312yes—
178C2×Dic7⋊C4C2314yes—
179C2×Dic7⋊C4C2314yes—
180C2×Dic7⋊C4C2312yes—
181C2×Dic7⋊C4C2314yes—
182C2×Dic7⋊C4C2314yes—
183C2×Dic7⋊C4C2314yes—
184C2×C4×Dic7C2312yes—
185C2×C4×Dic7C2312yes—
186C2×C4×Dic7C2312yes—
187C2×C4×Dic7C2314yes—
188C2×C4×Dic7C2314yes—
189C2×C4×Dic7C2314yes—
190#6461C23132yes—
191#6461C23132yes—
192#6461C23132yes—
193#6460C23132yes—
194#6460C23116yes—
195#6460C23116yes—
196#6459C23132yes—
197#6456C23116yes—
198#6455C23116yes—
199D7×C4⋊C4C23116yes—
200#6453C23116yes—
201#6453C23132yes—
202#6453C23132yes—
203#6453C23116yes—
204#6452C23132yes—
205#6452C23132yes—
206#6451C23116yes—
207#6451C23132yes—
208#6451C23116yes—
209#6450C23116yes—
210#6450C23116yes—
211#6450C23116yes—
212#6448C23132yes—
213#6446C23132yes—
214#6442C23132yes—
215#6442C23132yes—
216#6439C23116yes—
217#6439C23132yes—
218#6438C2318yes—
219C4×D28C2318yes—
220#6435C23116yes—
221#6435C23132yes—
222#6433C23116yes—
223#6433C2318yes—
224#6433C23132yes—
225#6432C2318yes—
226#6432C2318yes—
227C4×Dic14C2318yes—
228C4×Dic14C2318yes—
229C4×Dic14C2318yes—
230C4×Dic14C23116yes—
231C4×Dic14C23132yes—
232#3555—732no—
233C2×#563—74no—
234C2×Q82—71no—
235C2×#557—71no—
236C2×#557—72no—
237C2×#556—71no—
238C2×#556—72no—
239C2×#556—72no—
240C2×#554—71no—
241C2×#552—72no—
242C2×#544—72no—
243C2×#542—72no—
244C2×#541—72no—
245C2×#541—72no—
246C2×#541—74no—
247C2×#533—71no—
248C2×#533D711yescharacteristic, complemented
249C2×#529—71no—
250C24×C7C2411yescharacteristic
251C23×D7C2412yes—
252C2×C7×Q8—28no—
253C2×C7×Q8—44no—
254C2×C7×Q8C2418yes—
255C2×C7×Q8C2418yes—
256C22×C4×C7—24no—
257C22×C4×C7—24no—
258C22×C4×C7—42no—
259C22×C4×C7C2414yes—
260C22×C4×C7C2414yes—
261C22×C4×C7C2411yescharacteristic
262C22×C4×C7C2411yescharacteristic
263C22×C4×C7C2411yescharacteristic
264C22×C4×C7C2411yescharacteristic
265C22×C4×C7C2414yes—
266C22×C4×C7C2414yes—
267C22×C4×C7C2414yes—
268C22×C4×C7C2411yescharacteristic
269C22×C4×C7C2411yescharacteristic
270C2×C22⋊D7—44no—
271C2×C22⋊D7C2418yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C22×Dic7C2412yes—
275C22×Dic7C2412yes—
276C22×Dic7C2412yes—
277C22×Dic7C2412yes—
278C22×Dic7C2412yes—
279C2×D28—24no—
280C2×D28C2414yes—
281C2×C4×D7—28no—
282C2×C4×D7—48no—
283C2×C4×D7C2418yes—
284C2×C4×D7C24116yes—
285C2×Dic14—24no—
286C2×Dic14—24no—
287C2×Dic14—24no—
288C2×Dic14—48no—
289C2×Dic14—44no—
290C2×Dic14C2414yes—
291C2×Dic14C2414yes—
292C2×Dic14C2414yes—
293C2×Dic14C2418yes—
294C2×Dic14C24116yes—
295C7×C4⋊C4C2418yes—
296C7×C4⋊C4C2418yes—
297C7×C4⋊C4C2418yes—
298C7×C4⋊C4C24116yes—
299C7×C4⋊C4C2418yes—
300C7×C4⋊C4C24116yes—
301C7×C22⋊C4C24116yes—
302C42×C7C2414yes—
303C42×C7C2414yes—
304C42×C7C24116yes—
305C42×C7C2414yes—
306C42×C7C2414yes—
307C22⋊Dic7C2418yes—
308C22⋊Dic7C2418yes—
309C22⋊Dic7C2418yes—
310(C2×D7)⋊C4C2418yes—
311(C2×D7)⋊C4C2418yes—
312(C2×D7)⋊C4C2418yes—
313(C2×D7)⋊C4C24116yes—
314(C2×D7)⋊C4C2418yes—
315(C2×D7)⋊C4C24116yes—
316(C2×D7)⋊C4C24116yes—
317C4⋊Dic7C2414yes—
318C4⋊Dic7C2414yes—
319C4⋊Dic7C2418yes—
320C4⋊Dic7C2414yes—
321C4⋊Dic7C24116yes—
322C4⋊Dic7C2418yes—
323C4⋊Dic7C2418yes—
324C4⋊Dic7C2414yes—
325C4⋊Dic7C24116yes—
326C4⋊Dic7C24116yes—
327Dic7⋊C4C2418yes—
328Dic7⋊C4C2418yes—
329Dic7⋊C4C2418yes—
330Dic7⋊C4C2418yes—
331Dic7⋊C4C2418yes—
332Dic7⋊C4C2418yes—
333Dic7⋊C4C2418yes—
334Dic7⋊C4C24116yes—
335Dic7⋊C4C24116yes—
336Dic7⋊C4C2418yes—
337Dic7⋊C4C24116yes—
338Dic7⋊C4C24116yes—
339Dic7⋊C4C24116yes—
340C4×Dic7C2418yes—
341C4×Dic7C2418yes—
342C4×Dic7C2418yes—
343C4×Dic7C24116yes—
344C4×Dic7C24116yes—
345C4×Dic7C24116yes—
346#563—764no—
347Q82—716no—
348#557—716no—
349#557—732no—
350#556—716no—
351#556—732no—
352#556—732no—
353#554—716no—
354#552—732no—
355#544—732no—
356#542—732no—
357#541—732no—
358#541—732no—
359#541—764no—
360#533—716no—
361#533C2×D7116yescomplemented
362C2×C4⋊Q8—72no—
363C2×C4⋊Q8—74no—
364C2×C4⋊Q8—72no—
365C2×C4⋊Q8—72no—
366C2×C4⋊Q8—74no—
367C2×C4⋊Q8—71no—
368C2×C4⋊Q8—71no—
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—72no—
378C2×#126—74no—
379C2×#125—74no—
380C2×#125—74no—
381C2×#125—74no—
382C2×#125—72no—
383C2×#125—74no—
384C2×#125—72no—
385C2×#125—71no—
386C2×#125—72no—
387C2×#125—74no—
388C2×#125C2×D712yes—
389C2×#124—72no—
390C2×#124—74no—
391C2×#124—71no—
392C2×#123—72no—
393C2×#123—74no—
394C2×C22⋊Q8—74no—
395C2×C22⋊Q8—71no—
396C2×C22⋊Q8—71no—
397C2×C22⋊Q8—71no—
398C2×C22⋊Q8—72no—
399C2×C22⋊Q8—74no—
400C2×C22⋊Q8—74no—
401C2×C22⋊Q8—72no—
402C2×C22⋊Q8—72no—
403C2×C22⋊Q8C2×D712yes—
404C2×C22⋊Q8C2×D712yes—
405C2×#121—71no—
406C2×C4×Q8—72no—
407C2×C4×Q8—72no—
408C2×C4×Q8—72no—
409C2×C4×Q8—72no—
410C2×C4×Q8—72no—
411C2×C4×Q8—71no—
412C2×C4×Q8—71no—
413C2×C4×Q8—72no—
414C2×C4×Q8—71no—
415C2×C4×Q8—74no—
416C2×C4×Q8C2×D712yes—
417C2×C4×Q8C2×D712yes—
418C2×C4×D4—72no—
419C2×C4×D4—72no—
420C2×C4×D4—71no—
421C2×#117—72no—
422C2×#117—72no—
423C2×#117—72no—
424C2×#117—74no—
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—216no—
438C7×Q8—48no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—28no—
442C2×C4×C7—22no—
443C2×C4×C7—28no—
444C2×C4×C7—22no—
445C2×C4×C7—28no—
446C2×C4×C7—28no—
447C2×C4×C7—44no—
448C2×C4×C72−1+414yes—
449C2×C4×C72−1+414yes—
450C2×C4×C7C2518yes—
451C2×C4×C7C2518yes—
452C2×C4×C7C2512yes—
453C2×C4×C7C2512yes—
454C2×C4×C7C2512yes—
455C2×C4×C7C2512yes—
456C2×C4×C7C2512yes—
457C2×C4×C7C2512yes—
458C22⋊D7—48no—
459C2×Dic7—24no—
460C2×Dic7—24no—
461C2×Dic7—24no—
462C2×Dic7—24no—
463C2×Dic7—24no—
464C2×Dic7—24no—
465C2×Dic7—24no—
466C2×Dic7C2514yes—
467C2×Dic7C2514yes—
468C2×Dic7C2514yes—
469C2×Dic7C2514yes—
470C2×Dic7C2514yes—
471C2×Dic7C2514yes—
472C2×Dic7C2514yes—
473D28—28no—
474C4×D7—216no—
475C4×D7—416no—
476Dic14—28no—
477Dic14—28no—
478Dic14—28no—
479Dic14—416no—
480Dic14—48no—
481C22×Q8—71no—
482C22×Q8—71no—
483C22×Q8—71no—
484C22×Q8—72no—
485C22×Q8—74no—
486C22×Q8C22×D712yes—
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—716no—
496C4⋊Q8—732no—
497C4⋊Q8—716no—
498C4⋊Q8—716no—
499C4⋊Q8—732no—
500C4⋊Q8—78no—
501C4⋊Q8—78no—
502C4⋊Q8C22×D718yes—
503C4⋊Q8C22×D718yes—
504#126—732no—
505#126—732no—
506#126—732no—
507#126—732no—
508#126—732no—
509#126—716no—
510#126—732no—
511#125—732no—
512#125—732no—
513#125—716no—
514#125—732no—
515#125—732no—
516#125—716no—
517#125—78no—
518#125—716no—
519#125—732no—
520#125C22×D7116yes—
521#124—716no—
522#124—732no—
523#124—78no—
524#123—716no—
525#123—732no—
526C22⋊Q8—732no—
527C22⋊Q8—78no—
528C22⋊Q8—78no—
529C22⋊Q8—78no—
530C22⋊Q8—716no—
531C22⋊Q8—732no—
532C22⋊Q8—716no—
533C22⋊Q8—716no—
534C22⋊Q8—732no—
535C22⋊Q8C22×D7116yes—
536C22⋊Q8C22×D7116yes—
537#121—78no—
538C4×Q8—716no—
539C4×Q8—716no—
540C4×Q8—716no—
541C4×Q8—716no—
542C4×Q8—716no—
543C4×Q8—78no—
544C4×Q8—78no—
545C4×Q8—716no—
546C4×Q8—78no—
547C4×Q8—732no—
548C4×Q8C22×D7116yes—
549C4×Q8C22×D7116yes—
550C4×D4—716no—
551C4×D4—716no—
552C4×D4—78no—
553#117—716no—
554#117—716no—
555#117—716no—
556#117—732no—
557#117C22×D7116yes—
558C2×C4⋊C4—71no—
559C2×C4⋊C4—74no—
560C2×C4⋊C4—72no—
561C2×C4⋊C4—71no—
562C2×C4⋊C4—72no—
563C2×C4⋊C4—72no—
564C2×C4⋊C4—74no—
565C2×C4⋊C4—72no—
566C2×C4⋊C4—72no—
567C2×C4⋊C4—71no—
568C2×C4⋊C4—72no—
569C2×C4⋊C4—71no—
570C2×C4⋊C4—72no—
571C2×C4⋊C4—72no—
572C2×C4⋊C4—74no—
573C2×C4⋊C4—74no—
574C2×C4⋊C4—74no—
575C2×C4⋊C4—72no—
576C2×C4⋊C4—74no—
577C2×C4⋊C4—72no—
578C2×C4⋊C4—74no—
579C2×C4⋊C4—72no—
580C2×C4⋊C4—74no—
581C2×C4⋊C4—716no—
582C2×C4⋊C4C22×D712yes—
583C2×C4⋊C4C22×D712yes—
584C2×C4⋊C4C22×D712yes—
585C2×C4⋊C4C22×D714yes—
586C2×C4⋊C4C22×D714yes—
587C2×C4⋊C4C22×D712yes—
588C2×C22⋊C4—72no—
589C2×C22⋊C4—72no—
590C2×C22⋊C4—72no—
591C2×C22⋊C4—72no—
592C2×C22⋊C4—72no—
593C2×C22⋊C4—72no—
594C2×C22⋊C4—74no—
595C2×C22⋊C4—74no—
596C2×C22⋊C4—72no—
597C2×C22⋊C4—74no—
598C2×C22⋊C4C22×D714yes—
599C2×C42—72no—
600C2×C42—72no—
601C2×C42—72no—
602C2×C42—74no—
603C2×C42—74no—
604C2×C42—74no—
605C2×C42C22×D711yescharacteristic
606C2×C42C22×D714yes—
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—28no—
626C4×C7—22no—
627C4×C7—28no—
628C4×C7—22no—
629C4×C7C2×2−1+414yes—
630C4×C7C2×2−1+414yes—
631Dic7—24no—
632Dic7—24no—
633Dic7—24no—
634Dic7—24no—
635Dic7—24no—
636Dic7—24no—
637Dic7—24no—
638C24—72no—
639C24C23×D711yescharacteristic
640C2×Q8—28no—
641C2×Q8—44no—
642C2×Q8—74no—
643C2×Q8—74no—
644C2×Q8—74no—
645C2×Q8—78no—
646C2×Q8—716no—
647C2×Q8—144no—
648C2×Q8—144no—
649C2×Q8—144no—
650C2×Q8—284no—
651C2×Q8—288no—
652C2×Q8C23×D718yes—
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—72no—
662C22×C4—72no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—78no—
669C22×C4—716no—
670C22×C4—148no—
671C22×C4—288no—
672C22×C4C23×D714yes—
673C22×C4C23×D714yes—
674C22×C4C23×D714yes—
675C22×C4C23×D714yes—
676C22×C4C23×D711yescharacteristic
677C22×C4C23×D711yescharacteristic
678C22×C4C23×D711yescharacteristic
679C22×C4C23×D711yescharacteristic
680C22×C4C23×D714yes—
681C22×C4C23×D711yescharacteristic
682C22×C4C23×D711yescharacteristic
683C4⋊C4—716no—
684C4⋊C4—78no—
685C4⋊C4—78no—
686C4⋊C4—716no—
687C4⋊C4—78no—
688C4⋊C4—78no—
689C4⋊C4—78no—
690C4⋊C4—78no—
691C4⋊C4—716no—
692C4⋊C4—78no—
693C4⋊C4—716no—
694C4⋊C4—78no—
695C4⋊C4—716no—
696C4⋊C4—74no—
697C4⋊C4—74no—
698C4⋊C4—78no—
699C4⋊C4—78no—
700C4⋊C4—74no—
701C4⋊C4—74no—
702C4⋊C4—716no—
703C4⋊C4—716no—
704C4⋊C4—716no—
705C4⋊C4—78no—
706C4⋊C4C23×D718yes—
707C4⋊C4C23×D718yes—
708C4⋊C4C23×D718yes—
709C4⋊C4C23×D7116yes—
710C4⋊C4C23×D7116yes—
711C4⋊C4C23×D718yes—
712C22⋊C4—78no—
713C22⋊C4—78no—
714C22⋊C4—78no—
715C22⋊C4—78no—
716C22⋊C4—78no—
717C22⋊C4—78no—
718C22⋊C4—716no—
719C22⋊C4—716no—
720C22⋊C4—78no—
721C22⋊C4—716no—
722C22⋊C4C23×D7116yes—
723C42—78no—
724C42—78no—
725C42—78no—
726C42—716no—
727C42—716no—
728C42—716no—
729C42C23×D714yes—
730C42C23×D714yes—
731C42C23×D714yes—
732C42C23×D714yes—
733C42C23×D7116yes—
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—216no—
750Q8—48no—
751Q8—148no—
752Q8—148no—
753Q8—148no—
754Q8—288no—
755Q8—2816no—
756D4—148no—
757D4—288no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—44no—
767C2×C4—74no—
768C2×C4—74no—
769C2×C4—74no—
770C2×C4—74no—
771C2×C4—74no—
772C2×C4—74no—
773C2×C4—74no—
774C2×C4—144no—
775C2×C4—144no—
776C2×C4—144no—
777C2×C4—144no—
778C2×C4—144no—
779C2×C4—144no—
780C2×C4—144no—
781C2×C4—1416no—
782C2×C4—2816no—
783C2×C4#655114yes—
784C2×C4#655414yes—
785C2×C4C24×D718yes—
786C2×C4C24×D718yes—
787C2×C4C24×D712yes—
788C2×C4C24×D712yes—
789C2×C4C24×D712yes—
790C2×C4C24×D712yes—
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—28no—
809C4—22no—
810C4—22no—
811C4—28no—
812C4—144no—
813C4—144no—
814C4—144no—
815C4—144no—
816C4—144no—
817C4—144no—
818C4—144no—
819C4C2×#655114yes—
820C4C2×#655414yes—
821C2—42no—
822C2—284no—
823C2#1174333714yesdirect 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. #11743337C2direct (N × H)
3. C2×#90421C2semidirect
4. C2×#90413C2semidirect
5. C2×#90412C2semidirect
6. C2×#90423C2semidirect
7. C2×#90380C2semidirect
8. C2×#90388C2semidirect
9. C2×#90337C2semidirect
11. C2×#90316C2semidirect
12. C2×#90274C2semidirect
13. C2×#90260C2semidirect
14. C2×#90259C2semidirect
15. C2×#90224C2semidirect
16. C2×#90220C2semidirect
18. C2×#90161C2semidirect
19. C7×#533C22semidirect
43. #90423C22semidirect
44. #90421C22semidirect
45. #90413C22semidirect
46. #90412C22semidirect
47. #90388C22semidirect
48. #90380C22semidirect
49. #90337C22semidirect
51. #90316C22semidirect
52. #90274C22semidirect
53. #90260C22semidirect
54. #90259C22semidirect
55. #90224C22semidirect
56. #90220C22semidirect
90. #90161C22semidirect
248. C2×#533D7semidirect
361. #533C2×D7semidirect
735. C2×C7#3555semidirect
793. C7C2×#3555semidirect
823. C2#11743337direct (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
#117433372
C2×#904212
C2×#904132
C2×#904122
C2×#904232
C2×#903802
C2×#903882
C2×#903372
C2×#903342
C2×#903162
C2×#902742
C2×#902602
C2×#902592
C2×#902242
C2×#902202
C2×#901702
C2×#901612
C2×#35557