Finite Group Databasebeta

← C2×#11743171 #14261163

Subgroups — C2×#11743171 #14261163

Order 1792.

7194 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
1C22×C7×#125C211yesmaximal, characteristic, complemented
2#11743171C2132yesmaximal, direct product factor
3C2×#90390C212yesmaximal, complemented
4C2×#90391C212yesmaximal, complemented
5C2×#90386C212yesmaximal, complemented
6C2×#90380C212yesmaximal, complemented
7C2×#90389C212yesmaximal, complemented
8C2×#90383C214yesmaximal, complemented
9C2×#90381C212yesmaximal, complemented
10C2×#90205C212yesmaximal, complemented
11C2×#90198C212yesmaximal, complemented
12C2×#90198C214yesmaximal, complemented
13C2×#90206C212yesmaximal, complemented
14C2×#90201C212yesmaximal, complemented
15C2×#90168C211yesmaximal, characteristic, complemented
16C2×#90170C211yesmaximal, characteristic, complemented
17C22×#1157C2212yes—
18C22×#1157C2214yes—
19C2×C7×#125C2212yes—
20C2×C7×#125C2212yes—
21C2×C7×#125C2212yes—
22C2×C7×#125C2212yes—
23C2×C7×#125C22116yescomplemented
24C22×C7×C4⋊C4C2212yes—
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2212yes—
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C2×#6493C2211yescharacteristic
30C2×#6493C2212yes—
31C2×#6493C2212yes—
32C2×#6493C2214yes—
33C2×#6492C2212yes—
34C2×#6492C2214yes—
35C2×C4×C22⋊D7C2212yes—
36C2×C4×C22⋊D7C2214yes—
37C2×#6487C2211yescharacteristic
38#90391C22132yescomplemented
39#90390C22132yescomplemented
40#90389C22132yescomplemented
41#90386C22132yescomplemented
42#90383C22164yescomplemented
43#90381C22132yescomplemented
44#90380C22132yescomplemented
45#90206C22132yescomplemented
46#90205C22132yescomplemented
47C2×#6461C2214yes—
48C2×#6461C2214yes—
49#90201C22132yescomplemented
50C2×#6460C2214yes—
51C2×#6460C2214yes—
52C2×#6459C2214yes—
53C2×#6459C2214yes—
54C2×#6459C2214yes—
55C2×#6459C2214yes—
56#90198C22132yescomplemented
57#90198C22164yescomplemented
58C2×#6458C2214yes—
59C2×#6458C2214yes—
60C2×#6458C2212yes—
61C2×#6458C2214yes—
62C2×#6458C2212yes—
63C2×#6457C2214yes—
64C2×#6457C2214yes—
65C2×#6457C2214yes—
66C2×#6457C2214yes—
67C2×#6457C2214yes—
68C2×#6456C2212yes—
69C2×#6456C2214yes—
70C2×#6456C2212yes—
71C2×#6455C2212yes—
72C2×D7×C4⋊C4C2214yes—
73C2×D7×C4⋊C4C2212yes—
74C2×#6453C2212yes—
75C2×#6452C2214yes—
76C2×#6451C2212yes—
77C2×#6451C2214yes—
78#90170C22116yescomplemented
79C2×#6439C2212yes—
80#90168C22116yescomplemented
81C2×#6438C2211yescharacteristic
82C2×#6438C2212yes—
83C2×#6437C2211yescharacteristic
84C2×C4×D28C2211yescharacteristic
85C2×C4×D28C2212yes—
86C2×C4×D28C2212yes—
87C2×#6435C2212yes—
88C2×#6433C2211yescharacteristic
89C2×#6432C2211yescharacteristic
90C2×C4×Dic14C2211yescharacteristic
91C2×#3559—71nomaximal, Sylow
92C23×C4×C7C2311yescharacteristic
93C23×C4×C7C2311yescharacteristic
94C23×C4×C7C2312yes—
95C23×C4×C7C2311yescharacteristic
96C23×C4×C7C2312yes—
97C22×C22⋊D7C2312yes—
98C22×C22⋊D7C2314yes—
99C2×#1157—48no—
100C2×#1157—416no—
101C2×#1157C23116yes—
102C2×#1157C23132yes—
103C22×D28C2312yes—
104C22×D28C2312yes—
105C22×D28C2311yescharacteristic
106C22×D28C2312yes—
107C22×D28C2314yes—
108C22×D28C2314yes—
109C22×C4×D7C2312yes—
110C22×C4×D7C2314yes—
111C22×C4×D7C2314yes—
112C22×C4×D7C2314yes—
113C22×C4×D7C2314yes—
114C22×Dic14C2311yescharacteristic
115C22×Dic14C2312yes—
116C22×Dic14C2314yes—
117C7×#125C23116yes—
118C7×#125C23116yes—
119C7×#125C23116yes—
120C7×#125C23116yes—
121C2×C7×C4⋊C4C2312yes—
122C2×C7×C4⋊C4C2314yes—
123C2×C7×C4⋊C4C2314yes—
124C2×C7×C4⋊C4C2312yes—
125C2×C7×C4⋊C4C2314yes—
126C2×C7×C4⋊C4C2312yes—
127C2×C7×C4⋊C4C2312yes—
128C2×C7×C4⋊C4C2314yes—
129C2×C7×C4⋊C4C2318yes—
130C2×C7×C4⋊C4C23116yes—
131C2×C7×C4⋊C4C23116yes—
132C2×C7×C4⋊C4C2318yes—
133C2×C42×C7C2311yescharacteristic
134C2×C42×C7C2311yescharacteristic
135C2×C42×C7C2311yescharacteristic
136C2×C42×C7C2311yescharacteristic
137C2×C42×C7C2318yes—
138C2×C22⋊Dic7C2312yes—
139#6493C23116yes—
140#6493C23116yes—
141#6493C2318yes—
142#6493C23132yes—
143#6492C23116yes—
144#6492C23132yes—
145C4×C22⋊D7C23116yes—
146C4×C22⋊D7C23132yes—
147C2×(C2×D7)⋊C4C2312yes—
148C2×(C2×D7)⋊C4C2312yes—
149C2×(C2×D7)⋊C4C2314yes—
150C2×(C2×D7)⋊C4C2314yes—
151C2×(C2×D7)⋊C4C2312yes—
152C2×(C2×D7)⋊C4C2312yes—
153C2×(C2×D7)⋊C4C2314yes—
154C2×(C2×D7)⋊C4C2314yes—
155C2×(C2×D7)⋊C4C2314yes—
156C2×(C2×D7)⋊C4C2314yes—
157C2×(C2×D7)⋊C4C2314yes—
158C2×C4⋊Dic7C2311yescharacteristic
159C2×C4⋊Dic7C2312yes—
160C2×C4⋊Dic7C2312yes—
161C2×C4⋊Dic7C2311yescharacteristic
162C2×C4⋊Dic7C2314yes—
163#6487C2318yes—
164C2×Dic7⋊C4C2312yes—
165C2×Dic7⋊C4C2312yes—
166C2×Dic7⋊C4C2312yes—
167C2×Dic7⋊C4C2312yes—
168C2×Dic7⋊C4C2314yes—
169C2×Dic7⋊C4C2314yes—
170C2×Dic7⋊C4C2314yes—
171C2×C4×Dic7C2312yes—
172C2×C4×Dic7C2314yes—
173#6461C23132yes—
174#6461C23132yes—
175#6460C23132yes—
176#6460C23132yes—
177#6459C23132yes—
178#6459C23132yes—
179#6459C23132yes—
180#6459C23132yes—
181#6458C23132yes—
182#6458C23116yes—
183#6458C23116yes—
184#6458C23132yes—
185#6458C23132yes—
186#6457C23132yes—
187#6457C23132yes—
188#6457C23132yes—
189#6457C23132yes—
190#6457C23132yes—
191#6456C23116yes—
192#6456C23116yes—
193#6456C23132yes—
194#6455C23116yes—
195D7×C4⋊C4C23116yes—
196D7×C4⋊C4C23132yes—
197#6453C23116yes—
198#6452C23132yes—
199#6451C23116yes—
200#6451C23132yes—
201#6439C23116yes—
202#6438C23116yes—
203#6438C2318yes—
204#6437C2318yes—
205C4×D28C23116yes—
206C4×D28C23116yes—
207C4×D28C2318yes—
208#6435C23116yes—
209#6433C2318yes—
210#6432C2318yes—
211C4×Dic14C2318yes—
212#3559—732no—
213C2×#563—72no—
214C2×#562—72no—
215C2×#554—72no—
216C2×#553—72no—
217C2×#553—72no—
218C2×#547—74no—
219C2×#547—72no—
220C2×#544—72no—
221C2×#540—72no—
222C2×#539—74no—
223C2×#539—72no—
224C2×#537—72no—
225C2×#532—71no—
226C2×#529—71no—
227C22×#125D711yescharacteristic, complemented
228C24×C7C2411yescharacteristic
229C23×D7C2412yes—
230C23×D7C2414yes—
231C22×C4×C7—24no—
232C22×C4×C7—28no—
233C22×C4×C7—24no—
234C22×C4×C7—42no—
235C22×C4×C7—44no—
236C22×C4×C7C2414yes—
237C22×C4×C7C2411yescharacteristic
238C22×C4×C7C2411yescharacteristic
239C22×C4×C7C2411yescharacteristic
240C22×C4×C7C2411yescharacteristic
241C22×C4×C7C2414yes—
242C22×C4×C7C2411yescharacteristic
243C22×C4×C7C2414yes—
244C22×C4×C7C2414yes—
245C22×C4×C7C2418yes—
246C22×C4×C7C2414yes—
247C22×C4×C7C2418yes—
248C22×C4×C7C2411yescharacteristic
249C2×C22⋊D7—216no—
250C2×C22⋊D7—28no—
251C2×C22⋊D7C2418yes—
252C2×C22⋊D7C24116yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C22×Dic7C2414yes—
257#1157—432no—
258#1157—464no—
259C2×D28—28no—
260C2×D28—42no—
261C2×D28—48no—
262C2×D28—44no—
263C2×D28—44no—
264C2×D28—48no—
265C2×D28C2418yes—
266C2×D28C2418yes—
267C2×D28C2414yes—
268C2×D28C2418yes—
269C2×D28C24116yes—
270C2×D28C24116yes—
271C2×C4×D7—28no—
272C2×C4×D7—48no—
273C2×C4×D7—48no—
274C2×C4×D7—48no—
275C2×C4×D7—48no—
276C2×C4×D7C2418yes—
277C2×C4×D7C24116yes—
278C2×C4×D7C24116yes—
279C2×C4×D7C24116yes—
280C2×C4×D7C24116yes—
281C2×Dic14—42no—
282C2×Dic14—44no—
283C2×Dic14—48no—
284C2×Dic14C2414yes—
285C2×Dic14C2418yes—
286C2×Dic14C24116yes—
287C7×C4⋊C4C2418yes—
288C7×C4⋊C4C24116yes—
289C7×C4⋊C4C24116yes—
290C7×C4⋊C4C2418yes—
291C7×C4⋊C4C24116yes—
292C7×C4⋊C4C2418yes—
293C7×C4⋊C4C2418yes—
294C7×C4⋊C4C24116yes—
295C42×C7C2414yes—
296C42×C7C2414yes—
297C42×C7C2414yes—
298C42×C7C2414yes—
299C22⋊Dic7C2418yes—
300(C2×D7)⋊C4C2418yes—
301(C2×D7)⋊C4C2418yes—
302(C2×D7)⋊C4C24116yes—
303(C2×D7)⋊C4C24116yes—
304(C2×D7)⋊C4C2418yes—
305(C2×D7)⋊C4C2418yes—
306(C2×D7)⋊C4C24116yes—
307(C2×D7)⋊C4C24116yes—
308(C2×D7)⋊C4C24116yes—
309(C2×D7)⋊C4C24116yes—
310(C2×D7)⋊C4C24116yes—
311C4⋊Dic7C2414yes—
312C4⋊Dic7C2418yes—
313C4⋊Dic7C2418yes—
314C4⋊Dic7C2414yes—
315C4⋊Dic7C24116yes—
316Dic7⋊C4C2418yes—
317Dic7⋊C4C2418yes—
318Dic7⋊C4C2418yes—
319Dic7⋊C4C2418yes—
320Dic7⋊C4C24116yes—
321Dic7⋊C4C24116yes—
322Dic7⋊C4C24116yes—
323C4×Dic7C2418yes—
324C4×Dic7C24116yes—
325C22×#41—72no—
326C22×#41—74no—
327#563—732no—
328#562—732no—
329#554—732no—
330#553—732no—
331#553—732no—
332#547—764no—
333#547—732no—
334#544—732no—
335#540—732no—
336#539—764no—
337#539—732no—
338#537—732no—
339#532—716no—
340C2×C4⋊Q8—72no—
341C2×C4⋊Q8—74no—
342C2×C4⋊Q8—71no—
343C2×#127—71no—
344#529—716no—
345C2×#126—74no—
346C2×#126—74no—
347C2×#126—72no—
348C2×#125—74no—
349C2×#125—72no—
350C2×#125—71no—
351C2×#125C2×D712yes—
352C2×#125C2×D712yes—
353C2×#125C2×D712yes—
354C2×#125C2×D712yes—
355C2×#125C2×D7116yescomplemented
356C2×#124—71no—
357C2×#124—72no—
358C2×#123—72no—
359C2×#123—74no—
360C2×#123—74no—
361C2×#123—74no—
362C2×#123—74no—
363C2×#123—74no—
364C2×#123—74no—
365C2×C22⋊Q8—71no—
366C2×C22⋊Q8—74no—
367C2×C22⋊Q8—74no—
368C2×C22⋊Q8—74no—
369C2×C22⋊Q8—74no—
370C2×C22⋊Q8—74no—
371C2×C22⋊Q8—74no—
372C2×#121—71no—
373C2×#121—72no—
374C2×#121—72no—
375C2×#121—74no—
376C2×#121—74no—
377C2×#121—74no—
378C2×#121—72no—
379C2×#121—74no—
380C2×#121—72no—
381C2×C4×Q8—71no—
382C2×C4×D4—72no—
383C2×C4×D4—74no—
384C2×C4×D4—74no—
385C2×C4×D4—72no—
386C2×C4×D4—72no—
387C2×C4×D4—71no—
388C2×C4×D4—72no—
389C2×C4×D4—72no—
390C2×#117—72no—
391C2×#117—72no—
392C22×C4⋊C4—74no—
393C22×C4⋊C4—72no—
394C22×C4⋊C4C2×D712yes—
395C22×C4⋊C4C2×D711yescharacteristic
396C22×C4⋊C4C2×D712yes—
397C22×C4⋊C4C2×D711yescharacteristic
398C22×C42C2×D711yescharacteristic
399C23×C7—22no—
400C23×C7—22no—
401C23×C7H(5,𝔽2)14yes—
402C23×C7C2512yes—
403C23×C7C2511yescharacteristic
404C22×D7—24no—
405C22×D7—28no—
406C22×D7—24no—
407C22×D7—28no—
408C22×D7—28no—
409C22×D7—24no—
410C22×D7C2514yes—
411C22×D7C2518yes—
412C2×C4×C7—22no—
413C2×C4×C7—28no—
414C2×C4×C7—22no—
415C2×C4×C7—28no—
416C2×C4×C7—216no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—28no—
420C2×C4×C7—22no—
421C2×C4×C7—28no—
422C2×C4×C7—44no—
423C2×C4×C7—48no—
424C2×C4×C72−1+414yes—
425C2×C4×C7C2518yes—
426C2×C4×C7C2512yes—
427C2×C4×C7C2512yes—
428C2×C4×C7C2512yes—
429C2×C4×C7C2512yes—
430C2×C4×C7C2518yes—
431C2×C4×C7C2512yes—
432C2×C4×C7C2512yes—
433C22⋊D7—232no—
434C22⋊D7—216no—
435C2×Dic7—28no—
436C2×Dic7—24no—
437C2×Dic7—24no—
438C2×Dic7—24no—
439C2×Dic7C2514yes—
440C2×Dic7C2514yes—
441C2×Dic7C2514yes—
442C2×Dic7C2518yes—
443D28—216no—
444D28—44no—
445D28—416no—
446D28—48no—
447D28—48no—
448D28—416no—
449C4×D7—216no—
450C4×D7—416no—
451C4×D7—416no—
452C4×D7—416no—
453C4×D7—416no—
454Dic14—44no—
455Dic14—48no—
456Dic14—416no—
457C2×#41—716no—
458C2×#41—732no—
459C2×#41—288no—
460C2×#41—2816no—
461C22×Q8—71no—
462C22×Q8—74no—
463C22×Q8—72no—
464C22×D4—72no—
465C22×D4—74no—
466C22×D4—72no—
467C22×D4—74no—
468C22×D4—71no—
469C22×D4—72no—
470C22×D4—74no—
471C22×D4—72no—
472C23×C4—72no—
473C23×C4—74no—
474C23×C4—74no—
475C23×C4—74no—
476C23×C4—74no—
477C23×C4C22×D712yes—
478C23×C4C22×D711yescharacteristic
479C23×C4C22×D711yescharacteristic
480C23×C4C22×D712yes—
481C23×C4C22×D711yescharacteristic
482C4⋊Q8—716no—
483C4⋊Q8—732no—
484C4⋊Q8—78no—
485#127—78no—
486#126—732no—
487#126—732no—
488#126—716no—
489#125—732no—
490#125—716no—
491#125—78no—
492#125C22×D7116yes—
493#125C22×D7116yes—
494#125C22×D7116yes—
495#125C22×D7116yes—
496#124—78no—
497#124—716no—
498#123—716no—
499#123—732no—
500#123—732no—
501#123—732no—
502#123—732no—
503#123—732no—
504#123—732no—
505C22⋊Q8—78no—
506C22⋊Q8—732no—
507C22⋊Q8—732no—
508C22⋊Q8—732no—
509C22⋊Q8—732no—
510C22⋊Q8—732no—
511C22⋊Q8—732no—
512#121—78no—
513#121—716no—
514#121—716no—
515#121—732no—
516#121—732no—
517#121—732no—
518#121—716no—
519#121—732no—
520#121—716no—
521C4×Q8—78no—
522C4×D4—716no—
523C4×D4—732no—
524C4×D4—732no—
525C4×D4—716no—
526C4×D4—716no—
527C4×D4—78no—
528C4×D4—716no—
529C4×D4—716no—
530#117—716no—
531#117—716no—
532C2×C4⋊C4—72no—
533C2×C4⋊C4—72no—
534C2×C4⋊C4—74no—
535C2×C4⋊C4—74no—
536C2×C4⋊C4—74no—
537C2×C4⋊C4—72no—
538C2×C4⋊C4—72no—
539C2×C4⋊C4—72no—
540C2×C4⋊C4—74no—
541C2×C4⋊C4—72no—
542C2×C4⋊C4—71no—
543C2×C4⋊C4—71no—
544C2×C4⋊C4—732no—
545C2×C4⋊C4—716no—
546C2×C4⋊C4C22×D712yes—
547C2×C4⋊C4C22×D714yes—
548C2×C4⋊C4C22×D712yes—
549C2×C4⋊C4C22×D714yes—
550C2×C4⋊C4C22×D714yes—
551C2×C4⋊C4C22×D714yes—
552C2×C4⋊C4C22×D712yes—
553C2×C4⋊C4C22×D712yes—
554C2×C4⋊C4C22×D7116yes—
555C2×C4⋊C4C22×D718yes—
556C2×C4⋊C4C22×D7116yes—
557C2×C4⋊C4C22×D718yes—
558C2×C22⋊C4—72no—
559C2×C22⋊C4—72no—
560C2×C22⋊C4—74no—
561C2×C22⋊C4—72no—
562C2×C22⋊C4—72no—
563C2×C22⋊C4—74no—
564C2×C22⋊C4—74no—
565C2×C22⋊C4—74no—
566C2×C22⋊C4—74no—
567C2×C22⋊C4—74no—
568C2×C22⋊C4—74no—
569C2×C22⋊C4—72no—
570C2×C42—72no—
571C2×C42—74no—
572C2×C42C22×D711yescharacteristic
573C2×C42C22×D711yescharacteristic
574C2×C42C22×D711yescharacteristic
575C2×C42C22×D711yescharacteristic
576C2×C42C22×D718yes—
577C22×C7—22no—
578C22×C7—22no—
579C22×C7—28no—
580C22×C7C2×H(5,𝔽2)14yes—
581C22×C7C2×H(5,𝔽2)12yes—
582C22×C7C2×2−1+412yes—
583C22×C7#58512yes—
584C22×C7C2611yescharacteristic
585C2×D7—24no—
586C2×D7—28no—
587C2×D7—24no—
588C2×D7—28no—
589C2×D7—28no—
590C2×D7—24no—
591C2×D7—48no—
592C2×D7—416no—
593C4×C7—22no—
594C4×C7—28no—
595C4×C7—22no—
596C4×C7—22no—
597C4×C7—22no—
598C4×C7—28no—
599C4×C7—22no—
600C4×C7C2×2−1+414yes—
601Dic7—28no—
602Dic7—24no—
603Dic7—24no—
604Dic7—24no—
605C24—72no—
606C24—74no—
607C24C23×D711yescharacteristic
608#41—2832no—
609#41—2864no—
610C2×Q8—74no—
611C2×Q8—716no—
612C2×Q8—78no—
613C2×Q8—282no—
614C2×Q8—288no—
615C2×Q8—284no—
616C2×D4—78no—
617C2×D4—716no—
618C2×D4—78no—
619C2×D4—716no—
620C2×D4—74no—
621C2×D4—78no—
622C2×D4—716no—
623C2×D4—78no—
624C2×D4—148no—
625C2×D4—1416no—
626C2×D4—148no—
627C2×D4—288no—
628C2×D4—284no—
629C2×D4—282no—
630C2×D4—288no—
631C2×D4—284no—
632C22×C4—24no—
633C22×C4—28no—
634C22×C4—24no—
635C22×C4—44no—
636C22×C4—42no—
637C22×C4—72no—
638C22×C4—72no—
639C22×C4—72no—
640C22×C4—74no—
641C22×C4—78no—
642C22×C4—716no—
643C22×C4—716no—
644C22×C4—716no—
645C22×C4—716no—
646C22×C4—148no—
647C22×C4—288no—
648C22×C4—288no—
649C22×C4—288no—
650C22×C4—288no—
651C22×C4C23×D714yes—
652C22×C4C23×D714yes—
653C22×C4C23×D718yes—
654C22×C4C23×D714yes—
655C22×C4C23×D711yescharacteristic
656C22×C4C23×D711yescharacteristic
657C22×C4C23×D711yescharacteristic
658C22×C4C23×D711yescharacteristic
659C22×C4C23×D711yescharacteristic
660C22×C4C23×D714yes—
661C22×C4C23×D714yes—
662C22×C4C23×D718yes—
663C22×C4C23×D711yescharacteristic
664C4⋊C4—78no—
665C4⋊C4—716no—
666C4⋊C4—716no—
667C4⋊C4—78no—
668C4⋊C4—78no—
669C4⋊C4—716no—
670C4⋊C4—78no—
671C4⋊C4—78no—
672C4⋊C4—716no—
673C4⋊C4—78no—
674C4⋊C4—74no—
675C4⋊C4—74no—
676C4⋊C4C23×D718yes—
677C4⋊C4C23×D7116yes—
678C4⋊C4C23×D718yes—
679C4⋊C4C23×D7116yes—
680C4⋊C4C23×D7116yes—
681C4⋊C4C23×D7116yes—
682C4⋊C4C23×D718yes—
683C4⋊C4C23×D718yes—
684C22⋊C4—78no—
685C22⋊C4—78no—
686C22⋊C4—716no—
687C22⋊C4—78no—
688C22⋊C4—78no—
689C22⋊C4—716no—
690C22⋊C4—716no—
691C22⋊C4—716no—
692C22⋊C4—716no—
693C22⋊C4—716no—
694C22⋊C4—716no—
695C22⋊C4—78no—
696C42—78no—
697C42—716no—
698C42C23×D714yes—
699C42C23×D714yes—
700C42C23×D714yes—
701C42C23×D714yes—
702C2×C7—24no—
703C2×C7#355914yescomplemented
704C2×C7C22×H(5,𝔽2)11yescharacteristic
705C2×C7C22×2−1+411yescharacteristic
706C2×C7C2×#58511yescharacteristic
707D7—44no—
708D7—48no—
709C23—22no—
710C23—22no—
711C23—74no—
712C23—78no—
713C23—144no—
714C23—148no—
715C23—144no—
716C23—148no—
717C23—148no—
718C23—144no—
719C23#655314yes—
720C23C24×D712yes—
721C23C24×D711yescharacteristic
722Q8—284no—
723Q8—2816no—
724Q8—288no—
725D4—1416no—
726D4—1432no—
727D4—1416no—
728D4—2816no—
729D4—288no—
730D4—284no—
731D4—2816no—
732D4—288no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—216no—
739C2×C4—28no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—28no—
743C2×C4—48no—
744C2×C4—44no—
745C2×C4—74no—
746C2×C4—74no—
747C2×C4—74no—
748C2×C4—78no—
749C2×C4—144no—
750C2×C4—144no—
751C2×C4—148no—
752C2×C4—144no—
753C2×C4—1416no—
754C2×C4—2816no—
755C2×C4—2816no—
756C2×C4—2816no—
757C2×C4—2816no—
758C2×C4#655114yes—
759C2×C4C24×D718yes—
760C2×C4C24×D712yes—
761C2×C4C24×D712yes—
762C2×C4C24×D712yes—
763C2×C4C24×D712yes—
764C2×C4C24×D712yes—
765C2×C4C24×D718yes—
766C2×C4C24×D712yes—
767C7C2×#355911yescharacteristic, complemented, Sylow
768C22—22no—
769C22—22no—
770C22—28no—
771C22—144no—
772C22—148no—
773C22—144no—
774C22—148no—
775C22—148no—
776C22—144no—
777C22—288no—
778C22—2816no—
779C22C2×#655112yes—
780C22C2×#655314yes—
781C22C2×#655312yes—
782C22#9061612yes—
783C22C25×D711yescharacteristic
784C4—22no—
785C4—22no—
786C4—28no—
787C4—22no—
788C4—28no—
789C4—22no—
790C4—22no—
791C4—144no—
792C4—144no—
793C4—148no—
794C4—144no—
795C4C2×#655114yes—
796C2—24no—
797C2—284no—
798C2—288no—
799C2#1174317114yesdirect product factor
800C2C22×#655111yescharacteristic
801C2C22×#655311yescharacteristic
802C2C2×#9061611yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC22×C7×#125C2
socleC23×C7C25
hypercenterC22×#125D7
hypocenterC7C2×#3559
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. C22×C7×#125C2semidirect
2. #11743171C2direct (N × H)
3. C2×#90390C2semidirect
4. C2×#90391C2semidirect
5. C2×#90386C2semidirect
6. C2×#90380C2semidirect
7. C2×#90389C2semidirect
8. C2×#90383C2semidirect
9. C2×#90381C2semidirect
10. C2×#90205C2semidirect
11. C2×#90198C2semidirect
12. C2×#90198C2semidirect
13. C2×#90206C2semidirect
14. C2×#90201C2semidirect
15. C2×#90168C2semidirect
16. C2×#90170C2semidirect
23. C2×C7×#125C22semidirect
38. #90391C22semidirect
39. #90390C22semidirect
40. #90389C22semidirect
41. #90386C22semidirect
42. #90383C22semidirect
43. #90381C22semidirect
44. #90380C22semidirect
45. #90206C22semidirect
46. #90205C22semidirect
49. #90201C22semidirect
56. #90198C22semidirect
57. #90198C22semidirect
78. #90170C22semidirect
80. #90168C22semidirect
227. C22×#125D7semidirect
355. C2×#125C2×D7semidirect
703. C2×C7#3559semidirect
767. C7C2×#3559semidirect
799. C2#11743171direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1252
#117431712
C2×#903902
C2×#903912
C2×#903862
C2×#903802
C2×#903892
C2×#903832
C2×#903812
C2×#902052
C2×#901982
C2×#902062
C2×#902012
C2×#901682
C2×#901702
C2×#35597