Finite Group Databasebeta

← C2×#11737957 #14226586

Subgroups — C2×#11737957 #14226586

Order 1792.

2210 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90371C211yesmaximal, characteristic, complemented
2C2×#90239C211yesmaximal, characteristic, complemented
3C2×C7×#463C211yesmaximal, characteristic, complemented
4C2×#89943C211yesmaximal, characteristic, complemented
5C2×#89935C211yesmaximal, characteristic, complemented
6C2×#89929C211yesmaximal, characteristic, complemented
7C2×#89922C211yesmaximal, characteristic, complemented
8C2×#89829C211yesmaximal, characteristic, complemented
9C2×#89781C211yesmaximal, characteristic, complemented
10#11737957C2116yesmaximal, direct product factor
11C2×#89619C211yesmaximal, characteristic, complemented
12C2×D7×C4⋊C8C211yesmaximal, characteristic, complemented
13C2×#89579C211yesmaximal, characteristic, complemented
14C2×#89566C211yesmaximal, characteristic, complemented
15C2×#89547C211yesmaximal, characteristic, complemented
16C2×#89533C211yesmaximal, characteristic, complemented
17C22×#1157—21no—
18C22×C7×SD16C2211yescharacteristic
19C22×C7×D8C2211yescharacteristic
20C2×C7×#124C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×#6509C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C22×#1143C2211yescharacteristic
25C2×#6503C2211yescharacteristic
26C2×#6501C2211yescharacteristic
27C2×#6501C2211yescharacteristic
28C2×D4×Dic7C2211yescharacteristic
29C22×#1141C2211yescharacteristic
30C2×C4×C22⋊D7—21no—
31C22×C8×D7C2211yescharacteristic
32C22×C8×D7C2211yescharacteristic
33#90371—24no—
34#90371C2218yescomplemented
35#90239—24no—
36#90239C2218yescomplemented
37C2×#6458C2211yescharacteristic
38C2×#6451C2211yescharacteristic
39C2×#6448—21no—
40C2×#6447—21no—
41C2×#6446—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×#6442—21no—
44C2×#6440—21no—
45C2×C4×D28C2211yescharacteristic
46C2×C42×D7C2211yescharacteristic
47C2×#6433C2211yescharacteristic
48C7×#463C2218yescomplemented
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×#6406C2211yescharacteristic
56#89943C2218yescomplemented
57#89935C2218yescomplemented
58#89929C2218yescomplemented
59#89922C2218yescomplemented
60C2×#6395C2211yescharacteristic
61C2×#6395C2211yescharacteristic
62C2×#6392C2211yescharacteristic
63C2×#6391C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66#89829C2218yescomplemented
67#89781C2218yescomplemented
68C2×#6382C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×C4⋊(C7⋊C8)C2211yescharacteristic
71#89619C2218yescomplemented
72D7×C4⋊C8C2218yescomplemented
73#89579C2218yescomplemented
74#89566C2218yescomplemented
75#89547C2218yescomplemented
76#89533C2218yescomplemented
77C2×#3247—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C23×Dic7—21no—
87C2×#1157—28no—
88C2×#1157—48no—
89C22×D28—21no—
90C22×D28C2311yescharacteristic
91C22×C4×D7—21no—
92C22×C4×D7D411yescharacteristic
93C22×C4×D7D411yescharacteristic
94C22×C4×D7C2311yescharacteristic
95C22×Dic14—21no—
96C2×C7×SD16—42no—
97C2×C7×SD16C2314yes—
98C2×C7×D8—42no—
99C2×C7×D8C2314yes—
100C22×C7×C8C2311yescharacteristic
101C22×C7×C8C2311yescharacteristic
102C7×#124—22no—
103C7×#124C2314yes—
104C4×C7×D4—22no—
105C4×C7×D4C2314yes—
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C22⋊C4—21no—
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C42×C7C2311yescharacteristic
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7—21no—
113C2×C22⋊Dic7—21no—
114#6509—22no—
115#6509C2314yes—
116Q8×Dic7—22no—
117Q8×Dic7C2314yes—
118C2×#1143—42no—
119C2×#1143C2314yes—
120#6503—22no—
121#6503C2314yes—
122#6501—22no—
123#6501—22no—
124#6501C2314yes—
125#6501C2314yes—
126D4×Dic7—22no—
127D4×Dic7C2314yes—
128C2×#1141—42no—
129C2×#1141C2314yes—
130C4×C22⋊D7—28no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×C4⋊Dic7—21no—
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×C4×Dic7—21no—
143C2×C4×Dic7D411yescharacteristic
144C2×C4×Dic7D411yescharacteristic
145C2×C4×Dic7C2311yescharacteristic
146C22×C7⋊C8C2311yescharacteristic
147C22×C7⋊C8C2311yescharacteristic
148C2×C8×D7—42no—
149C2×C8×D7—42no—
150C2×C8×D7C2314yes—
151C2×C8×D7C2314yes—
152#6458—22no—
153#6458C2314yes—
154#6451—22no—
155#6451C2314yes—
156#6448—28no—
157#6447—28no—
158#6446—28no—
159(C22⋊D7)⋊C4—28no—
160#6442—28no—
161#6440—28no—
162C4×D28—22no—
163C4×D28C2314yes—
164C42×D7D414yes—
165C42×D7C2314yes—
166#6433—22no—
167#6433C2314yes—
168C7×C4⋊C8C2314yes—
169C7×#103C2314yes—
170C7×#102C2314yes—
171#6409C2314yes—
172#6406C2314yes—
173#6406C2314yes—
174#6406C2314yes—
175#6395C2314yes—
176#6395C2314yes—
177#6392C2314yes—
178#6391C2314yes—
179Dic7⋊C8C2314yes—
180Dic7⋊C8C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183C4⋊(C7⋊C8)C2314yes—
184C2×#532—71no—
185C2×#529—71no—
186#3247—716no—
187C2×#477—71no—
188C2×#478—71no—
189C2×#478—71no—
190C2×#476—71no—
191C2×#466—71no—
192C2×#466—71no—
193C2×#465—71no—
194C2×#465—71no—
195C2×#460—71no—
196C2×#463—71no—
197C2×#463D711yescharacteristic, complemented
198C2×#459—71no—
199C22×C4⋊C8—71no—
200C24×C7—21no—
201C24×C7—21no—
202C23×D7—21no—
203C23×D7C2×D411yescharacteristic
204C2×C7×Q8—21no—
205C2×C7×Q8—22no—
206C2×C7×Q8—22no—
207C2×C7×Q8C2412yes—
208C2×C7×D4—21no—
209C2×C7×D4—21no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4—22no—
214C2×C7×D4C2412yes—
215C2×C7×D4C2412yes—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—24no—
219C22×C4×C7—44no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2411yescharacteristic
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—24no—
226C2×C22⋊D7—24no—
227C2×C22⋊D7—44no—
228C2×C22⋊D7—44no—
229C2×C22⋊D7—44no—
230C2×C22⋊D7—44no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—24no—
235C22×Dic7—44no—
236C22×Dic7C2×D411yescharacteristic
237C22×Dic7C2×D411yescharacteristic
238C22×Dic7C2×D411yescharacteristic
239#1157—432no—
240C2×D28—22no—
241C2×D28—22no—
242C2×D28—24no—
243C2×D28—21no—
244C2×D28—44no—
245C2×D28C2412yes—
246C2×C4×D7—24no—
247C2×C4×D7—22no—
248C2×C4×D7—22no—
249C2×C4×D7—24no—
250C2×C4×D7—24no—
251C2×C4×D7—44no—
252C2×C4×D7C2×D412yes—
253C2×C4×D7C2×D414yes—
254C2×C4×D7C2×D414yes—
255C2×C4×D7C2412yes—
256C2×Dic14—24no—
257C2×Dic14—44no—
258C7×SD16—44no—
259C7×D8—44no—
260C2×C7×C8—22no—
261C2×C7×C8—22no—
262C2×C7×C8C2412yes—
263C2×C7×C8C2412yes—
264C7×C4⋊C4—21no—
265C7×C4⋊C4C2412yes—
266C7×C22⋊C4—24no—
267C7×C22⋊C4—24no—
268C7×C22⋊C4—24no—
269C42×C7C2×D412yes—
270C42×C7C2412yes—
271C22⋊Dic7—24no—
272C22⋊Dic7—24no—
273C22⋊Dic7—24no—
274#1143—44no—
275#1141—44no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279C4⋊Dic7—21no—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—24no—
283C4⋊Dic7C2412yes—
284C4⋊Dic7C2412yes—
285C4⋊Dic7C2412yes—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290C4×Dic7—24no—
291C4×Dic7C2×D412yes—
292C4×Dic7C2×D414yes—
293C4×Dic7C2×D414yes—
294C4×Dic7C2412yes—
295C2×C7⋊C8—22no—
296C2×C7⋊C8—22no—
297C2×C7⋊C8C2412yes—
298C2×C7⋊C8C2412yes—
299C8×D7—44no—
300C8×D7—44no—
301C22×#41—141no—
302C22×SD16—71no—
303C22×SD16C2×D711yescharacteristic
304C22×D8—71no—
305C22×D8C2×D711yescharacteristic
306C23×C8—71no—
307C23×C8—71no—
308#532—78no—
309#532—144no—
310C2×C4⋊Q8—71no—
311C2×#127—71no—
312#529—78no—
313#529—144no—
314C2×#126—141no—
315C2×#125—71no—
316C2×#124—141no—
317C2×#124C2×D711yescharacteristic
318C2×#123—141no—
319C2×C22⋊Q8—71no—
320C2×#121—71no—
321C2×#121—71no—
322C2×#121—71no—
323C2×#121—141no—
324C2×C4×Q8—71no—
325C2×C4×D4—71no—
326C2×C4×D4—71no—
327C2×C4×D4—141no—
328C2×C4×D4—141no—
329C2×C4×D4C2×D711yescharacteristic
330C2×#117—141no—
331C22×C42—71no—
332#478—78no—
333#478—78no—
334#477—78no—
335#476—78no—
336#466—78no—
337#466—78no—
338#465—78no—
339#465—78no—
340#463—78no—
341#463C2×D718yescomplemented
342#460—78no—
343#459—78no—
344C2×#107—71no—
345C2×#107—71no—
346C2×#106—71no—
347C2×#106—71no—
348C2×C4⋊C8—71no—
349C2×C4⋊C8—71no—
350C2×C4⋊C8—71no—
351C2×C4⋊C8—78no—
352C2×C4⋊C8C2×D711yescharacteristic
353C2×#103—71no—
354C2×#103C2×D711yescharacteristic
355C2×#102—71no—
356C2×#102—71no—
357C2×#102—71no—
358C2×#102—71no—
359C2×#102—71no—
360C2×#102C2×D711yescharacteristic
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7—42no—
369C23×C7C22×D411yescharacteristic
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—42no—
374C22×D7—42no—
375C22×D7—42no—
376C22×D7AGL(1,ℤ/8)14yes—
377C22×D7C22×D412yes—
378C7×Q8—22no—
379C7×Q8—22no—
380C7×Q8—42no—
381C7×D4—22no—
382C7×D4—22no—
383C7×D4—22no—
384C7×D4—22no—
385C7×D4—42no—
386C7×D4—42no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—48no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7C22×D412yes—
395C2×C4×C7C22×D412yes—
396C2×C4×C7C22×D411yescharacteristic
397C2×C4×C7H(5,𝔽2)12yes—
398C2×C4×C72−1+412yes—
399C2×C4×C7C2511yescharacteristic
400C22⋊D7—48no—
401C22⋊D7—48no—
402C22⋊D7—48no—
403C22⋊D7—48no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7—42no—
412C2×Dic7—48no—
413C2×Dic7#13514yes—
414C2×Dic7C22×D412yes—
415C2×Dic7C22×D412yes—
416C2×Dic7C22×D412yes—
417D28—22no—
418D28—22no—
419D28—48no—
420D28—42no—
421C4×D7—28no—
422C4×D7—24no—
423C4×D7—22no—
424C4×D7—22no—
425C4×D7—28no—
426C4×D7—48no—
427Dic14—48no—
428C7×C8—22no—
429C7×C8—22no—
430C7⋊C8—22no—
431C7⋊C8—22no—
432C2×#41—148no—
433C2×#41—288no—
434C22×Q8—141no—
435C22×Q8C22×D711yescharacteristic
436C22×D4—71no—
437C22×D4—141no—
438C22×D4—141no—
439C22×D4—141no—
440C22×D4—141no—
441C22×D4—141no—
442C22×D4C22×D711yescharacteristic
443C22×D4C22×D711yescharacteristic
444C23×C4—21no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—141no—
449C23×C4—141no—
450C2×SD16—42no—
451C2×SD16—74no—
452C2×SD16—282no—
453C2×SD16C22×D714yes—
454C2×D8—42no—
455C2×D8—74no—
456C2×D8—282no—
457C2×D8C22×D714yes—
458C22×C8—71no—
459C22×C8—71no—
460C22×C8—74no—
461C22×C8—74no—
462C22×C8—282no—
463C22×C8—282no—
464C22×C8C22×D711yescharacteristic
465C22×C8C22×D711yescharacteristic
466C4⋊Q8—74no—
467C4⋊Q8—142no—
468#127—74no—
469#127—142no—
470#126—148no—
471#125—74no—
472#125—142no—
473#124—22no—
474#124—148no—
475#124C22×D714yes—
476#123—148no—
477C22⋊Q8—74no—
478C22⋊Q8—142no—
479#121—74no—
480#121—74no—
481#121—74no—
482#121—148no—
483#121—142no—
484#121—142no—
485#121—142no—
486C4×Q8—74no—
487C4×Q8—142no—
488C4×D4—22no—
489C4×D4—74no—
490C4×D4—74no—
491C4×D4—148no—
492C4×D4—142no—
493C4×D4—148no—
494C4×D4—142no—
495C4×D4C22×D714yes—
496#117—148no—
497C2×C4⋊C4—71no—
498C2×C4⋊C4—71no—
499C2×C4⋊C4—71no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4C22×D711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C22⋊C4—141no—
514C2×C22⋊C4—141no—
515C2×C42—71no—
516C2×C42—71no—
517C2×C42—71no—
518C2×C42—74no—
519C2×C42—74no—
520C2×C42—141no—
521C2×C42C22×D711yescharacteristic
522#107—74no—
523#107—74no—
524#106—74no—
525#106—74no—
526C4⋊C8—74no—
527C4⋊C8—74no—
528C4⋊C8—74no—
529C4⋊C8C22×D714yes—
530#103—74no—
531#103C22×D714yes—
532#102—74no—
533#102—74no—
534#102—74no—
535#102—74no—
536#102—74no—
537#102C22×D714yes—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—84no—
545C22×C7—84no—
546C22×C7#53712yes—
547C22×C7C2×#13512yes—
548C22×C7C2×AGL(1,ℤ/8)12yes—
549C22×C7C23×D411yescharacteristic
550C2×D7—22no—
551C2×D7—28no—
552C2×D7—22no—
553C2×D7—42no—
554C2×D7—42no—
555C2×D7—42no—
556C2×D7—84no—
557C2×D7C2×AGL(1,ℤ/8)14yes—
558C4×C7—22no—
559C4×C7—22no—
560C4×C7—42no—
561C4×C7—42no—
562C4×C7#53712yes—
563C4×C7C2×H(5,𝔽2)11yescharacteristic
564C4×C7C2×2−1+411yescharacteristic
565Dic7—22no—
566Dic7—22no—
567Dic7—42no—
568Dic7—42no—
569Dic7—42no—
570Dic7C2×#13514yes—
571C24—21no—
572C24—21no—
573C24—71no—
574C24—141no—
575#41—2832no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—144no—
580C2×Q8—284no—
581C2×Q8C23×D712yes—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—72no—
589C2×D4—144no—
590C2×D4—144no—
591C2×D4—144no—
592C2×D4—144no—
593C2×D4—144no—
594C2×D4—141no—
595C2×D4—142no—
596C2×D4—142no—
597C2×D4—284no—
598C2×D4—284no—
599C2×D4—284no—
600C2×D4—284no—
601C2×D4—284no—
602C2×D4C23×D712yes—
603C2×D4C23×D712yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—44no—
608C22×C4—71no—
609C22×C4—71no—
610C22×C4—71no—
611C22×C4—74no—
612C22×C4—72no—
613C22×C4—74no—
614C22×C4—72no—
615C22×C4—144no—
616C22×C4—144no—
617C22×C4—144no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—144no—
624C22×C4—284no—
625C22×C4—284no—
626C22×C4D4×D711yescharacteristic
627C22×C4D4×D711yescharacteristic
628C22×C4C23×D711yescharacteristic
629SD16—44no—
630SD16—284no—
631D8—44no—
632D8—284no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—72no—
636C2×C8—72no—
637C2×C8—142no—
638C2×C8—142no—
639C2×C8—284no—
640C2×C8—284no—
641C2×C8C23×D712yes—
642C2×C8C23×D712yes—
643C4⋊C4—21no—
644C4⋊C4—72no—
645C4⋊C4—72no—
646C4⋊C4—72no—
647C4⋊C4—144no—
648C4⋊C4—144no—
649C4⋊C4—144no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—141no—
653C4⋊C4—141no—
654C4⋊C4—141no—
655C4⋊C4C23×D712yes—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—144no—
660C22⋊C4—144no—
661C22⋊C4—144no—
662C22⋊C4—144no—
663C22⋊C4—144no—
664C22⋊C4—144no—
665C42—74no—
666C42—72no—
667C42—74no—
668C42—72no—
669C42—144no—
670C42D4×D712yes—
671C42C23×D712yes—
672C2×C7—82no—
673C2×C7—82no—
674C2×C7#324714yescomplemented
675C2×C7C2×#53711yescharacteristic
676C2×C7C22×#13511yescharacteristic
677C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
678D7—24no—
679D7—82no—
680C23—22no—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—74no—
689C23—72no—
690C23—142no—
691C23—142no—
692C23—142no—
693C23—282no—
694C23—282no—
695C23—282no—
696C23C2×D4×D711yescharacteristic
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—288no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—42no—
706D4—42no—
707D4—142no—
708D4—142no—
709D4—288no—
710D4—288no—
711D4—288no—
712D4—288no—
713D4—288no—
714D4—282no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—48no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—74no—
723C2×C4—72no—
724C2×C4—72no—
725C2×C4—72no—
726C2×C4—148no—
727C2×C4—148no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—144no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—288no—
737C2×C4—288no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—282no—
741C2×C4C2×D4×D712yes—
742C2×C4C2×D4×D712yes—
743C2×C4C2×D4×D711yescharacteristic
744C2×C4#654812yes—
745C2×C4#655412yes—
746C2×C4C24×D711yescharacteristic
747C8—22no—
748C8—22no—
749C8—142no—
750C8—142no—
751C7C2×#324711yescharacteristic, complemented, Sylow
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—74no—
759C22—84no—
760C22—84no—
761C22—142no—
762C22—148no—
763C22—142no—
764C22—282no—
765C22—282no—
766C22—282no—
767C22—564no—
768C22#9029912yes—
769C22D7×#13512yes—
770C22D7×AGL(1,ℤ/8)12yes—
771C22C22×D4×D711yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—74no—
777C4—142no—
778C4—142no—
779C4—282no—
780C4—282no—
781C4—282no—
782C4#9029912yes—
783C4C2×#654811yescharacteristic
784C4C2×#655411yescharacteristic
785C2—82no—
786C2—82no—
787C2—144no—
788C2—562no—
789C2#1173795714yesdirect product factor
790C2C2×#9029911yescharacteristic
791C2C2×D7×#13511yescharacteristic
792C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#463C2
socleC23×C7C22×D4
hypercenterC2×#463D7
hypocenterC7C2×#3247
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#90371C2semidirect
2. C2×#90239C2semidirect
3. C2×C7×#463C2semidirect
4. C2×#89943C2semidirect
5. C2×#89935C2semidirect
6. C2×#89929C2semidirect
7. C2×#89922C2semidirect
8. C2×#89829C2semidirect
9. C2×#89781C2semidirect
10. #11737957C2direct (N × H)
11. C2×#89619C2semidirect
12. C2×D7×C4⋊C8C2semidirect
13. C2×#89579C2semidirect
14. C2×#89566C2semidirect
15. C2×#89547C2semidirect
16. C2×#89533C2semidirect
34. #90371C22semidirect
36. #90239C22semidirect
48. C7×#463C22semidirect
56. #89943C22semidirect
57. #89935C22semidirect
58. #89929C22semidirect
59. #89922C22semidirect
66. #89829C22semidirect
67. #89781C22semidirect
71. #89619C22semidirect
72. D7×C4⋊C8C22semidirect
73. #89579C22semidirect
74. #89566C22semidirect
75. #89547C22semidirect
76. #89533C22semidirect
197. C2×#463D7semidirect
341. #463C2×D7semidirect
674. C2×C7#3247semidirect
751. C7C2×#3247semidirect
789. C2#11737957direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903712
C2×#902392
C2×C7×#4632
C2×#899432
C2×#899352
C2×#899292
C2×#899222
C2×#898292
C2×#897812
#117379572
C2×#896192
C2×D7×C4⋊C82
C2×#895792
C2×#895662
C2×#895472
C2×#895332
C2×#32477