Finite Group Databasebeta

← C2×#11737321 #14223705

Subgroups — C2×#11737321 #14223705

Order 1792.

2278 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×#90239C211yesmaximal, characteristic, complemented
2C2×#90248C211yesmaximal, characteristic, complemented
3C2×C7×#442C211yesmaximal, characteristic, complemented
4C2×#89929C211yesmaximal, characteristic, complemented
5C2×#89926C211yesmaximal, characteristic, complemented
6C2×#89786C211yesmaximal, characteristic, complemented
7C2×#89790C211yesmaximal, characteristic, complemented
8#11737321C2116yesmaximal, direct product factor
9C2×#89636C211yesmaximal, characteristic, complemented
10C2×#89628C211yesmaximal, characteristic, complemented
11C2×#89547C211yesmaximal, characteristic, complemented
12C2×#89550C211yesmaximal, characteristic, complemented
13C2×#89536C211yesmaximal, characteristic, complemented
14C2×#89537C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×D7×#97C211yesmaximal, characteristic, complemented
17C22×#1157—21no—
18C22×C7×D8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6503C2211yescharacteristic
22C2×#6501C2211yescharacteristic
23C2×#6501C2211yescharacteristic
24C2×#6499C2211yescharacteristic
25C22×#1142C2211yescharacteristic
26C22×#1141C2211yescharacteristic
27C2×C4×C22⋊D7—21no—
28C2×C4×C22⋊D7—21no—
29C2×#6489—21no—
30C22×#1132C2211yescharacteristic
31C22×C8×D7C2211yescharacteristic
32C22×C8×D7C2211yescharacteristic
33#90248—24no—
34#90248C2218yescomplemented
35#90239—24no—
36#90239C2218yescomplemented
37C2×#6460C2211yescharacteristic
38C2×#6458C2211yescharacteristic
39C2×#6453C2211yescharacteristic
40C2×#6451C2211yescharacteristic
41C2×#6448—21no—
42C2×#6447—21no—
43C2×#6446—21no—
44C2×#6442—21no—
45C2×C4×D28C2211yescharacteristic
46C2×C42×D7C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C7×#442C2218yescomplemented
49C2×C7×#106C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C7×#97C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55#89929C2218yescomplemented
56#89926C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×#6389C2211yescharacteristic
61C2×#6389C2211yescharacteristic
62#89790C2218yescomplemented
63#89786C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6377C2211yescharacteristic
69#89636C2218yescomplemented
70#89628C2218yescomplemented
71#89550C2218yescomplemented
72#89547C2218yescomplemented
73#89537C2218yescomplemented
74#89536C2218yescomplemented
75#89482C2218yescomplemented
76D7×#97C2218yescomplemented
77C2×#3180—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C2×#1157—28no—
87C2×#1157—48no—
88C22×D28—21no—
89C22×D28C2311yescharacteristic
90C22×C4×D7—21no—
91C22×C4×D7D411yescharacteristic
92C22×C4×D7D411yescharacteristic
93C22×C4×D7C2311yescharacteristic
94C22×Dic14—21no—
95C22×Dic14C2311yescharacteristic
96C2×C7×D8—24no—
97C2×C7×D8C2314yes—
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C4×C7×D4—22no—
101C4×C7×D4—22no—
102C4×C7×D4C2314yes—
103C4×C7×D4C2314yes—
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C22⋊C4—21no—
107C2×C7×C22⋊C4—21no—
108C2×C42×C7C2311yescharacteristic
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7—21no—
113#6503—22no—
114#6503C2314yes—
115#6501—22no—
116#6501—22no—
117#6501C2314yes—
118#6501C2314yes—
119#6499—22no—
120#6499C2314yes—
121C2×#1142—24no—
122C2×#1142C2314yes—
123C2×#1141—24no—
124C2×#1141C2314yes—
125C4×C22⋊D7—28no—
126C4×C22⋊D7—28no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130#6489—28no—
131C2×C4⋊Dic7—21no—
132C2×C4⋊Dic7—21no—
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2311yescharacteristic
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×C4×Dic7—21no—
139C2×C4×Dic7D411yescharacteristic
140C2×C4×Dic7D411yescharacteristic
141C2×C4×Dic7C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C2×#1132—24no—
145C2×#1132C2314yes—
146C2×C8×D7—24no—
147C2×C8×D7—24no—
148C2×C8×D7C2314yes—
149C2×C8×D7C2314yes—
150#6460—22no—
151#6460C2314yes—
152#6458—22no—
153#6458C2314yes—
154#6453—22no—
155#6453C2314yes—
156#6451—22no—
157#6451C2314yes—
158#6448—28no—
159#6447—28no—
160#6446—28no—
161#6442—28no—
162C4×D28—22no—
163C4×D28C2314yes—
164C42×D7D414yes—
165C42×D7C2314yes—
166C4×Dic14—22no—
167C4×Dic14C2314yes—
168C7×#106C2314yes—
169C7×#102C2314yes—
170C7×#102C2314yes—
171C7×#97C2314yes—
172#6406C2314yes—
173#6406C2314yes—
174#6395C2314yes—
175#6392C2314yes—
176#6390C2314yes—
177#6389C2314yes—
178#6389C2314yes—
179#6384C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183#6377C2314yes—
184C2×#532—71no—
185C2×#529—71no—
186#3180—716no—
187C2×#501—71no—
188C2×#496—71no—
189C2×#490—71no—
190C2×#489—71no—
191C2×#466—71no—
192C2×#466—71no—
193C2×#465—71no—
194C2×#465—71no—
195C2×#442—71no—
196C2×#442D711yescharacteristic, complemented
197C2×#440—71no—
198C2×#440—71no—
199C22×#97—71no—
200C24×C7—21no—
201C24×C7—21no—
202C23×D7—21no—
203C23×D7C2×D411yescharacteristic
204C2×C7×D4—21no—
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4C2412yes—
211C2×C7×D4C2412yes—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—24no—
215C22×C4×C7—24no—
216C22×C4×C7—44no—
217C22×C4×C7—44no—
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2411yescharacteristic
221C2×C22⋊D7—24no—
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—44no—
226C2×C22⋊D7—44no—
227C2×C22⋊D7—44no—
228C2×C22⋊D7—44no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235#1157—432no—
236C2×D28—22no—
237C2×D28—22no—
238C2×D28—24no—
239C2×D28—21no—
240C2×D28—44no—
241C2×D28C2412yes—
242C2×C4×D7—24no—
243C2×C4×D7—22no—
244C2×C4×D7—22no—
245C2×C4×D7—24no—
246C2×C4×D7—42no—
247C2×C4×D7—44no—
248C2×C4×D7C2×D412yes—
249C2×C4×D7C2×D414yes—
250C2×C4×D7C2×D414yes—
251C2×C4×D7C2412yes—
252C2×Dic14—22no—
253C2×Dic14—22no—
254C2×Dic14—21no—
255C2×Dic14—24no—
256C2×Dic14—44no—
257C2×Dic14C2412yes—
258C7×D8—28no—
259C2×C7×C8—22no—
260C2×C7×C8#4114yescomplemented
261C2×C7×C8C2412yes—
262C2×C7×C8C2412yes—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4C2412yes—
266C7×C4⋊C4C2412yes—
267C7×C22⋊C4—24no—
268C7×C22⋊C4—24no—
269C42×C7C2×D412yes—
270C42×C7C2412yes—
271C22⋊Dic7—24no—
272C22⋊Dic7—24no—
273C22⋊Dic7—24no—
274C22⋊Dic7—24no—
275#1142—28no—
276#1141—28no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—24no—
283C4⋊Dic7—24no—
284C4⋊Dic7C2412yes—
285C4⋊Dic7C2412yes—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289C4×Dic7—24no—
290C4×Dic7C2×D412yes—
291C4×Dic7C2×D414yes—
292C4×Dic7C2×D414yes—
293C4×Dic7C2412yes—
294C2×C7⋊C8—22no—
295C2×C7⋊C8#4114yescomplemented
296C2×C7⋊C8C2412yes—
297C2×C7⋊C8C2412yes—
298#1132—28no—
299C8×D7—28no—
300C8×D7—28no—
301C22×#41—141no—
302C22×SD16—71no—
303C22×SD16—71no—
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—71no—
317C2×#124—141no—
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—141no—
327C2×C4×D4—141no—
328C2×C4×D4C2×D711yescharacteristic
329C2×C4×D4C2×D711yescharacteristic
330C2×#117—141no—
331C22×C42—71no—
332#501—78no—
333#496—78no—
334#490—78no—
335#489—78no—
336#466—78no—
337#466—78no—
338#465—78no—
339#465—78no—
340#442—78no—
341#442C2×D718yescomplemented
342#440—78no—
343#440—78no—
344C2×#107—71no—
345C2×#107—71no—
346C2×#106—71no—
347C2×#106C2×D711yescharacteristic
348C2×#103—71no—
349C2×#103—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102C2×D711yescharacteristic
355C2×#102C2×D711yescharacteristic
356C2×#97—71no—
357C2×#97—71no—
358C2×#97—71no—
359C2×#97—78no—
360C2×#97C2×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×D4—22no—
379C7×D4—22no—
380C7×D4—22no—
381C7×D4—22no—
382C7×D4—42no—
383C7×D4—42no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—48no—
389C2×C4×C7—48no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D411yescharacteristic
395C2×C4×C7C2×#4112yes—
396C2×C4×C7C2×#4112yes—
397C2×C4×C7C2511yescharacteristic
398C22⋊D7—48no—
399C22⋊D7—48no—
400C22⋊D7—48no—
401C22⋊D7—48no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—42no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7C22×D412yes—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414D28—22no—
415D28—22no—
416D28—48no—
417D28—42no—
418C4×D7—28no—
419C4×D7—24no—
420C4×D7—22no—
421C4×D7—22no—
422C4×D7—44no—
423C4×D7—48no—
424Dic14—22no—
425Dic14—22no—
426Dic14—48no—
427Dic14—42no—
428C7×C8—22no—
429C7×C8C2×#4114yescomplemented
430C7⋊C8—22no—
431C7⋊C8C2×#4114yescomplemented
432C2×#41—148no—
433C2×#41—288no—
434C22×Q8—71no—
435C22×Q8—141no—
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—21no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4—141no—
450C2×SD16—74no—
451C2×SD16—74no—
452C2×SD16—144no—
453C2×SD16—144no—
454C2×D8—24no—
455C2×D8—74no—
456C2×D8—144no—
457C2×D8C22×D714yes—
458C22×C8—71no—
459C22×C8—71no—
460C22×C8—74no—
461C22×C8—74no—
462C22×C8—144no—
463C22×C8—144no—
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—74no—
474#124—148no—
475#124—142no—
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—22no—
490C4×D4—74no—
491C4×D4—148no—
492C4×D4—148no—
493C4×D4—142no—
494C4×D4C22×D714yes—
495C4×D4C22×D714yes—
496#117—148no—
497C2×C4⋊C4—71no—
498C2×C4⋊C4—71no—
499C2×C4⋊C4—141no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4C22×D711yescharacteristic
505C2×C4⋊C4C22×D711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—141no—
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#106C22×D714yes—
526#103—74no—
527#103—74no—
528#102—74no—
529#102—74no—
530#102—74no—
531#102—74no—
532#102C22×D714yes—
533#102C22×D714yes—
534#97—74no—
535#97—74no—
536#97—74no—
537#97C22×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#53212yes—
547C22×C7C2×AGL(1,ℤ/8)12yes—
548C22×C7#57512yes—
549C22×C7C23×D411yescharacteristic
550C2×D7—28no—
551C2×D7—22no—
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#53212yes—
563C4×C7C22×#4111yescharacteristic
564C4×C7C22×#4111yescharacteristic
565Dic7—22no—
566Dic7—22no—
567Dic7—22no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571C24—21no—
572C24—21no—
573C24—71no—
574C24—141no—
575#41—2832no—
576C2×Q8—72no—
577C2×Q8—144no—
578C2×Q8—141no—
579C2×Q8—142no—
580C2×Q8—142no—
581C2×Q8—284no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
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—142no—
595C2×D4—141no—
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—24no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—71no—
611C22×C4—71no—
612C22×C4—71no—
613C22×C4—72no—
614C22×C4—74no—
615C22×C4—72no—
616C22×C4—74no—
617C22×C4—144no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—144no—
624C22×C4—282no—
625C22×C4—284no—
626C22×C4D4×D711yescharacteristic
627C22×C4D4×D711yescharacteristic
628C22×C4C23×D711yescharacteristic
629SD16—148no—
630SD16—148no—
631D8—28no—
632D8—148no—
633C2×C8—22no—
634C2×C8—74no—
635C2×C8—72no—
636C2×C8—72no—
637C2×C8—148no—
638C2×C8—142no—
639C2×C8—148no—
640C2×C8#115714yescomplemented
641C2×C8C23×D712yes—
642C2×C8C23×D712yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
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⋊C4C23×D712yes—
655C4⋊C4C23×D712yes—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—144no—
659C22⋊C4—144no—
660C22⋊C4—144no—
661C22⋊C4—144no—
662C22⋊C4—144no—
663C22⋊C4—144no—
664C22⋊C4—144no—
665C42—74no—
666C42—74no—
667C42—72no—
668C42—72no—
669C42—144no—
670C42D4×D712yes—
671C42C23×D712yes—
672C2×C7—82no—
673C2×C7—82no—
674C2×C7#318014yescomplemented
675C2×C7C2×#53211yescharacteristic
676C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
677C2×C7C2×#57511yescharacteristic
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—142no—
698Q8—142no—
699Q8—288no—
700Q8—282no—
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—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—72no—
724C2×C4—72no—
725C2×C4—72no—
726C2×C4—148no—
727C2×C4—142no—
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—284no—
737C2×C4—288no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—282no—
741C2×C4C2×#115712yes—
742C2×C4C2×D4×D712yes—
743C2×C4C2×D4×D712yes—
744C2×C4C2×D4×D711yescharacteristic
745C2×C4D7×#4112yes—
746C2×C4C24×D711yescharacteristic
747C8—22no—
748C8—74no—
749C8—142no—
750C8C2×#115714yescomplemented
751C7C2×#318011yescharacteristic, complemented, Sylow
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—74no—
759C22—84no—
760C22—84no—
761C22—142no—
762C22—142no—
763C22—148no—
764C22—282no—
765C22—282no—
766C22—282no—
767C22—564no—
768C22#9023912yes—
769C22D7×AGL(1,ℤ/8)12yes—
770C22#9046412yes—
771C22C22×D4×D711yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—142no—
777C4—142no—
778C4—142no—
779C4—282no—
780C4—282no—
781C4—282no—
782C4#9023912yes—
783C4C22×#115711yescharacteristic
784C4C2×D7×#4111yescharacteristic
785C2—82no—
786C2—82no—
787C2—144no—
788C2—562no—
789C2#1173732114yesdirect product factor
790C2C2×#9023911yescharacteristic
791C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
792C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#442C2
socleC23×C7C22×D4
hypercenterC2×#442D7
hypocenterC7C2×#3180
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#90239C2semidirect
2. C2×#90248C2semidirect
3. C2×C7×#442C2semidirect
4. C2×#89929C2semidirect
5. C2×#89926C2semidirect
6. C2×#89786C2semidirect
7. C2×#89790C2semidirect
8. #11737321C2direct (N × H)
9. C2×#89636C2semidirect
10. C2×#89628C2semidirect
11. C2×#89547C2semidirect
12. C2×#89550C2semidirect
13. C2×#89536C2semidirect
14. C2×#89537C2semidirect
15. C2×#89482C2semidirect
16. C2×D7×#97C2semidirect
34. #90248C22semidirect
36. #90239C22semidirect
48. C7×#442C22semidirect
55. #89929C22semidirect
56. #89926C22semidirect
62. #89790C22semidirect
63. #89786C22semidirect
69. #89636C22semidirect
70. #89628C22semidirect
71. #89550C22semidirect
72. #89547C22semidirect
73. #89537C22semidirect
74. #89536C22semidirect
75. #89482C22semidirect
76. D7×#97C22semidirect
196. C2×#442D7semidirect
260. C2×C7×C8#41semidirect
295. C2×C7⋊C8#41semidirect
341. #442C2×D7semidirect
429. C7×C8C2×#41semidirect
431. C7⋊C8C2×#41semidirect
640. C2×C8#1157semidirect
674. C2×C7#3180semidirect
750. C8C2×#1157semidirect
751. C7C2×#3180semidirect
789. C2#11737321direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902392
C2×#902482
C2×C7×#4422
C2×#899292
C2×#899262
C2×#897862
C2×#897902
#117373212
C2×#896362
C2×#896282
C2×#895472
C2×#895502
C2×#895362
C2×#895372
C2×#894822
C2×D7×#972
C2×#31807