Finite Group Databasebeta

← C2×#11736949 #14230452

Subgroups — C2×#11736949 #14230452

Order 1792.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90242C211yesmaximal, characteristic
2C2×#90232C211yesmaximal, characteristic, complemented
3C2×C7×#435C211yesmaximal, characteristic, complemented
4C2×#89909C211yesmaximal, characteristic, complemented
5C2×#89905C211yesmaximal, characteristic, complemented
6C2×#89888C211yesmaximal, characteristic, complemented
7C2×#89885C211yesmaximal, characteristic, complemented
8#11736949C2116yesmaximal, direct product factor
9C2×#89621C211yesmaximal, characteristic, complemented
10C2×#89619C211yesmaximal, characteristic, complemented
11C2×#89505C211yesmaximal, characteristic, complemented
12C2×#89505C211yesmaximal, characteristic, complemented
13C2×#89494C211yesmaximal, characteristic, complemented
14C2×#89495C211yesmaximal, characteristic, complemented
15C2×#89475C211yesmaximal, characteristic, complemented
16C2×#89482C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C22×#1157C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C23×C7×C8C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×#6501—21no—
23C2×#6498—21no—
24C2×#6489C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C2×#6487C2211yescharacteristic
27C2×#6487C2211yescharacteristic
28C2×#6487C2211yescharacteristic
29C2×#6487C2211yescharacteristic
30C22×Dic28C2211yescharacteristic
31C22×Dic28C2211yescharacteristic
32C22×#1132C2211yescharacteristic
33#90242—24no—
34#90242C2218yes—
35#90232—24no—
36#90232C2218yescomplemented
37C2×D7×C4⋊C4—21no—
38C2×#6452—21no—
39C2×#6446—21no—
40C2×#6446—21no—
41C2×#6442—21no—
42C2×#6440—21no—
43C2×C4×D28C2211yescharacteristic
44C2×#6433C2211yescharacteristic
45C2×#6432C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C7×#435C2218yescomplemented
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×C7×#97C2211yescharacteristic
52#89909C2218yescomplemented
53#89905C2218yescomplemented
54#89888C2218yescomplemented
55#89885C2218yescomplemented
56C2×#6395C2211yescharacteristic
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2211yescharacteristic
69#89621C2218yescomplemented
70#89619C2218yescomplemented
71#89505C2218yescomplemented
72#89505C2218yescomplemented
73#89495C2218yescomplemented
74#89494C2218yescomplemented
75#89482C2218yescomplemented
76#89475C2218yescomplemented
77C2×#3315—71nomaximal, Sylow
78C22×C7×D4D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C2×#1157—22no—
85C2×#1157—22no—
86C2×#1157—24no—
87C2×#1157—24no—
88C2×#1157—42no—
89C2×#1157—42no—
90C2×#1157C2314yes—
91C2×#1157C2314yes—
92C22×D28C2311yescharacteristic
93C22×C4×D7—21no—
94C22×C4×D7—21no—
95C22×C4×D7—21no—
96C22×Dic14C2311yescharacteristic
97C22×Dic14C2311yescharacteristic
98C22×Dic14C2311yescharacteristic
99C2×C7×M16—42no—
100C2×C7×M16C2314yes—
101C22×C7×C8—42no—
102C22×C7×C8C2311yescharacteristic
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2311yescharacteristic
105C22×C7×C8C2311yescharacteristic
106C22×C7×C8C2314yes—
107C4×C7×D4D414yes—
108C4×C7×D4C2314yes—
109C2×C7×C4⋊C4D411yescharacteristic
110C2×C7×C22⋊C4D411yescharacteristic
111C2×C7×C22⋊C4D411yescharacteristic
112C2×C42×C7C2311yescharacteristic
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118#6501—28no—
119#6498—28no—
120C2×(C2×D7)⋊C4—21no—
121#6489—22no—
122#6489C2314yes—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—22no—
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2314yes—
132#6487—22no—
133#6487—22no—
134#6487—22no—
135#6487—22no—
136#6487C2314yes—
137#6487C2314yes—
138#6487C2314yes—
139#6487C2314yes—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×C4×Dic7—21no—
148C2×C4×Dic7—21no—
149C2×Dic28—42no—
150C2×Dic28—42no—
151C2×Dic28C2314yes—
152C2×Dic28C2314yes—
153C2×#1132—24no—
154C2×#1132C2314yes—
155D7×C4⋊C4—28no—
156#6452—28no—
157#6446—28no—
158#6446—28no—
159#6442—28no—
160#6440—28no—
161C4×D28—22no—
162C4×D28C2314yes—
163#6433—22no—
164#6433C2314yes—
165#6432—22no—
166#6432C2314yes—
167C4×Dic14—22no—
168C4×Dic14C2314yes—
169C7×C4⋊C8C2314yes—
170C7×C22⋊C8C2314yes—
171C7×C22⋊C8C2314yes—
172C7×#97C2314yes—
173#6395C2314yes—
174#6395C2314yes—
175#6395C2314yes—
176#6392C2314yes—
177#6392C2314yes—
178#6391C2314yes—
179#6390C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182#6390C2314yes—
183#6390C2314yes—
184#6390C2314yes—
185#6390C2314yes—
186C2×#552—71no—
187C2×#547—71no—
188#3315—716no—
189C2×#491—71no—
190C2×#484—71no—
191C2×#485—71no—
192C2×#478—71no—
193C2×#470—71no—
194C2×#467—71no—
195C2×#462—71no—
196C2×#452—71no—
197C2×#452—71no—
198C2×#440—71no—
199C2×#435D711yescharacteristic, complemented
200C2×#417—71no—
201C2×#416—71no—
202C24×C7C2×D411yescharacteristic
203C24×C7C2×D411yescharacteristic
204C23×D7—21no—
205C2×C7×D4—42no—
206C2×C7×D4C2×D414yes—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2411yescharacteristic
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—44no—
223C2×C22⋊D7—44no—
224C22×Dic7—24no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—44no—
233#1157—28no—
234#1157—28no—
235#1157—44no—
236#1157—44no—
237#1157—48no—
238#1157—48no—
239C2×D28—21no—
240C2×D28—22no—
241C2×D28#4114yes—
242C2×D28C2412yes—
243C2×C4×D7—24no—
244C2×C4×D7—24no—
245C2×C4×D7—24no—
246C2×C4×D7—44no—
247C2×C4×D7—44no—
248C2×C4×D7—44no—
249C2×Dic14—22no—
250C2×Dic14—22no—
251C2×Dic14—22no—
252C2×Dic14—22no—
253C2×Dic14—22no—
254C2×Dic14—22no—
255C2×Dic14—21no—
256C2×Dic14—21no—
257C2×Dic14—21no—
258C2×Dic14C2412yes—
259C2×Dic14C2412yes—
260C2×Dic14C2412yes—
261C7×M16—44no—
262C2×C7×C8—22no—
263C2×C7×C8—22no—
264C2×C7×C8—22no—
265C2×C7×C8—22no—
266C2×C7×C8—44no—
267C2×C7×C8C2412yes—
268C2×C7×C8C2412yes—
269C2×C7×C8C2412yes—
270C2×C7×C8C2412yes—
271C7×C4⋊C4C2×D414yes—
272C7×C22⋊C4C2×D414yes—
273C7×C22⋊C4C2×D414yes—
274C42×C7C2×D412yes—
275C42×C7C2412yes—
276C22⋊Dic7—24no—
277C22⋊Dic7—24no—
278C22⋊Dic7—24no—
279C22⋊Dic7—24no—
280C22⋊Dic7—24no—
281(C2×D7)⋊C4—24no—
282C4⋊Dic7—21no—
283C4⋊Dic7—24no—
284C4⋊Dic7—24no—
285C4⋊Dic7—21no—
286C4⋊Dic7—21no—
287C4⋊Dic7—21no—
288C4⋊Dic7—24no—
289C4⋊Dic7C2412yes—
290C4⋊Dic7C2412yes—
291C4⋊Dic7C2412yes—
292C4⋊Dic7C2412yes—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4—24no—
296Dic7⋊C4—24no—
297Dic7⋊C4—24no—
298Dic7⋊C4—24no—
299Dic7⋊C4—24no—
300C4×Dic7—24no—
301C4×Dic7—24no—
302Dic28—44no—
303Dic28—44no—
304#1132—28no—
305C22×#41—71no—
306C22×#41—71no—
307C22×Q16—71no—
308C22×Q16—71no—
309C22×SD16—71no—
310C22×M16C2×D711yescharacteristic
311C23×C8C2×D711yescharacteristic
312#552—78no—
313#552—144no—
314#547—78no—
315#547—144no—
316C2×C4⋊Q8—71no—
317C2×#126—141no—
318C2×#125—71no—
319C2×#125—141no—
320C2×#123—141no—
321C2×#123—141no—
322C2×#123—141no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—71no—
326C2×C22⋊Q8—71no—
327C2×#121—141no—
328C2×C4×Q8—71no—
329C2×C4×D4—71no—
330C2×C4×D4C2×D711yescharacteristic
331C2×#117—71no—
332C2×#117—141no—
333C22×C4⋊C4—71no—
334C22×C4⋊C4—141no—
335#491—78no—
336#485—78no—
337#484—78no—
338#478—78no—
339#470—78no—
340#467—78no—
341#462—78no—
342#452—78no—
343#452—78no—
344#440—78no—
345#435C2×D718yescomplemented
346C2×#107—71no—
347C2×#107—71no—
348C2×#106—71no—
349C2×C4⋊C8C2×D711yescharacteristic
350#417—78no—
351#416—78no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#102—71no—
360C2×#102—71no—
361C2×#102—71no—
362C2×C22⋊C8C2×D711yescharacteristic
363C2×C22⋊C8C2×D711yescharacteristic
364C2×#97C2×D711yescharacteristic
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7C22×D412yes—
372C23×C7C22×D412yes—
373C23×C7C22×D411yescharacteristic
374C22×D7—24no—
375C22×D7—22no—
376C22×D7—42no—
377C22×D7—42no—
378C7×D4—44no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—24no—
384C2×C4×C7—24no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D411yescharacteristic
394C2×C4×C7C2×#4112yes—
395C2×C4×C7H(5,𝔽2)12yes—
396C2×C4×C7C2511yescharacteristic
397C22⋊D7—48no—
398C22⋊D7—48no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—48no—
407C2×Dic7—42no—
408C2×Dic7—42no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7—42no—
412C2×Dic7—42no—
413C2×Dic7—42no—
414D28—24no—
415D28—22no—
416D28C2×#4114yes—
417C4×D7—48no—
418C4×D7—48no—
419C4×D7—48no—
420Dic14—22no—
421Dic14—22no—
422Dic14—22no—
423Dic14—22no—
424Dic14—22no—
425Dic14—22no—
426Dic14—42no—
427Dic14—42no—
428Dic14—42no—
429C7×C8—22no—
430C7×C8—22no—
431C7×C8—22no—
432C7×C8—22no—
433C2×#41—74no—
434C2×#41—74no—
435C2×#41—144no—
436C2×#41—144no—
437C2×#41—142no—
438C2×#41—142no—
439C2×#41—282no—
440C2×#41—282no—
441C22×Q8—71no—
442C22×Q8—71no—
443C22×Q8—71no—
444C22×D4—71no—
445C22×D4—141no—
446C22×D4—141no—
447C22×D4D2811yescharacteristic
448C23×C4—141no—
449C23×C4—141no—
450C23×C4—141no—
451C23×C4—141no—
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C2×Q16—74no—
455C2×Q16—74no—
456C2×Q16—282no—
457C2×Q16—282no—
458C2×SD16—74no—
459C2×SD16—144no—
460C2×M16—42no—
461C2×M16C22×D714yes—
462C22×C8—42no—
463C22×C8C22×D711yescharacteristic
464C22×C8C22×D711yescharacteristic
465C22×C8C22×D711yescharacteristic
466C22×C8C22×D711yescharacteristic
467C22×C8C22×D714yes—
468C4⋊Q8—74no—
469C4⋊Q8—142no—
470#126—148no—
471#125—74no—
472#125—148no—
473#125—142no—
474#123—148no—
475#123—148no—
476#123—148no—
477C22⋊Q8—74no—
478C22⋊Q8—74no—
479C22⋊Q8—74no—
480C22⋊Q8—74no—
481C22⋊Q8—142no—
482C22⋊Q8—142no—
483C22⋊Q8—142no—
484C22⋊Q8—142no—
485#121—148no—
486C4×Q8—74no—
487C4×Q8—142no—
488C4×D4—74no—
489C4×D4—142no—
490C4×D4D2814yes—
491C4×D4C22×D714yes—
492#117—74no—
493#117—142no—
494#117—148no—
495C2×C4⋊C4—71no—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—74no—
498C2×C4⋊C4—71no—
499C2×C4⋊C4—71no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—142no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4—141no—
506C2×C4⋊C4—141no—
507C2×C4⋊C4—141no—
508C2×C4⋊C4—141no—
509C2×C4⋊C4—141no—
510C2×C4⋊C4—141no—
511C2×C4⋊C4—148no—
512C2×C4⋊C4D2811yescharacteristic
513C2×C22⋊C4—141no—
514C2×C22⋊C4—141no—
515C2×C22⋊C4—141no—
516C2×C22⋊C4—141no—
517C2×C22⋊C4—141no—
518C2×C22⋊C4—141no—
519C2×C22⋊C4D2811yescharacteristic
520C2×C22⋊C4D2811yescharacteristic
521C2×C42—141no—
522C2×C42—141no—
523C2×C42C22×D711yescharacteristic
524#107—74no—
525#107—74no—
526#106—74no—
527C4⋊C8C22×D714yes—
528#103—74no—
529#103—74no—
530#103—74no—
531#103—74no—
532#103—74no—
533#103—74no—
534#103—74no—
535#102—74no—
536#102—74no—
537#102—74no—
538C22⋊C8C22×D714yes—
539C22⋊C8C22×D714yes—
540#97C22×D714yes—
541C22×C7—22no—
542C22×C7—22no—
543C22×C7—22no—
544C22×C7—22no—
545C22×C7—22no—
546C22×C7—22no—
547C22×C7—44no—
548C22×C7—44no—
549C22×C7#54612yes—
550C22×C7#57512yes—
551C22×C7#57812yes—
552C22×C7C23×D411yescharacteristic
553C2×D7—24no—
554C2×D7—48no—
555C2×D7—42no—
556C2×D7—42no—
557C4×C7—22no—
558C4×C7—22no—
559C4×C7—22no—
560C4×C7—22no—
561C4×C7#54612yes—
562C4×C7C22×#4111yescharacteristic
563C4×C7C2×H(5,𝔽2)11yescharacteristic
564Dic7—42no—
565Dic7—42no—
566Dic7—42no—
567Dic7—42no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571C24—141no—
572C24C2×D2811yescharacteristic
573C24C2×D2811yescharacteristic
574#41—148no—
575#41—148no—
576#41—284no—
577#41—284no—
578#41—288no—
579#41—288no—
580C2×Q8—72no—
581C2×Q8—72no—
582C2×Q8—72no—
583C2×Q8—141no—
584C2×Q8—141no—
585C2×Q8—141no—
586C2×Q8—142no—
587C2×Q8—142no—
588C2×Q8—142no—
589C2×Q8—142no—
590C2×Q8—142no—
591C2×Q8—142no—
592C2×D4—42no—
593C2×D4—74no—
594C2×D4—72no—
595C2×D4—144no—
596C2×D4—144no—
597C2×D4—141no—
598C2×D4—142no—
599C2×D4—284no—
600C2×D4—284no—
601C2×D4C2×D2814yes—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—144no—
607C22×C4—141no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—141no—
612C22×C4—141no—
613C22×C4—141no—
614C22×C4—144no—
615C22×C4—144no—
616C22×C4—144no—
617C22×C4—284no—
618C22×C4—284no—
619C22×C4—284no—
620C22×C4—284no—
621C22×C4C2×D2812yes—
622C22×C4C2×D2812yes—
623C22×C4C2×D2811yescharacteristic
624C22×C4C2×D2811yescharacteristic
625C22×C4C2×D2811yescharacteristic
626C22×C4C2×D2811yescharacteristic
627C22×C4C23×D712yes—
628C22×C4C23×D712yes—
629C22×C4C23×D711yescharacteristic
630Q16—284no—
631Q16—284no—
632SD16—148no—
633M16—44no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—44no—
639C2×C8C23×D712yes—
640C2×C8C23×D712yes—
641C2×C8C23×D712yes—
642C2×C8C23×D712yes—
643C4⋊C4—72no—
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—144no—
653C4⋊C4—144no—
654C4⋊C4—141no—
655C4⋊C4—141no—
656C4⋊C4—144no—
657C4⋊C4—141no—
658C4⋊C4—141no—
659C4⋊C4—144no—
660C4⋊C4—144no—
661C4⋊C4C2×D2814yes—
662C22⋊C4—144no—
663C22⋊C4—144no—
664C22⋊C4—144no—
665C22⋊C4—144no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C22⋊C4C2×D2814yes—
669C22⋊C4C2×D2814yes—
670C42—144no—
671C42—144no—
672C42C2×D2812yes—
673C42C23×D712yes—
674C2×C7—42no—
675C2×C7—42no—
676C2×C7#331514yescomplemented
677C2×C7C2×#54611yescharacteristic
678C2×C7C2×#57511yescharacteristic
679C2×C7C2×#57811yescharacteristic
680D7—44no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—144no—
688C23—142no—
689C23—282no—
690C23—282no—
691C23C22×D2812yes—
692C23C22×D2812yes—
693C23C22×D2811yescharacteristic
694Q8—142no—
695Q8—142no—
696Q8—142no—
697Q8—142no—
698Q8—142no—
699Q8—142no—
700Q8—282no—
701Q8—282no—
702Q8—282no—
703D4—44no—
704D4—74no—
705D4—144no—
706D4—142no—
707D4—288no—
708D4—288no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—288no—
727C2×C4—288no—
728C2×C4—288no—
729C2×C4—288no—
730C2×C4—282no—
731C2×C4—282no—
732C2×C4—282no—
733C2×C4—282no—
734C2×C4—282no—
735C2×C4—282no—
736C2×C4—282no—
737C2×C4C22×D2812yes—
738C2×C4C22×D2812yes—
739C2×C4C22×D2812yes—
740C2×C4C22×D2812yes—
741C2×C4C22×D2811yescharacteristic
742C2×C4#654812yes—
743C2×C4D7×#4112yes—
744C2×C4C24×D711yescharacteristic
745C8—22no—
746C8—22no—
747C8—22no—
748C8—22no—
749C7C2×#331511yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—144no—
759C22—288no—
760C22—282no—
761C22—282no—
762C22#9024512yes—
763C22#9043912yes—
764C22#9044412yes—
765C22C23×D2811yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—282no—
771C4—282no—
772C4—282no—
773C4—282no—
774C4—282no—
775C4—282no—
776C4—282no—
777C4#9024512yes—
778C4C2×#654811yescharacteristic
779C4C2×D7×#4111yescharacteristic
780C2—42no—
781C2—42no—
782C2—284no—
783C2#1173694914yesdirect product factor
784C2C2×#9024511yescharacteristic
785C2C2×#9043911yescharacteristic
786C2C2×#9044411yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
prime radicalC2×#90242C2
hypercenterC2×#435D7
hypocenterC7C2×#3315
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#90232C2semidirect
3. C2×C7×#435C2semidirect
4. C2×#89909C2semidirect
5. C2×#89905C2semidirect
6. C2×#89888C2semidirect
7. C2×#89885C2semidirect
8. #11736949C2direct (N × H)
9. C2×#89621C2semidirect
10. C2×#89619C2semidirect
11. C2×#89505C2semidirect
12. C2×#89505C2semidirect
13. C2×#89494C2semidirect
14. C2×#89495C2semidirect
15. C2×#89475C2semidirect
16. C2×#89482C2semidirect
36. #90232C22semidirect
47. C7×#435C22semidirect
52. #89909C22semidirect
53. #89905C22semidirect
54. #89888C22semidirect
55. #89885C22semidirect
69. #89621C22semidirect
70. #89619C22semidirect
71. #89505C22semidirect
72. #89505C22semidirect
73. #89495C22semidirect
74. #89494C22semidirect
75. #89482C22semidirect
76. #89475C22semidirect
199. C2×#435D7semidirect
345. #435C2×D7semidirect
676. C2×C7#3315semidirect
749. C7C2×#3315semidirect
783. C2#11736949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902422
C2×#902322
C2×C7×#4352
C2×#899092
C2×#899052
C2×#898882
C2×#898852
#117369492
C2×#896212
C2×#896192
C2×#895052
C2×#894942
C2×#894952
C2×#894752
C2×#894822
C2×#33157