Finite Group Databasebeta

← C2×#11738856 #14230663

Subgroups — C2×#11738856 #14230663

Order 1792.

2114 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×#90289C211yesmaximal, characteristic
2C2×#90220C211yesmaximal, characteristic, complemented
3C2×C7×#482C211yesmaximal, characteristic, complemented
4C2×#89814C211yesmaximal, characteristic, complemented
5C2×#89776C211yesmaximal, characteristic, complemented
6#11738856C2116yesmaximal, direct product factor
7C2×#89656C211yesmaximal, characteristic, complemented
8C2×#89645C211yesmaximal, characteristic, complemented
9C2×#89629C211yesmaximal, characteristic, complemented
10C2×#89640C211yesmaximal, characteristic, complemented
11C2×#89539C211yesmaximal, characteristic, complemented
12C2×#89555C211yesmaximal, characteristic, complemented
13C2×#89543C211yesmaximal, characteristic, complemented
14C2×#89540C211yesmaximal, characteristic, complemented
15C2×#89511C211yesmaximal, characteristic, complemented
16C2×#89501C211yesmaximal, characteristic, complemented
17C22×#1159C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C2×C7×#121C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21C2×#6502—21no—
22C2×#6499C2211yescharacteristic
23C2×D4×Dic7—21no—
24C22×#1142C2211yescharacteristic
25C2×C4×C22⋊D7C2211yescharacteristic
26C2×#6487C2211yescharacteristic
27C22×#1136C2211yescharacteristic
28C22×Dic28C2211yescharacteristic
29C22×Dic28C2211yescharacteristic
30C22×#1131C2211yescharacteristic
31#90289—24no—
32#90289C2218yes—
33#90220—24no—
34#90220C2218yescomplemented
35C2×#6460C2211yescharacteristic
36C2×#6460C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×#6453C2211yescharacteristic
39C2×#6450C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×#6448—21no—
42C2×#6446—21no—
43C2×#6442—21no—
44C2×#6441—21no—
45C2×#6435—21no—
46C2×#6433—21no—
47C7×#482C2218yescomplemented
48C2×C7×#107C2211yescharacteristic
49C2×C7×#106C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C7×C22⋊C8C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89814C2218yescomplemented
60#89776C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89656C2218yescomplemented
68#89645C2218yescomplemented
69#89640C2218yescomplemented
70#89629C2218yescomplemented
71#89555C2218yescomplemented
72#89543C2218yescomplemented
73#89540C2218yescomplemented
74#89539C2218yescomplemented
75#89511C2218yescomplemented
76#89501C2218yescomplemented
77C2×#3327—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C23×Dic7—21no—
84C23×Dic7—21no—
85C2×#1159—22no—
86C2×#1159—24no—
87C2×#1159—42no—
88C2×#1159C2314yes—
89C22×C4×D7—21no—
90C22×C4×D7C2311yescharacteristic
91C22×Dic14—24no—
92C22×Dic14—21no—
93C22×Dic14—22no—
94C22×Dic14—42no—
95C22×Dic14C2311yescharacteristic
96C22×Dic14C2311yescharacteristic
97C22×Dic14C2314yes—
98C22×Dic14C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C22×C7×C8C2311yescharacteristic
101C7×#121—22no—
102C7×#121C2314yes—
103C7×#117—22no—
104C7×#117C2314yes—
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C42×C7—21no—
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7D411yescharacteristic
115#6502—28no—
116#6499—22no—
117#6499C2314yes—
118D4×Dic7—28no—
119C2×#1142—42no—
120C2×#1142C2314yes—
121C4×C22⋊D7D414yes—
122C4×C22⋊D7C2314yes—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4D411yescharacteristic
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7C2311yescharacteristic
130#6487—22no—
131#6487C2314yes—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4D411yescharacteristic
138C2×C4×Dic7—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7C2311yescharacteristic
141C2×#1136—42no—
142C2×#1136C2314yes—
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C2×Dic28—24no—
146C2×Dic28—42no—
147C2×Dic28C2314yes—
148C2×Dic28C2314yes—
149C2×#1131—42no—
150C2×#1131C2314yes—
151#6460—22no—
152#6460—22no—
153#6460C2314yes—
154#6460C2314yes—
155D7×C4⋊C4—22no—
156D7×C4⋊C4C2314yes—
157#6453—22no—
158#6453C2314yes—
159#6450—22no—
160#6450—22no—
161#6450C2314yes—
162#6450C2314yes—
163#6448—28no—
164#6446—28no—
165#6442—28no—
166#6441—28no—
167#6435—28no—
168#6433—28no—
169C7×#107C2314yes—
170C7×#106C2314yes—
171C7×#102C2314yes—
172C7×#102C2314yes—
173C7×C22⋊C8C2314yes—
174#6406C2314yes—
175(C2×D7)⋊C8C2314yes—
176#6390C2314yes—
177#6390C2314yes—
178Dic7⋊C8C2314yes—
179C8×Dic7C2314yes—
180#6384C2314yes—
181#6384C2314yes—
182#6384C2314yes—
183#6384C2314yes—
184#6384C2314yes—
185#6381C2314yes—
186C2×#552—71no—
187C2×#548—71no—
188#3327—716no—
189C2×#488—71no—
190C2×#484—71no—
191C2×#482D711yescharacteristic, complemented
192C2×#479—71no—
193C2×#470—71no—
194C2×#468—71no—
195C2×#464—71no—
196C2×#452—71no—
197C2×#451—71no—
198C2×C4×Q16—71no—
199C2×#436—71no—
200C2×#417—71no—
201C2×#419—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C23×D7C2×D411yescharacteristic
205C2×C7×D4—24no—
206C2×C7×D4—21no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—44no—
210C2×C7×D4C2412yes—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2411yescharacteristic
220C2×C22⋊D7—24no—
221C2×C22⋊D7—42no—
222C2×C22⋊D7—44no—
223C2×C22⋊D7C2×D414yes—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—24no—
229C22×Dic7—24no—
230C22×Dic7—44no—
231C22×Dic7—44no—
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235#1159—28no—
236#1159—44no—
237#1159—48no—
238C2×C4×D7—22no—
239C2×C4×D7—22no—
240C2×C4×D7—24no—
241C2×C4×D7—44no—
242C2×C4×D7C2×D412yes—
243C2×C4×D7C2412yes—
244C2×Dic14—21no—
245C2×Dic14—22no—
246C2×Dic14—22no—
247C2×Dic14—22no—
248C2×Dic14—22no—
249C2×Dic14—22no—
250C2×Dic14—28no—
251C2×Dic14—24no—
252C2×Dic14—21no—
253C2×Dic14—21no—
254C2×Dic14—44no—
255C2×Dic14—48no—
256C2×Dic14—44no—
257C2×Dic14#4114yes—
258C2×Dic14C2412yes—
259C2×Dic14C2412yes—
260C2×Dic14C2412yes—
261C2×C7×C8—22no—
262C2×C7×C8—22no—
263C2×C7×C8C2412yes—
264C2×C7×C8C2412yes—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—21no—
267C7×C4⋊C4—21no—
268C7×C4⋊C4C2412yes—
269C7×C4⋊C4C2412yes—
270C7×C4⋊C4C2412yes—
271C7×C22⋊C4—24no—
272C7×C22⋊C4—24no—
273C42×C7—24no—
274C22⋊Dic7—24no—
275C22⋊Dic7—24no—
276C22⋊Dic7—24no—
277C22⋊Dic7C2×D414yes—
278#1142—44no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4C2×D414yes—
282C4⋊Dic7—21no—
283C4⋊Dic7—24no—
284C4⋊Dic7—24no—
285C4⋊Dic7—24no—
286C4⋊Dic7C2412yes—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292Dic7⋊C4C2×D414yes—
293C4×Dic7—24no—
294C4×Dic7—24no—
295C4×Dic7C2×D412yes—
296C4×Dic7C2412yes—
297#1136—44no—
298C2×C7⋊C8—22no—
299C2×C7⋊C8—22no—
300C2×C7⋊C8C2412yes—
301C2×C7⋊C8C2412yes—
302Dic28—28no—
303Dic28—44no—
304#1131—44no—
305C22×#41—71no—
306C23×Q8—71no—
307C22×Q16—71no—
308C22×Q16—71no—
309C22×SD16—71no—
310C22×M16—71no—
311C22×M16—71no—
312#552—78no—
313#552—144no—
314#548—78no—
315#548—144no—
316C2×#126—141no—
317C2×#125—71no—
318C2×#125—141no—
319C2×#124—71no—
320C2×#124—141no—
321C2×#123—141no—
322C2×C22⋊Q8—71no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—141no—
326C2×#121—141no—
327C2×#121C2×D711yescharacteristic
328C2×C4×Q8—71no—
329C2×C4×Q8—71no—
330C2×C4×D4—71no—
331C2×C4×D4—141no—
332C2×#117—141no—
333C2×#117C2×D711yescharacteristic
334C22×C4⋊C4—71no—
335#488—78no—
336#484—78no—
337#482C2×D718yescomplemented
338#479—78no—
339#470—78no—
340#468—78no—
341#464—78no—
342#452—78no—
343#451—78no—
344C4×Q16—78no—
345#436—78no—
346C2×#107—71no—
347C2×#107C2×D711yescharacteristic
348C2×#106C2×D711yescharacteristic
349C2×C4⋊C8—71no—
350#419—78no—
351#417—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×#102C2×D711yescharacteristic
361C2×#102C2×D711yescharacteristic
362C2×C22⋊C8—71no—
363C2×C22⋊C8C2×D711yescharacteristic
364C2×C4×C8—71no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—42no—
370C23×C7—42no—
371C23×C7—42no—
372C23×C7C22×D412yes—
373C23×C7C22×D411yescharacteristic
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7C22×D412yes—
378C7×D4—22no—
379C7×D4—22no—
380C7×D4—48no—
381C7×D4—42no—
382C2×C4×C7—22no—
383C2×C4×C7—24no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D411yescharacteristic
394C2×C4×C7C2×#4112yes—
395C2×C4×C7H(5,𝔽2)12yes—
396C2×C4×C7C2511yescharacteristic
397C22⋊D7—44no—
398C22⋊D7—48no—
399C2×Dic7—24no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—48no—
408C2×Dic7—48no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7—42no—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414C2×Dic7C22×D412yes—
415C4×D7—24no—
416C4×D7—22no—
417C4×D7—22no—
418C4×D7—48no—
419Dic14—24no—
420Dic14—22no—
421Dic14—22no—
422Dic14—22no—
423Dic14—22no—
424Dic14—22no—
425Dic14—48no—
426Dic14—42no—
427Dic14—42no—
428Dic14C2×#4114yes—
429C7×C8—22no—
430C7×C8—22no—
431C7⋊C8—22no—
432C7⋊C8—22no—
433C2×#41—74no—
434C2×#41—142no—
435C2×#41—144no—
436C2×#41—282no—
437C22×Q8—71no—
438C22×Q8—71no—
439C22×Q8—71no—
440C22×Q8—74no—
441C22×Q8—144no—
442C22×Q8—141no—
443C22×Q8—142no—
444C22×Q8—282no—
445C22×D4—21no—
446C22×D4—71no—
447C22×D4—141no—
448C22×D4C22×D711yescharacteristic
449C23×C4—71no—
450C23×C4—141no—
451C23×C4—141no—
452C23×C4—141no—
453C23×C4C22×D711yescharacteristic
454C2×Q16—74no—
455C2×Q16—74no—
456C2×Q16—144no—
457C2×Q16—282no—
458C2×SD16—74no—
459C2×SD16—282no—
460C2×M16—74no—
461C2×M16—74no—
462C2×M16—282no—
463C2×M16—282no—
464C22×C8—71no—
465C22×C8—71no—
466C22×C8C22×D711yescharacteristic
467C22×C8C22×D711yescharacteristic
468#126—148no—
469#125—74no—
470#125—148no—
471#125—142no—
472#124—74no—
473#124—142no—
474#124—148no—
475#123—148no—
476C22⋊Q8—74no—
477C22⋊Q8—74no—
478C22⋊Q8—74no—
479C22⋊Q8—148no—
480C22⋊Q8—142no—
481C22⋊Q8—142no—
482C22⋊Q8—142no—
483#121—22no—
484#121—148no—
485#121C22×D714yes—
486C4×Q8—74no—
487C4×Q8—74no—
488C4×Q8—142no—
489C4×Q8—142no—
490C4×D4—74no—
491C4×D4—74no—
492C4×D4—148no—
493#117—22no—
494#117—148no—
495#117C22×D714yes—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—71no—
498C2×C4⋊C4—74no—
499C2×C4⋊C4—142no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
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⋊C4C22×D711yescharacteristic
509C2×C4⋊C4C22×D711yescharacteristic
510C2×C4⋊C4C22×D711yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—71no—
514C2×C22⋊C4—71no—
515C2×C22⋊C4—141no—
516C2×C22⋊C4—141no—
517C2×C22⋊C4—141no—
518C2×C22⋊C4—141no—
519C2×C22⋊C4—141no—
520C2×C42—21no—
521C2×C42—71no—
522C2×C42—141no—
523C2×C42—141no—
524#107—74no—
525#107C22×D714yes—
526#106C22×D714yes—
527C4⋊C8—74no—
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#102C22×D714yes—
537#102C22×D714yes—
538C22⋊C8—74no—
539C22⋊C8C22×D714yes—
540C4×C8—74no—
541C22×C7—22no—
542C22×C7—22no—
543C22×C7—22no—
544C22×C7—44no—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—84no—
549C22×C7#54612yes—
550C22×C7#57512yes—
551C22×C7#57812yes—
552C22×C7C23×D411yescharacteristic
553C2×D7—22no—
554C2×D7—22no—
555C2×D7—22no—
556C2×D7—44no—
557C4×C7—22no—
558C4×C7—42no—
559C4×C7—42no—
560C4×C7—42no—
561C4×C7#54612yes—
562C4×C7C22×#4111yescharacteristic
563C4×C7C2×H(5,𝔽2)11yescharacteristic
564Dic7—24no—
565Dic7—22no—
566Dic7—22no—
567Dic7—22no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571C24—21no—
572C24—71no—
573C24D4×D711yescharacteristic
574#41—148no—
575#41—284no—
576#41—288no—
577C2×Q8—74no—
578C2×Q8—72no—
579C2×Q8—72no—
580C2×Q8—72no—
581C2×Q8—148no—
582C2×Q8—141no—
583C2×Q8—141no—
584C2×Q8—144no—
585C2×Q8—141no—
586C2×Q8—142no—
587C2×Q8—142no—
588C2×Q8—142no—
589C2×Q8—142no—
590C2×Q8—142no—
591C2×Q8—284no—
592C2×Q8—284no—
593C2×Q8—288no—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—44no—
599C2×D4—74no—
600C2×D4—144no—
601C2×D4—282no—
602C2×D4—284no—
603C2×D4C23×D712yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—71no—
610C22×C4—71no—
611C22×C4—71no—
612C22×C4—72no—
613C22×C4—72no—
614C22×C4—144no—
615C22×C4—144no—
616C22×C4—141no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—144no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—284no—
624C22×C4—284no—
625C22×C4—284no—
626C22×C4D4×D712yes—
627C22×C4D4×D711yescharacteristic
628C22×C4C23×D712yes—
629C22×C4C23×D711yescharacteristic
630Q16—148no—
631Q16—284no—
632SD16—284no—
633M16—284no—
634M16—284no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—72no—
638C2×C8—72no—
639C2×C8—142no—
640C2×C8—142no—
641C2×C8C23×D712yes—
642C2×C8C23×D712yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—74no—
647C4⋊C4—72no—
648C4⋊C4—144no—
649C4⋊C4—144no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—144no—
653C4⋊C4—144no—
654C4⋊C4—144no—
655C4⋊C4—144no—
656C4⋊C4—141no—
657C4⋊C4C23×D712yes—
658C4⋊C4C23×D712yes—
659C4⋊C4C23×D712yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—74no—
663C22⋊C4—74no—
664C22⋊C4—144no—
665C22⋊C4—144no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C22⋊C4—144no—
669C42—24no—
670C42—72no—
671C42—72no—
672C42—144no—
673C42—144no—
674C2×C7—42no—
675C2×C7—82no—
676C2×C7#332714yescomplemented
677C2×C7C2×#54611yescharacteristic
678C2×C7C2×#57511yescharacteristic
679C2×C7C2×#57811yescharacteristic
680D7—42no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—72no—
689C23—142no—
690C23—142no—
691C23—142no—
692C23C2×D4×D712yes—
693C23C2×D4×D711yescharacteristic
694Q8—74no—
695Q8—144no—
696Q8—142no—
697Q8—142no—
698Q8—142no—
699Q8—142no—
700Q8—142no—
701Q8—288no—
702Q8—282no—
703Q8—282no—
704D4—22no—
705D4—22no—
706D4—48no—
707D4—42no—
708D4—284no—
709D4—288no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—72no—
721C2×C4—72no—
722C2×C4—72no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—144no—
727C2×C4—142no—
728C2×C4—144no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—288no—
735C2×C4—288no—
736C2×C4—288no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4C2×D4×D712yes—
741C2×C4C2×D4×D711yescharacteristic
742C2×C4D7×#4112yes—
743C2×C4#655312yes—
744C2×C4C24×D711yescharacteristic
745C8—22no—
746C8—22no—
747C8—142no—
748C8—142no—
749C7C2×#332711yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—142no—
759C22—142no—
760C22—142no—
761C22—284no—
762C22#9034512yes—
763C22#9046212yes—
764C22#9046412yes—
765C22C22×D4×D711yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—142no—
771C4—142no—
772C4—144no—
773C4—142no—
774C4—282no—
775C4—282no—
776C4—282no—
777C4#9034512yes—
778C4C2×D7×#4111yescharacteristic
779C4C2×#655311yescharacteristic
780C2—42no—
781C2—82no—
782C2—282no—
783C2#1173885614yesdirect product factor
784C2C2×#9034511yescharacteristic
785C2C2×#9046211yescharacteristic
786C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#482C2
socleC23×C7C22×D4
prime radicalC2×#90289C2
hypercenterC2×#482D7
hypocenterC7C2×#3327
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#90220C2semidirect
3. C2×C7×#482C2semidirect
4. C2×#89814C2semidirect
5. C2×#89776C2semidirect
6. #11738856C2direct (N × H)
7. C2×#89656C2semidirect
8. C2×#89645C2semidirect
9. C2×#89629C2semidirect
10. C2×#89640C2semidirect
11. C2×#89539C2semidirect
12. C2×#89555C2semidirect
13. C2×#89543C2semidirect
14. C2×#89540C2semidirect
15. C2×#89511C2semidirect
16. C2×#89501C2semidirect
34. #90220C22semidirect
47. C7×#482C22semidirect
59. #89814C22semidirect
60. #89776C22semidirect
67. #89656C22semidirect
68. #89645C22semidirect
69. #89640C22semidirect
70. #89629C22semidirect
71. #89555C22semidirect
72. #89543C22semidirect
73. #89540C22semidirect
74. #89539C22semidirect
75. #89511C22semidirect
76. #89501C22semidirect
191. C2×#482D7semidirect
337. #482C2×D7semidirect
676. C2×C7#3327semidirect
749. C7C2×#3327semidirect
783. C2#11738856direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902892
C2×#902202
C2×C7×#4822
C2×#898142
C2×#897762
#117388562
C2×#896562
C2×#896452
C2×#896292
C2×#896402
C2×#895392
C2×#895552
C2×#895432
C2×#895402
C2×#895112
C2×#895012
C2×#33277