Finite Group Databasebeta

← C2×#11736412 #14230531

Subgroups — C2×#11736412 #14230531

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×#90508C211yesmaximal, characteristic
2C2×#90224C211yesmaximal, characteristic, complemented
3C2×C7×#419C211yesmaximal, characteristic, complemented
4C2×#90000C211yesmaximal, characteristic, complemented
5C2×#89906C211yesmaximal, characteristic, complemented
6C2×#89899C211yesmaximal, characteristic, complemented
7C2×#89775C211yesmaximal, characteristic, complemented
8#11736412C2116yesmaximal, direct product factor
9C2×#89570C211yesmaximal, characteristic, complemented
10C2×#89585C211yesmaximal, characteristic, complemented
11C2×#89582C211yesmaximal, characteristic, complemented
12C2×#89576C211yesmaximal, characteristic, complemented
13C2×#89567C211yesmaximal, characteristic, complemented
14C2×#89586C211yesmaximal, characteristic, complemented
15C2×#89566C211yesmaximal, characteristic, complemented
16C2×#89561C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C22×#1161C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21#90508—24no—
22#90508C2218yes—
23C2×#6510—21no—
24C2×#6510C2211yescharacteristic
25C2×#6509—21no—
26C2×#6509C2211yescharacteristic
27C2×Q8×Dic7C2211yescharacteristic
28C22×#1144C2211yescharacteristic
29C22×#1144C2211yescharacteristic
30C2×#6493—21no—
31C2×#6493C2211yescharacteristic
32C2×C4×C22⋊D7—21no—
33C2×C4×C22⋊D7C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C22×#1132C2211yescharacteristic
36C22×C8×D7C2211yescharacteristic
37#90224—24no—
38#90224C2218yescomplemented
39C2×#6460C2211yescharacteristic
40C2×#6455C2211yescharacteristic
41C2×#6451C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×#6448—21no—
44C2×#6442—21no—
45C2×#6439—21no—
46C2×C4×Dic14—21no—
47C7×#419C2218yescomplemented
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#103C2211yescharacteristic
52#90000C2218yescomplemented
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89906C2218yescomplemented
57#89899C2218yescomplemented
58C2×#6395C2211yescharacteristic
59C2×(C2×D7)⋊C8C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6389C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64#89775C2218yescomplemented
65C2×#6383C2211yescharacteristic
66C2×#6383C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69#89586C2218yescomplemented
70#89585C2218yescomplemented
71#89582C2218yescomplemented
72#89576C2218yescomplemented
73#89570C2218yescomplemented
74#89567C2218yescomplemented
75#89566C2218yescomplemented
76#89561C2218yescomplemented
77C2×#3313—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—22no—
80C22×C7×Q8—24no—
81C22×C7×Q8—42no—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×Q8C2314yes—
84C22×C7×Q8C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7C2311yescharacteristic
87C22×C22⋊D7—21no—
88C22×C22⋊D7D411yescharacteristic
89C2×#1161—22no—
90C2×#1161—24no—
91C2×#1161—42no—
92C2×#1161C2314yes—
93C22×D28—21no—
94C22×D28C2311yescharacteristic
95C22×C4×D7—21no—
96C22×C4×D7C2311yescharacteristic
97C22×Dic14—21no—
98C22×Dic14C2311yescharacteristic
99C2×C7×M16—42no—
100C2×C7×M16C2314yes—
101C22×C7×C8C2311yescharacteristic
102C22×C7×C8C2311yescharacteristic
103C7×#117—22no—
104C7×#117C2314yes—
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C22⋊C4—21no—
108C2×C42×C7—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7D411yescharacteristic
111#6510—28no—
112#6510—22no—
113#6510C2314yes—
114#6509—22no—
115#6509—28no—
116#6509C2314yes—
117Q8×Dic7—22no—
118Q8×Dic7C2314yes—
119C2×#1144—24no—
120C2×#1144—42no—
121C2×#1144C2314yes—
122C2×#1144C2314yes—
123#6493—22no—
124#6493—28no—
125#6493C2314yes—
126C4×C22⋊D7—28no—
127C4×C22⋊D7D414yes—
128C4×C22⋊D7C2314yes—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4D411yescharacteristic
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140#6487—22no—
141#6487C2314yes—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4D411yescharacteristic
147C2×C4×Dic7—21no—
148C2×C4×Dic7—21no—
149C2×C4×Dic7—21no—
150C2×C4×Dic7C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C2×#1132—42no—
154C2×#1132C2314yes—
155C2×C8×D7—42no—
156C2×C8×D7C2314yes—
157#6460—22no—
158#6460C2314yes—
159#6455—22no—
160#6455C2314yes—
161#6451—22no—
162#6451C2314yes—
163#6450—22no—
164#6450C2314yes—
165#6448—28no—
166#6442—28no—
167#6439—28no—
168C4×Dic14—28no—
169C7×#103C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172C7×#103C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175C22⋊(C7⋊C8)C2314yes—
176#6395C2314yes—
177(C2×D7)⋊C8C2314yes—
178#6392C2314yes—
179#6390C2314yes—
180#6389C2314yes—
181Dic7⋊C8C2314yes—
182#6383C2314yes—
183#6383C2314yes—
184#6382C2314yes—
185#6381C2314yes—
186C2×#556—71no—
187C2×#548—71no—
188#3313—716no—
189C2×#489—71no—
190C2×#485—71no—
191C2×#482—71no—
192C2×#477—71no—
193C2×#468—71no—
194C2×#467—71no—
195C2×#464—71no—
196C2×#452—71no—
197C2×#451—71no—
198C2×#441—71no—
199C2×#435—71no—
200C2×#419D711yescharacteristic, complemented
201C2×#416—71no—
202C24×C7C2×D411yescharacteristic
203C23×D7—21no—
204C23×D7C2×D411yescharacteristic
205C2×C7×Q8—21no—
206C2×C7×Q8—24no—
207C2×C7×Q8—21no—
208C2×C7×Q8—22no—
209C2×C7×Q8—28no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8—44no—
213C2×C7×Q8—44no—
214C2×C7×Q8—48no—
215C2×C7×Q8#4114yes—
216C2×C7×Q8C2412yes—
217C2×C7×Q8C2412yes—
218C22×C4×C7—21no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—24no—
225C22×C4×C7—44no—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2411yescharacteristic
230C2×C22⋊D7—24no—
231C2×C22⋊D7—42no—
232C2×C22⋊D7—44no—
233C2×C22⋊D7C2×D414yes—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7C2×D411yescharacteristic
238C22×Dic7C2×D411yescharacteristic
239C22×Dic7C2×D411yescharacteristic
240#1161—28no—
241#1161—44no—
242#1161—48no—
243C2×D28—22no—
244C2×D28—22no—
245C2×D28—24no—
246C2×D28—21no—
247C2×D28—44no—
248C2×D28C2412yes—
249C2×C4×D7—22no—
250C2×C4×D7—22no—
251C2×C4×D7—24no—
252C2×C4×D7—44no—
253C2×C4×D7C2×D412yes—
254C2×C4×D7C2412yes—
255C2×Dic14—22no—
256C2×Dic14—22no—
257C2×Dic14—21no—
258C2×Dic14—24no—
259C2×Dic14—44no—
260C2×Dic14C2412yes—
261C7×M16—44no—
262C2×C7×C8—22no—
263C2×C7×C8—22no—
264C2×C7×C8C2412yes—
265C2×C7×C8C2412yes—
266C7×C4⋊C4—21no—
267C7×C4⋊C4—21no—
268C7×C4⋊C4C2412yes—
269C7×C4⋊C4C2412yes—
270C7×C22⋊C4—24no—
271C42×C7—24no—
272C22⋊Dic7—24no—
273C22⋊Dic7C2×D414yes—
274#1144—28no—
275#1144—44no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4C2×D414yes—
283C4⋊Dic7—21no—
284C4⋊Dic7—21no—
285C4⋊Dic7—24no—
286C4⋊Dic7—24no—
287C4⋊Dic7C2412yes—
288C4⋊Dic7C2412yes—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292Dic7⋊C4—24no—
293Dic7⋊C4C2×D414yes—
294C4×Dic7—24no—
295C4×Dic7—24no—
296C4×Dic7—24no—
297C4×Dic7C2×D412yes—
298C4×Dic7C2412yes—
299C2×C7⋊C8—22no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8C2412yes—
302C2×C7⋊C8C2412yes—
303#1132—44no—
304C8×D7—44no—
305C22×#41—71no—
306C23×Q8C2×D711yescharacteristic
307C22×Q16—71no—
308C22×Q16—71no—
309C22×SD16—71no—
310C22×M16C2×D711yescharacteristic
311C23×C8—71no—
312#556—78no—
313#556—144no—
314#548—78no—
315#548—144no—
316C2×C4⋊Q8—71no—
317C2×#126—141no—
318C2×#126—141no—
319C2×#124—71no—
320C2×#124—141no—
321C2×#124—141no—
322C2×C22⋊Q8—71no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—141no—
326C2×#121—71no—
327C2×#121—141no—
328C2×C4×Q8—71no—
329C2×C4×Q8—71no—
330C2×C4×Q8—141no—
331C2×C4×D4—71no—
332C2×C4×D4—141no—
333C2×#117—71no—
334C2×#117C2×D711yescharacteristic
335#489—78no—
336#485—78no—
337#482—78no—
338#477—78no—
339#468—78no—
340#467—78no—
341#464—78no—
342#452—78no—
343#451—78no—
344#441—78no—
345#435—78no—
346C2×#107—71no—
347C2×#107—71no—
348C2×#106—71no—
349C2×C4⋊C8—71no—
350#419C2×D718yescomplemented
351#416—78no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103C2×D711yescharacteristic
356C2×#103C2×D711yescharacteristic
357C2×#103C2×D711yescharacteristic
358C2×#103C2×D711yescharacteristic
359C2×#102—71no—
360C2×#102—71no—
361C2×#102—71no—
362C2×C22⋊C8—71no—
363C2×C22⋊C8—71no—
364C2×#97—71no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7C22×D412yes—
369C23×C7C22×D411yescharacteristic
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—42no—
375C22×D7—42no—
376C22×D7—42no—
377C22×D7C22×D412yes—
378C7×Q8—24no—
379C7×Q8—22no—
380C7×Q8—22no—
381C7×Q8—22no—
382C7×Q8—48no—
383C7×Q8—42no—
384C7×Q8C2×#4114yes—
385C2×C4×C7—24no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—24no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—48no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D411yescharacteristic
400C2×C4×C7C2×#4112yes—
401C2×C4×C7H(5,𝔽2)12yes—
402C2×C4×C7C2511yescharacteristic
403C22⋊D7—44no—
404C22⋊D7—48no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—42no—
412C2×Dic7—42no—
413C2×Dic7—42no—
414C2×Dic7C22×D412yes—
415C2×Dic7C22×D412yes—
416C2×Dic7C22×D412yes—
417D28—22no—
418D28—22no—
419D28—48no—
420D28—42no—
421C4×D7—24no—
422C4×D7—22no—
423C4×D7—22no—
424C4×D7—48no—
425Dic14—22no—
426Dic14—22no—
427Dic14—48no—
428Dic14—42no—
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—21no—
438C22×Q8—22no—
439C22×Q8—24no—
440C22×Q8—42no—
441C22×Q8—71no—
442C22×Q8—141no—
443C22×Q8C22×D711yescharacteristic
444C22×Q8C22×D714yes—
445C22×Q8C22×D711yescharacteristic
446C22×D4—71no—
447C22×D4—71no—
448C22×D4—141no—
449C22×D4—141no—
450C23×C4—21no—
451C23×C4—71no—
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—42no—
461C2×M16C22×D714yes—
462C22×C8—71no—
463C22×C8—71no—
464C22×C8—74no—
465C22×C8—282no—
466C22×C8C22×D711yescharacteristic
467C22×C8C22×D711yescharacteristic
468C4⋊Q8—74no—
469C4⋊Q8—142no—
470#126—148no—
471#126—148no—
472#124—74no—
473#124—142no—
474#124—148no—
475#124—148no—
476C22⋊Q8—74no—
477C22⋊Q8—74no—
478C22⋊Q8—74no—
479C22⋊Q8—142no—
480C22⋊Q8—148no—
481C22⋊Q8—142no—
482C22⋊Q8—142no—
483#121—74no—
484#121—148no—
485#121—142no—
486C4×Q8—74no—
487C4×Q8—74no—
488C4×Q8—148no—
489C4×Q8—142no—
490C4×Q8—142no—
491C4×D4—74no—
492C4×D4—74no—
493C4×D4—148no—
494#117—22no—
495#117—74no—
496#117—142no—
497#117C22×D714yes—
498C2×C4⋊C4—71no—
499C2×C4⋊C4—71no—
500C2×C4⋊C4—71no—
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⋊C4C22×D711yescharacteristic
508C2×C4⋊C4C22×D711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—71no—
511C2×C22⋊C4—71no—
512C2×C22⋊C4—141no—
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×C42—21no—
520C2×C42—71no—
521C2×C42—141no—
522C2×C42—141no—
523C2×C42—141no—
524#107—74no—
525#107—74no—
526#106—74no—
527C4⋊C8—74no—
528#103—74no—
529#103—74no—
530#103—74no—
531#103C22×D714yes—
532#103C22×D714yes—
533#103C22×D714yes—
534#103C22×D714yes—
535#102—74no—
536#102—74no—
537#102—74no—
538C22⋊C8—74no—
539C22⋊C8—74no—
540#97—74no—
541C22×C7—22no—
542C22×C7—22no—
543C22×C7—22no—
544C22×C7—44no—
545C22×C7#54612yes—
546C22×C7#57512yes—
547C22×C7#57812yes—
548C22×C7C23×D411yescharacteristic
549C2×D7—22no—
550C2×D7—22no—
551C2×D7—22no—
552C2×D7—44no—
553C2×D7—42no—
554C2×D7—42no—
555C2×D7—42no—
556C2×D7—84no—
557C4×C7—24no—
558C4×C7—22no—
559C4×C7—42no—
560C4×C7—42no—
561C4×C7—42no—
562C4×C7#54612yes—
563C4×C7C22×#4111yescharacteristic
564C4×C7C2×H(5,𝔽2)11yescharacteristic
565Dic7—22no—
566Dic7—22no—
567Dic7—22no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571C24—71no—
572C24—141no—
573C24D4×D711yescharacteristic
574#41—148no—
575#41—284no—
576#41—288no—
577C2×Q8—21no—
578C2×Q8—24no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—28no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—48no—
587C2×Q8—72no—
588C2×Q8—144no—
589C2×Q8—141no—
590C2×Q8—142no—
591C2×Q8—142no—
592C2×Q8—284no—
593C2×Q8#115714yes—
594C2×Q8C23×D712yes—
595C2×Q8C23×D712yes—
596C2×D4—74no—
597C2×D4—72no—
598C2×D4—144no—
599C2×D4—144no—
600C2×D4—142no—
601C2×D4—141no—
602C2×D4—142no—
603C2×D4—284no—
604C2×D4—282no—
605C2×D4—284no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—44no—
614C22×C4—71no—
615C22×C4—71no—
616C22×C4—71no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—144no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—141no—
625C22×C4—284no—
626C22×C4D4×D712yes—
627C22×C4D4×D711yescharacteristic
628C22×C4C23×D712yes—
629C22×C4C23×D711yescharacteristic
630Q16—148no—
631Q16—284no—
632SD16—284no—
633M16—44no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—72no—
637C2×C8—72no—
638C2×C8—142no—
639C2×C8—142no—
640C2×C8—284no—
641C2×C8C23×D712yes—
642C2×C8C23×D712yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—74no—
646C4⋊C4—72no—
647C4⋊C4—72no—
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⋊C4C23×D712yes—
657C4⋊C4C23×D712yes—
658C22⋊C4—24no—
659C22⋊C4—74no—
660C22⋊C4—74no—
661C22⋊C4—144no—
662C22⋊C4—144no—
663C22⋊C4—144no—
664C22⋊C4—144no—
665C22⋊C4—144no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C42—24no—
669C42—72no—
670C42—72no—
671C42—144no—
672C42—144no—
673C42—144no—
674C2×C7—42no—
675C2×C7#331314yescomplemented
676C2×C7C2×#54611yescharacteristic
677C2×C7C2×#57511yescharacteristic
678C2×C7C2×#57811yescharacteristic
679D7—42no—
680D7—82no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—72no—
685C23—142no—
686C23—142no—
687C23—142no—
688C23—142no—
689C23—282no—
690C23—282no—
691C23—282no—
692C23C2×D4×D712yes—
693C23C2×D4×D711yescharacteristic
694Q8—24no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—48no—
699Q8—42no—
700Q8—142no—
701Q8—142no—
702Q8—288no—
703Q8—282no—
704Q8C2×#115714yes—
705D4—142no—
706D4—142no—
707D4—288no—
708D4—284no—
709D4—288no—
710D4—282no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—72no—
725C2×C4—72no—
726C2×C4—72no—
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—288no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4C2×#115712yes—
741C2×C4C2×D4×D712yes—
742C2×C4C2×D4×D711yescharacteristic
743C2×C4#654812yes—
744C2×C4C24×D711yescharacteristic
745C8—22no—
746C8—22no—
747C8—142no—
748C8—142no—
749C7C2×#331311yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—142no—
755C22—142no—
756C22—142no—
757C22—284no—
758C22—282no—
759C22—282no—
760C22—282no—
761C22—564no—
762C22#9018112yes—
763C22#9046812yes—
764C22#9047012yes—
765C22C22×D4×D711yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—142no—
772C4—142no—
773C4—142no—
774C4—282no—
775C4—282no—
776C4—282no—
777C4#9018112yes—
778C4C22×#115711yescharacteristic
779C4C2×#654811yescharacteristic
780C2—42no—
781C2—282no—
782C2—562no—
783C2#1173641214yesdirect product factor
784C2C2×#9018111yescharacteristic
785C2C2×#9046811yescharacteristic
786C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#419C2
socleC23×C7C22×D4
prime radicalC2×#90508C2
hypercenterC2×#419D7
hypocenterC7C2×#3313
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×#90224C2semidirect
3. C2×C7×#419C2semidirect
4. C2×#90000C2semidirect
5. C2×#89906C2semidirect
6. C2×#89899C2semidirect
7. C2×#89775C2semidirect
8. #11736412C2direct (N × H)
9. C2×#89570C2semidirect
10. C2×#89585C2semidirect
11. C2×#89582C2semidirect
12. C2×#89576C2semidirect
13. C2×#89567C2semidirect
14. C2×#89586C2semidirect
15. C2×#89566C2semidirect
16. C2×#89561C2semidirect
38. #90224C22semidirect
47. C7×#419C22semidirect
52. #90000C22semidirect
56. #89906C22semidirect
57. #89899C22semidirect
64. #89775C22semidirect
69. #89586C22semidirect
70. #89585C22semidirect
71. #89582C22semidirect
72. #89576C22semidirect
73. #89570C22semidirect
74. #89567C22semidirect
75. #89566C22semidirect
76. #89561C22semidirect
200. C2×#419D7semidirect
350. #419C2×D7semidirect
675. C2×C7#3313semidirect
749. C7C2×#3313semidirect
783. C2#11736412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905082
C2×#902242
C2×C7×#4192
C2×#900002
C2×#899062
C2×#898992
C2×#897752
#117364122
C2×#895702
C2×#895852
C2×#895822
C2×#895762
C2×#895672
C2×#895862
C2×#895662
C2×#895612
C2×#33137