Finite Group Databasebeta

← C2×#11738036 #14234791

Subgroups — C2×#11738036 #14234791

Order 1792.

1970 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90372C211yesmaximal, characteristic
2C2×#90258C211yesmaximal, characteristic, complemented
3C2×C7×#464C211yesmaximal, characteristic, complemented
4C2×#89962C211yesmaximal, characteristic, complemented
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×#89947C211yesmaximal, characteristic
7C2×#89934C211yesmaximal, characteristic, complemented
8C2×#89832C211yesmaximal, characteristic, complemented
9C2×#89798C211yesmaximal, characteristic, complemented
10#11738036C2116yesmaximal, direct product factor
11C2×#89613C211yesmaximal, characteristic, complemented
12C2×#89600C211yesmaximal, characteristic, complemented
13C2×#89570C211yesmaximal, characteristic, complemented
14C2×#89562C211yesmaximal, characteristic, complemented
15C2×#89534C211yesmaximal, characteristic
16C2×#89529C211yesmaximal, characteristic, complemented
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C2×C7×#124C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6507C2211yescharacteristic
24C2×#6507C2211yescharacteristic
25C22×#1144C2211yescharacteristic
26C22×#1144C2211yescharacteristic
27C22×#1143C2211yescharacteristic
28C2×#6503C2211yescharacteristic
29C2×D4×Dic7C2211yescharacteristic
30C22×#1142C2211yescharacteristic
31C22×#1142C2211yescharacteristic
32C22×#1132C2211yescharacteristic
33C22×#1132C2211yescharacteristic
34#90372—24no—
35#90372C2218yes—
36#90258—24no—
37#90258C2218yescomplemented
38C2×#6452—21no—
39C2×#6452—21no—
40C2×#6450C2211yescharacteristic
41C2×#6450C2211yescharacteristic
42C2×#6449—21no—
43C2×#6448—21no—
44C2×#6446—21no—
45C2×(C22⋊D7)⋊C4—21no—
46C2×C4×D28C2211yescharacteristic
47C2×#6433—21no—
48C2×#6432C2211yescharacteristic
49C2×C4×Dic14—21no—
50C2×C4×Dic14C2211yescharacteristic
51C7×#464C2218yescomplemented
52C2×C7×C4⋊C8C2211yescharacteristic
53C2×C7×#103C2211yescharacteristic
54C2×C7×#102C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56#89962C2218yescomplemented
57#89954C2218yescomplemented
58#89947C2218yes—
59#89934C2218yescomplemented
60C2×#6390C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6389C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×C8×Dic7C2211yescharacteristic
66#89832C2218yescomplemented
67#89798C2218yescomplemented
68C2×#6383C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6377C2211yescharacteristic
71#89613C2218yescomplemented
72#89600C2218yescomplemented
73#89570C2218yescomplemented
74#89562C2218yescomplemented
75#89534C2218yes—
76#89529C2218yescomplemented
77C2×#3400—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C22×D28C2311yescharacteristic
85C22×C4×D7—21no—
86C22×Dic14D411yescharacteristic
87C22×Dic14C2311yescharacteristic
88C22×Dic14C2311yescharacteristic
89C2×C7×Q16—42no—
90C2×C7×Q16C2314yes—
91C2×C7×SD16—42no—
92C2×C7×SD16C2314yes—
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C7×#124—22no—
96C7×#124C2314yes—
97C4×C7×Q8—22no—
98C4×C7×Q8C2314yes—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—21no—
103C2×C42×C7—21no—
104C2×C42×C7C2311yescharacteristic
105C2×C22⋊Dic7—21no—
106#6510—22no—
107#6510C2314yes—
108Q8×Dic7—22no—
109Q8×Dic7C2314yes—
110#6507—22no—
111#6507—22no—
112#6507C2314yes—
113#6507C2314yes—
114C2×#1144—24no—
115C2×#1144—42no—
116C2×#1144C2314yes—
117C2×#1144C2314yes—
118C2×#1143—24no—
119C2×#1143C2314yes—
120#6503—22no—
121#6503C2314yes—
122D4×Dic7—22no—
123D4×Dic7C2314yes—
124C2×#1142—24no—
125C2×#1142—42no—
126C2×#1142C2314yes—
127C2×#1142C2314yes—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×C4⋊Dic7—21no—
132C2×C4⋊Dic7—21no—
133C2×C4⋊Dic7—21no—
134C2×C4⋊Dic7D411yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4D411yescharacteristic
143C2×Dic7⋊C4D411yescharacteristic
144C2×C4×Dic7—21no—
145C2×C4×Dic7—21no—
146C2×C4×Dic7—21no—
147C2×C4×Dic7C2311yescharacteristic
148C2×C4×Dic7C2311yescharacteristic
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C2×#1132—42no—
152C2×#1132—42no—
153C2×#1132C2314yes—
154C2×#1132C2314yes—
155#6452—28no—
156#6452—28no—
157#6450—22no—
158#6450—22no—
159#6450C2314yes—
160#6450C2314yes—
161#6449—28no—
162#6448—28no—
163#6446—28no—
164(C22⋊D7)⋊C4—28no—
165C4×D28—22no—
166C4×D28C2314yes—
167#6433—28no—
168#6432—22no—
169#6432C2314yes—
170C4×Dic14—28no—
171C4×Dic14D414yes—
172C4×Dic14C2314yes—
173C7×C4⋊C8C2314yes—
174C7×#103C2314yes—
175C7×#102C2314yes—
176#6409C2314yes—
177#6390C2314yes—
178#6390C2314yes—
179#6389C2314yes—
180Dic7⋊C8C2314yes—
181Dic7⋊C8C2314yes—
182C8×Dic7C2314yes—
183#6383C2314yes—
184#6381C2314yes—
185#6377C2314yes—
186C2×#559—71no—
187C2×#557—71no—
188#3400—716no—
189C2×#497—71no—
190C2×#497—71no—
191C2×#492—71no—
192C2×#464—71no—
193C2×#464D711yescharacteristic, complemented
194C2×#462—71no—
195C2×#460—71no—
196C2×#461—71no—
197C2×#461—71no—
198C2×#446—71no—
199C2×#440—71no—
200C2×#440—71no—
201C2×C4×Q16—71no—
202C24×C7—21no—
203C23×D7—21no—
204C2×C7×Q8—21no—
205C2×C7×Q8—21no—
206C2×C7×Q8—22no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8C2412yes—
211C2×C7×Q8C2412yes—
212C2×C7×D4—21no—
213C2×C7×D4—22no—
214C2×C7×D4—22no—
215C2×C7×D4C2412yes—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2411yescharacteristic
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—44no—
225C2×C22⋊D7—82no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—24no—
230C22×Dic7—82no—
231C22×Dic7C2×D411yescharacteristic
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235C2×D28—22no—
236C2×D28—22no—
237C2×D28—21no—
238C2×D28C2412yes—
239C2×C4×D7—24no—
240C2×C4×D7—82no—
241C2×Dic14—24no—
242C2×Dic14—22no—
243C2×Dic14—22no—
244C2×Dic14—22no—
245C2×Dic14—22no—
246C2×Dic14—21no—
247C2×Dic14—21no—
248C2×Dic14C2×D414yes—
249C2×Dic14C2412yes—
250C2×Dic14C2412yes—
251C7×Q16—44no—
252C7×SD16—44no—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8C2412yes—
256C2×C7×C8C2412yes—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4C2412yes—
260C7×C22⋊C4—24no—
261C7×C22⋊C4—24no—
262C42×C7—24no—
263C42×C7C2×D412yes—
264C42×C7C2412yes—
265C22⋊Dic7—24no—
266#1144—28no—
267#1144—44no—
268#1143—28no—
269#1142—28no—
270#1142—44no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274C4⋊Dic7—24no—
275C4⋊Dic7—24no—
276C4⋊Dic7—21no—
277C4⋊Dic7—24no—
278C4⋊Dic7C2×D414yes—
279C4⋊Dic7C2412yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286Dic7⋊C4C2×D414yes—
287Dic7⋊C4C2×D414yes—
288C4×Dic7—24no—
289C4×Dic7—24no—
290C4×Dic7—24no—
291C4×Dic7C2×D412yes—
292C4×Dic7C2×D412yes—
293C4×Dic7C2412yes—
294C4×Dic7C2412yes—
295C2×C7⋊C8—22no—
296C2×C7⋊C8#4114yes—
297C2×C7⋊C8C2412yes—
298C2×C7⋊C8C2412yes—
299#1132—44no—
300#1132—44no—
301C22×Q16—71no—
302C22×Q16—71no—
303C22×Q16C2×D711yescharacteristic
304C22×SD16—71no—
305C22×SD16—71no—
306C22×SD16—71no—
307C22×SD16—71no—
308C22×SD16—71no—
309C22×SD16C2×D711yescharacteristic
310#559—78no—
311#559—144no—
312#557—78no—
313#557—144no—
314C2×C4⋊Q8—71no—
315C2×C4⋊Q8—71no—
316C2×C4⋊Q8—71no—
317C2×#127—71no—
318C2×#125—141no—
319C2×#125—141no—
320C2×#125—141no—
321C2×#124—71no—
322C2×#124—141no—
323C2×#124C2×D711yescharacteristic
324C2×#123—141no—
325C2×#123—141no—
326C2×C4×Q8—71no—
327C2×C4×Q8—71no—
328C2×C4×Q8—71no—
329C2×C4×Q8—71no—
330C2×C4×Q8—141no—
331C2×C4×Q8C2×D711yescharacteristic
332C2×C4×D4—71no—
333C2×C4×D4—71no—
334C2×C4×D4—141no—
335#497—78no—
336#497—78no—
337#492—78no—
338#464—78no—
339#464C2×D718yescomplemented
340#462—78no—
341#461—78no—
342#461—78no—
343#460—78no—
344#446—78no—
345#440—78no—
346#440—78no—
347C4×Q16—78no—
348C2×#107—71no—
349C2×C4⋊C8—71no—
350C2×C4⋊C8—71no—
351C2×C4⋊C8C2×D711yescharacteristic
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103C2×D711yescharacteristic
356C2×#102—71no—
357C2×#102C2×D711yescharacteristic
358C2×#97—71no—
359C2×#97—71no—
360C2×C4×C8—71no—
361C23×C7—22no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C7×Q8—22no—
371C7×Q8—22no—
372C7×Q8—22no—
373C7×Q8—22no—
374C7×Q8—42no—
375C7×Q8—42no—
376C7×D4—22no—
377C7×D4—22no—
378C7×D4—42no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7C22×D412yes—
388C2×C4×C7C22×D412yes—
389C2×C4×C7C22×D411yescharacteristic
390C2×C4×C7C2×#4112yes—
391C2×C4×C7H(5,𝔽2)12yes—
392C2×C4×C7C2511yescharacteristic
393C22⋊D7—48no—
394C22⋊D7—84no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—42no—
402C2×Dic7—42no—
403C2×Dic7—42no—
404C2×Dic7—84no—
405C2×Dic7#13714yes—
406C2×Dic7C22×D412yes—
407C2×Dic7C22×D412yes—
408C2×Dic7C22×D412yes—
409C2×Dic7C22×D412yes—
410D28—22no—
411D28—22no—
412D28—42no—
413C4×D7—84no—
414Dic14—28no—
415Dic14—22no—
416Dic14—22no—
417Dic14—22no—
418Dic14—22no—
419Dic14—42no—
420Dic14—42no—
421C7×C8—22no—
422C7×C8—22no—
423C7⋊C8—22no—
424C7⋊C8C2×#4114yes—
425C22×Q8—71no—
426C22×Q8—71no—
427C22×Q8—71no—
428C22×Q8C22×D711yescharacteristic
429C22×Q8C22×D711yescharacteristic
430C22×D4—71no—
431C22×D4—141no—
432C22×D4—141no—
433C22×D4C22×D711yescharacteristic
434C23×C4—141no—
435C23×C4—141no—
436C2×Q16—42no—
437C2×Q16—74no—
438C2×Q16—74no—
439C2×Q16—144no—
440C2×Q16—282no—
441C2×Q16C22×D714yes—
442C2×SD16—42no—
443C2×SD16—74no—
444C2×SD16—74no—
445C2×SD16—74no—
446C2×SD16—74no—
447C2×SD16—74no—
448C2×SD16—144no—
449C2×SD16—144no—
450C2×SD16—282no—
451C2×SD16—282no—
452C2×SD16—282no—
453C2×SD16C22×D714yes—
454C22×C8—71no—
455C22×C8—71no—
456C22×C8C22×D711yescharacteristic
457C22×C8C22×D711yescharacteristic
458C4⋊Q8—74no—
459C4⋊Q8—74no—
460C4⋊Q8—74no—
461C4⋊Q8—142no—
462C4⋊Q8—142no—
463C4⋊Q8—142no—
464#127—74no—
465#127—142no—
466#125—148no—
467#125—148no—
468#125—148no—
469#124—22no—
470#124—74no—
471#124—142no—
472#124—148no—
473#124C22×D714yes—
474#123—148no—
475#123—148no—
476C4×Q8—22no—
477C4×Q8—74no—
478C4×Q8—74no—
479C4×Q8—74no—
480C4×Q8—74no—
481C4×Q8—74no—
482C4×Q8—148no—
483C4×Q8—142no—
484C4×Q8—142no—
485C4×Q8—142no—
486C4×Q8C22×D714yes—
487C4×D4—74no—
488C4×D4—74no—
489C4×D4—142no—
490C4×D4—148no—
491C4×D4—142no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—71no—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—141no—
498C2×C4⋊C4—141no—
499C2×C4⋊C4—141no—
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⋊C4C22×D711yescharacteristic
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×C42—21no—
514C2×C42—71no—
515C2×C42—71no—
516C2×C42—141no—
517C2×C42—141no—
518C2×C42—141no—
519C2×C42C22×D711yescharacteristic
520#107—74no—
521C4⋊C8—74no—
522C4⋊C8—74no—
523C4⋊C8C22×D714yes—
524#103—74no—
525#103—74no—
526#103—74no—
527#103C22×D714yes—
528#102—74no—
529#102C22×D714yes—
530#97—74no—
531#97—74no—
532C4×C8—74no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—84no—
537C22×C7#55012yes—
538C22×C7C2×#13712yes—
539C22×C7#57712yes—
540C22×C7C23×D411yescharacteristic
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—84no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7#55012yes—
551C4×C7C22×#4111yescharacteristic
552C4×C7C2×H(5,𝔽2)11yescharacteristic
553Dic7—22no—
554Dic7—22no—
555Dic7—22no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7C2×#13714yes—
560C24—21no—
561C24—141no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—74no—
569C2×Q8—72no—
570C2×Q8—72no—
571C2×Q8—144no—
572C2×Q8—141no—
573C2×Q8—141no—
574C2×Q8—142no—
575C2×Q8—142no—
576C2×Q8—142no—
577C2×Q8—142no—
578C2×Q8C23×D712yes—
579C2×Q8C23×D712yes—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—72no—
584C2×D4—144no—
585C2×D4—144no—
586C2×D4—141no—
587C2×D4—142no—
588C2×D4—142no—
589C2×D4—284no—
590C2×D4—562no—
591C2×D4C23×D712yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—71no—
596C22×C4—71no—
597C22×C4—71no—
598C22×C4—71no—
599C22×C4—144no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—144no—
604C22×C4—562no—
605C22×C4—562no—
606C22×C4D4×D711yescharacteristic
607C22×C4D4×D711yescharacteristic
608C22×C4C23×D711yescharacteristic
609Q16—44no—
610Q16—148no—
611Q16—284no—
612SD16—44no—
613SD16—148no—
614SD16—148no—
615SD16—284no—
616SD16—284no—
617SD16—284no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—74no—
621C2×C8—72no—
622C2×C8—72no—
623C2×C8—142no—
624C2×C8C23×D712yes—
625C2×C8C23×D712yes—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—74no—
629C4⋊C4—74no—
630C4⋊C4—74no—
631C4⋊C4—72no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—144no—
636C4⋊C4—144no—
637C4⋊C4—144no—
638C4⋊C4—144no—
639C4⋊C4—141no—
640C4⋊C4—144no—
641C4⋊C4—144no—
642C4⋊C4C23×D712yes—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C42—24no—
650C42—72no—
651C42—72no—
652C42—72no—
653C42—72no—
654C42—144no—
655C42—144no—
656C42—144no—
657C42D4×D712yes—
658C42C23×D712yes—
659C2×C7—82no—
660C2×C7#340014yescomplemented
661C2×C7C2×#55011yescharacteristic
662C2×C7C22×#13711yescharacteristic
663C2×C7C2×#57711yescharacteristic
664D7—82no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—142no—
670C23—282no—
671C23—282no—
672C23—282no—
673C23C2×D4×D711yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—22no—
678Q8—42no—
679Q8—42no—
680Q8—148no—
681Q8—142no—
682Q8—142no—
683Q8—142no—
684Q8—142no—
685Q8—282no—
686Q8—282no—
687D4—22no—
688D4—22no—
689D4—42no—
690D4—142no—
691D4—142no—
692D4—288no—
693D4—282no—
694D4—564no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—74no—
704C2×C4—72no—
705C2×C4—72no—
706C2×C4—72no—
707C2×C4—72no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—564no—
718C2×C4—564no—
719C2×C4C2×D4×D712yes—
720C2×C4C2×D4×D712yes—
721C2×C4C2×D4×D711yescharacteristic
722C2×C4#654812yes—
723C2×C4D7×#4112yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—22no—
727C8—74no—
728C8—142no—
729C7C2×#340011yescharacteristic, complemented, Sylow
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—282no—
735C22—282no—
736C22—282no—
737C22—564no—
738C22#9029012yes—
739C22#9046112yes—
740C22D7×#13712yes—
741C22C22×D4×D711yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—74no—
748C4—142no—
749C4—142no—
750C4—142no—
751C4—282no—
752C4—282no—
753C4—282no—
754C4#9029012yes—
755C4C2×#654811yescharacteristic
756C4C2×D7×#4111yescharacteristic
757C2—82no—
758C2—562no—
759C2#1173803614yesdirect product factor
760C2C2×#9029011yescharacteristic
761C2C2×#9046111yescharacteristic
762C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#464C2
socleC23×C7C22×D4
prime radicalC2×#6503C22
hypercenterC2×#464D7
hypocenterC7C2×#3400
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×#90258C2semidirect
3. C2×C7×#464C2semidirect
4. C2×#89962C2semidirect
5. C2×#89954C2semidirect
7. C2×#89934C2semidirect
8. C2×#89832C2semidirect
9. C2×#89798C2semidirect
10. #11738036C2direct (N × H)
11. C2×#89613C2semidirect
12. C2×#89600C2semidirect
13. C2×#89570C2semidirect
14. C2×#89562C2semidirect
16. C2×#89529C2semidirect
37. #90258C22semidirect
51. C7×#464C22semidirect
56. #89962C22semidirect
57. #89954C22semidirect
59. #89934C22semidirect
66. #89832C22semidirect
67. #89798C22semidirect
71. #89613C22semidirect
72. #89600C22semidirect
73. #89570C22semidirect
74. #89562C22semidirect
76. #89529C22semidirect
193. C2×#464D7semidirect
339. #464C2×D7semidirect
660. C2×C7#3400semidirect
729. C7C2×#3400semidirect
759. C2#11738036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903722
C2×#902582
C2×C7×#4642
C2×#899622
C2×#899542
C2×#899472
C2×#899342
C2×#898322
C2×#897982
#117380362
C2×#896132
C2×#896002
C2×#895702
C2×#895622
C2×#895342
C2×#895292
C2×#34007