Finite Group Databasebeta

← C2×#11738587 #14221981

Subgroups — C2×#11738587 #14221981

Order 1792.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90382C211yesmaximal, characteristic, complemented
2C2×C4×#1159C211yesmaximal, characteristic, complemented
3C2×C7×#478C211yesmaximal, characteristic, complemented
4C2×#89835C211yesmaximal, characteristic, complemented
5C2×#89788C211yesmaximal, characteristic, complemented
6#11738587C2116yesmaximal, direct product factor
7C2×#89660C211yesmaximal, characteristic, complemented
8C2×#89661C211yesmaximal, characteristic, complemented
9C2×#89638C211yesmaximal, characteristic, complemented
10C2×#89625C211yesmaximal, characteristic, complemented
11C2×#89617C211yesmaximal, characteristic, complemented
12C2×#89607C211yesmaximal, characteristic, complemented
13C2×#89555C211yesmaximal, characteristic, complemented
14C2×#89553C211yesmaximal, characteristic
15C2×#89557C211yesmaximal, characteristic, complemented
16C2×#89529C211yesmaximal, characteristic, complemented
17C22×#1159C2211yescharacteristic
18C2×C7×#125C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×D4×Dic7C2211yescharacteristic
21C22×#1142C2211yescharacteristic
22C22×#1141C2211yescharacteristic
23C2×C4×C22⋊D7—21no—
24C22×C4×Dic7—21no—
25C22×Dic28C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27#90382—24no—
28#90382C2218yescomplemented
29C4×#1159—24no—
30C4×#1159C2218yescomplemented
31C2×#6461—21no—
32C2×#6460C2211yescharacteristic
33C2×#6458C2211yescharacteristic
34C2×#6457—21no—
35C2×#6456—21no—
36C2×#6456C2211yescharacteristic
37C2×#6455—21no—
38C2×#6455C2211yescharacteristic
39C2×#6450C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×(C22⋊D7)⋊C4—21no—
42C2×#6440—21no—
43C2×#6438C2211yescharacteristic
44C2×C42×D7C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C7×#478C2218yescomplemented
47C2×C7×#107C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6389C2211yescharacteristic
57C2×#6389C2211yescharacteristic
58#89835C2218yescomplemented
59#89788C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89661C2218yescomplemented
68#89660C2218yescomplemented
69#89638C2218yescomplemented
70#89625C2218yescomplemented
71#89617C2218yescomplemented
72#89607C2218yescomplemented
73#89557C2218yescomplemented
74#89555C2218yescomplemented
75#89553C2218yes—
76#89529C2218yescomplemented
77C2×#3111—71nomaximal, Sylow
78C22×C7×D4C2311yescharacteristic
79C23×C4×C7—21no—
80C22×C22⋊D7—21no—
81C23×Dic7—21no—
82C23×Dic7—21no—
83C2×#1159—24no—
84C2×#1159—22no—
85C2×#1159—24no—
86C2×#1159C2314yes—
87C22×D28—21no—
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×C4×D7D411yescharacteristic
91C22×C4×D7D411yescharacteristic
92C22×C4×D7C2311yescharacteristic
93C22×Dic14C2311yescharacteristic
94C22×Dic14C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C7×#125—22no—
98C7×#125C2314yes—
99C4×C7×D4—22no—
100C4×C7×D4C2314yes—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C22⋊C4—21no—
107C2×C42×C7C2311yescharacteristic
108C2×C22⋊Dic7—21no—
109D4×Dic7—22no—
110D4×Dic7C2314yes—
111C2×#1142—24no—
112C2×#1142C2314yes—
113C2×#1141—24no—
114C2×#1141C2314yes—
115C4×C22⋊D7—28no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7C2311yescharacteristic
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×C4×Dic7—21no—
128C2×C4×Dic7—21no—
129C2×C4×Dic7—21no—
130C2×C4×Dic7—21no—
131C2×C4×Dic7—28no—
132C2×C4×Dic7D411yescharacteristic
133C2×C4×Dic7D411yescharacteristic
134C2×C4×Dic7C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C2×Dic28—24no—
138C2×Dic28C2314yes—
139C2×#1132—24no—
140C2×#1132C2314yes—
141#6461—28no—
142#6460—22no—
143#6460C2314yes—
144#6458—22no—
145#6458C2314yes—
146#6457—28no—
147#6456—28no—
148#6456—22no—
149#6456C2314yes—
150#6455—22no—
151#6455—28no—
152#6455C2314yes—
153#6450—22no—
154#6450—22no—
155#6450C2314yes—
156#6450C2314yes—
157(C22⋊D7)⋊C4—28no—
158#6440—28no—
159#6438—22no—
160#6438C2314yes—
161C42×D7D414yes—
162C42×D7C2314yes—
163C4×Dic14—22no—
164C4×Dic14C2314yes—
165C7×#107C2314yes—
166C7×#106C2314yes—
167C7×C4⋊C8C2314yes—
168C7×#102C2314yes—
169C7×#102C2314yes—
170#6395C2314yes—
171(C2×D7)⋊C8C2314yes—
172(C2×D7)⋊C8C2314yes—
173#6390C2314yes—
174#6389C2314yes—
175#6389C2314yes—
176#6384C2314yes—
177#6384C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#529—71no—
184C2×C4×#41—71no—
185#3111—716no—
186C2×#485—71no—
187C2×#482—71no—
188C2×#479—71no—
189C2×#478D711yescharacteristic, complemented
190C2×#464—71no—
191C2×#463—71no—
192C2×#452—71no—
193C2×#449—71no—
194C2×#442—71no—
195C2×#441—71no—
196C2×#440—71no—
197C2×#440—71no—
198C2×#432—71no—
199C24×C7—21no—
200C23×D7—21no—
201C23×D7C2×D411yescharacteristic
202C2×C7×D4—21no—
203C2×C7×D4—22no—
204C2×C7×D4#4114yes—
205C2×C7×D4C2412yes—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—24no—
210C22×C4×C7—44no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2411yescharacteristic
214C2×C22⋊D7—28no—
215C2×C22⋊D7—24no—
216C22×Dic7—28no—
217C22×Dic7—21no—
218C22×Dic7—24no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—24no—
222C22×Dic7—44no—
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226#1159—216no—
227#1159—28no—
228#1159—28no—
229C2×D28—22no—
230C2×D28—22no—
231C2×D28—24no—
232C2×D28—21no—
233C2×D28—44no—
234C2×D28C2412yes—
235C2×C4×D7—22no—
236C2×C4×D7—22no—
237C2×C4×D7—24no—
238C2×C4×D7—42no—
239C2×C4×D7—42no—
240C2×C4×D7—44no—
241C2×C4×D7C2×D412yes—
242C2×C4×D7C2×D414yes—
243C2×C4×D7C2×D414yes—
244C2×C4×D7C2412yes—
245C2×Dic14—21no—
246C2×Dic14—22no—
247C2×Dic14—22no—
248C2×Dic14—22no—
249C2×Dic14—21no—
250C2×Dic14#4114yes—
251C2×Dic14C2412yes—
252C2×Dic14C2412yes—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8C2412yes—
256C2×C7×C8C2412yes—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—24no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4—24no—
262C7×C4⋊C4C2412yes—
263C7×C4⋊C4C2412yes—
264C7×C4⋊C4C2412yes—
265C7×C22⋊C4—24no—
266C42×C7C2×D412yes—
267C42×C7C2412yes—
268C22⋊Dic7—24no—
269#1142—28no—
270#1141—28no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275(C2×D7)⋊C4—24no—
276(C2×D7)⋊C4—24no—
277C4⋊Dic7—21no—
278C4⋊Dic7—24no—
279C4⋊Dic7C2412yes—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283C4×Dic7—24no—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7—24no—
287C4×Dic7C2×D412yes—
288C4×Dic7C2×D414yes—
289C4×Dic7C2×D414yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295Dic28—28no—
296#1132—28no—
297C22×#41—71no—
298C22×Q16—71no—
299C22×SD16—71no—
300C22×SD16—71no—
301C22×D8—71no—
302#529—78no—
303#529—144no—
304C2×#126—141no—
305C2×#125C2×D711yescharacteristic
306C2×#124—71no—
307C2×#123—141no—
308C2×C22⋊Q8—71no—
309C2×#121—71no—
310C4×#41—78no—
311C4×#41—144no—
312C2×C4×Q8—71no—
313C2×C4×Q8—71no—
314C2×C4×Q8—71no—
315C2×C4×D4—71no—
316C2×C4×D4—71no—
317C2×C4×D4—141no—
318C2×C4×D4—141no—
319C2×C4×D4—141no—
320C2×C4×D4C2×D711yescharacteristic
321C2×#117—71no—
322C2×#117—141no—
323C2×#117—141no—
324C22×C42—71no—
325C22×C42—141no—
326#485—78no—
327#482—78no—
328#479—78no—
329#478C2×D718yescomplemented
330#464—78no—
331#463—78no—
332#452—78no—
333#449—78no—
334#442—78no—
335#441—78no—
336#440—78no—
337#440—78no—
338#432—78no—
339C2×#107—71no—
340C2×#107C2×D711yescharacteristic
341C2×#106—71no—
342C2×#106C2×D711yescharacteristic
343C2×C4⋊C8—71no—
344C2×C4⋊C8C2×D711yescharacteristic
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#102—71no—
350C2×#102—71no—
351C2×#102C2×D711yescharacteristic
352C2×#102C2×D711yescharacteristic
353C2×C22⋊C8—71no—
354C2×C22⋊C8—71no—
355C2×#97—71no—
356C2×#97—71no—
357C23×C7—24no—
358C23×C7—22no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7C22×D411yescharacteristic
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—42no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7C22×D412yes—
370C7×D4—24no—
371C7×D4—22no—
372C7×D4C2×#4114yes—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—48no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D411yescharacteristic
385C2×C4×C7C2×#4112yes—
386C2×C4×C7C2×#4112yes—
387C2×C4×C7C2511yescharacteristic
388C22⋊D7—216no—
389C2×Dic7—216no—
390C2×Dic7—24no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—48no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403D28—22no—
404D28—22no—
405D28—48no—
406D28—42no—
407C4×D7—24no—
408C4×D7—22no—
409C4×D7—22no—
410C4×D7—44no—
411C4×D7—44no—
412C4×D7—48no—
413Dic14—24no—
414Dic14—22no—
415Dic14—22no—
416Dic14—22no—
417Dic14—42no—
418Dic14C2×#4114yes—
419C7×C8—22no—
420C7×C8—22no—
421C7⋊C8—22no—
422C7⋊C8—22no—
423C2×#41—74no—
424C2×#41—142no—
425C2×#41—144no—
426C2×#41—144no—
427C22×Q8—71no—
428C22×Q8—71no—
429C22×D4—71no—
430C22×D4—141no—
431C22×D4—141no—
432C22×D4C22×D711yescharacteristic
433C23×C4—21no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—71no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4—141no—
440C2×Q16—74no—
441C2×Q16—144no—
442C2×SD16—74no—
443C2×SD16—74no—
444C2×SD16—144no—
445C2×SD16—144no—
446C2×D8—74no—
447C2×D8—144no—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8C22×D711yescharacteristic
451C22×C8C22×D711yescharacteristic
452#126—148no—
453#125—22no—
454#125C22×D714yes—
455#124—74no—
456#124—142no—
457#123—148no—
458C22⋊Q8—74no—
459C22⋊Q8—142no—
460#121—74no—
461#121—142no—
462C4×Q8—74no—
463C4×Q8—74no—
464C4×Q8—74no—
465C4×Q8—142no—
466C4×Q8—142no—
467C4×Q8—142no—
468C4×D4—22no—
469C4×D4—74no—
470C4×D4—74no—
471C4×D4—142no—
472C4×D4—142no—
473C4×D4—148no—
474C4×D4—148no—
475C4×D4—148no—
476C4×D4C22×D714yes—
477#117—74no—
478#117—148no—
479#117—148no—
480#117—142no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C42—71no—
500C2×C42—71no—
501C2×C42—71no—
502C2×C42—74no—
503C2×C42—74no—
504C2×C42—148no—
505C2×C42—141no—
506C2×C42—141no—
507C2×C42—141no—
508C2×C42—141no—
509C2×C42C22×D711yescharacteristic
510#107—74no—
511#107C22×D714yes—
512#106—74no—
513#106C22×D714yes—
514C4⋊C8—74no—
515C4⋊C8C22×D714yes—
516#103—74no—
517#103—74no—
518#103—74no—
519#103—74no—
520#102—74no—
521#102—74no—
522#102C22×D714yes—
523#102C22×D714yes—
524C22⋊C8—74no—
525C22⋊C8—74no—
526#97—74no—
527#97—74no—
528C22×C7—24no—
529C22×C7—48no—
530C22×C7—42no—
531C22×C7—42no—
532C22×C7#52512yes—
533C22×C7#57512yes—
534C22×C7#57512yes—
535C22×C7C23×D411yescharacteristic
536C2×D7—22no—
537C2×D7—22no—
538C2×D7—22no—
539C2×D7—44no—
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—84no—
544C4×C7—22no—
545C4×C7—22no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7#52512yes—
550C4×C7C22×#4111yescharacteristic
551C4×C7C22×#4111yescharacteristic
552Dic7—24no—
553Dic7—22no—
554Dic7—22no—
555Dic7—22no—
556Dic7—42no—
557Dic7—42no—
558C24—21no—
559C24—71no—
560C24—141no—
561#41—148no—
562#41—1416no—
563#41—148no—
564C2×Q8—74no—
565C2×Q8—72no—
566C2×Q8—72no—
567C2×Q8—141no—
568C2×Q8—141no—
569C2×Q8—142no—
570C2×Q8—142no—
571C2×Q8—142no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—72no—
575C2×D4—144no—
576C2×D4—144no—
577C2×D4—148no—
578C2×D4—141no—
579C2×D4—142no—
580C2×D4—142no—
581C2×D4—284no—
582C2×D4#116114yes—
583C2×D4C23×D712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—71no—
590C22×C4—71no—
591C22×C4—71no—
592C22×C4—72no—
593C22×C4—72no—
594C22×C4—74no—
595C22×C4—74no—
596C22×C4—144no—
597C22×C4—144no—
598C22×C4—144no—
599C22×C4—148no—
600C22×C4—141no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—141no—
604C22×C4—141no—
605C22×C4—282no—
606C22×C4—282no—
607C22×C4—284no—
608C22×C4—284no—
609C22×C4D4×D711yescharacteristic
610C22×C4D4×D711yescharacteristic
611C22×C4C23×D711yescharacteristic
612Q16—148no—
613SD16—148no—
614SD16—148no—
615D8—148no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—72no—
619C2×C8—72no—
620C2×C8—142no—
621C2×C8—142no—
622C2×C8C23×D712yes—
623C2×C8C23×D712yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—72no—
630C4⋊C4—144no—
631C4⋊C4—144no—
632C4⋊C4—144no—
633C4⋊C4—144no—
634C4⋊C4—141no—
635C4⋊C4C23×D712yes—
636C4⋊C4C23×D712yes—
637C4⋊C4C23×D712yes—
638C22⋊C4—24no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C22⋊C4—144no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C42—74no—
647C42—74no—
648C42—72no—
649C42—72no—
650C42—144no—
651C42—144no—
652C42—144no—
653C42—144no—
654C42D4×D712yes—
655C42C23×D712yes—
656C2×C7—44no—
657C2×C7#311114yescomplemented
658C2×C7C2×#52511yescharacteristic
659C2×C7C2×#57511yescharacteristic
660C2×C7C2×#57511yescharacteristic
661D7—42no—
662D7—82no—
663C23—24no—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—72no—
668C23—142no—
669C23—142no—
670C23—142no—
671C23—142no—
672C23—282no—
673C23—282no—
674C23—282no—
675C23C2×D4×D711yescharacteristic
676Q8—74no—
677Q8—144no—
678Q8—142no—
679Q8—142no—
680Q8—142no—
681Q8—282no—
682D4—24no—
683D4—22no—
684D4—1416no—
685D4—142no—
686D4—142no—
687D4—288no—
688D4—282no—
689D4C2×#116114yes—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—72no—
700C2×C4—72no—
701C2×C4—72no—
702C2×C4—1416no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—144no—
707C2×C4—142no—
708C2×C4—144no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—284no—
714C2×C4—284no—
715C2×C4—288no—
716C2×C4—288no—
717C2×C4—282no—
718C2×C4—282no—
719C2×C4C2×D4×D712yes—
720C2×C4C2×D4×D712yes—
721C2×C4C2×D4×D711yescharacteristic
722C2×C4C2×#116112yes—
723C2×C4D7×#4112yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—22no—
727C8—142no—
728C8—142no—
729C7C2×#311111yescharacteristic, complemented, Sylow
730C22—24no—
731C22—42no—
732C22—48no—
733C22—42no—
734C22—142no—
735C22—142no—
736C22—142no—
737C22—284no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—564no—
742C22#9031812yes—
743C22#9045912yes—
744C22#9046412yes—
745C22C22×D4×D711yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—142no—
752C4—142no—
753C4—144no—
754C4—142no—
755C4—282no—
756C4—282no—
757C4#9031812yes—
758C4C22×#116111yescharacteristic
759C4C2×D7×#4111yescharacteristic
760C2—44no—
761C2—282no—
762C2—562no—
763C2#1173858714yesdirect product factor
764C2C2×#9031811yescharacteristic
765C2C2×#9045911yescharacteristic
766C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#478C2
socleC23×C7C22×D4
prime radicalC2×#89553C2
hypercenterC2×#478D7
hypocenterC7C2×#3111
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#90382C2semidirect
2. C2×C4×#1159C2semidirect
3. C2×C7×#478C2semidirect
4. C2×#89835C2semidirect
5. C2×#89788C2semidirect
6. #11738587C2direct (N × H)
7. C2×#89660C2semidirect
8. C2×#89661C2semidirect
9. C2×#89638C2semidirect
10. C2×#89625C2semidirect
11. C2×#89617C2semidirect
12. C2×#89607C2semidirect
13. C2×#89555C2semidirect
15. C2×#89557C2semidirect
16. C2×#89529C2semidirect
28. #90382C22semidirect
30. C4×#1159C22semidirect
46. C7×#478C22semidirect
58. #89835C22semidirect
59. #89788C22semidirect
67. #89661C22semidirect
68. #89660C22semidirect
69. #89638C22semidirect
70. #89625C22semidirect
71. #89617C22semidirect
72. #89607C22semidirect
73. #89557C22semidirect
74. #89555C22semidirect
76. #89529C22semidirect
189. C2×#478D7semidirect
329. #478C2×D7semidirect
657. C2×C7#3111semidirect
729. C7C2×#3111semidirect
763. C2#11738587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903822
C2×C4×#11592
C2×C7×#4782
C2×#898352
C2×#897882
#117385872
C2×#896602
C2×#896612
C2×#896382
C2×#896252
C2×#896172
C2×#896072
C2×#895552
C2×#895532
C2×#895572
C2×#895292
C2×#31117