Finite Group Databasebeta

← C2×#11737916 #14234811

Subgroups — C2×#11737916 #14234811

Order 1792.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90423C211yesmaximal, characteristic, complemented
2C2×#90259C211yesmaximal, characteristic, complemented
3C2×C7×#462C211yesmaximal, characteristic, complemented
4C2×#89962C211yesmaximal, characteristic, complemented
5C2×#89963C211yesmaximal, characteristic
6C2×#89957C211yesmaximal, characteristic, complemented
7C2×#89954C211yesmaximal, characteristic, complemented
8C2×#89858C211yesmaximal, characteristic, complemented
9C2×#89798C211yesmaximal, characteristic, complemented
10#11737916C2116yesmaximal, direct product factor
11C2×#89616C211yesmaximal, characteristic
12C2×#89600C211yesmaximal, characteristic, complemented
13C2×#89570C211yesmaximal, characteristic, complemented
14C2×#89591C211yesmaximal, characteristic
15C2×#89589C211yesmaximal, characteristic, complemented
16C2×#89562C211yesmaximal, characteristic, complemented
17C22×C7×Q16C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22C2×#6510C2211yescharacteristic
23C2×#6510C2211yescharacteristic
24C2×Q8×Dic7C2211yescharacteristic
25C2×Q8×Dic7C2211yescharacteristic
26C2×#6507C2211yescharacteristic
27C22×#1144C2211yescharacteristic
28C22×#1144C2211yescharacteristic
29C22×#1143C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C22×#1143C2211yescharacteristic
32C22×D56C2211yescharacteristic
33C22×#1132C2211yescharacteristic
34#90423—24no—
35#90423C2218yescomplemented
36#90259—24no—
37#90259C2218yescomplemented
38C2×#6461—21no—
39C2×#6461—21no—
40C2×#6461—21no—
41C2×#6460—21no—
42C2×#6459—21no—
43C2×#6456C2211yescharacteristic
44C2×#6455—21no—
45C2×#6450C2211yescharacteristic
46C2×#6439—21no—
47C2×#6438C2211yescharacteristic
48C2×C4×D28C2211yescharacteristic
49C2×#6435—21no—
50C2×C4×Dic14C2211yescharacteristic
51C7×#462C2218yescomplemented
52C2×C7×C4⋊C8C2211yescharacteristic
53C2×C7×#103C2211yescharacteristic
54C2×C7×#103C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56#89963C2218yes—
57#89962C2218yescomplemented
58#89957C2218yescomplemented
59#89954C2218yescomplemented
60C2×#6395C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6389C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×C8×Dic7C2211yescharacteristic
66#89858C2218yescomplemented
67#89798C2218yescomplemented
68C2×#6383C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6377C2211yescharacteristic
71#89616C2218yes—
72#89600C2218yescomplemented
73#89591C2218yes—
74#89589C2218yescomplemented
75#89570C2218yescomplemented
76#89562C2218yescomplemented
77C2×#3402—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×D28C2311yescharacteristic
82C22×D28C2311yescharacteristic
83C22×C4×D7—21no—
84C22×C4×D7—21no—
85C22×Dic14D411yescharacteristic
86C22×Dic14C2311yescharacteristic
87C2×C7×Q16—42no—
88C2×C7×Q16—42no—
89C2×C7×Q16C2314yes—
90C2×C7×Q16C2314yes—
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C7×C4⋊Q8—22no—
94C7×C4⋊Q8C2314yes—
95C4×C7×Q8—22no—
96C4×C7×Q8C2314yes—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C42×C7—21no—
102C2×C42×C7C2311yescharacteristic
103#6510—22no—
104#6510—22no—
105#6510—22no—
106#6510C2314yes—
107#6510C2314yes—
108#6510C2314yes—
109Q8×Dic7—22no—
110Q8×Dic7—22no—
111Q8×Dic7C2314yes—
112Q8×Dic7C2314yes—
113#6507—22no—
114#6507C2314yes—
115C2×#1144—24no—
116C2×#1144—42no—
117C2×#1144C2314yes—
118C2×#1144C2314yes—
119C2×#1143—24no—
120C2×#1143—24no—
121C2×#1143—42no—
122C2×#1143C2314yes—
123C2×#1143C2314yes—
124C2×#1143C2314yes—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
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×C4⋊Dic7—21no—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7D411yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
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×D56—42no—
152C2×D56C2314yes—
153C2×#1132—42no—
154C2×#1132C2314yes—
155#6461—28no—
156#6461—28no—
157#6461—28no—
158#6460—28no—
159#6459—28no—
160#6456—22no—
161#6456C2314yes—
162#6455—28no—
163#6450—22no—
164#6450C2314yes—
165#6439—28no—
166#6438—22no—
167#6438C2314yes—
168C4×D28—22no—
169C4×D28C2314yes—
170#6435—28no—
171C4×Dic14D414yes—
172C4×Dic14C2314yes—
173C7×C4⋊C8C2314yes—
174C7×#103C2314yes—
175C7×#103C2314yes—
176#6409C2314yes—
177#6395C2314yes—
178#6390C2314yes—
179#6389C2314yes—
180Dic7⋊C8C2314yes—
181Dic7⋊C8C2314yes—
182C8×Dic7C2314yes—
183#6383C2314yes—
184#6381C2314yes—
185#6377C2314yes—
186C2×#556—71no—
187C2×#556—71no—
188#3402—716no—
189C2×#497—71no—
190C2×#497—71no—
191C2×#495—71no—
192C2×#464—71no—
193C2×#464—71no—
194C2×#462—71no—
195C2×#462D711yescharacteristic, complemented
196C2×#463—71no—
197C2×#463—71no—
198C2×#446—71no—
199C2×#440—71no—
200C2×#440—71no—
201C2×C4×Q16—71no—
202C23×D7—21no—
203C23×D7—21no—
204C2×C7×Q8—21no—
205C2×C7×Q8—21no—
206C2×C7×Q8—21no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8—22no—
213C2×C7×Q8C2412yes—
214C2×C7×Q8C2412yes—
215C2×C7×Q8C2412yes—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2411yescharacteristic
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7C2×D411yescharacteristic
226C22×Dic7C2×D411yescharacteristic
227C22×Dic7C2×D411yescharacteristic
228C22×Dic7C2×D411yescharacteristic
229C2×D28—22no—
230C2×D28—22no—
231C2×D28—22no—
232C2×D28—22no—
233C2×D28—21no—
234C2×D28—21no—
235C2×D28C2412yes—
236C2×D28C2412yes—
237C2×C4×D7—24no—
238C2×C4×D7—24no—
239C2×C4×D7—44no—
240C2×C4×D7—44no—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14—42no—
245C2×Dic14C2×D414yes—
246C2×Dic14C2412yes—
247C7×Q16—44no—
248C7×Q16—44no—
249C2×C7×C8—22no—
250C2×C7×C8—22no—
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—24no—
257C7×C4⋊C4C2412yes—
258C42×C7—24no—
259C42×C7C2×D412yes—
260C42×C7C2412yes—
261#1144—28no—
262#1144—44no—
263#1143—28no—
264#1143—28no—
265#1143—44no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
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—
276C4⋊Dic7—21no—
277C4⋊Dic7—24no—
278C4⋊Dic7—24no—
279C4⋊Dic7C2×D414yes—
280C4⋊Dic7C2412yes—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4C2×D414yes—
285Dic7⋊C4C2×D414yes—
286C4×Dic7—24no—
287C4×Dic7—24no—
288C4×Dic7—24no—
289C4×Dic7C2×D412yes—
290C4×Dic7C2×D412yes—
291C4×Dic7C2412yes—
292C4×Dic7C2412yes—
293C2×C7⋊C8—22no—
294C2×C7⋊C8#4114yes—
295C2×C7⋊C8C2412yes—
296C2×C7⋊C8C2412yes—
297D56—44no—
298#1132—44no—
299C22×Q16—71no—
300C22×Q16—71no—
301C22×Q16C2×D711yescharacteristic
302C22×Q16C2×D711yescharacteristic
303C22×SD16—71no—
304C22×SD16—71no—
305C22×SD16—71no—
306C22×SD16—71no—
307C22×D8—71no—
308#556—78no—
309#556—78no—
310#556—144no—
311#556—144no—
312C2×C4⋊Q8—71no—
313C2×C4⋊Q8C2×D711yescharacteristic
314C2×#126—141no—
315C2×#126—141no—
316C2×#126—141no—
317C2×#126—141no—
318C2×#124—71no—
319C2×#124—71no—
320C2×#124—71no—
321C2×#124—71no—
322C2×C22⋊Q8—141no—
323C2×C22⋊Q8—141no—
324C2×C4×Q8—71no—
325C2×C4×Q8—71no—
326C2×C4×Q8—71no—
327C2×C4×Q8—71no—
328C2×C4×Q8C2×D711yescharacteristic
329C2×C4×D4—71no—
330C2×C4×D4—71no—
331C2×#117—141no—
332C2×#117—141no—
333#497—78no—
334#497—78no—
335#495—78no—
336#464—78no—
337#464—78no—
338#463—78no—
339#463—78no—
340#462—78no—
341#462C2×D718yescomplemented
342#446—78no—
343#440—78no—
344#440—78no—
345C4×Q16—78no—
346C2×#107—71no—
347C2×C4⋊C8—71no—
348C2×C4⋊C8—71no—
349C2×C4⋊C8C2×D711yescharacteristic
350C2×#103—71no—
351C2×#103—71no—
352C2×#103C2×D711yescharacteristic
353C2×#103C2×D711yescharacteristic
354C2×#102—71no—
355C2×#102—71no—
356C2×#97—71no—
357C2×#97—71no—
358C2×C4×C8—71no—
359C23×C7C22×D411yescharacteristic
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7—42no—
368C7×Q8—22no—
369C7×Q8—22no—
370C7×Q8—22no—
371C7×Q8—22no—
372C7×Q8—22no—
373C7×Q8—22no—
374C7×Q8—42no—
375C7×Q8—42no—
376C7×Q8—42no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—42no—
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
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403C2×Dic7C22×D412yes—
404C2×Dic7C22×D412yes—
405D28—22no—
406D28—22no—
407D28—22no—
408D28—22no—
409D28—42no—
410D28—42no—
411C4×D7—48no—
412C4×D7—48no—
413Dic14—22no—
414Dic14—22no—
415Dic14—44no—
416Dic14—42no—
417C7×C8—22no—
418C7×C8—22no—
419C7⋊C8—22no—
420C7⋊C8C2×#4114yes—
421C22×Q8—71no—
422C22×Q8—71no—
423C22×Q8C22×D711yescharacteristic
424C22×Q8C22×D711yescharacteristic
425C22×Q8C22×D711yescharacteristic
426C22×D4—71no—
427C22×D4—71no—
428C23×C4—141no—
429C23×C4—141no—
430C2×Q16—42no—
431C2×Q16—42no—
432C2×Q16—74no—
433C2×Q16—74no—
434C2×Q16—144no—
435C2×Q16—282no—
436C2×Q16C22×D714yes—
437C2×Q16C22×D714yes—
438C2×SD16—74no—
439C2×SD16—74no—
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—144no—
443C2×SD16—144no—
444C2×SD16—282no—
445C2×SD16—282no—
446C2×D8—74no—
447C2×D8—282no—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8C22×D711yescharacteristic
451C22×C8C22×D711yescharacteristic
452C4⋊Q8—22no—
453C4⋊Q8—74no—
454C4⋊Q8—142no—
455C4⋊Q8C22×D714yes—
456#126—148no—
457#126—148no—
458#126—148no—
459#126—148no—
460#124—74no—
461#124—74no—
462#124—74no—
463#124—74no—
464#124—142no—
465#124—142no—
466#124—142no—
467#124—142no—
468C22⋊Q8—148no—
469C22⋊Q8—148no—
470C4×Q8—22no—
471C4×Q8—74no—
472C4×Q8—74no—
473C4×Q8—74no—
474C4×Q8—74no—
475C4×Q8—74no—
476C4×Q8—142no—
477C4×Q8—142no—
478C4×Q8—142no—
479C4×Q8C22×D714yes—
480C4×D4—74no—
481C4×D4—74no—
482C4×D4—142no—
483C4×D4—142no—
484#117—148no—
485#117—148no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—71no—
490C2×C4⋊C4—71no—
491C2×C4⋊C4—71no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—141no—
494C2×C4⋊C4—141no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4—141no—
498C2×C4⋊C4C22×D711yescharacteristic
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C22⋊C4—141no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C42—21no—
510C2×C42—71no—
511C2×C42—71no—
512C2×C42—141no—
513C2×C42—141no—
514C2×C42—141no—
515C2×C42C22×D711yescharacteristic
516#107—74no—
517C4⋊C8—74no—
518C4⋊C8—74no—
519C4⋊C8C22×D714yes—
520#103—74no—
521#103—74no—
522#103C22×D714yes—
523#103C22×D714yes—
524#102—74no—
525#102—74no—
526#97—74no—
527#97—74no—
528C4×C8—74no—
529C22×C7#55012yes—
530C22×C7#57512yes—
531C22×C7#57812yes—
532C22×C7C23×D411yescharacteristic
533C2×D7—42no—
534C2×D7—42no—
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—42no—
538C2×D7—42no—
539C2×D7—84no—
540C2×D7—84no—
541C4×C7—22no—
542C4×C7—22no—
543C4×C7—42no—
544C4×C7—42no—
545C4×C7—42no—
546C4×C7—42no—
547C4×C7#55012yes—
548C4×C7C22×#4111yescharacteristic
549C4×C7C2×H(5,𝔽2)11yescharacteristic
550Dic7—22no—
551Dic7—22no—
552Dic7—22no—
553Dic7—22no—
554Dic7—42no—
555Dic7—42no—
556C24—141no—
557C24—141no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—74no—
568C2×Q8—72no—
569C2×Q8—141no—
570C2×Q8—142no—
571C2×Q8—142no—
572C2×Q8—282no—
573C2×Q8C23×D712yes—
574C2×Q8C23×D712yes—
575C2×Q8C23×D712yes—
576C2×D4—72no—
577C2×D4—72no—
578C2×D4—141no—
579C2×D4—141no—
580C2×D4—142no—
581C2×D4—142no—
582C2×D4—142no—
583C2×D4—142no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—71no—
589C22×C4—71no—
590C22×C4—71no—
591C22×C4—71no—
592C22×C4—144no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—144no—
596C22×C4—284no—
597C22×C4—284no—
598C22×C4D4×D711yescharacteristic
599C22×C4D4×D711yescharacteristic
600C22×C4C23×D711yescharacteristic
601Q16—44no—
602Q16—44no—
603Q16—148no—
604Q16—284no—
605SD16—148no—
606SD16—148no—
607SD16—284no—
608SD16—284no—
609D8—284no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—74no—
613C2×C8—72no—
614C2×C8—72no—
615C2×C8—142no—
616C2×C8C23×D712yes—
617C2×C8C23×D712yes—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—74no—
623C4⋊C4—74no—
624C4⋊C4—74no—
625C4⋊C4—72no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—144no—
629C4⋊C4—144no—
630C4⋊C4—144no—
631C4⋊C4—141no—
632C4⋊C4C23×D712yes—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C22⋊C4—144no—
643C42—24no—
644C42—72no—
645C42—72no—
646C42—72no—
647C42—72no—
648C42—144no—
649C42—144no—
650C42—144no—
651C42D4×D712yes—
652C42C23×D712yes—
653C2×C7#340214yescomplemented
654C2×C7C2×#55011yescharacteristic
655C2×C7C2×#57511yescharacteristic
656C2×C7C2×#57811yescharacteristic
657D7—82no—
658D7—82no—
659C23—142no—
660C23—142no—
661C23—282no—
662C23—282no—
663C23—282no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23C2×D4×D711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8—42no—
675Q8—42no—
676Q8—42no—
677Q8—142no—
678Q8—142no—
679Q8—284no—
680Q8—282no—
681D4—142no—
682D4—142no—
683D4—142no—
684D4—142no—
685D4—282no—
686D4—282no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—72no—
698C2×C4—72no—
699C2×C4—72no—
700C2×C4—72no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—142no—
707C2×C4—288no—
708C2×C4—288no—
709C2×C4—282no—
710C2×C4—282no—
711C2×C4C2×D4×D712yes—
712C2×C4C2×D4×D712yes—
713C2×C4C2×D4×D711yescharacteristic
714C2×C4#654812yes—
715C2×C4D7×#4112yes—
716C2×C4C24×D711yescharacteristic
717C8—22no—
718C8—22no—
719C8—74no—
720C8—142no—
721C7C2×#340211yescharacteristic, complemented, Sylow
722C22—282no—
723C22—282no—
724C22—282no—
725C22—282no—
726C22—282no—
727C22—282no—
728C22—564no—
729C22—564no—
730C22#9029012yes—
731C22#9045712yes—
732C22#9046812yes—
733C22C22×D4×D711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—142no—
741C4—142no—
742C4—142no—
743C4—142no—
744C4—282no—
745C4—282no—
746C4#9029012yes—
747C4C2×#654811yescharacteristic
748C4C2×D7×#4111yescharacteristic
749C2—562no—
750C2—562no—
751C2#1173791614yesdirect product factor
752C2C2×#9029011yescharacteristic
753C2C2×#9045711yescharacteristic
754C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#462C2
socleC23×C7C22×D4
prime radicalC22×D56C22
hypercenterC2×#462D7
hypocenterC7C2×#3402
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#90423C2semidirect
2. C2×#90259C2semidirect
3. C2×C7×#462C2semidirect
4. C2×#89962C2semidirect
6. C2×#89957C2semidirect
7. C2×#89954C2semidirect
8. C2×#89858C2semidirect
9. C2×#89798C2semidirect
10. #11737916C2direct (N × H)
12. C2×#89600C2semidirect
13. C2×#89570C2semidirect
15. C2×#89589C2semidirect
16. C2×#89562C2semidirect
35. #90423C22semidirect
37. #90259C22semidirect
51. C7×#462C22semidirect
57. #89962C22semidirect
58. #89957C22semidirect
59. #89954C22semidirect
66. #89858C22semidirect
67. #89798C22semidirect
72. #89600C22semidirect
74. #89589C22semidirect
75. #89570C22semidirect
76. #89562C22semidirect
195. C2×#462D7semidirect
341. #462C2×D7semidirect
653. C2×C7#3402semidirect
721. C7C2×#3402semidirect
751. C2#11737916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904232
C2×#902592
C2×C7×#4622
C2×#899622
C2×#899632
C2×#899572
C2×#899542
C2×#898582
C2×#897982
#117379162
C2×#896162
C2×#896002
C2×#895702
C2×#895912
C2×#895892
C2×#895622
C2×#34027