Finite Group Databasebeta

← C2×#11737914 #14234759

Subgroups — C2×#11737914 #14234759

Order 1792.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90412C211yesmaximal, characteristic, complemented
2C2×#90259C211yesmaximal, characteristic
3C2×C7×#462C211yesmaximal, characteristic, complemented
4C2×#89962C211yesmaximal, characteristic
5C2×#89953C211yesmaximal, characteristic, complemented
6C2×#89957C211yesmaximal, characteristic
7C2×#89954C211yesmaximal, characteristic, complemented
8C2×#89858C211yesmaximal, characteristic
9C2×#89802C211yesmaximal, characteristic, complemented
10#11737914C2116yesmaximal, direct product factor
11C2×#89617C211yesmaximal, characteristic
12C2×#89600C211yesmaximal, characteristic, complemented
13C2×#89565C211yesmaximal, characteristic, complemented
14C2×#89590C211yesmaximal, characteristic
15C2×#89561C211yesmaximal, characteristic, complemented
16C2×#89560C211yesmaximal, characteristic
17C22×C7×Q16C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C2×#6507C2211yescharacteristic
25C2×#6507C2211yescharacteristic
26C2×#6507C2211yescharacteristic
27C22×#1144C2211yescharacteristic
28C22×#1144C2211yescharacteristic
29C22×#1144C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C22×#1143C2211yescharacteristic
32C22×Dic28C2211yescharacteristic
33C22×#1132C2211yescharacteristic
34#90412—24no—
35#90412C2218yescomplemented
36#90259—24no—
37#90259C2218yes—
38C2×#6461—21no—
39C2×#6459—21no—
40C2×#6456C2211yescharacteristic
41C2×#6453—21no—
42C2×#6452—21no—
43C2×#6452—21no—
44C2×#6450—21no—
45C2×#6450C2211yescharacteristic
46C2×#6439—21no—
47C2×#6438C2211yescharacteristic
48C2×#6435—21no—
49C2×C4×Dic14C2211yescharacteristic
50C2×C4×Dic14C2211yescharacteristic
51C7×#462C2218yescomplemented
52C2×C7×C4⋊C8C2211yescharacteristic
53C2×C7×#103C2211yescharacteristic
54C2×C7×#103C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56#89962C2218yes—
57#89957C2218yes—
58#89954C2218yescomplemented
59#89953C2218yescomplemented
60C2×#6395C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6389C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×C8×Dic7C2211yescharacteristic
66#89858C2218yes—
67#89802C2218yescomplemented
68C2×#6384C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6377C2211yescharacteristic
71#89617C2218yes—
72#89600C2218yescomplemented
73#89590C2218yes—
74#89565C2218yescomplemented
75#89561C2218yescomplemented
76#89560C2218yes—
77C2×#3398—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×D28C2311yescharacteristic
82C22×C4×D7—21no—
83C22×Dic14D411yescharacteristic
84C22×Dic14C2311yescharacteristic
85C22×Dic14C2311yescharacteristic
86C2×C7×Q16—42no—
87C2×C7×Q16—42no—
88C2×C7×Q16C2314yes—
89C2×C7×Q16C2314yes—
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C7×C4⋊Q8—22no—
93C7×C4⋊Q8C2314yes—
94C4×C7×Q8—22no—
95C4×C7×Q8C2314yes—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C42×C7—21no—
101C2×C42×C7C2311yescharacteristic
102#6510—22no—
103#6510C2314yes—
104Q8×Dic7—22no—
105Q8×Dic7—22no—
106Q8×Dic7C2314yes—
107Q8×Dic7C2314yes—
108#6507—22no—
109#6507—22no—
110#6507—22no—
111#6507C2314yes—
112#6507C2314yes—
113#6507C2314yes—
114C2×#1144—24no—
115C2×#1144—24no—
116C2×#1144—42no—
117C2×#1144C2314yes—
118C2×#1144C2314yes—
119C2×#1144C2314yes—
120C2×#1143—24no—
121C2×#1143—42no—
122C2×#1143C2314yes—
123C2×#1143C2314yes—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7D411yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4D411yescharacteristic
142C2×Dic7⋊C4D411yescharacteristic
143C2×C4×Dic7—21no—
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×Dic28—42no—
152C2×Dic28C2314yes—
153C2×#1132—42no—
154C2×#1132C2314yes—
155#6461—28no—
156#6459—28no—
157#6456—22no—
158#6456C2314yes—
159#6453—28no—
160#6452—28no—
161#6452—28no—
162#6450—28no—
163#6450—22no—
164#6450C2314yes—
165#6439—28no—
166#6438—22no—
167#6438C2314yes—
168#6435—28no—
169C4×Dic14—22no—
170C4×Dic14D414yes—
171C4×Dic14C2314yes—
172C4×Dic14C2314yes—
173C7×C4⋊C8C2314yes—
174C7×#103C2314yes—
175C7×#103C2314yes—
176#6409C2314yes—
177#6395C2314yes—
178#6390C2314yes—
179#6389C2314yes—
180Dic7⋊C8C2314yes—
181Dic7⋊C8C2314yes—
182C8×Dic7C2314yes—
183#6384C2314yes—
184#6382C2314yes—
185#6377C2314yes—
186C2×#557—71no—
187C2×#556—71no—
188#3398—716no—
189C2×#497—71no—
190C2×#497—71no—
191C2×#494—71no—
192C2×#464—71no—
193C2×#464—71no—
194C2×#462—71no—
195C2×#462—71no—
196C2×#462D711yescharacteristic, complemented
197C2×#461—71no—
198C2×#446—71no—
199C2×#441—71no—
200C2×#441—71no—
201C2×C4×SD16—71no—
202C23×D7—21no—
203C2×C7×Q8—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×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8C2412yes—
213C2×C7×Q8C2412yes—
214C2×C7×Q8C2412yes—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2411yescharacteristic
222C22×Dic7—21no—
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—21no—
232C2×D28C2412yes—
233C2×C4×D7—24no—
234C2×C4×D7—44no—
235C2×Dic14—24no—
236C2×Dic14—22no—
237C2×Dic14—22no—
238C2×Dic14—22no—
239C2×Dic14—22no—
240C2×Dic14—21no—
241C2×Dic14—21no—
242C2×Dic14C2×D414yes—
243C2×Dic14C2412yes—
244C2×Dic14C2412yes—
245C7×Q16—44no—
246C7×Q16—44no—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8C2412yes—
250C2×C7×C8C2412yes—
251C7×C4⋊C4—24no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4C2412yes—
256C42×C7—24no—
257C42×C7C2×D412yes—
258C42×C7C2412yes—
259#1144—28no—
260#1144—28no—
261#1144—44no—
262#1143—28no—
263#1143—44no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269C4⋊Dic7—21no—
270C4⋊Dic7—24no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2×D414yes—
273C4⋊Dic7C2412yes—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4C2×D414yes—
283Dic7⋊C4C2×D414yes—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7—24no—
287C4×Dic7—24no—
288C4×Dic7C2×D412yes—
289C4×Dic7C2×D412yes—
290C4×Dic7C2412yes—
291C4×Dic7C2412yes—
292C2×C7⋊C8—22no—
293C2×C7⋊C8#4114yes—
294C2×C7⋊C8C2412yes—
295C2×C7⋊C8C2412yes—
296Dic28—44no—
297#1132—44no—
298C22×Q16—71no—
299C22×Q16—71no—
300C22×Q16—71no—
301C22×Q16—71no—
302C22×Q16C2×D711yescharacteristic
303C22×Q16C2×D711yescharacteristic
304C22×SD16—71no—
305C22×SD16—71no—
306C22×SD16—71no—
307#557—78no—
308#557—144no—
309#556—78no—
310#556—144no—
311C2×C4⋊Q8—71no—
312C2×C4⋊Q8—71no—
313C2×C4⋊Q8—71no—
314C2×C4⋊Q8C2×D711yescharacteristic
315C2×#126—141no—
316C2×#126—141no—
317C2×#125—141no—
318C2×#125—141no—
319C2×#125—141no—
320C2×#124—71no—
321C2×#124—71no—
322C2×C22⋊Q8—141no—
323C2×C4×Q8—71no—
324C2×C4×Q8—71no—
325C2×C4×Q8—71no—
326C2×C4×Q8—71no—
327C2×C4×Q8—71no—
328C2×C4×Q8—141no—
329C2×C4×Q8C2×D711yescharacteristic
330C2×C4×D4—71no—
331C2×#117—141no—
332#497—78no—
333#497—78no—
334#494—78no—
335#464—78no—
336#464—78no—
337#462—78no—
338#462—78no—
339#462C2×D718yescomplemented
340#461—78no—
341#446—78no—
342#441—78no—
343#441—78no—
344C4×SD16—78no—
345C2×#106—71no—
346C2×C4⋊C8—71no—
347C2×C4⋊C8—71no—
348C2×C4⋊C8C2×D711yescharacteristic
349C2×#103—71no—
350C2×#103—71no—
351C2×#103—71no—
352C2×#103C2×D711yescharacteristic
353C2×#103C2×D711yescharacteristic
354C2×#102—71no—
355C2×#97—71no—
356C2×#97—71no—
357C2×C4×C8—71no—
358C23×C7C22×D411yescharacteristic
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—22no—
366C7×Q8—22no—
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—42no—
370C7×Q8—42no—
371C7×Q8—42no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—42no—
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×C7H(5,𝔽2)12yes—
387C2×C4×C7C2511yescharacteristic
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7#13714yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402D28—22no—
403D28—22no—
404D28—42no—
405C4×D7—48no—
406Dic14—28no—
407Dic14—22no—
408Dic14—22no—
409Dic14—22no—
410Dic14—22no—
411Dic14—42no—
412Dic14—42no—
413C7×C8—22no—
414C7×C8—22no—
415C7⋊C8—22no—
416C7⋊C8C2×#4114yes—
417C22×Q8—71no—
418C22×Q8—71no—
419C22×Q8—71no—
420C22×Q8C22×D711yescharacteristic
421C22×Q8C22×D711yescharacteristic
422C22×Q8C22×D711yescharacteristic
423C22×D4—71no—
424C23×C4—141no—
425C2×Q16—42no—
426C2×Q16—42no—
427C2×Q16—74no—
428C2×Q16—74no—
429C2×Q16—74no—
430C2×Q16—74no—
431C2×Q16—144no—
432C2×Q16—144no—
433C2×Q16—282no—
434C2×Q16—282no—
435C2×Q16C22×D714yes—
436C2×Q16C22×D714yes—
437C2×SD16—74no—
438C2×SD16—74no—
439C2×SD16—74no—
440C2×SD16—144no—
441C2×SD16—282no—
442C2×SD16—282no—
443C22×C8—71no—
444C22×C8—71no—
445C22×C8C22×D711yescharacteristic
446C22×C8C22×D711yescharacteristic
447C4⋊Q8—22no—
448C4⋊Q8—74no—
449C4⋊Q8—74no—
450C4⋊Q8—74no—
451C4⋊Q8—142no—
452C4⋊Q8—142no—
453C4⋊Q8—142no—
454C4⋊Q8C22×D714yes—
455#126—148no—
456#126—148no—
457#125—148no—
458#125—148no—
459#125—148no—
460#124—74no—
461#124—74no—
462#124—142no—
463#124—142no—
464C22⋊Q8—148no—
465C4×Q8—22no—
466C4×Q8—74no—
467C4×Q8—74no—
468C4×Q8—74no—
469C4×Q8—74no—
470C4×Q8—74no—
471C4×Q8—74no—
472C4×Q8—142no—
473C4×Q8—142no—
474C4×Q8—142no—
475C4×Q8—148no—
476C4×Q8—142no—
477C4×Q8C22×D714yes—
478C4×D4—74no—
479C4×D4—142no—
480#117—148no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—71no—
486C2×C4⋊C4—71no—
487C2×C4⋊C4—71no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
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×C42—21no—
505C2×C42—71no—
506C2×C42—71no—
507C2×C42—141no—
508C2×C42—141no—
509C2×C42—141no—
510C2×C42—141no—
511C2×C42C22×D711yescharacteristic
512#106—74no—
513C4⋊C8—74no—
514C4⋊C8—74no—
515C4⋊C8C22×D714yes—
516#103—74no—
517#103—74no—
518#103—74no—
519#103C22×D714yes—
520#103C22×D714yes—
521#102—74no—
522#97—74no—
523#97—74no—
524C4×C8—74no—
525C22×C7#55012yes—
526C22×C7C2×#13712yes—
527C22×C7#57812yes—
528C22×C7C23×D411yescharacteristic
529C2×D7—42no—
530C2×D7—42no—
531C2×D7—42no—
532C2×D7—84no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7#55012yes—
540C4×C7C22×#4111yescharacteristic
541C4×C7C2×H(5,𝔽2)11yescharacteristic
542Dic7—22no—
543Dic7—22no—
544Dic7—22no—
545Dic7—42no—
546Dic7—42no—
547Dic7—42no—
548Dic7C2×#13714yes—
549C24—141no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—74no—
560C2×Q8—72no—
561C2×Q8—72no—
562C2×Q8—144no—
563C2×Q8—141no—
564C2×Q8—141no—
565C2×Q8—142no—
566C2×Q8—142no—
567C2×Q8—142no—
568C2×Q8—142no—
569C2×Q8C23×D712yes—
570C2×Q8C23×D712yes—
571C2×Q8C23×D712yes—
572C2×D4—72no—
573C2×D4—141no—
574C2×D4—142no—
575C2×D4—142no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—71no—
581C22×C4—71no—
582C22×C4—71no—
583C22×C4—71no—
584C22×C4—144no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—284no—
589C22×C4D4×D711yescharacteristic
590C22×C4D4×D711yescharacteristic
591C22×C4C23×D711yescharacteristic
592Q16—44no—
593Q16—44no—
594Q16—148no—
595Q16—148no—
596Q16—284no—
597Q16—284no—
598SD16—148no—
599SD16—284no—
600SD16—284no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—74no—
604C2×C8—72no—
605C2×C8—72no—
606C2×C8—142no—
607C2×C8C23×D712yes—
608C2×C8C23×D712yes—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—74no—
614C4⋊C4—74no—
615C4⋊C4—74no—
616C4⋊C4—72no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—141no—
628C4⋊C4C23×D712yes—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C42—24no—
635C42—72no—
636C42—72no—
637C42—72no—
638C42—72no—
639C42—144no—
640C42—144no—
641C42—144no—
642C42—144no—
643C42D4×D712yes—
644C42C23×D712yes—
645C2×C7#339814yescomplemented
646C2×C7C2×#55011yescharacteristic
647C2×C7C22×#13711yescharacteristic
648C2×C7C2×#57811yescharacteristic
649D7—82no—
650C23—142no—
651C23—282no—
652C23—282no—
653C23—282no—
654C23C2×D4×D711yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—148no—
665Q8—142no—
666Q8—142no—
667Q8—142no—
668Q8—142no—
669Q8—282no—
670Q8—282no—
671D4—142no—
672D4—142no—
673D4—282no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—74no—
685C2×C4—72no—
686C2×C4—72no—
687C2×C4—72no—
688C2×C4—72no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—288no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4C2×D4×D712yes—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D711yescharacteristic
702C2×C4#654812yes—
703C2×C4D7×#4112yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—74no—
708C8—142no—
709C7C2×#339811yescharacteristic, complemented, Sylow
710C22—282no—
711C22—282no—
712C22—282no—
713C22—564no—
714C22#9029012yes—
715C22#9045712yes—
716C22D7×#13712yes—
717C22C22×D4×D711yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—74no—
725C4—142no—
726C4—142no—
727C4—142no—
728C4—282no—
729C4—282no—
730C4—282no—
731C4#9029012yes—
732C4C2×#654811yescharacteristic
733C4C2×D7×#4111yescharacteristic
734C2—562no—
735C2#1173791414yesdirect product factor
736C2C2×#9029011yescharacteristic
737C2C2×#9045711yescharacteristic
738C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#462C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×#462D7
hypocenterC7C2×#3398
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×#90412C2semidirect
3. C2×C7×#462C2semidirect
5. C2×#89953C2semidirect
7. C2×#89954C2semidirect
9. C2×#89802C2semidirect
10. #11737914C2direct (N × H)
12. C2×#89600C2semidirect
13. C2×#89565C2semidirect
15. C2×#89561C2semidirect
35. #90412C22semidirect
51. C7×#462C22semidirect
58. #89954C22semidirect
59. #89953C22semidirect
67. #89802C22semidirect
72. #89600C22semidirect
74. #89565C22semidirect
75. #89561C22semidirect
196. C2×#462D7semidirect
339. #462C2×D7semidirect
645. C2×C7#3398semidirect
709. C7C2×#3398semidirect
735. C2#11737914direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904122
C2×#902592
C2×C7×#4622
C2×#899622
C2×#899532
C2×#899572
C2×#899542
C2×#898582
C2×#898022
#117379142
C2×#896172
C2×#896002
C2×#895652
C2×#895902
C2×#895612
C2×#895602
C2×#33987