Finite Group Databasebeta

← C2×#11730965 #13522746

Subgroups — C2×#11730965 #13522746

Order 1792.

2486 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×#89982C211yesmaximal, characteristic
3C22×C7⋊#95C211yesmaximal, characteristic
4C2×#89722C211yesmaximal, characteristic
5C2×#89722C211yesmaximal, characteristic
6C2×#89718C211yesmaximal, characteristic
7C2×#89714C211yesmaximal, characteristic
8C2×#89700C211yesmaximal, characteristic, complemented
9C2×#89705C211yesmaximal, characteristic, complemented
10C2×#89705C211yesmaximal, characteristic, complemented
11C2×#89708C211yesmaximal, characteristic, complemented
12#11730965C2116yesmaximal, direct product factor
13C2×#89432C211yesmaximal, characteristic, complemented
14C2×#89432C211yesmaximal, characteristic, complemented
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89429C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C4×C7×C22⋊C4C2218yes—
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39#89982C2218yes—
40C2×C7⋊#95C2218yes—
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89722C2218yes—
56#89722C2218yes—
57#89718C2218yes—
58#89714C2218yes—
59#89708C2218yescomplemented
60#89705C2218yescomplemented
61#89705C2218yescomplemented
62#89700C2218yescomplemented
63#89432C2218yescomplemented
64#89432C2218yescomplemented
65#89432C2218yescomplemented
66#89429C2218yescomplemented
67C2×#2505—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C23×C4×C7—24no—
70C23×C4×C7—24no—
71C23×C4×C7—42no—
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2314yes—
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×Dic7—24no—
80C23×Dic7—24no—
81C23×Dic7—24no—
82C23×Dic7—42no—
83C23×Dic7—42no—
84C23×Dic7—42no—
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2314yes—
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2314yes—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4Q818yes—
97C2×C7×C22⋊C4C2314yes—
98C2×C7×C22⋊C4C2314yes—
99C2×C42×C7—24no—
100C2×C42×C7—42no—
101C2×C42×C7C2314yes—
102C2×C42×C7C2314yes—
103C2×C22⋊Dic7—24no—
104C2×C22⋊Dic7—24no—
105C2×C22⋊Dic7C2314yes—
106C2×C22⋊Dic7C2314yes—
107C2×C4⋊Dic7—24no—
108C2×C4⋊Dic7—42no—
109C2×C4⋊Dic7—42no—
110C2×C4⋊Dic7—42no—
111C2×C4⋊Dic7C2314yes—
112C2×C4⋊Dic7C2314yes—
113C2×C4⋊Dic7C2314yes—
114C2×C4⋊Dic7C2314yes—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—42no—
118C2×Dic7⋊C4—42no—
119C2×Dic7⋊C4—42no—
120C2×Dic7⋊C4—42no—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×Dic7⋊C4C2314yes—
125C2×Dic7⋊C4C2314yes—
126C2×Dic7⋊C4C2314yes—
127C7×#95C2314yes—
128C7×#95C2314yes—
129C7⋊#95C2314yes—
130C7⋊#95C2314yes—
131C7⋊#95C2314yes—
132C7⋊#95C2314yes—
133C7⋊#95C2314yes—
134C7⋊#95C2314yes—
135C7⋊#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143#2505—716no—
144C2×#400—71no—
145C2×#400—71no—
146C2×#400—71no—
147C2×#398—71no—
148C2×#389—71no—
149C2×#387—71no—
150C2×#387—71no—
151C2×#385—71no—
152C2×#385—71no—
153C2×#385—71no—
154C2×#385—71no—
155C2×#382—71no—
156C2×#380—71no—
157C2×C4×C22⋊C4D711yescharacteristic
158C22×#95—71no—
159C24×C7—22no—
160C24×C7—22no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7C2×Q814yes—
164C24×C7#4114yes—
165C24×C7#4114yes—
166C24×C7C2412yes—
167C24×C7C2411yescharacteristic
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—28no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—28no—
185C22×C4×C7—44no—
186C22×C4×C7—416no—
187C22×C4×C7C2×Q814yes—
188C22×C4×C7C2×Q814yes—
189C22×C4×C7#4114yes—
190C22×C4×C7C2412yes—
191C22×C4×C7C2412yes—
192C22×C4×C7C2412yes—
193C22×C4×C7C2412yes—
194C22×C4×C7C2412yes—
195C22×C4×C7C2412yes—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—22no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—28no—
207C22×Dic7—28no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—28no—
222C22×Dic7—44no—
223C22×Dic7—44no—
224C22×Dic7—44no—
225C22×Dic7—416no—
226C22×Dic7—416no—
227C22×Dic7#4114yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C7×C22⋊C4—28no—
237C7×C22⋊C4C2×Q8116yes—
238C42×C7—28no—
239C42×C7—44no—
240C22⋊Dic7—28no—
241C22⋊Dic7—28no—
242C4⋊Dic7—28no—
243C4⋊Dic7—44no—
244C4⋊Dic7—44no—
245C4⋊Dic7—44no—
246Dic7⋊C4—28no—
247Dic7⋊C4—28no—
248Dic7⋊C4—44no—
249Dic7⋊C4—44no—
250Dic7⋊C4—44no—
251Dic7⋊C4—44no—
252C24×C4—71no—
253C24×C4—71no—
254C24×C4C2×D711yescharacteristic
255C22×C4⋊C4—71no—
256C22×C4⋊C4—71no—
257C22×C4⋊C4—71no—
258C22×C4⋊C4—71no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C22⋊C4—71no—
266C22×C22⋊C4—71no—
267C22×C22⋊C4C2×D711yescharacteristic
268C22×C22⋊C4C2×D711yescharacteristic
269C22×C42C2×D711yescharacteristic
270C22×C42C2×D711yescharacteristic
271#400—78no—
272#400—78no—
273#400—78no—
274#398—78no—
275#389—78no—
276#387—78no—
277#387—78no—
278#385—78no—
279#385—78no—
280#385—78no—
281#385—78no—
282#382—78no—
283#380—78no—
284C4×C22⋊C4C2×D718yes—
285C2×#95—71no—
286C2×#95—71no—
287C2×#95—71no—
288C2×#95—71no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—78no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95C2×D711yescharacteristic
301C2×#95C2×D711yescharacteristic
302C23×C7—28no—
303C23×C7—28no—
304C23×C7—28no—
305C23×C7—28no—
306C23×C7—28no—
307C23×C7—28no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7#125116yes—
313C23×C7C22×Q814yes—
314C23×C7C22×Q812yes—
315C23×C7C2×#4114yes—
316C23×C7C2×#4114yes—
317C23×C7C2×#4112yes—
318C23×C7C2×#4112yes—
319C23×C7C2×#4112yes—
320C23×C7C2×#4112yes—
321C23×C7H(5,𝔽2)12yes—
322C23×C7H(5,𝔽2)12yes—
323C23×C7C2511yescharacteristic
324C2×C4×C7—28no—
325C2×C4×C7—28no—
326C2×C4×C7—28no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—416no—
343C2×C4×C7—44no—
344C2×C4×C7—44no—
345C2×C4×C7—44no—
346C2×C4×C7C22×Q814yes—
347C2×C4×C7C22×Q814yes—
348C2×C4×C7C2×#4114yes—
349C2×Dic7—28no—
350C2×Dic7—22no—
351C2×Dic7—22no—
352C2×Dic7—22no—
353C2×Dic7—22no—
354C2×Dic7—22no—
355C2×Dic7—22no—
356C2×Dic7—22no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—416no—
374C2×Dic7—416no—
375C2×Dic7—44no—
376C2×Dic7—44no—
377C2×Dic7—44no—
378C2×Dic7—44no—
379C2×Dic7—44no—
380C2×Dic7—44no—
381C2×Dic7—44no—
382C2×Dic7C2×#4114yes—
383C25C22×D711yescharacteristic
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—42no—
387C23×C4—71no—
388C23×C4—71no—
389C23×C4—71no—
390C23×C4—71no—
391C23×C4—71no—
392C23×C4—71no—
393C23×C4—71no—
394C23×C4—71no—
395C23×C4—74no—
396C23×C4—74no—
397C23×C4—144no—
398C23×C4—144no—
399C23×C4—144no—
400C23×C4—282no—
401C23×C4—282no—
402C23×C4—282no—
403C23×C4C22×D711yescharacteristic
404C23×C4C22×D711yescharacteristic
405C23×C4C22×D711yescharacteristic
406C23×C4C22×D714yes—
407C23×C4C22×D711yescharacteristic
408C23×C4C22×D711yescharacteristic
409C23×C4C22×D711yescharacteristic
410C2×C4⋊C4—74no—
411C2×C4⋊C4—74no—
412C2×C4⋊C4—74no—
413C2×C4⋊C4—74no—
414C2×C4⋊C4—74no—
415C2×C4⋊C4—74no—
416C2×C4⋊C4—74no—
417C2×C4⋊C4—74no—
418C2×C4⋊C4—74no—
419C2×C4⋊C4—74no—
420C2×C4⋊C4—144no—
421C2×C4⋊C4—144no—
422C2×C4⋊C4—144no—
423C2×C4⋊C4—282no—
424C2×C4⋊C4—282no—
425C2×C4⋊C4—282no—
426C2×C4⋊C4—282no—
427C2×C4⋊C4—282no—
428C2×C4⋊C4—282no—
429C2×C4⋊C4—282no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—74no—
432C2×C22⋊C4—74no—
433C2×C22⋊C4—144no—
434C2×C22⋊C4—144no—
435C2×C22⋊C4Dic1418yes—
436C2×C22⋊C4C22×D714yes—
437C2×C22⋊C4C22×D714yes—
438C2×C42—24no—
439C2×C42—42no—
440C2×C42C22×D714yes—
441C2×C42C22×D714yes—
442#95—74no—
443#95—74no—
444#95—74no—
445#95—74no—
446#95—74no—
447#95—74no—
448#95—74no—
449#95—74no—
450#95—74no—
451#95—74no—
452#95—74no—
453#95—74no—
454#95—74no—
455#95—74no—
456#95C22×D714yes—
457#95C22×D714yes—
458C22×C7—24no—
459C22×C7—24no—
460C22×C7—24no—
461C22×C7—24no—
462C22×C7—24no—
463C22×C7—24no—
464C22×C7—232no—
465C22×C7C2×#12518yes—
466C22×C7C2×#12514yes—
467C22×C7#52914yes—
468C22×C7#53814yes—
469C22×C7#55114yes—
470C22×C7#55114yes—
471C22×C7#55414yes—
472C22×C7#55414yes—
473C22×C7C23×Q811yescharacteristic
474C22×C7C22×#4111yescharacteristic
475C22×C7C22×#4111yescharacteristic
476C22×C7C22×#4111yescharacteristic
477C22×C7C22×#4111yescharacteristic
478C22×C7C2×H(5,𝔽2)11yescharacteristic
479C22×C7C2×H(5,𝔽2)11yescharacteristic
480C4×C7—24no—
481C4×C7—24no—
482C4×C7—24no—
483C4×C7—42no—
484C4×C7—42no—
485C4×C7—42no—
486Dic7—24no—
487Dic7—42no—
488Dic7—42no—
489Dic7—42no—
490Dic7—42no—
491Dic7—42no—
492Dic7—42no—
493Dic7—42no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24C2×Dic1414yes—
499C24#115714yes—
500C24#115714yes—
501C24C23×D712yes—
502C24C23×D711yescharacteristic
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—28no—
520C22×C4—44no—
521C22×C4—416no—
522C22×C4—74no—
523C22×C4—72no—
524C22×C4—72no—
525C22×C4—72no—
526C22×C4—72no—
527C22×C4—72no—
528C22×C4—72no—
529C22×C4—72no—
530C22×C4—72no—
531C22×C4—148no—
532C22×C4—142no—
533C22×C4—142no—
534C22×C4—142no—
535C22×C4—142no—
536C22×C4—142no—
537C22×C4—142no—
538C22×C4—148no—
539C22×C4—148no—
540C22×C4—142no—
541C22×C4—142no—
542C22×C4—142no—
543C22×C4—142no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—142no—
557C22×C4—284no—
558C22×C4—284no—
559C22×C4—284no—
560C22×C4—2816no—
561C22×C4—2816no—
562C22×C4C2×Dic1414yes—
563C22×C4C2×Dic1414yes—
564C22×C4#115914yes—
565C22×C4C23×D712yes—
566C22×C4C23×D712yes—
567C22×C4C23×D712yes—
568C22×C4C23×D712yes—
569C22×C4C23×D712yes—
570C22×C4C23×D712yes—
571C4⋊C4—148no—
572C4⋊C4—148no—
573C4⋊C4—148no—
574C4⋊C4—284no—
575C4⋊C4—284no—
576C4⋊C4—284no—
577C4⋊C4—284no—
578C4⋊C4—284no—
579C4⋊C4—284no—
580C4⋊C4—284no—
581C22⋊C4—28no—
582C22⋊C4—148no—
583C22⋊C4—148no—
584C22⋊C4C2×Dic14116yes—
585C42—28no—
586C42—44no—
587C2×C7—28no—
588C2×C7#250518yescomplemented
589C2×C7C22×#12511yescharacteristic
590C2×C7C2×#52911yescharacteristic
591C2×C7C2×#53811yescharacteristic
592C2×C7C2×#55111yescharacteristic
593C2×C7C2×#55111yescharacteristic
594C2×C7C2×#55411yescharacteristic
595C2×C7C2×#55411yescharacteristic
596C23—28no—
597C23—28no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—28no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23#6433116yes—
607C23C22×Dic1414yes—
608C23C22×Dic1412yes—
609C23C2×#115714yes—
610C23C2×#115714yes—
611C23C2×#115712yes—
612C23C2×#115712yes—
613C23C2×#115912yes—
614C23#654812yes—
615C23D7×#4112yes—
616C23#655312yes—
617C23C24×D711yescharacteristic
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—416no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—74no—
641C2×C4—148no—
642C2×C4—142no—
643C2×C4—142no—
644C2×C4—142no—
645C2×C4—142no—
646C2×C4—142no—
647C2×C4—142no—
648C2×C4—142no—
649C2×C4—142no—
650C2×C4—142no—
651C2×C4—142no—
652C2×C4—142no—
653C2×C4—142no—
654C2×C4—142no—
655C2×C4—142no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—2816no—
666C2×C4—2816no—
667C2×C4—284no—
668C2×C4—284no—
669C2×C4—284no—
670C2×C4—284no—
671C2×C4—284no—
672C2×C4—284no—
673C2×C4—284no—
674C2×C4C22×Dic1414yes—
675C2×C4C22×Dic1414yes—
676C2×C4C2×#115914yes—
677C7C2×#250511yescharacteristic, complemented, Sylow
678C22—232no—
679C22—24no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—24no—
684C22—24no—
685C22C2×#643318yes—
686C22C2×#643314yes—
687C22#9018614yes—
688C22#9021814yes—
689C22#9022914yes—
690C22#9023014yes—
691C22#9023414yes—
692C22#9025114yes—
693C22C23×Dic1411yescharacteristic
694C22C22×#115711yescharacteristic
695C22C22×#115711yescharacteristic
696C22C22×#115911yescharacteristic
697C22C2×#654811yescharacteristic
698C22C2×D7×#4111yescharacteristic
699C22C2×#655311yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—144no—
707C4—282no—
708C4—282no—
709C4—282no—
710C4—282no—
711C4—282no—
712C4—282no—
713C4—282no—
714C2—28no—
715C2#1173096518yesdirect product factor
716C2C22×#643311yescharacteristic
717C2C2×#9018611yescharacteristic
718C2C2×#9021811yescharacteristic
719C2C2×#9022911yescharacteristic
720C2C2×#9023411yescharacteristic
721C2C2×#9023011yescharacteristic
722C2C2×#9025111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2505
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C2×#89700C2semidirect
9. C2×#89705C2semidirect
10. C2×#89705C2semidirect
11. C2×#89708C2semidirect
12. #11730965C2direct (N × H)
13. C2×#89432C2semidirect
14. C2×#89432C2semidirect
15. C2×#89432C2semidirect
16. C2×#89429C2semidirect
59. #89708C22semidirect
60. #89705C22semidirect
61. #89705C22semidirect
62. #89700C22semidirect
63. #89432C22semidirect
64. #89432C22semidirect
65. #89432C22semidirect
66. #89429C22semidirect
588. C2×C7#2505semidirect
677. C7C2×#2505semidirect
715. C2#11730965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×#899822
C22×C7⋊#952
C2×#897222
C2×#897182
C2×#897142
C2×#897002
C2×#897052
C2×#897082
#117309652
C2×#894322
C2×#894292
C2×#25057