Finite Group Databasebeta

← C2×#11735798 #13522739

Subgroups — C2×#11735798 #13522739

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×C7×#400C211yesmaximal, characteristic, complemented
2C2×#89761C211yesmaximal, characteristic
3C2×#89761C211yesmaximal, characteristic
4C2×#89755C211yesmaximal, characteristic, complemented
5C2×#89745C211yesmaximal, characteristic, complemented
6#11735798C2116yesmaximal, direct product factor
7C2×#89440C211yesmaximal, characteristic
8C2×#89440C211yesmaximal, characteristic
9C2×#89439C211yesmaximal, characteristic
10C2×D7×#95C211yesmaximal, characteristic
11C2×#89432C211yesmaximal, characteristic, complemented
12C2×#89430C211yesmaximal, characteristic, complemented
13C2×#89427C211yesmaximal, characteristic, complemented
14C2×#89424C211yesmaximal, characteristic, complemented
15C2×#89422C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C23×C4×D7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C7×#400C2218yescomplemented
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
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
53#89761C2218yes—
54#89761C2218yes—
55#89755C2218yescomplemented
56#89745C2218yescomplemented
57#89440C2218yes—
58#89440C2218yes—
59#89439C2218yes—
60#89438C2218yes—
61D7×#95C2218yes—
62#89432C2218yescomplemented
63#89430C2218yescomplemented
64#89427C2218yescomplemented
65#89424C2218yescomplemented
66#89422C2218yescomplemented
67C2×#2505—71nomaximal, Sylow
68C24×D7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C22×C4×D7—24no—
84C22×C4×D7—24no—
85C22×C4×D7—24no—
86C22×C4×D7—24no—
87C22×C4×D7—24no—
88C22×C4×D7—42no—
89C22×C4×D7—42no—
90C22×C4×D7—42no—
91C22×C4×D7—42no—
92C22×C4×D7C2314yes—
93C22×C4×D7C2314yes—
94C22×C4×D7C2314yes—
95C2×C7×C4⋊C4—42no—
96C2×C7×C4⋊C4—42no—
97C2×C7×C4⋊C4C2314yes—
98C2×C7×C4⋊C4C2314yes—
99C2×(C2×D7)⋊C4—24no—
100C2×(C2×D7)⋊C4—24no—
101C2×(C2×D7)⋊C4—24no—
102C2×(C2×D7)⋊C4Q818yes—
103C2×(C2×D7)⋊C4C2314yes—
104C2×(C2×D7)⋊C4C2314yes—
105C2×(C2×D7)⋊C4C2314yes—
106C2×(C2×D7)⋊C4C2314yes—
107C2×C4⋊Dic7—24no—
108C2×C4⋊Dic7—42no—
109C2×C4⋊Dic7C2314yes—
110C2×C4⋊Dic7C2314yes—
111C2×Dic7⋊C4—24no—
112C2×Dic7⋊C4—24no—
113C2×Dic7⋊C4—42no—
114C2×Dic7⋊C4—42no—
115C2×Dic7⋊C4—42no—
116C2×Dic7⋊C4—42no—
117C2×Dic7⋊C4C2314yes—
118C2×Dic7⋊C4C2314yes—
119C2×Dic7⋊C4C2314yes—
120C2×Dic7⋊C4C2314yes—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×C4×Dic7—24no—
124C2×C4×Dic7—42no—
125C2×C4×Dic7C2314yes—
126C2×C4×Dic7C2314yes—
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×#400D711yescharacteristic, complemented
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⋊C4—71no—
158C22×#95—71no—
159C24×C7C2411yescharacteristic
160C23×D7—22no—
161C23×D7—22no—
162C23×D7—22no—
163C23×D7—22no—
164C23×D7C2×Q814yes—
165C23×D7#4114yes—
166C23×D7#4114yes—
167C23×D7C2412yes—
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—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7C2×Q814yes—
189C22×C4×C7C2412yes—
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—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7C2×Q814yes—
215C22×Dic7#4114yes—
216C22×Dic7#4114yes—
217C22×Dic7C2412yes—
218C22×Dic7C2412yes—
219C22×Dic7C2412yes—
220C22×Dic7C2412yes—
221C22×Dic7C2412yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C2×C4×D7—28no—
225C2×C4×D7—28no—
226C2×C4×D7—28no—
227C2×C4×D7—28no—
228C2×C4×D7—28no—
229C2×C4×D7—44no—
230C2×C4×D7—44no—
231C2×C4×D7—44no—
232C2×C4×D7—44no—
233C2×C4×D7—416no—
234C2×C4×D7—416no—
235C2×C4×D7—416no—
236C7×C4⋊C4—44no—
237C7×C4⋊C4—44no—
238(C2×D7)⋊C4—28no—
239(C2×D7)⋊C4—28no—
240(C2×D7)⋊C4—28no—
241(C2×D7)⋊C4C2×Q8116yes—
242C4⋊Dic7—28no—
243C4⋊Dic7—44no—
244Dic7⋊C4—28no—
245Dic7⋊C4—28no—
246Dic7⋊C4—44no—
247Dic7⋊C4—44no—
248Dic7⋊C4—44no—
249Dic7⋊C4—44no—
250C4×Dic7—28no—
251C4×Dic7—44no—
252C24×C4—71no—
253C24×C4—71no—
254C24×C4—71no—
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⋊C4C2×D711yescharacteristic
264C22×C4⋊C4C2×D711yescharacteristic
265C22×C22⋊C4—71no—
266C22×C22⋊C4—71no—
267C22×C22⋊C4—71no—
268C22×C22⋊C4—71no—
269C22×C42—71no—
270C22×C42—71no—
271#400—78no—
272#400—78no—
273#400C2×D718yescomplemented
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⋊C4—78no—
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×#95C2×D711yescharacteristic
298C2×#95C2×D711yescharacteristic
299C2×#95C2×D711yescharacteristic
300C2×#95C2×D711yescharacteristic
301C2×#95C2×D711yescharacteristic
302C23×C7C22×Q812yes—
303C23×C7C2×#4112yes—
304C23×C7C2×#4112yes—
305C23×C7C2×#4112yes—
306C23×C7C2×#4112yes—
307C23×C7H(5,𝔽2)12yes—
308C23×C7H(5,𝔽2)12yes—
309C23×C7C2511yescharacteristic
310C22×D7—28no—
311C22×D7—28no—
312C22×D7—28no—
313C22×D7—28no—
314C22×D7—28no—
315C22×D7—28no—
316C22×D7—22no—
317C22×D7—22no—
318C22×D7—22no—
319C22×D7—22no—
320C22×D7#125116yes—
321C22×D7C22×Q814yes—
322C22×D7C2×#4114yes—
323C22×D7C2×#4114yes—
324C2×C4×C7—28no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
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—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—44no—
346C2×C4×C7—44no—
347C2×C4×C7—44no—
348C2×C4×C7—44no—
349C2×C4×C7—44no—
350C2×C4×C7—44no—
351C2×C4×C7C22×Q814yes—
352C2×Dic7—28no—
353C2×Dic7—28no—
354C2×Dic7—28no—
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—44no—
374C2×Dic7—44no—
375C2×Dic7—44no—
376C2×Dic7—44no—
377C2×Dic7C22×Q814yes—
378C2×Dic7C2×#4114yes—
379C2×Dic7C2×#4114yes—
380C4×D7—416no—
381C4×D7—416no—
382C4×D7—416no—
383C25—71no—
384C23×C4—71no—
385C23×C4—71no—
386C23×C4—71no—
387C23×C4—71no—
388C23×C4—71no—
389C23×C4—71no—
390C23×C4—71no—
391C23×C4—74no—
392C23×C4—74no—
393C23×C4—74no—
394C23×C4—144no—
395C23×C4—144no—
396C23×C4—144no—
397C23×C4—144no—
398C23×C4—144no—
399C23×C4—282no—
400C23×C4—282no—
401C23×C4—282no—
402C23×C4—282no—
403C23×C4C22×D711yescharacteristic
404C23×C4C22×D711yescharacteristic
405C23×C4C22×D711yescharacteristic
406C23×C4C22×D711yescharacteristic
407C23×C4C22×D711yescharacteristic
408C23×C4C22×D711yescharacteristic
409C23×C4C22×D711yescharacteristic
410C2×C4⋊C4—42no—
411C2×C4⋊C4—42no—
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⋊C4C22×D714yes—
429C2×C4⋊C4C22×D714yes—
430C2×C22⋊C4—78no—
431C2×C22⋊C4—74no—
432C2×C22⋊C4—74no—
433C2×C22⋊C4—74no—
434C2×C22⋊C4—74no—
435C2×C22⋊C4—144no—
436C2×C22⋊C4—144no—
437C2×C22⋊C4—144no—
438C2×C42—74no—
439C2×C42—74no—
440C2×C42—144no—
441C2×C42—282no—
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#95C22×D714yes—
454#95C22×D714yes—
455#95C22×D714yes—
456#95C22×D714yes—
457#95C22×D714yes—
458C22×C7C2×#12514yes—
459C22×C7#52914yes—
460C22×C7#53814yes—
461C22×C7#55114yes—
462C22×C7#55114yes—
463C22×C7#55414yes—
464C22×C7#55414yes—
465C22×C7C23×Q811yescharacteristic
466C22×C7C22×#4111yescharacteristic
467C22×C7C22×#4111yescharacteristic
468C22×C7C22×#4111yescharacteristic
469C22×C7C22×#4111yescharacteristic
470C22×C7C2×H(5,𝔽2)11yescharacteristic
471C22×C7C2×H(5,𝔽2)11yescharacteristic
472C2×D7—24no—
473C2×D7—24no—
474C2×D7—24no—
475C2×D7—24no—
476C2×D7—24no—
477C2×D7—24no—
478C2×D7—232no—
479C2×D7C2×#12518yes—
480C4×C7—24no—
481C4×C7—42no—
482C4×C7—42no—
483C4×C7—42no—
484C4×C7—42no—
485C4×C7—42no—
486C4×C7—42no—
487Dic7—24no—
488Dic7—24no—
489Dic7—24no—
490Dic7—42no—
491Dic7—42no—
492Dic7—42no—
493Dic7—42no—
494C24—74no—
495C24—74no—
496C24—74no—
497C24—72no—
498C24—142no—
499C24—142no—
500C24—142no—
501C24—142no—
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—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—74no—
524C22×C4—74no—
525C22×C4—74no—
526C22×C4—72no—
527C22×C4—72no—
528C22×C4—72no—
529C22×C4—72no—
530C22×C4—72no—
531C22×C4—72no—
532C22×C4—72no—
533C22×C4—148no—
534C22×C4—148no—
535C22×C4—148no—
536C22×C4—148no—
537C22×C4—148no—
538C22×C4—142no—
539C22×C4—142no—
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—284no—
557C22×C4—284no—
558C22×C4—284no—
559C22×C4—284no—
560C22×C4—2816no—
561C22×C4—2816no—
562C22×C4—2816no—
563C22×C4Q8×D714yes—
564C22×C4C23×D712yes—
565C22×C4C23×D712yes—
566C22×C4C23×D712yes—
567C22×C4C23×D712yes—
568C22×C4C23×D712yes—
569C22×C4C23×D712yes—
570C22×C4C23×D712yes—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—148no—
574C4⋊C4—148no—
575C4⋊C4—148no—
576C4⋊C4—284no—
577C4⋊C4—284no—
578C4⋊C4—284no—
579C4⋊C4—284no—
580C4⋊C4—284no—
581C22⋊C4—716no—
582C22⋊C4—148no—
583C22⋊C4—148no—
584C22⋊C4—148no—
585C42—148no—
586C42—284no—
587C2×C7#250518yescomplemented
588C2×C7C22×#12511yescharacteristic
589C2×C7C2×#52911yescharacteristic
590C2×C7C2×#53811yescharacteristic
591C2×C7C2×#55111yescharacteristic
592C2×C7C2×#55111yescharacteristic
593C2×C7C2×#55411yescharacteristic
594C2×C7C2×#55411yescharacteristic
595D7—28no—
596C23—716no—
597C23—74no—
598C23—74no—
599C23—74no—
600C23—148no—
601C23—148no—
602C23—148no—
603C23—148no—
604C23—148no—
605C23—148no—
606C23—142no—
607C23—142no—
608C23—142no—
609C23—142no—
610C23#654812yes—
611C23C2×Q8×D712yes—
612C23D7×#4112yes—
613C23D7×#4112yes—
614C23D7×#4112yes—
615C23D7×#4112yes—
616C23#655312yes—
617C23C24×D711yescharacteristic
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
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—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—74no—
646C2×C4—74no—
647C2×C4—74no—
648C2×C4—148no—
649C2×C4—148no—
650C2×C4—148no—
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—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—2816no—
670C2×C4—2816no—
671C2×C4—2816no—
672C2×C4—284no—
673C2×C4—284no—
674C2×C4—284no—
675C2×C4—284no—
676C2×C4C2×Q8×D714yes—
677C7C2×#250511yescharacteristic, complemented, Sylow
678C22—78no—
679C22—144no—
680C22—144no—
681C22—144no—
682C22—144no—
683C22—144no—
684C22—144no—
685C22—1432no—
686C22#9032714yes—
687C22#9034814yes—
688C22#9037014yes—
689C22D7×#12514yes—
690C22#9038114yes—
691C22#9039614yes—
692C22#9039714yes—
693C22C2×#654811yescharacteristic
694C22C22×Q8×D711yescharacteristic
695C22C2×D7×#4111yescharacteristic
696C22C2×D7×#4111yescharacteristic
697C22C2×D7×#4111yescharacteristic
698C22C2×D7×#4111yescharacteristic
699C22C2×#655311yescharacteristic
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—144no—
708C4—144no—
709C4—144no—
710C4—282no—
711C4—282no—
712C4—282no—
713C4—282no—
714C2—148no—
715C2#1173579818yesdirect product factor
716C2C2×#9032711yescharacteristic
717C2C2×#9034811yescharacteristic
718C2C2×#9037011yescharacteristic
719C2C2×#9038111yescharacteristic
720C2C2×D7×#12511yescharacteristic
721C2C2×#9039711yescharacteristic
722C2C2×#9039611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#400C2
socleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#400D7
hypocenterC7C2×#2505
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C2×C7×#400C2semidirect
4. C2×#89755C2semidirect
5. C2×#89745C2semidirect
6. #11735798C2direct (N × H)
11. C2×#89432C2semidirect
12. C2×#89430C2semidirect
13. C2×#89427C2semidirect
14. C2×#89424C2semidirect
15. C2×#89422C2semidirect
36. C7×#400C22semidirect
55. #89755C22semidirect
56. #89745C22semidirect
62. #89432C22semidirect
63. #89430C22semidirect
64. #89427C22semidirect
65. #89424C22semidirect
66. #89422C22semidirect
146. C2×#400D7semidirect
273. #400C2×D7semidirect
587. C2×C7#2505semidirect
677. C7C2×#2505semidirect
715. C2#11735798direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4002
C2×#897612
C2×#897552
C2×#897452
#117357982
C2×#894402
C2×#894392
C2×D7×#952
C2×#894322
C2×#894302
C2×#894272
C2×#894242
C2×#894222
C2×#894382
C2×#25057