Finite Group Databasebeta

← C2×#11732937 #13516404

Subgroups — C2×#11732937 #13516404

Order 1792.

2566 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
1C22×#6441C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic
3C2×#89745C211yesmaximal, characteristic, complemented
4C2×#89750C211yesmaximal, characteristic, complemented
5C2×#89717C211yesmaximal, characteristic
6C2×#89717C211yesmaximal, characteristic
7C2×#89723C211yesmaximal, characteristic
8C2×#89715C211yesmaximal, characteristic
9C2×#89714C211yesmaximal, characteristic
10C2×#89701C211yesmaximal, characteristic, complemented
11C2×#89705C211yesmaximal, characteristic, complemented
12#11732937C2116yesmaximal, direct product factor
13C2×#89418C211yesmaximal, characteristic, complemented
14C2×#89419C211yesmaximal, characteristic, complemented
15C2×#89425C211yesmaximal, characteristic, complemented
16C2×#89424C211yesmaximal, characteristic, complemented
17C24×Dic7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C2×#6441C4116yescomplemented
39C2×#6441C2218yes—
40C7×#388C2218yes—
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#89750C2218yescomplemented
56#89745C2218yescomplemented
57#89723C2218yes—
58#89717C2218yes—
59#89717C2218yes—
60#89715C2218yes—
61#89714C2218yes—
62#89705C2218yescomplemented
63#89701C2218yescomplemented
64#89425C2218yescomplemented
65#89424C2218yescomplemented
66#89419C2218yescomplemented
67#89418C2218yescomplemented
68C2×#2378—71nomaximal, Sylow
69C25×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×Dic7—42no—
77C23×Dic7—42no—
78C23×Dic7C2×C418yes—
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2314yes—
88C22×Dic14—42no—
89C22×Dic14—42no—
90C22×Dic14C2×C418yes—
91C22×Dic14C2314yes—
92C2×C7×C4⋊C4—42no—
93C2×C7×C4⋊C4C2314yes—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4—42no—
96C2×C7×C22⋊C4C2×C418yes—
97C2×C7×C22⋊C4C2314yes—
98C2×C7×C22⋊C4C2314yes—
99C2×C7×C22⋊C4C2314yes—
100C2×C42×C7—42no—
101C2×C42×C7C2314yes—
102C2×C22⋊Dic7—42no—
103C2×C22⋊Dic7—42no—
104C2×C22⋊Dic7C2×C418yes—
105C2×C22⋊Dic7C2314yes—
106C2×C22⋊Dic7C2314yes—
107C2×C22⋊Dic7C2314yes—
108C2×C4⋊Dic7—42no—
109C2×C4⋊Dic7C2×C418yes—
110C2×C4⋊Dic7C2314yes—
111C2×C4⋊Dic7C2314yes—
112C2×Dic7⋊C4—42no—
113C2×Dic7⋊C4—42no—
114C2×Dic7⋊C4—42no—
115C2×Dic7⋊C4—42no—
116C2×Dic7⋊C4C2×C418yes—
117C2×Dic7⋊C4C2×C418yes—
118C2×Dic7⋊C4C2314yes—
119C2×Dic7⋊C4C2314yes—
120C2×Dic7⋊C4C2314yes—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×C4×Dic7—42no—
125C2×C4×Dic7—42no—
126C2×C4×Dic7—42no—
127C2×C4×Dic7C2314yes—
128C2×C4×Dic7C2314yes—
129C2×C4×Dic7C2314yes—
130#6441C2×C4164yescomplemented
131C7×#95C2314yes—
132C7×#95C2314yes—
133C7⋊#95C2314yes—
134C7⋊#95C2314yes—
135C7⋊#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C22×C22⋊Q8—71no—
146#2378—716no—
147C2×#391—71no—
148C2×#391—71no—
149C2×#389—71no—
150C2×#389—71no—
151C2×#388—71no—
152C2×#388—71no—
153C2×#388—71no—
154C2×#388D711yescharacteristic
155C2×#387—71no—
156C2×#387—71no—
157C2×#387—71no—
158C2×#387—71no—
159C2×#381—71no—
160C2×#380—71no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7C22×C414yes—
168C24×C7C2412yes—
169C24×C7C2411yescharacteristic
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×C7C22×C414yes—
187C22×C4×C7C22×C414yes—
188C22×C4×C7C2412yes—
189C22×C4×C7C2412yes—
190C22×C4×C7C2412yes—
191C22×C4×C7C2412yes—
192C22×C4×C7C2412yes—
193C22×C4×C7C2412yes—
194C22×Dic7—22no—
195C22×Dic7—22no—
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×Dic7—416no—
215C22×Dic7—44no—
216C22×Dic7—44no—
217C22×Dic7C22×C414yes—
218C22×Dic7C22×C414yes—
219C22×Dic7C22×C414yes—
220C22×Dic7C22×C414yes—
221C22×Dic7C22×C4116yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C2×Dic14—416no—
231C2×Dic14—44no—
232C2×Dic14—44no—
233C2×Dic14C22×C4116yes—
234C7×C4⋊C4—44no—
235C7×C22⋊C4—44no—
236C7×C22⋊C4—44no—
237C7×C22⋊C4C22×C4116yes—
238C42×C7—44no—
239C22⋊Dic7—44no—
240C22⋊Dic7—44no—
241C22⋊Dic7C22×C4116yes—
242C4⋊Dic7—44no—
243C4⋊Dic7C22×C4116yes—
244Dic7⋊C4—44no—
245Dic7⋊C4—44no—
246Dic7⋊C4—44no—
247Dic7⋊C4—44no—
248Dic7⋊C4C22×C4116yes—
249Dic7⋊C4C22×C4116yes—
250C4×Dic7—44no—
251C4×Dic7—44no—
252C4×Dic7—44no—
253C23×Q8—71no—
254C24×C4—71no—
255C2×C22⋊Q8—716no—
256C2×C22⋊Q8—78no—
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×C4⋊C4C2×D711yescharacteristic
266C22×C22⋊C4—71no—
267C22×C22⋊C4—71no—
268C22×C22⋊C4—71no—
269C22×C22⋊C4C2×D711yescharacteristic
270C22×C22⋊C4C2×D711yescharacteristic
271C22×C22⋊C4C2×D711yescharacteristic
272C22×C42—71no—
273C22×C42—71no—
274C22×C42—71no—
275C22×C42C2×D711yescharacteristic
276#391—78no—
277#391—78no—
278#389—78no—
279#389—78no—
280#388—78no—
281#388—78no—
282#388—78no—
283#388C2×D718yes—
284#387—78no—
285#387—78no—
286#387—78no—
287#387—78no—
288#381—78no—
289#380—78no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95C2×D711yescharacteristic
303C2×#95C2×D711yescharacteristic
304C23×C7—28no—
305C23×C7—28no—
306C23×C7—28no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—44no—
314C23×C7—44no—
315C23×C7—44no—
316C23×C7—44no—
317C23×C7C23×C414yes—
318C23×C7C23×C412yes—
319C23×C7H(5,𝔽2)12yes—
320C23×C7H(5,𝔽2)12yes—
321C23×C7H(5,𝔽2)12yes—
322C23×C72−1+412yes—
323C23×C72−1+412yes—
324C23×C72−1+412yes—
325C23×C7C2511yescharacteristic
326C2×C4×C7—28no—
327C2×C4×C7—28no—
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—44no—
345C2×C4×C7—44no—
346C2×C4×C7—44no—
347C2×C4×C7—44no—
348C2×C4×C7C23×C414yes—
349C2×C4×C7C23×C414yes—
350C2×Dic7—28no—
351C2×Dic7—28no—
352C2×Dic7—28no—
353C2×Dic7—28no—
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—22no—
374C2×Dic7—416no—
375C2×Dic7—44no—
376C2×Dic7—44no—
377C2×Dic7—44no—
378C2×Dic7—44no—
379C2×Dic7C23×C414yes—
380C2×Dic7C23×C414yes—
381C2×Dic7C23×C414yes—
382C2×Dic7C23×C414yes—
383Dic14—416no—
384C25C22×D711yescharacteristic
385C22×Q8—78no—
386C22×Q8—74no—
387C22×Q8—282no—
388C22×Q8—282no—
389C23×C4—71no—
390C23×C4—71no—
391C23×C4—71no—
392C23×C4—71no—
393C23×C4—78no—
394C23×C4—74no—
395C23×C4—71no—
396C23×C4—71no—
397C23×C4—71no—
398C23×C4—71no—
399C23×C4—282no—
400C23×C4—282no—
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404C23×C4C22×D711yescharacteristic
405C23×C4C22×D711yescharacteristic
406C23×C4C22×D711yescharacteristic
407C22⋊Q8—764no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—78no—
410C2×C4⋊C4—78no—
411C2×C4⋊C4—78no—
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—282no—
421C2×C4⋊C4—282no—
422C2×C4⋊C4—282no—
423C2×C4⋊C4—282no—
424C2×C4⋊C4—282no—
425C2×C4⋊C4C22×D714yes—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—78no—
429C2×C22⋊C4—74no—
430C2×C22⋊C4—74no—
431C2×C22⋊C4—74no—
432C2×C22⋊C4—282no—
433C2×C22⋊C4—282no—
434C2×C22⋊C4C4×D718yes—
435C2×C22⋊C4C22×D714yes—
436C2×C22⋊C4C22×D714yes—
437C2×C22⋊C4C22×D714yes—
438C2×C42—42no—
439C2×C42—74no—
440C2×C42—74no—
441C2×C42—74no—
442C2×C42—282no—
443C2×C42—282no—
444C2×C42—282no—
445C2×C42C22×D714yes—
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#95—74no—
457#95—74no—
458#95C22×D714yes—
459#95C22×D714yes—
460C22×C7—24no—
461C22×C7—24no—
462C22×C7—24no—
463C22×C7—416no—
464C22×C7—42no—
465C22×C7—42no—
466C22×C7—42no—
467C22×C7—42no—
468C22×C7#51814yes—
469C22×C7#51914yes—
470C22×C7#52014yes—
471C22×C7#56214yes—
472C22×C7#56214yes—
473C22×C7#56314yes—
474C22×C7#56314yes—
475C22×C7C24×C411yescharacteristic
476C22×C7C2×H(5,𝔽2)11yescharacteristic
477C22×C7C2×H(5,𝔽2)11yescharacteristic
478C22×C7C2×H(5,𝔽2)11yescharacteristic
479C22×C7C2×2−1+411yescharacteristic
480C22×C7C2×2−1+411yescharacteristic
481C22×C7C2×2−1+411yescharacteristic
482C4×C7—24no—
483C4×C7—24no—
484C4×C7—42no—
485C4×C7—42no—
486C4×C7—42no—
487C4×C7—42no—
488Dic7—24no—
489Dic7—24no—
490Dic7—24no—
491Dic7—24no—
492Dic7—42no—
493Dic7—42no—
494Dic7—42no—
495Dic7—42no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24C2×C4×D714yes—
503C24C23×D712yes—
504C24C23×D711yescharacteristic
505C2×Q8—716no—
506C2×Q8—2816no—
507C2×Q8—284no—
508C2×Q8—284no—
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—22no—
524C22×C4—22no—
525C22×C4—74no—
526C22×C4—74no—
527C22×C4—74no—
528C22×C4—74no—
529C22×C4—72no—
530C22×C4—72no—
531C22×C4—72no—
532C22×C4—72no—
533C22×C4—716no—
534C22×C4—72no—
535C22×C4—72no—
536C22×C4—72no—
537C22×C4—72no—
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—142no—
557C22×C4—142no—
558C22×C4—2816no—
559C22×C4—284no—
560C22×C4—284no—
561C22×C4C2×C4×D714yes—
562C22×C4C2×C4×D714yes—
563C22×C4C23×D712yes—
564C22×C4C23×D712yes—
565C22×C4C23×D712yes—
566C22×C4C23×D712yes—
567C22×C4C23×D712yes—
568C22×C4C23×D712yes—
569C4⋊C4—44no—
570C4⋊C4—716no—
571C4⋊C4—716no—
572C4⋊C4—716no—
573C4⋊C4—284no—
574C4⋊C4—284no—
575C4⋊C4—284no—
576C4⋊C4—284no—
577C4⋊C4—284no—
578C22⋊C4—44no—
579C22⋊C4—44no—
580C22⋊C4—716no—
581C22⋊C4—284no—
582C22⋊C4—284no—
583C22⋊C4C2×C4×D7116yes—
584C42—44no—
585C42—284no—
586C42—284no—
587C42—284no—
588C2×C7—44no—
589C2×C7#237818yescomplemented
590C2×C7C2×#51811yescharacteristic
591C2×C7C2×#51911yescharacteristic
592C2×C7C2×#52011yescharacteristic
593C2×C7C2×#56211yescharacteristic
594C2×C7C2×#56211yescharacteristic
595C2×C7C2×#56311yescharacteristic
596C2×C7C2×#56311yescharacteristic
597C23—28no—
598C23—28no—
599C23—28no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23C22×C4×D714yes—
611C23C22×C4×D712yes—
612C23#654812yes—
613C23#654812yes—
614C23#655312yes—
615C23#655412yes—
616C23#655412yes—
617C23#655412yes—
618C23C24×D711yescharacteristic
619Q8—2816no—
620C2×C4—28no—
621C2×C4—28no—
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—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—74no—
643C2×C4—74no—
644C2×C4—74no—
645C2×C4—74no—
646C2×C4—148no—
647C2×C4—148no—
648C2×C4—148no—
649C2×C4—148no—
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—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—2816no—
671C2×C4—284no—
672C2×C4—284no—
673C2×C4—284no—
674C2×C4—284no—
675C2×C4C22×C4×D714yes—
676C2×C4C22×C4×D714yes—
677C7C2×#237811yescharacteristic, complemented, Sylow
678C22—24no—
679C22—24no—
680C22—24no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—416no—
685C22—42no—
686C22#9020714yes—
687C22#9023614yes—
688C22#9023714yes—
689C22#9031214yes—
690C22#9034214yes—
691C22#9037514yes—
692C22#9040314yes—
693C22C23×C4×D711yescharacteristic
694C22C2×#654811yescharacteristic
695C22C2×#654811yescharacteristic
696C22C2×#655311yescharacteristic
697C22C2×#655411yescharacteristic
698C22C2×#655411yescharacteristic
699C22C2×#655411yescharacteristic
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—144no—
707C4—144no—
708C4—144no—
709C4—144no—
710C4—282no—
711C4—282no—
712C4—282no—
713C4—282no—
714C2—44no—
715C2#1173293718yesdirect product factor
716C2C2×#9020711yescharacteristic
717C2C2×#9023711yescharacteristic
718C2C2×#9023611yescharacteristic
719C2C2×#9031211yescharacteristic
720C2C2×#9034211yescharacteristic
721C2C2×#9037511yescharacteristic
722C2C2×#9040311yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#388C2
socleC24×C7C24
prime radicalC25×C7C23
cosocleC23×C7C25
hypercenterC2×#388D7
hypocenterC7C2×#2378
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×#89745C2semidirect
4. C2×#89750C2semidirect
10. C2×#89701C2semidirect
11. C2×#89705C2semidirect
12. #11732937C2direct (N × H)
13. C2×#89418C2semidirect
14. C2×#89419C2semidirect
15. C2×#89425C2semidirect
16. C2×#89424C2semidirect
38. C2×#6441C4semidirect
55. #89750C22semidirect
56. #89745C22semidirect
62. #89705C22semidirect
63. #89701C22semidirect
64. #89425C22semidirect
65. #89424C22semidirect
66. #89419C22semidirect
67. #89418C22semidirect
130. #6441C2×C4semidirect
589. C2×C7#2378semidirect
677. C7C2×#2378semidirect
715. C2#11732937direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64412
C2×C7×#3882
C2×#897452
C2×#897502
C2×#897172
C2×#897232
C2×#897152
C2×#897142
C2×#897012
C2×#897052
#117329372
C2×#894182
C2×#894192
C2×#894252
C2×#894242
C2×#23787