Finite Group Databasebeta

← #13387816

Subgroups — #13387816

Order 1792.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#552C211yesmaximal, characteristic
2C2×#89835C211yesmaximal, characteristic, complemented
3C2×C4×#1144C211yesmaximal, characteristic, complemented
4#11739820C211yesmaximal, characteristic
5#11729494C211yesmaximal, characteristic, complemented
6#11729454C211yesmaximal, characteristic, complemented
7#11729454C211yesmaximal, characteristic, complemented
8#11729449C211yesmaximal, characteristic, complemented
9#11729448C211yesmaximal, characteristic, complemented
10#11729381C211yesmaximal, characteristic, complemented
11#11729368C211yesmaximal, characteristic
12#11729339C211yesmaximal, characteristic, complemented
13#11729330C211yesmaximal, characteristic, complemented
14#11729313C211yesmaximal, characteristic, complemented
15#11729309C211yesmaximal, characteristic, complemented
16C7×#552—24no—
17C7×#552—24no—
18C2×C7×#126—21no—
19C2×C7×#125—21no—
20C2×C7×#125C2211yescharacteristic
21C2×C7×#123—21no—
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C2×C7×#117—21no—
27C2×C7×#117C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×#1144C2211yescharacteristic
30C2×#6487C2211yescharacteristic
31C2×#6487C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36#89994—21no—
37#89984C2211yescharacteristic
38#89984C2211yescharacteristic
39C2×C22⋊(C7⋊C8)C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43#89835—24no—
44C4×#1144—24no—
45#89752—21no—
46C2×#6384C2211yescharacteristic
47C2×#6384C2211yescharacteristic
48C2×#6384C2211yescharacteristic
49C2×#6382C2211yescharacteristic
50C2×#6381C2211yescharacteristic
51C2×#6381C2211yescharacteristic
52#89716—21no—
53#89716—21no—
54#89708C2211yescharacteristic
55C2×C4⋊(C7⋊C8)C2211yescharacteristic
56C2×C4×C7⋊C8C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#89324C2211yescharacteristic
63#24127—71nomaximal, Sylow
64C22×C7×Q8C2311yescharacteristic
65C22×C7×D4D411yescharacteristic
66C23×C4×C7—21no—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C22×Dic14C2311yescharacteristic
70C7×#126—28no—
71C7×#125—28no—
72C7×#125—22no—
73C7×#125D414yes—
74C7×#123—28no—
75C7×C22⋊Q8—22no—
76C7×C22⋊Q8—22no—
77C7×C22⋊Q8—22no—
78C7×C22⋊Q8—22no—
79C4×C7×Q8—22no—
80C4×C7×Q8D414yes—
81C4×C7×D4—22no—
82C4×C7×D4—22no—
83C7×#117—28no—
84C7×#117—22no—
85C7×#117—22no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4D411yescharacteristic
95C2×C7×C4⋊C4C2311yescharacteristic
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4D411yescharacteristic
102C2×C7×C22⋊C4D411yescharacteristic
103C2×C42×C7—21no—
104C2×C42×C7—21no—
105C2×C42×C7C2311yescharacteristic
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×#1144—22no—
111C2×#1144—22no—
112C2×#1144—22no—
113C2×C4⋊Dic7C2311yescharacteristic
114C2×C4⋊Dic7C2311yescharacteristic
115C2×C4⋊Dic7C2311yescharacteristic
116#6487—22no—
117#6487—22no—
118#6487—41no—
119#6487—41no—
120C2×Dic7⋊C4—21no—
121C2×Dic7⋊C4—21no—
122C2×Dic7⋊C4—21no—
123C2×C4×Dic7—21no—
124C22×C7⋊C8C2311yescharacteristic
125C22×C7⋊C8C2311yescharacteristic
126C22×C7⋊C8C2311yescharacteristic
127C22×C7⋊C8C2311yescharacteristic
128C4×Dic14—22no—
129C4×Dic14—22no—
130#6409—22no—
131#6409—41no—
132#6409—41no—
133C7⋊#95—21no—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C22⋊(C7⋊C8)—22no—
138C22⋊(C7⋊C8)—22no—
139C22⋊(C7⋊C8)—41no—
140C22⋊(C7⋊C8)—41no—
141#6384—22no—
142#6384—22no—
143#6384—22no—
144#6382—22no—
145#6381—22no—
146#6381—22no—
147C4⋊(C7⋊C8)—22no—
148C4×C7⋊C8—22no—
149C2×#552D711yescharacteristic
150C2×#479—71no—
151C2×C4×Q16—71no—
152#2536—71no—
153#2036—71no—
154#2035—71no—
155#2001—71no—
156#2001—71no—
157#1991—71no—
158#1954—71no—
159#1873—71no—
160#1872—71no—
161#1854—71no—
162#1852—71no—
163#1805—71no—
164C24×C7C2×D411yescharacteristic
165C24×C7C2×D411yescharacteristic
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8C2×D412yes—
172C2×C7×D4—22no—
173C2×C7×D4—22no—
174C2×C7×D4—41no—
175C22×C4×C7—24no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—42no—
193C22×C4×C7—42no—
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2411yescharacteristic
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C2×Dic14—21no—
204C2×Dic14—21no—
205C2×Dic14—21no—
206C2×Dic14—21no—
207C2×Dic14—21no—
208C2×Dic14#4112yes—
209C7×C4⋊C4—24no—
210C7×C4⋊C4—24no—
211C7×C4⋊C4—24no—
212C7×C4⋊C4—24no—
213C7×C4⋊C4—24no—
214C7×C4⋊C4—24no—
215C7×C4⋊C4—22no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4C2×D412yes—
220C7×C4⋊C4C2×D412yes—
221C7×C4⋊C4C2×D412yes—
222C7×C22⋊C4—24no—
223C7×C22⋊C4—24no—
224C7×C22⋊C4—24no—
225C7×C22⋊C4—22no—
226C7×C22⋊C4—22no—
227C42×C7—24no—
228C42×C7—24no—
229C42×C7C2×D412yes—
230C42×C7C2×D412yes—
231C22⋊Dic7—42no—
232C22⋊Dic7—42no—
233C22⋊Dic7—42no—
234C22⋊Dic7—42no—
235#1144—28no—
236C4⋊Dic7—21no—
237C4⋊Dic7—21no—
238C4⋊Dic7—21no—
239C4⋊Dic7—21no—
240C4⋊Dic7—21no—
241C4⋊Dic7—21no—
242Dic7⋊C4—42no—
243Dic7⋊C4—42no—
244Dic7⋊C4—42no—
245C4×Dic7—42no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8—21no—
256C2×C7⋊C8—21no—
257C2×C7⋊C8#4112yes—
258C22×Q16—71no—
259#552—24no—
260#552—24no—
261C2×#126—21no—
262C2×#125—21no—
263C2×#125C2×D711yescharacteristic
264C2×#123—21no—
265C2×C22⋊Q8—71no—
266C2×C22⋊Q8—71no—
267C2×C22⋊Q8C2×D711yescharacteristic
268C2×C22⋊Q8C2×D711yescharacteristic
269C2×C4×Q8—71no—
270C2×C4×Q8C2×D711yescharacteristic
271C2×C4×D4C2×D711yescharacteristic
272C2×#117—21no—
273C2×#117C2×D711yescharacteristic
274C22×C4⋊C4C2×D711yescharacteristic
275#479—144no—
276C4×Q16—144no—
277C2×#107—71no—
278C2×#107—71no—
279C2×#106—71no—
280C2×C4⋊C8—71no—
281C2×#103—71no—
282C2×#103—71no—
283C2×#103—71no—
284C2×#103—71no—
285C2×#103—71no—
286C2×#103—71no—
287C2×C22⋊C8—71no—
288C2×C22⋊C8—71no—
289C2×C22⋊C8—71no—
290C2×C22⋊C8—71no—
291C2×C4×C8—71no—
292#398—141no—
293#394—141no—
294#388—141no—
295#388—141no—
296#382—71no—
297#380—71no—
298#380—71no—
299#340—71no—
300#340—71no—
301#340—71no—
302#340—71no—
303#340—71no—
304#340—71no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—21no—
316C23×C7—21no—
317C23×C7—21no—
318C23×C7#13512yes—
319C23×C7C22×D411yescharacteristic
320C7×Q8—22no—
321C7×Q8—22no—
322C7×Q8—41no—
323C7×Q8—41no—
324C7×D4—44no—
325C2×C4×C7—21no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—21no—
329C2×C4×C7—21no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—21no—
334C2×C4×C7—22no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—48no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7#12012yes—
357C2×C4×C7#12012yes—
358C2×C4×C7C22×D411yescharacteristic
359C2×C4×C7C22×D411yescharacteristic
360C2×C4×C7C2×#4111yescharacteristic
361C2×C4×C7C2×#4111yescharacteristic
362C2×C4×C7H(5,𝔽2)11yescharacteristic
363C2×C4×C72−1+411yescharacteristic
364C2×Dic7—22no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376Dic14—22no—
377Dic14—22no—
378Dic14—41no—
379Dic14—41no—
380C7⋊C8—22no—
381C7⋊C8—41no—
382C7⋊C8—41no—
383C7⋊C8—41no—
384C22×Q8—71no—
385C22×Q8C22×D711yescharacteristic
386C22×D4C22⋊D711yescharacteristic
387C23×C4—21no—
388C23×C4C22×D711yescharacteristic
389C23×C4C22×D711yescharacteristic
390C2×Q16—142no—
391C2×Q16—142no—
392C2×Q16—142no—
393C22×C8—71no—
394C22×C8—71no—
395C22×C8—71no—
396C22×C8—71no—
397#126—28no—
398#125—28no—
399#125—22no—
400#125C22⋊D714yes—
401#123—28no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—142no—
407C22⋊Q8—142no—
408C22⋊Q8—281no—
409C22⋊Q8—281no—
410C4×Q8—22no—
411C4×Q8—142no—
412C4×Q8—142no—
413C4×Q8C22⋊D714yes—
414C4×D4—22no—
415C4×D4—22no—
416#117—28no—
417#117—22no—
418#117—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—71no—
428C2×C4⋊C4—71no—
429C2×C4⋊C4—71no—
430C2×C4⋊C4—141no—
431C2×C4⋊C4—141no—
432C2×C4⋊C4—141no—
433C2×C4⋊C4C22⋊D711yescharacteristic
434C2×C4⋊C4C22×D711yescharacteristic
435C2×C4⋊C4C22×D711yescharacteristic
436C2×C4⋊C4C22×D711yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—141no—
441C2×C22⋊C4—141no—
442C2×C22⋊C4—141no—
443C2×C22⋊C4—141no—
444C2×C22⋊C4C22⋊D711yescharacteristic
445C2×C22⋊C4C22⋊D711yescharacteristic
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—141no—
449C2×C42C22×D711yescharacteristic
450#107—142no—
451#107—142no—
452#106—142no—
453C4⋊C8—142no—
454#103—142no—
455#103—142no—
456#103—142no—
457#103—142no—
458#103—281no—
459#103—281no—
460C22⋊C8—142no—
461C22⋊C8—142no—
462C22⋊C8—281no—
463C22⋊C8—281no—
464C4×C8—142no—
465#95—141no—
466#95—141no—
467#95—141no—
468#95—141no—
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—41no—
473C22×C7—41no—
474C22×C7—41no—
475C22×C7—41no—
476C22×C7—41no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—41no—
481C22×C7—41no—
482C22×C7—41no—
483C22×C7C2×#12011yescharacteristic
484C22×C7#54611yescharacteristic
485C22×C7#54711yescharacteristic
486C22×C7C2×#13511yescharacteristic
487C22×C7#57511yescharacteristic
488C22×C7#57811yescharacteristic
489C22×C7#57811yescharacteristic
490C4×C7—22no—
491C4×C7—22no—
492C4×C7—41no—
493C4×C7—41no—
494C4×C7—42no—
495C4×C7—42no—
496C4×C7—42no—
497C4×C7—42no—
498C4×C7#52511yescharacteristic
499C4×C7#53711yescharacteristic
500C4×C7#54811yescharacteristic
501C4×C7#55011yescharacteristic
502Dic7—42no—
503Dic7—81no—
504Dic7—81no—
505Dic7—81no—
506C24C2×C22⋊D711yescharacteristic
507C24C2×C22⋊D711yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—72no—
514C2×Q8—141no—
515C2×Q8—141no—
516C2×Q8—141no—
517C2×Q8—141no—
518C2×Q8—141no—
519C2×Q8C2×C22⋊D712yes—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—141no—
543C22×C4—141no—
544C22×C4—141no—
545C22×C4—141no—
546C22×C4C2×C22⋊D711yescharacteristic
547C22×C4C2×C22⋊D711yescharacteristic
548C22×C4C2×C22⋊D711yescharacteristic
549C22×C4C2×C22⋊D711yescharacteristic
550C22×C4C23×D711yescharacteristic
551Q16—148no—
552C2×C8—72no—
553C2×C8—141no—
554C2×C8—141no—
555C2×C8—141no—
556C2×C8—141no—
557C2×C8—141no—
558C2×C8—141no—
559C2×C8—141no—
560C2×C8—141no—
561C2×C8—141no—
562C2×C8—141no—
563C2×C8—141no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—141no—
575C4⋊C4—141no—
576C4⋊C4—141no—
577C4⋊C4—141no—
578C4⋊C4—141no—
579C4⋊C4—141no—
580C4⋊C4—282no—
581C4⋊C4—282no—
582C4⋊C4—282no—
583C4⋊C4C2×C22⋊D712yes—
584C4⋊C4C2×C22⋊D712yes—
585C4⋊C4C2×C22⋊D712yes—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—282no—
592C22⋊C4—282no—
593C22⋊C4—282no—
594C22⋊C4—282no—
595C42—24no—
596C42—24no—
597C42—282no—
598C42C2×C22⋊D712yes—
599C42C2×C22⋊D712yes—
600C2×C7—42no—
601C2×C7—81no—
602C2×C7#240711yescharacteristic
603C2×C7#300211yescharacteristic
604C2×C7#301111yescharacteristic
605C2×C7#330011yescharacteristic
606C2×C7#332711yescharacteristic
607C2×C7#333611yescharacteristic
608C2×C7#335211yescharacteristic
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23#651312yes—
623C23C22×C22⋊D711yescharacteristic
624Q8—22no—
625Q8—22no—
626Q8—41no—
627Q8—41no—
628Q8—142no—
629Q8—142no—
630Q8—281no—
631Q8—281no—
632D4—44no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—48no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—142no—
665C2×C4—281no—
666C2×C4—281no—
667C2×C4—281no—
668C2×C4—281no—
669C2×C4—281no—
670C2×C4—281no—
671C2×C4—281no—
672C2×C4—281no—
673C2×C4—281no—
674C2×C4—281no—
675C2×C4—281no—
676C2×C4#651612yes—
677C2×C4#651612yes—
678C2×C4D7×#4111yescharacteristic
679C2×C4D7×#4111yescharacteristic
680C2×C4#655311yescharacteristic
681C2×C4#655411yescharacteristic
682C2×C4C22×C22⋊D711yescharacteristic
683C2×C4C22×C22⋊D711yescharacteristic
684C8—142no—
685C8—281no—
686C8—281no—
687C8—281no—
688C7#2412711yescharacteristic, complemented, Sylow
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22C2×#651311yescharacteristic
704C22#9051311yescharacteristic
705C22#9051511yescharacteristic
706C22#9052011yescharacteristic
707C22#9052911yescharacteristic
708C22#9052911yescharacteristic
709C22C2×#651611yescharacteristic
710C4—22no—
711C4—22no—
712C4—42no—
713C4—42no—
714C4—41no—
715C4—41no—
716C4—42no—
717C4—42no—
718C4—282no—
719C4—561no—
720C4—561no—
721C4—561no—
722C4#9051911yescharacteristic
723C4#9052211yescharacteristic
724C4#9052411yescharacteristic
725C4#9052511yescharacteristic
726C2—42no—
727C2—81no—
728C2#1174103511yescharacteristic
729C2#1174104211yescharacteristic
730C2#1174104711yescharacteristic
731C2#1174105011yescharacteristic
732C2#1174152511yescharacteristic
733C2#1174154211yescharacteristic
734C2#1174156211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#552C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
hypercenterC2×#552D7
hypocenterC7#24127
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. C2×#89835C2semidirect
3. C2×C4×#1144C2semidirect
5. #11729494C2semidirect
6. #11729454C2semidirect
7. #11729454C2semidirect
8. #11729449C2semidirect
9. #11729448C2semidirect
10. #11729381C2semidirect
12. #11729339C2semidirect
13. #11729330C2semidirect
14. #11729313C2semidirect
15. #11729309C2semidirect
688. C7#24127semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5522
C2×#898352
C2×C4×#11442
#117398202
#117294942
#117294542
#117294492
#117294482
#117293812
#117293682
#117293392
#117293302
#117293132
#117293092
#241277