Finite Group Databasebeta

← #13410970

Subgroups — #13410970

Order 1792.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2440C211yesmaximal, characteristic, complemented
2C2×#89856C211yesmaximal, characteristic, complemented
3C22×#6383C211yesmaximal, characteristic
4C22⋊C4×D28C211yesmaximal, characteristic
5#11729546C211yesmaximal, characteristic, complemented
6#11729310C211yesmaximal, characteristic, complemented
7#11727383C211yesmaximal, characteristic, complemented
8#11727383C211yesmaximal, characteristic, complemented
9#11727380C211yesmaximal, characteristic, complemented
10#11727380C211yesmaximal, characteristic, complemented
11#11727341C211yesmaximal, characteristic, complemented
12#11727338C211yesmaximal, characteristic, complemented
13#11727275C211yesmaximal, characteristic
14#11727265C211yesmaximal, characteristic, complemented
15#11727203C211yesmaximal, characteristic, complemented
16C23×D28C2211yescharacteristic
17C2×C7×C4⋊Q8C2211yescharacteristic, complemented
18C2×C7×C22⋊Q8—21no—
19C22×C7×C4⋊C4C2211yescharacteristic
20C23×C7⋊C8C2211yescharacteristic
21C2×D7×C22⋊C4—21no—
22C2×C4×D28C2211yescharacteristic
23C2×C4×D28C2211yescharacteristic
24C7×#398—21no—
25C7×#395—21no—
26C7×#389C2211yescharacteristic, complemented
27C7×#389C2211yescharacteristic, complemented
28C7×#385—21no—
29C7×#384C2211yescharacteristic, complemented
30C7×#380C2211yescharacteristic
31C4×C7×C22⋊C4C2211yescharacteristic
32#89984C2211yescharacteristic
33C2×C22⋊(C7⋊C8)C2211yescharacteristic
34#89856—24no—
35C2×#6383—24no—
36C2×#6383C2211yescharacteristic
37C2×#6383C2211yescharacteristic
38C2×#6383C2211yescharacteristic
39C2×#6383C2211yescharacteristic
40C2×#6383C2211yescharacteristic
41C2×#6383C2211yescharacteristic
42C2×#6383C2211yescharacteristic
43C2×#6383C2211yescharacteristic
44C2×#6382C2211yescharacteristic, complemented
45C2×#6382C2211yescharacteristic, complemented
46C2×#6382C2211yescharacteristic, complemented
47C2×#6382C2211yescharacteristic, complemented
48#89727—21no—
49#89711C2211yescharacteristic
50#89711C2211yescharacteristic
51C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
52C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
53#89437—21no—
54#89437—21no—
55#89324C2211yescharacteristic, complemented
56#89324C2211yescharacteristic, complemented
57#89324C2211yescharacteristic, complemented
58#89324C2211yescharacteristic, complemented
59#89319C2211yescharacteristic, complemented
60#89319C2211yescharacteristic, complemented
61#25958—71nomaximal, Sylow
62C24×D7—21no—
63C22×C7×Q8—21no—
64C23×C4×C7—21no—
65C23×C4×C7C2311yescharacteristic
66C22×D28—22no—
67C22×D28—22no—
68C22×D28—21no—
69C22×D28—22no—
70C22×D28—41no—
71C22×D28—41no—
72C22×D28Q814yescomplemented
73C22×D28C2311yescharacteristic
74C22×D28C2311yescharacteristic
75C22×C4×D7—21no—
76C22×C4×D7—21no—
77C7×C4⋊Q8—22no—
78C7×C4⋊Q8—41no—
79C7×C22⋊Q8—44no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—21no—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—21no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—41no—
88C2×C7×C4⋊C4C2311yescharacteristic
89C2×C7×C4⋊C4C2311yescharacteristic
90C2×C7×C4⋊C4C2311yescharacteristic
91C2×C7×C4⋊C4C2311yescharacteristic
92C2×C7×C22⋊C4—21no—
93C2×C7×C22⋊C4D411yescharacteristic
94C2×C7×C22⋊C4D411yescharacteristic
95C2×C42×C7C2311yescharacteristic
96C2×C42×C7C2311yescharacteristic
97C2×C22⋊Dic7—21no—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—21no—
100C2×(C2×D7)⋊C4—21no—
101C2×(C2×D7)⋊C4—21no—
102C2×(C2×D7)⋊C4—21no—
103C2×(C2×D7)⋊C4—21no—
104C2×C4⋊Dic7C2311yescharacteristic
105C2×C4⋊Dic7C2311yescharacteristic
106C22×C7⋊C8—22no—
107C22×C7⋊C8—22no—
108C22×C7⋊C8—41no—
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113D7×C22⋊C4—44no—
114C4×D28—22no—
115C4×D28—22no—
116C4×D28—41no—
117C4×D28—41no—
118C7×#95—21no—
119C7×#95—21no—
120C7×#95—21no—
121C7×#95D411yescharacteristic
122C7×#95D411yescharacteristic
123C7⋊#95—21no—
124C22⋊(C7⋊C8)—22no—
125#6383—22no—
126#6383—22no—
127#6383—22no—
128#6383—22no—
129#6383—22no—
130#6383—41no—
131#6383—41no—
132#6383D414yes—
133#6382—22no—
134#6382—22no—
135#6382—41no—
136#6382—41no—
137C4⋊(C7⋊C8)—22no—
138C4⋊(C7⋊C8)—41no—
139C2×#476—71no—
140C22×#102—71no—
141#2440D711yescharacteristic, complemented
142D4×C22⋊C4—71no—
143#2094—71no—
144#2065—71no—
145#2065—71no—
146#2023—71no—
147#1864—71no—
148#1864—71no—
149#1853—71no—
150#1850—71no—
151#1807—71no—
152#1802—71no—
153#1786—71no—
154C24×C7C2×D411yescharacteristic
155C23×D7—21no—
156C23×D7—21no—
157C23×D7—24no—
158C23×D7—42no—
159C23×D7—42no—
160C23×D7—42no—
161C23×D7—42no—
162C23×D7—81no—
163C23×D7—81no—
164C2×C7×Q8—42no—
165C2×C7×Q8—42no—
166C2×C7×Q8—81no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—42no—
176C22×C4×C7—42no—
177C22×C4×C7—81no—
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7C2×D411yescharacteristic
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×Q812yes—
184C22×C4×C7#4112yes—
185C22×C4×C7C2411yescharacteristic
186C22×Dic7—21no—
187C22×Dic7—21no—
188C2×D28—21no—
189C2×D28—21no—
190C2×D28—21no—
191C2×D28—21no—
192C2×D28—21no—
193C2×D28—21no—
194C2×D28—21no—
195C2×D28—28no—
196C2×D28—24no—
197C2×D28—21no—
198C2×D28—44no—
199C2×D28—44no—
200C2×D28—44no—
201C2×D28—42no—
202C2×D28—42no—
203C2×D28C2×D412yes—
204C2×D28C2×Q812yes—
205C2×D28C2×Q812yes—
206C2×D28#4112yes—
207C2×C4×D7—42no—
208C2×C4×D7—42no—
209C2×C4×D7—42no—
210C2×C4×D7—42no—
211C2×C4×D7—81no—
212C2×C4×D7—81no—
213C7×C4⋊C4—21no—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—42no—
221C7×C4⋊C4—42no—
222C7×C4⋊C4—42no—
223C7×C4⋊C4—42no—
224C7×C4⋊C4—42no—
225C7×C4⋊C4—81no—
226C7×C4⋊C4C2×D412yes—
227C7×C22⋊C4—22no—
228C7×C22⋊C4—42no—
229C7×C22⋊C4SD1614yes—
230C42×C7—21no—
231C42×C7—21no—
232C42×C7—21no—
233C42×C7—21no—
234C22⋊Dic7—42no—
235(C2×D7)⋊C4—42no—
236(C2×D7)⋊C4—42no—
237(C2×D7)⋊C4—42no—
238(C2×D7)⋊C4—42no—
239(C2×D7)⋊C4—81no—
240(C2×D7)⋊C4—81no—
241C4⋊Dic7—21no—
242C4⋊Dic7—21no—
243C4⋊Dic7—21no—
244C4⋊Dic7—21no—
245C2×C7⋊C8—21no—
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—44no—
257C2×C7⋊C8C2×D412yes—
258C23×D4—71no—
259C23×C8—71no—
260C2×C4⋊Q8C2×D711yescharacteristic, complemented
261C2×C22⋊Q8—21no—
262C2×C4×D4—71no—
263C2×C4×D4—71no—
264C22×C4⋊C4C2×D711yescharacteristic
265C22×C22⋊C4—141no—
266#476—144no—
267C2×#106—71no—
268C2×#106—71no—
269C2×#106—71no—
270C2×#106—71no—
271C2×C4⋊C8—71no—
272C2×C4⋊C8—71no—
273C2×#102—71no—
274C2×#102—71no—
275C2×#102—71no—
276C2×#102—71no—
277C2×#102—71no—
278C2×#102—71no—
279C2×#102—71no—
280C2×#102—71no—
281C2×#102—144no—
282C2×C22⋊C8—71no—
283#398—21no—
284#395—21no—
285#390—71no—
286#390—71no—
287#389C2×D711yescharacteristic, complemented
288#389C2×D711yescharacteristic, complemented
289#386—141no—
290#386—141no—
291#385—21no—
292#384C2×D711yescharacteristic, complemented
293#380—71no—
294#380C2×D711yescharacteristic
295#379—141no—
296C4×C22⋊C4C2×D711yescharacteristic
297#340—71no—
298#340—71no—
299#340—71no—
300#340—71no—
301#336—71no—
302#336—71no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7C22⋊Q812yes—
308C23×C7C2×SD1612yes—
309C23×C7AGL(1,ℤ/8)12yes—
310C23×C7C22×D411yescharacteristic
311C22×D7—22no—
312C22×D7—22no—
313C22×D7—22no—
314C22×D7—22no—
315C22×D7—48no—
316C22×D7—41no—
317C22×D7—41no—
318C22×D7—41no—
319C22×D7—41no—
320C22×D7—41no—
321C22×D7—41no—
322C22×D7—41no—
323C22×D7—41no—
324C22×D7—41no—
325C22×D7—41no—
326C22×D7—48no—
327C22×D7—84no—
328C22×D7—84no—
329C22×D7—84no—
330C22×D7—84no—
331C22×D7—84no—
332C7×Q8—84no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—21no—
344C2×C4×C7—22no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
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—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—84no—
362C2×C4×C7C22⋊Q812yes—
363C2×C4×C7C2×SD1612yes—
364C2×C4×C7C2×SD1612yes—
365C2×C4×C7C22×D411yescharacteristic
366C2×C4×C7C22×Q811yescharacteristic
367C2×C4×C7C2×#4111yescharacteristic
368C2×C4×C7C2×#4111yescharacteristic
369C2×C4×C7H(5,𝔽2)11yescharacteristic
370C2×C4×C7H(5,𝔽2)11yescharacteristic
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377D28—22no—
378D28—22no—
379D28—22no—
380D28—22no—
381D28—22no—
382D28—48no—
383D28—41no—
384D28—41no—
385D28C22⋊Q814yescomplemented
386C4×D7—84no—
387C4×D7—84no—
388C7⋊C8—22no—
389C7⋊C8—41no—
390C7⋊C8—41no—
391C7⋊C8—41no—
392C25—141no—
393C22×Q8—21no—
394C22×D4—74no—
395C22×D4—71no—
396C22×D4—71no—
397C22×D4—142no—
398C22×D4—142no—
399C22×D4—142no—
400C22×D4—141no—
401C22×D4—281no—
402C22×D4—281no—
403C23×C4—21no—
404C23×C4—141no—
405C23×C4—141no—
406C23×C4C22×D711yescharacteristic
407C22×C8—71no—
408C22×C8—71no—
409C22×C8—71no—
410C22×C8—71no—
411C22×C8—142no—
412C22×C8—142no—
413C22×C8—281no—
414C4⋊Q8—22no—
415C4⋊Q8—41no—
416C22⋊Q8—44no—
417C4×D4—142no—
418C4×D4—142no—
419C4×D4—281no—
420C4×D4—281no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—71no—
430C2×C4⋊C4—71no—
431C2×C4⋊C4C22×D711yescharacteristic
432C2×C4⋊C4C22×D711yescharacteristic
433C2×C4⋊C4C22×D711yescharacteristic
434C2×C4⋊C4C22×D711yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—141no—
437C2×C22⋊C4—141no—
438C2×C22⋊C4—141no—
439C2×C22⋊C4—141no—
440C2×C22⋊C4—141no—
441C2×C22⋊C4—141no—
442C2×C22⋊C4—141no—
443C2×C22⋊C4—284no—
444C2×C22⋊C4C22⋊D711yescharacteristic
445C2×C22⋊C4C22⋊D711yescharacteristic
446C2×C42C22×D711yescharacteristic
447C2×C42C22×D711yescharacteristic
448#106—142no—
449#106—142no—
450#106—281no—
451#106—281no—
452C4⋊C8—142no—
453C4⋊C8—281no—
454#102—74no—
455#102—142no—
456#102—142no—
457#102—142no—
458#102—142no—
459#102—142no—
460#102—281no—
461#102—281no—
462C22⋊C8—142no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—141no—
467#95C22⋊D711yescharacteristic
468#95C22⋊D711yescharacteristic
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7#47614yescomplemented
476C22×C7C2×C22⋊Q811yescharacteristic
477C22×C7D4211yescharacteristic
478C22×C7#54611yescharacteristic
479C22×C7C22×SD1611yescharacteristic
480C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
481C22×C7#57611yescharacteristic
482C22×C7#57711yescharacteristic
483C2×D7—24no—
484C2×D7—42no—
485C2×D7—42no—
486C2×D7—42no—
487C2×D7—42no—
488C2×D7—42no—
489C2×D7—42no—
490C2×D7—42no—
491C2×D7—42no—
492C2×D7—42no—
493C2×D7—816no—
494C2×D7—81no—
495C2×D7—81no—
496C2×D7—81no—
497C2×D7—81no—
498C4×C7—22no—
499C4×C7—22no—
500C4×C7—22no—
501C4×C7—41no—
502C4×C7—42no—
503C4×C7—41no—
504C4×C7—81no—
505C4×C7—81no—
506C4×C7—81no—
507C4×C7C2×C22⋊Q811yescharacteristic
508C4×C7#54311yescharacteristic
509C4×C7#54611yescharacteristic
510C4×C7#55111yescharacteristic
511Dic7—81no—
512Dic7—81no—
513C24—141no—
514C24—141no—
515C24—144no—
516C24—282no—
517C24—282no—
518C24—282no—
519C24—282no—
520C24—561no—
521C24—561no—
522C24C2×C22⋊D711yescharacteristic
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—81no—
526C2×D4—72no—
527C2×D4—72no—
528C2×D4—72no—
529C2×D4—72no—
530C2×D4—148no—
531C2×D4—144no—
532C2×D4—141no—
533C2×D4—141no—
534C2×D4—141no—
535C2×D4—141no—
536C2×D4—141no—
537C2×D4—141no—
538C2×D4—141no—
539C2×D4—141no—
540C2×D4—284no—
541C2×D4—284no—
542C2×D4—284no—
543C2×D4—282no—
544C2×D4—282no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—141no—
557C22×C4—141no—
558C22×C4—282no—
559C22×C4—282no—
560C22×C4—282no—
561C22×C4—282no—
562C22×C4—561no—
563C22×C4—561no—
564C22×C4Q8×D712yes—
565C22×C4#116112yes—
566C22×C4C2×C22⋊D711yescharacteristic
567C22×C4C2×C22⋊D711yescharacteristic
568C22×C4C2×C22⋊D711yescharacteristic
569C22×C4C2×C22⋊D711yescharacteristic
570C22×C4C2×C22⋊D711yescharacteristic
571C22×C4C23×D711yescharacteristic
572C2×C8—72no—
573C2×C8—141no—
574C2×C8—141no—
575C2×C8—141no—
576C2×C8—141no—
577C2×C8—141no—
578C2×C8—141no—
579C2×C8—141no—
580C2×C8—141no—
581C2×C8—141no—
582C2×C8—141no—
583C2×C8—141no—
584C2×C8—284no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—81no—
598C4⋊C4—141no—
599C4⋊C4—141no—
600C4⋊C4—141no—
601C4⋊C4—141no—
602C4⋊C4D4×D712yes—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—282no—
606C22⋊C4—282no—
607C22⋊C4—282no—
608C22⋊C4—282no—
609C22⋊C4—282no—
610C22⋊C4—561no—
611C22⋊C4—561no—
612C22⋊C4#114314yes—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C2×C7—24no—
618C2×C7#243711yescharacteristic
619C2×C7C2×#47611yescharacteristic
620C2×C7#308111yescharacteristic
621C2×C7#326411yescharacteristic
622C2×C7D4×SD1611yescharacteristic
623C2×C7#329511yescharacteristic
624C2×C7#330611yescharacteristic
625D7—44no—
626D7—82no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—142no—
632C23—142no—
633C23—142no—
634C23—142no—
635C23—288no—
636C23—281no—
637C23—281no—
638C23—281no—
639C23—281no—
640C23—288no—
641C23—281no—
642C23—281no—
643C23—281no—
644C23—281no—
645C23—281no—
646C23—281no—
647C23—564no—
648C23—564no—
649C23—564no—
650C23—564no—
651C23—564no—
652C23#649512yes—
653C23C2×#114312yes—
654C23#650912yes—
655C23C22×C22⋊D711yescharacteristic
656Q8—84no—
657D4—74no—
658D4—142no—
659D4—142no—
660D4—142no—
661D4—142no—
662D4—142no—
663D4—288no—
664D4—281no—
665D4—281no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—84no—
695C2×C4—281no—
696C2×C4—281no—
697C2×C4—281no—
698C2×C4—281no—
699C2×C4—281no—
700C2×C4—281no—
701C2×C4—564no—
702C2×C4—564no—
703C2×C4C2×#114312yes—
704C2×C4C2×#114312yes—
705C2×C4#650912yes—
706C2×C4C2×D4×D711yescharacteristic
707C2×C4#654811yescharacteristic
708C2×C4C2×Q8×D711yescharacteristic
709C2×C4C2×#116111yescharacteristic
710C2×C4D7×#4111yescharacteristic
711C2×C4#655311yescharacteristic
712C8—142no—
713C8—281no—
714C8—281no—
715C8—281no—
716C7#2595811yescharacteristic, complemented, Sylow
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—144no—
724C22—282no—
725C22—282no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—282no—
730C22—282no—
731C22—282no—
732C22—282no—
733C22—5616no—
734C22—561no—
735C22—561no—
736C22—561no—
737C22—561no—
738C22#8985614yescomplemented
739C22C2×#649511yescharacteristic
740C22D4×C22⋊D711yescharacteristic
741C22C22×#114311yescharacteristic
742C22C2×#650911yescharacteristic
743C22#9052011yescharacteristic
744C22#9052611yescharacteristic
745C22#9052811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—561no—
756C4—561no—
757C4D7×C22⋊Q811yescharacteristic
758C4#9032111yescharacteristic
759C4#9032511yescharacteristic
760C4#9032811yescharacteristic
761C2—24no—
762C2—284no—
763C2—562no—
764C2#1174026111yescharacteristic
765C2C2×#8985611yescharacteristic
766C2#1174091911yescharacteristic
767C2#1174093311yescharacteristic
768C2#1174097111yescharacteristic
769C2D4×#114311yescharacteristic
770C2#1174107911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2440C2
socleC23×C7C22×D4
prime radicalC23×D28C22
hypercenter#2440D7
hypocenterC7#25958
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C7×#2440C2semidirect
2. C2×#89856C2semidirect
5. #11729546C2semidirect
6. #11729310C2semidirect
7. #11727383C2semidirect
8. #11727383C2semidirect
9. #11727380C2semidirect
10. #11727380C2semidirect
11. #11727341C2semidirect
12. #11727338C2semidirect
14. #11727265C2semidirect
15. #11727203C2semidirect
17. C2×C7×C4⋊Q8C22semidirect
26. C7×#389C22semidirect
27. C7×#389C22semidirect
29. C7×#384C22semidirect
44. C2×#6382C22semidirect
45. C2×#6382C22semidirect
46. C2×#6382C22semidirect
47. C2×#6382C22semidirect
51. C2×C4⋊(C7⋊C8)C22semidirect
52. C2×C4⋊(C7⋊C8)C22semidirect
55. #89324C22semidirect
56. #89324C22semidirect
57. #89324C22semidirect
58. #89324C22semidirect
59. #89319C22semidirect
60. #89319C22semidirect
72. C22×D28Q8semidirect
141. #2440D7semidirect
260. C2×C4⋊Q8C2×D7semidirect
287. #389C2×D7semidirect
288. #389C2×D7semidirect
292. #384C2×D7semidirect
385. D28C22⋊Q8semidirect
475. C22×C7#476semidirect
716. C7#25958semidirect
738. C22#89856semidirect

Maximal subgroups

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

subgroupindex
C7×#24402
C2×#898562
C22×#63832
C22⋊C4×D282
#117295462
#117293102
#117273832
#117273802
#117273412
#117273382
#117272752
#117272652
#117272032
#259587