Finite Group Databasebeta

← #13410883

Subgroups — #13410883

Order 1792.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D4×C22⋊C4C211yesmaximal, characteristic
2C22×#6406C211yesmaximal, characteristic
3C2×#89781C211yesmaximal, characteristic, complemented
4#11730940C211yesmaximal, characteristic, complemented
5#11729882C211yesmaximal, characteristic
6#11729361C211yesmaximal, characteristic, complemented
7#11729360C211yesmaximal, characteristic, complemented
8#11729359C211yesmaximal, characteristic, complemented
9#11727408C211yesmaximal, characteristic, complemented
10#11727407C211yesmaximal, characteristic, complemented
11#11727406C211yesmaximal, characteristic, complemented
12#11727393C211yesmaximal, characteristic, complemented
13#11727266C211yesmaximal, characteristic, complemented
14#11727259C211yesmaximal, characteristic, complemented
15#11727203C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×C7×C22⋊C4—21no—
20C22×C4⋊Dic7C2211yescharacteristic
21C23×C7⋊C8C2211yescharacteristic
22C2×#6433C2211yescharacteristic, complemented
23C7×#390C2211yescharacteristic
24C7×#390C2211yescharacteristic
25C7×#386—21no—
26C7×#386—21no—
27C7×#380C2211yescharacteristic
28C7×#379—21no—
29C4×C7×C22⋊C4C2211yescharacteristic
30C2×#6406—24no—
31C2×#6406C2211yescharacteristic
32C2×#6406C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36C2×#6406C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39#89984C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41#89781—24no—
42C2×#6382C2211yescharacteristic, complemented
43C2×#6382C2211yescharacteristic, complemented
44C2×#6381C2211yescharacteristic, complemented
45C2×#6381C2211yescharacteristic, complemented
46#89718—21no—
47#89714—21no—
48#89708C2211yescharacteristic, complemented
49#89700C2211yescharacteristic, complemented
50#89700C2211yescharacteristic, complemented
51C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
52C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
53#89432—21no—
54#89429—21no—
55#89324C2211yescharacteristic, complemented
56#89324C2211yescharacteristic, complemented
57#89324C2211yescharacteristic, complemented
58#89324C2211yescharacteristic, complemented
59#89319C2211yescharacteristic, complemented
60#89319C2211yescharacteristic, complemented
61#25952—71nomaximal, Sylow
62C25×C7—21no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—21no—
66C22×C7×D4—22no—
67C22×C7×D4—41no—
68C22×C7×D4—41no—
69C22×C7×D4Q814yes—
70C22×C7×D4C2311yescharacteristic
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7—21no—
74C23×C4×C7C2311yescharacteristic
75C23×Dic7—21no—
76C4×C7×D4—22no—
77C4×C7×D4—22no—
78C4×C7×D4—41no—
79C4×C7×D4—41no—
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—44no—
90C2×C7×C22⋊C4D411yescharacteristic
91C2×C7×C22⋊C4D411yescharacteristic
92C2×C42×C7C2311yescharacteristic
93C2×C42×C7C2311yescharacteristic
94C2×C22⋊Dic7—21no—
95C2×C4⋊Dic7—22no—
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7—41no—
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2311yescharacteristic
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102C2×Dic7⋊C4—21no—
103C2×Dic7⋊C4—21no—
104C2×Dic7⋊C4—21no—
105C2×Dic7⋊C4—21no—
106C22×C7⋊C8—22no—
107C22×C7⋊C8—22no—
108C22×C7⋊C8—41no—
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113#6433—22no—
114#6433—41no—
115C7×#95—21no—
116C7×#95D411yescharacteristic
117C7×#95D411yescharacteristic
118#6406—22no—
119#6406—22no—
120#6406—22no—
121#6406—22no—
122#6406—22no—
123#6406—41no—
124#6406—41no—
125#6406D414yes—
126C7⋊#95—21no—
127C7⋊#95—21no—
128C7⋊#95—21no—
129C7⋊#95—21no—
130C7⋊#95—21no—
131C22⋊(C7⋊C8)—22no—
132#6382—22no—
133#6382—41no—
134#6381—22no—
135#6381—41no—
136C4⋊(C7⋊C8)—22no—
137C4⋊(C7⋊C8)—41no—
138C2×#478—71no—
139C22×#102—71no—
140#2442—71no—
141D4×C22⋊C4D711yescharacteristic
142#2092—71no—
143#2067—71no—
144#2065—71no—
145#2025—71no—
146#1864—71no—
147#1862—71no—
148#1853—71no—
149#1850—71no—
150#1808—71no—
151#1804—71no—
152#1786—71no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—24no—
156C24×C7—42no—
157C24×C7—42no—
158C24×C7—42no—
159C24×C7—42no—
160C24×C7—81no—
161C24×C7—81no—
162C24×C7C2×D411yescharacteristic
163C2×C7×D4—28no—
164C2×C7×D4—24no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—21no—
173C2×C7×D4—44no—
174C2×C7×D4—44no—
175C2×C7×D4—44no—
176C2×C7×D4—42no—
177C2×C7×D4—42no—
178C2×C7×D4C2×D412yes—
179C2×C7×D4C2×Q812yes—
180C2×C7×D4C2×Q812yes—
181C2×C7×D4#4112yes—
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—42no—
189C22×C4×C7—42no—
190C22×C4×C7—42no—
191C22×C4×C7—42no—
192C22×C4×C7—81no—
193C22×C4×C7—81no—
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×Q812yes—
200C22×C4×C7#4112yes—
201C22×C4×C7C2411yescharacteristic
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—42no—
207C22×Dic7—42no—
208C22×Dic7—81no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4—21no—
211C7×C4⋊C4—21no—
212C7×C4⋊C4—21no—
213C7×C22⋊C4—22no—
214C7×C22⋊C4—22no—
215C7×C22⋊C4—42no—
216C7×C22⋊C4—42no—
217C7×C22⋊C4—42no—
218C7×C22⋊C4—42no—
219C7×C22⋊C4—42no—
220C7×C22⋊C4—81no—
221C7×C22⋊C4—81no—
222C42×C7—21no—
223C42×C7—21no—
224C42×C7—21no—
225C42×C7—21no—
226C22⋊Dic7—42no—
227C4⋊Dic7—21no—
228C4⋊Dic7—21no—
229C4⋊Dic7—21no—
230C4⋊Dic7—21no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—42no—
235C4⋊Dic7C2×D412yes—
236Dic7⋊C4—42no—
237Dic7⋊C4—42no—
238Dic7⋊C4—81no—
239Dic7⋊C4—81no—
240C2×C7⋊C8—21no—
241C2×C7⋊C8—21no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—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—44no—
252C2×C7⋊C8C2×D412yes—
253C23×D4C2×D711yescharacteristic
254C23×C8—71no—
255C2×#125—71no—
256C2×C4×D4C2×D711yescharacteristic
257C2×C4×D4C2×D711yescharacteristic
258C22×C4⋊C4—71no—
259C22×C22⋊C4—21no—
260#478—144no—
261C2×#107—71no—
262C2×#107—71no—
263C2×#106—71no—
264C2×#106—71no—
265C2×C4⋊C8—71no—
266C2×C4⋊C8—71no—
267C2×#102—71no—
268C2×#102—71no—
269C2×#102—71no—
270C2×#102—71no—
271C2×#102—71no—
272C2×#102—71no—
273C2×#102—71no—
274C2×#102—71no—
275C2×#102—144no—
276C2×C22⋊C8—71no—
277#400—141no—
278#398—141no—
279#390C2×D711yescharacteristic
280#390C2×D711yescharacteristic
281#389—71no—
282#389—71no—
283#386—21no—
284#386—21no—
285#385—141no—
286#382—71no—
287#380—71no—
288#380—141no—
289#380C2×D711yescharacteristic
290#379—21no—
291C4×C22⋊C4C2×D711yescharacteristic
292#340—71no—
293#340—71no—
294#340—71no—
295#340—71no—
296#336—71no—
297#336—71no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—22no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—48no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—48no—
318C23×C7—84no—
319C23×C7—84no—
320C23×C7—84no—
321C23×C7—84no—
322C23×C7—84no—
323C23×C7C22⋊Q812yes—
324C23×C7#13512yes—
325C23×C7AGL(1,ℤ/8)12yes—
326C23×C7C22×D411yescharacteristic
327C7×D4—22no—
328C7×D4—22no—
329C7×D4—22no—
330C7×D4—22no—
331C7×D4—22no—
332C7×D4—48no—
333C7×D4—41no—
334C7×D4—41no—
335C7×D4C22⋊Q814yes—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—21no—
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—84no—
361C2×C4×C7—84no—
362C2×C4×C7C22⋊Q812yes—
363C2×C4×C7C22×D411yescharacteristic
364C2×C4×C7C22×Q811yescharacteristic
365C2×C4×C7C2×#4111yescharacteristic
366C2×C4×C7C2×#4111yescharacteristic
367C2×C4×C7H(5,𝔽2)11yescharacteristic
368C2×C4×C7H(5,𝔽2)11yescharacteristic
369C2×Dic7—22no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—84no—
382C7⋊C8—22no—
383C7⋊C8—41no—
384C7⋊C8—41no—
385C7⋊C8—41no—
386C25—21no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—22no—
390C22×D4—21no—
391C22×D4—41no—
392C22×D4—41no—
393C22×D4Dic1414yes—
394C22×D4C22×D711yescharacteristic
395C22×D4C22×D711yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—141no—
399C23×C4C22×D711yescharacteristic
400C22×C8—71no—
401C22×C8—71no—
402C22×C8—71no—
403C22×C8—71no—
404C22×C8—142no—
405C22×C8—142no—
406C22×C8—281no—
407#125—142no—
408#125—281no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—41no—
412C4×D4—41no—
413C2×C4⋊C4—71no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—142no—
418C2×C4⋊C4—141no—
419C2×C4⋊C4—141no—
420C2×C4⋊C4—141no—
421C2×C4⋊C4—141no—
422C2×C4⋊C4—141no—
423C2×C4⋊C4—281no—
424C2×C4⋊C4C22×D711yescharacteristic
425C2×C4⋊C4C22×D711yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—141no—
435C2×C22⋊C4C22⋊D711yescharacteristic
436C2×C22⋊C4C22⋊D711yescharacteristic
437C2×C42C22×D711yescharacteristic
438C2×C42C22×D711yescharacteristic
439#107—142no—
440#107—281no—
441#106—142no—
442#106—281no—
443C4⋊C8—142no—
444C4⋊C8—281no—
445#102—74no—
446#102—142no—
447#102—142no—
448#102—142no—
449#102—142no—
450#102—142no—
451#102—281no—
452#102—281no—
453C22⋊C8—142no—
454#95—21no—
455#95—141no—
456#95—141no—
457#95—141no—
458#95—141no—
459#95—141no—
460#95C22⋊D711yescharacteristic
461#95C22⋊D711yescharacteristic
462C22×C7—22no—
463C22×C7—22no—
464C22×C7—22no—
465C22×C7—22no—
466C22×C7—22no—
467C22×C7—22no—
468C22×C7—24no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7—42no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—816no—
479C22×C7—81no—
480C22×C7—81no—
481C22×C7—81no—
482C22×C7—81no—
483C22×C7#47814yescomplemented
484C22×C7C2×C22⋊Q811yescharacteristic
485C22×C7D4211yescharacteristic
486C22×C7#54611yescharacteristic
487C22×C7C2×#13511yescharacteristic
488C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
489C22×C7#57611yescharacteristic
490C22×C7#57711yescharacteristic
491C4×C7—22no—
492C4×C7—41no—
493C4×C7—41no—
494C4×C7—41no—
495C4×C7—41no—
496C4×C7—81no—
497C4×C7—81no—
498C4×C7C2×C22⋊Q811yescharacteristic
499C4×C7#54311yescharacteristic
500C4×C7#54611yescharacteristic
501C4×C7#55111yescharacteristic
502Dic7—42no—
503Dic7—81no—
504Dic7—81no—
505Dic7—81no—
506C24—21no—
507C24—21no—
508C24—24no—
509C24—42no—
510C24—42no—
511C24—42no—
512C24—42no—
513C24—81no—
514C24—81no—
515C24C2×C22⋊D711yescharacteristic
516C2×D4—28no—
517C2×D4—24no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4C2×Dic1412yes—
532C2×D4C2×Dic1412yes—
533C2×D4D4×D712yes—
534C2×D4#115912yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—141no—
550C22×C4—141no—
551C22×C4—282no—
552C22×C4—282no—
553C22×C4—561no—
554C22×C4C2×Dic1412yes—
555C22×C4#115712yes—
556C22×C4C2×C22⋊D711yescharacteristic
557C22×C4C2×C22⋊D711yescharacteristic
558C22×C4C2×C22⋊D711yescharacteristic
559C22×C4C2×C22⋊D711yescharacteristic
560C22×C4C2×C22⋊D711yescharacteristic
561C22×C4C23×D711yescharacteristic
562C2×C8—72no—
563C2×C8—141no—
564C2×C8—141no—
565C2×C8—141no—
566C2×C8—141no—
567C2×C8—141no—
568C2×C8—141no—
569C2×C8—141no—
570C2×C8—141no—
571C2×C8—141no—
572C2×C8—141no—
573C2×C8—141no—
574C2×C8—284no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—72no—
580C4⋊C4—141no—
581C4⋊C4—141no—
582C4⋊C4—141no—
583C4⋊C4—141no—
584C4⋊C4—141no—
585C4⋊C4—141no—
586C4⋊C4—141no—
587C4⋊C4—282no—
588C4⋊C4—282no—
589C4⋊C4—282no—
590C4⋊C4—561no—
591C4⋊C4—561no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C22⋊C4—282no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C2×C7—24no—
607C2×C7—44no—
608C2×C7—82no—
609C2×C7#243711yescharacteristic
610C2×C7C2×#47811yescharacteristic
611C2×C7#308111yescharacteristic
612C2×C7#326511yescharacteristic
613C2×C7#328011yescharacteristic
614C2×C7#329611yescharacteristic
615C2×C7#331811yescharacteristic
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—48no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—48no—
636C23—84no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23#648712yes—
642C23#649512yes—
643C23#651312yes—
644C23C22×C22⋊D711yescharacteristic
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—48no—
651D4—41no—
652D4—41no—
653D4#644114yes—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4—142no—
681C2×C4—281no—
682C2×C4—281no—
683C2×C4—281no—
684C2×C4—281no—
685C2×C4—281no—
686C2×C4—281no—
687C2×C4—281no—
688C2×C4—281no—
689C2×C4—281no—
690C2×C4—281no—
691C2×C4—281no—
692C2×C4—564no—
693C2×C4#648712yes—
694C2×C4C22×Dic1411yescharacteristic
695C2×C4C2×#115711yescharacteristic
696C2×C4C2×D4×D711yescharacteristic
697C2×C4C2×#115911yescharacteristic
698C2×C4#654811yescharacteristic
699C2×C4#654811yescharacteristic
700C8—142no—
701C8—281no—
702C8—281no—
703C8—281no—
704C7#2595211yescharacteristic, complemented, Sylow
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—24no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—816no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22#8978114yescomplemented
727C22C2×#648711yescharacteristic
728C22C2×#649511yescharacteristic
729C22D4×C22⋊D711yescharacteristic
730C22#9049711yescharacteristic
731C22C2×#651311yescharacteristic
732C22#9052611yescharacteristic
733C22#9052711yescharacteristic
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—81no—
740C4—81no—
741C4—282no—
742C4—561no—
743C4—561no—
744C4—561no—
745C4C2×#644111yescharacteristic
746C4#9017411yescharacteristic
747C4#9018111yescharacteristic
748C4#9018611yescharacteristic
749C2—24no—
750C2—44no—
751C2—82no—
752C2#1173955511yescharacteristic
753C2C2×#8978111yescharacteristic
754C2#1173998411yescharacteristic
755C2#1174093011yescharacteristic
756C2#1174093611yescharacteristic
757C2#1174093911yescharacteristic
758C2#1174095011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×D4×C22⋊C4C2
socleC23×C7C22×D4
prime radicalC23×C7×D4C22
hypercenterD4×C22⋊C4D7
hypocenterC7#25952
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#89781C2semidirect
4. #11730940C2semidirect
6. #11729361C2semidirect
7. #11729360C2semidirect
8. #11729359C2semidirect
9. #11727408C2semidirect
10. #11727407C2semidirect
11. #11727406C2semidirect
12. #11727393C2semidirect
13. #11727266C2semidirect
14. #11727259C2semidirect
15. #11727203C2semidirect
22. C2×#6433C22semidirect
42. C2×#6382C22semidirect
43. C2×#6382C22semidirect
44. C2×#6381C22semidirect
45. C2×#6381C22semidirect
48. #89708C22semidirect
49. #89700C22semidirect
50. #89700C22semidirect
51. C2×C4⋊(C7⋊C8)C22semidirect
52. C2×C4⋊(C7⋊C8)C22semidirect
55. #89324C22semidirect
56. #89324C22semidirect
57. #89324C22semidirect
58. #89324C22semidirect
59. #89319C22semidirect
60. #89319C22semidirect
483. C22×C7#478semidirect
704. C7#25952semidirect
726. C22#89781semidirect

Maximal subgroups

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

subgroupindex
C7×D4×C22⋊C42
C22×#64062
C2×#897812
#117309402
#117298822
#117293612
#117293602
#117293592
#117274082
#117274072
#117274062
#117273932
#117272662
#117272592
#117272032
#259527