Finite Group Databasebeta

← #13370823

Subgroups — #13370823

Order 1792.

1010 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11741531C211yesmaximal, characteristic
2C2×#90006C211yesmaximal, characteristic
3C2×#89492C211yesmaximal, characteristic, complemented
4C7×#1780C211yesmaximal, characteristic
5#11727705C211yesmaximal, characteristic, complemented
6#11727704C211yesmaximal, characteristic, complemented
7#11727703C211yesmaximal, characteristic, complemented
8#11727701C211yesmaximal, characteristic, complemented
9#11727669C211yesmaximal, characteristic, complemented
10#11727667C211yesmaximal, characteristic, complemented
11#11727666C211yesmaximal, characteristic, complemented
12#11727666C211yesmaximal, characteristic, complemented
13#11727665C211yesmaximal, characteristic, complemented
14#11727662C211yesmaximal, characteristic, complemented
15Dic7×C22⋊C8C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C2×#6489C2211yescharacteristic
18C22×C4×Dic7C2211yescharacteristic
19C22×#1136C2211yescharacteristic
20C23×C7⋊C8C2211yescharacteristic
21C2×C7×C22⋊C8C2211yescharacteristic
22C2×C7×C22⋊C8C2211yescharacteristic
23C2×C7×C22⋊C8C2211yescharacteristic
24C2×C7×C22⋊C8C2211yescharacteristic
25C2×C7×C22⋊C8C2211yescharacteristic
26C2×C7×C22⋊C8C2211yescharacteristic
27#90006—24no—
28#90002C411yescharacteristic
29#90002C411yescharacteristic
30#89993C411yescharacteristic
31#89993C411yescharacteristic
32#89992C411yescharacteristic
33#89992C411yescharacteristic
34#89992C411yescharacteristic
35#89992C411yescharacteristic
36C4×C22⋊Dic7C2211yescharacteristic
37C4×C22⋊Dic7C2211yescharacteristic
38C4×C22⋊Dic7C2211yescharacteristic
39C4×C22⋊Dic7C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43C2×C22⋊(C7⋊C8)C2211yescharacteristic
44C2×#6389C2211yescharacteristic
45C2×Dic7⋊C8C2211yescharacteristic
46C2×Dic7⋊C8C2211yescharacteristic
47C2×Dic7⋊C8C2211yescharacteristic
48C2×Dic7⋊C8C2211yescharacteristic
49C2×C8×Dic7C2211yescharacteristic
50C2×C8×Dic7C2211yescharacteristic
51C2×C8×Dic7C2211yescharacteristic
52#89492—24no—
53#89345C2211yescharacteristic
54#89345C2211yescharacteristic
55#89345C2211yescharacteristic
56#89345C2211yescharacteristic
57#89345C2211yescharacteristic
58#89345C2211yescharacteristic
59#89345C2211yescharacteristic
60#89345C2211yescharacteristic
61#22560—71nomaximal, Sylow
62C2×C7×#41—22no—
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—41no—
67C2×C7×#41—41no—
68C22×C7×Q8C2×C411yescharacteristic
69C22×C7×D4C2×C411yescharacteristic
70C22×C7×D4C2×C411yescharacteristic
71C22×C7×D4C2×C411yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×Dic7C2×C411yescharacteristic
76C23×Dic7C2×C411yescharacteristic
77C22×C7×C8C2311yescharacteristic
78C22×C7×C8C2311yescharacteristic
79C22×C7×C8C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C2×C22⋊Dic7C2×C411yescharacteristic
82C2×C22⋊Dic7C2×C411yescharacteristic
83C2×C22⋊Dic7C2×C411yescharacteristic
84C2×C22⋊Dic7C2×C411yescharacteristic
85C2×C22⋊Dic7C2×C411yescharacteristic
86C2×C22⋊Dic7C2×C411yescharacteristic
87C2×C22⋊Dic7C2×C411yescharacteristic
88C2×C22⋊Dic7C2×C411yescharacteristic
89C2×C22⋊Dic7C2×C411yescharacteristic
90C2×C22⋊Dic7C2×C411yescharacteristic
91#6489—22no—
92#6489—22no—
93C2×C4⋊Dic7C2×C411yescharacteristic
94C2×C4⋊Dic7C2×C411yescharacteristic
95C2×C4×Dic7—41no—
96C2×C4×Dic7—41no—
97C2×C4×Dic7C2×C411yescharacteristic
98C2×C4×Dic7C2×C411yescharacteristic
99C2×C4×Dic7C2311yescharacteristic
100C2×C4×Dic7C2311yescharacteristic
101C2×C4×Dic7C2311yescharacteristic
102C2×C4×Dic7C2311yescharacteristic
103C2×#1136—22no—
104C2×#1136—22no—
105C2×#1136—41no—
106C22×C7⋊C8—22no—
107C22×C7⋊C8—22no—
108C22×C7⋊C8—41no—
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113C7×C22⋊C8—22no—
114C7×C22⋊C8—22no—
115C7×C22⋊C8—22no—
116C7×C22⋊C8—22no—
117C7×C22⋊C8—41no—
118C7×C22⋊C8—41no—
119C7⋊#95C2×C411yescharacteristic
120C7⋊#95C2×C411yescharacteristic
121C7⋊#95C2×C411yescharacteristic
122C7⋊#95C2×C411yescharacteristic
123C7⋊#95C2×C411yescharacteristic
124C7⋊#95C2×C411yescharacteristic
125C7⋊#95C2×C411yescharacteristic
126C7⋊#95C2×C411yescharacteristic
127C22⋊(C7⋊C8)—22no—
128C22⋊(C7⋊C8)—22no—
129C22⋊(C7⋊C8)—22no—
130C22⋊(C7⋊C8)D414yes—
131#6389—22no—
132Dic7⋊C8—22no—
133Dic7⋊C8—22no—
134Dic7⋊C8—41no—
135Dic7⋊C8—41no—
136C8×Dic7—22no—
137C8×Dic7—41no—
138C8×Dic7—41no—
139C2×#433—71no—
140C2×#408—71no—
141#2297—71no—
142#1924—71no—
143#1923—71no—
144#1923—71no—
145#1923—71no—
146#1851—71no—
147#1850—71no—
148#1818—71no—
149#1797—71no—
150#1780D711yescharacteristic
151#1753—71no—
152C8×C22⋊C4—71no—
153C4×C22⋊C8—71no—
154C24×C7C22×C411yescharacteristic
155C24×C7C22×C411yescharacteristic
156C24×C7C22×C411yescharacteristic
157C7×#41—44no—
158C7×#41—44no—
159C7×#41—44no—
160C7×#41—44no—
161C2×C7×Q8—22no—
162C2×C7×Q8—22no—
163C2×C7×Q8—41no—
164C2×C7×D4—22no—
165C2×C7×D4—22no—
166C2×C7×D4—22no—
167C2×C7×D4—22no—
168C2×C7×D4—22no—
169C2×C7×D4—22no—
170C2×C7×D4—41no—
171C2×C7×D4—41no—
172C2×C7×D4—41no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
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×C7C22×C411yescharacteristic
188C22×C4×C7C22×C411yescharacteristic
189C22×C4×C7C22×C411yescharacteristic
190C22×C4×C7C2×D412yes—
191C22×C4×C7#4112yes—
192C22×C4×C7#4112yes—
193C22×C4×C7#4112yes—
194C22×C4×C7C2411yescharacteristic
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
198C22×Dic7—41no—
199C22×Dic7—41no—
200C22×Dic7—41no—
201C22×Dic7C22×C411yescharacteristic
202C22×Dic7C22×C411yescharacteristic
203C22×Dic7C22×C411yescharacteristic
204C22×Dic7C22×C411yescharacteristic
205C22×Dic7C22×C411yescharacteristic
206C22×Dic7C22×C411yescharacteristic
207C22×Dic7C22×C411yescharacteristic
208C22×Dic7C22×C411yescharacteristic
209C2×C7×C8—21no—
210C2×C7×C8—21no—
211C2×C7×C8—21no—
212C2×C7×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C22⋊Dic7—22no—
222C22⋊Dic7—22no—
223C22⋊Dic7—22no—
224C22⋊Dic7—22no—
225C22⋊Dic7—22no—
226C22⋊Dic7—22no—
227C22⋊Dic7—22no—
228C22⋊Dic7—22no—
229C22⋊Dic7—41no—
230C22⋊Dic7—41no—
231C4⋊Dic7—22no—
232C4⋊Dic7—22no—
233C4×Dic7—21no—
234C4×Dic7—21no—
235C4×Dic7—21no—
236C4×Dic7—21no—
237C4×Dic7—21no—
238C4×Dic7—21no—
239C4×Dic7—21no—
240C4×Dic7—21no—
241C4×Dic7—41no—
242C4×Dic7—41no—
243#1136—44no—
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—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—44no—
255C2×C7⋊C8C2×D412yes—
256C2×C7⋊C8C2×D412yes—
257C22×#41C2×D711yescharacteristic
258C22×M16—71no—
259C23×C8—71no—
260C2×#117—71no—
261C22×C42—71no—
262#433—144no—
263C2×C4⋊C8—71no—
264C2×C4⋊C8—71no—
265C2×C4⋊C8—71no—
266C2×C4⋊C8—71no—
267#408—144no—
268C2×C22⋊C8—71no—
269C2×C22⋊C8—71no—
270C2×C22⋊C8—71no—
271C2×C22⋊C8—71no—
272C2×C22⋊C8C2×D711yescharacteristic
273C2×C22⋊C8C2×D711yescharacteristic
274C2×C22⋊C8C2×D711yescharacteristic
275C2×C22⋊C8C2×D711yescharacteristic
276C2×C22⋊C8C2×D711yescharacteristic
277C2×C22⋊C8C2×D711yescharacteristic
278C2×#97—71no—
279C2×C4×C8—71no—
280C2×C4×C8—71no—
281C2×C4×C8—71no—
282#391—71no—
283#391—71no—
284#390—71no—
285#390—71no—
286#386—71no—
287#386—71no—
288#386—71no—
289#386—71no—
290C4×C22⋊C4—71no—
291C4×C22⋊C4—71no—
292C4×C22⋊C4—71no—
293C4×C22⋊C4—71no—
294#336—71no—
295#336—71no—
296#336—71no—
297#336—71no—
298#336—71no—
299#336—71no—
300#336—71no—
301#336—71no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
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—21no—
319C23×C7—21no—
320C23×C7—21no—
321C23×C7#11712yes—
322C23×C7C4×D412yes—
323C23×C7C23×C411yescharacteristic
324C7×Q8—44no—
325C7×D4—44no—
326C7×D4—44no—
327C7×D4—44no—
328C2×C4×C7—21no—
329C2×C4×C7—21no—
330C2×C4×C7—21no—
331C2×C4×C7—21no—
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—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7#11712yes—
348C2×C4×C7C4×D412yes—
349C2×C4×C7C22×D411yescharacteristic
350C2×C4×C7C2×#4111yescharacteristic
351C2×C4×C7C2×#4111yescharacteristic
352C2×C4×C7C2×#4111yescharacteristic
353C2×C4×C7H(5,𝔽2)11yescharacteristic
354C2×C4×C7H(5,𝔽2)11yescharacteristic
355C2×Dic7—21no—
356C2×Dic7—21no—
357C2×Dic7—21no—
358C2×Dic7—21no—
359C2×Dic7—21no—
360C2×Dic7—21no—
361C2×Dic7—21no—
362C2×Dic7—21no—
363C2×Dic7—21no—
364C2×Dic7—21no—
365C2×Dic7—21no—
366C2×Dic7—21no—
367C2×Dic7—21no—
368C2×Dic7—21no—
369C2×Dic7—21no—
370C2×Dic7—21no—
371C2×Dic7—21no—
372C2×Dic7—21no—
373C2×Dic7—21no—
374C2×Dic7—21no—
375C2×Dic7—21no—
376C2×Dic7—44no—
377C2×Dic7—44no—
378C2×Dic7#13112yes—
379C2×Dic7#13112yes—
380C2×Dic7#13112yes—
381C7×C8—41no—
382C7×C8—41no—
383C7×C8—41no—
384C7×C8—41no—
385C7⋊C8—22no—
386C7⋊C8—22no—
387C7⋊C8—41no—
388C7⋊C8—41no—
389C2×#41—22no—
390C2×#41—22no—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41—41no—
394C2×#41—41no—
395C22×Q8C4×D711yescharacteristic
396C22×D4C4×D711yescharacteristic
397C22×D4C4×D711yescharacteristic
398C22×D4C4×D711yescharacteristic
399C23×C4—71no—
400C23×C4—71no—
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404C2×M16—142no—
405C2×M16—142no—
406C2×M16—281no—
407C22×C8—71no—
408C22×C8—71no—
409C22×C8—71no—
410C22×C8—71no—
411C22×C8—142no—
412C22×C8—142no—
413C22×C8—281no—
414C22×C8C22×D711yescharacteristic
415C22×C8C22×D711yescharacteristic
416C22×C8C22×D711yescharacteristic
417C22×C8C22×D711yescharacteristic
418#117—142no—
419#117—142no—
420C2×C4⋊C4—71no—
421C2×C4⋊C4—71no—
422C2×C22⋊C4—71no—
423C2×C22⋊C4—71no—
424C2×C22⋊C4—71no—
425C2×C22⋊C4—71no—
426C2×C22⋊C4—71no—
427C2×C22⋊C4—71no—
428C2×C22⋊C4—71no—
429C2×C22⋊C4—71no—
430C2×C22⋊C4—71no—
431C2×C22⋊C4—71no—
432C2×C42—71no—
433C2×C42—71no—
434C2×C42—71no—
435C2×C42—71no—
436C2×C42—71no—
437C2×C42—71no—
438C2×C42—281no—
439C2×C42—281no—
440C4⋊C8—142no—
441C4⋊C8—142no—
442C4⋊C8—281no—
443C4⋊C8—281no—
444C22⋊C8—22no—
445C22⋊C8—22no—
446C22⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—41no—
449C22⋊C8—41no—
450C22⋊C8—74no—
451C22⋊C8—142no—
452C22⋊C8—142no—
453C22⋊C8—142no—
454#97—142no—
455C4×C8—142no—
456C4×C8—281no—
457C4×C8—281no—
458#95—71no—
459#95—71no—
460#95—71no—
461#95—71no—
462#95—71no—
463#95—71no—
464#95—71no—
465#95—71no—
466C22×C7—22no—
467C22×C7—22no—
468C22×C7—22no—
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×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—41no—
487C22×C7C2×#11711yescharacteristic
488C22×C7C2×C4×D411yescharacteristic
489C22×C7#51811yescharacteristic
490C22×C7C2×#13111yescharacteristic
491C22×C7C2×#13111yescharacteristic
492C22×C7C2×#13111yescharacteristic
493C22×C7#56811yescharacteristic
494C4×C7—22no—
495C4×C7—22no—
496C4×C7—41no—
497C4×C7#54611yescharacteristic
498C4×C7#54611yescharacteristic
499C4×C7#55111yescharacteristic
500C4×C7#55111yescharacteristic
501Dic7—22no—
502Dic7—22no—
503Dic7—22no—
504Dic7—41no—
505Dic7—41no—
506Dic7—41no—
507Dic7—41no—
508Dic7—41no—
509C24C2×C4×D711yescharacteristic
510C24C2×C4×D711yescharacteristic
511C24C2×C4×D711yescharacteristic
512#41—44no—
513#41—44no—
514#41—44no—
515#41—44no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—41no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
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—21no—
541C22×C4—21no—
542C22×C4—71no—
543C22×C4—71no—
544C22×C4—71no—
545C22×C4—71no—
546C22×C4—71no—
547C22×C4—71no—
548C22×C4—71no—
549C22×C4—71no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—281no—
554C22×C4—281no—
555C22×C4—281no—
556C22×C4C2×C4×D711yescharacteristic
557C22×C4C2×C4×D711yescharacteristic
558C22×C4C2×C4×D711yescharacteristic
559C22×C4D4×D712yes—
560C22×C4#115912yes—
561C22×C4#115912yes—
562C22×C4#115912yes—
563C22×C4C23×D711yescharacteristic
564M16—284no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—72no—
578C2×C8—72no—
579C2×C8—141no—
580C2×C8—141no—
581C2×C8—141no—
582C2×C8—141no—
583C2×C8—141no—
584C2×C8—141no—
585C2×C8—141no—
586C2×C8—141no—
587C2×C8—141no—
588C2×C8—141no—
589C2×C8—284no—
590C4⋊C4—142no—
591C4⋊C4—142no—
592C22⋊C4—142no—
593C22⋊C4—142no—
594C22⋊C4—142no—
595C22⋊C4—142no—
596C22⋊C4—142no—
597C22⋊C4—142no—
598C22⋊C4—142no—
599C22⋊C4—142no—
600C22⋊C4—281no—
601C22⋊C4—281no—
602C42—141no—
603C42—141no—
604C42—141no—
605C42—141no—
606C42—141no—
607C42—141no—
608C42—141no—
609C42—141no—
610C42—281no—
611C42—281no—
612C2×C7—42no—
613C2×C7—42no—
614C2×C7—81no—
615C2×C7#234211yescharacteristic
616C2×C7#292211yescharacteristic
617C2×C7#292511yescharacteristic
618C2×C7#293111yescharacteristic
619C2×C7#293511yescharacteristic
620C2×C7#297611yescharacteristic
621C2×C7#297711yescharacteristic
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23#644012yes—
642C23(C22⋊D7)⋊C412yes—
643C23C22×C4×D711yescharacteristic
644Q8—44no—
645D4—44no—
646D4—44no—
647D4—44no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—72no—
668C2×C4—72no—
669C2×C4—72no—
670C2×C4—141no—
671C2×C4—141no—
672C2×C4—141no—
673C2×C4—141no—
674C2×C4—141no—
675C2×C4—141no—
676C2×C4—141no—
677C2×C4—141no—
678C2×C4—141no—
679C2×C4—141no—
680C2×C4—141no—
681C2×C4—141no—
682C2×C4—141no—
683C2×C4—141no—
684C2×C4—141no—
685C2×C4—141no—
686C2×C4—141no—
687C2×C4—141no—
688C2×C4—141no—
689C2×C4—141no—
690C2×C4—141no—
691C2×C4—284no—
692C2×C4—284no—
693C2×C4#644012yes—
694C2×C4(C22⋊D7)⋊C412yes—
695C2×C4C2×D4×D711yescharacteristic
696C2×C4C2×#115911yescharacteristic
697C2×C4C2×#115911yescharacteristic
698C2×C4C2×#115911yescharacteristic
699C2×C4#654811yescharacteristic
700C2×C4#654811yescharacteristic
701C8—41no—
702C8—41no—
703C8—41no—
704C8—41no—
705C8—142no—
706C8—142no—
707C8—281no—
708C8—281no—
709C7#2256011yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22C2×#644011yescharacteristic
732C22C2×(C22⋊D7)⋊C411yescharacteristic
733C22#9017711yescharacteristic
734C22D7×#13111yescharacteristic
735C22D7×#13111yescharacteristic
736C22D7×#13111yescharacteristic
737C22#9044111yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—142no—
742C4—142no—
743C4—142no—
744C4—281no—
745C4—281no—
746C4—281no—
747C4—281no—
748C4—281no—
749C4#9027811yescharacteristic
750C4#9027811yescharacteristic
751C4#9028211yescharacteristic
752C4#9028211yescharacteristic
753C2—42no—
754C2—42no—
755C2—81no—
756C2#1173126711yescharacteristic
757C2#1173609311yescharacteristic
758C2#1173609511yescharacteristic
759C2#1173610211yescharacteristic
760C2#1173610511yescharacteristic
761C2#1173610911yescharacteristic
762C2#1173611011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC7×#1780C2
prime radicalC22×C7×#41C22
cosocleC22×C4×C7C24
hypercenter#1780D7
hypocenterC7#22560
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
3. C2×#89492C2semidirect
5. #11727705C2semidirect
6. #11727704C2semidirect
7. #11727703C2semidirect
8. #11727701C2semidirect
9. #11727669C2semidirect
10. #11727667C2semidirect
11. #11727666C2semidirect
12. #11727666C2semidirect
13. #11727665C2semidirect
14. #11727662C2semidirect
15. Dic7×C22⋊C8C2semidirect
709. C7#22560semidirect

Maximal subgroups

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

subgroupindex
#117415312
C2×#900062
C2×#894922
C7×#17802
#117277052
#117277042
#117277032
#117277012
#117276692
#117276672
#117276662
#117276652
#117276622
Dic7×C22⋊C82
#225607