Finite Group Databasebeta

← #13370808

Subgroups — #13370808

Order 1792.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11741472C211yesmaximal, characteristic
2C2×#89979C211yesmaximal, characteristic
3C2×#89492C211yesmaximal, characteristic, complemented
4C7×#1779C211yesmaximal, characteristic
5#11727705C211yesmaximal, characteristic, complemented
6#11727705C211yesmaximal, characteristic, complemented
7#11727703C211yesmaximal, characteristic, complemented
8#11727703C211yesmaximal, characteristic, complemented
9#11727669C211yesmaximal, characteristic, complemented
10#11727668C211yesmaximal, characteristic, complemented
11#11727667C211yesmaximal, characteristic, complemented
12#11727666C211yesmaximal, characteristic, complemented
13#11727665C211yesmaximal, characteristic, complemented
14#11727663C211yesmaximal, characteristic, complemented
15#11727661C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C2×#6489C2211yescharacteristic
18C2×#6489C2211yescharacteristic
19C22×#1136C2211yescharacteristic
20C22×#1136C2211yescharacteristic
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#90019C411yescharacteristic
28#90019C411yescharacteristic
29#89984C411yescharacteristic
30#89984C411yescharacteristic
31#89984C411yescharacteristic
32#89984C411yescharacteristic
33#89983C411yescharacteristic
34#89983C411yescharacteristic
35C4×C22⋊Dic7C2211yescharacteristic
36C4×C22⋊Dic7C2211yescharacteristic
37C4×C22⋊Dic7C2211yescharacteristic
38C4×C22⋊Dic7C2211yescharacteristic
39#89979—24no—
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43C2×C22⋊(C7⋊C8)C2211yescharacteristic
44C2×#6389C2211yescharacteristic, complemented
45C2×#6389C2211yescharacteristic, complemented
46C2×Dic7⋊C8C2211yescharacteristic, complemented
47C2×Dic7⋊C8C2211yescharacteristic, complemented
48C2×Dic7⋊C8C2211yescharacteristic, complemented
49C2×Dic7⋊C8C2211yescharacteristic, complemented
50C2×C8×Dic7C2211yescharacteristic, complemented
51C2×C8×Dic7C2211yescharacteristic, complemented
52#89492—24no—
53#89345C2211yescharacteristic, complemented
54#89345C2211yescharacteristic, complemented
55#89345C2211yescharacteristic, complemented
56#89345C2211yescharacteristic, complemented
57#89345C2211yescharacteristic, complemented
58#89345C2211yescharacteristic, complemented
59#89345C2211yescharacteristic, complemented
60#89345C2211yescharacteristic, complemented
61#22559—71nomaximal, Sylow
62C25×C7C2×C411yescharacteristic
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—22no—
66C23×C4×C7—22no—
67C23×C4×C7—41no—
68C23×C4×C7—41no—
69C23×C4×C7C2×C411yescharacteristic
70C23×C4×C7C2×C411yescharacteristic
71C23×C4×C7C2×C411yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C22×C7×C8C2311yescharacteristic
76C22×C7×C8C2311yescharacteristic
77C22×C7×C8C2311yescharacteristic
78C22×C7×C8C2311yescharacteristic
79C2×C22⋊Dic7C2×C411yescharacteristic
80C2×C22⋊Dic7C2×C411yescharacteristic
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—
93#6489—41no—
94#6489—41no—
95C2×C4⋊Dic7C2×C411yescharacteristic
96C2×C4⋊Dic7C2×C411yescharacteristic
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—22no—
106C2×#1136—22no—
107C2×#1136—41no—
108C2×#1136—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—
132#6389—41no—
133Dic7⋊C8—22no—
134Dic7⋊C8—22no—
135Dic7⋊C8—41no—
136Dic7⋊C8—41no—
137C8×Dic7—22no—
138C8×Dic7—41no—
139C2×#433—71no—
140C2×#407—71no—
141#2280—71no—
142#1924—71no—
143#1924—71no—
144#1923—71no—
145#1923—71no—
146#1851—71no—
147#1851—71no—
148#1818—71no—
149#1798—71no—
150#1779D711yescharacteristic
151#1753—71no—
152#1753—71no—
153#1750—71no—
154C24×C7—22no—
155C24×C7—22no—
156C24×C7—22no—
157C24×C7—41no—
158C24×C7—41no—
159C24×C7—41no—
160C24×C7—41no—
161C24×C7C22×C411yescharacteristic
162C24×C7C22×C411yescharacteristic
163C24×C7C22×C411yescharacteristic
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
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—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—41no—
185C22×C4×C7—41no—
186C22×C4×C7—41no—
187C22×C4×C7—44no—
188C22×C4×C7—44no—
189C22×C4×C7—44no—
190C22×C4×C7—44no—
191C22×C4×C7C22×C411yescharacteristic
192C22×C4×C7C22×C411yescharacteristic
193C22×C4×C7C22×C411yescharacteristic
194C22×C4×C7C2×D412yes—
195C22×C4×C7#4112yes—
196C22×C4×C7#4112yes—
197C22×C4×C7#4112yes—
198C22×C4×C7C2411yescharacteristic
199C22×Dic7C22×C411yescharacteristic
200C22×Dic7C22×C411yescharacteristic
201C22×Dic7C22×C411yescharacteristic
202C22×Dic7C22×C411yescharacteristic
203C22×Dic7C22×C411yescharacteristic
204C22×Dic7C22×C411yescharacteristic
205C22×Dic7C22×C411yescharacteristic
206C22×Dic7C22×C411yescharacteristic
207C2×C7×C8—21no—
208C2×C7×C8—21no—
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—
219C22⋊Dic7—22no—
220C22⋊Dic7—22no—
221C22⋊Dic7—22no—
222C22⋊Dic7—22no—
223C22⋊Dic7—41no—
224C22⋊Dic7—41no—
225C22⋊Dic7—41no—
226C22⋊Dic7—41no—
227C22⋊Dic7—41no—
228C22⋊Dic7—41no—
229C22⋊Dic7—41no—
230C22⋊Dic7—41no—
231C4⋊Dic7—22no—
232C4⋊Dic7—22no—
233C4⋊Dic7—41no—
234C4⋊Dic7—41no—
235C4×Dic7—21no—
236C4×Dic7—21no—
237C4×Dic7—21no—
238C4×Dic7—21no—
239C4×Dic7—21no—
240C4×Dic7—21no—
241C4×Dic7—21no—
242C4×Dic7—21no—
243#1136—44no—
244#1136—44no—
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⋊C8C2×D412yes—
256C2×C7⋊C8C2×D412yes—
257C24×C4C2×D711yescharacteristic
258C22×M16—71no—
259C22×M16—71no—
260C2×#117—71no—
261C2×#117—71no—
262#433—144no—
263C2×C4⋊C8—71no—
264C2×C4⋊C8—71no—
265C2×C4⋊C8—71no—
266C2×C4⋊C8—71no—
267#407—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×#97—71no—
280C2×C4×C8—71no—
281C2×C4×C8—71no—
282#381—71no—
283#381—71no—
284#380—71no—
285#380—71no—
286#380—71no—
287#380—71no—
288#379—71no—
289#379—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—44no—
321C23×C7—44no—
322C23×C7—44no—
323C23×C7—44no—
324C23×C7—44no—
325C23×C7—44no—
326C23×C7—44no—
327C23×C7#11712yes—
328C23×C7C4×D412yes—
329C23×C7#13112yes—
330C23×C7C23×C411yescharacteristic
331C2×C4×C7—21no—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
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—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—44no—
347C2×C4×C7—44no—
348C2×C4×C7—44no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7#11712yes—
354C2×C4×C7C4×D412yes—
355C2×C4×C7C22×D411yescharacteristic
356C2×C4×C7C2×#4111yescharacteristic
357C2×C4×C7C2×#4111yescharacteristic
358C2×C4×C7C2×#4111yescharacteristic
359C2×C4×C7H(5,𝔽2)11yescharacteristic
360C2×C4×C7H(5,𝔽2)11yescharacteristic
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—21no—
377C2×Dic7—21no—
378C2×Dic7—21no—
379C2×Dic7—21no—
380C2×Dic7—21no—
381C2×Dic7—21no—
382C2×Dic7—21no—
383C2×Dic7—21no—
384C2×Dic7—21no—
385C7×C8—41no—
386C7×C8—41no—
387C7×C8—41no—
388C7×C8—41no—
389C7⋊C8—22no—
390C7⋊C8—22no—
391C7⋊C8—41no—
392C7⋊C8—41no—
393C25C4×D711yescharacteristic
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—41no—
399C23×C4—41no—
400C23×C4C4×D711yescharacteristic
401C23×C4C4×D711yescharacteristic
402C23×C4C4×D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404C23×C4C22×D711yescharacteristic
405C23×C4C22×D711yescharacteristic
406C2×M16—142no—
407C2×M16—142no—
408C2×M16—142no—
409C2×M16—142no—
410C2×M16—281no—
411C2×M16—281no—
412C22×C8—71no—
413C22×C8—71no—
414C22×C8—71no—
415C22×C8—71no—
416C22×C8C22×D711yescharacteristic
417C22×C8C22×D711yescharacteristic
418C22×C8C22×D711yescharacteristic
419C22×C8C22×D711yescharacteristic
420#117—142no—
421#117—142no—
422#117—281no—
423#117—281no—
424C2×C4⋊C4—71no—
425C2×C4⋊C4—71no—
426C2×C4⋊C4—71no—
427C2×C4⋊C4—71no—
428C2×C22⋊C4—71no—
429C2×C22⋊C4—71no—
430C2×C22⋊C4—71no—
431C2×C22⋊C4—71no—
432C2×C22⋊C4—71no—
433C2×C22⋊C4—71no—
434C2×C22⋊C4—71no—
435C2×C22⋊C4—71no—
436C2×C22⋊C4—71no—
437C2×C22⋊C4—71no—
438C2×C22⋊C4—71no—
439C2×C22⋊C4—71no—
440C2×C42—71no—
441C2×C42—71no—
442C2×C42—71no—
443C2×C42—71no—
444C4⋊C8—142no—
445C4⋊C8—142no—
446C4⋊C8—281no—
447C4⋊C8—281no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452C22⋊C8—41no—
453C22⋊C8—41no—
454C22⋊C8—74no—
455C22⋊C8—142no—
456C22⋊C8—142no—
457C22⋊C8—142no—
458#97—142no—
459#97—281no—
460C4×C8—142no—
461C4×C8—281no—
462#95—71no—
463#95—71no—
464#95—71no—
465#95—71no—
466#95—71no—
467#95—71no—
468#95—71no—
469#95—71no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—22no—
476C22×C7—22no—
477C22×C7—22no—
478C22×C7—22no—
479C22×C7—416no—
480C22×C7—41no—
481C22×C7—41no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—41no—
487C22×C7—41no—
488C22×C7—41no—
489C22×C7—41no—
490C22×C7—41no—
491C22×C7—41no—
492C22×C7C2×#11711yescharacteristic
493C22×C7C2×C4×D411yescharacteristic
494C22×C7#51811yescharacteristic
495C22×C7C2×#13111yescharacteristic
496C22×C7#56811yescharacteristic
497C22×C7#56811yescharacteristic
498C22×C7#56811yescharacteristic
499C4×C7—22no—
500C4×C7—22no—
501C4×C7—41no—
502C4×C7#54611yescharacteristic
503C4×C7#54611yescharacteristic
504C4×C7#55111yescharacteristic
505C4×C7#55111yescharacteristic
506Dic7—41no—
507Dic7—41no—
508Dic7—41no—
509Dic7—41no—
510Dic7—41no—
511Dic7—41no—
512Dic7—41no—
513Dic7—41no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—41no—
518C24—41no—
519C24—41no—
520C24—41no—
521C24C2×C4×D711yescharacteristic
522C24C2×C4×D711yescharacteristic
523C24C2×C4×D711yescharacteristic
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—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—71no—
552C22×C4—71no—
553C22×C4—71no—
554C22×C4—71no—
555C22×C4—71no—
556C22×C4—71no—
557C22×C4—71no—
558C22×C4—71no—
559C22×C4C2×C4×D711yescharacteristic
560C22×C4C2×C4×D711yescharacteristic
561C22×C4C2×C4×D711yescharacteristic
562C22×C4D4×D712yes—
563C22×C4#115912yes—
564C22×C4#115912yes—
565C22×C4#115912yes—
566C22×C4C23×D711yescharacteristic
567M16—284no—
568M16—284no—
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—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—72no—
582C2×C8—72no—
583C2×C8—141no—
584C2×C8—141no—
585C2×C8—141no—
586C2×C8—141no—
587C2×C8—141no—
588C2×C8—141no—
589C2×C8—141no—
590C2×C8—141no—
591C2×C8—141no—
592C2×C8—141no—
593C4⋊C4—142no—
594C4⋊C4—142no—
595C4⋊C4—281no—
596C4⋊C4—281no—
597C22⋊C4—142no—
598C22⋊C4—142no—
599C22⋊C4—142no—
600C22⋊C4—142no—
601C22⋊C4—281no—
602C22⋊C4—281no—
603C22⋊C4—281no—
604C22⋊C4—281no—
605C22⋊C4—281no—
606C22⋊C4—281no—
607C22⋊C4—281no—
608C22⋊C4—281no—
609C42—141no—
610C42—141no—
611C42—141no—
612C42—141no—
613C42—141no—
614C42—141no—
615C42—141no—
616C42—141no—
617C2×C7—42no—
618C2×C7—42no—
619C2×C7—42no—
620C2×C7#234211yescharacteristic
621C2×C7#292111yescharacteristic
622C2×C7#292411yescharacteristic
623C2×C7#293011yescharacteristic
624C2×C7#293311yescharacteristic
625C2×C7#297611yescharacteristic
626C2×C7#297811yescharacteristic
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—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23#644012yes—
653C23(C22⋊D7)⋊C412yes—
654C23#646412yes—
655C23C22×C4×D711yescharacteristic
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
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—141no—
692C2×C4—141no—
693C2×C4—141no—
694C2×C4—141no—
695C2×C4—141no—
696C2×C4—141no—
697C2×C4—141no—
698C2×C4—141no—
699C2×C4—141no—
700C2×C4—141no—
701C2×C4—141no—
702C2×C4#644012yes—
703C2×C4(C22⋊D7)⋊C412yes—
704C2×C4C2×D4×D711yescharacteristic
705C2×C4C2×#115911yescharacteristic
706C2×C4C2×#115911yescharacteristic
707C2×C4C2×#115911yescharacteristic
708C2×C4#654811yescharacteristic
709C2×C4#654811yescharacteristic
710C8—41no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—142no—
715C8—142no—
716C8—281no—
717C8—281no—
718C7#2255911yescharacteristic, complemented, Sylow
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—416no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22C2×#644011yescharacteristic
742C22C2×(C22⋊D7)⋊C411yescharacteristic
743C22#9017711yescharacteristic
744C22C2×#646411yescharacteristic
745C22#9043611yescharacteristic
746C22#9043611yescharacteristic
747C22#9043611yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—281no—
752C4—281no—
753C4—281no—
754C4—281no—
755C4—281no—
756C4—281no—
757C4—281no—
758C4—281no—
759C4#9027811yescharacteristic
760C4#9027811yescharacteristic
761C4#9028211yescharacteristic
762C4#9028211yescharacteristic
763C2—42no—
764C2—42no—
765C2—42no—
766C2#1173126711yescharacteristic
767C2#1173602911yescharacteristic
768C2#1173604111yescharacteristic
769C2#1173604911yescharacteristic
770C2#1173606511yescharacteristic
771C2#1173607211yescharacteristic
772C2#1173608111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC7×#1779C2
prime radicalC25×C7C2×C4
cosocleC22×C4×C7C24
hypercenter#1779D7
hypocenterC7#22559
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#89492C2semidirect
5. #11727705C2semidirect
6. #11727705C2semidirect
7. #11727703C2semidirect
8. #11727703C2semidirect
9. #11727669C2semidirect
10. #11727668C2semidirect
11. #11727667C2semidirect
12. #11727666C2semidirect
13. #11727665C2semidirect
14. #11727663C2semidirect
15. #11727661C2semidirect
44. C2×#6389C22semidirect
45. C2×#6389C22semidirect
46. C2×Dic7⋊C8C22semidirect
47. C2×Dic7⋊C8C22semidirect
48. C2×Dic7⋊C8C22semidirect
49. C2×Dic7⋊C8C22semidirect
50. C2×C8×Dic7C22semidirect
51. C2×C8×Dic7C22semidirect
53. #89345C22semidirect
54. #89345C22semidirect
55. #89345C22semidirect
56. #89345C22semidirect
57. #89345C22semidirect
58. #89345C22semidirect
59. #89345C22semidirect
60. #89345C22semidirect
718. C7#22559semidirect

Maximal subgroups

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

subgroupindex
#117414722
C2×#899792
C2×#894922
C7×#17792
#117277052
#117277032
#117276692
#117276682
#117276672
#117276662
#117276652
#117276632
#117276612
#225597