Finite Group Databasebeta

← #13370117

Subgroups — #13370117

Order 1792.

1258 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
1C2×#90305C211yesmaximal, characteristic
2C4⋊C4×C22⋊D7C211yesmaximal, characteristic, complemented
3C2×#89500C211yesmaximal, characteristic, complemented
4C7×#1874C211yesmaximal, characteristic, complemented
5#11729436C211yesmaximal, characteristic, complemented
6#11729312C211yesmaximal, characteristic, complemented
7#11727956C211yesmaximal, characteristic, complemented
8#11727954C211yesmaximal, characteristic, complemented
9#11727907C211yesmaximal, characteristic, complemented
10#11727906C211yesmaximal, characteristic, complemented
11#11727680C211yesmaximal, characteristic, complemented
12#11726626C211yesmaximal, characteristic, complemented
13D7×#340C211yesmaximal, characteristic, complemented
14#11726559C211yesmaximal, characteristic, complemented
15#11726556C211yesmaximal, characteristic, complemented
16C2×C7×#121C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C2×#6501—21no—
19C2×#6501C2211yescharacteristic
20C2×#6498—21no—
21C2×D4×Dic7C2211yescharacteristic
22C2×C4×C22⋊D7—21no—
23C2×C4×C22⋊D7C2211yescharacteristic
24C2×#6489C2211yescharacteristic
25C22×#1136C2211yescharacteristic
26C22×C8×D7C2211yescharacteristic
27#90305—24no—
28#90305C418yescomplemented
29C2×D7×C4⋊C4C2211yescharacteristic
30C2×D7×C4⋊C4C2211yescharacteristic
31C2×#6453C2211yescharacteristic
32C2×(C22⋊D7)⋊C4—21no—
33C2×#6442—21no—
34C2×C7×#102C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C2×C7×C22⋊C8C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39#89984C2211yescharacteristic
40#89982—21no—
41C2×(C2×D7)⋊C8C2211yescharacteristic
42C2×#6389C2211yescharacteristic
43C2×Dic7⋊C8C2211yescharacteristic
44#89761—21no—
45#89759C2211yescharacteristic
46#89748C2211yescharacteristic
47C4⋊C4×Dic7C2211yescharacteristic
48#89744—21no—
49#89500—24no—
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22493—71nomaximal, Sylow
63C22×C7×D4—21no—
64C22×C7×D4C2311yescharacteristic
65C23×C4×C7—21no—
66C23×C4×C7C2311yescharacteristic
67C22×C22⋊D7—21no—
68C22×C22⋊D7D411yescharacteristic
69C23×Dic7—21no—
70C22×C4×D7—21no—
71C22×C4×D7—21no—
72C22×C4×D7C2311yescharacteristic
73C22×C7×C8C2311yescharacteristic
74C22×C7×C8C2311yescharacteristic
75C7×#121—22no—
76C7×#121C2×C414yescomplemented
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—41no—
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C22⋊C4—21no—
84C2×C22⋊Dic7—21no—
85C2×C22⋊Dic7—21no—
86C2×C22⋊Dic7—21no—
87C2×C22⋊Dic7—21no—
88C2×C22⋊Dic7D411yescharacteristic
89#6501—28no—
90#6501—22no—
91#6501C2×C414yescomplemented
92#6498—28no—
93D4×Dic7—22no—
94D4×Dic7C2×C414yescomplemented
95C4×C22⋊D7—44no—
96C4×C22⋊D7C2×C414yes—
97C4×C22⋊D7D414yes—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4D411yescharacteristic
100#6489—22no—
101#6489C2×C414yescomplemented
102C2×C4⋊Dic7—21no—
103C2×C4⋊Dic7C2311yescharacteristic
104C2×C4⋊Dic7C2311yescharacteristic
105C2×C4⋊Dic7C2311yescharacteristic
106C2×C4⋊Dic7C2311yescharacteristic
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—21no—
109C2×Dic7⋊C4—21no—
110C2×Dic7⋊C4—21no—
111C2×Dic7⋊C4—21no—
112C2×Dic7⋊C4D411yescharacteristic
113C2×C4×Dic7—21no—
114C2×C4×Dic7—21no—
115C2×C4×Dic7C2311yescharacteristic
116C2×#1136—22no—
117C2×#1136—22no—
118C2×#1136—41no—
119C22×C7⋊C8C2311yescharacteristic
120C22×C7⋊C8C2311yescharacteristic
121C2×C8×D7—22no—
122C2×C8×D7—22no—
123C2×C8×D7—41no—
124D7×C4⋊C4—22no—
125D7×C4⋊C4—22no—
126D7×C4⋊C4—41no—
127D7×C4⋊C4C2×C414yescomplemented
128#6453—22no—
129#6453C2×C414yescomplemented
130(C22⋊D7)⋊C4—28no—
131#6442—28no—
132C7×#102—22no—
133C7×#102—41no—
134C7×C22⋊C8—22no—
135#6406—22no—
136#6406—41no—
137C7⋊#95—21no—
138C7⋊#95—21no—
139C7⋊#95—21no—
140(C2×D7)⋊C8—22no—
141#6389—22no—
142Dic7⋊C8—22no—
143C2×#553—71no—
144C2×#435—71no—
145D4×C4⋊C4—71no—
146#1992—71no—
147#1989—71no—
148#1895—71no—
149#1893—71no—
150#1874—71no—
151#1874D711yescharacteristic, complemented
152#1825—71no—
153#1824—71no—
154#1802—71no—
155#1762—71no—
156#1736—71no—
157C2×#340—71no—
158C24×C7—21no—
159C24×C7C2×D411yescharacteristic
160C23×D7C2×D411yescharacteristic
161C2×C7×D4—24no—
162C2×C7×D4—21no—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—81no—
168C2×C7×D4—81no—
169C2×C7×D4C22×C412yes—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—42no—
178C22×C4×C7—42no—
179C22×C4×C7—81no—
180C22×C4×C7C22×C412yes—
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D412yes—
183C22×C4×C7C2411yescharacteristic
184C2×C22⋊D7—22no—
185C2×C22⋊D7—22no—
186C2×C22⋊D7—24no—
187C2×C22⋊D7—42no—
188C2×C22⋊D7—42no—
189C2×C22⋊D7C22⋊C414yes—
190C22×Dic7—21no—
191C22×Dic7—21no—
192C22×Dic7—24no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—81no—
196C22×Dic7—81no—
197C22×Dic7C2×D411yescharacteristic
198C22×Dic7C2×D411yescharacteristic
199C22×Dic7C2×D411yescharacteristic
200C2×C4×D7—21no—
201C2×C4×D7—21no—
202C2×C4×D7—21no—
203C2×C4×D7—21no—
204C2×C4×D7—24no—
205C2×C4×D7—42no—
206C2×C4×D7—42no—
207C2×C4×D7—81no—
208C2×C4×D7—81no—
209C2×C4×D7—81no—
210C2×C4×D7C22×C412yes—
211C2×C4×D7C2×D412yes—
212C2×C7×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—42no—
223C7×C4⋊C4C22×C412yes—
224C7×C4⋊C4#4112yes—
225C7×C22⋊C4—24no—
226C22⋊Dic7—24no—
227C22⋊Dic7—24no—
228C22⋊Dic7—24no—
229C22⋊Dic7—42no—
230C22⋊Dic7C22⋊C414yes—
231(C2×D7)⋊C4—42no—
232(C2×D7)⋊C4C22⋊C414yes—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—24no—
236C4⋊Dic7—21no—
237C4⋊Dic7—21no—
238C4⋊Dic7—21no—
239C4⋊Dic7—21no—
240C4⋊Dic7C22×C412yes—
241C4⋊Dic7C22×C412yes—
242Dic7⋊C4—24no—
243Dic7⋊C4—24no—
244Dic7⋊C4—42no—
245Dic7⋊C4—42no—
246Dic7⋊C4—81no—
247Dic7⋊C4C22⋊C414yes—
248C4×Dic7—24no—
249C4×Dic7—42no—
250C4×Dic7C22×C412yes—
251C4×Dic7C2×D412yes—
252#1136—44no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8—21no—
256C2×C7⋊C8—21no—
257C2×C7⋊C8—21no—
258C2×C7⋊C8#4112yes—
259C8×D7—44no—
260C22×M16—71no—
261C23×C8—71no—
262#553—78no—
263#553—144no—
264C2×#126—141no—
265C2×#125—71no—
266C2×#123—141no—
267C2×#121—71no—
268C2×#121—141no—
269C2×#121C2×D711yescharacteristic
270C2×C4×D4—71no—
271C2×C4×D4—71no—
272C2×C4×D4—141no—
273C2×C4×D4—141no—
274C2×#117—71no—
275C22×C4⋊C4—71no—
276C22×C4⋊C4—71no—
277C22×C4⋊C4C2×D711yescharacteristic
278#435—144no—
279C2×C4⋊C8—71no—
280C2×#102—71no—
281C2×#102—71no—
282C2×#102C2×D711yescharacteristic
283C2×#102C2×D711yescharacteristic
284C2×C22⋊C8—71no—
285C2×C22⋊C8C2×D711yescharacteristic
286C2×#97—71no—
287#389—141no—
288#385—141no—
289#385—141no—
290#384—71no—
291#380—71no—
292#380—71no—
293C4×C4⋊C4—71no—
294#340—71no—
295#340—71no—
296#340—71no—
297#340—71no—
298#340—71no—
299#340—71no—
300#340—71no—
301#340—71no—
302#340—71no—
303#340—71no—
304#340C2×D711yescharacteristic
305#340C2×D711yescharacteristic
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—22no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7C2×C22⋊C412yes—
320C23×C7C22×D411yescharacteristic
321C22×D7—21no—
322C22×D7—21no—
323C22×D7—21no—
324C22×D7—21no—
325C22×D7C2×C22⋊C412yes—
326C22×D7AGL(1,ℤ/8)12yes—
327C22×D7#13712yes—
328C7×D4—22no—
329C7×D4—22no—
330C7×D4—41no—
331C7×D4—41no—
332C7×D4—84no—
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—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—84no—
349C2×C4×C7C2×C22⋊C412yes—
350C2×C4×C7C23×C411yescharacteristic
351C2×C4×C7C22×D411yescharacteristic
352C2×C4×C7C2×#4111yescharacteristic
353C2×C4×C7C2×#4111yescharacteristic
354C2×C4×C7H(5,𝔽2)11yescharacteristic
355C2×C4×C72−1+411yescharacteristic
356C22⋊D7—28no—
357C22⋊D7—48no—
358C2×Dic7—21no—
359C2×Dic7—21no—
360C2×Dic7—21no—
361C2×Dic7—21no—
362C2×Dic7—21no—
363C2×Dic7—21no—
364C2×Dic7—22no—
365C2×Dic7—22no—
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—
376C2×Dic7—84no—
377C2×Dic7C2×C22⋊C412yes—
378C2×Dic7C2×C22⋊C412yes—
379C2×Dic7C2×C22⋊C412yes—
380C4×D7—22no—
381C4×D7—22no—
382C4×D7—22no—
383C4×D7—22no—
384C4×D7—84no—
385C4×D7—84no—
386C7×C8—41no—
387C7×C8—41no—
388C7⋊C8—22no—
389C7⋊C8—41no—
390C22×D4—21no—
391C22×D4—71no—
392C22×D4—141no—
393C22×D4C22×D711yescharacteristic
394C23×C4—21no—
395C23×C4—71no—
396C23×C4—141no—
397C23×C4—141no—
398C23×C4—141no—
399C23×C4C22×D711yescharacteristic
400C2×M16—142no—
401C2×M16—142no—
402C2×M16—281no—
403C22×C8—71no—
404C22×C8—71no—
405C22×C8—142no—
406C22×C8—142no—
407C22×C8—281no—
408C22×C8C22×D711yescharacteristic
409C22×C8C22×D711yescharacteristic
410#126—148no—
411#125—74no—
412#125—142no—
413#123—148no—
414#121—22no—
415#121—74no—
416#121—142no—
417#121—148no—
418#121C4×D714yescomplemented
419C4×D4—74no—
420C4×D4—74no—
421C4×D4—74no—
422C4×D4—142no—
423C4×D4—148no—
424C4×D4—284no—
425#117—74no—
426#117—142no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4—71no—
431C2×C4⋊C4—71no—
432C2×C4⋊C4—71no—
433C2×C4⋊C4—74no—
434C2×C4⋊C4—71no—
435C2×C4⋊C4—71no—
436C2×C4⋊C4—142no—
437C2×C4⋊C4—141no—
438C2×C4⋊C4—141no—
439C2×C4⋊C4—141no—
440C2×C4⋊C4—142no—
441C2×C4⋊C4—141no—
442C2×C4⋊C4—141no—
443C2×C4⋊C4—141no—
444C2×C4⋊C4—281no—
445C2×C4⋊C4C22×D711yescharacteristic
446C2×C4⋊C4C22×D711yescharacteristic
447C2×C4⋊C4C22×D711yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—71no—
450C2×C22⋊C4—71no—
451C2×C22⋊C4—141no—
452C2×C22⋊C4—141no—
453C2×C22⋊C4—141no—
454C2×C22⋊C4—141no—
455C2×C22⋊C4—141no—
456C2×C42—71no—
457C2×C42—141no—
458C2×C42—141no—
459C4⋊C8—142no—
460#102—22no—
461#102—41no—
462#102—142no—
463#102—281no—
464C22⋊C8—22no—
465C22⋊C8—142no—
466#97—142no—
467#95—141no—
468#95—141no—
469#95—141no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—41no—
474C22×C7—41no—
475C22×C7—41no—
476C22×C7—41no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—81no—
481C22×C7—81no—
482C22×C7—81no—
483C22×C7—81no—
484C22×C7C22×C22⋊C411yescharacteristic
485C22×C7#54611yescharacteristic
486C22×C7#54711yescharacteristic
487C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
488C22×C7C2×#13711yescharacteristic
489C22×C7#57611yescharacteristic
490C22×C7#57711yescharacteristic
491C2×D7—22no—
492C2×D7—22no—
493C2×D7—22no—
494C2×D7—22no—
495C2×D7—22no—
496C2×D7—22no—
497C2×D7#41714yes—
498C4×C7—22no—
499C4×C7—42no—
500C4×C7—42no—
501C4×C7—81no—
502C4×C7C4×#4111yescharacteristic
503C4×C7#52011yescharacteristic
504C4×C7#54611yescharacteristic
505C4×C7#54711yescharacteristic
506Dic7—22no—
507Dic7—22no—
508Dic7—22no—
509Dic7—42no—
510Dic7—42no—
511Dic7—81no—
512Dic7—81no—
513C24—21no—
514C24—71no—
515C24D4×D711yescharacteristic
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—74no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4—142no—
526C2×D4—142no—
527C2×D4—144no—
528C2×D4—282no—
529C2×D4—282no—
530C2×D4C2×C4×D712yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—71no—
541C22×C4—71no—
542C22×C4—71no—
543C22×C4—72no—
544C22×C4—72no—
545C22×C4—81no—
546C22×C4—144no—
547C22×C4—144no—
548C22×C4—141no—
549C22×C4—141no—
550C22×C4—141no—
551C22×C4—141no—
552C22×C4—141no—
553C22×C4—141no—
554C22×C4—141no—
555C22×C4—141no—
556C22×C4—282no—
557C22×C4—282no—
558C22×C4—561no—
559C22×C4—561no—
560C22×C4—561no—
561C22×C4—561no—
562C22×C4—561no—
563C22×C4C2×C4×D712yes—
564C22×C4D4×D711yescharacteristic
565C22×C4D4×D712yes—
566C22×C4C23×D711yescharacteristic
567M16—284no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—72no—
575C2×C8—141no—
576C2×C8—141no—
577C2×C8—141no—
578C2×C8—141no—
579C2×C8—141no—
580C2×C8—284no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—74no—
587C4⋊C4—72no—
588C4⋊C4—72no—
589C4⋊C4—144no—
590C4⋊C4—144no—
591C4⋊C4—144no—
592C4⋊C4—141no—
593C4⋊C4—141no—
594C4⋊C4—141no—
595C4⋊C4—141no—
596C4⋊C4—141no—
597C4⋊C4—141no—
598C4⋊C4—282no—
599C4⋊C4—282no—
600C4⋊C4—561no—
601C4⋊C4C2×C4×D712yes—
602C4⋊C4#115912yes—
603C22⋊C4—24no—
604C22⋊C4—74no—
605C22⋊C4—74no—
606C22⋊C4—144no—
607C22⋊C4—144no—
608C22⋊C4—144no—
609C22⋊C4—282no—
610C22⋊C4—282no—
611C42—72no—
612C42—72no—
613C42—144no—
614C42—282no—
615C2×C7—42no—
616C2×C7—82no—
617C2×C7#233911yescharacteristic
618C2×C7C2×#41711yescharacteristic
619C2×C7#289711yescharacteristic
620C2×C7#331811yescharacteristic
621C2×C7#332011yescharacteristic
622C2×C7#334511yescharacteristic
623C2×C7#334611yescharacteristic
624D7—24no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—72no—
639C23—72no—
640C23—72no—
641C23—141no—
642C23—141no—
643C23—141no—
644C23—141no—
645C23D7×C22⋊C412yes—
646C23C2×D4×D711yescharacteristic
647D4—22no—
648D4—22no—
649D4—41no—
650D4—41no—
651D4—84no—
652D4—148no—
653D4—288no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—72no—
670C2×C4—72no—
671C2×C4—72no—
672C2×C4—84no—
673C2×C4—141no—
674C2×C4—141no—
675C2×C4—141no—
676C2×C4—141no—
677C2×C4—141no—
678C2×C4—141no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—281no—
686C2×C4—281no—
687C2×C4—281no—
688C2×C4—281no—
689C2×C4—281no—
690C2×C4—281no—
691C2×C4—281no—
692C2×C4—281no—
693C2×C4—281no—
694C2×C4—281no—
695C2×C4—564no—
696C2×C4—564no—
697C2×C4—564no—
698C2×C4D7×C22⋊C412yes—
699C2×C4C22×C4×D711yescharacteristic
700C2×C4C2×D4×D711yescharacteristic
701C2×C4C2×#115911yescharacteristic
702C2×C4#654811yescharacteristic
703C2×C4D7×#4111yescharacteristic
704C2×C4#655411yescharacteristic
705C8—41no—
706C8—41no—
707C8—142no—
708C8—281no—
709C7#2249311yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—74no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—142no—
726C22—142no—
727C22—142no—
728C22—142no—
729C22—142no—
730C22—142no—
731C22C2×D7×C22⋊C411yescharacteristic
732C22#9028211yescharacteristic
733C22#9034611yescharacteristic
734C22#9044811yescharacteristic
735C22#9045311yescharacteristic
736C22D7×AGL(1,ℤ/8)11yescharacteristic
737C22D7×#13711yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—81no—
742C4—142no—
743C4—142no—
744C4—142no—
745C4—282no—
746C4—282no—
747C4—561no—
748C4—561no—
749C4C4×#115911yescharacteristic
750C4#9023711yescharacteristic
751C4#9030111yescharacteristic
752C4#9030211yescharacteristic
753C2—42no—
754C2—82no—
755C2—144no—
756C2#1173211711yescharacteristic
757C2#1173618711yescharacteristic
758C2D7×#41711yescharacteristic
759C2#1173746311yescharacteristic
760C2#1173749811yescharacteristic
761C2#1173874011yescharacteristic
762C2#1173878011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1874C2
socleC23×C7C22×D4
prime radicalC2×#90305C2
cosocleC22×C4×C7C24
hypercenter#1874D7
hypocenterC7#22493
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C22⋊D7C2semidirect
3. C2×#89500C2semidirect
4. C7×#1874C2semidirect
5. #11729436C2semidirect
6. #11729312C2semidirect
7. #11727956C2semidirect
8. #11727954C2semidirect
9. #11727907C2semidirect
10. #11727906C2semidirect
11. #11727680C2semidirect
12. #11726626C2semidirect
13. D7×#340C2semidirect
14. #11726559C2semidirect
15. #11726556C2semidirect
28. #90305C4semidirect
76. C7×#121C2×C4semidirect
91. #6501C2×C4semidirect
94. D4×Dic7C2×C4semidirect
101. #6489C2×C4semidirect
127. D7×C4⋊C4C2×C4semidirect
129. #6453C2×C4semidirect
151. #1874D7semidirect
418. #121C4×D7semidirect
709. C7#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#903052
C4⋊C4×C22⋊D72
C2×#895002
C7×#18742
#117294362
#117293122
#117279562
#117279542
#117279072
#117279062
#117276802
#117266262
D7×#3402
#117265592
#117265562
#224937