Finite Group Databasebeta

← #13353324

Subgroups — #13353324

Order 1792.

1462 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
1C2×#90237C211yesmaximal, characteristic
2C2×#89611C211yesmaximal, characteristic, complemented
3C2×#89543C211yesmaximal, characteristic
4C2×#89544C211yesmaximal, characteristic
5#11731670C211yesmaximal, characteristic, complemented
6C7×#1804C211yesmaximal, characteristic, complemented
7#11729358C211yesmaximal, characteristic, complemented
8#11728239C211yesmaximal, characteristic, complemented
9#11727908C211yesmaximal, characteristic, complemented
10#11727907C211yesmaximal, characteristic, complemented
11#11727313C211yesmaximal, characteristic, complemented
12#11726659C211yesmaximal, characteristic, complemented
13#11726658C211yesmaximal, characteristic, complemented
14#11726621C211yesmaximal, characteristic, complemented
15D7×#340C211yesmaximal, characteristic, complemented
16C22×#1159C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×D4×Dic7C2211yescharacteristic
19C2×C4×C22⋊D7—21no—
20C22×Dic7⋊C4—21no—
21C22×#1131C2211yescharacteristic
22C22×C8×D7C2211yescharacteristic
23#90237—24no—
24#90237C418yescomplemented
25C2×#6455C2211yescharacteristic
26C2×D7×C4⋊C4C2211yescharacteristic
27C2×D7×C4⋊C4C2211yescharacteristic
28C2×#6450C2211yescharacteristic
29C2×(C22⋊D7)⋊C4—21no—
30C2×#6440—21no—
31C2×#6435C2211yescharacteristic
32C2×C4×Dic14C2211yescharacteristic
33C2×C7×C4⋊C8C2211yescharacteristic
34C2×C7×#102C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C7×#382C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39C2×#6390C2211yescharacteristic
40C2×#6390C2211yescharacteristic
41C2×Dic7⋊C8C2211yescharacteristic
42C2×Dic7⋊C8C2211yescharacteristic
43#89749C2211yescharacteristic
44#89748C2211yescharacteristic
45C2×#6384C2211yescharacteristic
46C2×#6384C2211yescharacteristic
47#89707C2211yescharacteristic
48C2×C4⋊(C7⋊C8)C2211yescharacteristic
49#89611—24no—
50#89544—24no—
51#89543—24no—
52#89440—21no—
53#89440—21no—
54#89419—21no—
55#89419—21no—
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#89324C2211yescharacteristic
63#89324C2211yescharacteristic
64#20652—71nomaximal, Sylow
65C22×C7×D4C2311yescharacteristic
66C23×C4×C7—21no—
67C22×C22⋊D7—21no—
68C23×Dic7—21no—
69C23×Dic7—21no—
70C2×#1159—22no—
71C2×#1159—22no—
72C2×#1159—22no—
73C2×#1159C2×C414yes—
74C2×#1159D414yes—
75C2×#1159Q814yes—
76C22×C4×D7—21no—
77C22×C4×D7—21no—
78C22×C4×D7C2311yescharacteristic
79C22×Dic14C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C22×C7×C8C2311yescharacteristic
82C4×C7×D4—22no—
83C4×C7×D4C2×C414yescomplemented
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C4⋊C4C2311yescharacteristic
87C2×C7×C22⋊C4—21no—
88C2×C42×C7C2311yescharacteristic
89C2×C22⋊Dic7—21no—
90D4×Dic7—22no—
91D4×Dic7C2×C414yescomplemented
92C4×C22⋊D7—28no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4D411yescharacteristic
95C2×(C2×D7)⋊C4D411yescharacteristic
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2311yescharacteristic
100C2×C4⋊Dic7C2311yescharacteristic
101C2×Dic7⋊C4—21no—
102C2×Dic7⋊C4—21no—
103C2×Dic7⋊C4—21no—
104C2×Dic7⋊C4—28no—
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4D411yescharacteristic
109C2×Dic7⋊C4D411yescharacteristic
110C2×C4×Dic7—21no—
111C2×C4×Dic7—21no—
112C2×C4×Dic7—21no—
113C2×C4×Dic7C2311yescharacteristic
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C2×#1131—22no—
117C2×#1131—22no—
118C2×#1131—22no—
119C2×C8×D7—22no—
120C2×C8×D7—22no—
121C2×C8×D7—22no—
122#6455—22no—
123#6455—22no—
124D7×C4⋊C4—22no—
125D7×C4⋊C4—22no—
126D7×C4⋊C4—22no—
127D7×C4⋊C4C2×C414yes—
128#6450—22no—
129#6450C2×C414yescomplemented
130(C22⋊D7)⋊C4—28no—
131#6440—28no—
132#6435C2×C414yes—
133#6435D414yes—
134C4×Dic14—22no—
135C4×Dic14C2×C414yescomplemented
136C7×C4⋊C8—22no—
137C7×#102—22no—
138C7×#102—22no—
139C7×#95—21no—
140C7×#95—21no—
141#6406—22no—
142#6406—22no—
143C7⋊#95—21no—
144C7⋊#95—21no—
145#6390—22no—
146#6390—22no—
147Dic7⋊C8—22no—
148Dic7⋊C8—22no—
149#6384—22no—
150#6384—22no—
151C4⋊(C7⋊C8)—22no—
152C2×#520—71no—
153C2×#424—71no—
154C2×#417—71no—
155C2×#416—71no—
156#2317—71no—
157#1805—71no—
158#1805—71no—
159#1804—71no—
160#1804D711yescharacteristic, complemented
161#1803—71no—
162#1803—71no—
163#1802—71no—
164#1802—71no—
165#1736—71no—
166C2×#340—71no—
167C24×C7—21no—
168C23×D7C2×D411yescharacteristic
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4C22×C412yes—
173C2×C7×D4C2×D412yes—
174C2×C7×D4C2×Q812yes—
175C22×C4×C7—21no—
176C22×C4×C7—24no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—81no—
180C22×C4×C7—81no—
181C22×C4×C7C2×D411yescharacteristic
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2411yescharacteristic
184C2×C22⋊D7—24no—
185C2×C22⋊D7—24no—
186C2×C22⋊D7—24no—
187C22×Dic7—21no—
188C22×Dic7—24no—
189C22×Dic7—24no—
190C22×Dic7—24no—
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
200#1159—28no—
201#1159—28no—
202#1159—28no—
203#1159C4⋊C4116yescomplemented
204C2×C4×D7—24no—
205C2×C4×D7—42no—
206C2×C4×D7—81no—
207C2×C4×D7—81no—
208C2×C4×D7—81no—
209C2×C4×D7—81no—
210C2×C4×D7C22×C412yes—
211C2×C4×D7C2×D412yes—
212C2×C4×D7C2×D412yes—
213C2×C4×D7C2×Q812yes—
214C2×C4×D7#4112yes—
215C2×C4×D7#4112yes—
216C2×Dic14—21no—
217C2×Dic14—21no—
218C2×Dic14—21no—
219C2×Dic14C22×C412yes—
220C2×Dic14C2×D412yes—
221C2×Dic14C2×Q812yes—
222C2×C7×C8—21no—
223C2×C7×C8—21no—
224C2×C7×C8—21no—
225C2×C7×C8—21no—
226C2×C7×C8—21no—
227C2×C7×C8—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4C22×C412yes—
234C7×C22⋊C4—24no—
235C42×C7C22×C412yes—
236C42×C7C2×D412yes—
237C22⋊Dic7—24no—
238(C2×D7)⋊C4—42no—
239(C2×D7)⋊C4C22⋊C414yes—
240(C2×D7)⋊C4C22⋊C414yes—
241C4⋊Dic7—21no—
242C4⋊Dic7—21no—
243C4⋊Dic7—21no—
244C4⋊Dic7—21no—
245C4⋊Dic7—21no—
246C4⋊Dic7—81no—
247C4⋊Dic7—81no—
248C4⋊Dic7C22×C412yes—
249Dic7⋊C4—24no—
250Dic7⋊C4—24no—
251Dic7⋊C4—24no—
252Dic7⋊C4—42no—
253Dic7⋊C4—81no—
254Dic7⋊C4—81no—
255Dic7⋊C4C22⋊C414yes—
256Dic7⋊C4C22⋊C414yes—
257C4×Dic7—24no—
258C4×Dic7—24no—
259C4×Dic7—42no—
260C4×Dic7C22×C412yes—
261C4×Dic7C2×D412yes—
262C2×C7⋊C8—21no—
263C2×C7⋊C8—21no—
264C2×C7⋊C8—21no—
265C2×C7⋊C8—21no—
266C2×C7⋊C8—21no—
267C2×C7⋊C8—21no—
268#1131—44no—
269C8×D7—44no—
270C22×#41—71no—
271C22×M16—71no—
272C23×C8—71no—
273#520—78no—
274#520—144no—
275C2×C4×Q8—71no—
276C2×C4×Q8—71no—
277C2×C4×D4—71no—
278C2×C4×D4—141no—
279C2×C4×D4—141no—
280C2×C4×D4C2×D711yescharacteristic
281C2×#117—71no—
282C2×#117—71no—
283C2×#117—141no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—141no—
287#424—144no—
288C2×C4⋊C8—71no—
289C2×C4⋊C8—71no—
290C2×C4⋊C8—71no—
291C2×C4⋊C8C2×D711yescharacteristic
292#417—144no—
293#416—144no—
294C2×#103—71no—
295C2×#103—71no—
296C2×#103—71no—
297C2×#103—71no—
298C2×#102—71no—
299C2×#102—71no—
300C2×#102C2×D711yescharacteristic
301C2×#102C2×D711yescharacteristic
302#389—141no—
303#389—141no—
304#385—141no—
305#385—141no—
306#384—71no—
307#384—71no—
308#382—71no—
309#382C2×D711yescharacteristic
310#340—71no—
311#340—71no—
312#340—71no—
313#340—71no—
314#340—71no—
315#340—71no—
316#340C2×D711yescharacteristic
317#340C2×D711yescharacteristic
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7C22×D411yescharacteristic
326C22×D7—21no—
327C22×D7—21no—
328C22×D7—21no—
329C22×D7—21no—
330C22×D7C2×C22⋊C412yes—
331C22×D7#12112yes—
332C22×D7C22⋊Q812yes—
333C7×D4—22no—
334C7×D4—22no—
335C7×D4—22no—
336C7×D4C2×C4⋊C414yes—
337C2×C4×C7—21no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
341C2×C4×C7—22no—
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—41no—
349C2×C4×C7—41no—
350C2×C4×C7—84no—
351C2×C4×C7C2×C22⋊C412yes—
352C2×C4×C7C2×C22⋊C412yes—
353C2×C4×C7C23×C411yescharacteristic
354C2×C4×C7C22×D411yescharacteristic
355C2×C4×C7C22×D411yescharacteristic
356C2×C4×C7C22×Q811yescharacteristic
357C2×C4×C7C2×#4111yescharacteristic
358C2×C4×C7C2×#4111yescharacteristic
359C22⋊D7—216no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—21no—
364C2×Dic7—21no—
365C2×Dic7—21no—
366C2×Dic7—21no—
367C2×Dic7—216no—
368C2×Dic7—22no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—84no—
378C2×Dic7C2×C22⋊C412yes—
379C2×Dic7C2×C22⋊C412yes—
380C2×Dic7C2×C22⋊C412yes—
381C2×Dic7#12112yes—
382C2×Dic7C22⋊Q812yes—
383C4×D7—84no—
384C4×D7—84no—
385C4×D7C2×C4⋊C414yes—
386C4×D7#11714yes—
387C4×D7#12114yes—
388C4×D7C22⋊Q814yes—
389Dic14—22no—
390Dic14—22no—
391Dic14—22no—
392Dic14C2×C4⋊C414yes—
393C7×C8—41no—
394C7×C8—41no—
395C7⋊C8—41no—
396C7⋊C8—41no—
397C2×#41—74no—
398C2×#41—74no—
399C2×#41—74no—
400C2×#41—142no—
401C2×#41—142no—
402C2×#41—142no—
403C22×Q8—71no—
404C22×D4—141no—
405C22×D4C22×D711yescharacteristic
406C23×C4—21no—
407C23×C4—71no—
408C23×C4—141no—
409C23×C4—141no—
410C23×C4—141no—
411C23×C4—141no—
412C2×M16—142no—
413C2×M16—142no—
414C2×M16—142no—
415C22×C8—71no—
416C22×C8—71no—
417C22×C8—142no—
418C22×C8—142no—
419C22×C8—142no—
420C22×C8C22×D711yescharacteristic
421C22×C8C22×D711yescharacteristic
422C4×Q8—74no—
423C4×Q8—74no—
424C4×Q8—142no—
425C4×Q8—142no—
426C4×D4—22no—
427C4×D4—74no—
428C4×D4—142no—
429C4×D4—148no—
430C4×D4—148no—
431C4×D4C4×D714yescomplemented
432#117—74no—
433#117—74no—
434#117—148no—
435#117—142no—
436#117—142no—
437C2×C4⋊C4—71no—
438C2×C4⋊C4—71no—
439C2×C4⋊C4—71no—
440C2×C4⋊C4—74no—
441C2×C4⋊C4—71no—
442C2×C4⋊C4—71no—
443C2×C4⋊C4—142no—
444C2×C4⋊C4—142no—
445C2×C4⋊C4—142no—
446C2×C4⋊C4—148no—
447C2×C4⋊C4—141no—
448C2×C4⋊C4—141no—
449C2×C4⋊C4—141no—
450C2×C4⋊C4—141no—
451C2×C4⋊C4—141no—
452C2×C4⋊C4—141no—
453C2×C4⋊C4—141no—
454C2×C4⋊C4—141no—
455C2×C4⋊C4C22×D711yescharacteristic
456C2×C4⋊C4C22×D711yescharacteristic
457C2×C4⋊C4C22×D711yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—71no—
460C2×C22⋊C4—71no—
461C2×C22⋊C4—141no—
462C2×C22⋊C4—141no—
463C2×C42—71no—
464C2×C42—141no—
465C2×C42—141no—
466C2×C42—141no—
467C2×C42C22×D711yescharacteristic
468C4⋊C8—22no—
469C4⋊C8—142no—
470C4⋊C8—142no—
471C4⋊C8—142no—
472#103—142no—
473#103—142no—
474#103—142no—
475#103—142no—
476#102—22no—
477#102—22no—
478#102—142no—
479#102—142no—
480#95—21no—
481#95—21no—
482#95—141no—
483#95—141no—
484C22×C7—24no—
485C22×C7—42no—
486C22×C7—42no—
487C22×C7—42no—
488C22×C7—42no—
489C22×C7—42no—
490C22×C7—42no—
491C22×C7C22×C22⋊C411yescharacteristic
492C22×C7C2×#12111yescharacteristic
493C22×C7C2×C22⋊Q811yescharacteristic
494C22×C7#57611yescharacteristic
495C22×C7#57711yescharacteristic
496C22×C7#57711yescharacteristic
497C22×C7#57811yescharacteristic
498C2×D7—22no—
499C2×D7—22no—
500C2×D7—22no—
501C2×D7—22no—
502C2×D7—22no—
503C2×D7—22no—
504C2×D7#38014yes—
505C4×C7—22no—
506C4×C7—22no—
507C4×C7—42no—
508C4×C7—81no—
509C4×C7—81no—
510C4×C7C22×C4⋊C411yescharacteristic
511C4×C7C2×#11711yescharacteristic
512C4×C7C2×#12111yescharacteristic
513C4×C7C2×C22⋊Q811yescharacteristic
514Dic7—22no—
515Dic7—22no—
516Dic7—24no—
517Dic7—42no—
518Dic7—81no—
519Dic7—81no—
520Dic7#38014yes—
521C24—21no—
522C24—71no—
523#41—716no—
524#41—148no—
525#41—148no—
526#41—148no—
527C2×Q8—72no—
528C2×Q8—72no—
529C2×Q8—72no—
530C2×Q8—141no—
531C2×Q8—141no—
532C2×Q8—141no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—144no—
537C2×D4—144no—
538C2×D4—144no—
539C2×D4C2×C4×D712yes—
540C2×D4D4×D712yes—
541C2×D4Q8×D712yes—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—71no—
547C22×C4—72no—
548C22×C4—72no—
549C22×C4—72no—
550C22×C4—72no—
551C22×C4—72no—
552C22×C4—72no—
553C22×C4—71no—
554C22×C4—71no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—144no—
558C22×C4—144no—
559C22×C4—144no—
560C22×C4—144no—
561C22×C4—144no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—282no—
567C22×C4—561no—
568C22×C4—561no—
569C22×C4—561no—
570C22×C4—561no—
571C22×C4—561no—
572C22×C4—561no—
573C22×C4D4×D711yescharacteristic
574C22×C4D4×D711yescharacteristic
575C22×C4C23×D711yescharacteristic
576M16—284no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—141no—
584C2×C8—141no—
585C2×C8—141no—
586C2×C8—141no—
587C2×C8—141no—
588C2×C8—141no—
589C2×C8—284no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—74no—
596C4⋊C4—74no—
597C4⋊C4—72no—
598C4⋊C4—144no—
599C4⋊C4—144no—
600C4⋊C4—144no—
601C4⋊C4—141no—
602C4⋊C4—141no—
603C4⋊C4—141no—
604C4⋊C4—141no—
605C4⋊C4—141no—
606C4⋊C4—282no—
607C4⋊C4—561no—
608C4⋊C4—561no—
609C4⋊C4—561no—
610C4⋊C4—561no—
611C4⋊C4C2×C4×D712yes—
612C22⋊C4—24no—
613C22⋊C4—74no—
614C22⋊C4—74no—
615C22⋊C4—144no—
616C22⋊C4—282no—
617C42—72no—
618C42—72no—
619C42—144no—
620C42—144no—
621C42—282no—
622C42C2×C4×D712yes—
623C42D4×D712yes—
624C2×C7—44no—
625C2×C7C2×#38011yescharacteristic
626C2×C7#289711yescharacteristic
627C2×C7#289811yescharacteristic
628C2×C7#304511yescharacteristic
629C2×C7#304611yescharacteristic
630C2×C7#308311yescharacteristic
631C2×C7#308411yescharacteristic
632D7—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—72no—
641C23—72no—
642C23—72no—
643C23—141no—
644C23—141no—
645C23—141no—
646C23—141no—
647C23C2×D4×D711yescharacteristic
648Q8—74no—
649Q8—142no—
650Q8—142no—
651Q8—142no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—1416no—
656D4D7×C4⋊C414yes—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
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—41no—
670C2×C4—72no—
671C2×C4—72no—
672C2×C4—72no—
673C2×C4—74no—
674C2×C4—74no—
675C2×C4—74no—
676C2×C4—74no—
677C2×C4—72no—
678C2×C4—72no—
679C2×C4—84no—
680C2×C4—1416no—
681C2×C4—142no—
682C2×C4—141no—
683C2×C4—141no—
684C2×C4—141no—
685C2×C4—141no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—281no—
690C2×C4—281no—
691C2×C4—281no—
692C2×C4—281no—
693C2×C4—281no—
694C2×C4—281no—
695C2×C4—281no—
696C2×C4—281no—
697C2×C4—564no—
698C2×C4—564no—
699C2×C4—564no—
700C2×C4D7×C22⋊C412yes—
701C2×C4D7×C22⋊C412yes—
702C2×C4C22×C4×D711yescharacteristic
703C2×C4C2×D4×D711yescharacteristic
704C2×C4C2×D4×D711yescharacteristic
705C2×C4C2×Q8×D711yescharacteristic
706C2×C4D7×#4111yescharacteristic
707C2×C4D7×#4111yescharacteristic
708C8—41no—
709C8—41no—
710C8—281no—
711C8—281no—
712C7#2065211yescharacteristic, complemented, Sylow
713C22—24no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—74no—
721C22—142no—
722C22—142no—
723C22—142no—
724C22—142no—
725C22—142no—
726C22—142no—
727C22C2×D7×C22⋊C411yescharacteristic
728C22D7×#12111yescharacteristic
729C22D7×C22⋊Q811yescharacteristic
730C22#9046111yescharacteristic
731C22#9046211yescharacteristic
732C22#9046511yescharacteristic
733C22#9046611yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—74no—
738C4—81no—
739C4—81no—
740C4—142no—
741C4—142no—
742C4—144no—
743C4—282no—
744C4—561no—
745C4—561no—
746C4C2×D7×C4⋊C411yescharacteristic
747C4D7×#11711yescharacteristic
748C4D7×#12111yescharacteristic
749C4D7×C22⋊Q811yescharacteristic
750C2—44no—
751C2—144no—
752C2D7×#38011yescharacteristic
753C2#1173627711yescharacteristic
754C2#1173637011yescharacteristic
755C2#1173798311yescharacteristic
756C2#1173798411yescharacteristic
757C2#1173861511yescharacteristic
758C2#1173861611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1804C2
socleC23×C7C22×D4
prime radicalC22×#1159C22
cosocleC22×C4×C7C24
hypercenter#1804D7
hypocenterC7#20652
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#89611C2semidirect
5. #11731670C2semidirect
6. C7×#1804C2semidirect
7. #11729358C2semidirect
8. #11728239C2semidirect
9. #11727908C2semidirect
10. #11727907C2semidirect
11. #11727313C2semidirect
12. #11726659C2semidirect
13. #11726658C2semidirect
14. #11726621C2semidirect
15. D7×#340C2semidirect
24. #90237C4semidirect
83. C4×C7×D4C2×C4semidirect
91. D4×Dic7C2×C4semidirect
129. #6450C2×C4semidirect
135. C4×Dic14C2×C4semidirect
160. #1804D7semidirect
203. #1159C4⋊C4semidirect
431. C4×D4C4×D7semidirect
712. C7#20652semidirect

Maximal subgroups

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

subgroupindex
C2×#902372
C2×#896112
C2×#895432
C2×#895442
#117316702
C7×#18042
#117293582
#117282392
#117279082
#117279072
#117273132
#117266592
#117266582
#117266212
D7×#3402
#206527