Finite Group Databasebeta

← #13354571

Subgroups — #13354571

Order 1792.

1462 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90195C211yesmaximal, characteristic
2C2×#89633C211yesmaximal, characteristic, complemented
3C2×#89632C211yesmaximal, characteristic, complemented
4C2×#89499C211yesmaximal, characteristic
5#11731448C211yesmaximal, characteristic
6C7×#1853C211yesmaximal, characteristic, complemented
7#11729309C211yesmaximal, characteristic, complemented
8#11728334C211yesmaximal, characteristic, complemented
9#11728333C211yesmaximal, characteristic, complemented
10#11727683C211yesmaximal, characteristic, complemented
11#11727260C211yesmaximal, characteristic, complemented
12#11726630C211yesmaximal, characteristic, complemented
13#11726628C211yesmaximal, characteristic, complemented
14#11726621C211yesmaximal, characteristic, complemented
15D7×#340C211yesmaximal, characteristic, complemented
16C22×#1157C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C2×C4×C22⋊D7—21no—
19C2×C4×C22⋊D7—21no—
20C2×#6489C2211yescharacteristic
21C22×#1131C2211yescharacteristic
22C22×C8×D7C2211yescharacteristic
23#90195—24no—
24#90195—24no—
25C2×#6456—21no—
26C2×#6455C2211yescharacteristic
27C2×#6455C2211yescharacteristic
28C2×#6455C2211yescharacteristic
29C2×D7×C4⋊C4C2211yescharacteristic
30C2×D7×C4⋊C4C2211yescharacteristic
31C2×D7×C4⋊C4C2211yescharacteristic
32C2×#6450—21no—
33C2×C7×#106C2211yescharacteristic
34C2×C7×#106C2211yescharacteristic
35C2×C7×C22⋊C8C2211yescharacteristic
36C7×#380C2211yescharacteristic
37#89984C2211yescharacteristic
38C2×C22⋊(C7⋊C8)C2211yescharacteristic
39C2×(C2×D7)⋊C8C2211yescharacteristic
40C2×(C2×D7)⋊C8C2211yescharacteristic
41C2×#6392C2211yescharacteristic
42C2×#6391C2211yescharacteristic
43#89759C2211yescharacteristic
44#89759C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47C2×#6381C2211yescharacteristic
48C2×#6381C2211yescharacteristic
49#89729—21no—
50#89728—21no—
51#89633—24no—
52#89632—24no—
53#89499C418yescomplemented
54#89437—21no—
55#89418—21no—
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#89324C2211yescharacteristic
63#89324C2211yescharacteristic
64#20849—71nomaximal, Sylow
65C23×C4×C7—21no—
66C23×C4×C7C2311yescharacteristic
67C22×C22⋊D7D411yescharacteristic
68C22×C22⋊D7D411yescharacteristic
69C2×#1157—22no—
70C2×#1157—22no—
71C2×#1157—22no—
72C2×#1157—22no—
73C2×#1157C2×C414yes—
74C2×#1157Q814yes—
75C22×D28D411yescharacteristic
76C22×C4×D7—21no—
77C22×C4×D7—21no—
78C22×C4×D7—21no—
79C22×C4×D7C2311yescharacteristic
80C22×C4×D7C2311yescharacteristic
81C22×Dic14D411yescharacteristic
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4C2311yescharacteristic
88C2×C7×C4⋊C4C2311yescharacteristic
89C2×C7×C4⋊C4C2311yescharacteristic
90C2×C7×C4⋊C4C2311yescharacteristic
91C2×C7×C22⋊C4—21no—
92C2×C22⋊Dic7—21no—
93C2×C22⋊Dic7—21no—
94C4×C22⋊D7—28no—
95C4×C22⋊D7—28no—
96C2×(C2×D7)⋊C4—21no—
97C2×(C2×D7)⋊C4—21no—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—21no—
100C2×(C2×D7)⋊C4—21no—
101#6489—22no—
102#6489—22no—
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×C4×Dic7—21no—
111C2×C4×Dic7—21no—
112C2×C4×Dic7—21no—
113C2×C4×Dic7—21no—
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C2×#1131—22no—
117C2×#1131—22no—
118C2×#1131C2×C414yescomplemented
119C2×C8×D7—22no—
120C2×C8×D7—22no—
121C2×C8×D7C2×C414yescomplemented
122#6456—28no—
123#6455—22no—
124#6455—22no—
125#6455—22no—
126#6455—22no—
127#6455—22no—
128#6455D414yes—
129D7×C4⋊C4—22no—
130D7×C4⋊C4—22no—
131D7×C4⋊C4—22no—
132D7×C4⋊C4—22no—
133D7×C4⋊C4—22no—
134D7×C4⋊C4D414yes—
135#6450—28no—
136C7×#106—22no—
137C7×#106—22no—
138C7×C22⋊C8C2×C414yescomplemented
139C7×#95—21no—
140C7⋊#95—21no—
141C7⋊#95—21no—
142C7⋊#95—21no—
143C22⋊(C7⋊C8)C2×C414yescomplemented
144(C2×D7)⋊C8C2×C414yescomplemented
145(C2×D7)⋊C8C2×C414yescomplemented
146#6392—22no—
147#6391—22no—
148#6382—22no—
149#6381—22no—
150#6381—22no—
151#6381—22no—
152C2×#520—71no—
153C2×#428—71no—
154C2×#427—71no—
155C2×#408—71no—
156#2311—71no—
157#1854—71no—
158#1854—71no—
159#1854—71no—
160#1854—71no—
161#1853—71no—
162#1853D711yescharacteristic, complemented
163#1852—71no—
164#1852—71no—
165#1736—71no—
166C2×#340—71no—
167C24×C7C2×D411yescharacteristic
168C23×D7C2×D411yescharacteristic
169C23×D7C2×D411yescharacteristic
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—24no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—81no—
180C22×C4×C7—81no—
181C22×C4×C7C22×C412yes—
182C22×C4×C7C2×D411yescharacteristic
183C22×C4×C7C2×Q812yes—
184C22×C4×C7C2411yescharacteristic
185C2×C22⋊D7—22no—
186C2×C22⋊D7—22no—
187C2×C22⋊D7—22no—
188C2×C22⋊D7—22no—
189C2×C22⋊D7C4⋊C414yes—
190C2×C22⋊D7C4⋊C414yes—
191C22×Dic7—21no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7C2×D411yescharacteristic
196C22×Dic7C2×D411yescharacteristic
197#1157—28no—
198#1157—28no—
199#1157—28no—
200#1157—28no—
201C2×D28—22no—
202C2×D28—22no—
203C2×D28C4⋊C414yes—
204C2×C4×D7—21no—
205C2×C4×D7—21no—
206C2×C4×D7—21no—
207C2×C4×D7—21no—
208C2×C4×D7—24no—
209C2×C4×D7—24no—
210C2×C4×D7—42no—
211C2×C4×D7—81no—
212C2×C4×D7—81no—
213C2×C4×D7—81no—
214C2×C4×D7—81no—
215C2×C4×D7—81no—
216C2×C4×D7—81no—
217C2×C4×D7C22×C412yes—
218C2×C4×D7C22×C412yes—
219C2×C4×D7C2×D412yes—
220C2×C4×D7C2×D412yes—
221C2×C4×D7C2×Q812yes—
222C2×C4×D7C2×Q812yes—
223C2×C4×D7#4112yes—
224C2×C4×D7#4112yes—
225C2×Dic14—22no—
226C2×Dic14—22no—
227C2×Dic14C4⋊C414yes—
228C2×C7×C8—21no—
229C2×C7×C8—21no—
230C2×C7×C8—21no—
231C2×C7×C8—21no—
232C2×C7×C8C22×C412yes—
233C2×C7×C8C22×C412yes—
234C7×C4⋊C4—24no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—21no—
238C7×C4⋊C4—21no—
239C7×C4⋊C4—21no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4C2×D412yes—
242C7×C4⋊C4C2×D412yes—
243C7×C22⋊C4—81no—
244C22⋊Dic7—24no—
245C22⋊Dic7—81no—
246(C2×D7)⋊C4—24no—
247(C2×D7)⋊C4—24no—
248(C2×D7)⋊C4—42no—
249(C2×D7)⋊C4—81no—
250(C2×D7)⋊C4—81no—
251C4⋊Dic7—21no—
252C4⋊Dic7—21no—
253C4⋊Dic7—21no—
254C4⋊Dic7—21no—
255C4⋊Dic7—21no—
256C4⋊Dic7—21no—
257C4⋊Dic7C2×D412yes—
258C4⋊Dic7C2×D412yes—
259Dic7⋊C4—24no—
260Dic7⋊C4—24no—
261Dic7⋊C4—42no—
262C4×Dic7—24no—
263C4×Dic7—24no—
264C4×Dic7—24no—
265C4×Dic7—42no—
266C2×C7⋊C8—21no—
267C2×C7⋊C8—21no—
268C2×C7⋊C8—21no—
269C2×C7⋊C8—21no—
270C2×C7⋊C8C22×C412yes—
271C2×C7⋊C8C22×C412yes—
272#1131—28no—
273C8×D7—28no—
274C22×#41—71no—
275C22×M16—71no—
276C23×C8—71no—
277#520—144no—
278#520—144no—
279C2×C4×Q8—141no—
280C2×C4×D4—141no—
281C2×C4×D4—141no—
282C2×C4×D4—141no—
283C2×#117—71no—
284C2×#117—71no—
285C2×#117—71no—
286C2×#117—71no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4—71no—
289C22×C4⋊C4—71no—
290C22×C4⋊C4C2×D711yescharacteristic
291#428—144no—
292#427—144no—
293C2×#107—71no—
294C2×#107—71no—
295C2×#107—71no—
296C2×#107—71no—
297C2×#106—71no—
298C2×#106—71no—
299C2×#106C2×D711yescharacteristic
300C2×#106C2×D711yescharacteristic
301#408—78no—
302C2×C22⋊C8—71no—
303C2×C22⋊C8—71no—
304C2×C22⋊C8—71no—
305C2×C22⋊C8C2×D711yescharacteristic
306#391—141no—
307#390—141no—
308#386—141no—
309#386—141no—
310#380—71no—
311#380—71no—
312#380—71no—
313#380C2×D711yescharacteristic
314#340—71no—
315#340—71no—
316#340—71no—
317#340—71no—
318#340—71no—
319#340—71no—
320#340C2×D711yescharacteristic
321#340C2×D711yescharacteristic
322C23×C7—21no—
323C23×C7—21no—
324C23×C7—21no—
325C23×C7—21no—
326C23×C7—21no—
327C23×C7—21no—
328C23×C7C2×C4⋊C412yes—
329C23×C7C22×D411yescharacteristic
330C22×D7—21no—
331C22×D7—21no—
332C22×D7—21no—
333C22×D7—21no—
334C22×D7—21no—
335C22×D7—21no—
336C22×D7—21no—
337C22×D7—21no—
338C22×D7—21no—
339C22×D7—21no—
340C22×D7C2×C4⋊C412yes—
341C22×D7C2×C4⋊C412yes—
342C22×D7#12012yes—
343C22×D7#12312yes—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
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—41no—
361C2×C4×C7—41no—
362C2×C4×C7—84no—
363C2×C4×C7C2×C4⋊C412yes—
364C2×C4×C7C23×C411yescharacteristic
365C2×C4×C7C22×D411yescharacteristic
366C2×C4×C7C22×D411yescharacteristic
367C2×C4×C7C22×Q811yescharacteristic
368C2×C4×C7C2×#4111yescharacteristic
369C2×C4×C7C2×#4111yescharacteristic
370C22⋊D7—28no—
371C22⋊D7—28no—
372C2×Dic7—21no—
373C2×Dic7—21no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—41no—
386C2×Dic7C2×C4⋊C412yes—
387C2×Dic7C2×C4⋊C412yes—
388C2×Dic7#12012yes—
389C2×Dic7#12312yes—
390D28—28no—
391C4×D7—22no—
392C4×D7—22no—
393C4×D7—22no—
394C4×D7—22no—
395C4×D7—84no—
396C4×D7—84no—
397C4×D7—84no—
398C4×D7C4×D414yes—
399C4×D7C4×D414yes—
400C4×D7C22⋊Q814yes—
401C4×D7C22⋊Q814yes—
402Dic14—28no—
403C7×C8—22no—
404C7×C8—22no—
405C7⋊C8—22no—
406C7⋊C8—22no—
407C2×#41—74no—
408C2×#41—74no—
409C2×#41—142no—
410C2×#41—142no—
411C2×#41—142no—
412C2×#41—142no—
413C22×Q8—71no—
414C22×D4—71no—
415C22×D4—71no—
416C22×D4—71no—
417C23×C4—21no—
418C23×C4—71no—
419C23×C4—71no—
420C23×C4—141no—
421C23×C4—141no—
422C23×C4—141no—
423C23×C4C22×D711yescharacteristic
424C2×M16—74no—
425C2×M16—142no—
426C2×M16—142no—
427C22×C8—71no—
428C22×C8—71no—
429C22×C8—74no—
430C22×C8—142no—
431C22×C8—142no—
432C22×C8C22×D711yescharacteristic
433C22×C8C22×D711yescharacteristic
434C4×Q8—148no—
435C4×D4—148no—
436C4×D4—148no—
437C4×D4—148no—
438#117—74no—
439#117—142no—
440#117—142no—
441#117—142no—
442#117—142no—
443#117—142no—
444#117—142no—
445#117—142no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—71no—
450C2×C4⋊C4—71no—
451C2×C4⋊C4—74no—
452C2×C4⋊C4—71no—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—142no—
455C2×C4⋊C4—142no—
456C2×C4⋊C4—142no—
457C2×C4⋊C4—142no—
458C2×C4⋊C4—141no—
459C2×C4⋊C4—141no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—141no—
462C2×C4⋊C4C22×D711yescharacteristic
463C2×C4⋊C4C22×D711yescharacteristic
464C2×C4⋊C4C22×D711yescharacteristic
465C2×C4⋊C4C22×D711yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—141no—
468C2×C22⋊C4—141no—
469C2×C22⋊C4—141no—
470C2×C22⋊C4—141no—
471C2×C22⋊C4—141no—
472C2×C22⋊C4—141no—
473C2×C22⋊C4—141no—
474C2×C42—141no—
475C2×C42—141no—
476C2×C42—141no—
477C2×C42—141no—
478#107—142no—
479#107—142no—
480#107—142no—
481#107—142no—
482#106—22no—
483#106—22no—
484#106—142no—
485#106—142no—
486C22⋊C8—74no—
487C22⋊C8—74no—
488C22⋊C8—74no—
489C22⋊C8C4×D714yescomplemented
490#95—21no—
491#95—141no—
492#95—141no—
493#95—141no—
494C22×C7—22no—
495C22×C7—22no—
496C22×C7—22no—
497C22×C7—41no—
498C22×C7—41no—
499C22×C7—41no—
500C22×C7—41no—
501C22×C7C22×C4⋊C411yescharacteristic
502C22×C7C2×#12011yescharacteristic
503C22×C7C2×#12311yescharacteristic
504C22×C7#57611yescharacteristic
505C22×C7#57711yescharacteristic
506C22×C7#57711yescharacteristic
507C22×C7#57811yescharacteristic
508C2×D7—22no—
509C2×D7—22no—
510C2×D7—22no—
511C2×D7—22no—
512C2×D7—22no—
513C2×D7—22no—
514C2×D7—22no—
515C2×D7—22no—
516C2×D7—22no—
517C2×D7—41no—
518C2×D7—41no—
519C2×D7—41no—
520C2×D7—41no—
521C2×D7#38514yes—
522C4×C7—22no—
523C4×C7—42no—
524C4×C7—42no—
525C4×C7—81no—
526C4×C7—81no—
527C4×C7C2×C4×D411yescharacteristic
528C4×C7C2×C4×D411yescharacteristic
529C4×C7C2×C22⋊Q811yescharacteristic
530C4×C7C2×C22⋊Q811yescharacteristic
531Dic7—22no—
532Dic7—42no—
533Dic7—42no—
534Dic7—81no—
535Dic7—81no—
536Dic7#38514yes—
537C24—71no—
538C24—71no—
539C24D4×D711yescharacteristic
540#41—148no—
541#41—148no—
542#41—148no—
543#41—148no—
544C2×Q8—74no—
545C2×Q8—142no—
546C2×Q8—142no—
547C2×D4—74no—
548C2×D4—74no—
549C2×D4—74no—
550C2×D4—142no—
551C2×D4—142no—
552C2×D4—142no—
553C2×D4—142no—
554C2×D4—142no—
555C2×D4—142no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—71no—
566C22×C4—72no—
567C22×C4—72no—
568C22×C4—72no—
569C22×C4—72no—
570C22×C4—72no—
571C22×C4—72no—
572C22×C4—71no—
573C22×C4—72no—
574C22×C4—72no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—144no—
578C22×C4—144no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—282no—
588C22×C4—561no—
589C22×C4—561no—
590C22×C4—561no—
591C22×C4—561no—
592C22×C4—561no—
593C22×C4—561no—
594C22×C4C2×C4×D712yes—
595C22×C4D4×D711yescharacteristic
596C22×C4Q8×D712yes—
597C22×C4C23×D711yescharacteristic
598M16—148no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—72no—
604C2×C8—72no—
605C2×C8—148no—
606C2×C8—141no—
607C2×C8—141no—
608C2×C8—141no—
609C2×C8—141no—
610C2×C8C2×C4×D712yes—
611C2×C8C2×C4×D712yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—72no—
620C4⋊C4—72no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—141no—
624C4⋊C4—141no—
625C4⋊C4—141no—
626C4⋊C4—141no—
627C4⋊C4—141no—
628C4⋊C4—141no—
629C4⋊C4—282no—
630C4⋊C4D4×D712yes—
631C4⋊C4D4×D712yes—
632C22⋊C4—81no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—282no—
637C22⋊C4—561no—
638C22⋊C4—561no—
639C22⋊C4—561no—
640C42—144no—
641C42—144no—
642C42—144no—
643C42—282no—
644C2×C7—42no—
645C2×C7C2×#38511yescharacteristic
646C2×C7#291211yescharacteristic
647C2×C7#291311yescharacteristic
648C2×C7#301211yescharacteristic
649C2×C7#301311yescharacteristic
650C2×C7#309611yescharacteristic
651C2×C7#309711yescharacteristic
652D7—24no—
653D7—42no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—72no—
661C23—72no—
662C23—72no—
663C23—72no—
664C23—141no—
665C23—141no—
666C23—141no—
667C23—141no—
668C23—141no—
669C23—141no—
670C23—141no—
671C23—141no—
672C23—141no—
673C23—141no—
674C23D7×C4⋊C412yes—
675C23C2×D4×D711yescharacteristic
676Q8—148no—
677D4—148no—
678D4—148no—
679D4—148no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—72no—
699C2×C4—72no—
700C2×C4—72no—
701C2×C4—74no—
702C2×C4—74no—
703C2×C4—74no—
704C2×C4—74no—
705C2×C4—72no—
706C2×C4—84no—
707C2×C4—141no—
708C2×C4—141no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—281no—
716C2×C4—281no—
717C2×C4—281no—
718C2×C4—281no—
719C2×C4—281no—
720C2×C4—281no—
721C2×C4—281no—
722C2×C4—281no—
723C2×C4—281no—
724C2×C4—281no—
725C2×C4—564no—
726C2×C4—564no—
727C2×C4—564no—
728C2×C4D7×C4⋊C412yes—
729C2×C4C22×C4×D711yescharacteristic
730C2×C4C2×D4×D711yescharacteristic
731C2×C4C2×D4×D711yescharacteristic
732C2×C4C2×Q8×D711yescharacteristic
733C2×C4D7×#4111yescharacteristic
734C2×C4D7×#4111yescharacteristic
735C8—22no—
736C8—22no—
737C8—142no—
738C8—142no—
739C7#2084911yescharacteristic, complemented, Sylow
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—74no—
748C22—142no—
749C22—142no—
750C22—142no—
751C22—142no—
752C22—142no—
753C22—142no—
754C22—142no—
755C22—142no—
756C22—142no—
757C22—281no—
758C22—281no—
759C22—281no—
760C22—281no—
761C22C2×D7×C4⋊C411yescharacteristic
762C22D7×#12011yescharacteristic
763C22D7×#12311yescharacteristic
764C22#9045311yescharacteristic
765C22#9045311yescharacteristic
766C22#9046511yescharacteristic
767C22#9047011yescharacteristic
768C4—22no—
769C4—42no—
770C4—42no—
771C4—74no—
772C4—81no—
773C4—81no—
774C4—142no—
775C4—282no—
776C4—282no—
777C4—561no—
778C4—561no—
779C4C4×D4×D711yescharacteristic
780C4C4×D4×D711yescharacteristic
781C4D7×C22⋊Q811yescharacteristic
782C4D7×C22⋊Q811yescharacteristic
783C2—42no—
784C2—144no—
785C2—282no—
786C2D7×#38511yescharacteristic
787C2#1173656111yescharacteristic
788C2#1173665511yescharacteristic
789C2#1173748711yescharacteristic
790C2#1173759411yescharacteristic
791C2#1173877211yescharacteristic
792C2#1173887411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1853C2
socleC23×C7C22×D4
prime radicalC22×#1157C22
cosocleC22×C4×C7C24
hypercenter#1853D7
hypocenterC7#20849
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C2×#89633C2semidirect
3. C2×#89632C2semidirect
6. C7×#1853C2semidirect
7. #11729309C2semidirect
8. #11728334C2semidirect
9. #11728333C2semidirect
10. #11727683C2semidirect
11. #11727260C2semidirect
12. #11726630C2semidirect
13. #11726628C2semidirect
14. #11726621C2semidirect
15. D7×#340C2semidirect
53. #89499C4semidirect
118. C2×#1131C2×C4semidirect
121. C2×C8×D7C2×C4semidirect
138. C7×C22⋊C8C2×C4semidirect
143. C22⋊(C7⋊C8)C2×C4semidirect
144. (C2×D7)⋊C8C2×C4semidirect
145. (C2×D7)⋊C8C2×C4semidirect
162. #1853D7semidirect
489. C22⋊C8C4×D7semidirect
739. C7#20849semidirect

Maximal subgroups

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

subgroupindex
C2×#901952
C2×#896332
C2×#896322
C2×#894992
#117314482
C7×#18532
#117293092
#117283342
#117283332
#117276832
#117272602
#117266302
#117266282
#117266212
D7×#3402
#208497