Finite Group Databasebeta

← #31925867

Subgroups — #31925867

Order 18176.

2118 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×#17985901C211yesmaximal, characteristic
2C2×#17985877C212yesmaximal
3C2×#17985873C212yesmaximal, complemented
4C2×#17985870C212yesmaximal, complemented
5#22586592C212yesmaximal, complemented
6#22586586C212yesmaximal, complemented
7#22586582C212yesmaximal, complemented
8#22586570C211yesmaximal, characteristic, complemented
9C71×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D284C2211yescharacteristic
11C23×C4×D71C2212yes—
12C22×C4⋊Dic71C2211yescharacteristic
13C22×C4⋊Dic71C2211yescharacteristic
14C22×C4⋊Dic71C2211yescharacteristic
15C22×Dic71⋊C4C2212yes—
16C22×(C2×D71)⋊C4C2212yes—
17C22×(C2×D71)⋊C4C2212yes—
18C22×(C2×D71)⋊C4C2212yes—
19C22×(C2×D71)⋊C4C2212yes—
20C22×(C2×D71)⋊C4C2212yes—
21#17985901C418yescomplemented
22#17985877—28no—
23#17985873—28no—
24#17985870—28no—
25C2×C71⋊#95C2212yes—
26C2×C71⋊#95C2212yes—
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C22×C4⋊C4×C71C2211yescharacteristic
31C22×C4⋊C4×C71C2211yescharacteristic
32C22×C42×C71C2211yescharacteristic
33C2×#95×C71C2212yes—
34C2×#95×C71C2212yes—
35C24×D71C2312yes—
36C22×D284—41no—
37C22×D284—41no—
38C22×D284—41no—
39C22×D284—41no—
40C22×D284C2×C414yes—
41C22×D284D414yes—
42C22×D284Q814yes—
43C23×Dic71C2312yes—
44C23×Dic71C2312yes—
45C23×Dic71C2312yes—
46C22×C4×D71—24no—
47C22×C4×D71—24no—
48C22×C4×D71—24no—
49C22×C4×D71—42no—
50C22×C4×D71—42no—
51C22×C4×D71—42no—
52C22×C4×D71—42no—
53C2×C4⋊Dic71—22no—
54C2×C4⋊Dic71—41no—
55C2×C4⋊Dic71—41no—
56C2×C4⋊Dic71—41no—
57C2×C4⋊Dic71—41no—
58C2×C4⋊Dic71—41no—
59C2×C4⋊Dic71—41no—
60C2×C4⋊Dic71C2×C414yescomplemented
61C2×C4⋊Dic71D414yescomplemented
62C2×Dic71⋊C4—24no—
63C2×Dic71⋊C4—24no—
64C2×Dic71⋊C4—42no—
65C2×(C2×D71)⋊C4—24no—
66C2×(C2×D71)⋊C4—24no—
67C2×(C2×D71)⋊C4—24no—
68C2×(C2×D71)⋊C4—24no—
69C2×(C2×D71)⋊C4—24no—
70C2×(C2×D71)⋊C4—24no—
71C2×(C2×D71)⋊C4—24no—
72C2×(C2×D71)⋊C4—24no—
73C2×(C2×D71)⋊C4—24no—
74C2×(C2×D71)⋊C4—42no—
75C2×(C2×D71)⋊C4—42no—
76C2×(C2×D71)⋊C4—42no—
77C2×(C2×D71)⋊C4—42no—
78C2×(C2×D71)⋊C4C2×C418yescomplemented
79C2×(C2×D71)⋊C4C2×C418yescomplemented
80C71⋊#95—24no—
81C71⋊#95—24no—
82C71⋊#95—24no—
83C71⋊#95—24no—
84C71⋊#95—42no—
85C23×C4×C71C2312yes—
86C23×C4×C71C2312yes—
87C23×C4×C71C2311yescharacteristic
88C23×C4×C71C2311yescharacteristic
89C23×C4×C71C2311yescharacteristic
90C2×C4⋊C4×C71—22no—
91C2×C4⋊C4×C71—41no—
92C2×C4⋊C4×C71—41no—
93C2×C4⋊C4×C71—41no—
94C2×C4⋊C4×C71—41no—
95C2×C4⋊C4×C71D414yescomplemented
96C2×C42×C71—41no—
97C2×C42×C71—41no—
98C2×C42×C71C2×C414yescomplemented
99#95×C71—24no—
100#95×C71—24no—
101C23×D71—22no—
102C23×D71—22no—
103C23×D71—22no—
104C23×D71—22no—
105C23×D71—22no—
106C23×D71—22no—
107C23×D71—22no—
108C23×D71—22no—
109C23×D71—22no—
110C23×D71—22no—
111C23×D71—22no—
112C23×D71—22no—
113C23×D71C22×C414yes—
114C23×D71C2×D414yes—
115C23×D71C2×Q814yes—
116C2×D284—44no—
117C2×D284—44no—
118C2×D284—44no—
119C2×D284—44no—
120C2×D284—44no—
121C2×D284—44no—
122C2×D284C4⋊C4116yescomplemented
123C22×Dic71—22no—
124C22×Dic71—22no—
125C22×Dic71—22no—
126C22×Dic71—22no—
127C22×Dic71—22no—
128C22×Dic71—22no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71—22no—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71—22no—
142C22×Dic71C22×C414yes—
143C22×Dic71C2×D414yes—
144C2×C4×D71—48no—
145C2×C4×D71—48no—
146C2×C4×D71—48no—
147C2×C4×D71—48no—
148C2×C4×D71—48no—
149C2×C4×D71—48no—
150C2×C4×D71—48no—
151C4⋊Dic71—44no—
152C4⋊Dic71—44no—
153C4⋊Dic71—44no—
154Dic71⋊C4—48no—
155(C2×D71)⋊C4—216no—
156(C2×D71)⋊C4—216no—
157(C2×D71)⋊C4—48no—
158(C2×D71)⋊C4—48no—
159(C2×D71)⋊C4—48no—
160C24×C71C2411yescharacteristic
161C22×C4×C71—21no—
162C22×C4×C71—21no—
163C22×C4×C71—21no—
164C22×C4×C71—21no—
165C22×C4×C71—21no—
166C22×C4×C71—21no—
167C22×C4×C71—21no—
168C22×C4×C71—21no—
169C22×C4×C71—21no—
170C22×C4×C71—21no—
171C22×C4×C71—21no—
172C22×C4×C71—21no—
173C22×C4×C71—22no—
174C22×C4×C71—22no—
175C22×C4×C71—22no—
176C22×C4×C71—22no—
177C22×C4×C71—22no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—22no—
181C22×C4×C71—22no—
182C22×C4×C71—22no—
183C22×C4×C71—22no—
184C22×C4×C71—22no—
185C22×C4×C71—22no—
186C22×C4×C71C22×C412yes—
187C22×C4×C71C22×C412yes—
188C22×C4×C71C22×C412yes—
189C22×C4×C71C2×D412yes—
190C22×C4×C71C2×D412yes—
191C22×C4×C71C2×D414yes—
192C22×C4×C71C2×D412yes—
193C22×C4×C71C2×Q812yes—
194C22×C4×C71#4112yes—
195C22×C4×C71#4112yes—
196C4⋊C4×C71—44no—
197C4⋊C4×C71—44no—
198C42×C71—44no—
199C23×C71C23×C411yescharacteristic
200C23×C71C22×D411yescharacteristic
201C23×C71C22×D411yescharacteristic
202C23×C71C22×D411yescharacteristic
203C23×C71C22×Q811yescharacteristic
204C23×C71C2×#4111yescharacteristic
205C23×C71C2×#4111yescharacteristic
206C23×C71H(5,𝔽2)11yescharacteristic
207C23×C71H(5,𝔽2)11yescharacteristic
208C23×C71H(5,𝔽2)11yescharacteristic
209C23×C71H(5,𝔽2)11yescharacteristic
210C23×C71H(5,𝔽2)11yescharacteristic
211C23×C71H(5,𝔽2)11yescharacteristic
212C23×C712−1+411yescharacteristic
213C23×C712−1+411yescharacteristic
214C22×D71—24no—
215C22×D71—24no—
216C22×D71—24no—
217C22×D71—24no—
218C22×D71—24no—
219C22×D71—24no—
220C22×D71—24no—
221C22×D71—24no—
222C22×D71—24no—
223C22×D71—24no—
224C22×D71—24no—
225C22×D71—24no—
226C22×D71—24no—
227C22×D71—24no—
228C22×D71—24no—
229C22×D71—24no—
230C22×D71—24no—
231C22×D71—24no—
232C22×D71—42no—
233C22×D71—42no—
234C22×D71—42no—
235C22×D71—42no—
236C22×D71—42no—
237C22×D71—42no—
238C22×D71—42no—
239C22×D71—42no—
240C22×D71—42no—
241C22×D71—42no—
242C22×D71—42no—
243C22×D71—42no—
244C22×D71—42no—
245C22×D71—42no—
246C22×D71—42no—
247C22×D71—42no—
248C22×D71C2×C4⋊C418yes—
249C2×C4×C71—22no—
250C2×C4×C71—22no—
251C2×C4×C71—22no—
252C2×C4×C71—22no—
253C2×C4×C71—22no—
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—22no—
259C2×C4×C71—22no—
260C2×C4×C71—22no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—24no—
268C2×C4×C71—24no—
269C2×C4×C71—24no—
270C2×C4×C71—42no—
271C2×C4×C71—42no—
272C2×C4×C71—42no—
273C2×C4×C71—42no—
274C2×C4×C71—42no—
275C2×C4×C71—42no—
276C2×C4×C71—42no—
277C2×C4×C71—42no—
278C2×C4×C71—42no—
279C2×C4×C71—42no—
280C2×C4×C71—42no—
281C2×C4×C71C2×C4⋊C414yes—
282C2×C4×C71C4×D414yes—
283C2×C4×C71C4×D414yes—
284C2×Dic71—24no—
285C2×Dic71—24no—
286C2×Dic71—24no—
287C2×Dic71—24no—
288C2×Dic71—24no—
289C2×Dic71—24no—
290C2×Dic71—42no—
291C2×Dic71—42no—
292C2×Dic71—42no—
293C2×Dic71—42no—
294C2×Dic71—42no—
295C2×Dic71—42no—
296C2×Dic71—42no—
297C2×Dic71—42no—
298C2×Dic71—42no—
299C2×Dic71—42no—
300C2×Dic71—42no—
301C2×Dic71—42no—
302C2×Dic71—42no—
303C2×Dic71—42no—
304C2×Dic71—42no—
305D284—416no—
306C4×D71—432no—
307C22×C71C22×C4⋊C411yescharacteristic
308C22×C71C2×C4×D411yescharacteristic
309C22×C71C2×C4×D411yescharacteristic
310C22×C71#51811yescharacteristic
311C22×C71#51811yescharacteristic
312C22×C71#52011yescharacteristic
313C22×C71#52011yescharacteristic
314C22×C71#53411yescharacteristic
315C22×C71#53411yescharacteristic
316C22×C71#53411yescharacteristic
317C22×C71#53411yescharacteristic
318C22×C71#53711yescharacteristic
319C22×C71#53711yescharacteristic
320C22×C71#53811yescharacteristic
321C22×C71#53811yescharacteristic
322C22×C71#53911yescharacteristic
323C22×C71#53911yescharacteristic
324C22×C71#54311yescharacteristic
325C22×C71#54311yescharacteristic
326C22×C71D4211yescharacteristic
327C22×C71D4211yescharacteristic
328C22×C71D4211yescharacteristic
329C22×C71#54711yescharacteristic
330C22×C71#54711yescharacteristic
331C22×C71D4×Q811yescharacteristic
332C22×C71D4×Q811yescharacteristic
333C22×C71#55011yescharacteristic
334C22×C71#55011yescharacteristic
335C22×C71#55411yescharacteristic
336C22×C71#55411yescharacteristic
337C22×C71#55911yescharacteristic
338C22×C71H(3,𝔽4)11yescharacteristic
339C22×C71#56211yescharacteristic
340C22×C71#56211yescharacteristic
341C22×C71#56311yescharacteristic
342C2×D71—28no—
343C2×D71—28no—
344C2×D71—28no—
345C2×D71—44no—
346C2×D71—44no—
347C2×D71—44no—
348C2×D71—44no—
349C2×D71—44no—
350C2×D71—44no—
351C2×D71—44no—
352C2×D71—44no—
353C2×D71—44no—
354C2×D71—44no—
355C2×D71—44no—
356C2×D71—44no—
357C4×C71—24no—
358C4×C71—24no—
359C4×C71—24no—
360C4×C71—44no—
361C4×C71—82no—
362Dic71—44no—
363Dic71—44no—
364Dic71—82no—
365#14440—711nomaximal, Sylow
366C2×C71#231511yescharacteristic
367C2×C71#232511yescharacteristic
368C2×C71#232511yescharacteristic
369C2×C71D4×C4⋊C411yescharacteristic
370C2×C71D4×C4⋊C411yescharacteristic
371C2×C71#236611yescharacteristic
372C2×C71#237911yescharacteristic
373C2×C71#267911yescharacteristic
374C2×C71#268211yescharacteristic
375C2×C71#268211yescharacteristic
376C2×C71#268311yescharacteristic
377C2×C71#272411yescharacteristic
378C2×C71#273211yescharacteristic
379C2×C71#273211yescharacteristic
380C2×C71#280411yescharacteristic
381D71—48no—
382C2×#390—711no—
383C2×#386—712no—
384C2×#385—712no—
385C2×#385—712no—
386#1441—712no—
387#1439—712no—
388#1439—712no—
389C4⋊#95—711no—
390C4⋊#95D7111yescharacteristic, complemented
391C71#1444011yescharacteristic, complemented, Sylow
392C23×D4—711no—
393C24×C4—712no—
394C22×C4⋊C4—711no—
395C22×C4⋊C4—711no—
396C22×C4⋊C4—711no—
397C22×C4⋊C4—712no—
398C22×C4⋊C4C2×D7111yescharacteristic
399C22×C4⋊C4C2×D7111yescharacteristic
400C22×C22⋊C4—712no—
401C22×C22⋊C4—712no—
402C22×C22⋊C4—712no—
403C22×C22⋊C4—712no—
404C22×C22⋊C4—712no—
405C22×C42C2×D7111yescharacteristic
406#390—718no—
407#386—1428no—
408#385—1428no—
409#385—1428no—
410C2×#95—712no—
411C2×#95—712no—
412C2×#95—712no—
413C2×#95—712no—
414C2×#95—712no—
415C2×#95C2×D7112yes—
416C2×#95C2×D7112yes—
417C25—712no—
418C22×D4—2841no—
419C22×D4—2841no—
420C22×D4—2841no—
421C22×D4—2841no—
422C22×D4—714no—
423C22×D4—714no—
424C22×D4—714no—
425C23×C4—2842no—
426C23×C4—2842no—
427C23×C4—2842no—
428C23×C4—2842no—
429C23×C4—712no—
430C23×C4—712no—
431C23×C4—712no—
432C23×C4—1424no—
433C23×C4—1424no—
434C23×C4—1424no—
435C23×C4C22×D7112yes—
436C23×C4C22×D7112yes—
437C23×C4C22×D7111yescharacteristic
438C23×C4C22×D7111yescharacteristic
439C23×C4C22×D7111yescharacteristic
440C2×C4⋊C4—22no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—2842no—
446C2×C4⋊C4—2841no—
447C2×C4⋊C4—2841no—
448C2×C4⋊C4—2841no—
449C2×C4⋊C4—2841no—
450C2×C4⋊C4—2841no—
451C2×C4⋊C4—2841no—
452C2×C4⋊C4—714no—
453C2×C4⋊C4—714no—
454C2×C4⋊C4—1424no—
455C2×C4⋊C4—1424no—
456C2×C4⋊C4—1422no—
457C2×C4⋊C4D28414yescomplemented
458C2×C22⋊C4—2842no—
459C2×C22⋊C4—2842no—
460C2×C22⋊C4—2842no—
461C2×C22⋊C4—2842no—
462C2×C22⋊C4—718no—
463C2×C22⋊C4—718no—
464C2×C22⋊C4—1424no—
465C2×C22⋊C4—1424no—
466C2×C22⋊C4—1424no—
467C2×C22⋊C4—1424no—
468C2×C22⋊C4—1424no—
469C2×C22⋊C4—1424no—
470C2×C22⋊C4—1424no—
471C2×C22⋊C4—1424no—
472C2×C22⋊C4—1424no—
473C2×C42—41no—
474C2×C42—41no—
475C2×C42C4×D7114yescomplemented
476#95—24no—
477#95—24no—
478#95—2842no—
479#95—1424no—
480#95—1424no—
481#95—1424no—
482#95—1424no—
483C24—714no—
484C24—714no—
485C24—714no—
486C24—1422no—
487C24—1422no—
488C24—1422no—
489C24—1422no—
490C24—1422no—
491C24—1422no—
492C24—1422no—
493C24—1422no—
494C24—1422no—
495C24—1422no—
496C24—1422no—
497C24—1422no—
498C24C23×D7111yescharacteristic
499C2×D4—2844no—
500C2×D4—2844no—
501C2×D4—2844no—
502C2×D4—2844no—
503C2×D4—2844no—
504C2×D4—2844no—
505C2×D4—7116no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—2848no—
532C22×C4—2848no—
533C22×C4—2848no—
534C22×C4—2848no—
535C22×C4—2848no—
536C22×C4—2848no—
537C22×C4—2848no—
538C22×C4—714no—
539C22×C4—714no—
540C22×C4—1422no—
541C22×C4—1422no—
542C22×C4—1422no—
543C22×C4—1422no—
544C22×C4—1422no—
545C22×C4—1422no—
546C22×C4—1422no—
547C22×C4—1422no—
548C22×C4—1422no—
549C22×C4—1422no—
550C22×C4—1422no—
551C22×C4—1422no—
552C22×C4—1422no—
553C22×C4—1422no—
554C22×C4—1422no—
555C22×C4—1422no—
556C22×C4—1422no—
557C22×C4—1422no—
558C22×C4—1422no—
559C22×C4C2×C4×D7112yes—
560C22×C4C2×C4×D7112yes—
561C22×C4C2×C4×D7112yes—
562C22×C4D4×D7112yes—
563C22×C4D4×D7112yes—
564C22×C4C2×D28414yes—
565C22×C4C2×D28412yes—
566C22×C4Q8×D7112yes—
567C22×C4#1176586512yes—
568C22×C4#1176586612yes—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—2844no—
572C4⋊C4—2848no—
573C4⋊C4—2844no—
574C4⋊C4—2844no—
575C22⋊C4—2848no—
576C22⋊C4—2848no—
577C22⋊C4—2848no—
578C22⋊C4—14216no—
579C22⋊C4—14216no—
580C42—44no—
581C23—2842no—
582C23—2842no—
583C23—2842no—
584C23—2842no—
585C23—2842no—
586C23—2842no—
587C23—2842no—
588C23—2842no—
589C23—2842no—
590C23—2842no—
591C23—2842no—
592C23—2842no—
593C23—2842no—
594C23—2842no—
595C23—2842no—
596C23—2842no—
597C23—718no—
598C23—1424no—
599C23—1424no—
600C23—1424no—
601C23—1424no—
602C23—1424no—
603C23—1424no—
604C23—1424no—
605C23—1424no—
606C23—1424no—
607C23—1424no—
608C23—1424no—
609C23—1424no—
610C23—1424no—
611C23—1424no—
612C23—1424no—
613C23—1424no—
614C23—1424no—
615C23—1424no—
616C23C22×C4×D7111yescharacteristic
617C23C2×D4×D7111yescharacteristic
618C23C2×D4×D7111yescharacteristic
619C23C22×D28411yescharacteristic
620C23C2×Q8×D7111yescharacteristic
621C23C2×#1176586511yescharacteristic
622C23C2×#1176586611yescharacteristic
623C23#1455617311yescharacteristic
624C23#1455617311yescharacteristic
625C23#1455617311yescharacteristic
626C23#1455617411yescharacteristic
627C23#1455617411yescharacteristic
628C23#1455617411yescharacteristic
629C23#1455617511yescharacteristic
630C23#1455617611yescharacteristic
631D4—28416no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—28432no—
665C2×C4—2842no—
666C2×C4—2842no—
667C2×C4—2842no—
668C2×C4—2842no—
669C2×C4—2842no—
670C2×C4—2842no—
671C2×C4—2842no—
672C2×C4—2842no—
673C2×C4—2842no—
674C2×C4—2842no—
675C2×C4—2842no—
676C2×C4—2842no—
677C2×C4—2842no—
678C2×C4—2842no—
679C2×C4—2842no—
680C2×C4—1424no—
681C2×C4—1424no—
682C2×C4—1424no—
683C2×C4—1424no—
684C2×C4—1424no—
685C2×C4—1424no—
686C2×C4C4⋊C4×D7114yes—
687C2×C4#1455609014yes—
688C2×C4C4×D28414yes—
689C22—2844no—
690C22—2844no—
691C22—2844no—
692C22—2844no—
693C22—2844no—
694C22—2844no—
695C22—2844no—
696C22—2844no—
697C22—2844no—
698C22—2844no—
699C22—2844no—
700C22—2844no—
701C22—1428no—
702C22—1428no—
703C22—1428no—
704C22C2×C4⋊C4×D7111yescharacteristic
705C22C2×#1455609011yescharacteristic
706C22C2×C4×D28411yescharacteristic
707C22#1798647211yescharacteristic
708C22#1798647311yescharacteristic
709C22#1798647911yescharacteristic
710C22#1798648011yescharacteristic
711C22#1798655711yescharacteristic
712C22#1798655711yescharacteristic
713C22#1798655711yescharacteristic
714C22#1798656111yescharacteristic
715C22#1798657611yescharacteristic
716C22#1798658011yescharacteristic
717C22#1798658711yescharacteristic
718C22#1798658911yescharacteristic
719C22#1798659611yescharacteristic
720C22#1798659811yescharacteristic
721C22#1798662411yescharacteristic
722C22#1798662411yescharacteristic
723C22#1798663411yescharacteristic
724C22D4×D28411yescharacteristic
725C22D4×D28411yescharacteristic
726C22#1798665211yescharacteristic
727C22#1798665411yescharacteristic
728C22#1798666411yescharacteristic
729C22Q8×D28411yescharacteristic
730C22#1798667011yescharacteristic
731C22#1798667111yescharacteristic
732C22#1798670911yescharacteristic
733C22#1798671011yescharacteristic
734C22#1798673411yescharacteristic
735C22#1798674111yescharacteristic
736C22#1798674311yescharacteristic
737C22#1798674711yescharacteristic
738C22#1798675311yescharacteristic
739C4—24no—
740C4—24no—
741C4—24no—
742C4—44no—
743C4—82no—
744C4—2844no—
745C4—2844no—
746C4—5682no—
747C2—2848no—
748C2#2259095311yescharacteristic
749C2#2259104011yescharacteristic
750C2#2259104311yescharacteristic
751C2#2259124011yescharacteristic
752C2C4⋊C4×D28411yescharacteristic
753C2#2259140411yescharacteristic
754C2#2259151111yescharacteristic
755C2#2259467511yescharacteristic
756C2#2259470211yescharacteristic
757C2#2259470311yescharacteristic
758C2#2259471111yescharacteristic
759C2#2259526911yescharacteristic
760C2#2259535611yescharacteristic
761C2#2259535811yescharacteristic
762C2#2259628411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC71×C4⋊#95C2
socle, cosocleC24×C71C24
prime radicalC23×D284C22
hypercenterC4⋊#95D71
hypocenterC71#14440
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#17985873C2semidirect
4. C2×#17985870C2semidirect
5. #22586592C2semidirect
6. #22586586C2semidirect
7. #22586582C2semidirect
8. #22586570C2semidirect
9. C71×C4⋊#95C2semidirect
21. #17985901C4semidirect
60. C2×C4⋊Dic71C2×C4semidirect
61. C2×C4⋊Dic71D4semidirect
78. C2×(C2×D71)⋊C4C2×C4semidirect
79. C2×(C2×D71)⋊C4C2×C4semidirect
95. C2×C4⋊C4×C71D4semidirect
98. C2×C42×C71C2×C4semidirect
122. C2×D284C4⋊C4semidirect
390. C4⋊#95D71semidirect
391. C71#14440semidirect
457. C2×C4⋊C4D284semidirect
475. C2×C42C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179859012
C2×#179858772
C2×#179858732
C2×#179858702
#225865922
#225865862
#225865822
#225865702
C71×C4⋊#952
#1444071