Finite Group Databasebeta

← #31921183

Subgroups — #31921183

Order 18176.

1586 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985898C211yesmaximal, characteristic
2C2×#17985898C211yesmaximal, characteristic
3C2×#17985897C212yesmaximal
4C2×#17985897C211yesmaximal, characteristic
5C2×C4×Dic71⋊C4C211yesmaximal, characteristic
6#22586596C212yesmaximal
7#22586592C212yesmaximal
8#22586573C212yesmaximal
9#22586569C211yesmaximal, characteristic
10#22586569C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C71C211yesmaximal, characteristic
12C22×C4⋊Dic71C2211yescharacteristic
13C22×C4⋊Dic71C2212yes—
14C22×C4⋊Dic71C2211yescharacteristic
15C22×C4⋊Dic71C2212yes—
16C22×Dic71⋊C4C2212yes—
17C22×Dic71⋊C4C2211yescharacteristic
18C22×Dic71⋊C4C2211yescharacteristic
19C22×C4×Dic71C2211yescharacteristic
20C22×C4×Dic71C2211yescharacteristic
21#17985898—24no—
22#17985898C418yescomplemented
23#17985897—28no—
24#17985897—24no—
25C4×Dic71⋊C4—24no—
26C2×C71⋊#95C2212yes—
27C2×C71⋊#95C2212yes—
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2211yescharacteristic
32C2×C71⋊#95C2211yescharacteristic
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C22×C4⋊C4×C71C2211yescharacteristic
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C42×C71C2212yes—
38C22×C42×C71C2211yescharacteristic
39C4×C4⋊C4×C71—24no—
40C2×#95×C71C2212yes—
41C23×Dic71C2312yes—
42C23×Dic71C2311yescharacteristic
43C23×Dic71C2312yes—
44C23×Dic71C2311yescharacteristic
45C23×Dic71C2311yescharacteristic
46C23×Dic71C2311yescharacteristic
47C2×C4⋊Dic71—24no—
48C2×C4⋊Dic71—24no—
49C2×C4⋊Dic71—24no—
50C2×C4⋊Dic71—22no—
51C2×C4⋊Dic71—22no—
52C2×C4⋊Dic71—24no—
53C2×C4⋊Dic71—22no—
54C2×C4⋊Dic71—22no—
55C2×C4⋊Dic71—22no—
56C2×C4⋊Dic71—42no—
57C2×C4⋊Dic71C2×C418yes—
58C2×C4⋊Dic71C2×C414yes—
59C2×Dic71⋊C4—22no—
60C2×Dic71⋊C4—22no—
61C2×Dic71⋊C4—22no—
62C2×Dic71⋊C4—22no—
63C2×Dic71⋊C4—24no—
64C2×Dic71⋊C4—24no—
65C2×Dic71⋊C4—22no—
66C2×Dic71⋊C4—24no—
67C2×Dic71⋊C4D414yes—
68C2×C4×Dic71—22no—
69C2×C4×Dic71—22no—
70C2×C4×Dic71—22no—
71C2×C4×Dic71—22no—
72C2×C4×Dic71—22no—
73C2×C4×Dic71C2×C414yes—
74C71⋊#95—24no—
75C71⋊#95—24no—
76C71⋊#95—24no—
77C71⋊#95—22no—
78C71⋊#95—22no—
79C71⋊#95—24no—
80C71⋊#95—24no—
81C71⋊#95—42no—
82C71⋊#95C2×C418yes—
83C23×C4×C71C2311yescharacteristic
84C23×C4×C71C2312yes—
85C23×C4×C71C2312yes—
86C23×C4×C71C2311yescharacteristic
87C23×C4×C71C2311yescharacteristic
88C2×C4⋊C4×C71—22no—
89C2×C4⋊C4×C71—22no—
90C2×C4⋊C4×C71C2×C414yes—
91C2×C4⋊C4×C71D414yes—
92C2×C4⋊C4×C71Q814yes—
93C2×C4⋊C4×C71Q814yes—
94C2×C42×C71—22no—
95C2×C42×C71—22no—
96C2×C42×C71—24no—
97C2×C42×C71—24no—
98C2×C42×C71—42no—
99C2×C42×C71D414yes—
100#95×C71—24no—
101C22×Dic71—21no—
102C22×Dic71—21no—
103C22×Dic71—21no—
104C22×Dic71—21no—
105C22×Dic71—21no—
106C22×Dic71—21no—
107C22×Dic71—21no—
108C22×Dic71—21no—
109C22×Dic71—22no—
110C22×Dic71—22no—
111C22×Dic71—21no—
112C22×Dic71—22no—
113C22×Dic71—21no—
114C22×Dic71—21no—
115C22×Dic71—21no—
116C22×Dic71—21no—
117C22×Dic71—22no—
118C22×Dic71—21no—
119C22×Dic71—22no—
120C22×Dic71—22no—
121C22×Dic71—21no—
122C22×Dic71—21no—
123C22×Dic71—21no—
124C22×Dic71—21no—
125C22×Dic71—21no—
126C22×Dic71—21no—
127C22×Dic71—21no—
128C22×Dic71—21no—
129C22×Dic71—22no—
130C22×Dic71—22no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71—22no—
136C22×Dic71C22×C412yes—
137C22×Dic71C22×C414yes—
138C22×Dic71C22×C412yes—
139C22×Dic71C2×D412yes—
140C22×Dic71C2×D412yes—
141C22×Dic71#4112yes—
142C22×Dic71#4112yes—
143C4⋊Dic71—28no—
144C4⋊Dic71—216no—
145C4⋊Dic71—48no—
146C4⋊Dic71—44no—
147Dic71⋊C4—28no—
148Dic71⋊C4—28no—
149Dic71⋊C4—48no—
150C4×Dic71—28no—
151C4×Dic71—44no—
152C24×C71C2411yescharacteristic
153C22×C4×C71—21no—
154C22×C4×C71—22no—
155C22×C4×C71—21no—
156C22×C4×C71—22no—
157C22×C4×C71—21no—
158C22×C4×C71—22no—
159C22×C4×C71—22no—
160C22×C4×C71—21no—
161C22×C4×C71—21no—
162C22×C4×C71—22no—
163C22×C4×C71—22no—
164C22×C4×C71—21no—
165C22×C4×C71—22no—
166C22×C4×C71—22no—
167C22×C4×C71—21no—
168C22×C4×C71—21no—
169C22×C4×C71—22no—
170C22×C4×C71—21no—
171C22×C4×C71—21no—
172C22×C4×C71—22no—
173C22×C4×C71C22×C414yes—
174C22×C4×C71C22×C412yes—
175C22×C4×C71C2×D412yes—
176C22×C4×C71C2×D414yes—
177C22×C4×C71C2×D412yes—
178C22×C4×C71C2×D412yes—
179C22×C4×C71C2×D412yes—
180C22×C4×C71C2×D412yes—
181C22×C4×C71C2×Q814yes—
182C22×C4×C71C2×Q814yes—
183C22×C4×C71C2×Q812yes—
184C22×C4×C71C2×Q812yes—
185C22×C4×C71#4112yes—
186C22×C4×C71#4112yes—
187C22×C4×C71#4112yes—
188C4⋊C4×C71—28no—
189C4⋊C4×C71C4⋊C4116yescomplemented
190C42×C71—28no—
191C42×C71—48no—
192C23×C71C23×C411yescharacteristic
193C23×C71C22×D411yescharacteristic
194C23×C71C22×D411yescharacteristic
195C23×C71C22×D411yescharacteristic
196C23×C71C22×Q811yescharacteristic
197C23×C71C22×Q811yescharacteristic
198C23×C71C2×#4111yescharacteristic
199C23×C71C2×#4111yescharacteristic
200C23×C71C2×#4111yescharacteristic
201C23×C71C2×#4111yescharacteristic
202C23×C71C2×#4111yescharacteristic
203C23×C71H(5,𝔽2)11yescharacteristic
204C23×C712−1+411yescharacteristic
205C23×C712−1+411yescharacteristic
206C23×C712−1+411yescharacteristic
207C2×C4×C71—24no—
208C2×C4×C71—24no—
209C2×C4×C71—22no—
210C2×C4×C71—22no—
211C2×C4×C71—22no—
212C2×C4×C71—24no—
213C2×C4×C71—24no—
214C2×C4×C71—22no—
215C2×C4×C71—22no—
216C2×C4×C71—24no—
217C2×C4×C71—22no—
218C2×C4×C71—24no—
219C2×C4×C71—22no—
220C2×C4×C71—24no—
221C2×C4×C71—22no—
222C2×C4×C71—22no—
223C2×C4×C71—24no—
224C2×C4×C71—24no—
225C2×C4×C71—42no—
226C2×C4×C71—42no—
227C2×C4×C71—42no—
228C2×C4×C71—41no—
229C2×C4×C71—41no—
230C2×C4×C71—42no—
231C2×C4×C71—41no—
232C2×C4×C71—41no—
233C2×C4×C71C2×C4⋊C418yes—
234C2×C4×C71C2×C4⋊C414yes—
235C2×C4×C71C4×D414yes—
236C2×C4×C71C4×Q814yes—
237C2×C4×C71#12114yes—
238C2×C4×C71#12114yes—
239C2×C4×C71C22⋊Q814yes—
240C2×C4×C71#12514yes—
241C2×C4×C71C4⋊Q814yes—
242C2×Dic71—22no—
243C2×Dic71—22no—
244C2×Dic71—22no—
245C2×Dic71—22no—
246C2×Dic71—22no—
247C2×Dic71—22no—
248C2×Dic71—22no—
249C2×Dic71—24no—
250C2×Dic71—24no—
251C2×Dic71—24no—
252C2×Dic71—22no—
253C2×Dic71—22no—
254C2×Dic71—22no—
255C2×Dic71—22no—
256C2×Dic71—22no—
257C2×Dic71—22no—
258C2×Dic71—22no—
259C2×Dic71—22no—
260C2×Dic71—41no—
261C2×Dic71—41no—
262C2×Dic71—42no—
263C2×Dic71—42no—
264C2×Dic71—42no—
265C2×Dic71—42no—
266C2×Dic71—41no—
267C2×Dic71—41no—
268C2×Dic71—41no—
269C2×Dic71—41no—
270C2×Dic71—41no—
271C2×Dic71—41no—
272C2×Dic71—41no—
273C2×Dic71—41no—
274C2×Dic71—41no—
275C2×Dic71—41no—
276C2×Dic71—42no—
277C2×Dic71—42no—
278C2×Dic71—42no—
279C2×Dic71—42no—
280C2×Dic71—42no—
281C2×Dic71—42no—
282C2×Dic71—42no—
283C2×Dic71C4×D414yes—
284C22×C71C22×C4⋊C411yescharacteristic
285C22×C71C2×C4×D411yescharacteristic
286C22×C71C2×C4×D411yescharacteristic
287C22×C71C2×C4×Q811yescharacteristic
288C22×C71C4×#4111yescharacteristic
289C22×C71#51911yescharacteristic
290C22×C71#52011yescharacteristic
291C22×C71C2×#12111yescharacteristic
292C22×C71C2×#12111yescharacteristic
293C22×C71C2×C22⋊Q811yescharacteristic
294C22×C71#52511yescharacteristic
295C22×C71C2×#12511yescharacteristic
296C22×C71#52911yescharacteristic
297C22×C71C2×C4⋊Q811yescharacteristic
298C22×C71#53211yescharacteristic
299C22×C71#53611yescharacteristic
300C22×C71#53711yescharacteristic
301C22×C71#54111yescharacteristic
302C22×C71#54211yescharacteristic
303C22×C71D4211yescharacteristic
304C22×C71#54711yescharacteristic
305C22×C71#54711yescharacteristic
306C22×C71#54811yescharacteristic
307C22×C71#54811yescharacteristic
308C22×C71D4×Q811yescharacteristic
309C22×C71D4×Q811yescharacteristic
310C22×C71#55211yescharacteristic
311C22×C71#55311yescharacteristic
312C22×C71#55411yescharacteristic
313C22×C71#55411yescharacteristic
314C22×C71#55611yescharacteristic
315C22×C71#55711yescharacteristic
316C22×C71#55711yescharacteristic
317C22×C71#55711yescharacteristic
318C22×C71#55711yescharacteristic
319C4×C71—28no—
320C4×C71—24no—
321C4×C71—42no—
322C4×C71—44no—
323C4×C71#38918yescomplemented
324Dic71—24no—
325Dic71—42no—
326Dic71—42no—
327Dic71—42no—
328Dic71—44no—
329Dic71—82no—
330#14046—711nomaximal, Sylow
331C2×C71C2×#38911yescharacteristic
332C2×C71C4×#12111yescharacteristic
333C2×C71#232311yescharacteristic
334C2×C71D4×C4⋊C411yescharacteristic
335C2×C71#235111yescharacteristic
336C2×C71#236511yescharacteristic
337C2×C71#237011yescharacteristic
338C2×C71#241511yescharacteristic
339C2×C71#241611yescharacteristic
340C2×C71#245211yescharacteristic
341C2×C71#245311yescharacteristic
342C2×C71#250611yescharacteristic
343C2×C71#250911yescharacteristic
344C2×C71#254611yescharacteristic
345C2×C71#258411yescharacteristic
346C2×#389—712no—
347C2×#389—711no—
348C2×#389—711no—
349C2×#389—711no—
350C2×C4×C4⋊C4—711no—
351C2×C4×C4⋊C4D7111yescharacteristic
352#1442—712no—
353#1441—712no—
354#1436—712no—
355C4⋊#95—711no—
356C4⋊#95—711no—
357C71#1404611yescharacteristic, complemented, Sylow
358C22×C4⋊C4—712no—
359C22×C4⋊C4—711no—
360C22×C4⋊C4—711no—
361C22×C4⋊C4—712no—
362C22×C4⋊C4—712no—
363C22×C4⋊C4—711no—
364C22×C4⋊C4—711no—
365C22×C4⋊C4C2×D7111yescharacteristic
366C22×C4⋊C4C2×D7111yescharacteristic
367C22×C42—711no—
368C22×C42—711no—
369C22×C42C2×D7112yes—
370C22×C42C2×D7111yescharacteristic
371#389—718no—
372#389—1428no—
373#389—1424no—
374#389—1424no—
375C4×C4⋊C4—24no—
376C4×C4⋊C4—1424no—
377C2×#95—712no—
378C2×#95—712no—
379C2×#95—712no—
380C2×#95—712no—
381C2×#95—712no—
382C2×#95—711no—
383C2×#95—712no—
384C2×#95—712no—
385C2×#95—711no—
386C2×#95C2×D7112yes—
387C23×C4—711no—
388C23×C4—712no—
389C23×C4—711no—
390C23×C4—711no—
391C23×C4—711no—
392C23×C4—712no—
393C23×C4C22×D7111yescharacteristic
394C23×C4C22×D7112yes—
395C23×C4C22×D7112yes—
396C23×C4C22×D7111yescharacteristic
397C23×C4C22×D7111yescharacteristic
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—2842no—
401C2×C4⋊C4—718no—
402C2×C4⋊C4—714no—
403C2×C4⋊C4—714no—
404C2×C4⋊C4—1424no—
405C2×C4⋊C4—1424no—
406C2×C4⋊C4—1424no—
407C2×C4⋊C4—1422no—
408C2×C4⋊C4—1424no—
409C2×C4⋊C4—1422no—
410C2×C4⋊C4—1422no—
411C2×C4⋊C4—1424no—
412C2×C4⋊C4—1424no—
413C2×C4⋊C4—1422no—
414C2×C4⋊C4—1422no—
415C2×C4⋊C4—1424no—
416C2×C4⋊C4—1422no—
417C2×C4⋊C4—1422no—
418C2×C4⋊C4—1422no—
419C2×C4⋊C4—1422no—
420C2×C4⋊C4—1422no—
421C2×C4⋊C4Dic14214yes—
422C2×C4⋊C4Dic14214yes—
423C2×C4⋊C4C4×D7114yes—
424C2×C4⋊C4C22⋊D7114yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—42no—
430C2×C42—714no—
431C2×C42—1422no—
432C2×C42—1422no—
433C2×C42—1422no—
434C2×C42—1422no—
435C2×C42—1422no—
436C2×C42D28414yes—
437#95—24no—
438#95—2842no—
439#95—718no—
440#95—1424no—
441#95—1424no—
442#95—1424no—
443#95—1424no—
444#95—1422no—
445#95—1422no—
446#95—1424no—
447C24C23×D7111yescharacteristic
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—712no—
469C22×C4—712no—
470C22×C4—712no—
471C22×C4—712no—
472C22×C4—714no—
473C22×C4—712no—
474C22×C4—712no—
475C22×C4—1422no—
476C22×C4—1422no—
477C22×C4—1422no—
478C22×C4—1422no—
479C22×C4—1422no—
480C22×C4—1422no—
481C22×C4—1422no—
482C22×C4—1422no—
483C22×C4—1421no—
484C22×C4—1421no—
485C22×C4—1421no—
486C22×C4—1421no—
487C22×C4—1421no—
488C22×C4—1422no—
489C22×C4—1422no—
490C22×C4—1421no—
491C22×C4—1422no—
492C22×C4—1421no—
493C22×C4—1421no—
494C22×C4—1421no—
495C22×C4—1422no—
496C22×C4—1421no—
497C22×C4—1422no—
498C22×C4—1421no—
499C22×C4—1421no—
500C22×C4—1421no—
501C22×C4—1421no—
502C22×C4—1421no—
503C22×C4—1421no—
504C22×C4—1421no—
505C22×C4—1421no—
506C22×C4—1421no—
507C22×C4—1421no—
508C22×C4—1421no—
509C22×C4—1421no—
510C22×C4C2×C4×D7114yes—
511C22×C4C2×C4×D7112yes—
512C22×C4D4×D7112yes—
513C22×C4C2×C22⋊D7114yes—
514C22×C4C2×C22⋊D7112yes—
515C22×C4C2×D28412yes—
516C22×C4C2×D28412yes—
517C22×C4C2×D28412yes—
518C22×C4C2×Dic14214yes—
519C22×C4C2×Dic14214yes—
520C22×C4C2×Dic14212yes—
521C22×C4C2×Dic14212yes—
522C22×C4#1176586512yes—
523C22×C4#1176586512yes—
524C22×C4#1176586612yes—
525C4⋊C4—28no—
526C4⋊C4—2848no—
527C4⋊C4—2844no—
528C4⋊C4—2848no—
529C4⋊C4—14216no—
530C4⋊C4—1428no—
531C4⋊C4—1428no—
532C4⋊C4—1428no—
533C4⋊C4Dic71⋊C4116yescomplemented
534C42—28no—
535C42—48no—
536C42—2844no—
537C42—1428no—
538C23C22×C4×D7111yescharacteristic
539C23C2×D4×D7111yescharacteristic
540C23C22×C22⋊D7111yescharacteristic
541C23C22×D28411yescharacteristic
542C23C22×Dic14211yescharacteristic
543C23C22×Dic14211yescharacteristic
544C23#41×D7111yescharacteristic
545C23#41×D7111yescharacteristic
546C23C2×#1176586511yescharacteristic
547C23C2×#1176586511yescharacteristic
548C23C2×#1176586611yescharacteristic
549C23#1455617311yescharacteristic
550C23#1455617511yescharacteristic
551C23#1455617511yescharacteristic
552C23#1455617611yescharacteristic
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—2841no—
580C2×C4—2841no—
581C2×C4—2841no—
582C2×C4—2841no—
583C2×C4—2841no—
584C2×C4—2841no—
585C2×C4—2841no—
586C2×C4—2841no—
587C2×C4—2841no—
588C2×C4—2841no—
589C2×C4—2841no—
590C2×C4—2841no—
591C2×C4—2842no—
592C2×C4—2842no—
593C2×C4—2842no—
594C2×C4—2842no—
595C2×C4—2842no—
596C2×C4—2842no—
597C2×C4—2842no—
598C2×C4—2842no—
599C2×C4—2842no—
600C2×C4—2842no—
601C2×C4—2842no—
602C2×C4—714no—
603C2×C4—1422no—
604C2×C4—1422no—
605C2×C4—1422no—
606C2×C4—1422no—
607C2×C4—1424no—
608C2×C4—1422no—
609C2×C4—1424no—
610C2×C4—1424no—
611C2×C4—1422no—
612C2×C4—1422no—
613C2×C4—1422no—
614C2×C4—1422no—
615C2×C4—1422no—
616C2×C4—1422no—
617C2×C4—1422no—
618C2×C4—1422no—
619C2×C4—1422no—
620C2×C4—1422no—
621C2×C4C2×Dic71⋊C418yes—
622C2×C4C2×Dic71⋊C414yes—
623C2×C4C4×D28414yes—
624C2×C4C4×Dic14214yes—
625C2×C4#1455610214yes—
626C2×C4#1455610314yes—
627C2×C4#1455610714yes—
628C2×C4#1455612014yes—
629C2×C4#1455612814yes—
630C22C22×Dic71⋊C411yescharacteristic
631C22C4×D4×D7111yescharacteristic
632C22C2×C4×D28411yescharacteristic
633C22C2×C4×Dic14211yescharacteristic
634C22C4×#1176586611yescharacteristic
635C22#1798647511yescharacteristic
636C22#1798647811yescharacteristic
637C22C2×#1455610211yescharacteristic
638C22C2×#1455610311yescharacteristic
639C22C2×#1455610711yescharacteristic
640C22#1798651111yescharacteristic
641C22C2×#1455612011yescharacteristic
642C22#1798653611yescharacteristic
643C22C2×#1455612811yescharacteristic
644C22#1798654611yescharacteristic
645C22#1798657511yescharacteristic
646C22#1798658011yescharacteristic
647C22#1798660711yescharacteristic
648C22#1798661411yescharacteristic
649C22D4×C22⋊D7111yescharacteristic
650C22#1798664811yescharacteristic
651C22#1798665011yescharacteristic
652C22#1798665611yescharacteristic
653C22#1798666011yescharacteristic
654C22D4×Dic14211yescharacteristic
655C22D4×Dic14211yescharacteristic
656C22#1798668811yescharacteristic
657C22#1798669711yescharacteristic
658C22#1798670811yescharacteristic
659C22#1798670811yescharacteristic
660C22#1798671711yescharacteristic
661C22#1798672511yescharacteristic
662C22#1798672511yescharacteristic
663C22#1798672811yescharacteristic
664C22#1798672811yescharacteristic
665C4—28no—
666C4—24no—
667C4—42no—
668C4—44no—
669C4—2842no—
670C4—2842no—
671C4—2842no—
672C4—2844no—
673C4—5682no—
674C4—1424no—
675C4#1798589718yescomplemented
676C2C2×#1798589711yescharacteristic
677C2C4×#1455610311yescharacteristic
678C2#2259102311yescharacteristic
679C2D4×Dic71⋊C411yescharacteristic
680C2#2259125811yescharacteristic
681C2#2259139911yescharacteristic
682C2#2259143211yescharacteristic
683C2#2259176311yescharacteristic
684C2#2259177411yescharacteristic
685C2#2259218411yescharacteristic
686C2#2259219511yescharacteristic
687C2#2259285011yescharacteristic
688C2#2259288311yescharacteristic
689C2#2259332811yescharacteristic
690C2#2259372311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×C4×C4⋊C4×C71C2
socle, prime radical, cosocleC24×C71C24
hypercenterC2×C4×C4⋊C4D71
hypocenterC71#14046
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #17985898C4semidirect
189. C4⋊C4×C71C4⋊C4semidirect
323. C4×C71#389semidirect
357. C71#14046semidirect
533. C4⋊C4Dic71⋊C4semidirect
675. C4#17985897semidirect

Maximal subgroups

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

subgroupindex
C2×#179858982
C2×#179858972
C2×C4×Dic71⋊C42
#225865962
#225865922
#225865732
#225865692
C2×C4×C4⋊C4×C712
#1404671