Finite Group Databasebeta

← #31964841

Subgroups — #31964841

Order 18176.

1762 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556102C211yesmaximal, characteristic
2C2×#17985963C211yesmaximal, characteristic, complemented
3#22586907C214yesmaximal, complemented
4#22586868C214yesmaximal, complemented
5#22586855C214yesmaximal, complemented
6C71×#2280C211yesmaximal, characteristic, complemented
7C23×D284C411yescharacteristic, complemented
8C23×C22⋊D71—21no—
9C22×#11765849—21no—
10C2×#14556102—21no—
11C2×#14556102—21no—
12C2×#14556102—21no—
13C2×#14556102—21no—
14C2×#14556102—21no—
15C2×#14556102—21no—
16C2×#14556102C412yescomplemented
17C2×#14556102C412yescomplemented
18C2×#14556102C412yescomplemented
19C2×#14556102C2212yes—
20C2×#14556102C2212yes—
21C2×#14556102C2212yes—
22C22×C4⋊Dic71C411yescharacteristic, complemented
23C22×(C2×D71)⋊C4—21no—
24#17985963—21no—
25#17985963—21no—
26#17985963C2212yescomplemented
27#17985963C2212yescomplemented
28C2×C22⋊(C71⋊C8)—21no—
29C2×C22⋊(C71⋊C8)C2212yescomplemented
30#17985732C22116yescomplemented
31C24×C4×C71C2211yescharacteristic
32C2×#117×C71—21no—
33#381×C71C2212yescomplemented
34#380×C71—21no—
35#380×C71C2212yescomplemented
36#379×C71—21no—
37C4×C22⋊C4×C71—21no—
38C4×C22⋊C4×C71C2212yescomplemented
39C24×D71—21no—
40C22×D284—21no—
41C22×D284—21no—
42C22×D284—21no—
43C22×D284—44no—
44C22×D284C2×C412yes—
45C22×D284C2×C412yes—
46C22×D284C2×C412yes—
47C22×C22⋊D71—22no—
48C22×C22⋊D71—22no—
49C22×C22⋊D71—22no—
50C22×C22⋊D71—22no—
51C22×C22⋊D71—22no—
52C22×C22⋊D71—22no—
53C22×C22⋊D71—48no—
54C23×Dic71—21no—
55C2×#11765849—22no—
56C2×#11765849—22no—
57C2×#11765849—44no—
58C22×C71⋊C8—22no—
59#14556102—22no—
60#14556102—22no—
61#14556102—22no—
62#14556102—22no—
63#14556102—22no—
64#14556102—22no—
65#14556102—22no—
66#14556102—22no—
67#14556102—22no—
68#14556102—22no—
69#14556102—22no—
70#14556102—22no—
71#14556102C2×C414yes—
72#14556102C2×C414yes—
73#14556102C2×C414yes—
74#14556102C2314yes—
75C2×C4⋊Dic71—21no—
76C2×C4⋊Dic71—21no—
77C2×C4⋊Dic71—21no—
78C2×C4⋊Dic71C2×C412yes—
79C2×C4⋊Dic71C2×C412yes—
80C2×C4⋊Dic71C2×C412yes—
81C2×(C2×D71)⋊C4—22no—
82C2×(C2×D71)⋊C4—22no—
83C2×(C2×D71)⋊C4—22no—
84C2×(C2×D71)⋊C4—22no—
85C2×(C2×D71)⋊C4—22no—
86C2×(C2×D71)⋊C4—22no—
87C22⋊(C71⋊C8)—22no—
88C22⋊(C71⋊C8)—22no—
89C22⋊(C71⋊C8)—22no—
90C22⋊(C71⋊C8)C2314yescomplemented
91C25×C71D411yescharacteristic
92C23×C4×C71—44no—
93C23×C4×C71C2×C411yescharacteristic
94C23×C4×C71C2×C411yescharacteristic
95C23×C4×C71C2×C411yescharacteristic
96C23×C4×C71C2×C411yescharacteristic
97C23×C4×C71D411yescharacteristic
98C23×C4×C71D411yescharacteristic
99C23×C4×C71D411yescharacteristic
100C23×C4×C71D411yescharacteristic
101C23×C4×C71D411yescharacteristic
102C23×C4×C71D411yescharacteristic
103C23×C4×C71D411yescharacteristic
104C23×C4×C71C2311yescharacteristic
105C23×C4×C71C2311yescharacteristic
106C23×C4×C71C2311yescharacteristic
107#117×C71—44no—
108C2×C4⋊C4×C71—22no—
109C2×C22⋊C4×C71—22no—
110C2×C22⋊C4×C71—22no—
111C2×C22⋊C4×C71—22no—
112C2×C42×C71—22no—
113#95×C71—22no—
114#95×C71C2314yescomplemented
115C23×D71—22no—
116C23×D71—22no—
117C23×D71—22no—
118C23×D71—44no—
119C23×D71—44no—
120C23×D71—44no—
121C2×D284—22no—
122C2×D284—22no—
123C2×D284—22no—
124C2×D284—44no—
125C2×D284—44no—
126C2×D284—44no—
127C2×D284—44no—
128C2×D284—44no—
129C2×D284—44no—
130C2×D284C22×C414yes—
131C2×C22⋊D71—24no—
132C2×C22⋊D71—24no—
133C2×C22⋊D71—24no—
134C2×C22⋊D71—24no—
135C2×C22⋊D71—48no—
136C2×C22⋊D71—48no—
137C2×C22⋊D71—48no—
138C2×C22⋊D71—48no—
139C2×C22⋊D71—48no—
140C2×C22⋊D71—48no—
141C22×Dic71—22no—
142C22×Dic71—22no—
143C22×Dic71—22no—
144C22×Dic71—44no—
145#11765849—44no—
146#11765849—44no—
147C2×C71⋊C8—24no—
148C2×C71⋊C8—44no—
149C4⋊Dic71—22no—
150C4⋊Dic71—22no—
151C4⋊Dic71—22no—
152C4⋊Dic71C22×C414yes—
153(C2×D71)⋊C4—24no—
154(C2×D71)⋊C4—24no—
155(C2×D71)⋊C4—24no—
156(C2×D71)⋊C4—24no—
157C24×C71—24no—
158C24×C71—42no—
159C24×C71—42no—
160C24×C71C22⋊C411yescharacteristic
161C24×C71C22⋊C411yescharacteristic
162C24×C71C22⋊C411yescharacteristic
163C24×C71C22⋊C411yescharacteristic
164C24×C71C2×D411yescharacteristic
165C24×C71C2×D411yescharacteristic
166C24×C71C2×D411yescharacteristic
167C22×C4×C71—24no—
168C22×C4×C71—24no—
169C22×C4×C71—24no—
170C22×C4×C71—24no—
171C22×C4×C71—42no—
172C22×C4×C71—42no—
173C22×C4×C71—42no—
174C22×C4×C71—42no—
175C22×C4×C71—42no—
176C22×C4×C71—42no—
177C22×C4×C71—42no—
178C22×C4×C71—42no—
179C22×C4×C71—42no—
180C22×C4×C71—42no—
181C22×C4×C71—42no—
182C22×C4×C71C22⋊C411yescharacteristic
183C22×C4×C71C22⋊C411yescharacteristic
184C22×C4×C71C22⋊C411yescharacteristic
185C22×C4×C71C22⋊C411yescharacteristic
186C22×C4×C71C22⋊C411yescharacteristic
187C22×C4×C71C22⋊C411yescharacteristic
188C22×C4×C71C22⋊C411yescharacteristic
189C22×C4×C71C22⋊C411yescharacteristic
190C22×C4×C71C22⋊C411yescharacteristic
191C22×C4×C71C22⋊C411yescharacteristic
192C22×C4×C71C22⋊C411yescharacteristic
193C22×C4×C71C22⋊C411yescharacteristic
194C22×C4×C71C22×C411yescharacteristic
195C22×C4×C71C22×C411yescharacteristic
196C22×C4×C71C22×C411yescharacteristic
197C22×C4×C71C22×C411yescharacteristic
198C22×C4×C71C22×C411yescharacteristic
199C22×C4×C71C22×C411yescharacteristic
200C22×C4×C71C2×D411yescharacteristic
201C22×C4×C71C2×D411yescharacteristic
202C22×C4×C71C2×D411yescharacteristic
203C22×C4×C71C2×D411yescharacteristic
204C22×C4×C71C2×D411yescharacteristic
205C22×C4×C71C2×D411yescharacteristic
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D411yescharacteristic
209C22×C4×C71C2411yescharacteristic
210C4⋊C4×C71—44no—
211C22⋊C4×C71—44no—
212C22⋊C4×C71—44no—
213C22⋊C4×C71—44no—
214C42×C71—44no—
215C23×C71—22no—
216C23×C71—22no—
217C23×C71—22no—
218C23×C71—22no—
219C23×C71—22no—
220C23×C71—22no—
221C23×C71—22no—
222C23×C71—22no—
223C23×C71—22no—
224C23×C71—22no—
225C23×C71—22no—
226C23×C71—22no—
227C23×C71—41no—
228C23×C71—41no—
229C23×C71—41no—
230C23×C71—41no—
231C23×C71—41no—
232C23×C71—41no—
233C23×C71—41no—
234C23×C71—41no—
235C23×C71—416no—
236C23×C71C2×C22⋊C411yescharacteristic
237C23×C71C2×C22⋊C411yescharacteristic
238C23×C71C2×C22⋊C411yescharacteristic
239C23×C71C2×C22⋊C411yescharacteristic
240C23×C71C2×C22⋊C411yescharacteristic
241C23×C71C2×C22⋊C411yescharacteristic
242C23×C71AGL(1,ℤ/8)14yes—
243C23×C71C22×D411yescharacteristic
244C22×D71—24no—
245C22×D71—44no—
246C22×D71—44no—
247C22×D71—44no—
248C22×D71—44no—
249C22×D71—44no—
250C22×D71—44no—
251C22×D71—44no—
252C22×D71—44no—
253C22×D71—44no—
254C22×D71—816no—
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—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—41no—
271C2×C4×C71—41no—
272C2×C4×C71—41no—
273C2×C4×C71—41no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71—41no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—41no—
282C2×C4×C71—44no—
283C2×C4×C71—44no—
284C2×C4×C71—44no—
285C2×C4×C71#9914yes—
286C2×C4×C71C2×C22⋊C411yescharacteristic
287C2×C4×C71C2×C22⋊C411yescharacteristic
288C2×C4×C71C2×C22⋊C411yescharacteristic
289C2×C4×C71C2×C22⋊C411yescharacteristic
290C2×C4×C71C2×C22⋊C411yescharacteristic
291C2×C4×C71C2×C22⋊C411yescharacteristic
292C2×C4×C71C23×C411yescharacteristic
293C2×C4×C71C22×D411yescharacteristic
294C22⋊D71—48no—
295C22⋊D71—48no—
296C22⋊D71—48no—
297C22⋊D71—48no—
298C2×Dic71—24no—
299C2×Dic71—44no—
300C2×Dic71—44no—
301C2×Dic71—44no—
302D284—44no—
303D284—44no—
304D284—44no—
305D284—44no—
306C71⋊C8—44no—
307C22×C71—28no—
308C22×C71—21no—
309C22×C71—21no—
310C22×C71—21no—
311C22×C71—21no—
312C22×C71—21no—
313C22×C71—21no—
314C22×C71—21no—
315C22×C71—21no—
316C22×C71—21no—
317C22×C71—21no—
318C22×C71—21no—
319C22×C71—21no—
320C22×C71—21no—
321C22×C71—21no—
322C22×C71—21no—
323C22×C71—21no—
324C22×C71—44no—
325C22×C71—44no—
326C22×C71—44no—
327C22×C71—44no—
328C22×C71—44no—
329C22×C71—44no—
330C22×C71C2×#9912yes—
331C22×C71#41812yes—
332C22×C71#41812yes—
333C22×C71#42112yes—
334C22×C71C22×C22⋊C411yescharacteristic
335C22×C71C2×AGL(1,ℤ/8)12yes—
336C2×D71—44no—
337C2×D71—44no—
338C2×D71—44no—
339C2×D71—88no—
340C2×D71—88no—
341C2×D71—88no—
342C4×C71—21no—
343C4×C71—21no—
344C4×C71—21no—
345C4×C71—21no—
346C4×C71—21no—
347C4×C71—21no—
348C4×C71—84no—
349C4×C71C2×#9912yes—
350C4×C71C2×#9912yes—
351Dic71—44no—
352#17577—711nomaximal, Sylow
353C2×C71—22no—
354C2×C71—22no—
355C2×C71—22no—
356C2×C71—22no—
357C2×C71—22no—
358C2×C71—41no—
359C2×C71—41no—
360C2×C71C22×#9911yescharacteristic
361C2×C71C2×#41811yescharacteristic
362C2×C71C2×#42111yescharacteristic
363D71—84no—
364C22×#121—711no—
365C2×#407—711no—
366#2280D7111yescharacteristic, complemented
367#1519—714no—
368#1510—714no—
369#1507—714no—
370C71#1757711yescharacteristic, complemented, Sylow
371C23×D4—711no—
372C23×D4—1421no—
373C24×C4C2×D7111yescharacteristic
374C22×M16—1421no—
375C2×#121—712no—
376C2×#121—712no—
377C2×#121—712no—
378C2×#121—712no—
379C2×#121—712no—
380C2×#121—712no—
381C2×#121—1421no—
382C2×#121—1421no—
383C2×#121—1421no—
384C2×#121—1421no—
385C2×#121—1421no—
386C2×#121—1421no—
387C2×#117—21no—
388C22×C4⋊C4—711no—
389C22×C22⋊C4—1421no—
390#407—712no—
391#407—712no—
392#407—1421no—
393#407—1421no—
394C2×C22⋊C8—712no—
395C2×C22⋊C8—1421no—
396#381C2×D7112yescomplemented
397#380—21no—
398#380C2×D7112yescomplemented
399#379—21no—
400C4×C22⋊C4—21no—
401C4×C22⋊C4C2×D7112yescomplemented
402#327—7116no—
403C25—1421no—
404C25C22⋊D7111yescharacteristic
405C22×D4—2844no—
406C22×D4—2848no—
407C22×D4—712no—
408C22×D4—712no—
409C22×D4—712no—
410C22×D4—1422no—
411C22×D4—1422no—
412C22×D4—1422no—
413C22×D4—1422no—
414C22×D4—1422no—
415C22×D4—1422no—
416C22×D4—1421no—
417C22×D4—1421no—
418C22×D4—1421no—
419C23×C4—44no—
420C23×C4—1421no—
421C23×C4C4×D7111yescharacteristic
422C23×C4C4×D7111yescharacteristic
423C23×C4C4×D7111yescharacteristic
424C23×C4C4×D7111yescharacteristic
425C23×C4D28411yescharacteristic
426C23×C4D28411yescharacteristic
427C23×C4D28411yescharacteristic
428C23×C4D28411yescharacteristic
429C23×C4C22⋊D7111yescharacteristic
430C23×C4C22⋊D7111yescharacteristic
431C23×C4C22⋊D7111yescharacteristic
432C23×C4C22×D7111yescharacteristic
433C23×C4C22×D7111yescharacteristic
434C23×C4C22×D7111yescharacteristic
435C2×M16—2844no—
436C2×M16—1422no—
437C2×M16—1422no—
438C22×C8—1422no—
439#121—714no—
440#121—714no—
441#121—714no—
442#121—714no—
443#121—1422no—
444#121—1422no—
445#121—1422no—
446#121—1422no—
447#121—1422no—
448#121—1422no—
449#121—1422no—
450#121—1422no—
451#121—1422no—
452#121—1422no—
453#121—1422no—
454#121—1422no—
455#117—44no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—712no—
458C2×C4⋊C4—712no—
459C2×C4⋊C4—712no—
460C2×C4⋊C4—1421no—
461C2×C4⋊C4—1421no—
462C2×C4⋊C4—1421no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—1422no—
467C2×C22⋊C4—1422no—
468C2×C22⋊C4—1422no—
469C2×C22⋊C4—1422no—
470C2×C22⋊C4—1422no—
471C2×C22⋊C4—1422no—
472C2×C42—22no—
473C22⋊C8—714no—
474C22⋊C8—1422no—
475C22⋊C8—1422no—
476C22⋊C8—1422no—
477#95—22no—
478#95C22×D7114yescomplemented
479C24—24no—
480C24—42no—
481C24—42no—
482C24—2844no—
483C24—2844no—
484C24—2844no—
485C24—1422no—
486C24—1422no—
487C24—1422no—
488C24(C2×D71)⋊C411yescharacteristic
489C24(C2×D71)⋊C411yescharacteristic
490C24(C2×D71)⋊C411yescharacteristic
491C24(C2×D71)⋊C411yescharacteristic
492C24C2×C22⋊D7111yescharacteristic
493C24C2×C22⋊D7111yescharacteristic
494C24C2×C22⋊D7111yescharacteristic
495C2×D4—2844no—
496C2×D4—2844no—
497C2×D4—2844no—
498C2×D4—2844no—
499C2×D4—2844no—
500C2×D4—2848no—
501C2×D4—2848no—
502C2×D4—2848no—
503C2×D4—2848no—
504C2×D4—2848no—
505C2×D4—2848no—
506C2×D4—2844no—
507C2×D4—714no—
508C2×D4—1424no—
509C2×D4—1424no—
510C2×D4—1424no—
511C2×D4—1424no—
512C2×D4—1422no—
513C2×D4—1422no—
514C2×D4—1422no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—2844no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—1422no—
534C22×C4(C2×D71)⋊C411yescharacteristic
535C22×C4(C2×D71)⋊C411yescharacteristic
536C22×C4(C2×D71)⋊C411yescharacteristic
537C22×C4(C2×D71)⋊C411yescharacteristic
538C22×C4(C2×D71)⋊C411yescharacteristic
539C22×C4(C2×D71)⋊C411yescharacteristic
540C22×C4(C2×D71)⋊C411yescharacteristic
541C22×C4(C2×D71)⋊C411yescharacteristic
542C22×C4(C2×D71)⋊C411yescharacteristic
543C22×C4(C2×D71)⋊C411yescharacteristic
544C22×C4(C2×D71)⋊C411yescharacteristic
545C22×C4(C2×D71)⋊C411yescharacteristic
546C22×C4C2×C4×D7111yescharacteristic
547C22×C4C2×C4×D7111yescharacteristic
548C22×C4C2×C4×D7111yescharacteristic
549C22×C4C2×C4×D7111yescharacteristic
550C22×C4C2×C4×D7111yescharacteristic
551C22×C4C2×C4×D7111yescharacteristic
552C22×C4C2×C22⋊D7111yescharacteristic
553C22×C4C2×C22⋊D7111yescharacteristic
554C22×C4C2×C22⋊D7111yescharacteristic
555C22×C4C2×D28411yescharacteristic
556C22×C4C2×D28411yescharacteristic
557C22×C4C2×D28411yescharacteristic
558C22×C4C2×D28411yescharacteristic
559C22×C4C2×D28411yescharacteristic
560C22×C4C2×D28411yescharacteristic
561C22×C4C23×D7111yescharacteristic
562M16—2844no—
563M16—2844no—
564C2×C8—2844no—
565C2×C8—1424no—
566C4⋊C4—44no—
567C4⋊C4—714no—
568C4⋊C4—1422no—
569C4⋊C4—1422no—
570C4⋊C4—1422no—
571C22⋊C4—44no—
572C22⋊C4—44no—
573C22⋊C4—44no—
574C22⋊C4—1424no—
575C22⋊C4—1424no—
576C22⋊C4—1424no—
577C22⋊C4—1424no—
578C42—44no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—416no—
600C23—2844no—
601C23—2844no—
602C23—2844no—
603C23—2844no—
604C23—2844no—
605C23—2844no—
606C23—2844no—
607C23—2844no—
608C23—2844no—
609C23—56816no—
610C23—1424no—
611C23C2×(C2×D71)⋊C411yescharacteristic
612C23C2×(C2×D71)⋊C411yescharacteristic
613C23C2×(C2×D71)⋊C411yescharacteristic
614C23C2×(C2×D71)⋊C411yescharacteristic
615C23C2×(C2×D71)⋊C411yescharacteristic
616C23C2×(C2×D71)⋊C411yescharacteristic
617C23#1455615314yes—
618C23C22×C22⋊D7111yescharacteristic
619D4—2844no—
620D4—2844no—
621D4—2848no—
622D4—2848no—
623D4—2848no—
624D4—2848no—
625D4—2844no—
626D4—2844no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
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—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—2844no—
658C2×C4—2844no—
659C2×C4—2844no—
660C2×C4—1424no—
661C2×C4#1455604214yes—
662C2×C4C2×(C2×D71)⋊C411yescharacteristic
663C2×C4C2×(C2×D71)⋊C411yescharacteristic
664C2×C4C2×(C2×D71)⋊C411yescharacteristic
665C2×C4C2×(C2×D71)⋊C411yescharacteristic
666C2×C4C2×(C2×D71)⋊C411yescharacteristic
667C2×C4C2×(C2×D71)⋊C411yescharacteristic
668C2×C4C22×C4×D7111yescharacteristic
669C2×C4C22×D28411yescharacteristic
670C8—2844no—
671C22—28no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—2844no—
695C22—2844no—
696C22—2844no—
697C22—5688no—
698C22—5688no—
699C22—5688no—
700C22C2×#1455604212yes—
701C22#1798600312yes—
702C22#1798600312yes—
703C22#1798601712yes—
704C22C22×(C2×D71)⋊C411yescharacteristic
705C22C2×#1455615312yes—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—84no—
713C4—2844no—
714C4C2×#1455604212yes—
715C4C2×#1455604212yes—
716C2—22no—
717C2—22no—
718C2—22no—
719C2—22no—
720C2—22no—
721C2—41no—
722C2—41no—
723C2—5684no—
724C2C22×#1455604211yescharacteristic
725C2C2×#1798600311yescharacteristic
726C2C2×#1798601711yescharacteristic
subgroupG/H
centerC22C22×(C2×D71)⋊C4
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2280C2
socleC22×C71C22×C22⋊C4
prime radicalC22×#14556102C2
cosocleC22×C4×C71C24
hypercenter#2280D71
hypocenterC71#17577
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#17985963C2semidirect
3. #22586907C2semidirect
4. #22586868C2semidirect
5. #22586855C2semidirect
6. C71×#2280C2semidirect
7. C23×D284C4semidirect
16. C2×#14556102C4semidirect
17. C2×#14556102C4semidirect
18. C2×#14556102C4semidirect
22. C22×C4⋊Dic71C4semidirect
26. #17985963C22semidirect
27. #17985963C22semidirect
29. C2×C22⋊(C71⋊C8)C22semidirect
30. #17985732C22semidirect
33. #381×C71C22semidirect
35. #380×C71C22semidirect
38. C4×C22⋊C4×C71C22semidirect
90. C22⋊(C71⋊C8)C23semidirect
114. #95×C71C23semidirect
366. #2280D71semidirect
370. C71#17577semidirect
396. #381C2×D71semidirect
398. #380C2×D71semidirect
401. C4×C22⋊C4C2×D71semidirect
478. #95C22×D71semidirect

Maximal subgroups

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

subgroupindex
C22×#145561022
C2×#179859632
#225869072
#225868682
#225868552
C71×#22802
#1757771