Finite Group Databasebeta

← #32006888

Subgroups — #32006888

Order 18176.

1006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986553C211yesmaximal, characteristic
2C2×#17986059C211yesmaximal, characteristic
3C2×#17986058C211yesmaximal, characteristic
4#22589281C211yesmaximal, characteristic, complemented
5#22589279C211yesmaximal, characteristic, complemented
6#22589278C211yesmaximal, characteristic, complemented
7#22589278C211yesmaximal, characteristic, complemented
8#22589276C211yesmaximal, characteristic, complemented
9#22589274C211yesmaximal, characteristic, complemented
10#22589274C211yesmaximal, characteristic, complemented
11#22588410C211yesmaximal, characteristic
12#22588410C211yesmaximal, characteristic
13#22588407C211yesmaximal, characteristic
14#22588407C211yesmaximal, characteristic
15C71×#1984C211yesmaximal, characteristic, complemented
16#17986553—24no—
17#17986553—24no—
18C2×#14556127C411yescharacteristic
19C2×#14556126C411yescharacteristic
20C2×#14556118C411yescharacteristic
21C2×#14556118C411yescharacteristic
22C2×#14556108C411yescharacteristic
23C2×#14556106C411yescharacteristic
24C2×#14556106C411yescharacteristic
25C2×#14556104C411yescharacteristic
26C2×C4×Dic142C2211yescharacteristic
27C2×C4×Dic142C2211yescharacteristic
28C2×C4×Dic142C2211yescharacteristic
29C2×#14556085C2211yescharacteristic
30C2×#14556085C2211yescharacteristic
31C2×C42×D71C2211yescharacteristic
32#17986059—24no—
33#17986058—24no—
34C2×C4⋊(C71⋊C8)C2211yescharacteristic
35C2×Dic71⋊C8C2211yescharacteristic
36C2×Dic71⋊C8C2211yescharacteristic
37C2×(C2×D71)⋊C8C2211yescharacteristic
38C2×(C2×D71)⋊C8C2211yescharacteristic
39C2×(C2×D71)⋊C8C2211yescharacteristic
40C2×(C2×D71)⋊C8C2211yescharacteristic
41C2×#14556039C2211yescharacteristic
42C2×#14556038C2211yescharacteristic
43C2×C8×Dic71C2211yescharacteristic
44#17985754C2211yescharacteristic
45#17985754C2211yescharacteristic
46#17985754C2211yescharacteristic
47#17985754C2211yescharacteristic
48#17985753C2211yescharacteristic
49#17985753C2211yescharacteristic
50#17985753C2211yescharacteristic
51#17985753C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54#17985753C2211yescharacteristic
55#17985753C2211yescharacteristic
56C2×C4×Q8×C71C2211yescharacteristic
57C2×C4⋊C8×C71C2211yescharacteristic
58C2×C4×C8×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic
60#336×C71C2211yescharacteristic
61#336×C71C2211yescharacteristic
62#336×C71C2211yescharacteristic
63C22×Dic142C2×C411yescharacteristic
64C22×Dic142C2×C411yescharacteristic
65C22×Dic142C2×C411yescharacteristic
66C22×C4×D71C2×C411yescharacteristic
67C22×C4×D71C2×C411yescharacteristic
68C22×C4×D71C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73#14556127—24no—
74#14556126—24no—
75#14556118—24no—
76#14556118—24no—
77#14556108—24no—
78#14556106—24no—
79#14556106—24no—
80#14556104—24no—
81C4×Dic142—22no—
82C4×Dic142—22no—
83C4×Dic142—22no—
84C4×Dic142—22no—
85C4×Dic142—22no—
86C4×Dic142—22no—
87#14556085—22no—
88#14556085—22no—
89#14556085D414yes—
90#14556085D414yes—
91C2×C4⋊Dic71C2×C411yescharacteristic
92C2×C4⋊Dic71C2×C411yescharacteristic
93C2×C4⋊Dic71C2×C411yescharacteristic
94C2×Dic71⋊C4C2×C411yescharacteristic
95C2×Dic71⋊C4C2×C411yescharacteristic
96C2×Dic71⋊C4C2×C411yescharacteristic
97C2×Dic71⋊C4C2×C411yescharacteristic
98C2×Dic71⋊C4C2×C411yescharacteristic
99C2×Dic71⋊C4C2×C411yescharacteristic
100C2×Dic71⋊C4C2×C411yescharacteristic
101C2×Dic71⋊C4C2×C411yescharacteristic
102C2×Dic71⋊C4C2×C411yescharacteristic
103C2×Dic71⋊C4C2×C411yescharacteristic
104C2×(C2×D71)⋊C4C2×C411yescharacteristic
105C2×(C2×D71)⋊C4C2×C411yescharacteristic
106C2×(C2×D71)⋊C4C2×C411yescharacteristic
107C2×(C2×D71)⋊C4C2×C411yescharacteristic
108C2×C4×Dic71C2×C411yescharacteristic
109C2×C4×Dic71C2×C411yescharacteristic
110C2×C4×Dic71C2311yescharacteristic
111C2×C4×Dic71C2311yescharacteristic
112C2×C4×Dic71C2311yescharacteristic
113C42×D71—22no—
114C42×D71—22no—
115C4⋊(C71⋊C8)—22no—
116Dic71⋊C8—22no—
117Dic71⋊C8—22no—
118(C2×D71)⋊C8—22no—
119(C2×D71)⋊C8—22no—
120(C2×D71)⋊C8—22no—
121(C2×D71)⋊C8—22no—
122#14556039—22no—
123#14556038—22no—
124C8×Dic71—22no—
125C22×Q8×C71C2×C411yescharacteristic
126C22×C8×C71C2311yescharacteristic
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C22×C8×C71C2311yescharacteristic
130C4×Q8×C71—22no—
131C4×Q8×C71—22no—
132C2×C4⋊C4×C71C2×C411yescharacteristic
133C2×C4⋊C4×C71C2×C411yescharacteristic
134C2×C4⋊C4×C71C2×C411yescharacteristic
135C2×C42×C71C2311yescharacteristic
136C2×C42×C71C2311yescharacteristic
137C2×C42×C71C2311yescharacteristic
138C4⋊C8×C71—22no—
139C4×C8×C71—22no—
140C23×D71C22×C411yescharacteristic
141C2×Dic142—22no—
142C2×Dic142—22no—
143C2×Dic142—22no—
144C2×Dic142—22no—
145C2×Dic142—22no—
146C2×Dic142—22no—
147C2×Dic142—41no—
148C2×Dic142—41no—
149C2×Dic142—41no—
150C22×Dic71C22×C411yescharacteristic
151C22×Dic71C22×C411yescharacteristic
152C22×Dic71C22×C411yescharacteristic
153C22×Dic71C22×C411yescharacteristic
154C22×Dic71C22×C411yescharacteristic
155C22×Dic71C22×C411yescharacteristic
156C22×Dic71C22×C411yescharacteristic
157C2×C4×D71—21no—
158C2×C4×D71—21no—
159C2×C4×D71—21no—
160C2×C4×D71—21no—
161C2×C4×D71—22no—
162C2×C4×D71—22no—
163C2×C4×D71—22no—
164C2×C4×D71—22no—
165C2×C4×D71—41no—
166C2×C4×D71—41no—
167C2×C4×D71C2×D412yes—
168C2×C4×D71C2×D412yes—
169C2×C71⋊C8—21no—
170C2×C71⋊C8—21no—
171C2×C71⋊C8—21no—
172C2×C71⋊C8—21no—
173C2×C71⋊C8—21no—
174C2×C71⋊C8—21no—
175C2×C71⋊C8—21no—
176C2×C71⋊C8—21no—
177C2×C71⋊C8—21no—
178C2×C71⋊C8—21no—
179C2×C71⋊C8—21no—
180C2×C71⋊C8—21no—
181C4⋊Dic71—22no—
182C4⋊Dic71—22no—
183C4⋊Dic71—22no—
184Dic71⋊C4—22no—
185Dic71⋊C4—22no—
186Dic71⋊C4—22no—
187Dic71⋊C4—22no—
188Dic71⋊C4—22no—
189Dic71⋊C4—22no—
190Dic71⋊C4—22no—
191Dic71⋊C4—22no—
192Dic71⋊C4C22⋊C414yes—
193Dic71⋊C4C22⋊C414yes—
194(C2×D71)⋊C4—22no—
195(C2×D71)⋊C4—22no—
196(C2×D71)⋊C4C22⋊C414yes—
197(C2×D71)⋊C4C22⋊C414yes—
198C4×Dic71—21no—
199C4×Dic71—21no—
200C4×Dic71—21no—
201C4×Dic71—21no—
202C4×Dic71—22no—
203C4×Dic71—22no—
204C4×Dic71C2×D412yes—
205C4×Dic71C2×D412yes—
206C2×Q8×C71—22no—
207C2×Q8×C71—22no—
208C2×Q8×C71—41no—
209C22×C4×C71C22×C411yescharacteristic
210C22×C4×C71C22×C411yescharacteristic
211C22×C4×C71C22×C411yescharacteristic
212C22×C4×C71C22×C411yescharacteristic
213C22×C4×C71C22×C411yescharacteristic
214C22×C4×C71C22×C411yescharacteristic
215C22×C4×C71C2411yescharacteristic
216C2×C8×C71—21no—
217C2×C8×C71—21no—
218C2×C8×C71—21no—
219C2×C8×C71—21no—
220C2×C8×C71—21no—
221C2×C8×C71—21no—
222C2×C8×C71—21no—
223C2×C8×C71—21no—
224C2×C8×C71—21no—
225C2×C8×C71—21no—
226C2×C8×C71—21no—
227C2×C8×C71—21no—
228C4⋊C4×C71—22no—
229C4⋊C4×C71—22no—
230C4⋊C4×C71—22no—
231C42×C71—21no—
232C42×C71—21no—
233C42×C71—21no—
234C42×C71—21no—
235C42×C71C2×D412yes—
236C42×C71C2×D412yes—
237C23×C71C23×C411yescharacteristic
238C22×D71—21no—
239C22×D71—21no—
240C22×D71—21no—
241C22×D71—21no—
242C22×D71—21no—
243C22×D71—21no—
244C22×D71C2×C22⋊C412yes—
245Q8×C71—44no—
246C2×C4×C71—21no—
247C2×C4×C71—21no—
248C2×C4×C71—21no—
249C2×C4×C71—21no—
250C2×C4×C71—21no—
251C2×C4×C71—21no—
252C2×C4×C71—21no—
253C2×C4×C71—21no—
254C2×C4×C71—21no—
255C2×C4×C71—21no—
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71C2×C22⋊C412yes—
262C2×C4×C71C2×C22⋊C412yes—
263C2×C4×C71#13112yes—
264C2×C4×C71C22×D411yescharacteristic
265C2×C4×C71C22×D411yescharacteristic
266C2×C4×C712−1+411yescharacteristic
267C2×C4×C712−1+411yescharacteristic
268C2×C4×C712−1+411yescharacteristic
269C2×C4×C712−1+411yescharacteristic
270C2×Dic71—21no—
271C2×Dic71—21no—
272C2×Dic71—21no—
273C2×Dic71—21no—
274C2×Dic71—21no—
275C2×Dic71—21no—
276C2×Dic71—21no—
277C2×Dic71—21no—
278C2×Dic71—21no—
279C2×Dic71—21no—
280C2×Dic71—21no—
281C2×Dic71—21no—
282C2×Dic71—21no—
283C2×Dic71—21no—
284C2×Dic71—21no—
285C2×Dic71—21no—
286C2×Dic71—21no—
287C2×Dic71C2×C22⋊C412yes—
288C2×Dic71C2×C22⋊C412yes—
289C2×Dic71C2×C22⋊C412yes—
290C2×Dic71#13112yes—
291C4×D71—22no—
292C4×D71—22no—
293C4×D71—22no—
294C4×D71—22no—
295C4×D71—44no—
296C4×D71—44no—
297Dic142—44no—
298Dic142—44no—
299Dic142—44no—
300C8×C71—41no—
301C8×C71—41no—
302C8×C71—41no—
303C8×C71—41no—
304C71⋊C8—41no—
305C71⋊C8—41no—
306C71⋊C8—41no—
307C71⋊C8—41no—
308C22×C71C22×C22⋊C411yescharacteristic
309C22×C71#51911yescharacteristic
310C22×C71#51911yescharacteristic
311C22×C71C2×#13111yescharacteristic
312C22×C71C2×#13111yescharacteristic
313C22×C71#56811yescharacteristic
314C22×C71#56811yescharacteristic
315C2×D71—22no—
316C2×D71—22no—
317C2×D71—22no—
318C2×D71—41no—
319C2×D71—41no—
320C2×D71—41no—
321C2×D71—41no—
322C4×C71—22no—
323C4×C71—22no—
324C4×C71—22no—
325C4×C71—41no—
326C4×C71—41no—
327C4×C71—41no—
328C4×C71#53611yescharacteristic
329C4×C71#53611yescharacteristic
330C4×C71#53611yescharacteristic
331C4×C71#53611yescharacteristic
332Dic71—22no—
333Dic71—22no—
334Dic71—22no—
335Dic71—22no—
336Dic71—41no—
337Dic71—41no—
338Dic71—41no—
339#21824—711nomaximal, Sylow
340C2×C71#231011yescharacteristic
341C2×C71#288011yescharacteristic
342C2×C71#288011yescharacteristic
343C2×C71#298511yescharacteristic
344C2×C71#298511yescharacteristic
345C2×C71#298611yescharacteristic
346C2×C71#298711yescharacteristic
347D71—42no—
348C2×#533—711no—
349C2×#433—711no—
350C2×#433—711no—
351#1985—711no—
352#1985—711no—
353#1985—711no—
354#1985—711no—
355#1984—711no—
356#1984—711no—
357#1984—711no—
358#1984D7111yescharacteristic, complemented
359#1818—711no—
360#1818—711no—
361#1817—711no—
362#1817—711no—
363C71#2182411yescharacteristic, complemented, Sylow
364#533—1424no—
365#533—1424no—
366C2×C4⋊Q8—711no—
367C2×C4⋊Q8—711no—
368C2×#125—711no—
369C2×#125—711no—
370C2×C22⋊Q8—711no—
371C2×C22⋊Q8—711no—
372C2×C22⋊Q8—711no—
373C2×C22⋊Q8—711no—
374C2×C4×Q8—711no—
375C2×C4×Q8—711no—
376C2×C4×Q8—711no—
377C2×C4×Q8C2×D7111yescharacteristic
378C2×#117—711no—
379C2×#117—711no—
380C22×C42—711no—
381#433—1424no—
382#433—1424no—
383C2×C4⋊C8—711no—
384C2×C4⋊C8—711no—
385C2×C4⋊C8—711no—
386C2×C4⋊C8C2×D7111yescharacteristic
387C2×C22⋊C8—711no—
388C2×C22⋊C8—711no—
389C2×C22⋊C8—711no—
390C2×C22⋊C8—711no—
391C2×#97—711no—
392C2×#97—711no—
393C2×C4×C8—711no—
394C2×C4×C8C2×D7111yescharacteristic
395#336—711no—
396#336—711no—
397#336—711no—
398#336—711no—
399#336—711no—
400#336—711no—
401#336—711no—
402#336—711no—
403#336—711no—
404#336—711no—
405#336—711no—
406#336—711no—
407#336C2×D7111yescharacteristic
408#336C2×D7111yescharacteristic
409#336C2×D7111yescharacteristic
410#336C2×D7111yescharacteristic
411C22×Q8—711no—
412C22×Q8—711no—
413C22×Q8—711no—
414C22×Q8C4×D7111yescharacteristic
415C23×C4—711no—
416C23×C4—711no—
417C23×C4—711no—
418C22×C8—711no—
419C22×C8—711no—
420C22×C8—711no—
421C22×C8—711no—
422C22×C8C22×D7111yescharacteristic
423C22×C8C22×D7111yescharacteristic
424C22×C8C22×D7111yescharacteristic
425C22×C8C22×D7111yescharacteristic
426C4⋊Q8—1424no—
427C4⋊Q8—1424no—
428#125—1424no—
429#125—1424no—
430C22⋊Q8—1424no—
431C22⋊Q8—1424no—
432C22⋊Q8—1424no—
433C22⋊Q8—1424no—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—1422no—
437C4×Q8—1422no—
438C4×Q8—1422no—
439C4×Q8—1422no—
440C4×Q8—1422no—
441C4×Q8—1422no—
442#117—714no—
443#117—714no—
444#117—1422no—
445#117—1422no—
446C2×C4⋊C4—711no—
447C2×C4⋊C4—711no—
448C2×C4⋊C4—711no—
449C2×C4⋊C4—711no—
450C2×C4⋊C4—711no—
451C2×C4⋊C4—711no—
452C2×C4⋊C4—711no—
453C2×C4⋊C4—711no—
454C2×C4⋊C4—711no—
455C2×C4⋊C4—711no—
456C2×C4⋊C4—711no—
457C2×C4⋊C4—711no—
458C2×C4⋊C4—711no—
459C2×C4⋊C4C4×D7111yescharacteristic
460C2×C4⋊C4C4×D7111yescharacteristic
461C2×C4⋊C4C4×D7111yescharacteristic
462C2×C22⋊C4—711no—
463C2×C22⋊C4—711no—
464C2×C22⋊C4—711no—
465C2×C22⋊C4—711no—
466C2×C42—711no—
467C2×C42—711no—
468C2×C42—711no—
469C2×C42—711no—
470C2×C42—711no—
471C2×C42—1422no—
472C2×C42—1422no—
473C2×C42C22×D7111yescharacteristic
474C2×C42C22×D7111yescharacteristic
475C2×C42C22×D7111yescharacteristic
476C4⋊C8—22no—
477C4⋊C8—1422no—
478C4⋊C8—1422no—
479C4⋊C8—1422no—
480C22⋊C8—1422no—
481C22⋊C8—1422no—
482C22⋊C8—1422no—
483C22⋊C8—1422no—
484#97—1422no—
485#97—1422no—
486C4×C8—22no—
487C4×C8—1422no—
488C24—711no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—41no—
492C2×Q8—2841no—
493C2×Q8—2841no—
494C2×Q8—2841no—
495C2×Q8—1422no—
496C2×Q8—1422no—
497C2×Q8—1422no—
498C2×Q8—1422no—
499C2×Q8—1422no—
500C2×Q8—1422no—
501C22×C4—2841no—
502C22×C4—2841no—
503C22×C4—711no—
504C22×C4—711no—
505C22×C4—711no—
506C22×C4—711no—
507C22×C4—712no—
508C22×C4—712no—
509C22×C4—711no—
510C22×C4—711no—
511C22×C4—711no—
512C22×C4—1422no—
513C22×C4—1422no—
514C22×C4—1422no—
515C22×C4—1422no—
516C22×C4—1421no—
517C22×C4—1421no—
518C22×C4—1421no—
519C22×C4—1421no—
520C22×C4C2×C4×D7111yescharacteristic
521C22×C4C2×C4×D7111yescharacteristic
522C22×C4C2×C4×D7111yescharacteristic
523C22×C4C2×C4×D7111yescharacteristic
524C22×C4C2×C4×D7111yescharacteristic
525C22×C4C2×C4×D7111yescharacteristic
526C22×C4C23×D7111yescharacteristic
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—1421no—
540C2×C8—1421no—
541C2×C8—1421no—
542C2×C8—1421no—
543C2×C8—1421no—
544C2×C8—1421no—
545C2×C8—1421no—
546C2×C8—1421no—
547C2×C8—1421no—
548C2×C8—1421no—
549C2×C8—1421no—
550C2×C8—1421no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—714no—
555C4⋊C4—714no—
556C4⋊C4—1422no—
557C4⋊C4—1422no—
558C4⋊C4—1422no—
559C4⋊C4—1422no—
560C4⋊C4—1422no—
561C4⋊C4—1422no—
562C4⋊C4—1422no—
563C4⋊C4—1422no—
564C4⋊C4—1422no—
565C4⋊C4—1422no—
566C4⋊C4—1422no—
567C22⋊C4—714no—
568C22⋊C4—714no—
569C22⋊C4—1422no—
570C22⋊C4—1422no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—712no—
576C42—712no—
577C42—1422no—
578C42—1422no—
579C42—1421no—
580C42—1421no—
581C42—1421no—
582C42—1421no—
583C42D4×D7112yes—
584C42D4×D7112yes—
585C23—712no—
586C23—1421no—
587C23—1421no—
588C23—1421no—
589C23—1421no—
590C23—1421no—
591C23—1421no—
592C23C22×C4×D7111yescharacteristic
593Q8—44no—
594Q8—2844no—
595Q8—2844no—
596Q8—2844no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—2844no—
613C2×C4—2844no—
614C2×C4—712no—
615C2×C4—712no—
616C2×C4—712no—
617C2×C4—712no—
618C2×C4—1421no—
619C2×C4—1421no—
620C2×C4—1421no—
621C2×C4—1421no—
622C2×C4—1421no—
623C2×C4—1421no—
624C2×C4—1421no—
625C2×C4—1421no—
626C2×C4—1421no—
627C2×C4—1421no—
628C2×C4—1421no—
629C2×C4—1421no—
630C2×C4—1421no—
631C2×C4—1421no—
632C2×C4—1421no—
633C2×C4—1421no—
634C2×C4—1421no—
635C2×C4—1422no—
636C2×C4—1422no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4C22⋊C4×D7112yes—
640C2×C4C22⋊C4×D7112yes—
641C2×C4#1455613412yes—
642C2×C4C2×D4×D7111yescharacteristic
643C2×C4C2×D4×D7111yescharacteristic
644C2×C4#1455617511yescharacteristic
645C2×C4#1455617511yescharacteristic
646C2×C4#1455617611yescharacteristic
647C2×C4#1455617611yescharacteristic
648C8—41no—
649C8—41no—
650C8—41no—
651C8—41no—
652C8—2841no—
653C8—2841no—
654C8—2841no—
655C8—2841no—
656C22—2841no—
657C22—2841no—
658C22—2841no—
659C22—2841no—
660C22—1422no—
661C22—1422no—
662C22—1422no—
663C22C2×C22⋊C4×D7111yescharacteristic
664C22#1798647511yescharacteristic
665C22#1798647511yescharacteristic
666C22#131×D7111yescharacteristic
667C22C2×#1455613411yescharacteristic
668C22#1798676411yescharacteristic
669C22#1798676511yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—2841no—
677C4—2841no—
678C4—2841no—
679C4—1422no—
680C4—1422no—
681C4—1422no—
682C4—1422no—
683C4#1798656911yescharacteristic
684C4#1798657211yescharacteristic
685C4#1798657211yescharacteristic
686C4#1798657411yescharacteristic
687C2—2842no—
688C2#2259092311yescharacteristic
689C2#2259678611yescharacteristic
690C2#2259678811yescharacteristic
691C2#2259743111yescharacteristic
692C2#2259743311yescharacteristic
693C2#2259744011yescharacteristic
694C2#2259744311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1984C2
prime radicalC23×D71C22×C4
cosocleC22×C4×C71C24
hypercenter#1984D71
hypocenterC71#21824
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1984

Complements

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

NH ≅ G/Ntype
4. #22589281C2semidirect
5. #22589279C2semidirect
6. #22589278C2semidirect
7. #22589278C2semidirect
8. #22589276C2semidirect
9. #22589274C2semidirect
10. #22589274C2semidirect
15. C71×#1984C2semidirect
358. #1984D71semidirect
363. C71#21824semidirect

Maximal subgroups

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

subgroupindex
C2×#179865532
C2×#179860592
C2×#179860582
#225892812
#225892792
#225892782
#225892762
#225892742
#225884102
#225884072
C71×#19842
#2182471