Finite Group Databasebeta

← #32015514

Subgroups — #32015514

Order 18176.

980 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986078C211yesmaximal, characteristic
2C2×#17986072C211yesmaximal, characteristic
3C2×#17986024C211yesmaximal, characteristic, complemented
4C2×#17986021C211yesmaximal, characteristic, complemented
5#22590784C211yesmaximal, characteristic
6#22589063C211yesmaximal, characteristic, complemented
7#22589058C211yesmaximal, characteristic, complemented
8#22588524C211yesmaximal, characteristic, complemented
9#22588524C211yesmaximal, characteristic, complemented
10#22588524C211yesmaximal, characteristic, complemented
11#22588519C211yesmaximal, characteristic, complemented
12#22588494C211yesmaximal, characteristic, complemented
13#22588321C211yesmaximal, characteristic, complemented
14#22588317C211yesmaximal, characteristic, complemented
15C71×#1768C211yesmaximal, characteristic, complemented
16C22×#11765848C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20C2×C4×D284C2211yescharacteristic
21C2×#14556085C2211yescharacteristic
22C2×C42×D71C2211yescharacteristic
23#17986078—24no—
24#17986072—24no—
25#17986024—24no—
26#17986021—24no—
27C2×C4⋊(C71⋊C8)C2211yescharacteristic
28C2×C4⋊(C71⋊C8)C2211yescharacteristic
29C2×C4⋊(C71⋊C8)C2211yescharacteristic
30C2×C4⋊(C71⋊C8)C2211yescharacteristic
31C2×C4⋊(C71⋊C8)C2211yescharacteristic
32C2×C4⋊(C71⋊C8)C2211yescharacteristic
33C2×Dic71⋊C8C2211yescharacteristic
34C2×Dic71⋊C8C2211yescharacteristic
35C2×Dic71⋊C8C2211yescharacteristic
36C2×Dic71⋊C8C2211yescharacteristic
37C2×(C2×D71)⋊C8C2211yescharacteristic
38C2×(C2×D71)⋊C8C2211yescharacteristic
39C2×(C2×D71)⋊C8C2211yescharacteristic
40C2×(C2×D71)⋊C8C2211yescharacteristic
41#17985891C411yescharacteristic
42#17985891C411yescharacteristic
43#17985884C411yescharacteristic
44#17985884C411yescharacteristic
45#17985877C411yescharacteristic
46#17985877C411yescharacteristic
47#17985873C411yescharacteristic
48#17985873C411yescharacteristic
49C4×C4⋊Dic71C2211yescharacteristic
50C4×(C2×D71)⋊C4C2211yescharacteristic
51C4×(C2×D71)⋊C4C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54#17985753C2211yescharacteristic
55#17985753C2211yescharacteristic
56C2×C4⋊C8×C71C2211yescharacteristic
57C2×C4⋊C8×C71C2211yescharacteristic
58C2×#97×C71C2211yescharacteristic
59C2×C4×C8×C71C2211yescharacteristic
60#376×C71C2211yescharacteristic
61#336×C71C2211yescharacteristic
62#336×C71C2211yescharacteristic
63C22×D284C2×C411yescharacteristic
64C22×C4×D71C2×C411yescharacteristic
65C22×C4×D71C2×C411yescharacteristic
66C22×C4×D71C2311yescharacteristic
67C22×C4×D71C2311yescharacteristic
68C2×#11765848—22no—
69C2×#11765848—22no—
70C2×#11765848—22no—
71C2×#11765848—22no—
72C2×#11765848—22no—
73C2×#11765848—22no—
74C2×#11765848—41no—
75C2×#11765848—41no—
76C2×#11765848—41no—
77C22×C71⋊C8C2311yescharacteristic
78C22×C71⋊C8C2311yescharacteristic
79C22×C71⋊C8C2311yescharacteristic
80C22×C71⋊C8C2311yescharacteristic
81C2×C8×D71—22no—
82C2×C8×D71—22no—
83C2×C8×D71—41no—
84C4×D284D414yes—
85C4×D284Q814yes—
86#14556085—22no—
87#14556085—22no—
88C2×C4⋊Dic71C2×C411yescharacteristic
89C2×C4⋊Dic71C2×C411yescharacteristic
90C2×C4⋊Dic71C2×C411yescharacteristic
91C2×Dic71⋊C4C2×C411yescharacteristic
92C2×Dic71⋊C4C2×C411yescharacteristic
93C2×(C2×D71)⋊C4C2×C411yescharacteristic
94C2×(C2×D71)⋊C4C2×C411yescharacteristic
95C2×(C2×D71)⋊C4C2×C411yescharacteristic
96C2×(C2×D71)⋊C4C2×C411yescharacteristic
97C2×(C2×D71)⋊C4C2×C411yescharacteristic
98C2×(C2×D71)⋊C4C2×C411yescharacteristic
99C2×(C2×D71)⋊C4C2×C411yescharacteristic
100C2×(C2×D71)⋊C4C2×C411yescharacteristic
101C2×C4×Dic71C2×C411yescharacteristic
102C2×C4×Dic71C2×C411yescharacteristic
103C2×C4×Dic71C2311yescharacteristic
104C2×C4×Dic71C2311yescharacteristic
105C42×D71—22no—
106C42×D71—22no—
107C4⋊(C71⋊C8)—22no—
108C4⋊(C71⋊C8)—22no—
109C4⋊(C71⋊C8)—22no—
110C4⋊(C71⋊C8)—22no—
111C4⋊(C71⋊C8)—41no—
112C4⋊(C71⋊C8)—41no—
113Dic71⋊C8—22no—
114Dic71⋊C8—22no—
115Dic71⋊C8—22no—
116Dic71⋊C8—22no—
117(C2×D71)⋊C8—22no—
118(C2×D71)⋊C8—22no—
119(C2×D71)⋊C8—22no—
120(C2×D71)⋊C8—22no—
121C71⋊#95C2×C411yescharacteristic
122C71⋊#95C2×C411yescharacteristic
123C71⋊#95C2×C411yescharacteristic
124C71⋊#95C2×C411yescharacteristic
125C71⋊#95C2×C411yescharacteristic
126C71⋊#95C2×C411yescharacteristic
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C22×C8×C71C2311yescharacteristic
130C22×C8×C71C2311yescharacteristic
131C2×C42×C71C2311yescharacteristic
132C2×C42×C71C2311yescharacteristic
133C2×C42×C71C2311yescharacteristic
134C4⋊C8×C71—22no—
135C4⋊C8×C71D414yescomplemented
136#97×C71—22no—
137C4×C8×C71—22no—
138#95×C71C2×C411yescharacteristic
139#95×C71C2×C411yescharacteristic
140#95×C71C2×C411yescharacteristic
141#95×C71C2×C411yescharacteristic
142C23×D71C22×C411yescharacteristic
143C23×D71C22×C411yescharacteristic
144C2×D284—41no—
145C2×D284—41no—
146C2×D284C4⋊C414yes—
147C22×Dic71C22×C411yescharacteristic
148C22×Dic71C22×C411yescharacteristic
149C22×Dic71C22×C411yescharacteristic
150C22×Dic71C22×C411yescharacteristic
151C22×Dic71C22×C411yescharacteristic
152C22×Dic71C22×C411yescharacteristic
153C2×C4×D71—21no—
154C2×C4×D71—21no—
155C2×C4×D71—21no—
156C2×C4×D71—21no—
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—41no—
165C2×C4×D71—41no—
166C2×C4×D71—41no—
167C2×C4×D71C2×D412yes—
168C2×C4×D71C2×D412yes—
169C2×C4×D71C2×Q812yes—
170C2×C4×D71C2×Q812yes—
171#11765848—44no—
172#11765848—44no—
173#11765848—44no—
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—
181C2×C71⋊C8—21no—
182C2×C71⋊C8—21no—
183C2×C71⋊C8—21no—
184C2×C71⋊C8—21no—
185C2×C71⋊C8—21no—
186C8×D71—44no—
187C4⋊Dic71—22no—
188C4⋊Dic71—41no—
189C4⋊Dic71C4⋊C414yes—
190Dic71⋊C4—22no—
191Dic71⋊C4—22no—
192(C2×D71)⋊C4—22no—
193(C2×D71)⋊C4—22no—
194(C2×D71)⋊C4—22no—
195(C2×D71)⋊C4—41no—
196(C2×D71)⋊C4—41no—
197(C2×D71)⋊C4—41no—
198(C2×D71)⋊C4C4⋊C414yes—
199(C2×D71)⋊C4C4⋊C414yes—
200C4×Dic71—22no—
201C4×Dic71—22no—
202C4×Dic71—21no—
203C4×Dic71—21no—
204C4×Dic71—21no—
205C4×Dic71—21no—
206C22×C4×C71C22×C411yescharacteristic
207C22×C4×C71C22×C411yescharacteristic
208C22×C4×C71C22×C411yescharacteristic
209C22×C4×C71C22×C411yescharacteristic
210C22×C4×C71C22×C411yescharacteristic
211C22×C4×C71C22×C411yescharacteristic
212C22×C4×C71C2411yescharacteristic
213C2×C8×C71—21no—
214C2×C8×C71—21no—
215C2×C8×C71—21no—
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×C71C2×D412yes—
224C2×C8×C71C2×D412yes—
225C42×C71—21no—
226C42×C71—21no—
227C42×C71C2×D412yes—
228C42×C71C2×D412yes—
229C42×C71C2×Q812yes—
230C42×C71#4112yes—
231C23×C71C23×C411yescharacteristic
232C22×D71—21no—
233C22×D71—21no—
234C22×D71—21no—
235C22×D71—21no—
236C22×D71—21no—
237C22×D71—21no—
238C22×D71—21no—
239C22×D71—21no—
240C22×D71—21no—
241C22×D71—21no—
242C22×D71—21no—
243C22×D71—21no—
244C22×D71C2×C4⋊C412yes—
245C22×D71C2×C4⋊C412yes—
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×C71C2×C4⋊C412yes—
261C2×C4×C71C2×C4⋊C412yes—
262C2×C4×C71C4×D412yes—
263C2×C4×C71C4×D412yes—
264C2×C4×C71C22×D411yescharacteristic
265C2×C4×C71C22×D411yescharacteristic
266C2×C4×C71C22×Q811yescharacteristic
267C2×C4×C71C2×#4111yescharacteristic
268C2×C4×C71H(5,𝔽2)11yescharacteristic
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×Dic71C2×C4⋊C412yes—
286C2×Dic71C2×C4⋊C412yes—
287C2×Dic71#13112yes—
288D284—44no—
289C4×D71—22no—
290C4×D71—22no—
291C4×D71—22no—
292C4×D71—22no—
293C4×D71—22no—
294C4×D71—22no—
295C4×D71—22no—
296C4×D71—22no—
297C4×D71—44no—
298C4×D71—44no—
299C8×C71—22no—
300C8×C71—22no—
301C8×C71—41no—
302C8×C71—41no—
303C71⋊C8—41no—
304C71⋊C8—41no—
305C71⋊C8—41no—
306C71⋊C8—41no—
307C22×C71C22×C4⋊C411yescharacteristic
308C22×C71C2×C4×D411yescharacteristic
309C22×C71#52011yescharacteristic
310C22×C71C2×#13111yescharacteristic
311C22×C71#56811yescharacteristic
312C22×C71#56811yescharacteristic
313C22×C71#56811yescharacteristic
314C2×D71—22no—
315C2×D71—22no—
316C2×D71—22no—
317C2×D71—22no—
318C2×D71—22no—
319C2×D71—22no—
320C2×D71—41no—
321C2×D71—41no—
322C2×D71—41no—
323C2×D71—41no—
324C2×D71—41no—
325C2×D71—41no—
326C2×D71—41no—
327C2×D71—41no—
328C4×C71—22no—
329C4×C71—22no—
330C4×C71—22no—
331C4×C71—22no—
332C4×C71—41no—
333C4×C71—41no—
334C4×C71D4211yescharacteristic
335C4×C71#54711yescharacteristic
336C4×C71D4×Q811yescharacteristic
337C4×C71#55411yescharacteristic
338Dic71—22no—
339Dic71—22no—
340Dic71—22no—
341Dic71—41no—
342Dic71—41no—
343Dic71—41no—
344#22649—711nomaximal, Sylow
345C2×C71D4×C4⋊C411yescharacteristic
346C2×C71#290511yescharacteristic
347C2×C71#290611yescharacteristic
348C2×C71#293011yescharacteristic
349C2×C71#293311yescharacteristic
350C2×C71#299311yescharacteristic
351C2×C71#299511yescharacteristic
352D71—42no—
353D71—42no—
354C2×#436—711no—
355C2×#435—711no—
356C2×#424—711no—
357C2×#423—711no—
358#2290—711no—
359#1940—711no—
360#1939—711no—
361#1851—711no—
362#1851—711no—
363#1851—711no—
364#1850—711no—
365#1843—711no—
366#1798—711no—
367#1797—711no—
368#1768D7111yescharacteristic, complemented
369C71#2264911yescharacteristic, complemented, Sylow
370C22×M16—711no—
371C22×M16—711no—
372C22×M16—711no—
373C23×C8—711no—
374C2×C4×D4—711no—
375C2×#117—711no—
376C22×C42—711no—
377#436—1424no—
378#435—1424no—
379#424—1424no—
380#423—1424no—
381C2×C4⋊C8—711no—
382C2×C4⋊C8—711no—
383C2×C4⋊C8—711no—
384C2×C4⋊C8—711no—
385C2×C4⋊C8—711no—
386C2×C4⋊C8—711no—
387C2×C4⋊C8—711no—
388C2×C4⋊C8—711no—
389C2×C4⋊C8—711no—
390C2×C4⋊C8—711no—
391C2×C4⋊C8C2×D7111yescharacteristic
392C2×C4⋊C8C2×D7111yescharacteristic
393C2×C22⋊C8—711no—
394C2×C22⋊C8—711no—
395C2×C22⋊C8—711no—
396C2×C22⋊C8—711no—
397C2×#97C2×D7111yescharacteristic
398C2×C4×C8C2×D7111yescharacteristic
399#388—711no—
400#388—711no—
401#387—711no—
402#387—711no—
403#386—711no—
404#386—711no—
405#385—711no—
406#385—711no—
407C4×C4⋊C4—711no—
408C4×C22⋊C4—711no—
409C4×C22⋊C4—711no—
410#376C2×D7111yescharacteristic
411#336—711no—
412#336—711no—
413#336—711no—
414#336—711no—
415#336C2×D7111yescharacteristic
416#336C2×D7111yescharacteristic
417C22×D4—711no—
418C23×C4—711no—
419C23×C4—711no—
420C23×C4—711no—
421C23×C4—711no—
422C2×M16—2841no—
423C2×M16—2841no—
424C2×M16—2841no—
425C2×M16—1422no—
426C2×M16—1422no—
427C2×M16—1422no—
428C2×M16—1422no—
429C2×M16—1422no—
430C2×M16—1422no—
431C22×C8—2841no—
432C22×C8—711no—
433C22×C8—711no—
434C22×C8—711no—
435C22×C8—711no—
436C22×C8—1422no—
437C22×C8—1422no—
438C22×C8C22×D7111yescharacteristic
439C22×C8C22×D7111yescharacteristic
440C22×C8C22×D7111yescharacteristic
441C22×C8C22×D7111yescharacteristic
442C4×D4—714no—
443C4×D4—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×C22⋊C4—711no—
452C2×C22⋊C4—711no—
453C2×C22⋊C4—711no—
454C2×C22⋊C4—711no—
455C2×C22⋊C4—711no—
456C2×C22⋊C4—711no—
457C2×C22⋊C4—711no—
458C2×C22⋊C4—711no—
459C2×C42—711no—
460C2×C42—711no—
461C2×C42—711no—
462C2×C42—711no—
463C2×C42—1422no—
464C2×C42—1422no—
465C2×C42C22×D7111yescharacteristic
466C2×C42C22×D7111yescharacteristic
467C2×C42C22×D7111yescharacteristic
468C4⋊C8—22no—
469C4⋊C8—2841no—
470C4⋊C8—2841no—
471C4⋊C8—1422no—
472C4⋊C8—1422no—
473C4⋊C8—1422no—
474C4⋊C8—1422no—
475C4⋊C8—1422no—
476C4⋊C8—1422no—
477C4⋊C8—1422no—
478C4⋊C8—1422no—
479C4⋊C8D28414yescomplemented
480C22⋊C8—1422no—
481C22⋊C8—1422no—
482C22⋊C8—1422no—
483C22⋊C8—1422no—
484#97—22no—
485C4×C8—22no—
486#95—711no—
487#95—711no—
488#95—711no—
489#95—711no—
490#95—711no—
491#95—711no—
492#95C4×D7111yescharacteristic
493#95C4×D7111yescharacteristic
494#95C4×D7111yescharacteristic
495#95C4×D7111yescharacteristic
496C24—711no—
497C24—711no—
498C2×D4—2841no—
499C2×D4—2841no—
500C2×D4—714no—
501C22×C4—2841no—
502C22×C4—2841no—
503C22×C4—2841no—
504C22×C4—711no—
505C22×C4—711no—
506C22×C4—711no—
507C22×C4—712no—
508C22×C4—712no—
509C22×C4—712no—
510C22×C4—712no—
511C22×C4—711no—
512C22×C4—711no—
513C22×C4—711no—
514C22×C4—1422no—
515C22×C4—1422no—
516C22×C4—1422no—
517C22×C4—1421no—
518C22×C4—1421no—
519C22×C4—1421no—
520C22×C4—1421no—
521C22×C4—1421no—
522C22×C4—1421no—
523C22×C4—1421no—
524C22×C4—1421no—
525C22×C4C2×C4×D7111yescharacteristic
526C22×C4C2×C4×D7111yescharacteristic
527C22×C4C2×C4×D7111yescharacteristic
528C22×C4C2×C4×D7111yescharacteristic
529C22×C4C2×C4×D7111yescharacteristic
530C22×C4C2×C4×D7111yescharacteristic
531C22×C4C23×D7111yescharacteristic
532M16—2844no—
533M16—2844no—
534M16—2844no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—2844no—
546C2×C8—1421no—
547C2×C8—1421no—
548C2×C8—1421no—
549C2×C8—1421no—
550C2×C8—1421no—
551C2×C8—1421no—
552C2×C8—1421no—
553C2×C8—1421no—
554C2×C8—1421no—
555C2×C8—1421no—
556C2×C8—1421no—
557C2×C8—1421no—
558C2×C8C2×D28412yes—
559C2×C8C2×D28412yes—
560C4⋊C4—2841no—
561C4⋊C4—714no—
562C4⋊C4—1422no—
563C4⋊C4—1422no—
564C4⋊C4—1422no—
565C22⋊C4—2841no—
566C22⋊C4—2841no—
567C22⋊C4—2841no—
568C22⋊C4—714no—
569C22⋊C4—714no—
570C22⋊C4—1422no—
571C22⋊C4—1422no—
572C22⋊C4—1422no—
573C42—21no—
574C42—21no—
575C42—1421no—
576C42—1421no—
577C42—1421no—
578C42—1421no—
579C42—1422no—
580C42—1422no—
581C42D4×D7112yes—
582C42C2×D28412yes—
583C42Q8×D7112yes—
584C42#1176586512yes—
585C23—712no—
586C23—712no—
587C23—1421no—
588C23—1421no—
589C23—1421no—
590C23—1421no—
591C23—1421no—
592C23—1421no—
593C23—1421no—
594C23—1421no—
595C23—1421no—
596C23—1421no—
597C23—1421no—
598C23—1421no—
599C23C22×C4×D7111yescharacteristic
600D4—2844no—
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—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—2844no—
616C2×C4—2844no—
617C2×C4—712no—
618C2×C4—712no—
619C2×C4—712no—
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×C4—1422no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1422no—
643C2×C4C4⋊C4×D7112yes—
644C2×C4C4⋊C4×D7112yes—
645C2×C4C4×D28412yes—
646C2×C4C4×D28412yes—
647C2×C4C2×D4×D7111yescharacteristic
648C2×C4C22×D28411yescharacteristic
649C2×C4C2×Q8×D7111yescharacteristic
650C2×C4C2×#1176586511yescharacteristic
651C2×C4#1455617411yescharacteristic
652C2×C4#1455617511yescharacteristic
653C8—22no—
654C8—22no—
655C8—41no—
656C8—41no—
657C8—2841no—
658C8—2841no—
659C8—2841no—
660C8—2841no—
661C22—2841no—
662C22—2841no—
663C22—2841no—
664C22—2841no—
665C22—2841no—
666C22—2841no—
667C22—2841no—
668C22—2841no—
669C22—1422no—
670C22—1422no—
671C22—1422no—
672C22—1422no—
673C22—1422no—
674C22—1422no—
675C22C2×C4⋊C4×D7111yescharacteristic
676C22C2×C4×D28411yescharacteristic
677C22#1798647911yescharacteristic
678C22#131×D7111yescharacteristic
679C22#1798676411yescharacteristic
680C22#1798676411yescharacteristic
681C22#1798676411yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—2841no—
689C4—2841no—
690C4—2841no—
691C4—1422no—
692C4—1422no—
693C4—1422no—
694C4D4×D28411yescharacteristic
695C4#1798665411yescharacteristic
696C4Q8×D28411yescharacteristic
697C4#1798670911yescharacteristic
698C2—2842no—
699C2—2842no—
700C2C4⋊C4×D28411yescharacteristic
701C2#2259690111yescharacteristic
702C2#2259690711yescharacteristic
703C2#2259704511yescharacteristic
704C2#2259706811yescharacteristic
705C2#2259748311yescharacteristic
706C2#2259750511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1768C2
prime radicalC22×D284C2×C4
cosocleC22×C4×C71C24
hypercenter#1768D71
hypocenterC71#22649
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1768

Complements

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

NH ≅ G/Ntype
3. C2×#17986024C2semidirect
4. C2×#17986021C2semidirect
6. #22589063C2semidirect
7. #22589058C2semidirect
8. #22588524C2semidirect
9. #22588524C2semidirect
10. #22588524C2semidirect
11. #22588519C2semidirect
12. #22588494C2semidirect
13. #22588321C2semidirect
14. #22588317C2semidirect
15. C71×#1768C2semidirect
135. C4⋊C8×C71D4semidirect
368. #1768D71semidirect
369. C71#22649semidirect
479. C4⋊C8D284semidirect

Maximal subgroups

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

subgroupindex
C2×#179860782
C2×#179860722
C2×#179860242
C2×#179860212
#225907842
#225890632
#225890582
#225885242
#225885192
#225884942
#225883212
#225883172
C71×#17682
#2264971