Finite Group Databasebeta

← #32013854

Subgroups — #32013854

Order 18176.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986689C211yesmaximal, characteristic
2C2×#17986077C211yesmaximal, characteristic
3#22589304C211yesmaximal, characteristic, complemented
4#22589297C211yesmaximal, characteristic, complemented
5#22588771C211yesmaximal, characteristic, complemented
6#22588771C211yesmaximal, characteristic, complemented
7#22588652C211yesmaximal, characteristic, complemented
8#22588647C211yesmaximal, characteristic, complemented
9#22588432C211yesmaximal, characteristic, complemented
10#22588428C211yesmaximal, characteristic, complemented
11#22588352C211yesmaximal, characteristic, complemented
12C4×#14556051C211yesmaximal, characteristic, complemented
13#22588061C211yesmaximal, characteristic, complemented
14#22588059C211yesmaximal, characteristic, complemented
15C71×#2352C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C22×#11765849C2211yescharacteristic
18#17986689—24no—
19#17986689C418yescomplemented
20C2×#14556121—21no—
21C2×#14556120C2211yescharacteristic
22C2×#14556118—21no—
23C2×#14556109—21no—
24C2×#14556107C2211yescharacteristic
25C2×#14556107C2211yescharacteristic
26C2×C4×Dic142C2211yescharacteristic
27C2×#14556087C2211yescharacteristic
28C2×#14556084—21no—
29C22×C4⋊Dic71C2211yescharacteristic
30#17986077—24no—
31C2×C4⋊(C71⋊C8)C2211yescharacteristic
32C2×#14556051C2211yescharacteristic
33C2×#14556051C2211yescharacteristic
34C2×#14556051C2211yescharacteristic
35C2×#14556051C2211yescharacteristic
36C2×C22⋊(C71⋊C8)C2211yescharacteristic
37C2×C22⋊(C71⋊C8)C2211yescharacteristic
38C2×C4×C71⋊C8C2211yescharacteristic
39#17985761C2211yescharacteristic
40#17985761C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#17985761C2211yescharacteristic
50#17985761C2211yescharacteristic
51C2×C4×D4×C71C2211yescharacteristic
52C2×#117×C71C2211yescharacteristic
53C22×C4⋊C4×C71C2211yescharacteristic
54#388×C71—21no—
55#387×C71—21no—
56#386×C71—21no—
57#382×C71C2211yescharacteristic
58#380×C71C2211yescharacteristic
59#380×C71C2211yescharacteristic
60C4×C4⋊C4×C71C2211yescharacteristic
61C4×C22⋊C4×C71—21no—
62C22×Dic142C2311yescharacteristic
63C23×Dic71—21no—
64C2×#11765849—22no—
65C2×#11765849—22no—
66C2×#11765849—22no—
67C2×#11765849—22no—
68C2×#11765849—41no—
69C2×#11765849—41no—
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74#14556121—28no—
75#14556120—22no—
76#14556120C2×C414yescomplemented
77#14556118—28no—
78#14556109—28no—
79#14556107—22no—
80#14556107—22no—
81#14556107C2×C414yes—
82#14556107C2×C414yescomplemented
83C4×Dic142—22no—
84C4×Dic142C2×C414yescomplemented
85#14556087—22no—
86#14556087C2×C414yes—
87#14556084—28no—
88C2×C4⋊Dic71—22no—
89C2×C4⋊Dic71—21no—
90C2×C4⋊Dic71C2×C414yescomplemented
91C2×C4⋊Dic71C2311yescharacteristic
92C2×C4⋊Dic71C2311yescharacteristic
93C2×C4⋊Dic71C2311yescharacteristic
94C2×Dic71⋊C4—21no—
95C2×Dic71⋊C4—21no—
96C2×Dic71⋊C4—21no—
97C2×Dic71⋊C4—21no—
98C2×Dic71⋊C4—21no—
99C2×C22⋊Dic71—21no—
100C2×C22⋊Dic71—21no—
101C2×C22⋊Dic71—21no—
102C2×C4×Dic71—21no—
103C2×C4×Dic71—21no—
104C4⋊(C71⋊C8)—22no—
105#14556051—22no—
106#14556051—22no—
107#14556051—41no—
108#14556051—41no—
109C22⋊(C71⋊C8)—22no—
110C22⋊(C71⋊C8)—22no—
111C4×C71⋊C8—22no—
112C22×D4×C71D411yescharacteristic
113C23×C4×C71—21no—
114C23×C4×C71C2311yescharacteristic
115C23×C4×C71C2311yescharacteristic
116C4×D4×C71C2×C414yes—
117C4×D4×C71D414yes—
118#117×C71—22no—
119#117×C71—41no—
120C2×C4⋊C4×C71—22no—
121C2×C4⋊C4×C71—21no—
122C2×C4⋊C4×C71—41no—
123C2×C4⋊C4×C71D411yescharacteristic
124C2×C4⋊C4×C71C2311yescharacteristic
125C2×C4⋊C4×C71C2311yescharacteristic
126C2×C4⋊C4×C71C2311yescharacteristic
127C2×C4⋊C4×C71C2311yescharacteristic
128C2×C22⋊C4×C71—21no—
129C2×C22⋊C4×C71—21no—
130C2×C22⋊C4×C71—21no—
131C2×C22⋊C4×C71D411yescharacteristic
132C2×C22⋊C4×C71D411yescharacteristic
133C2×C42×C71—21no—
134C2×C42×C71—21no—
135C2×C42×C71C2311yescharacteristic
136#95×C71—21no—
137#95×C71—21no—
138#95×C71—21no—
139#95×C71—21no—
140#95×C71—21no—
141C2×Dic142—21no—
142C2×Dic142—21no—
143C2×Dic142—21no—
144C2×Dic142—21no—
145C2×Dic142—21no—
146C2×Dic142C22×C412yes—
147C22×Dic71—24no—
148C22×Dic71—21no—
149C22×Dic71—21no—
150C22×Dic71—21no—
151C22×Dic71—21no—
152C22×Dic71—42no—
153C22×Dic71—42no—
154#11765849—44no—
155#11765849—44no—
156C2×C71⋊C8—21no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161C2×C71⋊C8—21no—
162C2×C71⋊C8—21no—
163C2×C71⋊C8—21no—
164C2×C71⋊C8—21no—
165C2×C71⋊C8—21no—
166C2×C71⋊C8—21no—
167C2×C71⋊C8#4112yes—
168C4⋊Dic71—24no—
169C4⋊Dic71—21no—
170C4⋊Dic71—21no—
171C4⋊Dic71—21no—
172C4⋊Dic71C22×C412yes—
173C4⋊Dic71C22×C412yes—
174C4⋊Dic71C22×C412yes—
175Dic71⋊C4—24no—
176Dic71⋊C4—24no—
177Dic71⋊C4—24no—
178Dic71⋊C4—24no—
179Dic71⋊C4—24no—
180C22⋊Dic71—24no—
181C22⋊Dic71—24no—
182C22⋊Dic71—24no—
183C4×Dic71—24no—
184C4×Dic71—24no—
185C24×C71C2×D411yescharacteristic
186C24×C71C2×D411yescharacteristic
187C2×D4×C71—41no—
188C2×D4×C71—41no—
189C2×D4×C71C22⋊C414yes—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—42no—
203C22×C4×C71—42no—
204C22×C4×C71—81no—
205C22×C4×C71C22×C412yes—
206C22×C4×C71C22×C412yes—
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D411yescharacteristic
209C22×C4×C71C2×D411yescharacteristic
210C22×C4×C71C2×D411yescharacteristic
211C22×C4×C71C2×D412yes—
212C22×C4×C71C2×D412yes—
213C22×C4×C71C2411yescharacteristic
214C4⋊C4×C71—21no—
215C4⋊C4×C71—21no—
216C4⋊C4×C71—21no—
217C4⋊C4×C71—21no—
218C4⋊C4×C71—21no—
219C4⋊C4×C71—21no—
220C4⋊C4×C71—21no—
221C4⋊C4×C71—42no—
222C4⋊C4×C71C22⋊C414yes—
223C4⋊C4×C71#4112yes—
224C22⋊C4×C71—42no—
225C22⋊C4×C71—42no—
226C22⋊C4×C71—81no—
227C22⋊C4×C71C22⋊C414yes—
228C22⋊C4×C71C22⋊C414yes—
229C42×C71—42no—
230C42×C71—81no—
231C42×C71C22×C412yes—
232C42×C71C2×D412yes—
233C23×C71—21no—
234C23×C71—21no—
235C23×C71—21no—
236C23×C71—21no—
237C23×C71—21no—
238C23×C71—21no—
239C23×C71—21no—
240C23×C71—21no—
241C23×C71—21no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71C2×C22⋊C412yes—
246C23×C71C2×C22⋊C412yes—
247C23×C71C22×D411yescharacteristic
248D4×C71—44no—
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—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—41no—
267C2×C4×C71—41no—
268C2×C4×C71—41no—
269C2×C4×C71—41no—
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—84no—
278C2×C4×C71C2×C22⋊C412yes—
279C2×C4×C71C2×C22⋊C412yes—
280C2×C4×C71C2×C22⋊C412yes—
281C2×C4×C71C2×C22⋊C412yes—
282C2×C4×C71C23×C411yescharacteristic
283C2×C4×C71C22×D411yescharacteristic
284C2×C4×C71C2×#4111yescharacteristic
285C2×C4×C71C2×#4111yescharacteristic
286C2×C4×C71H(5,𝔽2)11yescharacteristic
287C2×C4×C712−1+411yescharacteristic
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—48no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—41no—
297C2×Dic71—41no—
298C2×Dic71—41no—
299C2×Dic71—41no—
300C2×Dic71—41no—
301Dic142—22no—
302Dic142—22no—
303Dic142—41no—
304Dic142—41no—
305C71⋊C8—22no—
306C71⋊C8—41no—
307C71⋊C8—41no—
308C71⋊C8—41no—
309C22×C71—22no—
310C22×C71—22no—
311C22×C71—22no—
312C22×C71—22no—
313C22×C71—22no—
314C22×C71—22no—
315C22×C71—41no—
316C22×C71—41no—
317C22×C71—41no—
318C22×C71—41no—
319C22×C71—41no—
320C22×C71—41no—
321C22×C71—41no—
322C22×C71—41no—
323C22×C71C22×C22⋊C411yescharacteristic
324C22×C71#54611yescharacteristic
325C22×C71#54711yescharacteristic
326C22×C71#57511yescharacteristic
327C22×C71#57511yescharacteristic
328C22×C71#57711yescharacteristic
329C22×C71#57811yescharacteristic
330C4×C71—22no—
331C4×C71—22no—
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—42no—
335C4×C71—81no—
336C4×C71—81no—
337C4×C71—81no—
338C4×C71C4×#4111yescharacteristic
339C4×C71#52011yescharacteristic
340C4×C71#54611yescharacteristic
341C4×C71#54711yescharacteristic
342Dic71—42no—
343Dic71—42no—
344Dic71—42no—
345Dic71—42no—
346#22499—711nomaximal, Sylow
347C2×C71—42no—
348C2×C71—42no—
349C2×C71#233911yescharacteristic
350C2×C71#289611yescharacteristic
351C2×C71#289811yescharacteristic
352C2×C71#332311yescharacteristic
353C2×C71#332711yescharacteristic
354C2×C71#335111yescharacteristic
355C2×C71#335211yescharacteristic
356C2×#552—711no—
357C2×#436—711no—
358#2352D7111yescharacteristic
359#1991—711no—
360#1989—711no—
361#1894—711no—
362#1894—711no—
363#1873—711no—
364#1872—711no—
365#1825—711no—
366#1824—711no—
367#1805—711no—
368C4×#103—711no—
369#1736—711no—
370#1736—711no—
371C71#2249911yescharacteristic, complemented, Sylow
372C22×M16—711no—
373C22×M16—711no—
374#552—718no—
375#552—1424no—
376C2×#126—1421no—
377C2×#125—711no—
378C2×#125—1421no—
379C2×#123—1421no—
380C2×C22⋊Q8—711no—
381C2×C22⋊Q8—711no—
382C2×C4×Q8—711no—
383C2×C4×D4C2×D7111yescharacteristic
384C2×#117—711no—
385C2×#117—1421no—
386C2×#117C2×D7111yescharacteristic
387C22×C4⋊C4—711no—
388C22×C4⋊C4C2×D7111yescharacteristic
389#436—1424no—
390C2×C4⋊C8—711no—
391C2×#103—711no—
392C2×#103—711no—
393C2×#103—711no—
394C2×#103—711no—
395C2×C22⋊C8—711no—
396C2×C22⋊C8—711no—
397C2×C4×C8—711no—
398#388—21no—
399#387—21no—
400#386—21no—
401#382C2×D7111yescharacteristic
402#380C2×D7111yescharacteristic
403#380C2×D7111yescharacteristic
404C4×C4⋊C4C2×D7111yescharacteristic
405C4×C22⋊C4—21no—
406#340—711no—
407#340—711no—
408#340—711no—
409#340—711no—
410#340—711no—
411#340—711no—
412#340—711no—
413#340—711no—
414#340—711no—
415#340—711no—
416#340—711no—
417#340—711no—
418C22×Q8—711no—
419C22×D4C22⋊D7111yescharacteristic
420C23×C4—21no—
421C23×C4—1421no—
422C23×C4C22×D7111yescharacteristic
423C23×C4C22×D7111yescharacteristic
424C2×M16—2841no—
425C2×M16—2841no—
426C2×M16—1422no—
427C2×M16—1422no—
428C2×M16—1422no—
429C2×M16—1422no—
430C22×C8—711no—
431C22×C8—711no—
432C22×C8—711no—
433C22×C8—711no—
434#126—1428no—
435#125—714no—
436#125—1428no—
437#125—1422no—
438#123—1428no—
439C22⋊Q8—714no—
440C22⋊Q8—714no—
441C22⋊Q8—1422no—
442C22⋊Q8—1422no—
443C4×Q8—714no—
444C4×Q8—1422no—
445C4×D4C4×D7114yes—
446C4×D4D28414yes—
447#117—22no—
448#117—41no—
449#117—714no—
450#117—1422no—
451#117—1428no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—714no—
456C2×C4⋊C4—711no—
457C2×C4⋊C4—711no—
458C2×C4⋊C4—711no—
459C2×C4⋊C4—1421no—
460C2×C4⋊C4—1421no—
461C2×C4⋊C4—1421no—
462C2×C4⋊C4—1421no—
463C2×C4⋊C4—1421no—
464C2×C4⋊C4—1421no—
465C2×C4⋊C4—1422no—
466C2×C4⋊C4C22⋊D7111yescharacteristic
467C2×C4⋊C4C22×D7111yescharacteristic
468C2×C4⋊C4C22×D7111yescharacteristic
469C2×C4⋊C4C22×D7111yescharacteristic
470C2×C4⋊C4C22×D7111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1421no—
475C2×C22⋊C4—1421no—
476C2×C22⋊C4—1421no—
477C2×C22⋊C4C22⋊D7111yescharacteristic
478C2×C22⋊C4C22⋊D7111yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—1421no—
482C2×C42—1421no—
483C2×C42C22×D7111yescharacteristic
484C4⋊C8—1422no—
485#103—2841no—
486#103—2841no—
487#103—1422no—
488#103—1422no—
489C22⋊C8—1422no—
490C22⋊C8—1422no—
491C4×C8—1422no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24C2×C22⋊D7111yescharacteristic
498C24C2×C22⋊D7111yescharacteristic
499C2×Q8—712no—
500C2×Q8—1421no—
501C2×Q8—1421no—
502C2×Q8—1421no—
503C2×Q8—1421no—
504C2×Q8—1421no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4(C2×D71)⋊C414yes—
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—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—2842no—
524C22×C4—2842no—
525C22×C4—1421no—
526C22×C4—1421no—
527C22×C4—1421no—
528C22×C4—1421no—
529C22×C4—1424no—
530C22×C4C2×C4×D7112yes—
531C22×C4C2×C4×D7112yes—
532C22×C4C2×C22⋊D7111yescharacteristic
533C22×C4C2×C22⋊D7111yescharacteristic
534C22×C4C2×C22⋊D7111yescharacteristic
535C22×C4C2×C22⋊D7111yescharacteristic
536C22×C4C2×D28412yes—
537C22×C4C2×D28412yes—
538C22×C4C23×D7111yescharacteristic
539M16—2844no—
540M16—2844no—
541C2×C8—712no—
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—
551C2×C8—1421no—
552C2×C8—1421no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—712no—
562C4⋊C4—712no—
563C4⋊C4—712no—
564C4⋊C4—1421no—
565C4⋊C4—1421no—
566C4⋊C4—1421no—
567C4⋊C4—1424no—
568C4⋊C4—1424no—
569C4⋊C4—1424no—
570C4⋊C4—1424no—
571C4⋊C4—1424no—
572C4⋊C4—1424no—
573C4⋊C4(C2×D71)⋊C414yes—
574C4⋊C4#1176586412yes—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C22⋊C4—1424no—
579C22⋊C4—1424no—
580C22⋊C4—1424no—
581C22⋊C4(C2×D71)⋊C414yes—
582C22⋊C4(C2×D71)⋊C414yes—
583C42—42no—
584C42—81no—
585C42—1424no—
586C42—1424no—
587C42C2×C4×D7112yes—
588C42C2×D28412yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×(C2×D71)⋊C412yes—
602C23C2×(C2×D71)⋊C412yes—
603C23C22×C22⋊D7111yescharacteristic
604Q8—2841no—
605Q8—2841no—
606Q8—1422no—
607Q8—1422no—
608D4—44no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—2848no—
639C2×C4—2841no—
640C2×C4—2841no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—2841no—
644C2×C4—2841no—
645C2×C4—2841no—
646C2×C4—2841no—
647C2×C4—1422no—
648C2×C4—1422no—
649C2×C4—1422no—
650C2×C4—1422no—
651C2×C4C2×(C2×D71)⋊C412yes—
652C2×C4C2×(C2×D71)⋊C412yes—
653C2×C4C2×(C2×D71)⋊C412yes—
654C2×C4C2×(C2×D71)⋊C412yes—
655C2×C4C22×C4×D7111yescharacteristic
656C2×C4C22×D28411yescharacteristic
657C2×C4#41×D7111yescharacteristic
658C2×C4C2×#1176586411yescharacteristic
659C2×C4#1455617311yescharacteristic
660C2×C4#1455617511yescharacteristic
661C8—2841no—
662C8—2841no—
663C8—2841no—
664C8—1422no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×(C2×D71)⋊C411yescharacteristic
680C22#1798664311yescharacteristic
681C22#1798664811yescharacteristic
682C22#1798679711yescharacteristic
683C22#1798679711yescharacteristic
684C22#1798681011yescharacteristic
685C22#1798681411yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—2842no—
695C4—2842no—
696C4—2842no—
697C4—2842no—
698C4C4×#1176586411yescharacteristic
699C4#1798647811yescharacteristic
700C4#1798664411yescharacteristic
701C4#1798665311yescharacteristic
702C2—42no—
703C2—42no—
704C2#2259116511yescharacteristic
705C2#2259685711yescharacteristic
706C2#2259687011yescharacteristic
707C2#2260055611yescharacteristic
708C2#2260060811yescharacteristic
709C2#2260089411yescharacteristic
710C2#2260090911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2352C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
cosocleC22×C4×C71C24
hypercenter#2352D71
hypocenterC71#22499
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. #22589304C2semidirect
4. #22589297C2semidirect
5. #22588771C2semidirect
6. #22588771C2semidirect
7. #22588652C2semidirect
8. #22588647C2semidirect
9. #22588432C2semidirect
10. #22588428C2semidirect
11. #22588352C2semidirect
12. C4×#14556051C2semidirect
13. #22588061C2semidirect
14. #22588059C2semidirect
19. #17986689C4semidirect
76. #14556120C2×C4semidirect
82. #14556107C2×C4semidirect
84. C4×Dic142C2×C4semidirect
90. C2×C4⋊Dic71C2×C4semidirect
371. C71#22499semidirect

Maximal subgroups

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

subgroupindex
C2×#179866892
C2×#179860772
#225893042
#225892972
#225887712
#225886522
#225886472
#225884322
#225884282
#225883522
C4×#145560512
#225880612
#225880592
C71×#23522
#2249971