Finite Group Databasebeta

← #32015995

Subgroups — #32015995

Order 18176.

944 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×#17986070C211yesmaximal, characteristic
2C2×C8×C22⋊D71C211yesmaximal, characteristic
3#22590783C211yesmaximal, characteristic
4#22589062C211yesmaximal, characteristic, complemented
5#22589057C211yesmaximal, characteristic, complemented
6#22588524C211yesmaximal, characteristic, complemented
7#22588519C211yesmaximal, characteristic, complemented
8#22588518C211yesmaximal, characteristic, complemented
9#22588518C211yesmaximal, characteristic, complemented
10#22588458C211yesmaximal, characteristic, complemented
11#22588323C211yesmaximal, characteristic, complemented
12#22588320C211yesmaximal, characteristic, complemented
13#22588196C211yesmaximal, characteristic, complemented
14#22588035C211yesmaximal, characteristic, complemented
15C2×#336×C71C211yesmaximal, characteristic, complemented
16C22×#11765848C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C2×C4×C22⋊D71C2211yescharacteristic
19C2×#14556085C2211yescharacteristic
20#17986070—24no—
21C8×C22⋊D71—24no—
22C2×C4⋊(C71⋊C8)C2211yescharacteristic
23C2×C4⋊(C71⋊C8)C2211yescharacteristic
24C2×Dic71⋊C8C2211yescharacteristic
25C2×Dic71⋊C8C2211yescharacteristic
26C2×Dic71⋊C8C2211yescharacteristic
27C2×Dic71⋊C8C2211yescharacteristic
28C2×Dic71⋊C8C2211yescharacteristic
29C2×Dic71⋊C8C2211yescharacteristic
30C2×C22⋊(C71⋊C8)C2211yescharacteristic
31C2×C22⋊(C71⋊C8)C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×#14556038C2211yescharacteristic
35C2×C8×Dic71C2211yescharacteristic
36#17985890C411yescharacteristic
37#17985890C411yescharacteristic
38#17985883C411yescharacteristic
39#17985883C411yescharacteristic
40#17985878C411yescharacteristic
41#17985878C411yescharacteristic
42#17985872C411yescharacteristic
43#17985872C411yescharacteristic
44C4×Dic71⋊C4C2211yescharacteristic
45C4×(C2×D71)⋊C4C2211yescharacteristic
46C4×C22⋊Dic71C2211yescharacteristic
47#17985845C2211yescharacteristic
48#17985754C2211yescharacteristic
49#17985754C2211yescharacteristic
50#17985753C2211yescharacteristic
51#17985753C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54C23×C8×C71C2211yescharacteristic
55C23×C8×C71C2211yescharacteristic
56C22×C42×C71C2211yescharacteristic
57#336×C71C2211yescharacteristic
58#336×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic
60#336×C71C2211yescharacteristic
61C22×C22⋊D71C2×C411yescharacteristic
62C22×C4×D71C2311yescharacteristic
63C2×#11765848—22no—
64C2×#11765848—22no—
65C2×#11765848—41no—
66C22×C71⋊C8C2311yescharacteristic
67C22×C71⋊C8C2311yescharacteristic
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C2×C8×D71—22no—
71C2×C8×D71—22no—
72C2×C8×D71—41no—
73C4×C22⋊D71D414yes—
74C4×C22⋊D71Q814yes—
75#14556085—41no—
76#14556085—41no—
77C2×Dic71⋊C4C2×C411yescharacteristic
78C2×Dic71⋊C4C2×C411yescharacteristic
79C2×Dic71⋊C4C2×C411yescharacteristic
80C2×Dic71⋊C4C2×C411yescharacteristic
81C2×Dic71⋊C4C2×C411yescharacteristic
82C2×C22⋊Dic71C2×C411yescharacteristic
83C2×C22⋊Dic71C2×C411yescharacteristic
84C2×C22⋊Dic71C2×C411yescharacteristic
85C2×(C2×D71)⋊C4C2×C411yescharacteristic
86C2×(C2×D71)⋊C4C2×C411yescharacteristic
87C2×(C2×D71)⋊C4C2×C411yescharacteristic
88C2×(C2×D71)⋊C4C2×C411yescharacteristic
89C2×(C2×D71)⋊C4C2×C411yescharacteristic
90C2×C4×Dic71C2311yescharacteristic
91C2×C4×Dic71C2311yescharacteristic
92C2×C4×Dic71C2311yescharacteristic
93C4⋊(C71⋊C8)—41no—
94C4⋊(C71⋊C8)—41no—
95Dic71⋊C8—22no—
96Dic71⋊C8—22no—
97Dic71⋊C8—22no—
98Dic71⋊C8—22no—
99Dic71⋊C8—41no—
100Dic71⋊C8—41no—
101C22⋊(C71⋊C8)—22no—
102C22⋊(C71⋊C8)—22no—
103(C2×D71)⋊C8—22no—
104(C2×D71)⋊C8—22no—
105#14556038—22no—
106C8×Dic71—22no—
107C71⋊#95C2×C411yescharacteristic
108C71⋊#95C2×C411yescharacteristic
109C71⋊#95C2×C411yescharacteristic
110C71⋊#95C2×C411yescharacteristic
111C71⋊#95C2×C411yescharacteristic
112C71⋊#95C2×C411yescharacteristic
113C71⋊#95C2×C411yescharacteristic
114C71⋊#95C2×C411yescharacteristic
115C71⋊#95C2×C411yescharacteristic
116C71⋊#95C2×C411yescharacteristic
117C23×C4×C71C2×C411yescharacteristic
118C23×C4×C71C2×C411yescharacteristic
119C23×C4×C71C2311yescharacteristic
120C22×C8×C71—22no—
121C22×C8×C71—22no—
122C22×C8×C71—22no—
123C22×C8×C71—22no—
124C22×C8×C71—41no—
125C22×C8×C71—41no—
126C22×C8×C71C2311yescharacteristic
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C22×C8×C71C2311yescharacteristic
130C2×C42×C71—41no—
131C2×C42×C71—41no—
132C2×C42×C71C2×C411yescharacteristic
133C2×C42×C71C2×C411yescharacteristic
134C2×C42×C71C2311yescharacteristic
135C2×C42×C71C2311yescharacteristic
136C23×D71C22×C411yescharacteristic
137C2×C22⋊D71—22no—
138C2×C22⋊D71—22no—
139C2×C22⋊D71C4⋊C414yes—
140C22×Dic71C22×C411yescharacteristic
141C22×Dic71C22×C411yescharacteristic
142C22×Dic71C22×C411yescharacteristic
143C22×Dic71C22×C411yescharacteristic
144C22×Dic71C22×C411yescharacteristic
145C22×Dic71C22×C411yescharacteristic
146C22×Dic71C22×C411yescharacteristic
147C2×C4×D71—21no—
148C2×C4×D71—21no—
149C2×C4×D71—21no—
150C2×C4×D71—21no—
151C2×C4×D71C2×D412yes—
152C2×C4×D71C2×Q812yes—
153#11765848—44no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
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—
166C8×D71—44no—
167Dic71⋊C4—22no—
168Dic71⋊C4—41no—
169Dic71⋊C4—41no—
170Dic71⋊C4—41no—
171Dic71⋊C4C4⋊C414yes—
172C22⋊Dic71—22no—
173C22⋊Dic71—22no—
174C22⋊Dic71C4⋊C414yes—
175(C2×D71)⋊C4—22no—
176(C2×D71)⋊C4—41no—
177(C2×D71)⋊C4—41no—
178(C2×D71)⋊C4—41no—
179(C2×D71)⋊C4C4⋊C414yes—
180C4×Dic71—21no—
181C4×Dic71—21no—
182C4×Dic71—21no—
183C4×Dic71—21no—
184C4×Dic71C2×D412yes—
185C4×Dic71C2×Q812yes—
186C24×C71C22×C411yescharacteristic
187C22×C4×C71—21no—
188C22×C4×C71—21no—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—22no—
192C22×C4×C71—22no—
193C22×C4×C71—22no—
194C22×C4×C71—41no—
195C22×C4×C71—41no—
196C22×C4×C71—41no—
197C22×C4×C71C22×C411yescharacteristic
198C22×C4×C71C22×C411yescharacteristic
199C22×C4×C71C22×C411yescharacteristic
200C22×C4×C71C22×C411yescharacteristic
201C22×C4×C71C22×C411yescharacteristic
202C22×C4×C71C2×D412yes—
203C22×C4×C71C2×Q812yes—
204C22×C4×C71C2411yescharacteristic
205C2×C8×C71—21no—
206C2×C8×C71—21no—
207C2×C8×C71—21no—
208C2×C8×C71—21no—
209C2×C8×C71—21no—
210C2×C8×C71—21no—
211C2×C8×C71—21no—
212C2×C8×C71—21no—
213C2×C8×C71—21no—
214C2×C8×C71—21no—
215C2×C8×C71—44no—
216C2×C8×C71—44no—
217C2×C8×C71#4112yes—
218C2×C8×C71#4112yes—
219C42×C71—21no—
220C42×C71—21no—
221C42×C71—21no—
222C42×C71—21no—
223C42×C71—41no—
224C42×C71—41no—
225C23×C71—21no—
226C23×C71—21no—
227C23×C71—21no—
228C23×C71—21no—
229C23×C71C2×C4⋊C412yes—
230C23×C71#13112yes—
231C23×C71#13112yes—
232C23×C71C23×C411yescharacteristic
233C22×D71—21no—
234C22×D71—21no—
235C22×D71—21no—
236C22×D71—21no—
237C22×D71—21no—
238C22×D71—21no—
239C22×D71C2×C4⋊C412yes—
240C2×C4×C71—21no—
241C2×C4×C71—21no—
242C2×C4×C71—21no—
243C2×C4×C71—21no—
244C2×C4×C71—22no—
245C2×C4×C71—22no—
246C2×C4×C71—22no—
247C2×C4×C71—22no—
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—44no—
258C2×C4×C71—44no—
259C2×C4×C71C2×C4⋊C412yes—
260C2×C4×C71#13112yes—
261C2×C4×C71C22×D411yescharacteristic
262C2×C4×C71C22×Q811yescharacteristic
263C2×C4×C71C2×#4111yescharacteristic
264C2×C4×C71C2×#4111yescharacteristic
265C2×C4×C71H(5,𝔽2)11yescharacteristic
266C2×C4×C71H(5,𝔽2)11yescharacteristic
267C22⋊D71—28no—
268C2×Dic71—21no—
269C2×Dic71—21no—
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×Dic71C2×C4⋊C412yes—
287C2×Dic71C2×C4⋊C412yes—
288C2×Dic71C2×C4⋊C412yes—
289C4×D71—22no—
290C4×D71—22no—
291C4×D71—22no—
292C4×D71—22no—
293C8×C71—22no—
294C8×C71—22no—
295C8×C71—41no—
296C8×C71—41no—
297C71⋊C8—41no—
298C71⋊C8—41no—
299C71⋊C8—41no—
300C71⋊C8—41no—
301C22×C71—22no—
302C22×C71—22no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—22no—
306C22×C71—22no—
307C22×C71#42414yes—
308C22×C71C22×C4⋊C411yescharacteristic
309C22×C71C4×#4111yescharacteristic
310C22×C71#51811yescharacteristic
311C22×C71C2×#13111yescharacteristic
312C22×C71C2×#13111yescharacteristic
313C22×C71C2×#13111yescharacteristic
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—41no—
325C4×C71—41no—
326C4×C71—41no—
327C4×C71#54611yescharacteristic
328C4×C71#54611yescharacteristic
329C4×C71#55411yescharacteristic
330C4×C71#55411yescharacteristic
331Dic71—22no—
332Dic71—22no—
333Dic71—22no—
334Dic71—41no—
335Dic71—41no—
336Dic71—41no—
337Dic71—41no—
338#22697—711nomaximal, Sylow
339C2×C71—24no—
340C2×C71#234911yescharacteristic
341C2×C71C2×#42411yescharacteristic
342C2×C71#290611yescharacteristic
343C2×C71#296611yescharacteristic
344C2×C71#296811yescharacteristic
345C2×C71#297611yescharacteristic
346C2×C71#297711yescharacteristic
347D71—42no—
348C2×#435—711no—
349C2×C8×D4—711no—
350#2290—711no—
351#1940—711no—
352#1939—711no—
353#1851—711no—
354#1850—711no—
355#1850—711no—
356#1850—711no—
357#1832—711no—
358#1798—711no—
359#1797—711no—
360#1768—711no—
361#1729—711no—
362C2×#336D7111yescharacteristic, complemented
363C71#2269711yescharacteristic, complemented, Sylow
364C22×M16—711no—
365C23×C8—711no—
366C23×C8C2×D7111yescharacteristic
367C23×C8C2×D7111yescharacteristic
368C2×C4×D4—711no—
369C2×#117—711no—
370C22×C42C2×D7111yescharacteristic
371#435—1424no—
372C8×D4—1424no—
373C2×C4⋊C8—711no—
374C2×C4⋊C8—711no—
375C2×C4⋊C8—711no—
376C2×C4⋊C8—711no—
377C2×C4⋊C8—711no—
378C2×C4⋊C8—711no—
379C2×C4⋊C8—711no—
380C2×C4⋊C8—711no—
381C2×C22⋊C8—711no—
382C2×C22⋊C8—711no—
383C2×C22⋊C8—711no—
384C2×C22⋊C8—711no—
385C2×#97—711no—
386C2×C4×C8—711no—
387#388—711no—
388#388—711no—
389#387—711no—
390#387—711no—
391#386—711no—
392#386—711no—
393#385—711no—
394#385—711no—
395C4×C4⋊C4—711no—
396C4×C22⋊C4—711no—
397C4×C22⋊C4—711no—
398#376—711no—
399#336—711no—
400#336—711no—
401#336—711no—
402#336—711no—
403#336—711no—
404#336—711no—
405#336C2×D7111yescharacteristic
406#336C2×D7111yescharacteristic
407#336C2×D7111yescharacteristic
408#336C2×D7111yescharacteristic
409C22×D4—711no—
410C23×C4—711no—
411C23×C4C4×D7111yescharacteristic
412C23×C4C4×D7111yescharacteristic
413C23×C4C22×D7111yescharacteristic
414C2×M16—2841no—
415C2×M16—1422no—
416C2×M16—1422no—
417C22×C8—22no—
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—22no—
421C22×C8—41no—
422C22×C8—41no—
423C22×C8—2841no—
424C22×C8—711no—
425C22×C8—711no—
426C22×C8—711no—
427C22×C8—711no—
428C22×C8—1422no—
429C22×C8—1422no—
430C22×C8C22×D7111yescharacteristic
431C22×C8C22×D7111yescharacteristic
432C22×C8C22×D7111yescharacteristic
433C22×C8C22×D7111yescharacteristic
434C4×D4—714no—
435C4×D4—714no—
436#117—2841no—
437#117—2841no—
438C2×C4⋊C4—711no—
439C2×C4⋊C4—711no—
440C2×C4⋊C4—711no—
441C2×C4⋊C4—711no—
442C2×C4⋊C4—711no—
443C2×C22⋊C4—711no—
444C2×C22⋊C4—711no—
445C2×C22⋊C4—711no—
446C2×C22⋊C4—711no—
447C2×C22⋊C4—711no—
448C2×C22⋊C4—711no—
449C2×C22⋊C4—711no—
450C2×C22⋊C4—711no—
451C2×C42—41no—
452C2×C42—41no—
453C2×C42—711no—
454C2×C42—711no—
455C2×C42—711no—
456C2×C42C4×D7111yescharacteristic
457C2×C42C4×D7111yescharacteristic
458C2×C42C22×D7111yescharacteristic
459C2×C42C22×D7111yescharacteristic
460C4⋊C8—2841no—
461C4⋊C8—2841no—
462C4⋊C8—2841no—
463C4⋊C8—2841no—
464C4⋊C8—1422no—
465C4⋊C8—1422no—
466C4⋊C8—1422no—
467C4⋊C8—1422no—
468C22⋊C8—1422no—
469C22⋊C8—1422no—
470C22⋊C8—1422no—
471C22⋊C8—1422no—
472#97—1422no—
473C4×C8—1422no—
474#95—711no—
475#95—711no—
476#95—711no—
477#95—711no—
478#95—711no—
479#95—711no—
480#95—711no—
481#95—711no—
482#95—711no—
483#95—711no—
484C24—711no—
485C24C2×C4×D7111yescharacteristic
486C2×D4—714no—
487C2×D4—1422no—
488C2×D4—1422no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—711no—
500C22×C4—711no—
501C22×C4—711no—
502C22×C4—712no—
503C22×C4—712no—
504C22×C4—711no—
505C22×C4—711no—
506C22×C4—711no—
507C22×C4—711no—
508C22×C4—1421no—
509C22×C4—1421no—
510C22×C4—1421no—
511C22×C4—1421no—
512C22×C4C2×C4×D7111yescharacteristic
513C22×C4C2×C4×D7111yescharacteristic
514C22×C4C2×C4×D7111yescharacteristic
515C22×C4C2×C4×D7111yescharacteristic
516C22×C4C2×C4×D7111yescharacteristic
517C22×C4D4×D7112yes—
518C22×C4Q8×D7112yes—
519C22×C4C23×D7111yescharacteristic
520M16—2844no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—44no—
532C2×C8—44no—
533C2×C8—2844no—
534C2×C8—1421no—
535C2×C8—1421no—
536C2×C8—1421no—
537C2×C8—1421no—
538C2×C8—1421no—
539C2×C8—1421no—
540C2×C8—1421no—
541C2×C8—1421no—
542C2×C8—1421no—
543C2×C8—1421no—
544C2×C8—1421no—
545C2×C8—1421no—
546C2×C8#1176586512yes—
547C2×C8#1176586512yes—
548C4⋊C4—2841no—
549C4⋊C4—2841no—
550C4⋊C4—2841no—
551C4⋊C4—714no—
552C4⋊C4—1422no—
553C22⋊C4—2841no—
554C22⋊C4—2841no—
555C22⋊C4—2841no—
556C22⋊C4—714no—
557C22⋊C4—714no—
558C22⋊C4—1422no—
559C22⋊C4—1422no—
560C22⋊C4—1422no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—41no—
566C42—41no—
567C42—712no—
568C42—712no—
569C42—1421no—
570C42—1421no—
571C42—1421no—
572C42—1421no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—712no—
578C23—1421no—
579C23—1421no—
580C23—1421no—
581C23—1421no—
582C23—1421no—
583C23—1421no—
584C23C4⋊C4×D7112yes—
585C23#1455613412yes—
586C23#1455613612yes—
587C23C22×C4×D7111yescharacteristic
588D4—1428no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
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—44no—
607C2×C4—44no—
608C2×C4—712no—
609C2×C4—712no—
610C2×C4—712no—
611C2×C4—1421no—
612C2×C4—1421no—
613C2×C4—1421no—
614C2×C4—1421no—
615C2×C4—1421no—
616C2×C4—1421no—
617C2×C4—1421no—
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—1422no—
630C2×C4—1422no—
631C2×C4—1422no—
632C2×C4—1422no—
633C2×C4C4⋊C4×D7112yes—
634C2×C4#1455613412yes—
635C2×C4C2×D4×D7111yescharacteristic
636C2×C4C2×Q8×D7111yescharacteristic
637C2×C4C2×#1176586511yescharacteristic
638C2×C4C2×#1176586511yescharacteristic
639C2×C4#1455617311yescharacteristic
640C2×C4#1455617311yescharacteristic
641C8—22no—
642C8—22no—
643C8—41no—
644C8—41no—
645C8—2841no—
646C8—2841no—
647C8—2841no—
648C8—2841no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—2841no—
656C22—2841no—
657C22—2841no—
658C22—2841no—
659C22—1422no—
660C22—1422no—
661C22—1422no—
662C22#1798602414yes—
663C22C2×C4⋊C4×D7111yescharacteristic
664C22C4×#1176586511yescharacteristic
665C22#1798647211yescharacteristic
666C22C2×#1455613411yescharacteristic
667C22C2×#1455613411yescharacteristic
668C22C2×#1455613611yescharacteristic
669C22#1798676511yescharacteristic
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—2841no—
676C4—2841no—
677C4—2841no—
678C4—2841no—
679C4—1422no—
680C4—1422no—
681C4—1422no—
682C4#1798663911yescharacteristic
683C4#1798663911yescharacteristic
684C4#1798670411yescharacteristic
685C4#1798670411yescharacteristic
686C2—24no—
687C2—2842no—
688C2#2259124711yescharacteristic
689C2C2×#1798602411yescharacteristic
690C2#2259690511yescharacteristic
691C2#2259731511yescharacteristic
692C2#2259733411yescharacteristic
693C2#2259738511yescharacteristic
694C2#2259739411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC2×#336×C71C2
prime radicalC22×C22⋊D71C2×C4
cosocleC22×C4×C71C24
hypercenterC2×#336D71
hypocenterC71#22697
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. #22589062C2semidirect
5. #22589057C2semidirect
6. #22588524C2semidirect
7. #22588519C2semidirect
8. #22588518C2semidirect
9. #22588518C2semidirect
10. #22588458C2semidirect
11. #22588323C2semidirect
12. #22588320C2semidirect
13. #22588196C2semidirect
14. #22588035C2semidirect
15. C2×#336×C71C2semidirect
362. C2×#336D71semidirect
363. C71#22697semidirect

Maximal subgroups

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

subgroupindex
C2×#179860702
C2×C8×C22⋊D712
#225907832
#225890622
#225890572
#225885242
#225885192
#225885182
#225884582
#225883232
#225883202
#225881962
#225880352
C2×#336×C712
#2269771