Finite Group Databasebeta

← #32016935

Subgroups — #32016935

Order 18176.

960 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
1C4×(C22⋊D71)⋊C4C211yesmaximal, characteristic
2#22588948C211yesmaximal, characteristic, complemented
3#22588900C211yesmaximal, characteristic, complemented
4#22588894C211yesmaximal, characteristic, complemented
5#22588629C211yesmaximal, characteristic
6#22588629C211yesmaximal, characteristic
7#22588482C211yesmaximal, characteristic, complemented
8#22588406C211yesmaximal, characteristic, complemented
9#22588317C211yesmaximal, characteristic, complemented
10C8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
11#22588110C211yesmaximal, characteristic, complemented
12C22⋊C8×Dic71C211yesmaximal, characteristic, complemented
13#22588085C211yesmaximal, characteristic, complemented
14#336×D71C211yesmaximal, characteristic, complemented
15C71×#1923C211yesmaximal, characteristic, complemented
16C22×C8×D71C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C2×C4×C22⋊D71C2211yescharacteristic
19C2×(C22⋊D71)⋊C4C411yescharacteristic
20C2×(C22⋊D71)⋊C4C411yescharacteristic
21C22×C4×Dic71C2211yescharacteristic
22C2×C42×D71C2211yescharacteristic
23C2×C4⋊(C71⋊C8)C2211yescharacteristic
24C2×C22⋊(C71⋊C8)C2211yescharacteristic
25C2×C22⋊(C71⋊C8)C2211yescharacteristic
26C2×(C2×D71)⋊C8C2211yescharacteristic
27C2×(C2×D71)⋊C8C2211yescharacteristic
28C2×C4×C71⋊C8C2211yescharacteristic
29C2×C8×Dic71C2211yescharacteristic
30C2×C8×Dic71C2211yescharacteristic
31C4×Dic71⋊C4C2211yescharacteristic
32#17985850C411yescharacteristic
33#17985850C411yescharacteristic
34C22⋊C4×Dic71C411yescharacteristic
35C22⋊C4×Dic71C411yescharacteristic
36C4×(C2×D71)⋊C4C2211yescharacteristic
37#17985846C411yescharacteristic
38#17985846C411yescharacteristic
39C42×Dic71C2211yescharacteristic
40#17985754C2211yescharacteristic
41#17985754C2211yescharacteristic
42#17985753C2211yescharacteristic
43#17985753C2211yescharacteristic
44#17985753C2211yescharacteristic
45#17985753C2211yescharacteristic
46#17985753C2211yescharacteristic
47#17985753C2211yescharacteristic
48#17985753C2211yescharacteristic
49#17985753C2211yescharacteristic
50#17985753C2211yescharacteristic
51#17985753C2211yescharacteristic
52C2×C4⋊C8×C71C2211yescharacteristic
53C2×C22⋊C8×C71C2211yescharacteristic
54C2×C22⋊C8×C71C2211yescharacteristic
55C2×C4×C8×C71C2211yescharacteristic
56C4×C22⋊C4×C71C2211yescharacteristic
57#336×C71C2211yescharacteristic
58#336×C71C2211yescharacteristic
59C22×C22⋊D71C2×C411yescharacteristic
60C23×Dic71C2×C411yescharacteristic
61C23×Dic71C2×C411yescharacteristic
62C22×C4×D71C2×C411yescharacteristic
63C22×C4×D71C2×C411yescharacteristic
64C22×C4×D71C2311yescharacteristic
65C22×C71⋊C8C2311yescharacteristic
66C22×C71⋊C8C2311yescharacteristic
67C22×C71⋊C8C2311yescharacteristic
68C22×C71⋊C8C2311yescharacteristic
69C2×C8×D71—22no—
70C2×C8×D71—22no—
71C2×C8×D71—22no—
72C2×C8×D71—22no—
73C2×C8×D71—41no—
74C2×C8×D71—41no—
75C4×C22⋊D71—22no—
76C4×C22⋊D71—22no—
77(C22⋊D71)⋊C4—24no—
78(C22⋊D71)⋊C4C818yescomplemented
79C2×Dic71⋊C4C2×C411yescharacteristic
80C2×Dic71⋊C4C2×C411yescharacteristic
81C2×Dic71⋊C4C2×C411yescharacteristic
82C2×C22⋊Dic71C2×C411yescharacteristic
83C2×(C2×D71)⋊C4C2×C411yescharacteristic
84C2×(C2×D71)⋊C4C2×C411yescharacteristic
85C2×(C2×D71)⋊C4C2×C411yescharacteristic
86C2×C4×Dic71—41no—
87C2×C4×Dic71—41no—
88C2×C4×Dic71C2×C411yescharacteristic
89C2×C4×Dic71C2×C411yescharacteristic
90C2×C4×Dic71C2×C411yescharacteristic
91C2×C4×Dic71C2×C411yescharacteristic
92C2×C4×Dic71C2×C411yescharacteristic
93C2×C4×Dic71C2×C411yescharacteristic
94C2×C4×Dic71C2×C411yescharacteristic
95C2×C4×Dic71C2×C411yescharacteristic
96C2×C4×Dic71C2311yescharacteristic
97C2×C4×Dic71C2311yescharacteristic
98C2×C4×Dic71C2311yescharacteristic
99C42×D71—41no—
100C42×D71—41no—
101C4⋊(C71⋊C8)—41no—
102C22⋊(C71⋊C8)—22no—
103C22⋊(C71⋊C8)—41no—
104(C2×D71)⋊C8—22no—
105(C2×D71)⋊C8—22no—
106C4×C71⋊C8—22no—
107C8×Dic71—41no—
108C8×Dic71—41no—
109C71⋊#95C2×C411yescharacteristic
110C71⋊#95C2×C411yescharacteristic
111C71⋊#95C2×C411yescharacteristic
112C71⋊#95C2×C411yescharacteristic
113C23×C4×C71C2311yescharacteristic
114C22×C8×C71C2311yescharacteristic
115C22×C8×C71C2311yescharacteristic
116C22×C8×C71C2311yescharacteristic
117C22×C8×C71C2311yescharacteristic
118C2×C22⋊C4×C71C2×C411yescharacteristic
119C2×C22⋊C4×C71C2×C411yescharacteristic
120C2×C42×C71C2311yescharacteristic
121C2×C42×C71C2311yescharacteristic
122C4⋊C8×C71—41no—
123C22⋊C8×C71—22no—
124C22⋊C8×C71—41no—
125C4×C8×C71—22no—
126#95×C71C2×C411yescharacteristic
127#95×C71C2×C411yescharacteristic
128C23×D71C22×C411yescharacteristic
129C2×C22⋊D71—22no—
130C2×C22⋊D71—22no—
131C2×C22⋊D71C2×C814yes—
132C22×Dic71—22no—
133C22×Dic71—22no—
134C22×Dic71—41no—
135C22×Dic71—41no—
136C22×Dic71—41no—
137C22×Dic71C2×C814yescomplemented
138C22×Dic71C22×C411yescharacteristic
139C22×Dic71C22×C411yescharacteristic
140C22×Dic71C22×C411yescharacteristic
141C22×Dic71C22×C411yescharacteristic
142C22×Dic71C22×C411yescharacteristic
143C22×Dic71C22×C411yescharacteristic
144C22×Dic71C22×C411yescharacteristic
145C2×C4×D71—21no—
146C2×C4×D71—21no—
147C2×C4×D71—21no—
148C2×C4×D71—21no—
149C2×C4×D71—22no—
150C2×C4×D71—22no—
151C2×C4×D71—41no—
152C2×C4×D71—41no—
153C2×C4×D71—41no—
154C2×C4×D71C2×C814yes—
155C2×C4×D71#4112yes—
156C2×C4×D71#4112yes—
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—21no—
168C2×C71⋊C8#4112yes—
169C8×D71—44no—
170C8×D71—44no—
171Dic71⋊C4—22no—
172Dic71⋊C4—22no—
173Dic71⋊C4C2×C814yescomplemented
174C22⋊Dic71—22no—
175(C2×D71)⋊C4—22no—
176(C2×D71)⋊C4C2×C814yes—
177(C2×D71)⋊C4M1614yes—
178C4×Dic71—22no—
179C4×Dic71—21no—
180C4×Dic71—21no—
181C4×Dic71—21no—
182C4×Dic71—21no—
183C4×Dic71—21no—
184C4×Dic71—21no—
185C4×Dic71—22no—
186C4×Dic71—41no—
187C4×Dic71—41no—
188C4×Dic71—41no—
189C4×Dic71—41no—
190C4×Dic71—41no—
191C4×Dic71C2×C814yescomplemented
192C24×C71C22×C411yescharacteristic
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×C71C22×C411yescharacteristic
200C22×C4×C71C22×C411yescharacteristic
201C22×C4×C71C22×C411yescharacteristic
202C22×C4×C71C22×C411yescharacteristic
203C22×C4×C71C22×C411yescharacteristic
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—21no—
216C2×C8×C71#4112yes—
217C22⋊C4×C71—22no—
218C22⋊C4×C71C2×C814yescomplemented
219C42×C71—21no—
220C42×C71—21no—
221C42×C71—21no—
222C42×C71—21no—
223C23×C71—21no—
224C23×C71—21no—
225C23×C71—21no—
226C23×C71—21no—
227C23×C71—21no—
228C23×C71—21no—
229C23×C71C22×C812yes—
230C23×C71C23×C411yescharacteristic
231C22×D71—21no—
232C22×D71—21no—
233C22×D71—21no—
234C22×D71—21no—
235C22×D71#11712yes—
236C22×D71C22×C812yes—
237C22×D71C2×M1612yes—
238C2×C4×C71—21no—
239C2×C4×C71—21no—
240C2×C4×C71—21no—
241C2×C4×C71—21no—
242C2×C4×C71—21no—
243C2×C4×C71—21no—
244C2×C4×C71—21no—
245C2×C4×C71—21no—
246C2×C4×C71—21no—
247C2×C4×C71—21no—
248C2×C4×C71—21no—
249C2×C4×C71—21no—
250C2×C4×C71—41no—
251C2×C4×C71—41no—
252C2×C4×C71—41no—
253C2×C4×C71—41no—
254C2×C4×C71C22×C812yes—
255C2×C4×C71C22×C812yes—
256C2×C4×C71C2×M1612yes—
257C2×C4×C71C2×#4111yescharacteristic
258C2×C4×C71C2×#4111yescharacteristic
259C2×C4×C71C2×#4111yescharacteristic
260C2×C4×C71C2×#4111yescharacteristic
261C2×C4×C71H(5,𝔽2)11yescharacteristic
262C2×C4×C71H(5,𝔽2)11yescharacteristic
263C22⋊D71—28no—
264C2×Dic71—21no—
265C2×Dic71—21no—
266C2×Dic71—21no—
267C2×Dic71—21no—
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—44no—
280C2×Dic71—44no—
281C2×Dic71#11712yes—
282C2×Dic71C22×C812yes—
283C2×Dic71C22×C812yes—
284C2×Dic71C22×C812yes—
285C2×Dic71C2×M1612yes—
286C2×Dic71#13112yes—
287C4×D71—22no—
288C4×D71—22no—
289C4×D71—22no—
290C4×D71—22no—
291C4×D71—44no—
292C4×D71—44no—
293C8×C71—22no—
294C8×C71—41no—
295C8×C71—41no—
296C8×C71—41no—
297C71⋊C8—22no—
298C71⋊C8—41no—
299C71⋊C8—41no—
300C71⋊C8—41no—
301C22×C71—22no—
302C22×C71—22no—
303C22×C71—22no—
304C22×C71—41no—
305C22×C71—41no—
306C22×C71—41no—
307C22×C71—41no—
308C22×C71C2×#11711yescharacteristic
309C22×C71C4×#4111yescharacteristic
310C22×C71#51811yescharacteristic
311C22×C71C23×C811yescharacteristic
312C22×C71C22×M1611yescharacteristic
313C22×C71C2×#13111yescharacteristic
314C22×C71#56811yescharacteristic
315C2×D71—22no—
316C2×D71—22no—
317C2×D71—22no—
318C2×D71—22no—
319C2×D71—22no—
320C2×D71—22no—
321C2×D71#43114yes—
322C4×C71—22no—
323C4×C71—22no—
324C4×C71—22no—
325C4×C71—41no—
326C4×C71—41no—
327C4×C71#55111yescharacteristic
328C4×C71#55111yescharacteristic
329C4×C71#55311yescharacteristic
330C4×C71#55311yescharacteristic
331Dic71—22no—
332Dic71—22no—
333Dic71—22no—
334Dic71—22no—
335Dic71—22no—
336Dic71—22no—
337Dic71—41no—
338#22785—711nomaximal, Sylow
339C2×C71—42no—
340C2×C71#235311yescharacteristic
341C2×C71C2×#43111yescharacteristic
342C2×C71#292511yescharacteristic
343C2×C71C8×#4111yescharacteristic
344C2×C71#297011yescharacteristic
345C2×C71#297211yescharacteristic
346C2×C71#297411yescharacteristic
347D71—24no—
348C42×D4—711no—
349#1923—711no—
350#1923D7111yescharacteristic, complemented
351#1916—711no—
352#1916—711no—
353#1869—711no—
354#1869—711no—
355#1839—711no—
356#1817—711no—
357#1797—711no—
358C8×C22⋊C4—711no—
359C8×C22⋊C4—711no—
360C4×C22⋊C8—711no—
361#1744—711no—
362C2×#336—711no—
363C71#2278511yescharacteristic, complemented, Sylow
364C23×C8—711no—
365C23×C8—711no—
366C2×C4×D4—711no—
367C2×C4×D4—711no—
368C2×C4×D4—711no—
369C22×C42—711no—
370C22×C42—711no—
371C2×C4⋊C8—711no—
372C2×C4⋊C8C2×D7111yescharacteristic
373C2×C22⋊C8—711no—
374C2×C22⋊C8—711no—
375C2×C22⋊C8—711no—
376C2×C22⋊C8—711no—
377C2×C22⋊C8C2×D7111yescharacteristic
378C2×C22⋊C8C2×D7111yescharacteristic
379C2×C4×C8—711no—
380C2×C4×C8—711no—
381C2×C4×C8—711no—
382C2×C4×C8C2×D7111yescharacteristic
383C4×C4⋊C4—711no—
384C4×C4⋊C4—711no—
385C4×C4⋊C4—711no—
386C4×C22⋊C4—711no—
387C4×C22⋊C4—711no—
388C4×C22⋊C4—711no—
389C4×C22⋊C4—711no—
390C4×C22⋊C4—711no—
391C4×C22⋊C4C2×D7111yescharacteristic
392C43—711no—
393#336—711no—
394#336—711no—
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#336C2×D7111yescharacteristic
406#336C2×D7111yescharacteristic
407C22×D4—711no—
408C23×C4—711no—
409C23×C4—711no—
410C23×C4—711no—
411C23×C4—711no—
412C23×C4—711no—
413C23×C4C22×D7111yescharacteristic
414C22×C8—2841no—
415C22×C8—2841no—
416C22×C8—711no—
417C22×C8—711no—
418C22×C8—711no—
419C22×C8—711no—
420C22×C8—1422no—
421C22×C8—1422no—
422C22×C8—1422no—
423C22×C8—1422no—
424C22×C8C22×D7111yescharacteristic
425C22×C8C22×D7111yescharacteristic
426C22×C8C22×D7111yescharacteristic
427C22×C8C22×D7111yescharacteristic
428C4×D4—718no—
429C4×D4—1424no—
430C4×D4—1422no—
431C4×D4—1422no—
432C2×C4⋊C4—711no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—711no—
435C2×C22⋊C4—711no—
436C2×C22⋊C4—711no—
437C2×C22⋊C4—711no—
438C2×C22⋊C4—711no—
439C2×C22⋊C4C4×D7111yescharacteristic
440C2×C22⋊C4C4×D7111yescharacteristic
441C2×C42—2841no—
442C2×C42—2841no—
443C2×C42—2841no—
444C2×C42—2841no—
445C2×C42—711no—
446C2×C42—711no—
447C2×C42—711no—
448C2×C42—711no—
449C2×C42—711no—
450C2×C42—711no—
451C2×C42—711no—
452C2×C42—711no—
453C2×C42—711no—
454C2×C42—711no—
455C2×C42—711no—
456C2×C42C22×D7111yescharacteristic
457C2×C42C22×D7111yescharacteristic
458C4⋊C8—41no—
459C4⋊C8—2841no—
460C22⋊C8—22no—
461C22⋊C8—41no—
462C22⋊C8—2841no—
463C22⋊C8—1422no—
464C22⋊C8—1422no—
465C22⋊C8—1422no—
466C4×C8—22no—
467C4×C8—2841no—
468C4×C8—2841no—
469C4×C8—1422no—
470#95—711no—
471#95—711no—
472#95—711no—
473#95—711no—
474#95C4×D7111yescharacteristic
475#95C4×D7111yescharacteristic
476C24—711no—
477C24C2×C4×D7111yescharacteristic
478C2×D4—714no—
479C2×D4—1422no—
480C2×D4—1422no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—2841no—
488C22×C4—2841no—
489C22×C4—2841no—
490C22×C4—2841no—
491C22×C4—2841no—
492C22×C4—2841no—
493C22×C4—714no—
494C22×C4—714no—
495C22×C4—711no—
496C22×C4—711no—
497C22×C4—711no—
498C22×C4—711no—
499C22×C4—711no—
500C22×C4—711no—
501C22×C4—712no—
502C22×C4—712no—
503C22×C4—711no—
504C22×C4—1422no—
505C22×C4—1422no—
506C22×C4—1422no—
507C22×C4—1422no—
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×C4C23×D7111yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
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—2844no—
530C2×C8—2844no—
531C2×C8—712no—
532C2×C8—1421no—
533C2×C8—1421no—
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#1176586412yes—
544C4⋊C4—714no—
545C4⋊C4—1422no—
546C4⋊C4—1422no—
547C22⋊C4—22no—
548C22⋊C4—714no—
549C22⋊C4—714no—
550C22⋊C4—1422no—
551C22⋊C4—1422no—
552C22⋊C4C8×D7114yescomplemented
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—2841no—
558C42—2841no—
559C42—2841no—
560C42—2841no—
561C42—2841no—
562C42—714no—
563C42—1422no—
564C42—1421no—
565C42—1421no—
566C42—1421no—
567C42—1421no—
568C42—1421no—
569C42—1421no—
570C42—1422no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—712no—
578C23—712no—
579C23—712no—
580C23—1421no—
581C23—1421no—
582C23—1421no—
583C23—1421no—
584C23C2×C8×D7112yes—
585C23C22×C4×D7111yescharacteristic
586D4—1428no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—2844no—
604C2×C4—2844no—
605C2×C4—2844no—
606C2×C4—2844no—
607C2×C4—712no—
608C2×C4—712no—
609C2×C4—712no—
610C2×C4—712no—
611C2×C4—712no—
612C2×C4—712no—
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—1422no—
629C2×C4—1422no—
630C2×C4—1422no—
631C2×C4—1422no—
632C2×C4C2×C8×D7112yes—
633C2×C4C2×C8×D7112yes—
634C2×C4M16×D7112yes—
635C2×C4#41×D7111yescharacteristic
636C2×C4#41×D7111yescharacteristic
637C2×C4#41×D7111yescharacteristic
638C2×C4C2×#1176586411yescharacteristic
639C2×C4#1455617311yescharacteristic
640C2×C4#1455617411yescharacteristic
641C8—22no—
642C8—41no—
643C8—41no—
644C8—41no—
645C8—2841no—
646C8—2841no—
647C8—2841no—
648C8—1422no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—714no—
657C22—1422no—
658C22—1422no—
659C22—1422no—
660C22—1422no—
661C22—1422no—
662C22—1422no—
663C22#117×D7111yescharacteristic
664C22C4×#1176586411yescharacteristic
665C22#1798647111yescharacteristic
666C22C22×C8×D7111yescharacteristic
667C22C2×M16×D7111yescharacteristic
668C22#131×D7111yescharacteristic
669C22#1798676411yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—2841no—
676C4—1422no—
677C4—1422no—
678C4—1422no—
679C4—1422no—
680C4—1422no—
681C4—1422no—
682C4#1798667211yescharacteristic
683C4#1798667911yescharacteristic
684C4#1798669611yescharacteristic
685C4#1798670011yescharacteristic
686C2—42no—
687C2—1424no—
688C2#2259127511yescharacteristic
689C2#431×D7111yescharacteristic
690C2#2259700311yescharacteristic
691C2C8×#1176586411yescharacteristic
692C2#2259735011yescharacteristic
693C2#2259736111yescharacteristic
694C2#2259737211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC71×#1923C2
socleC23×C71C23×C4
prime radicalC22×C22⋊D71C2×C4
cosocleC22×C4×C71C24
hypercenter#1923D71
hypocenterC71#22785
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #22588948C2semidirect
3. #22588900C2semidirect
4. #22588894C2semidirect
7. #22588482C2semidirect
8. #22588406C2semidirect
9. #22588317C2semidirect
10. C8×(C2×D71)⋊C4C2semidirect
11. #22588110C2semidirect
12. C22⋊C8×Dic71C2semidirect
13. #22588085C2semidirect
14. #336×D71C2semidirect
15. C71×#1923C2semidirect
78. (C22⋊D71)⋊C4C8semidirect
137. C22×Dic71C2×C8semidirect
173. Dic71⋊C4C2×C8semidirect
191. C4×Dic71C2×C8semidirect
218. C22⋊C4×C71C2×C8semidirect
350. #1923D71semidirect
363. C71#22785semidirect
552. C22⋊C4C8×D71semidirect

Maximal subgroups

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

subgroupindex
C4×(C22⋊D71)⋊C42
#225889482
#225889002
#225888942
#225886292
#225884822
#225884062
#225883172
C8×(C2×D71)⋊C42
#225881102
C22⋊C8×Dic712
#225880852
#336×D712
C71×#19232
#2278571