Finite Group Databasebeta

← #32000227

Subgroups — #32000227

Order 18176.

1106 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×#17986051C211yesmaximal, characteristic, complemented
2C2×C4×C8×D71C211yesmaximal, characteristic, complemented
3C4×#14556090C211yesmaximal, characteristic
4#22588946C211yesmaximal, characteristic, complemented
5#22588944C211yesmaximal, characteristic, complemented
6#22588899C211yesmaximal, characteristic, complemented
7#22588631C211yesmaximal, characteristic
8#22588631C211yesmaximal, characteristic
9#22588519C211yesmaximal, characteristic, complemented
10#22588516C211yesmaximal, characteristic, complemented
11#22588188C211yesmaximal, characteristic, complemented
12#22588097C211yesmaximal, characteristic, complemented
13#22588097C211yesmaximal, characteristic, complemented
14#22588084C211yesmaximal, characteristic, complemented
15C71×#1916C211yesmaximal, characteristic, complemented
16C22×C8×D71C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C2×C4×D284C2211yescharacteristic
19C2×#14556090C411yescharacteristic
20C2×#14556090C411yescharacteristic
21C2×C42×D71C2211yescharacteristic
22C2×C42×D71C2211yescharacteristic
23#17986051—24no—
24C2×C4⋊(C71⋊C8)C2211yescharacteristic
25C2×Dic71⋊C8C2211yescharacteristic
26C2×Dic71⋊C8C2211yescharacteristic
27C2×(C2×D71)⋊C8C2211yescharacteristic
28C2×(C2×D71)⋊C8C2211yescharacteristic
29C2×(C2×D71)⋊C8C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×C4×C71⋊C8C2211yescharacteristic
34C2×C8×Dic71C2211yescharacteristic
35C2×C8×Dic71C2211yescharacteristic
36C2×C8×Dic71C2211yescharacteristic
37C2×C8×Dic71C2211yescharacteristic
38C4×C8×D71—24no—
39C4⋊C4×Dic71C411yescharacteristic
40C4⋊C4×Dic71C411yescharacteristic
41C4×(C2×D71)⋊C4C2211yescharacteristic
42C4×(C2×D71)⋊C4C2211yescharacteristic
43#17985846C411yescharacteristic
44#17985846C411yescharacteristic
45#17985846C411yescharacteristic
46#17985846C411yescharacteristic
47C42×Dic71C2211yescharacteristic
48#17985754C2211yescharacteristic
49#17985754C2211yescharacteristic
50#17985754C2211yescharacteristic
51#17985754C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54C2×C4⋊C8×C71C2211yescharacteristic
55C2×C4×C8×C71C2211yescharacteristic
56C4×C4⋊C4×C71C2211yescharacteristic
57#336×C71C2211yescharacteristic
58#336×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic
60#336×C71C2211yescharacteristic
61C22×D284C2×C411yescharacteristic
62C22×C4×D71C2×C411yescharacteristic
63C22×C4×D71C2×C411yescharacteristic
64C22×C4×D71C2×C411yescharacteristic
65C22×C4×D71C2×C411yescharacteristic
66C22×C4×D71C2311yescharacteristic
67C22×C4×D71C2311yescharacteristic
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C2×C8×D71—22no—
73C2×C8×D71—22no—
74C2×C8×D71—22no—
75C2×C8×D71—22no—
76C2×C8×D71—22no—
77C2×C8×D71—22no—
78C4×D284—22no—
79C4×D284—22no—
80#14556090—24no—
81#14556090C818yescomplemented
82C2×C4⋊Dic71C2×C411yescharacteristic
83C2×(C2×D71)⋊C4C2×C411yescharacteristic
84C2×(C2×D71)⋊C4C2×C411yescharacteristic
85C2×(C2×D71)⋊C4C2×C411yescharacteristic
86C2×(C2×D71)⋊C4C2×C411yescharacteristic
87C2×(C2×D71)⋊C4C2×C411yescharacteristic
88C2×(C2×D71)⋊C4C2×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×Dic71C2×C411yescharacteristic
97C2×C4×Dic71C2311yescharacteristic
98C2×C4×Dic71C2311yescharacteristic
99C42×D71—22no—
100C42×D71—22no—
101C42×D71—22no—
102C42×D71—22no—
103C4⋊(C71⋊C8)—22no—
104Dic71⋊C8—22no—
105Dic71⋊C8—22no—
106(C2×D71)⋊C8—22no—
107(C2×D71)⋊C8—22no—
108(C2×D71)⋊C8—22no—
109(C2×D71)⋊C8—22no—
110(C2×D71)⋊C8—22no—
111(C2×D71)⋊C8—22no—
112C4×C71⋊C8—22no—
113C8×Dic71—22no—
114C8×Dic71—22no—
115C8×Dic71—22no—
116C8×Dic71D414yescomplemented
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C71⋊#95C2×C411yescharacteristic
120C71⋊#95C2×C411yescharacteristic
121C22×C8×C71C2311yescharacteristic
122C22×C8×C71C2311yescharacteristic
123C22×C8×C71C2311yescharacteristic
124C22×C8×C71C2311yescharacteristic
125C2×C4⋊C4×C71C2×C411yescharacteristic
126C2×C4⋊C4×C71C2×C411yescharacteristic
127C2×C42×C71C2311yescharacteristic
128C2×C42×C71C2311yescharacteristic
129C2×C42×C71C2311yescharacteristic
130C4⋊C8×C71—22no—
131C4×C8×C71—22no—
132#95×C71C2×C411yescharacteristic
133#95×C71C2×C411yescharacteristic
134C23×D71C22×C411yescharacteristic
135C23×D71C22×C411yescharacteristic
136C2×D284—22no—
137C2×D284—22no—
138C2×D284C2×C814yes—
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—22no—
152C2×C4×D71—22no—
153C2×C4×D71—22no—
154C2×C4×D71—22no—
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×D71C2×C814yes—
165C2×C4×D71C2×C814yescomplemented
166C2×C4×D71M1614yes—
167C2×C4×D71#4112yes—
168C2×C4×D71#4112yes—
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⋊C8C2×D412yes—
180C2×C71⋊C8#4112yes—
181C8×D71—28no—
182C8×D71—28no—
183C4⋊Dic71—22no—
184(C2×D71)⋊C4—22no—
185(C2×D71)⋊C4—22no—
186(C2×D71)⋊C4—22no—
187(C2×D71)⋊C4—22no—
188(C2×D71)⋊C4C2×C814yes—
189(C2×D71)⋊C4C2×C814yescomplemented
190C4×Dic71—21no—
191C4×Dic71—21no—
192C4×Dic71—22no—
193C4×Dic71—22no—
194C4×Dic71—22no—
195C4×Dic71—22no—
196C4×Dic71—22no—
197C4×Dic71—22no—
198C4×Dic71—22no—
199C4×Dic71C2×C814yescomplemented
200C4×Dic71C2×D412yes—
201C4×Dic71#4112yes—
202C22×C4×C71C22×C411yescharacteristic
203C22×C4×C71C22×C411yescharacteristic
204C22×C4×C71C22×C411yescharacteristic
205C22×C4×C71C22×C411yescharacteristic
206C22×C4×C71C22×C411yescharacteristic
207C22×C4×C71C22×C411yescharacteristic
208C22×C4×C71C2411yescharacteristic
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—21no—
217C2×C8×C71—21no—
218C2×C8×C71—21no—
219C2×C8×C71C2×D412yes—
220C2×C8×C71#4112yes—
221C4⋊C4×C71—22no—
222C4⋊C4×C71C2×C814yescomplemented
223C42×C71—21no—
224C42×C71—21no—
225C42×C71—21no—
226C42×C71—21no—
227C42×C71—21no—
228C42×C71—21no—
229C23×C71C23×C411yescharacteristic
230C22×D71—21no—
231C22×D71—21no—
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#11712yes—
241C22×D71C22×C812yes—
242C22×D71C22×C812yes—
243C22×D71C2×M1612yes—
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—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×C71C22×C812yes—
259C2×C4×C71C22×C812yes—
260C2×C4×C71C22×C812yes—
261C2×C4×C71C2×M1612yes—
262C2×C4×C71C22×D411yescharacteristic
263C2×C4×C71C2×#4111yescharacteristic
264C2×C4×C71C2×#4111yescharacteristic
265C2×C4×C71C2×#4111yescharacteristic
266C2×C4×C71C2×#4111yescharacteristic
267C2×C4×C71C2×#4111yescharacteristic
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#11712yes—
279C2×Dic71C4×D412yes—
280C2×Dic71C4×D412yes—
281C2×Dic71C22×C812yes—
282C2×Dic71C22×C812yes—
283C2×Dic71C2×M1612yes—
284C2×Dic71#13112yes—
285C2×Dic71#13112yes—
286D284—28no—
287C4×D71—22no—
288C4×D71—22no—
289C4×D71—22no—
290C4×D71—22no—
291C4×D71—28no—
292C4×D71—28no—
293C4×D71—28no—
294C4×D71—41no—
295C4×D71—41no—
296C4×D71—41no—
297C4×D71—41no—
298C4×D71—44no—
299C8×C71—22no—
300C8×C71—22no—
301C8×C71—41no—
302C8×C71—41no—
303C71⋊C8—22no—
304C71⋊C8—22no—
305C71⋊C8—41no—
306C71⋊C8—41no—
307C22×C71C2×#11711yescharacteristic
308C22×C71C2×C4×D411yescharacteristic
309C22×C71C4×#4111yescharacteristic
310C22×C71C23×C811yescharacteristic
311C22×C71C22×M1611yescharacteristic
312C22×C71C2×#13111yescharacteristic
313C22×C71C2×#13111yescharacteristic
314C2×D71—22no—
315C2×D71—22no—
316C2×D71—22no—
317C2×D71—22no—
318C2×D71—22no—
319C2×D71—22no—
320C2×D71—22no—
321C2×D71—22no—
322C2×D71—22no—
323C2×D71—41no—
324C2×D71—41no—
325C2×D71—41no—
326C2×D71—41no—
327C2×D71#43114yescomplemented
328C4×C71—22no—
329C4×C71—22no—
330C4×C71—22no—
331C4×C71—22no—
332C4×C71—41no—
333C4×C71—41no—
334C4×C71#52511yescharacteristic
335C4×C71#52511yescharacteristic
336C4×C71#52911yescharacteristic
337C4×C71#52911yescharacteristic
338Dic71—22no—
339Dic71—22no—
340Dic71—41no—
341Dic71—41no—
342Dic71C8×D414yes—
343Dic71#43514yes—
344#21101—711nomaximal, Sylow
345C2×C71#229011yescharacteristic
346C2×C71C2×#43111yescharacteristic
347C2×C71#292211yescharacteristic
348C2×C71C2×C8×D411yescharacteristic
349C2×C71C2×#43511yescharacteristic
350C2×C71C8×#4111yescharacteristic
351C2×C71#296511yescharacteristic
352D71—24no—
353D71—42no—
354C2×#431—711no—
355C22×C4×C8—711no—
356C42×D4—711no—
357#1923—711no—
358#1923—711no—
359#1916—711no—
360#1916D7111yescharacteristic, complemented
361#1869—711no—
362#1869—711no—
363#1850—711no—
364#1850—711no—
365C4×C4⋊C8—711no—
366C4×C22⋊C8—711no—
367C4×C22⋊C8—711no—
368#1744—711no—
369C71#2110111yescharacteristic, complemented, Sylow
370C23×C8—711no—
371C23×C8—711no—
372C2×C4×D4—711no—
373C2×C4×D4—711no—
374C2×C4×D4—711no—
375C22×C42—711no—
376C22×C42—711no—
377#431—1424no—
378C2×C4⋊C8—711no—
379C2×C4⋊C8—711no—
380C2×C4⋊C8—711no—
381C2×C4⋊C8C2×D7111yescharacteristic
382C2×C22⋊C8—711no—
383C2×C22⋊C8—711no—
384C2×C22⋊C8—711no—
385C2×C22⋊C8—711no—
386C2×C22⋊C8—711no—
387C2×C22⋊C8—711no—
388C2×C4×C8—711no—
389C2×C4×C8—711no—
390C2×C4×C8—711no—
391C2×C4×C8—711no—
392C2×C4×C8—711no—
393C2×C4×C8—1424no—
394C2×C4×C8C2×D7111yescharacteristic
395C4×C4⋊C4—711no—
396C4×C4⋊C4—711no—
397C4×C4⋊C4C2×D7111yescharacteristic
398C4×C22⋊C4—711no—
399C4×C22⋊C4—711no—
400C4×C22⋊C4—711no—
401C4×C22⋊C4—711no—
402C4×C22⋊C4—711no—
403C4×C22⋊C4—711no—
404C43—711no—
405#336—711no—
406#336—711no—
407#336—711no—
408#336—711no—
409#336—711no—
410#336—711no—
411#336C2×D7111yescharacteristic
412#336C2×D7111yescharacteristic
413#336C2×D7111yescharacteristic
414#336C2×D7111yescharacteristic
415C22×D4—711no—
416C23×C4—711no—
417C23×C4—711no—
418C23×C4—711no—
419C23×C4—711no—
420C23×C4—711no—
421C23×C4—711no—
422C22×C8—711no—
423C22×C8—711no—
424C22×C8—711no—
425C22×C8—711no—
426C22×C8—1422no—
427C22×C8—1422no—
428C22×C8—1422no—
429C22×C8—1422no—
430C22×C8—1422no—
431C22×C8—1422no—
432C22×C8C22×D7111yescharacteristic
433C22×C8C22×D7111yescharacteristic
434C22×C8C22×D7111yescharacteristic
435C22×C8C22×D7111yescharacteristic
436C4×D4—718no—
437C4×D4—1422no—
438C4×D4—1422no—
439C4×D4—1424no—
440C2×C4⋊C4—711no—
441C2×C4⋊C4C4×D7111yescharacteristic
442C2×C4⋊C4C4×D7111yescharacteristic
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×C42—711no—
450C2×C42—711no—
451C2×C42—711no—
452C2×C42—711no—
453C2×C42—711no—
454C2×C42—711no—
455C2×C42—711no—
456C2×C42—711no—
457C2×C42—711no—
458C2×C42—711no—
459C2×C42—1422no—
460C2×C42—1422no—
461C2×C42—1422no—
462C2×C42—1422no—
463C2×C42C22×D7111yescharacteristic
464C2×C42C22×D7111yescharacteristic
465C2×C42C22×D7111yescharacteristic
466C4⋊C8—22no—
467C4⋊C8—1422no—
468C4⋊C8—1422no—
469C4⋊C8—1422no—
470C22⋊C8—1422no—
471C22⋊C8—1422no—
472C22⋊C8—1422no—
473C22⋊C8—1422no—
474C22⋊C8—1422no—
475C22⋊C8—1422no—
476C4×C8—22no—
477C4×C8—714no—
478C4×C8—1422no—
479C4×C8—1422no—
480C4×C8—1422no—
481C4×C8—1422no—
482#95—711no—
483#95—711no—
484#95—711no—
485#95—711no—
486#95C4×D7111yescharacteristic
487#95C4×D7111yescharacteristic
488C24—711no—
489C24—711no—
490C2×D4—714no—
491C2×D4—1422no—
492C2×D4—1422no—
493C22×C4—711no—
494C22×C4—711no—
495C22×C4—711no—
496C22×C4—711no—
497C22×C4—712no—
498C22×C4—712no—
499C22×C4—714no—
500C22×C4—714no—
501C22×C4—714no—
502C22×C4—711no—
503C22×C4—711no—
504C22×C4—1422no—
505C22×C4—1422no—
506C22×C4—1422no—
507C22×C4—1422no—
508C22×C4—1422no—
509C22×C4—1422no—
510C22×C4—1422no—
511C22×C4—1422no—
512C22×C4—1422no—
513C22×C4—1421no—
514C22×C4—1421no—
515C22×C4—1421no—
516C22×C4—1421no—
517C22×C4—1421no—
518C22×C4—1421no—
519C22×C4—1421no—
520C22×C4—1421no—
521C22×C4—1421no—
522C22×C4—1421no—
523C22×C4C2×C4×D7111yescharacteristic
524C22×C4C2×C4×D7111yescharacteristic
525C22×C4C2×C4×D7111yescharacteristic
526C22×C4C2×C4×D7111yescharacteristic
527C22×C4C2×C4×D7111yescharacteristic
528C22×C4C2×C4×D7111yescharacteristic
529C22×C4C23×D7111yescharacteristic
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—21no—
540C2×C8—712no—
541C2×C8—712no—
542C2×C8—1428no—
543C2×C8—1428no—
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—
553C2×C8—1421no—
554C2×C8D4×D7112yes—
555C2×C8#1176586612yes—
556C4⋊C4—22no—
557C4⋊C4—1422no—
558C4⋊C4C8×D7114yescomplemented
559C22⋊C4—714no—
560C22⋊C4—714no—
561C22⋊C4—1422no—
562C22⋊C4—1422no—
563C22⋊C4—1422no—
564C22⋊C4—1422no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—712no—
572C42—712no—
573C42—714no—
574C42—1422no—
575C42—1422no—
576C42—1422no—
577C42—1422no—
578C42—1422no—
579C42—1422no—
580C42—1422no—
581C42—1421no—
582C42—1421no—
583C23—712no—
584C23—712no—
585C23—712no—
586C23—712no—
587C23—1421no—
588C23—1421no—
589C23—1421no—
590C23—1421no—
591C23—1421no—
592C23—1421no—
593C23—1421no—
594C23—1421no—
595C23—1421no—
596C23—1421no—
597C23C22×C4×D7111yescharacteristic
598D4—1428no—
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—21no—
613C2×C4—2844no—
614C2×C4—2841no—
615C2×C4—2841no—
616C2×C4—2841no—
617C2×C4—2841no—
618C2×C4—712no—
619C2×C4—712no—
620C2×C4—712no—
621C2×C4—712no—
622C2×C4—712no—
623C2×C4—712no—
624C2×C4—712no—
625C2×C4—712no—
626C2×C4—1428no—
627C2×C4—1428no—
628C2×C4—1428no—
629C2×C4—1421no—
630C2×C4—1421no—
631C2×C4—1421no—
632C2×C4—1421no—
633C2×C4—1421no—
634C2×C4—1421no—
635C2×C4—1421no—
636C2×C4—1421no—
637C2×C4—1421no—
638C2×C4—1421no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1422no—
643C2×C4C2×C8×D7112yes—
644C2×C4C2×C8×D7112yes—
645C2×C4C2×C8×D7112yes—
646C2×C4M16×D7112yes—
647C2×C4C2×D4×D7111yescharacteristic
648C2×C4#41×D7111yescharacteristic
649C2×C4#41×D7111yescharacteristic
650C2×C4#41×D7111yescharacteristic
651C2×C4#41×D7111yescharacteristic
652C2×C4C2×#1176586611yescharacteristic
653C8—22no—
654C8—22no—
655C8—41no—
656C8—41no—
657C8—2841no—
658C8—2841no—
659C8—1422no—
660C8—1422no—
661C22—2841no—
662C22—2841no—
663C22—2841no—
664C22—2841no—
665C22—714no—
666C22—1422no—
667C22—1422no—
668C22—1422no—
669C22—1422no—
670C22—1422no—
671C22—1422no—
672C22—1422no—
673C22—1422no—
674C22—1422no—
675C22#117×D7111yescharacteristic
676C22C4×D4×D7111yescharacteristic
677C22C4×#1176586611yescharacteristic
678C22C22×C8×D7111yescharacteristic
679C22C2×M16×D7111yescharacteristic
680C22#131×D7111yescharacteristic
681C22#131×D7111yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—2841no—
689C4—2841no—
690C4—714no—
691C4—714no—
692C4—1422no—
693C4—1422no—
694C4#1798650711yescharacteristic
695C4#1798651211yescharacteristic
696C4#1798653211yescharacteristic
697C4#1798653411yescharacteristic
698C2—2842no—
699C2—1424no—
700C2#2259077811yescharacteristic
701C2#431×D7111yescharacteristic
702C2#2259698111yescharacteristic
703C2C8×D4×D7111yescharacteristic
704C2#435×D7111yescharacteristic
705C2C8×#1176586611yescharacteristic
706C2#2259730511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC71×#1916C2
socleC23×C71C23×C4
prime radicalC22×D284C2×C4
cosocleC22×C4×C71C24
hypercenter#1916D71
hypocenterC71#21101
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. C2×#17986051C2semidirect
2. C2×C4×C8×D71C2semidirect
4. #22588946C2semidirect
5. #22588944C2semidirect
6. #22588899C2semidirect
9. #22588519C2semidirect
10. #22588516C2semidirect
11. #22588188C2semidirect
12. #22588097C2semidirect
13. #22588097C2semidirect
14. #22588084C2semidirect
15. C71×#1916C2semidirect
81. #14556090C8semidirect
116. C8×Dic71D4semidirect
165. C2×C4×D71C2×C8semidirect
189. (C2×D71)⋊C4C2×C8semidirect
199. C4×Dic71C2×C8semidirect
222. C4⋊C4×C71C2×C8semidirect
327. C2×D71#431semidirect
360. #1916D71semidirect
369. C71#21101semidirect
558. C4⋊C4C8×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860512
C2×C4×C8×D712
C4×#145560902
#225889462
#225889442
#225888992
#225886312
#225885192
#225885162
#225881882
#225880972
#225880842
C71×#19162
#2110171