Finite Group Databasebeta

← #32018332

Subgroups — #32018332

Order 18176.

980 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986064C211yesmaximal, characteristic
2C2×#17986050C211yesmaximal, characteristic, complemented
3C4×#14556113C211yesmaximal, characteristic
4#22589055C211yesmaximal, characteristic, complemented
5#22588944C211yesmaximal, characteristic, complemented
6#22588944C211yesmaximal, characteristic, complemented
7#22588895C211yesmaximal, characteristic, complemented
8#22588631C211yesmaximal, characteristic
9#22588519C211yesmaximal, characteristic, complemented
10#22588519C211yesmaximal, characteristic, complemented
11C4⋊C4×C71⋊C8C211yesmaximal, characteristic, complemented
12C8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
13#22588110C211yesmaximal, characteristic, complemented
14#336×D71C211yesmaximal, characteristic, complemented
15C71×#1916C211yesmaximal, characteristic, complemented
16C22×C8×D71C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19C2×#14556113C411yescharacteristic
20C2×C4×D284C2211yescharacteristic
21C2×C42×D71C2211yescharacteristic
22#17986064—24no—
23#17986050—24no—
24C2×C4⋊(C71⋊C8)C2211yescharacteristic
25C2×Dic71⋊C8C2211yescharacteristic
26C2×Dic71⋊C8C2211yescharacteristic
27C2×Dic71⋊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×C4×C71⋊C8C2211yescharacteristic
35C2×C4×C71⋊C8C2211yescharacteristic
36C2×C8×Dic71C2211yescharacteristic
37#17985889C411yescharacteristic
38#17985888C411yescharacteristic
39#17985886C411yescharacteristic
40#17985885C411yescharacteristic
41#17985877C411yescharacteristic
42#17985870C411yescharacteristic
43#17985861C411yescharacteristic
44C4×Dic71⋊C4C2211yescharacteristic
45C4×(C2×D71)⋊C4C2211yescharacteristic
46C4×(C2×D71)⋊C4C2211yescharacteristic
47C4×(C2×D71)⋊C4C2211yescharacteristic
48#17985754C2211yescharacteristic
49#17985754C2211yescharacteristic
50#17985753C2211yescharacteristic
51#17985753C2211yescharacteristic
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×D71C2311yescharacteristic
65C22×C4×D71C2311yescharacteristic
66C22×C71⋊C8C2311yescharacteristic
67C22×C71⋊C8C2311yescharacteristic
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C2×C8×D71—22no—
71C2×C8×D71—22no—
72C2×C8×D71—22no—
73C2×C8×D71—22no—
74C2×C8×D71—22no—
75C2×C8×D71—22no—
76C2×C8×D71—41no—
77C2×C8×D71—41no—
78C2×C8×D71—41no—
79#14556113C818yescomplemented
80C4×D284—22no—
81C4×D284—22no—
82C2×C4⋊Dic71C2×C411yescharacteristic
83C2×Dic71⋊C4C2×C411yescharacteristic
84C2×Dic71⋊C4C2×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×(C2×D71)⋊C4C2×C411yescharacteristic
91C2×(C2×D71)⋊C4C2×C411yescharacteristic
92C2×(C2×D71)⋊C4C2×C411yescharacteristic
93C2×C4×Dic71C2×C411yescharacteristic
94C2×C4×Dic71C2×C411yescharacteristic
95C2×C4×Dic71C2311yescharacteristic
96C2×C4×Dic71C2311yescharacteristic
97C42×D71—22no—
98C42×D71—22no—
99C4⋊(C71⋊C8)—22no—
100Dic71⋊C8—22no—
101Dic71⋊C8—22no—
102Dic71⋊C8—41no—
103(C2×D71)⋊C8—22no—
104(C2×D71)⋊C8—22no—
105(C2×D71)⋊C8—22no—
106(C2×D71)⋊C8—41no—
107(C2×D71)⋊C8D414yes—
108C4×C71⋊C8—22no—
109C4×C71⋊C8—22no—
110C4×C71⋊C8—22no—
111C8×Dic71—41no—
112C71⋊#95C2×C411yescharacteristic
113C71⋊#95C2×C411yescharacteristic
114C71⋊#95C2×C411yescharacteristic
115C71⋊#95C2×C411yescharacteristic
116C71⋊#95C2×C411yescharacteristic
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C71⋊#95C2×C411yescharacteristic
120C22×C8×C71C2311yescharacteristic
121C22×C8×C71C2311yescharacteristic
122C22×C8×C71C2311yescharacteristic
123C22×C8×C71C2311yescharacteristic
124C2×C4⋊C4×C71C2×C411yescharacteristic
125C2×C4⋊C4×C71C2×C411yescharacteristic
126C2×C42×C71C2311yescharacteristic
127C2×C42×C71C2311yescharacteristic
128C2×C42×C71C2311yescharacteristic
129C4⋊C8×C71—22no—
130C4×C8×C71—22no—
131#95×C71C2×C411yescharacteristic
132#95×C71C2×C411yescharacteristic
133C23×D71C22×C411yescharacteristic
134C23×D71C22×C411yescharacteristic
135C2×D284—22no—
136C2×D284—22no—
137C2×D284C2×C814yes—
138C22×Dic71C22×C411yescharacteristic
139C22×Dic71C22×C411yescharacteristic
140C22×Dic71C22×C411yescharacteristic
141C22×Dic71C22×C411yescharacteristic
142C22×Dic71C22×C411yescharacteristic
143C22×Dic71C22×C411yescharacteristic
144C2×C4×D71—22no—
145C2×C4×D71—22no—
146C2×C4×D71—21no—
147C2×C4×D71—21no—
148C2×C4×D71—21no—
149C2×C4×D71—21no—
150C2×C4×D71—22no—
151C2×C4×D71—22no—
152C2×C4×D71—21no—
153C2×C4×D71—21no—
154C2×C4×D71—21no—
155C2×C4×D71—21no—
156C2×C4×D71—21no—
157C2×C4×D71—21no—
158C2×C4×D71—41no—
159C2×C4×D71C2×C814yescomplemented
160C2×C4×D71C2×D412yes—
161C2×C4×D71#4112yes—
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—21no—
169C2×C71⋊C8—21no—
170C2×C71⋊C8—21no—
171C2×C71⋊C8C2×D412yes—
172C2×C71⋊C8#4112yes—
173C2×C71⋊C8#4112yes—
174C8×D71—44no—
175C8×D71—44no—
176C8×D71—44no—
177C4⋊Dic71—22no—
178Dic71⋊C4—41no—
179Dic71⋊C4C2×C814yescomplemented
180(C2×D71)⋊C4—22no—
181(C2×D71)⋊C4—22no—
182(C2×D71)⋊C4—22no—
183(C2×D71)⋊C4—22no—
184(C2×D71)⋊C4—41no—
185(C2×D71)⋊C4C2×C814yescomplemented
186(C2×D71)⋊C4C2×C814yescomplemented
187(C2×D71)⋊C4C2×C814yescomplemented
188C4×Dic71—21no—
189C4×Dic71—21no—
190C4×Dic71—21no—
191C4×Dic71—21no—
192C4×Dic71—22no—
193C4×Dic71—22no—
194C22×C4×C71C22×C411yescharacteristic
195C22×C4×C71C22×C411yescharacteristic
196C22×C4×C71C22×C411yescharacteristic
197C22×C4×C71C22×C411yescharacteristic
198C22×C4×C71C22×C411yescharacteristic
199C22×C4×C71C22×C411yescharacteristic
200C22×C4×C71C2411yescharacteristic
201C2×C8×C71—21no—
202C2×C8×C71—21no—
203C2×C8×C71—21no—
204C2×C8×C71—21no—
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×C71C2×D412yes—
213C4⋊C4×C71—22no—
214C4⋊C4×C71C2×C814yescomplemented
215C42×C71—21no—
216C42×C71—21no—
217C42×C71—21no—
218C42×C71—21no—
219C42×C71—21no—
220C42×C71—21no—
221C23×C71C23×C411yescharacteristic
222C22×D71—21no—
223C22×D71—21no—
224C22×D71—21no—
225C22×D71—21no—
226C22×D71—21no—
227C22×D71—21no—
228C22×D71—21no—
229C22×D71—21no—
230C22×D71—21no—
231C22×D71—21no—
232C22×D71C4×D412yes—
233C22×D71C22×C812yes—
234C22×D71C22×C812yes—
235C22×D71#13112yes—
236C2×C4×C71—21no—
237C2×C4×C71—21no—
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×C71C22×C812yes—
251C2×C4×C71C22×C812yes—
252C2×C4×C71C22×C812yes—
253C2×C4×C71#13112yes—
254C2×C4×C71C22×D411yescharacteristic
255C2×C4×C71C2×#4111yescharacteristic
256C2×C4×C71C2×#4111yescharacteristic
257C2×C4×C71C2×#4111yescharacteristic
258C2×C4×C71H(5,𝔽2)11yescharacteristic
259C2×C4×C712−1+411yescharacteristic
260C2×Dic71—21no—
261C2×Dic71—21no—
262C2×Dic71—21no—
263C2×Dic71—21no—
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×Dic71C4×D412yes—
276C2×Dic71C22×C812yes—
277C2×Dic71C22×C812yes—
278D284—28no—
279C4×D71—28no—
280C4×D71—22no—
281C4×D71—22no—
282C4×D71—22no—
283C4×D71—22no—
284C4×D71—44no—
285C4×D71—41no—
286C4×D71—41no—
287C4×D71—41no—
288C4×D71—41no—
289C8×C71—22no—
290C8×C71—41no—
291C8×C71—41no—
292C8×C71—41no—
293C71⋊C8—22no—
294C71⋊C8—22no—
295C71⋊C8—22no—
296C71⋊C8—41no—
297C22×C71C2×C4×D411yescharacteristic
298C22×C71C4×#4111yescharacteristic
299C22×C71#52011yescharacteristic
300C22×C71C23×C811yescharacteristic
301C22×C71C2×#13111yescharacteristic
302C22×C71C2×#13111yescharacteristic
303C22×C71#56811yescharacteristic
304C2×D71—22no—
305C2×D71—22no—
306C2×D71—22no—
307C2×D71—22no—
308C2×D71—22no—
309C2×D71—22no—
310C2×D71—22no—
311C2×D71—22no—
312C2×D71—22no—
313C2×D71—41no—
314C2×D71—41no—
315C2×D71—41no—
316C2×D71—41no—
317C2×D71C8×D414yes—
318C4×C71—22no—
319C4×C71—22no—
320C4×C71—22no—
321C4×C71—22no—
322C4×C71—41no—
323C4×C71—41no—
324C4×C71#54611yescharacteristic
325C4×C71#54711yescharacteristic
326C4×C71#55111yescharacteristic
327C4×C71#55211yescharacteristic
328Dic71—22no—
329Dic71—22no—
330Dic71—22no—
331Dic71—41no—
332Dic71—41no—
333Dic71—41no—
334#22900—711nomaximal, Sylow
335C2×C71#235911yescharacteristic
336C2×C71C2×C8×D411yescharacteristic
337C2×C71#293311yescharacteristic
338C2×C71C8×#4111yescharacteristic
339C2×C71#296811yescharacteristic
340C2×C71#298811yescharacteristic
341C2×C71#299411yescharacteristic
342D71—24no—
343D71—42no—
344C2×C8×D4—711no—
345C2×#431—711no—
346C4×#123—711no—
347#1939—711no—
348#1923—711no—
349#1923—711no—
350#1916—711no—
351#1916D7111yescharacteristic, complemented
352#1869—711no—
353#1850—711no—
354#1850—711no—
355C8×C4⋊C4—711no—
356C8×C22⋊C4—711no—
357C8×C22⋊C4—711no—
358C2×#336—711no—
359C71#2290011yescharacteristic, complemented, Sylow
360C23×C8—711no—
361C23×C8—711no—
362C23×C8—711no—
363C2×#123—711no—
364C2×C4×D4—711no—
365C22×C42—711no—
366C8×D4—1424no—
367#431—1424no—
368C2×C4⋊C8—711no—
369C2×C4⋊C8—711no—
370C2×C4⋊C8—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⋊C8—711no—
378C2×C4×C8—711no—
379C2×C4×C8—711no—
380C2×C4×C8—711no—
381C2×C4×C8—711no—
382C2×C4×C8C2×D7111yescharacteristic
383#388—711no—
384#388—711no—
385#387—711no—
386#387—711no—
387#386—711no—
388#385—711no—
389#381—711no—
390C4×C4⋊C4—711no—
391C4×C4⋊C4C2×D7111yescharacteristic
392C4×C22⋊C4—711no—
393C4×C22⋊C4—711no—
394C4×C22⋊C4—711no—
395#336—711no—
396#336—711no—
397#336—711no—
398#336—711no—
399#336—711no—
400#336—711no—
401#336C2×D7111yescharacteristic
402#336C2×D7111yescharacteristic
403#336C2×D7111yescharacteristic
404#336C2×D7111yescharacteristic
405C22×D4—711no—
406C23×C4—711no—
407C23×C4—711no—
408C23×C4—711no—
409C23×C4—711no—
410C22×C8—2841no—
411C22×C8—2841no—
412C22×C8—2841no—
413C22×C8—711no—
414C22×C8—711no—
415C22×C8—711no—
416C22×C8—711no—
417C22×C8—1422no—
418C22×C8—1422no—
419C22×C8—1422no—
420C22×C8—1422no—
421C22×C8—1422no—
422C22×C8—1422no—
423C22×C8C22×D7111yescharacteristic
424C22×C8C22×D7111yescharacteristic
425C22×C8C22×D7111yescharacteristic
426C22×C8C22×D7111yescharacteristic
427#123—718no—
428C4×D4—1422no—
429C4×D4—1422no—
430C2×C4⋊C4—711no—
431C2×C4⋊C4—711no—
432C2×C4⋊C4—711no—
433C2×C4⋊C4C4×D7111yescharacteristic
434C2×C4⋊C4C4×D7111yescharacteristic
435C2×C22⋊C4—711no—
436C2×C22⋊C4—711no—
437C2×C22⋊C4—711no—
438C2×C22⋊C4—711no—
439C2×C22⋊C4—711no—
440C2×C22⋊C4—711no—
441C2×C22⋊C4—711no—
442C2×C22⋊C4—711no—
443C2×C42—711no—
444C2×C42—711no—
445C2×C42—711no—
446C2×C42—711no—
447C2×C42—1422no—
448C2×C42—1422no—
449C2×C42C22×D7111yescharacteristic
450C2×C42C22×D7111yescharacteristic
451C2×C42C22×D7111yescharacteristic
452C4⋊C8—22no—
453C4⋊C8—2841no—
454C4⋊C8—1422no—
455C4⋊C8—1422no—
456C4⋊C8—1422no—
457C22⋊C8—2841no—
458C22⋊C8—714no—
459C22⋊C8—1422no—
460C22⋊C8—1422no—
461C22⋊C8—1422no—
462C4×C8—22no—
463C4×C8—2841no—
464C4×C8—1422no—
465C4×C8—1422no—
466C4×C8—1422no—
467#95—711no—
468#95—711no—
469#95—711no—
470#95—711no—
471#95—711no—
472#95—711no—
473#95—711no—
474#95—711no—
475#95C4×D7111yescharacteristic
476#95C4×D7111yescharacteristic
477C24—711no—
478C24—711no—
479C2×D4—714no—
480C2×D4—1422no—
481C2×D4—1422no—
482C22×C4—2841no—
483C22×C4—711no—
484C22×C4—711no—
485C22×C4—711no—
486C22×C4—712no—
487C22×C4—712no—
488C22×C4—714no—
489C22×C4—711no—
490C22×C4—711no—
491C22×C4—711no—
492C22×C4—1422no—
493C22×C4—1422no—
494C22×C4—1422no—
495C22×C4—1421no—
496C22×C4—1421no—
497C22×C4—1421no—
498C22×C4—1421no—
499C22×C4—1421no—
500C22×C4—1421no—
501C22×C4—1422no—
502C22×C4—1421no—
503C22×C4—1421no—
504C22×C4—1421no—
505C22×C4—1421no—
506C22×C4C2×C4×D7111yescharacteristic
507C22×C4C2×C4×D7111yescharacteristic
508C22×C4C2×C4×D7111yescharacteristic
509C22×C4C2×C4×D7111yescharacteristic
510C22×C4C2×C4×D7111yescharacteristic
511C22×C4C2×C4×D7111yescharacteristic
512C22×C4C23×D7111yescharacteristic
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—2844no—
525C2×C8—2844no—
526C2×C8—2844no—
527C2×C8—712no—
528C2×C8—712no—
529C2×C8—712no—
530C2×C8—1421no—
531C2×C8—1421no—
532C2×C8—1421no—
533C2×C8—1421no—
534C2×C8—1421no—
535C2×C8—1421no—
536C2×C8—1421no—
537C2×C8—1421no—
538C2×C8—1421no—
539C2×C8D4×D7112yes—
540C4⋊C4—22no—
541C4⋊C4—2841no—
542C4⋊C4—714no—
543C4⋊C4—1422no—
544C4⋊C4C8×D7114yescomplemented
545C22⋊C4—2841no—
546C22⋊C4—714no—
547C22⋊C4—714no—
548C22⋊C4—714no—
549C22⋊C4—1422no—
550C22⋊C4—1422no—
551C22⋊C4—1422no—
552C22⋊C4—1422no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—1422no—
560C42—1422no—
561C42—1421no—
562C42—1421no—
563C42—1421no—
564C42—1421no—
565C23—712no—
566C23—712no—
567C23—712no—
568C23—712no—
569C23—1421no—
570C23—1421no—
571C23—1421no—
572C23—1421no—
573C23—1421no—
574C23—1421no—
575C23—1421no—
576C23—1421no—
577C23—1421no—
578C23—1421no—
579C23C22×C4×D7111yescharacteristic
580D4—1428no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
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—2844no—
596C2×C4—2841no—
597C2×C4—2841no—
598C2×C4—2841no—
599C2×C4—2841no—
600C2×C4—712no—
601C2×C4—712no—
602C2×C4—712no—
603C2×C4—1428no—
604C2×C4—1421no—
605C2×C4—1421no—
606C2×C4—1421no—
607C2×C4—1421no—
608C2×C4—1421no—
609C2×C4—1421no—
610C2×C4—1421no—
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—1422no—
620C2×C4—1422no—
621C2×C4—1422no—
622C2×C4—1422no—
623C2×C4C2×C8×D7112yes—
624C2×C4C2×C8×D7112yes—
625C2×C4C2×C8×D7112yes—
626C2×C4#1455613612yes—
627C2×C4C2×D4×D7111yescharacteristic
628C2×C4#41×D7111yescharacteristic
629C2×C4#41×D7111yescharacteristic
630C2×C4#41×D7111yescharacteristic
631C2×C4#1455617411yescharacteristic
632C2×C4#1455617611yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8—41no—
637C8—2841no—
638C8—1422no—
639C8—1422no—
640C8—1422no—
641C22—2841no—
642C22—2841no—
643C22—2841no—
644C22—2841no—
645C22—714no—
646C22—1422no—
647C22—1422no—
648C22—1422no—
649C22—1422no—
650C22—1422no—
651C22—1422no—
652C22—1422no—
653C22—1422no—
654C22—1422no—
655C22C4×D4×D7111yescharacteristic
656C22#1798646711yescharacteristic
657C22#1798648111yescharacteristic
658C22C22×C8×D7111yescharacteristic
659C22#131×D7111yescharacteristic
660C22C2×#1455613611yescharacteristic
661C22#1798676411yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—2841no—
669C4—2841no—
670C4—2841no—
671C4—1422no—
672C4—1422no—
673C4—1422no—
674C4#1798664111yescharacteristic
675C4#1798665111yescharacteristic
676C4#1798667411yescharacteristic
677C4#1798668111yescharacteristic
678C2—2842no—
679C2—1424no—
680C2#2259132511yescharacteristic
681C2C8×D4×D7111yescharacteristic
682C2#2259706611yescharacteristic
683C2#2259729611yescharacteristic
684C2#2259733211yescharacteristic
685C2#2259745011yescharacteristic
686C2#2259750311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC71×#1916C2
socleC23×C71C23×C4
prime radicalC22×D284C2×C4
cosocleC22×C4×C71C24
hypercenter#1916D71
hypocenterC71#22900
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. C2×#17986050C2semidirect
4. #22589055C2semidirect
5. #22588944C2semidirect
6. #22588944C2semidirect
7. #22588895C2semidirect
9. #22588519C2semidirect
10. #22588519C2semidirect
11. C4⋊C4×C71⋊C8C2semidirect
12. C8×(C2×D71)⋊C4C2semidirect
13. #22588110C2semidirect
14. #336×D71C2semidirect
15. C71×#1916C2semidirect
79. #14556113C8semidirect
159. C2×C4×D71C2×C8semidirect
179. Dic71⋊C4C2×C8semidirect
185. (C2×D71)⋊C4C2×C8semidirect
186. (C2×D71)⋊C4C2×C8semidirect
187. (C2×D71)⋊C4C2×C8semidirect
214. C4⋊C4×C71C2×C8semidirect
351. #1916D71semidirect
359. C71#22900semidirect
544. C4⋊C4C8×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860642
C2×#179860502
C4×#145561132
#225890552
#225889442
#225888952
#225886312
#225885192
C4⋊C4×C71⋊C82
C8×(C2×D71)⋊C42
#225881102
#336×D712
C71×#19162
#2290071