Finite Group Databasebeta

← C2×#22594421 #32164118

Subgroups — C2×#22594421 #32164118

Order 18176.

1962 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
1#22594421C2116yesmaximal, direct product factor
2C2×#17985941C211yesmaximal, characteristic, complemented
3C2×#17985936C211yesmaximal, characteristic
4C2×#17985931C211yesmaximal, characteristic, complemented
5C2×#17985931C211yesmaximal, characteristic, complemented
6C2×#17985926C211yesmaximal, characteristic
7C2×#17985925C211yesmaximal, characteristic
8C2×#17985921C211yesmaximal, characteristic
9C2×#17985898C211yesmaximal, characteristic, complemented
10C2×#17985891C211yesmaximal, characteristic
11C2×#17985888C211yesmaximal, characteristic
12C2×#17985888C211yesmaximal, characteristic
13C2×#17985886C211yesmaximal, characteristic, complemented
14C2×#17985881C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
16C2×#400×C71C211yesmaximal, characteristic, complemented
17C22×C4⋊Dic71C2211yescharacteristic
18C22×C4⋊Dic71C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C4⋊Dic71C2211yescharacteristic
21C22×C4⋊Dic71C2211yescharacteristic
22C22×C4⋊Dic71C2211yescharacteristic
23C22×Dic71⋊C4C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×(C2×D71)⋊C4C2211yescharacteristic
27C22×(C2×D71)⋊C4C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×C4×Dic71C2211yescharacteristic
34C22×C4×Dic71C2211yescharacteristic
35C22×C4×Dic71C2211yescharacteristic
36#17985941C2218yescomplemented
37#17985936C2218yes—
38#17985931C2218yescomplemented
39#17985931C2218yescomplemented
40#17985926C2218yes—
41#17985925C2218yes—
42#17985921C2218yes—
43#17985898C2218yescomplemented
44#17985891C2218yes—
45#17985888C2218yes—
46#17985888C2218yes—
47#17985886C2218yescomplemented
48#17985881C2218yescomplemented
49C4⋊C4×Dic71C2218yescomplemented
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C22×C4⋊C4×C71C2211yescharacteristic
60C22×C4⋊C4×C71C2211yescharacteristic
61#400×C71C2218yescomplemented
62C2×#95×C71C2211yescharacteristic
63C2×#95×C71C2211yescharacteristic
64C2×#95×C71C2211yescharacteristic
65C2×#95×C71C2211yescharacteristic
66C2×#95×C71C2211yescharacteristic
67C24×D71C2311yescharacteristic
68C23×Dic71C2311yescharacteristic
69C23×Dic71C2311yescharacteristic
70C23×Dic71C2311yescharacteristic
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2311yescharacteristic
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C2×C4⋊Dic71—24no—
76C2×C4⋊Dic71—42no—
77C2×C4⋊Dic71—42no—
78C2×C4⋊Dic71—42no—
79C2×C4⋊Dic71—42no—
80C2×C4⋊Dic71—42no—
81C2×C4⋊Dic71C2314yes—
82C2×C4⋊Dic71C2314yes—
83C2×C4⋊Dic71C2314yes—
84C2×C4⋊Dic71C2314yes—
85C2×C4⋊Dic71C2314yes—
86C2×C4⋊Dic71C2314yes—
87C2×Dic71⋊C4—24no—
88C2×Dic71⋊C4—24no—
89C2×Dic71⋊C4—42no—
90C2×Dic71⋊C4C2314yes—
91C2×Dic71⋊C4C2314yes—
92C2×Dic71⋊C4C2314yes—
93C2×(C2×D71)⋊C4—24no—
94C2×(C2×D71)⋊C4—24no—
95C2×(C2×D71)⋊C4—24no—
96C2×(C2×D71)⋊C4—42no—
97C2×(C2×D71)⋊C4—42no—
98C2×(C2×D71)⋊C4—42no—
99C2×(C2×D71)⋊C4—42no—
100C2×(C2×D71)⋊C4C2314yes—
101C2×(C2×D71)⋊C4C2314yes—
102C2×(C2×D71)⋊C4C2314yes—
103C2×(C2×D71)⋊C4C2314yes—
104C2×(C2×D71)⋊C4C2314yes—
105C2×(C2×D71)⋊C4C2314yes—
106C2×(C2×D71)⋊C4C2314yes—
107C2×C4×Dic71—24no—
108C2×C4×Dic71—42no—
109C2×C4×Dic71—42no—
110C2×C4×Dic71C2314yes—
111C2×C4×Dic71C2314yes—
112C2×C4×Dic71C2314yes—
113C71⋊#95C2314yes—
114C71⋊#95C2314yes—
115C71⋊#95C2314yes—
116C71⋊#95C2314yes—
117C71⋊#95C2314yes—
118C71⋊#95C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C23×C4×C71C2311yescharacteristic
123C23×C4×C71C2311yescharacteristic
124C23×C4×C71C2311yescharacteristic
125C23×C4×C71C2311yescharacteristic
126C23×C4×C71C2311yescharacteristic
127C23×C4×C71C2311yescharacteristic
128C23×C4×C71C2311yescharacteristic
129C2×C4⋊C4×C71—24no—
130C2×C4⋊C4×C71—24no—
131C2×C4⋊C4×C71C2314yes—
132C2×C4⋊C4×C71C2314yes—
133#95×C71C2314yes—
134#95×C71C2314yes—
135#95×C71C2314yes—
136#95×C71C2314yes—
137#95×C71C2314yes—
138C23×D71—22no—
139C23×D71—22no—
140C23×D71—22no—
141C23×D71—22no—
142C23×D71—22no—
143C23×D71—22no—
144C23×D71—22no—
145C23×D71C2412yes—
146C22×Dic71—22no—
147C22×Dic71—22no—
148C22×Dic71—22no—
149C22×Dic71—22no—
150C22×Dic71—22no—
151C22×Dic71—22no—
152C22×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71#4114yes—
167C22×Dic71C2412yes—
168C22×Dic71C2412yes—
169C22×Dic71C2412yes—
170C22×Dic71C2412yes—
171C22×Dic71C2412yes—
172C22×Dic71C2412yes—
173C22×Dic71C2412yes—
174C4⋊Dic71—28no—
175C4⋊Dic71—44no—
176C4⋊Dic71—44no—
177C4⋊Dic71—44no—
178C4⋊Dic71—44no—
179C4⋊Dic71—44no—
180Dic71⋊C4—28no—
181Dic71⋊C4—28no—
182Dic71⋊C4—44no—
183(C2×D71)⋊C4—28no—
184(C2×D71)⋊C4—28no—
185(C2×D71)⋊C4—28no—
186(C2×D71)⋊C4—44no—
187(C2×D71)⋊C4—44no—
188(C2×D71)⋊C4—44no—
189(C2×D71)⋊C4—44no—
190C4×Dic71—28no—
191C4×Dic71—44no—
192C4×Dic71—44no—
193C24×C71C2411yescharacteristic
194C22×C4×C71—22no—
195C22×C4×C71—22no—
196C22×C4×C71—22no—
197C22×C4×C71—22no—
198C22×C4×C71—22no—
199C22×C4×C71—22no—
200C22×C4×C71—22no—
201C22×C4×C71—22no—
202C22×C4×C71—22no—
203C22×C4×C71—22no—
204C22×C4×C71—22no—
205C22×C4×C71—22no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71#4114yes—
214C22×C4×C71#4114yes—
215C22×C4×C71C2412yes—
216C22×C4×C71C2412yes—
217C22×C4×C71C2412yes—
218C22×C4×C71C2412yes—
219C22×C4×C71C2412yes—
220C22×C4×C71C2412yes—
221C22×C4×C71C2412yes—
222C4⋊C4×C71—28no—
223C4⋊C4×C71—28no—
224C23×C71C2×#4112yes—
225C23×C71C2×#4112yes—
226C23×C71C2×#4112yes—
227C23×C71H(5,𝔽2)12yes—
228C23×C71H(5,𝔽2)12yes—
229C23×C712−1+412yes—
230C23×C712−1+412yes—
231C23×C71C2511yescharacteristic
232C22×D71—22no—
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—22no—
236C22×D71—22no—
237C22×D71—22no—
238C22×D71—22no—
239C22×D71—44no—
240C22×D71—44no—
241C22×D71—44no—
242C22×D71—44no—
243C22×D71—44no—
244C22×D71—44no—
245C22×D71—44no—
246C2×C4×C71—28no—
247C2×C4×C71—28no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—22no—
251C2×C4×C71—22no—
252C2×C4×C71—22no—
253C2×C4×C71—22no—
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
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—22no—
267C2×C4×C71—44no—
268C2×C4×C71—44no—
269C2×C4×C71—44no—
270C2×C4×C71—44no—
271C2×C4×C71—44no—
272C2×C4×C71C2×#4114yes—
273C2×C4×C71C2×#4114yes—
274C2×Dic71—28no—
275C2×Dic71—22no—
276C2×Dic71—22no—
277C2×Dic71—22no—
278C2×Dic71—22no—
279C2×Dic71—22no—
280C2×Dic71—22no—
281C2×Dic71—22no—
282C2×Dic71—22no—
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71—22no—
286C2×Dic71—22no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—44no—
296C2×Dic71—44no—
297C2×Dic71—44no—
298C2×Dic71—44no—
299C2×Dic71—44no—
300C2×Dic71—44no—
301C2×Dic71C2×#4114yes—
302C22×C71#52914yes—
303C22×C71#53914yes—
304C22×C71#53914yes—
305C22×C71#54014yes—
306C22×C71#54114yes—
307C22×C71#54214yes—
308C22×C71#54214yes—
309C22×C71C22×#4111yescharacteristic
310C22×C71C22×#4111yescharacteristic
311C22×C71C22×#4111yescharacteristic
312C22×C71C2×H(5,𝔽2)11yescharacteristic
313C22×C71C2×H(5,𝔽2)11yescharacteristic
314C22×C71C2×2−1+411yescharacteristic
315C22×C71C2×2−1+411yescharacteristic
316C2×D71—42no—
317C2×D71—42no—
318C2×D71—42no—
319C2×D71—42no—
320C2×D71—42no—
321C2×D71—42no—
322C2×D71—42no—
323C2×D71—88no—
324C4×C71—24no—
325C4×C71—24no—
326C4×C71—42no—
327C4×C71—42no—
328C4×C71—42no—
329C4×C71—42no—
330C4×C71—42no—
331Dic71—24no—
332Dic71—42no—
333Dic71—42no—
334Dic71—42no—
335Dic71—42no—
336Dic71—42no—
337Dic71—42no—
338C2×#2654—711nomaximal, Sylow
339C2×C71#265418yescomplemented
340C2×C71C2×#52911yescharacteristic
341C2×C71C2×#53911yescharacteristic
342C2×C71C2×#53911yescharacteristic
343C2×C71C2×#54011yescharacteristic
344C2×C71C2×#54111yescharacteristic
345C2×C71C2×#54211yescharacteristic
346C2×C71C2×#54211yescharacteristic
347D71—82no—
348#2654—7116no—
349C2×#400—711no—
350C2×#400D7111yescharacteristic, complemented
351C2×#399—711no—
352C2×#398—711no—
353C2×#398—711no—
354C2×#397—711no—
355C2×#397—711no—
356C2×#396—711no—
357C2×#389—711no—
358C2×#388—711no—
359C2×#388—711no—
360C2×#388—711no—
361C2×#387—711no—
362C2×#387—711no—
363C2×C4×C4⋊C4—711no—
364C71C2×#265411yescharacteristic, complemented, Sylow
365C22×C4⋊C4—711no—
366C22×C4⋊C4—711no—
367C22×C4⋊C4—711no—
368C22×C4⋊C4—711no—
369C22×C4⋊C4—711no—
370C22×C4⋊C4—711no—
371C22×C4⋊C4—711no—
372C22×C4⋊C4—711no—
373C22×C4⋊C4—711no—
374C22×C4⋊C4C2×D7111yescharacteristic
375C22×C4⋊C4C2×D7111yescharacteristic
376C22×C22⋊C4—711no—
377C22×C22⋊C4—711no—
378C22×C22⋊C4—711no—
379C22×C22⋊C4—711no—
380C22×C22⋊C4—711no—
381C22×C22⋊C4—711no—
382C22×C22⋊C4—711no—
383C22×C42—711no—
384C22×C42—711no—
385C22×C42—711no—
386#400—718no—
387#400C2×D7118yescomplemented
388#399—718no—
389#398—718no—
390#398—718no—
391#397—718no—
392#397—718no—
393#396—718no—
394#389—718no—
395#388—718no—
396#388—718no—
397#388—718no—
398#387—718no—
399#387—718no—
400C4×C4⋊C4—718no—
401C2×#95—711no—
402C2×#95—711no—
403C2×#95—711no—
404C2×#95—711no—
405C2×#95—711no—
406C2×#95—711no—
407C2×#95—711no—
408C2×#95—711no—
409C2×#95—711no—
410C2×#95C2×D7111yescharacteristic
411C2×#95C2×D7111yescharacteristic
412C2×#95C2×D7111yescharacteristic
413C2×#95C2×D7111yescharacteristic
414C2×#95C2×D7111yescharacteristic
415C25—711no—
416C23×C4—711no—
417C23×C4—711no—
418C23×C4—711no—
419C23×C4—711no—
420C23×C4—711no—
421C23×C4—711no—
422C23×C4—711no—
423C23×C4C22×D7111yescharacteristic
424C23×C4C22×D7111yescharacteristic
425C23×C4C22×D7111yescharacteristic
426C23×C4C22×D7111yescharacteristic
427C23×C4C22×D7111yescharacteristic
428C23×C4C22×D7111yescharacteristic
429C23×C4C22×D7111yescharacteristic
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—2842no—
433C2×C4⋊C4—2842no—
434C2×C4⋊C4—2842no—
435C2×C4⋊C4—2842no—
436C2×C4⋊C4—2842no—
437C2×C4⋊C4—2842no—
438C2×C4⋊C4—714no—
439C2×C4⋊C4—714no—
440C2×C4⋊C4—714no—
441C2×C4⋊C4—714no—
442C2×C4⋊C4—714no—
443C2×C4⋊C4—714no—
444C2×C4⋊C4—714no—
445C2×C4⋊C4—714no—
446C2×C4⋊C4—714no—
447C2×C4⋊C4—1424no—
448C2×C4⋊C4—1424no—
449C2×C4⋊C4—1424no—
450C2×C4⋊C4C22×D7114yes—
451C2×C4⋊C4C22×D7114yes—
452C2×C22⋊C4—2842no—
453C2×C22⋊C4—2842no—
454C2×C22⋊C4—2842no—
455C2×C22⋊C4—2842no—
456C2×C22⋊C4—714no—
457C2×C22⋊C4—714no—
458C2×C22⋊C4—714no—
459C2×C22⋊C4—714no—
460C2×C22⋊C4—714no—
461C2×C22⋊C4—714no—
462C2×C22⋊C4—714no—
463C2×C22⋊C4—1424no—
464C2×C22⋊C4—1424no—
465C2×C22⋊C4—1424no—
466C2×C42—2842no—
467C2×C42—2842no—
468C2×C42—714no—
469C2×C42—714no—
470C2×C42—714no—
471C2×C42—1424no—
472#95—714no—
473#95—714no—
474#95—714no—
475#95—714no—
476#95—714no—
477#95—714no—
478#95—714no—
479#95—714no—
480#95—714no—
481#95C22×D7114yes—
482#95C22×D7114yes—
483#95C22×D7114yes—
484#95C22×D7114yes—
485#95C22×D7114yes—
486C24—712no—
487C24—1422no—
488C24—1422no—
489C24—1422no—
490C24—1422no—
491C24—1422no—
492C24—1422no—
493C24—1422no—
494C24C23×D7111yescharacteristic
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—714no—
515C22×C4—712no—
516C22×C4—712no—
517C22×C4—712no—
518C22×C4—712no—
519C22×C4—712no—
520C22×C4—712no—
521C22×C4—712no—
522C22×C4—1422no—
523C22×C4—1422no—
524C22×C4—1422no—
525C22×C4—1422no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1422no—
529C22×C4—1422no—
530C22×C4—1422no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—1422no—
534C22×C4—1422no—
535C22×C4—1422no—
536C22×C4—1422no—
537C22×C4—1422no—
538C22×C4—1422no—
539C22×C4—1422no—
540C22×C4—1422no—
541C22×C4—1422no—
542C22×C4#1176586414yes—
543C22×C4#1176586614yes—
544C22×C4C23×D7112yes—
545C22×C4C23×D7112yes—
546C22×C4C23×D7112yes—
547C22×C4C23×D7112yes—
548C22×C4C23×D7112yes—
549C22×C4C23×D7112yes—
550C22×C4C23×D7112yes—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—2844no—
554C4⋊C4—2844no—
555C4⋊C4—2844no—
556C4⋊C4—2844no—
557C4⋊C4—2844no—
558C4⋊C4—2844no—
559C4⋊C4—1428no—
560C4⋊C4—1428no—
561C4⋊C4—1428no—
562C22⋊C4—2844no—
563C22⋊C4—2844no—
564C22⋊C4—2844no—
565C22⋊C4—2844no—
566C22⋊C4—1428no—
567C22⋊C4—1428no—
568C22⋊C4—1428no—
569C42—2844no—
570C42—2844no—
571C42—1428no—
572C23—2844no—
573C23—2844no—
574C23—2844no—
575C23—2844no—
576C23—2844no—
577C23—2844no—
578C23—2844no—
579C23—1422no—
580C23—1422no—
581C23—1422no—
582C23—1422no—
583C23—1422no—
584C23—1422no—
585C23—1422no—
586C23#41×D7112yes—
587C23C2×#1176586412yes—
588C23C2×#1176586612yes—
589C23#1455617412yes—
590C23#1455617412yes—
591C23#1455617512yes—
592C23#1455617512yes—
593C23C24×D7111yescharacteristic
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—28no—
599C2×C4—28no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—2844no—
621C2×C4—2844no—
622C2×C4—2844no—
623C2×C4—2844no—
624C2×C4—2844no—
625C2×C4—2844no—
626C2×C4—714no—
627C2×C4—1422no—
628C2×C4—1422no—
629C2×C4—1422no—
630C2×C4—1422no—
631C2×C4—1422no—
632C2×C4—1422no—
633C2×C4—1422no—
634C2×C4—1422no—
635C2×C4—1422no—
636C2×C4—1422no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4—1422no—
642C2×C4—1422no—
643C2×C4—1422no—
644C2×C4—1422no—
645C2×C4—1422no—
646C2×C4—1422no—
647C2×C4—1428no—
648C2×C4C2×#1176586414yes—
649C2×C4C2×#1176586614yes—
650C22—2842no—
651C22—2842no—
652C22—2842no—
653C22—2842no—
654C22—2842no—
655C22—2842no—
656C22—2842no—
657C22—5688no—
658C22#1798653514yes—
659C22#1798659014yes—
660C22#1798659314yes—
661C22#1798660514yes—
662C22#1798661214yes—
663C22#1798661514yes—
664C22#1798661814yes—
665C22C2×#41×D7111yescharacteristic
666C22C22×#1176586411yescharacteristic
667C22C22×#1176586611yescharacteristic
668C22C2×#1455617411yescharacteristic
669C22C2×#1455617411yescharacteristic
670C22C2×#1455617511yescharacteristic
671C22C2×#1455617511yescharacteristic
672C4—24no—
673C4—24no—
674C4—42no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—42no—
679C4—2842no—
680C4—2842no—
681C4—2842no—
682C4—2842no—
683C4—2842no—
684C4—2842no—
685C4—1424no—
686C2—5682no—
687C2#2259442118yesdirect product factor
688C2C2×#1798653511yescharacteristic
689C2C2×#1798659011yescharacteristic
690C2C2×#1798659311yescharacteristic
691C2C2×#1798660511yescharacteristic
692C2C2×#1798661211yescharacteristic
693C2C2×#1798661511yescharacteristic
694C2C2×#1798661811yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#400×C71C2
socleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×#400D71
hypocenterC71C2×#2654
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #22594421C2direct (N × H)
2. C2×#17985941C2semidirect
4. C2×#17985931C2semidirect
5. C2×#17985931C2semidirect
9. C2×#17985898C2semidirect
13. C2×#17985886C2semidirect
14. C2×#17985881C2semidirect
15. C2×C4⋊C4×Dic71C2semidirect
16. C2×#400×C71C2semidirect
36. #17985941C22semidirect
38. #17985931C22semidirect
39. #17985931C22semidirect
43. #17985898C22semidirect
47. #17985886C22semidirect
48. #17985881C22semidirect
49. C4⋊C4×Dic71C22semidirect
61. #400×C71C22semidirect
339. C2×C71#2654semidirect
350. C2×#400D71semidirect
364. C71C2×#2654semidirect
387. #400C2×D71semidirect
687. C2#22594421direct (N × H)

Maximal subgroups

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

subgroupindex
#225944212
C2×#179859412
C2×#179859362
C2×#179859312
C2×#179859262
C2×#179859252
C2×#179859212
C2×#179858982
C2×#179858912
C2×#179858882
C2×#179858862
C2×#179858812
C2×C4⋊C4×Dic712
C2×#400×C712
C2×#265471