Finite Group Databasebeta

← C2×#20255775 #27094734

Subgroups — C2×#20255775 #27094734

Order 12032.

1942 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689831C211yesmaximal, characteristic
2C2×#15689828C211yesmaximal, characteristic
3#20255775C2116yesmaximal, direct product factor
4C2×#15689527C211yesmaximal, characteristic, complemented
5C2×#15689460C211yesmaximal, characteristic, complemented
6C2×#15689459C211yesmaximal, characteristic, complemented
7C2×#15689457C211yesmaximal, characteristic, complemented
8C2×#15689417C211yesmaximal, characteristic, complemented
9C2×#15689416C211yesmaximal, characteristic, complemented
10C2×#15689363C211yesmaximal, characteristic, complemented
11C2×#15689362C211yesmaximal, characteristic, complemented
12C2×#15689215C211yesmaximal, characteristic, complemented
13C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic
14C22×#13093957C211yesmaximal, characteristic, complemented
15C2×#107×D47C211yesmaximal, characteristic, complemented
16C2×C47×#484C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689831—24no—
21#15689831C2218yes—
22#15689828—24no—
23#15689828C2218yes—
24C2×#13094023C2211yescharacteristic
25C2×#13094023C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094014—21no—
28C2×#13094004—21no—
29C2×#13094004C2211yescharacteristic
30C2×#13094003—21no—
31C2×#13094003C2211yescharacteristic
32C2×#13094002—21no—
33C2×#13094001—21no—
34C2×#13094000C2211yescharacteristic
35C2×Q8×Dic47C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×C4×C22⋊D47—21no—
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×(C22⋊D47)⋊C4—21no—
40C22×C4⋊Dic47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689527C2218yescomplemented
44#15689460C2218yescomplemented
45#15689459C2218yescomplemented
46#15689457C2218yescomplemented
47#15689417C2218yescomplemented
48#15689416C2218yescomplemented
49#15689363C2218yescomplemented
50#15689362C2218yescomplemented
51#15689215C2218yescomplemented
52(C22⋊D47)⋊C8C2218yes—
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093957C2211yescharacteristic
59C2×#13093957C2211yescharacteristic
60C2×#13093957C2218yescomplemented
61#107×D47C2218yescomplemented
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093947C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C22⋊Q8×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic
71C47×#484C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C22×C22⋊D47D411yescharacteristic
81C23×Dic47—21no—
82C22×C4×D47—21no—
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C2×#10625337—24no—
86C2×#10625337C2314yes—
87C22×C47⋊C8—24no—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2314yes—
90C22×C47⋊C8C2311yescharacteristic
91C2×C8×D47—24no—
92C2×C8×D47C2314yes—
93#13094023—22no—
94#13094023—22no—
95#13094023C2314yes—
96#13094023C2314yes—
97#13094014—28no—
98#13094014—28no—
99#13094004—22no—
100#13094004—28no—
101#13094004C2314yes—
102#13094003—22no—
103#13094003—28no—
104#13094003C2314yes—
105#13094002—28no—
106#13094001—28no—
107#13094000—22no—
108#13094000C2314yes—
109Q8×Dic47—22no—
110Q8×Dic47C2314yes—
111#13093989—22no—
112#13093989C2314yes—
113C4×C22⋊D47—28no—
114C4×C22⋊D47D414yes—
115C4×C22⋊D47C2314yes—
116(C22⋊D47)⋊C4—28no—
117C2×C4⋊Dic47—22no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2314yes—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4D411yescharacteristic
133C4⋊C4×D47—22no—
134C4⋊C4×D47—22no—
135C4⋊C4×D47C2314yes—
136C4⋊C4×D47C2314yes—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47D411yescharacteristic
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4D411yescharacteristic
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093958C2314yes—
146#13093958C2314yes—
147#13093957C2314yes—
148#13093957C2314yes—
149#13093957C2314yes—
150#13093957C2314yes—
151#13093957C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157(C2×D47)⋊C8C2314yes—
158C8×Dic47C2314yes—
159C22×Q8×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C23×C4×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C22⋊Q8×C47—22no—
165C22⋊Q8×C47C2314yes—
166C2×C4⋊C4×C47—22no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47C2314yes—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47—21no—
174#107×C47C2314yes—
175#107×C47C2314yes—
176#103×C47C2314yes—
177#103×C47C2314yes—
178C22⋊C8×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C23×D47C2×D411yescharacteristic
181C2×Q8×C47—21no—
182C2×Q8×C47—22no—
183C2×Q8×C47—22no—
184C2×Q8×C47C2412yes—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—24no—
192C22×C4×C47—82no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2411yescharacteristic
197C2×C22⋊D47Q1618yescomplemented
198C2×C22⋊D47C2×D414yes—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—24no—
204C22×Dic47—82no—
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C2×C4×D47—22no—
209C2×C4×D47—22no—
210C2×C4×D47—24no—
211C2×C4×D47—24no—
212C2×C4×D47—82no—
213C2×C4×D47—82no—
214C2×C4×D47C2×D412yes—
215C2×C4×D47C2412yes—
216C2×Dic94—22no—
217C2×Dic94—22no—
218C2×Dic94—21no—
219C2×Dic94—24no—
220C2×Dic94—24no—
221C2×Dic94—82no—
222C2×Dic94—82no—
223C2×Dic94C2412yes—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C2×C8×C47C2412yes—
227C2×C8×C47C2412yes—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47C2412yes—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C22⋊C4×C47—24no—
237C22⋊Dic47—24no—
238C22⋊Dic47C2×D414yes—
239#10625337—28no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4C2×D414yes—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—24no—
247C4⋊Dic47—24no—
248C4⋊Dic47—24no—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4C2×D414yes—
260C4×Dic47—24no—
261C4×Dic47—24no—
262C4×Dic47C2×D412yes—
263C4×Dic47C2412yes—
264C2×C47⋊C8—22no—
265C2×C47⋊C8—28no—
266C2×C47⋊C8#4114yes—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269C8×D47—28no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47C2×Q1614yes—
273C23×C47C22×D412yes—
274C23×C47C22×D411yescharacteristic
275C22×D47—22no—
276C22×D47—22no—
277C22×D47C2×Q1614yes—
278C22×D47C22×D412yes—
279Q8×C47—22no—
280Q8×C47—22no—
281Q8×C47—42no—
282C2×C4×C47—22no—
283C2×C4×C47—24no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—84no—
295C2×C4×C47C22×D412yes—
296C2×C4×C47C22×D411yescharacteristic
297C2×C4×C47C2×#4112yes—
298C2×C4×C472−1+412yes—
299C2×C4×C47C2511yescharacteristic
300C22⋊D47C2×Q16116yescomplemented
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—84no—
312C2×Dic47C2×Q1614yes—
313C2×Dic47C22×D412yes—
314C2×Dic47C22×D412yes—
315C2×Dic47C22×D412yes—
316C4×D47—24no—
317C4×D47—22no—
318C4×D47—22no—
319C4×D47—84no—
320C4×D47—84no—
321Dic94—22no—
322Dic94—22no—
323Dic94—42no—
324Dic94—84no—
325Dic94—84no—
326C8×C47—22no—
327C8×C47—22no—
328C47⋊C8—22no—
329C47⋊C8C2×#4114yes—
330C2×#3338—471nomaximal, Sylow
331C22×C47—28no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47#54712yes—
335C22×C47C22×Q1614yes—
336C22×C47C22×Q1612yes—
337C22×C47#57612yes—
338C22×C47C23×D411yescharacteristic
339C2×D47—28no—
340C2×D47—22no—
341C2×D47—22no—
342C2×D47C22×Q1614yes—
343C4×C47—22no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47—42no—
347C4×C47—42no—
348C4×C47#54712yes—
349C4×C47C22×#4111yescharacteristic
350C4×C47C2×2−1+411yescharacteristic
351Dic47—22no—
352Dic47—22no—
353Dic47—42no—
354Dic47—42no—
355Dic47—42no—
356Dic47—42no—
357Dic47C22×Q1614yes—
358C2×#554—471no—
359C2×#554—471no—
360#3338—4716no—
361C2×#500—471no—
362C2×#484—471no—
363C2×#484—471no—
364C2×#484—471no—
365C2×#484D4711yescharacteristic, complemented
366C2×#477—471no—
367C2×#477—471no—
368C2×#467—471no—
369C2×#467—471no—
370C2×C4×Q16—471no—
371C2×C8×D4—471no—
372C22×#107—471no—
373C22×#107—471no—
374C2×C47—24no—
375C2×C47#333814yescomplemented
376C2×C47C2×#54711yescharacteristic
377C2×C47C23×Q1611yescharacteristic
378C2×C47C2×#57611yescharacteristic
379D47—24no—
380C22×Q16—471no—
381C23×C8—471no—
382C23×C8—471no—
383#554—478no—
384#554—478no—
385#554—944no—
386#554—944no—
387C2×C4⋊Q8—471no—
388C2×C4⋊Q8—471no—
389C2×#125—941no—
390C2×#125—941no—
391C2×C22⋊Q8—471no—
392C2×C22⋊Q8—471no—
393C2×C22⋊Q8—471no—
394C2×C22⋊Q8—941no—
395C2×C22⋊Q8—941no—
396C2×C22⋊Q8—941no—
397C2×C22⋊Q8—941no—
398C2×C22⋊Q8C2×D4711yescharacteristic
399C2×C4×Q8—471no—
400C2×C4×Q8—471no—
401C2×C4×D4—471no—
402C2×C4×D4—941no—
403C2×C4×D4—941no—
404C22×C4⋊C4—471no—
405C22×C4⋊C4—471no—
406C22×C4⋊C4—471no—
407C22×C4⋊C4C2×D4711yescharacteristic
408#500—478no—
409#484—478no—
410#484—478no—
411#484—478no—
412#484C2×D4718yescomplemented
413#477—478no—
414#477—478no—
415#467—478no—
416#467—478no—
417C4×Q16—478no—
418C8×D4—478no—
419C2×#107—471no—
420C2×#107—471no—
421C2×#107—471no—
422C2×#107—471no—
423C2×#107—478no—
424C2×#107—471no—
425C2×#107—471no—
426C2×#107—471no—
427C2×#107—478no—
428C2×#107C2×D4711yescharacteristic
429C2×#107C2×D4711yescharacteristic
430C2×C4⋊C8—471no—
431C2×#103—471no—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103—471no—
435C2×#103C2×D4711yescharacteristic
436C2×#103C2×D4711yescharacteristic
437C2×C22⋊C8—471no—
438C2×C22⋊C8C2×D4711yescharacteristic
439C2×C4×C8—471no—
440C47C2×#333811yescharacteristic, complemented, Sylow
441C22×Q8—471no—
442C22×Q8—941no—
443C22×Q8—941no—
444C22×Q8C22×D4711yescharacteristic
445C22×D4—471no—
446C23×C4—21no—
447C23×C4—471no—
448C23×C4—941no—
449C23×C4—941no—
450C23×C4—941no—
451C23×C4C22×D4711yescharacteristic
452C2×Q16—474no—
453C2×Q16—944no—
454C22×C8—471no—
455C22×C8—471no—
456C22×C8—474no—
457C22×C8—474no—
458C22×C8—944no—
459C22×C8—944no—
460C22×C8C22×D4711yescharacteristic
461C22×C8C22×D4711yescharacteristic
462C4⋊Q8—474no—
463C4⋊Q8—474no—
464C4⋊Q8—942no—
465C4⋊Q8—942no—
466#125—948no—
467#125—948no—
468C22⋊Q8—22no—
469C22⋊Q8—474no—
470C22⋊Q8—474no—
471C22⋊Q8—474no—
472C22⋊Q8—948no—
473C22⋊Q8—948no—
474C22⋊Q8—948no—
475C22⋊Q8—948no—
476C22⋊Q8—942no—
477C22⋊Q8—942no—
478C22⋊Q8—942no—
479C22⋊Q8C22×D4714yes—
480C4×Q8—474no—
481C4×Q8—474no—
482C4×Q8—942no—
483C4×Q8—942no—
484C4×D4—474no—
485C4×D4—474no—
486C4×D4—948no—
487C4×D4—948no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—474no—
496C2×C4⋊C4—474no—
497C2×C4⋊C4—474no—
498C2×C4⋊C4—942no—
499C2×C4⋊C4—942no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4C22×D4711yescharacteristic
512C2×C4⋊C4C22×D4711yescharacteristic
513C2×C4⋊C4C22×D4711yescharacteristic
514C2×C4⋊C4C22×D4714yes—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—471no—
517C2×C22⋊C4—471no—
518C2×C22⋊C4—941no—
519C2×C22⋊C4—941no—
520C2×C22⋊C4—941no—
521C2×C42—471no—
522C2×C42—941no—
523C2×C42—941no—
524#107—474no—
525#107—474no—
526#107—474no—
527#107—474no—
528#107—474no—
529#107—474no—
530#107—474no—
531#107C22×D4714yes—
532#107C22×D4714yes—
533C4⋊C8—474no—
534#103—474no—
535#103—474no—
536#103—474no—
537#103—474no—
538#103C22×D4714yes—
539#103C22×D4714yes—
540C22⋊C8—474no—
541C22⋊C8C22×D4714yes—
542C4×C8—474no—
543C24—471no—
544C24D4×D4711yescharacteristic
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—472no—
549C2×Q8—944no—
550C2×Q8—944no—
551C2×Q8—941no—
552C2×Q8—942no—
553C2×Q8—942no—
554C2×Q8—3762no—
555C2×Q8—3762no—
556C2×Q8C23×D4712yes—
557C2×D4—478no—
558C2×D4—474no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—471no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—472no—
571C22×C4—472no—
572C22×C4—944no—
573C22×C4—944no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—944no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—3762no—
582C22×C4—3762no—
583C22×C4—3762no—
584C22×C4D4×D4712yes—
585C22×C4D4×D4711yescharacteristic
586C22×C4C23×D4712yes—
587C22×C4C23×D4711yescharacteristic
588Q16—948no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—474no—
592C2×C8—472no—
593C2×C8—472no—
594C2×C8—948no—
595C2×C8—948no—
596C2×C8—942no—
597C2×C8C23×D4712yes—
598C2×C8C23×D4712yes—
599C4⋊C4—21no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—474no—
605C4⋊C4—472no—
606C4⋊C4—472no—
607C4⋊C4—472no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—941no—
618C4⋊C4—944no—
619C4⋊C4—941no—
620C4⋊C4—941no—
621C4⋊C4C23×D4712yes—
622C4⋊C4C23×D4712yes—
623C4⋊C4C23×D4712yes—
624C22⋊C4—24no—
625C22⋊C4—474no—
626C22⋊C4—474no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C42—472no—
631C42—472no—
632C42—944no—
633C42—944no—
634C23—22no—
635C23—22no—
636C23—474no—
637C23—472no—
638C23—942no—
639C23—942no—
640C23Q16×D4714yes—
641C23C2×D4×D4712yes—
642C23C2×D4×D4711yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—942no—
647Q8—942no—
648Q8—3764no—
649Q8—3764no—
650Q8—1882no—
651D4—4716no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—474no—
666C2×C4—472no—
667C2×C4—472no—
668C2×C4—472no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—944no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—3764no—
679C2×C4—3764no—
680C2×C4—3764no—
681C2×C4—1882no—
682C2×C4—1882no—
683C2×C4—1882no—
684C2×C4—1882no—
685C2×C4C2×D4×D4712yes—
686C2×C4C2×D4×D4711yescharacteristic
687C2×C4#41×D4712yes—
688C2×C4#1309407112yes—
689C2×C4C24×D4711yescharacteristic
690C8—22no—
691C8—22no—
692C8—474no—
693C8—942no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—474no—
698C22—948no—
699C22—942no—
700C22—942no—
701C22#1568977112yes—
702C22C2×Q16×D4714yes—
703C22C2×Q16×D4712yes—
704C22#1568992712yes—
705C22C22×D4×D4711yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—474no—
712C4—942no—
713C4—942no—
714C4—1882no—
715C4—1882no—
716C4—1882no—
717C4—1882no—
718C4#1568977112yes—
719C4C2×#41×D4711yescharacteristic
720C4C2×#1309407111yescharacteristic
721C2—24no—
722C2—944no—
723C2#2025577514yesdirect product factor
724C2C2×#1568977111yescharacteristic
725C2C22×Q16×D4711yescharacteristic
726C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#484C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
hypercenterC2×#484D47
hypocenterC47C2×#3338
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #20255775C2direct (N × H)
4. C2×#15689527C2semidirect
5. C2×#15689460C2semidirect
6. C2×#15689459C2semidirect
7. C2×#15689457C2semidirect
8. C2×#15689417C2semidirect
9. C2×#15689416C2semidirect
10. C2×#15689363C2semidirect
11. C2×#15689362C2semidirect
12. C2×#15689215C2semidirect
14. C22×#13093957C2semidirect
15. C2×#107×D47C2semidirect
16. C2×C47×#484C2semidirect
43. #15689527C22semidirect
44. #15689460C22semidirect
45. #15689459C22semidirect
46. #15689457C22semidirect
47. #15689417C22semidirect
48. #15689416C22semidirect
49. #15689363C22semidirect
50. #15689362C22semidirect
51. #15689215C22semidirect
60. C2×#13093957C22semidirect
61. #107×D47C22semidirect
71. C47×#484C22semidirect
197. C2×C22⋊D47Q16semidirect
300. C22⋊D47C2×Q16semidirect
365. C2×#484D47semidirect
375. C2×C47#3338semidirect
412. #484C2×D47semidirect
440. C47C2×#3338semidirect
723. C2#20255775direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898312
C2×#156898282
#202557752
C2×#156895272
C2×#156894602
C2×#156894592
C2×#156894572
C2×#156894172
C2×#156894162
C2×#156893632
C2×#156893622
C2×#156892152
C2×(C22⋊D47)⋊C82
C22×#130939572
C2×#107×D472
C2×C47×#4842
C2×#333847