Finite Group Databasebeta

← C2×#20253686 #27084632

Subgroups — C2×#20253686 #27084632

Order 12032.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689734C211yesmaximal, characteristic
2C2×#15689599C211yesmaximal, characteristic
3#20253686C2116yesmaximal, direct product factor
4C2×#15689463C211yesmaximal, characteristic
5C2×#15689462C211yesmaximal, characteristic
6C2×#15689431C211yesmaximal, characteristic, complemented
7C2×#15689430C211yesmaximal, characteristic, complemented
8C2×#15689330C211yesmaximal, characteristic, complemented
9C2×#15689277C211yesmaximal, characteristic
10C2×#15689277C211yesmaximal, characteristic
11C2×#15689230C211yesmaximal, characteristic, complemented
12C2×#15689227C211yesmaximal, characteristic, complemented
13C2×Q16×Dic47C211yesmaximal, characteristic, complemented
14C2×#15689215C211yesmaximal, characteristic, complemented
15C2×#15689183C211yesmaximal, characteristic
16C2×C47×#462C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20#15689734—24no—
21#15689734C2218yes—
22C2×#13094019—21no—
23C2×#13094019—21no—
24C2×#13094016C2211yescharacteristic
25C2×#13094014—21no—
26C2×#13094014—21no—
27C2×#13094000C2211yescharacteristic
28C2×#13094000C2211yescharacteristic
29#15689599—24no—
30#15689599C2218yes—
31C2×Q8×Dic47C2211yescharacteristic
32C2×Q8×Dic47C2211yescharacteristic
33C2×Q8×Dic47C2211yescharacteristic
34C2×C4×Dic94—21no—
35C2×C4×Dic94C2211yescharacteristic
36C2×#13093989—21no—
37C2×#13093989C2211yescharacteristic
38C2×#13093982—21no—
39C2×#13093982C2211yescharacteristic
40C2×#13093981—21no—
41C2×#13093981C2211yescharacteristic
42#15689463C2218yes—
43#15689462C2218yes—
44#15689431C2218yescomplemented
45#15689430C2218yescomplemented
46#15689330C2218yescomplemented
47#15689277C2218yes—
48#15689277C2218yes—
49#15689230C2218yescomplemented
50#15689227C2218yescomplemented
51Q16×Dic47C2218yescomplemented
52#15689215C2218yescomplemented
53#15689183C2218yes—
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C2×C4⋊Q8×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C47×#462C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C2×Q8×D47—24no—
80C2×Q8×D47—22no—
81C2×Q8×D47—24no—
82C2×Q8×D47C2314yes—
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C2×#10625337—24no—
86C2×#10625337—24no—
87C2×#10625337C2314yes—
88C2×#10625337C2314yes—
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91#13094019—28no—
92#13094019—28no—
93#13094016—22no—
94#13094016C2314yes—
95#13094014—28no—
96#13094014—28no—
97#13094000—22no—
98#13094000—22no—
99#13094000C2314yes—
100#13094000C2314yes—
101Q8×Dic47—22no—
102Q8×Dic47—22no—
103Q8×Dic47—22no—
104Q8×Dic47C2314yes—
105Q8×Dic47C2314yes—
106Q8×Dic47C2314yes—
107C4×Dic94—22no—
108C4×Dic94—28no—
109C4×Dic94C2314yes—
110#13093989—28no—
111#13093989—22no—
112#13093989C2314yes—
113#13093982—22no—
114#13093982—28no—
115#13093982C2314yes—
116#13093981—28no—
117#13093981D414yes—
118#13093981C2314yes—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
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⋊C4D411yescharacteristic
132C2×Dic47⋊C4D411yescharacteristic
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4D411yescharacteristic
137C2×(C2×D47)⋊C4D411yescharacteristic
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093958C2314yes—
146#13093957C2314yes—
147#13093956C2314yes—
148#13093955C2314yes—
149C4⋊(C47⋊C8)C2314yes—
150#13093949C2314yes—
151#13093949C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158#13093934C2314yes—
159C8×Dic47C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×Q8×C47C2311yescharacteristic
162C22×Q8×C47C2311yescharacteristic
163C2×Q16×C47—24no—
164C2×Q16×C47—24no—
165C2×Q16×C47C2314yes—
166C2×Q16×C47C2314yes—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C4⋊Q8×C47—22no—
170C4⋊Q8×C47C2314yes—
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C4⋊C8×C47C2314yes—
180#103×C47C2314yes—
181#103×C47C2314yes—
182C23×D47C2×D411yescharacteristic
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47—22no—
191C2×Q8×C47#4114yes—
192C2×Q8×C47C2412yes—
193C2×Q8×C47C2412yes—
194C2×Q8×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2411yescharacteristic
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209Q8×D47—216no—
210Q8×D47—28no—
211Q8×D47—28no—
212C2×C4×D47—28no—
213C2×C4×D47—24no—
214C2×C4×D47—22no—
215C2×C4×D47—22no—
216C2×C4×D47C2×D412yes—
217C2×C4×D47C2412yes—
218C2×Dic94—28no—
219C2×Dic94—21no—
220C2×Dic94—22no—
221C2×Dic94—24no—
222C2×Dic94#4114yes—
223C2×Dic94C2412yes—
224Q16×C47—28no—
225Q16×C47—28no—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47C2412yes—
229C2×C8×C47C2412yes—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47C2412yes—
235C42×C47—24no—
236C42×C47C2×D412yes—
237C42×C47C2412yes—
238#10625337—28no—
239#10625337—28no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4C2×D414yes—
244(C2×D47)⋊C4C2×D414yes—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47—24no—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253C4⋊Dic47C2412yes—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4C2×D414yes—
261Dic47⋊C4C2×D414yes—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47—24no—
268C4×Dic47C2×D412yes—
269C4×Dic47C2412yes—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8C2412yes—
273C2×C47⋊C8C2412yes—
274C23×C47C22×D411yescharacteristic
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47C22×D412yes—
279Q8×C47—24no—
280Q8×C47—22no—
281Q8×C47—22no—
282Q8×C47—22no—
283Q8×C47—22no—
284Q8×C47—22no—
285Q8×C47—42no—
286Q8×C47—42no—
287Q8×C47C2×#4114yes—
288C2×C4×C47—24no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D412yes—
300C2×C4×C47C22×D411yescharacteristic
301C2×C4×C47C2×#4112yes—
302C2×C4×C47C2×#4112yes—
303C2×C4×C47C2511yescharacteristic
304C2×Dic47—22no—
305C2×Dic47—24no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47C22×D412yes—
316C2×Dic47C22×D412yes—
317C2×Dic47C22×D412yes—
318C4×D47—216no—
319C4×D47—24no—
320C4×D47—22no—
321C4×D47—22no—
322Dic94—216no—
323Dic94—24no—
324Dic94—22no—
325Dic94C2×#4114yes—
326C8×C47—22no—
327C8×C47—22no—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C2×#3127—471nomaximal, Sylow
331C22×C47#52512yes—
332C22×C47#57812yes—
333C22×C47#57812yes—
334C22×C47C23×D411yescharacteristic
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—44no—
339C4×C47—24no—
340C4×C47—22no—
341C4×C47—22no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47#52512yes—
346C4×C47C22×#4111yescharacteristic
347C4×C47C22×#4111yescharacteristic
348Dic47—22no—
349Dic47—24no—
350Dic47—22no—
351Dic47—22no—
352Dic47—42no—
353Dic47—42no—
354Dic47—42no—
355C2×#541—471no—
356C2×#519—471no—
357#3127—4716no—
358C2×#485—471no—
359C2×#485—471no—
360C2×#479—471no—
361C2×#479—471no—
362C2×#462—471no—
363C2×#462D4711yescharacteristic, complemented
364C2×#451—471no—
365C2×#451—471no—
366C2×#441—471no—
367C2×#441—471no—
368C2×C4×Q16—471no—
369C2×C4×Q16—471no—
370C2×#433—471no—
371C2×C47#312714yescomplemented
372C2×C47C2×#52511yescharacteristic
373C2×C47C2×#57811yescharacteristic
374C2×C47C2×#57811yescharacteristic
375D47—42no—
376C23×Q8—471no—
377C22×Q16—471no—
378C22×Q16—471no—
379C22×Q16C2×D4711yescharacteristic
380C22×Q16C2×D4711yescharacteristic
381#541—478no—
382#541—944no—
383C2×C4⋊Q8C2×D4711yescharacteristic
384C2×#126—941no—
385C2×#126—941no—
386C2×#125—471no—
387C2×#125—941no—
388C2×#125—941no—
389C2×C22⋊Q8—471no—
390C2×C22⋊Q8—471no—
391#519—478no—
392#519—944no—
393C2×C4×Q8—471no—
394C2×C4×Q8—471no—
395C2×C4×Q8—471no—
396C2×C4×Q8—471no—
397C2×C4×Q8—471no—
398C2×C4×Q8—941no—
399C2×C4×Q8—941no—
400C2×C4×Q8C2×D4711yescharacteristic
401C2×#117—471no—
402C2×#117—471no—
403C2×#117—941no—
404C2×#117—941no—
405#485—478no—
406#485—478no—
407#479—478no—
408#479—478no—
409#462—478no—
410#462C2×D4718yescomplemented
411#451—478no—
412#451—478no—
413#441—478no—
414#441—478no—
415C4×Q16—478no—
416C4×Q16—478no—
417#433—478no—
418C2×#107—471no—
419C2×#107—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×C4⋊C8—471no—
423C2×C4⋊C8C2×D4711yescharacteristic
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103C2×D4711yescharacteristic
431C2×#103C2×D4711yescharacteristic
432C2×C22⋊C8—471no—
433C2×C22⋊C8—471no—
434C2×#97—471no—
435C2×C4×C8—471no—
436C47C2×#312711yescharacteristic, complemented, Sylow
437C22×Q8—474no—
438C22×Q8—471no—
439C22×Q8—941no—
440C22×Q8—942no—
441C22×Q8—944no—
442C22×Q8—944no—
443C22×Q8C22×D4711yescharacteristic
444C22×Q8C22×D4711yescharacteristic
445C22×Q8C22×D4711yescharacteristic
446C23×C4—471no—
447C23×C4—941no—
448C2×Q16—24no—
449C2×Q16—24no—
450C2×Q16—474no—
451C2×Q16—474no—
452C2×Q16—944no—
453C2×Q16—944no—
454C2×Q16C22×D4714yes—
455C2×Q16C22×D4714yes—
456C22×C8—471no—
457C22×C8—471no—
458C22×C8C22×D4711yescharacteristic
459C22×C8C22×D4711yescharacteristic
460C4⋊Q8—22no—
461C4⋊Q8C22×D4714yes—
462#126—948no—
463#126—948no—
464#125—474no—
465#125—948no—
466#125—948no—
467#125—942no—
468C22⋊Q8—474no—
469C22⋊Q8—474no—
470C22⋊Q8—942no—
471C22⋊Q8—942no—
472C4×Q8—22no—
473C4×Q8—474no—
474C4×Q8—474no—
475C4×Q8—474no—
476C4×Q8—474no—
477C4×Q8—474no—
478C4×Q8—948no—
479C4×Q8—942no—
480C4×Q8—942no—
481C4×Q8—942no—
482C4×Q8—942no—
483C4×Q8—948no—
484C4×Q8—942no—
485C4×Q8C22×D4714yes—
486#117—474no—
487#117—474no—
488#117—474no—
489#117—948no—
490#117—948no—
491#117—942no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
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⋊C4C22×D4711yescharacteristic
510C2×C22⋊C4—471no—
511C2×C22⋊C4—471no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C42—21no—
516C2×C42—471no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42—941no—
520C2×C42—941no—
521C2×C42—941no—
522C2×C42—941no—
523C2×C42C22×D4711yescharacteristic
524#107—474no—
525#107—474no—
526#106—474no—
527#106—474no—
528C4⋊C8—474no—
529C4⋊C8C22×D4714yes—
530#103—474no—
531#103—474no—
532#103—474no—
533#103—474no—
534#103—474no—
535#103—474no—
536#103C22×D4714yes—
537#103C22×D4714yes—
538C22⋊C8—474no—
539C22⋊C8—474no—
540#97—474no—
541C4×C8—474no—
542C24—471no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—474no—
552C2×Q8—472no—
553C2×Q8—944no—
554C2×Q8—948no—
555C2×Q8—948no—
556C2×Q8—9416no—
557C2×Q8—948no—
558C2×Q8—941no—
559C2×Q8—942no—
560C2×Q8#1062535214yes—
561C2×Q8C23×D4712yes—
562C2×Q8C23×D4712yes—
563C2×Q8C23×D4712yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—471no—
571C22×C4—472no—
572C22×C4—472no—
573C22×C4—944no—
574C22×C4—948no—
575C22×C4—941no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4D4×D4711yescharacteristic
582C22×C4D4×D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584Q16—28no—
585Q16—28no—
586Q16—948no—
587Q16—948no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—472no—
591C2×C8—472no—
592C2×C8—942no—
593C2×C8—942no—
594C2×C8C23×D4712yes—
595C2×C8C23×D4712yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—474no—
601C4⋊C4—474no—
602C4⋊C4—472no—
603C4⋊C4—472no—
604C4⋊C4—472no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—941no—
615C4⋊C4—941no—
616C4⋊C4—941no—
617C4⋊C4C23×D4712yes—
618C22⋊C4—474no—
619C22⋊C4—474no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C42—24no—
624C42—472no—
625C42—472no—
626C42—944no—
627C42—944no—
628C42—944no—
629C42—944no—
630C42—944no—
631C42—944no—
632C42D4×D4712yes—
633C42C23×D4712yes—
634C23—472no—
635C23—942no—
636C23—942no—
637C23—942no—
638C23C2×D4×D4711yescharacteristic
639Q8—24no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—42no—
647Q8—474no—
648Q8—9416no—
649Q8—944no—
650Q8—942no—
651Q8C2×#1062535214yes—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—472no—
663C2×C4—472no—
664C2×C4—472no—
665C2×C4—9416no—
666C2×C4—942no—
667C2×C4—944no—
668C2×C4—942no—
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—1882no—
678C2×C4—1882no—
679C2×C4—1882no—
680C2×C4C2×D4×D4712yes—
681C2×C4C2×D4×D4712yes—
682C2×C4C2×D4×D4711yescharacteristic
683C2×C4#41×D4712yes—
684C2×C4C2×#1062535212yes—
685C2×C4C24×D4711yescharacteristic
686C8—22no—
687C8—22no—
688C8—942no—
689C8—942no—
690C22—942no—
691C22—942no—
692C22—942no—
693C22—1884no—
694C22#1568963312yes—
695C22#1568993612yes—
696C22#1568993912yes—
697C22C22×D4×D4711yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—942no—
705C4—942no—
706C4—942no—
707C4—944no—
708C4—1882no—
709C4—1882no—
710C4—1882no—
711C4#1568963312yes—
712C4C2×#41×D4711yescharacteristic
713C4C22×#1062535211yescharacteristic
714C2—1882no—
715C2#2025368614yesdirect product factor
716C2C2×#1568963311yescharacteristic
717C2C2×#1568993611yescharacteristic
718C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#462C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#462D47
hypocenterC47C2×#3127
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #20253686C2direct (N × H)
6. C2×#15689431C2semidirect
7. C2×#15689430C2semidirect
8. C2×#15689330C2semidirect
11. C2×#15689230C2semidirect
12. C2×#15689227C2semidirect
13. C2×Q16×Dic47C2semidirect
14. C2×#15689215C2semidirect
16. C2×C47×#462C2semidirect
44. #15689431C22semidirect
45. #15689430C22semidirect
46. #15689330C22semidirect
49. #15689230C22semidirect
50. #15689227C22semidirect
51. Q16×Dic47C22semidirect
52. #15689215C22semidirect
73. C47×#462C22semidirect
363. C2×#462D47semidirect
371. C2×C47#3127semidirect
410. #462C2×D47semidirect
436. C47C2×#3127semidirect
715. C2#20253686direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897342
C2×#156895992
#202536862
C2×#156894632
C2×#156894622
C2×#156894312
C2×#156894302
C2×#156893302
C2×#156892772
C2×#156892302
C2×#156892272
C2×Q16×Dic472
C2×#156892152
C2×#156891832
C2×C47×#4622
C2×#312747