Finite Group Databasebeta

← C2×#20253636 #27084578

Subgroups — C2×#20253636 #27084578

Order 12032.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689733C211yesmaximal, characteristic, complemented
2C2×#15689597C211yesmaximal, characteristic
3#20253636C2116yesmaximal, direct product factor
4C2×#15689464C211yesmaximal, characteristic, complemented
5C2×#15689426C211yesmaximal, characteristic, complemented
6C2×#15689422C211yesmaximal, characteristic, complemented
7C2×#15689327C211yesmaximal, characteristic, complemented
8C2×#15689327C211yesmaximal, characteristic, complemented
9C2×#15689276C211yesmaximal, characteristic
10C2×#15689273C211yesmaximal, characteristic
11C2×#15689226C211yesmaximal, characteristic, complemented
12C2×#15689222C211yesmaximal, characteristic, complemented
13C2×#15689210C211yesmaximal, characteristic, complemented
14C2×#15689208C211yesmaximal, characteristic, complemented
15C2×#15689181C211yesmaximal, characteristic, complemented
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22#15689733—24no—
23#15689733C2218yescomplemented
24C2×#13094022C2211yescharacteristic, complemented
25C2×#13094017—21no—
26C2×#13094017—21no—
27C2×#13094015—21no—
28C2×#13094015C2211yescharacteristic, complemented
29C2×#13094014—21no—
30C2×#13094003C2211yescharacteristic
31#15689597—24no—
32#15689597C2218yes—
33C2×Q8×Dic47C2211yescharacteristic, complemented
34C2×#13093989C2211yescharacteristic, complemented
35C2×C4×D188—21no—
36C2×C4×D188—21no—
37C2×#13093986C2211yescharacteristic
38C2×#13093986C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×#13093983C2211yescharacteristic
42C2×C22⋊C4×D47—21no—
43C2×C22⋊C4×D47—21no—
44#15689464C2218yescomplemented
45#15689426C2218yescomplemented
46#15689422C2218yescomplemented
47#15689327C2218yescomplemented
48#15689327C2218yescomplemented
49#15689276C2218yes—
50#15689273C2218yes—
51#15689226C2218yescomplemented
52#15689222C2218yescomplemented
53#15689210C2218yescomplemented
54#15689208C2218yescomplemented
55#15689181C2218yescomplemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×Dic47⋊C8C2211yescharacteristic, complemented
59C2×Dic47⋊C8C2211yescharacteristic, complemented
60C2×#13093947C2211yescharacteristic, complemented
61C2×#13093947C2211yescharacteristic, complemented
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×#13093934C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#485C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188—21no—
80C22×D188—22no—
81C22×D188—24no—
82C22×D188—24no—
83C22×D188C2314yes—
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C2×#10625325—24no—
91C2×#10625325—24no—
92C2×#10625325C2314yes—
93C2×#10625325C2314yes—
94C2×#10625336—24no—
95C2×#10625336—24no—
96C2×#10625336C2314yes—
97C2×#10625336C2314yes—
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100#13094022—22no—
101#13094022C2314yescomplemented
102#13094017—28no—
103#13094017—28no—
104#13094015—28no—
105#13094015—22no—
106#13094015C2314yescomplemented
107#13094014—28no—
108#13094003—22no—
109#13094003C2314yes—
110Q8×Dic47—22no—
111Q8×Dic47C2314yescomplemented
112#13093989—22no—
113#13093989C2314yescomplemented
114C4×D188—28no—
115C4×D188—28no—
116#13093986—22no—
117#13093986—22no—
118#13093986—22no—
119#13093986—22no—
120#13093986C2314yes—
121#13093986C2314yes—
122#13093986C2314yes—
123#13093986C2314yes—
124#13093983D414yes—
125#13093983C2314yes—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47D411yescharacteristic
129C2×C4⋊Dic47D411yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47D411yescharacteristic
138C2×C22⋊Dic47D411yescharacteristic
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C22⋊C4×D47—28no—
144C22⋊C4×D47—28no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47C2311yescharacteristic
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yescomplemented
150#13093955C2314yescomplemented
151Dic47⋊C8C2314yescomplemented
152Dic47⋊C8C2314yescomplemented
153#13093947C2314yescomplemented
154#13093947C2314yescomplemented
155#13093946C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160#13093934C2314yescomplemented
161C8×Dic47C2314yescomplemented
162C22×Q8×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22⋊Q8×C47—22no—
167C22⋊Q8×C47C2314yes—
168#117×C47—22no—
169#117×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177#107×C47C2314yescomplemented
178#106×C47C2314yescomplemented
179#103×C47C2314yescomplemented
180#103×C47C2314yescomplemented
181C22⋊C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C23×D47—21no—
185C23×D47—28no—
186C23×D47—24no—
187C23×D47—82no—
188C23×D47—82no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47C2412yes—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2411yescharacteristic
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C2×D188—28no—
210C2×D188—216no—
211C2×D188—21no—
212C2×D188—21no—
213C2×D188—24no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—28no—
217C2×D188—28no—
218C2×D188#4114yes—
219C2×D188#4114yes—
220C2×D188C2412yes—
221C2×D188C2412yes—
222C2×C4×D47—24no—
223C2×C4×D47—24no—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—82no—
227C2×C4×D47—82no—
228C2×C4×D47—82no—
229C2×C4×D47—82no—
230C2×Dic94—22no—
231C2×Dic94—22no—
232C2×Dic94—21no—
233C2×Dic94C2412yes—
234C2×C8×C47—22no—
235C2×C8×C47—22no—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47C2412yes—
243C4⋊C4×C47C2412yes—
244C4⋊C4×C47C2412yes—
245C22⋊C4×C47—24no—
246C22⋊C4×C47—24no—
247C42×C47—24no—
248C22⋊Dic47—24no—
249C22⋊Dic47C2×D414yes—
250C22⋊Dic47C2×D414yes—
251#10625336—28no—
252#10625336—28no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257C4⋊Dic47—21no—
258C4⋊Dic47—24no—
259C4⋊Dic47—24no—
260C4⋊Dic47C2×D414yes—
261C4⋊Dic47C2×D414yes—
262C4⋊Dic47C2412yes—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47C2×D412yes—
271C4×Dic47C2×D412yes—
272C4×Dic47C2412yes—
273C4×Dic47C2412yes—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—22no—
276C2×C47⋊C8C2412yes—
277C2×C47⋊C8C2412yes—
278#10625325—28no—
279#10625325—28no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47C22×D412yes—
284C23×C47C22×D411yescharacteristic
285C22×D47—24no—
286C22×D47—24no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—216no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—84no—
295C22×D47—84no—
296C22×D47—816no—
297Q8×C47—22no—
298Q8×C47—22no—
299Q8×C47—42no—
300C2×C4×C47—22no—
301C2×C4×C47—24no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47C22×D412yes—
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C2×#4112yes—
315C2×C4×C47C2×#4112yes—
316C2×C4×C47C2511yescharacteristic
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47C22×D412yes—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329D188—216no—
330D188—24no—
331D188—24no—
332D188—22no—
333D188—22no—
334D188C2×#4114yes—
335D188C2×#4114yes—
336C4×D47—84no—
337C4×D47—84no—
338C4×D47—84no—
339C4×D47—84no—
340Dic94—22no—
341Dic94—22no—
342Dic94—42no—
343C8×C47—22no—
344C8×C47—22no—
345C47⋊C8—22no—
346C47⋊C8—22no—
347C2×#3123—471nomaximal, Sylow
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—44no—
352C22×C47#52512yes—
353C22×C47#57712yes—
354C22×C47#57712yes—
355C22×C47C23×D411yescharacteristic
356C2×D47—24no—
357C2×D47—24no—
358C2×D47—48no—
359C2×D47—48no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—42no—
363C2×D47—42no—
364C2×D47—816no—
365C4×C47—22no—
366C4×C47—42no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47—42no—
370C4×C47#52512yes—
371C4×C47C22×#4111yescharacteristic
372C4×C47C22×#4111yescharacteristic
373Dic47—22no—
374Dic47—22no—
375Dic47—22no—
376Dic47—22no—
377Dic47—42no—
378Dic47—42no—
379C2×#541—471no—
380C2×#518—471no—
381#3123—4716no—
382C2×#485—471no—
383C2×#485D4711yescharacteristic, complemented
384C2×#478—471no—
385C2×#478—471no—
386C2×#461—471no—
387C2×#461—471no—
388C2×#450—471no—
389C2×#450—471no—
390C2×#440—471no—
391C2×#440—471no—
392C2×C4×SD16—471no—
393C2×C4×SD16—471no—
394C2×#433—471no—
395C2×C47—42no—
396C2×C47#312314yescomplemented
397C2×C47C2×#52511yescharacteristic
398C2×C47C2×#57711yescharacteristic
399C2×C47C2×#57711yescharacteristic
400D47—44no—
401D47—44no—
402C23×D4—471no—
403C22×SD16—471no—
404C22×SD16—471no—
405C22×SD16—471no—
406C22×SD16—471no—
407#541—478no—
408#541—944no—
409C2×C4⋊Q8—471no—
410C2×#126—941no—
411C2×#126—941no—
412C2×#125—471no—
413C2×#125—941no—
414C2×#125—941no—
415C2×C22⋊Q8—471no—
416C2×C22⋊Q8C2×D4711yescharacteristic
417#518—478no—
418#518—944no—
419C2×C4×Q8—471no—
420C2×C4×Q8—471no—
421C2×C4×D4—471no—
422C2×C4×D4—471no—
423C2×C4×D4—471no—
424C2×C4×D4—471no—
425C2×C4×D4—941no—
426C2×C4×D4—941no—
427C2×#117—471no—
428C2×#117C2×D4711yescharacteristic
429C22×C22⋊C4—941no—
430C22×C22⋊C4—941no—
431#485—478no—
432#485C2×D4718yescomplemented
433#478—478no—
434#478—478no—
435#461—478no—
436#461—478no—
437#450—478no—
438#450—478no—
439#440—478no—
440#440—478no—
441C4×SD16—478no—
442C4×SD16—478no—
443#433—478no—
444C2×#107—471no—
445C2×#107C2×D4711yescharacteristic, complemented
446C2×#106—471no—
447C2×#106C2×D4711yescharacteristic, complemented
448C2×C4⋊C8—471no—
449C2×C4⋊C8—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103C2×D4711yescharacteristic, complemented
453C2×#103C2×D4711yescharacteristic, complemented
454C2×#102—471no—
455C2×#102—471no—
456C2×#102—471no—
457C2×#102—471no—
458C2×C22⋊C8—471no—
459C2×C22⋊C8C2×D4711yescharacteristic
460C2×#97—471no—
461C2×C4×C8—471no—
462C47C2×#312311yescharacteristic, complemented, Sylow
463C25—941no—
464C22×Q8—471no—
465C22×Q8C22×D4711yescharacteristic
466C22×D4—471no—
467C22×D4—471no—
468C22×D4—474no—
469C22×D4—944no—
470C22×D4—944no—
471C22×D4—941no—
472C22×D4—942no—
473C23×C4—941no—
474C23×C4—941no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4C22×D4711yescharacteristic
478C2×SD16—474no—
479C2×SD16—474no—
480C2×SD16—474no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16—944no—
484C2×SD16—944no—
485C2×SD16—944no—
486C22×C8—471no—
487C22×C8—471no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490C4⋊Q8—474no—
491C4⋊Q8—942no—
492#126—948no—
493#126—948no—
494#125—474no—
495#125—942no—
496#125—948no—
497#125—948no—
498C22⋊Q8—22no—
499C22⋊Q8—474no—
500C22⋊Q8—942no—
501C22⋊Q8C22×D4714yes—
502C4×Q8—474no—
503C4×Q8—474no—
504C4×Q8—942no—
505C4×Q8—942no—
506C4×D4—474no—
507C4×D4—474no—
508C4×D4—474no—
509C4×D4—474no—
510C4×D4—948no—
511C4×D4—948no—
512C4×D4—942no—
513C4×D4—942no—
514C4×D4—942no—
515C4×D4—942no—
516#117—22no—
517#117—474no—
518#117—474no—
519#117C22×D4714yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4C22×D4711yescharacteristic
532C2×C4⋊C4C22×D4711yescharacteristic
533C2×C4⋊C4C22×D4711yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—471no—
537C2×C22⋊C4—471no—
538C2×C22⋊C4—948no—
539C2×C22⋊C4—948no—
540C2×C22⋊C4—941no—
541C2×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C22⋊C4—941no—
544C2×C22⋊C4—941no—
545C2×C42—21no—
546C2×C42—471no—
547C2×C42—471no—
548C2×C42—941no—
549C2×C42—941no—
550#107—474no—
551#107C22×D4714yescomplemented
552#106—474no—
553#106C22×D4714yescomplemented
554C4⋊C8—474no—
555C4⋊C8—474no—
556#103—474no—
557#103—474no—
558#103C22×D4714yescomplemented
559#103C22×D4714yescomplemented
560#102—474no—
561#102—474no—
562#102—474no—
563#102—474no—
564C22⋊C8—474no—
565C22⋊C8C22×D4714yes—
566#97—474no—
567C4×C8—474no—
568C24—948no—
569C24—944no—
570C24—941no—
571C24—941no—
572C24—3762no—
573C24—3762no—
574C24D4×D4711yescharacteristic
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—472no—
579C2×Q8—941no—
580C2×Q8—942no—
581C2×Q8—942no—
582C2×Q8C23×D4712yes—
583C2×D4—474no—
584C2×D4—474no—
585C2×D4—472no—
586C2×D4—472no—
587C2×D4—948no—
588C2×D4—948no—
589C2×D4—948no—
590C2×D4—9416no—
591C2×D4—944no—
592C2×D4—941no—
593C2×D4—941no—
594C2×D4—942no—
595C2×D4—942no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—471no—
603C22×C4—471no—
604C22×C4—471no—
605C22×C4—471no—
606C22×C4—944no—
607C22×C4—944no—
608C22×C4—944no—
609C22×C4—944no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—3762no—
613C22×C4—3762no—
614C22×C4—3762no—
615C22×C4—3762no—
616C22×C4D4×D4712yes—
617C22×C4D4×D4711yescharacteristic
618C22×C4C23×D4712yes—
619C22×C4C23×D4711yescharacteristic
620SD16—948no—
621SD16—948no—
622SD16—948no—
623SD16—948no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—472no—
627C2×C8—472no—
628C2×C8—942no—
629C2×C8—942no—
630C2×C8C23×D4712yes—
631C2×C8C23×D4712yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—474no—
637C4⋊C4—474no—
638C4⋊C4—472no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4—944no—
644C4⋊C4—944no—
645C4⋊C4—944no—
646C4⋊C4—941no—
647C4⋊C4C23×D4712yes—
648C4⋊C4C23×D4712yes—
649C4⋊C4C23×D4712yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—474no—
653C22⋊C4—474no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C22⋊C4—944no—
657C22⋊C4—944no—
658C22⋊C4—944no—
659C42—24no—
660C42—472no—
661C42—472no—
662C42—472no—
663C42—472no—
664C42—944no—
665C42—944no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—9416no—
670C23—944no—
671C23—944no—
672C23—942no—
673C23—942no—
674C23—3764no—
675C23—3764no—
676C23—37616no—
677C23—1882no—
678C23—1882no—
679C23—1882no—
680C23—1882no—
681C23C2×D4×D4712yes—
682C23C2×D4×D4711yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—942no—
687Q8—942no—
688Q8—1882no—
689D4—474no—
690D4—474no—
691D4—9416no—
692D4—944no—
693D4—944no—
694D4—942no—
695D4—942no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—472no—
709C2×C4—472no—
710C2×C4—472no—
711C2×C4—472no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—3764no—
719C2×C4—3764no—
720C2×C4—3764no—
721C2×C4—3764no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4C2×D4×D4712yes—
725C2×C4C2×D4×D4711yescharacteristic
726C2×C4#41×D4712yes—
727C2×C4#41×D4712yes—
728C2×C4C24×D4711yescharacteristic
729C8—22no—
730C8—22no—
731C8—942no—
732C8—942no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—944no—
738C22—944no—
739C22—37616no—
740C22—1882no—
741C22—1882no—
742C22—1882no—
743C22—1882no—
744C22—1888no—
745C22—1888no—
746C22#1568963112yes—
747C22#1568993012yes—
748C22#1568993212yes—
749C22C22×D4×D4711yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—942no—
756C4—942no—
757C4—942no—
758C4—942no—
759C4—1882no—
760C4—1882no—
761C4#1568963112yes—
762C4C2×#41×D4711yescharacteristic
763C4C2×#41×D4711yescharacteristic
764C2—42no—
765C2—1884no—
766C2—1884no—
767C2#2025363614yesdirect product factor
768C2C2×#1568963111yescharacteristic
769C2C2×#1568993011yescharacteristic
770C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
prime radicalC23×D188C22
hypercenterC2×#485D47
hypocenterC47C2×#3123
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#15689733C2semidirect
3. #20253636C2direct (N × H)
4. C2×#15689464C2semidirect
5. C2×#15689426C2semidirect
6. C2×#15689422C2semidirect
7. C2×#15689327C2semidirect
8. C2×#15689327C2semidirect
11. C2×#15689226C2semidirect
12. C2×#15689222C2semidirect
13. C2×#15689210C2semidirect
14. C2×#15689208C2semidirect
15. C2×#15689181C2semidirect
16. C2×C47×#485C2semidirect
23. #15689733C22semidirect
24. C2×#13094022C22semidirect
28. C2×#13094015C22semidirect
33. C2×Q8×Dic47C22semidirect
34. C2×#13093989C22semidirect
44. #15689464C22semidirect
45. #15689426C22semidirect
46. #15689422C22semidirect
47. #15689327C22semidirect
48. #15689327C22semidirect
51. #15689226C22semidirect
52. #15689222C22semidirect
53. #15689210C22semidirect
54. #15689208C22semidirect
55. #15689181C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093955C22semidirect
58. C2×Dic47⋊C8C22semidirect
59. C2×Dic47⋊C8C22semidirect
60. C2×#13093947C22semidirect
61. C2×#13093947C22semidirect
67. C2×#13093934C22semidirect
68. C2×C8×Dic47C22semidirect
71. C47×#485C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#103×C47C22semidirect
75. C2×#103×C47C22semidirect
101. #13094022C23semidirect
106. #13094015C23semidirect
111. Q8×Dic47C23semidirect
113. #13093989C23semidirect
149. #13093957C23semidirect
150. #13093955C23semidirect
151. Dic47⋊C8C23semidirect
152. Dic47⋊C8C23semidirect
153. #13093947C23semidirect
154. #13093947C23semidirect
160. #13093934C23semidirect
161. C8×Dic47C23semidirect
177. #107×C47C23semidirect
178. #106×C47C23semidirect
179. #103×C47C23semidirect
180. #103×C47C23semidirect
383. C2×#485D47semidirect
396. C2×C47#3123semidirect
432. #485C2×D47semidirect
445. C2×#107C2×D47semidirect
447. C2×#106C2×D47semidirect
452. C2×#103C2×D47semidirect
453. C2×#103C2×D47semidirect
462. C47C2×#3123semidirect
551. #107C22×D47semidirect
553. #106C22×D47semidirect
558. #103C22×D47semidirect
559. #103C22×D47semidirect
767. C2#20253636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897332
C2×#156895972
#202536362
C2×#156894642
C2×#156894262
C2×#156894222
C2×#156893272
C2×#156892762
C2×#156892732
C2×#156892262
C2×#156892222
C2×#156892102
C2×#156892082
C2×#156891812
C2×C47×#4852
C2×#312347