Finite Group Databasebeta

← C2×#20253748 #27085521

Subgroups — C2×#20253748 #27085521

Order 12032.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689750C211yesmaximal, characteristic, complemented
2C2×#15689698C211yesmaximal, characteristic
3#20253748C2116yesmaximal, direct product factor
4C2×#15689491C211yesmaximal, characteristic, complemented
5C2×#15689490C211yesmaximal, characteristic, complemented
6C2×#15689485C211yesmaximal, characteristic, complemented
7C2×#15689484C211yesmaximal, characteristic, complemented
8C2×#15689479C211yesmaximal, characteristic, complemented
9C2×#15689478C211yesmaximal, characteristic, complemented
10C2×#15689472C211yesmaximal, characteristic, complemented
11C2×#15689123C211yesmaximal, characteristic
12C2×#15689130C211yesmaximal, characteristic, complemented
13C2×#15689118C211yesmaximal, characteristic
14C2×#103×D47C211yesmaximal, characteristic, complemented
15C2×#15689077C211yesmaximal, characteristic, complemented
16C2×C47×#487C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689750—24no—
22#15689750C2218yescomplemented
23#15689698—24no—
24#15689698C2218yes—
25C2×#13094023C2211yescharacteristic
26C2×#13094022—21no—
27C2×#13094022C2211yescharacteristic
28C2×#13094016C2211yescharacteristic
29C2×#13094015C2211yescharacteristic
30C2×#13094014—21no—
31C2×#13094013C2211yescharacteristic
32C2×#13094012C2211yescharacteristic
33C2×#13094009—21no—
34C2×#13094009—21no—
35C2×#13094002—21no—
36C2×#13094002—21no—
37C2×#13094002—21no—
38C2×#13094000—21no—
39C2×#13093982C2211yescharacteristic
40C2×#13093981C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689491C2218yescomplemented
43#15689490C2218yescomplemented
44#15689485C2218yescomplemented
45#15689484C2218yescomplemented
46#15689479C2218yescomplemented
47#15689478C2218yescomplemented
48#15689472C2218yescomplemented
49#15689130C2218yescomplemented
50#15689123C2218yes—
51#15689118C2218yes—
52C2×#13093949C2211yescharacteristic
53C2×#13093949C2211yescharacteristic
54C2×#13093948C2211yescharacteristic
55C2×#13093948C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093947C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60#103×D47C2218yescomplemented
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65#15689077C2218yescomplemented
66C2×#13093935C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×C4⋊Q8×C47C2211yescharacteristic
71C47×#487C2218yescomplemented
72C2×#103×C47C2211yescharacteristic
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—24no—
80C2×#10625354C2314yes—
81C22×Dic94—21no—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C2×Q8×D47—22no—
85C2×Q8×D47—24no—
86C2×Q8×D47—24no—
87C2×Q8×D47C2314yes—
88C22×D188—21no—
89C22×D188C2311yescharacteristic
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47C2311yescharacteristic
94C2×#10625324—24no—
95C2×#10625324C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98C2×C8×D47—24no—
99C2×C8×D47C2314yes—
100#13094023—22no—
101#13094023C2314yes—
102#13094022—28no—
103#13094022—22no—
104#13094022C2314yes—
105#13094016—22no—
106#13094016C2314yes—
107#13094015—22no—
108#13094015C2314yes—
109#13094014—28no—
110#13094013—22no—
111#13094013C2314yes—
112#13094012—22no—
113#13094012C2314yes—
114#13094009—28no—
115#13094009—28no—
116#13094002—28no—
117#13094002—28no—
118#13094002—28no—
119#13094000—28no—
120#13093982—22no—
121#13093982C2314yes—
122#13093981D414yes—
123#13093981C2314yes—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4D411yescharacteristic
135C2×Dic47⋊C4D411yescharacteristic
136C4⋊C4×D47—22no—
137C4⋊C4×D47C2314yes—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093949C2314yes—
148#13093949C2314yes—
149#13093948C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159#13093935C2314yes—
160#13093934C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47—21no—
163C22×Q8×C47C2311yescharacteristic
164C22×Q8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4⋊Q8×C47—22no—
168C4⋊Q8×C47—22no—
169C4⋊Q8×C47C2314yes—
170C4⋊Q8×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C42×C47C2311yescharacteristic
177#103×C47C2314yes—
178#103×C47C2314yes—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C4×C8×C47C2314yes—
182C23×D47—21no—
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—24no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47—22no—
191C2×Q8×C47—82no—
192C2×Q8×C47C2412yes—
193C2×Q8×C47C2412yes—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207#10625354—28no—
208#10625354—28no—
209#10625354—48no—
210Q8×D47—28no—
211Q8×D47—28no—
212Q8×D47—48no—
213C2×D188—22no—
214C2×D188—22no—
215C2×D188—24no—
216C2×D188—21no—
217C2×D188—44no—
218C2×D188C2412yes—
219C2×C4×D47—24no—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—44no—
223C2×C4×D47—44no—
224C2×C4×D47—82no—
225C2×C4×D47C2×D412yes—
226C2×C4×D47#4114yes—
227C2×C4×D47#4114yes—
228C2×C4×D47C2412yes—
229C2×Dic94—22no—
230C2×Dic94—22no—
231C2×Dic94—21no—
232C2×Dic94—24no—
233C2×Dic94—24no—
234C2×Dic94—44no—
235C2×Dic94—82no—
236C2×Dic94C2412yes—
237C2×C8×C47—22no—
238C2×C8×C47—22no—
239C2×C8×C47C2412yes—
240C2×C8×C47C2412yes—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—24no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47C2412yes—
247C4⋊C4×C47C2412yes—
248C42×C47C2×D412yes—
249C42×C47C2412yes—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4C2×D414yes—
256(C2×D47)⋊C4C2×D414yes—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47—24no—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269Dic47⋊C4C2×D414yes—
270Dic47⋊C4C2×D414yes—
271C4×Dic47—24no—
272C4×Dic47C2×D412yes—
273C4×Dic47C2412yes—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—22no—
276C2×C47⋊C8C2412yes—
277C2×C47⋊C8C2412yes—
278#10625324—28no—
279C8×D47—28no—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47—42no—
287C22×D47#12414yes—
288C22×D47C22×D412yes—
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—42no—
294Q8×C47—42no—
295Q8×C47—84no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47C2×#4112yes—
310C2×C4×C47C2×#4112yes—
311C2×C4×C47C2511yescharacteristic
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47#12414yes—
321C2×Dic47C22×D412yes—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324D188—22no—
325D188—22no—
326D188—48no—
327D188—42no—
328C4×D47—48no—
329C4×D47—48no—
330C4×D47—84no—
331C4×D47#12418yes—
332C4×D47C2×#4114yes—
333C4×D47C2×#4114yes—
334Dic94—22no—
335Dic94—22no—
336Dic94—42no—
337Dic94—48no—
338Dic94—84no—
339C8×C47—22no—
340C8×C47—22no—
341C47⋊C8—22no—
342C47⋊C8—22no—
343C2×#3137—471nomaximal, Sylow
344C22×C47C2×#12412yes—
345C22×C47#57712yes—
346C22×C47#57812yes—
347C22×C47C23×D411yescharacteristic
348C2×D47—28no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—42no—
352C2×D47—42no—
353C2×D47—42no—
354C2×D47—84no—
355C2×D47C2×#12414yes—
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—42no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47C2×#12412yes—
363C4×C47C22×#4111yescharacteristic
364C4×C47C22×#4111yescharacteristic
365Dic47—22no—
366Dic47—22no—
367Dic47—42no—
368Dic47—42no—
369Dic47—42no—
370Dic47C2×#12414yes—
371C2×#544—471no—
372C2×#536—471no—
373#3137—4716no—
374C2×#491—471no—
375C2×#491—471no—
376C2×#489—471no—
377C2×#489—471no—
378C2×#488—471no—
379C2×#488—471no—
380C2×#487—471no—
381C2×#487D4711yescharacteristic, complemented
382C2×#417—471no—
383C2×#419—471no—
384C2×#416—471no—
385C22×#103—471no—
386C2×#405—471no—
387C2×C47#313714yescomplemented
388C2×C47C22×#12411yescharacteristic
389C2×C47C2×#57711yescharacteristic
390C2×C47C2×#57811yescharacteristic
391D47—24no—
392D47—82no—
393C22×#41—471no—
394C23×Q8—471no—
395C22×M16—471no—
396C23×C8—471no—
397#544—478no—
398#544—944no—
399#536—478no—
400#536—944no—
401C2×C4⋊Q8—471no—
402C2×C4⋊Q8—471no—
403C2×C4⋊Q8—941no—
404C2×C4⋊Q8C2×D4711yescharacteristic
405C2×C4⋊Q8C2×D4711yescharacteristic
406C2×#125—471no—
407C2×#125—471no—
408C2×#125—941no—
409C2×#124—471no—
410C2×#124—471no—
411C2×#123—941no—
412C2×#123—941no—
413C2×C22⋊Q8—941no—
414C2×C22⋊Q8—941no—
415C2×C22⋊Q8—941no—
416C2×C22⋊Q8—941no—
417C2×#117—471no—
418C2×#117—471no—
419C22×C4⋊C4—471no—
420#491—478no—
421#491—478no—
422#489—478no—
423#489—478no—
424#488—478no—
425#488—478no—
426#487—478no—
427#487C2×D4718yescomplemented
428#419—478no—
429#417—478no—
430#416—478no—
431C2×#103—471no—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103—471no—
435C2×#103—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—478no—
440C2×#103C2×D4711yescharacteristic
441C2×#103C2×D4711yescharacteristic
442C2×#103C2×D4711yescharacteristic
443C2×#103C2×D4711yescharacteristic
444C2×#102—471no—
445C2×#102—471no—
446C2×#102—471no—
447C2×#102—471no—
448#405—478no—
449C2×#97—471no—
450C2×#97—471no—
451C2×C4×C8—471no—
452C2×C4×C8C2×D4711yescharacteristic
453C47C2×#313711yescharacteristic, complemented, Sylow
454C2×#41—474no—
455C2×#41—942no—
456C2×#41—944no—
457C2×#41—944no—
458C22×Q8—21no—
459C22×Q8—474no—
460C22×Q8—471no—
461C22×Q8—941no—
462C22×Q8—941no—
463C22×Q8—942no—
464C22×Q8—944no—
465C22×Q8—944no—
466C22×Q8C22×D4711yescharacteristic
467C22×Q8C22×D4711yescharacteristic
468C22×D4—471no—
469C22×D4—941no—
470C23×C4—471no—
471C23×C4—941no—
472C23×C4—941no—
473C23×C4—941no—
474C2×M16—474no—
475C2×M16—944no—
476C22×C8—471no—
477C22×C8—471no—
478C22×C8—474no—
479C22×C8—944no—
480C22×C8C22×D4711yescharacteristic
481C22×C8C22×D4711yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—22no—
484C4⋊Q8—474no—
485C4⋊Q8—474no—
486C4⋊Q8—942no—
487C4⋊Q8—942no—
488C4⋊Q8—948no—
489C4⋊Q8C22×D4714yes—
490C4⋊Q8C22×D4714yes—
491#125—474no—
492#125—474no—
493#125—942no—
494#125—948no—
495#125—942no—
496#124—474no—
497#124—474no—
498#124—942no—
499#124—942no—
500#123—948no—
501#123—948no—
502C22⋊Q8—948no—
503C22⋊Q8—948no—
504C22⋊Q8—948no—
505C22⋊Q8—948no—
506#117—474no—
507#117—474no—
508#117—474no—
509#117—942no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—474no—
518C2×C4⋊C4—942no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—471no—
530C2×C22⋊C4—471no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C42—471no—
537C2×C42—941no—
538C2×C42C22×D4711yescharacteristic
539#103—474no—
540#103—474no—
541#103—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#103—474no—
546#103—474no—
547#103C22×D4714yes—
548#103C22×D4714yes—
549#103C22×D4714yes—
550#103C22×D4714yes—
551#102—474no—
552#102—474no—
553#102—474no—
554#102—474no—
555#97—474no—
556#97—474no—
557C4×C8—474no—
558C4×C8C22×D4714yes—
559C24—471no—
560C24—941no—
561#41—948no—
562#41—948no—
563#41—1888no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—24no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—82no—
572C2×Q8—472no—
573C2×Q8—944no—
574C2×Q8—944no—
575C2×Q8—948no—
576C2×Q8—948no—
577C2×Q8—941no—
578C2×Q8—942no—
579C2×Q8—942no—
580C2×Q8—3762no—
581C2×Q8—1884no—
582C2×Q8—1888no—
583C2×Q8C23×D4712yes—
584C2×Q8C23×D4712yes—
585C2×D4—472no—
586C2×D4—944no—
587C2×D4—941no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4—1884no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—471no—
596C22×C4—472no—
597C22×C4—474no—
598C22×C4—474no—
599C22×C4—472no—
600C22×C4—471no—
601C22×C4—471no—
602C22×C4—944no—
603C22×C4—944no—
604C22×C4—944no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—3762no—
609C22×C4—1884no—
610C22×C4—1884no—
611C22×C4D4×D4711yescharacteristic
612C22×C4D4×D4711yescharacteristic
613C22×C4C23×D4711yescharacteristic
614M16—948no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—472no—
618C2×C8—472no—
619C2×C8—948no—
620C2×C8—942no—
621C2×C8—942no—
622C2×C8C23×D4712yes—
623C2×C8C23×D4712yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—474no—
630C4⋊C4—474no—
631C4⋊C4—472no—
632C4⋊C4—472no—
633C4⋊C4—944no—
634C4⋊C4—944no—
635C4⋊C4—944no—
636C4⋊C4—944no—
637C4⋊C4—944no—
638C4⋊C4—944no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—941no—
642C4⋊C4—941no—
643C4⋊C4C23×D4712yes—
644C4⋊C4C23×D4712yes—
645C22⋊C4—474no—
646C22⋊C4—474no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C22⋊C4—944no—
651C22⋊C4—944no—
652C42—472no—
653C42—472no—
654C42—944no—
655C42D4×D4712yes—
656C42C23×D4712yes—
657C23—474no—
658C23—472no—
659C23—942no—
660C23—942no—
661C23—942no—
662C23—1882no—
663C23—1882no—
664C23—1882no—
665C23C2×D4×D4711yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—42no—
672Q8—84no—
673Q8—942no—
674Q8—942no—
675Q8—3764no—
676Q8—1888no—
677Q8—1882no—
678D4—942no—
679D4—942no—
680D4—1888no—
681D4—1882no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—474no—
693C2×C4—472no—
694C2×C4—478no—
695C2×C4—474no—
696C2×C4—474no—
697C2×C4—472no—
698C2×C4—472no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—3764no—
705C2×C4—1888no—
706C2×C4—1888no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4—1882no—
710C2×C4C2×D4×D4712yes—
711C2×C4C2×D4×D4712yes—
712C2×C4C2×D4×D4711yescharacteristic
713C2×C4#41×D4712yes—
714C2×C4#41×D4712yes—
715C2×C4C24×D4711yescharacteristic
716C8—22no—
717C8—22no—
718C8—942no—
719C8—942no—
720C22—474no—
721C22—948no—
722C22—942no—
723C22—942no—
724C22—3764no—
725C22—1882no—
726C22—1882no—
727C22—1882no—
728C22#124×D4712yes—
729C22#1568992912yes—
730C22#1568993612yes—
731C22C22×D4×D4711yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—474no—
739C4—942no—
740C4—942no—
741C4—1882no—
742C4—1882no—
743C4—1882no—
744C4#124×D4712yes—
745C4C2×#41×D4711yescharacteristic
746C4C2×#41×D4711yescharacteristic
747C2—944no—
748C2—3762no—
749C2#2025374814yesdirect product factor
750C2C2×#124×D4711yescharacteristic
751C2C2×#1568992911yescharacteristic
752C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#487C2
socleC23×C47C22×D4
prime radicalC22×#10625354C22
hypercenterC2×#487D47
hypocenterC47C2×#3137
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
1. C2×#15689750C2semidirect
3. #20253748C2direct (N × H)
4. C2×#15689491C2semidirect
5. C2×#15689490C2semidirect
6. C2×#15689485C2semidirect
7. C2×#15689484C2semidirect
8. C2×#15689479C2semidirect
9. C2×#15689478C2semidirect
10. C2×#15689472C2semidirect
12. C2×#15689130C2semidirect
14. C2×#103×D47C2semidirect
15. C2×#15689077C2semidirect
16. C2×C47×#487C2semidirect
22. #15689750C22semidirect
42. #15689491C22semidirect
43. #15689490C22semidirect
44. #15689485C22semidirect
45. #15689484C22semidirect
46. #15689479C22semidirect
47. #15689478C22semidirect
48. #15689472C22semidirect
49. #15689130C22semidirect
60. #103×D47C22semidirect
65. #15689077C22semidirect
71. C47×#487C22semidirect
381. C2×#487D47semidirect
387. C2×C47#3137semidirect
427. #487C2×D47semidirect
453. C47C2×#3137semidirect
749. C2#20253748direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897502
C2×#156896982
#202537482
C2×#156894912
C2×#156894902
C2×#156894852
C2×#156894842
C2×#156894792
C2×#156894782
C2×#156894722
C2×#156891232
C2×#156891302
C2×#156891182
C2×#103×D472
C2×#156890772
C2×C47×#4872
C2×#313747