Finite Group Databasebeta

← C2×#20253750 #27085523

Subgroups — C2×#20253750 #27085523

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×#15689693C211yesmaximal, characteristic
3#20253750C2116yesmaximal, direct product factor
4C2×#15689492C211yesmaximal, characteristic, complemented
5C2×#15689490C211yesmaximal, characteristic, complemented
6C2×#15689481C211yesmaximal, characteristic, complemented
7C2×#15689477C211yesmaximal, characteristic, complemented
8C2×#15689476C211yesmaximal, characteristic, complemented
9C2×#15689475C211yesmaximal, characteristic, complemented
10C2×#15689472C211yesmaximal, characteristic, complemented
11C2×#15689121C211yesmaximal, characteristic
12C2×#15689130C211yesmaximal, characteristic, complemented
13C2×#15689116C211yesmaximal, characteristic
14C2×#103×D47C211yesmaximal, characteristic, complemented
15C2×#15689080C211yesmaximal, characteristic, complemented
16C2×C47×#489C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689750—24no—
22#15689750C2218yescomplemented
23#15689693—24no—
24#15689693C2218yes—
25C2×#13094024C2211yescharacteristic
26C2×#13094023C2211yescharacteristic
27C2×#13094022—21no—
28C2×#13094022C2211yescharacteristic
29C2×#13094016C2211yescharacteristic
30C2×#13094015C2211yescharacteristic
31C2×#13094014—21no—
32C2×#13094011C2211yescharacteristic
33C2×#13094006—21no—
34C2×#13094006—21no—
35C2×#13094002—21no—
36C2×#13094001—21no—
37C2×#13094001—21no—
38C2×#13094000—21no—
39C2×#13093982C2211yescharacteristic
40C2×#13093981C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689492C2218yescomplemented
43#15689490C2218yescomplemented
44#15689481C2218yescomplemented
45#15689477C2218yescomplemented
46#15689476C2218yescomplemented
47#15689475C2218yescomplemented
48#15689472C2218yescomplemented
49#15689130C2218yescomplemented
50#15689121C2218yes—
51#15689116C2218yes—
52C2×#13093949C2211yescharacteristic
53C2×#13093949C2211yescharacteristic
54C2×#13093949C2211yescharacteristic
55C2×#13093949C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093947C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62#103×D47C2218yescomplemented
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65#15689080C2218yescomplemented
66C2×#13093934C2211yescharacteristic
67C2×C4×C47⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×#124×C47C2211yescharacteristic
71C47×#489C2218yescomplemented
72C2×#103×C47C2211yescharacteristic
73C2×#103×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C2×#10625352—22no—
78C2×#10625352—24no—
79C2×#10625352—24no—
80C2×#10625352C2314yes—
81C22×Dic94—21no—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C22×Dic94C2311yescharacteristic
85C2×Q8×D47—22no—
86C2×Q8×D47—24no—
87C2×Q8×D47—24no—
88C2×Q8×D47C2314yes—
89C22×C22⋊D47—21no—
90C23×Dic47—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#13094024—22no—
101#13094024C2314yes—
102#13094023—22no—
103#13094023C2314yes—
104#13094022—28no—
105#13094022—22no—
106#13094022C2314yes—
107#13094016—22no—
108#13094016C2314yes—
109#13094015—22no—
110#13094015C2314yes—
111#13094014—28no—
112#13094011—22no—
113#13094011C2314yes—
114#13094006—28no—
115#13094006—28no—
116#13094002—28no—
117#13094001—28no—
118#13094001—28no—
119#13094000—28no—
120#13093982—22no—
121#13093982C2314yes—
122#13093981D414yes—
123#13093981C2314yes—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4D411yescharacteristic
137C2×Dic47⋊C4D411yescharacteristic
138C4⋊C4×D47—22no—
139C4⋊C4×D47C2314yes—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47—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#13093949C2314yes—
150#13093949C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093947C2314yes—
156#13093947C2314yes—
157#13093945C2314yes—
158#13093945C2314yes—
159#13093934C2314yes—
160C4×C47⋊C8C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47—21no—
163C22×Q8×C47C2311yescharacteristic
164C22×D4×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4⋊Q8×C47—22no—
168C4⋊Q8×C47C2314yes—
169#124×C47—22no—
170#124×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#103×C47C2314yes—
178#103×C47C2314yes—
179#102×C47C2314yes—
180#102×C47C2314yes—
181#97×C47C2314yes—
182C24×C47—21no—
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—24no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—82no—
189C2×Q8×C47C2412yes—
190C2×D4×C47—21no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47C2412yes—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C2×C22⋊D47—24no—
201C2×C22⋊D47—44no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—24no—
207C22×Dic47—44no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211Q8×D47—28no—
212Q8×D47—28no—
213Q8×D47—48no—
214#10625352—28no—
215#10625352—28no—
216#10625352—48no—
217C2×C4×D47—24no—
218C2×C4×D47—24no—
219C2×C4×D47—44no—
220C2×C4×D47—82no—
221C2×C4×D47C2×D412yes—
222C2×C4×D47#4114yes—
223C2×C4×D47#4114yes—
224C2×C4×D47C2412yes—
225C2×Dic94—22no—
226C2×Dic94—22no—
227C2×Dic94—22no—
228C2×Dic94—22no—
229C2×Dic94—21no—
230C2×Dic94—21no—
231C2×Dic94—24no—
232C2×Dic94—24no—
233C2×Dic94—44no—
234C2×Dic94—82no—
235C2×Dic94C2412yes—
236C2×Dic94C2412yes—
237C2×C8×C47—22no—
238C2×C8×C47—22no—
239C2×C8×C47C2412yes—
240C2×C8×C47C2412yes—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47C2412yes—
245C4⋊C4×C47C2412yes—
246C22⋊C4×C47—24no—
247C22⋊C4×C47—24no—
248C42×C47C2×D412yes—
249C42×C47C2412yes—
250C22⋊Dic47—24no—
251C22⋊Dic47—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4C2×D414yes—
254(C2×D47)⋊C4C2×D414yes—
255C4⋊Dic47—21no—
256C4⋊Dic47—24no—
257C4⋊Dic47—24no—
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×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—22no—
287C22×D47#12414yes—
288C22×D47C22×D412yes—
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—42no—
292Q8×C47—84no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—42no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47C22×D412yes—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C47C2×#4112yes—
308C2×C4×C47C2×#4112yes—
309C2×C4×C47C2511yescharacteristic
310C22⋊D47—48no—
311C2×Dic47—22no—
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—42no—
321C2×Dic47—48no—
322C2×Dic47#12414yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326C4×D47—48no—
327C4×D47—84no—
328C4×D47#12418yes—
329C4×D47C2×#4114yes—
330C4×D47C2×#4114yes—
331Dic94—22no—
332Dic94—22no—
333Dic94—22no—
334Dic94—22no—
335Dic94—42no—
336Dic94—42no—
337Dic94—48no—
338Dic94—84no—
339C8×C47—22no—
340C8×C47—22no—
341C47⋊C8—22no—
342C47⋊C8—22no—
343C2×#3137—471nomaximal, Sylow
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—84no—
348C22×C47C2×#12412yes—
349C22×C47#57712yes—
350C22×C47#57812yes—
351C22×C47C23×D411yescharacteristic
352C2×D47—28no—
353C2×D47—22no—
354C2×D47—22no—
355C2×D47C2×#12414yes—
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—42no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47C2×#12412yes—
362C4×C47C22×#4111yescharacteristic
363C4×C47C22×#4111yescharacteristic
364Dic47—22no—
365Dic47—22no—
366Dic47—42no—
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×#489D4711yescharacteristic, complemented
378C2×#488—471no—
379C2×#488—471no—
380C2×#487—471no—
381C2×#487—471no—
382C2×#417—471no—
383C2×#419—471no—
384C2×#416—471no—
385C22×#103—471no—
386C2×#405—471no—
387C2×C47—82no—
388C2×C47#313714yescomplemented
389C2×C47C22×#12411yescharacteristic
390C2×C47C2×#57711yescharacteristic
391C2×C47C2×#57811yescharacteristic
392D47—24no—
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—471no—
404C2×C4⋊Q8—941no—
405C2×C4⋊Q8C2×D4711yescharacteristic
406C2×#125—471no—
407C2×#125—471no—
408C2×#125—941no—
409C2×#124—471no—
410C2×#124C2×D4711yescharacteristic
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#489C2×D4718yescomplemented
424#488—478no—
425#488—478no—
426#487—478no—
427#487—478no—
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—471no—
440C2×#103—471no—
441C2×#103—478no—
442C2×#103C2×D4711yescharacteristic
443C2×#103C2×D4711yescharacteristic
444C2×#102—471no—
445C2×#102—471no—
446C2×#102C2×D4711yescharacteristic
447C2×#102C2×D4711yescharacteristic
448#405—478no—
449C2×#97—471no—
450C2×#97C2×D4711yescharacteristic
451C2×C4×C8—471no—
452C2×C4×C8—471no—
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—471no—
462C22×Q8—941no—
463C22×Q8—941no—
464C22×Q8—942no—
465C22×Q8—944no—
466C22×Q8—944no—
467C22×Q8C22×D4711yescharacteristic
468C22×D4—941no—
469C22×D4C22×D4711yescharacteristic
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—474no—
484C4⋊Q8—474no—
485C4⋊Q8—474no—
486C4⋊Q8—942no—
487C4⋊Q8—942no—
488C4⋊Q8—948no—
489C4⋊Q8—942no—
490C4⋊Q8C22×D4714yes—
491#125—474no—
492#125—474no—
493#125—942no—
494#125—948no—
495#125—942no—
496#124—22no—
497#124—474no—
498#124—942no—
499#124C22×D4714yes—
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—471no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—474no—
516C2×C4⋊C4—942no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
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—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—471no—
532C2×C22⋊C4—471no—
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#103—474no—
548#103—474no—
549#103C22×D4714yes—
550#103C22×D4714yes—
551#102—474no—
552#102—474no—
553#102C22×D4714yes—
554#102C22×D4714yes—
555#97—474no—
556#97C22×D4714yes—
557C4×C8—474no—
558C4×C8—474no—
559C24—21no—
560C24—471no—
561#41—948no—
562#41—948no—
563#41—1888no—
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—472no—
570C2×Q8—472no—
571C2×Q8—944no—
572C2×Q8—944no—
573C2×Q8—948no—
574C2×Q8—948no—
575C2×Q8—941no—
576C2×Q8—941no—
577C2×Q8—942no—
578C2×Q8—942no—
579C2×Q8—942no—
580C2×Q8—942no—
581C2×Q8—3762no—
582C2×Q8—1884no—
583C2×Q8—1888no—
584C2×Q8C23×D4712yes—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—944no—
589C2×D4—1884no—
590C2×D4C23×D4712yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—471no—
595C22×C4—472no—
596C22×C4—474no—
597C22×C4—474no—
598C22×C4—472no—
599C22×C4—471no—
600C22×C4—471no—
601C22×C4—944no—
602C22×C4—944no—
603C22×C4—944no—
604C22×C4—941no—
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—21no—
626C4⋊C4—21no—
627C4⋊C4—474no—
628C4⋊C4—474no—
629C4⋊C4—472no—
630C4⋊C4—472no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—944no—
635C4⋊C4—944no—
636C4⋊C4—944no—
637C4⋊C4—944no—
638C4⋊C4—944no—
639C4⋊C4—941no—
640C4⋊C4—941no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4C23×D4712yes—
644C4⋊C4C23×D4712yes—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—474no—
648C22⋊C4—474no—
649C22⋊C4—944no—
650C22⋊C4—944no—
651C22⋊C4—944no—
652C42—472no—
653C42—472no—
654C42—944no—
655C42D4×D4712yes—
656C42C23×D4712yes—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—474no—
662C23—472no—
663C23—942no—
664C23—942no—
665C23C2×D4×D4711yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—84no—
670Q8—942no—
671Q8—942no—
672Q8—942no—
673Q8—942no—
674Q8—3764no—
675Q8—1888no—
676Q8—1882no—
677Q8—1882no—
678D4—22no—
679D4—22no—
680D4—42no—
681D4—1888no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—474no—
691C2×C4—472no—
692C2×C4—478no—
693C2×C4—474no—
694C2×C4—474no—
695C2×C4—472no—
696C2×C4—472no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—3764no—
704C2×C4—1888no—
705C2×C4—1888no—
706C2×C4—1882no—
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—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—474no—
725C22—948no—
726C22—942no—
727C22—942no—
728C22#124×D4712yes—
729C22#1568993312yes—
730C22#1568993912yes—
731C22C22×D4×D4711yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—474no—
738C4—942no—
739C4—942no—
740C4—1882no—
741C4—1882no—
742C4—1882no—
743C4—1882no—
744C4#124×D4712yes—
745C4C2×#41×D4711yescharacteristic
746C4C2×#41×D4711yescharacteristic
747C2—82no—
748C2—944no—
749C2#2025375014yesdirect product factor
750C2C2×#124×D4711yescharacteristic
751C2C2×#1568993311yescharacteristic
752C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#489C2
socleC23×C47C22×D4
prime radicalC22×#10625352C22
hypercenterC2×#489D47
hypocenterC47C2×#3137
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#15689750C2semidirect
3. #20253750C2direct (N × H)
4. C2×#15689492C2semidirect
5. C2×#15689490C2semidirect
6. C2×#15689481C2semidirect
7. C2×#15689477C2semidirect
8. C2×#15689476C2semidirect
9. C2×#15689475C2semidirect
10. C2×#15689472C2semidirect
12. C2×#15689130C2semidirect
14. C2×#103×D47C2semidirect
15. C2×#15689080C2semidirect
16. C2×C47×#489C2semidirect
22. #15689750C22semidirect
42. #15689492C22semidirect
43. #15689490C22semidirect
44. #15689481C22semidirect
45. #15689477C22semidirect
46. #15689476C22semidirect
47. #15689475C22semidirect
48. #15689472C22semidirect
49. #15689130C22semidirect
62. #103×D47C22semidirect
65. #15689080C22semidirect
71. C47×#489C22semidirect
377. C2×#489D47semidirect
388. C2×C47#3137semidirect
423. #489C2×D47semidirect
453. C47C2×#3137semidirect
749. C2#20253750direct (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×#156896932
#202537502
C2×#156894922
C2×#156894902
C2×#156894812
C2×#156894772
C2×#156894762
C2×#156894752
C2×#156894722
C2×#156891212
C2×#156891302
C2×#156891162
C2×#103×D472
C2×#156890802
C2×C47×#4892
C2×#313747