Finite Group Databasebeta

← C2×#20256442 #27097271

Subgroups — C2×#20256442 #27097271

Order 12032.

1970 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689856C211yesmaximal, characteristic
2C2×#15689851C211yesmaximal, characteristic, complemented
3#20256442C2116yesmaximal, direct product factor
4C2×#15689517C211yesmaximal, characteristic, complemented
5C2×#15689514C211yesmaximal, characteristic, complemented
6C2×#15689494C211yesmaximal, characteristic
7C2×#15689345C211yesmaximal, characteristic, complemented
8C2×#15689344C211yesmaximal, characteristic, complemented
9C2×#15689332C211yesmaximal, characteristic, complemented
10C2×#15689322C211yesmaximal, characteristic
11C2×#15689328C211yesmaximal, characteristic, complemented
12C2×#15689327C211yesmaximal, characteristic, complemented
13C2×#15689251C211yesmaximal, characteristic, complemented
14C2×#15689222C211yesmaximal, characteristic, complemented
15C2×#15689217C211yesmaximal, characteristic, complemented
16C2×C47×#440C211yesmaximal, characteristic, complemented
17C22×Dic188C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625325C2211yescharacteristic
22C22×#10625335C2211yescharacteristic
23C22×#10625335C2211yescharacteristic
24C22×#10625336C2211yescharacteristic
25#15689856—24no—
26#15689856C2218yes—
27#15689851—24no—
28#15689851C2218yescomplemented
29C2×#13094024C2211yescharacteristic
30C2×#13094022C2211yescharacteristic
31C2×#13094022C2211yescharacteristic
32C2×#13094020C2211yescharacteristic
33C2×#13094016—21no—
34C2×#13094014—21no—
35C2×#13094014—21no—
36C2×#13094012C2211yescharacteristic
37C2×#13094011C2211yescharacteristic
38C2×#13094010—21no—
39C2×#13094007—21no—
40C2×#13094006—21no—
41C2×C4×Dic94—21no—
42C2×C4×Dic94C2211yescharacteristic
43C2×#13093989C2211yescharacteristic
44C2×#13093989C2211yescharacteristic
45C2×#13093989C2211yescharacteristic
46C2×#13093986C2211yescharacteristic
47C2×C4×C22⋊D47—21no—
48#15689517C2218yescomplemented
49#15689514C2218yescomplemented
50#15689494C2218yes—
51#15689345C2218yescomplemented
52#15689344C2218yescomplemented
53#15689332C2218yescomplemented
54#15689328C2218yescomplemented
55#15689327C2218yescomplemented
56#15689322C2218yes—
57#15689251C2218yescomplemented
58#15689222C2218yescomplemented
59#15689217C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#440C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94D411yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×Dic94C2311yescharacteristic
81C22×D188C2311yescharacteristic
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C22×C4×D47—21no—
85C2×Dic188—24no—
86C2×Dic188—42no—
87C2×Dic188C2314yes—
88C2×Dic188C2314yes—
89C2×#10625337—42no—
90C2×#10625337C2314yes—
91C2×#10625325—24no—
92C2×#10625325—42no—
93C2×#10625325C2314yes—
94C2×#10625325C2314yes—
95C2×#10625335—42no—
96C2×#10625335—42no—
97C2×#10625335C2314yes—
98C2×#10625335C2314yes—
99C2×#10625336—42no—
100C2×#10625336C2314yes—
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103#13094024—22no—
104#13094024C2314yes—
105#13094022—22no—
106#13094022—22no—
107#13094022C2314yes—
108#13094022C2314yes—
109#13094020—22no—
110#13094020C2314yes—
111#13094016—28no—
112#13094014—28no—
113#13094014—28no—
114#13094012—22no—
115#13094012C2314yes—
116#13094011—22no—
117#13094011C2314yes—
118#13094010—28no—
119#13094007—28no—
120#13094006—28no—
121C4×Dic94—28no—
122C4×Dic94D414yes—
123C4×Dic94C2314yes—
124#13093989—22no—
125#13093989—22no—
126#13093989—22no—
127#13093989C2314yes—
128#13093989C2314yes—
129#13093989C2314yes—
130#13093986—22no—
131#13093986C2314yes—
132C4×C22⋊D47—28no—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47—21no—
135C2×C4⋊Dic47D411yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×Dic47⋊C4D411yescharacteristic
144C2×Dic47⋊C4D411yescharacteristic
145C2×C22⋊Dic47—21no—
146C2×C22⋊Dic47—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×C4×Dic47—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47—21no—
153C2×C4×Dic47C2311yescharacteristic
154C2×C4×Dic47C2311yescharacteristic
155C4⋊(C47⋊C8)C2314yes—
156Dic47⋊C8C2314yes—
157Dic47⋊C8C2314yes—
158#13093947C2314yes—
159#13093947C2314yes—
160#13093947C2314yes—
161#13093944C2314yes—
162#13093934C2314yes—
163C8×Dic47C2314yes—
164C22×Q8×C47C2311yescharacteristic
165C22×D4×C47C2311yescharacteristic
166C23×C4×C47—21no—
167C2×SD16×C47—24no—
168C2×SD16×C47C2314yes—
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yes—
173C4×D4×C47—22no—
174C4×D4×C47C2314yes—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#107×C47C2314yes—
182#103×C47C2314yes—
183#102×C47C2314yes—
184#97×C47C2314yes—
185C24×C47—21no—
186C23×D47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47C2412yes—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—24no—
199C22×C4×C47—82no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C2×C22⋊D47—24no—
204C2×C22⋊D47—24no—
205C2×C22⋊D47—44no—
206C2×C22⋊D47—82no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—21no—
217C2×D188C2412yes—
218C2×C4×D47—24no—
219C2×C4×D47—82no—
220C2×Dic94—24no—
221C2×Dic94—22no—
222C2×Dic94—22no—
223C2×Dic94—22no—
224C2×Dic94—22no—
225C2×Dic94—22no—
226C2×Dic94—22no—
227C2×Dic94—21no—
228C2×Dic94—21no—
229C2×Dic94—21no—
230C2×Dic94C2×D414yes—
231C2×Dic94C2412yes—
232C2×Dic94C2412yes—
233C2×Dic94C2412yes—
234SD16×C47—28no—
235C2×C8×C47—22no—
236C2×C8×C47#4114yes—
237C2×C8×C47C2412yes—
238C2×C8×C47C2412yes—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47C2412yes—
243C4⋊C4×C47C2412yes—
244C22⋊C4×C47—24no—
245C42×C47—24no—
246C42×C47C2×D412yes—
247C42×C47C2412yes—
248C22⋊Dic47—24no—
249C22⋊Dic47—24no—
250#10625337—44no—
251#10625336—44no—
252#10625335—44no—
253#10625335—44no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257C4⋊Dic47—24no—
258C4⋊Dic47—24no—
259C4⋊Dic47C2×D414yes—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4C2×D414yes—
268Dic47⋊C4C2×D414yes—
269C4×Dic47—24no—
270C4×Dic47—24no—
271C4×Dic47—24no—
272C4×Dic47C2×D412yes—
273C4×Dic47C2×D412yes—
274C4×Dic47C2412yes—
275C4×Dic47C2412yes—
276C2×C47⋊C8—22no—
277C2×C47⋊C8—22no—
278C2×C47⋊C8C2412yes—
279C2×C47⋊C8C2412yes—
280Dic188—28no—
281Dic188—44no—
282#10625325—28no—
283#10625325—44no—
284C23×C47—22no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47—42no—
288C23×C47C22×D411yescharacteristic
289C22×D47—22no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293Q8×C47—22no—
294Q8×C47—22no—
295Q8×C47—42no—
296D4×C47—22no—
297D4×C47—22no—
298D4×C47—42no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—84no—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C2×#4112yes—
312C2×C4×C47H(5,𝔽2)12yes—
313C2×C4×C47C2511yescharacteristic
314C22⋊D47—48no—
315C22⋊D47—84no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47#13714yes—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329C2×Dic47C22×D412yes—
330D188—22no—
331D188—22no—
332D188—42no—
333C4×D47—84no—
334Dic94—28no—
335Dic94—22no—
336Dic94—22no—
337Dic94—22no—
338Dic94—22no—
339Dic94—22no—
340Dic94—22no—
341Dic94—42no—
342Dic94—42no—
343Dic94—42no—
344C8×C47—22no—
345C8×C47C2×#4114yes—
346C47⋊C8—22no—
347C47⋊C8—22no—
348C2×#3400—471nomaximal, Sylow
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—84no—
353C22×C47#55012yes—
354C22×C47C2×#13712yes—
355C22×C47#57712yes—
356C22×C47C23×D411yescharacteristic
357C2×D47—42no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—84no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—42no—
364C4×C47—42no—
365C4×C47—42no—
366C4×C47#55012yes—
367C4×C47C22×#4111yescharacteristic
368C4×C47C2×H(5,𝔽2)11yescharacteristic
369Dic47—22no—
370Dic47—22no—
371Dic47—22no—
372Dic47—42no—
373Dic47—42no—
374Dic47—42no—
375Dic47C2×#13714yes—
376C2×#559—471no—
377C2×#557—471no—
378#3400—4716no—
379C2×#497—471no—
380C2×#497—471no—
381C2×#492—471no—
382C2×#464—471no—
383C2×#464—471no—
384C2×#462—471no—
385C2×#460—471no—
386C2×#461—471no—
387C2×#461—471no—
388C2×#446—471no—
389C2×#440—471no—
390C2×#440D4711yescharacteristic, complemented
391C2×C4×Q16—471no—
392C2×C47—82no—
393C2×C47#340014yescomplemented
394C2×C47C2×#55011yescharacteristic
395C2×C47C22×#13711yescharacteristic
396C2×C47C2×#57711yescharacteristic
397D47—82no—
398C22×Q16—471no—
399C22×Q16—471no—
400C22×Q16—471no—
401C22×SD16—471no—
402C22×SD16—471no—
403C22×SD16—471no—
404C22×SD16—471no—
405C22×SD16—471no—
406C22×SD16C2×D4711yescharacteristic
407#559—478no—
408#559—944no—
409#557—478no—
410#557—944no—
411C2×C4⋊Q8—471no—
412C2×C4⋊Q8—471no—
413C2×C4⋊Q8—471no—
414C2×#127—471no—
415C2×#125—941no—
416C2×#125—941no—
417C2×#125—941no—
418C2×#124—471no—
419C2×#124—471no—
420C2×#124—941no—
421C2×#123—941no—
422C2×#123—941no—
423C2×C4×Q8—471no—
424C2×C4×Q8—471no—
425C2×C4×Q8—471no—
426C2×C4×Q8—471no—
427C2×C4×Q8—941no—
428C2×C4×Q8C2×D4711yescharacteristic
429C2×C4×D4—471no—
430C2×C4×D4—941no—
431C2×C4×D4C2×D4711yescharacteristic
432#497—478no—
433#497—478no—
434#492—478no—
435#464—478no—
436#464—478no—
437#462—478no—
438#461—478no—
439#461—478no—
440#460—478no—
441#446—478no—
442#440—478no—
443#440C2×D4718yescomplemented
444C4×Q16—478no—
445C2×#107C2×D4711yescharacteristic
446C2×C4⋊C8—471no—
447C2×C4⋊C8—471no—
448C2×C4⋊C8—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103C2×D4711yescharacteristic
453C2×#102—471no—
454C2×#102C2×D4711yescharacteristic
455C2×#97—471no—
456C2×#97C2×D4711yescharacteristic
457C2×C4×C8—471no—
458C47C2×#340011yescharacteristic, complemented, Sylow
459C22×Q8—471no—
460C22×Q8—471no—
461C22×Q8—471no—
462C22×Q8—471no—
463C22×Q8C22×D4711yescharacteristic
464C22×D4—471no—
465C22×D4—941no—
466C22×D4—941no—
467C22×D4C22×D4711yescharacteristic
468C23×C4—21no—
469C23×C4—941no—
470C2×Q16—474no—
471C2×Q16—474no—
472C2×Q16—474no—
473C2×Q16—944no—
474C2×Q16—1882no—
475C2×Q16—1882no—
476C2×SD16—24no—
477C2×SD16—474no—
478C2×SD16—474no—
479C2×SD16—474no—
480C2×SD16—474no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16—1882no—
484C2×SD16—1882no—
485C2×SD16—1882no—
486C2×SD16—1882no—
487C2×SD16C22×D4714yes—
488C22×C8—471no—
489C22×C8—471no—
490C22×C8C22×D4711yescharacteristic
491C22×C8C22×D4711yescharacteristic
492C4⋊Q8—474no—
493C4⋊Q8—474no—
494C4⋊Q8—474no—
495C4⋊Q8—942no—
496C4⋊Q8—942no—
497C4⋊Q8—942no—
498#127—474no—
499#127—942no—
500#125—948no—
501#125—948no—
502#125—948no—
503#124—474no—
504#124—474no—
505#124—942no—
506#124—948no—
507#124—942no—
508#123—948no—
509#123—948no—
510C4×Q8—22no—
511C4×Q8—474no—
512C4×Q8—474no—
513C4×Q8—474no—
514C4×Q8—474no—
515C4×Q8—474no—
516C4×Q8—948no—
517C4×Q8—942no—
518C4×Q8—942no—
519C4×Q8—942no—
520C4×Q8C22×D4714yes—
521C4×D4—22no—
522C4×D4—474no—
523C4×D4—942no—
524C4×D4—948no—
525C4×D4C22×D4714yes—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—471no—
528C2×C4⋊C4—471no—
529C2×C4⋊C4—471no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—941no—
532C2×C4⋊C4—941no—
533C2×C4⋊C4—941no—
534C2×C4⋊C4—941no—
535C2×C4⋊C4—941no—
536C2×C4⋊C4—941no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4C22×D4711yescharacteristic
540C2×C4⋊C4C22×D4711yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—941no—
543C2×C22⋊C4—941no—
544C2×C22⋊C4—941no—
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C42—21no—
548C2×C42—471no—
549C2×C42—471no—
550C2×C42—941no—
551C2×C42—941no—
552C2×C42—941no—
553C2×C42C22×D4711yescharacteristic
554#107C22×D4714yes—
555C4⋊C8—474no—
556C4⋊C8—474no—
557C4⋊C8—474no—
558#103—474no—
559#103—474no—
560#103—474no—
561#103C22×D4714yes—
562#102—474no—
563#102C22×D4714yes—
564#97—474no—
565#97C22×D4714yes—
566C4×C8—474no—
567C24—21no—
568C24—941no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—474no—
573C2×Q8—472no—
574C2×Q8—472no—
575C2×Q8—472no—
576C2×Q8—944no—
577C2×Q8—941no—
578C2×Q8—941no—
579C2×Q8—941no—
580C2×Q8—942no—
581C2×Q8—942no—
582C2×Q8—942no—
583C2×Q8—942no—
584C2×Q8—942no—
585C2×Q8—942no—
586C2×Q8C23×D4712yes—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—472no—
591C2×D4—944no—
592C2×D4—944no—
593C2×D4—941no—
594C2×D4—942no—
595C2×D4—942no—
596C2×D4—3762no—
597C2×D4—1884no—
598C2×D4C23×D4712yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—82no—
604C22×C4—471no—
605C22×C4—471no—
606C22×C4—471no—
607C22×C4—471no—
608C22×C4—944no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—3762no—
613C22×C4D4×D4711yescharacteristic
614C22×C4D4×D4711yescharacteristic
615C22×C4C23×D4711yescharacteristic
616Q16—948no—
617Q16—1884no—
618Q16—1884no—
619SD16—28no—
620SD16—948no—
621SD16—1884no—
622SD16—1884no—
623SD16—1884no—
624SD16—1884no—
625C2×C8—22no—
626C2×C8—472no—
627C2×C8—472no—
628C2×C8—942no—
629C2×C8—942no—
630C2×C8#1062535014yes—
631C2×C8C23×D4712yes—
632C2×C8C23×D4712yes—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—474no—
637C4⋊C4—474no—
638C4⋊C4—474no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4—944no—
644C4⋊C4—944no—
645C4⋊C4—944no—
646C4⋊C4—944no—
647C4⋊C4—944no—
648C4⋊C4C23×D4712yes—
649C4⋊C4C23×D4712yes—
650C22⋊C4—24no—
651C22⋊C4—944no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C42—24no—
657C42—472no—
658C42—472no—
659C42—472no—
660C42—472no—
661C42—944no—
662C42—944no—
663C42—944no—
664C42D4×D4712yes—
665C42C23×D4712yes—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—942no—
671C23—1882no—
672C23—1882no—
673C23—1882no—
674C23C2×D4×D4711yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—42no—
678Q8—948no—
679Q8—942no—
680Q8—942no—
681Q8—942no—
682Q8—942no—
683Q8—942no—
684Q8—942no—
685Q8—1882no—
686Q8—1882no—
687Q8—1882no—
688D4—22no—
689D4—22no—
690D4—42no—
691D4—942no—
692D4—942no—
693D4—3764no—
694D4—1888no—
695D4—1882no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—474no—
706C2×C4—472no—
707C2×C4—472no—
708C2×C4—472no—
709C2×C4—472no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—3764no—
717C2×C4—1882no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4C2×D4×D4712yes—
721C2×C4C2×D4×D4712yes—
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4C2×#1062535012yes—
724C2×C4#1309407012yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—942no—
728C8—942no—
729C8C2×#1062535014yes—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—3764no—
735C22—1882no—
736C22—1882no—
737C22—1882no—
738C22#1568979412yes—
739C22#137×D4712yes—
740C22#1568993312yes—
741C22C22×D4×D4711yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—474no—
748C4—942no—
749C4—942no—
750C4—942no—
751C4—1882no—
752C4—1882no—
753C4—1882no—
754C4#1568979412yes—
755C4C22×#1062535011yescharacteristic
756C4C2×#1309407011yescharacteristic
757C2—82no—
758C2—3762no—
759C2#2025644214yesdirect product factor
760C2C2×#1568979411yescharacteristic
761C2C2×#137×D4711yescharacteristic
762C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#440C2
socleC23×C47C22×D4
prime radicalC2×#13094020C22
hypercenterC2×#440D47
hypocenterC47C2×#3400
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#15689851C2semidirect
3. #20256442C2direct (N × H)
4. C2×#15689517C2semidirect
5. C2×#15689514C2semidirect
7. C2×#15689345C2semidirect
8. C2×#15689344C2semidirect
9. C2×#15689332C2semidirect
11. C2×#15689328C2semidirect
12. C2×#15689327C2semidirect
13. C2×#15689251C2semidirect
14. C2×#15689222C2semidirect
15. C2×#15689217C2semidirect
16. C2×C47×#440C2semidirect
28. #15689851C22semidirect
48. #15689517C22semidirect
49. #15689514C22semidirect
51. #15689345C22semidirect
52. #15689344C22semidirect
53. #15689332C22semidirect
54. #15689328C22semidirect
55. #15689327C22semidirect
57. #15689251C22semidirect
58. #15689222C22semidirect
59. #15689217C22semidirect
72. C47×#440C22semidirect
390. C2×#440D47semidirect
393. C2×C47#3400semidirect
443. #440C2×D47semidirect
458. C47C2×#3400semidirect
759. C2#20256442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898562
C2×#156898512
#202564422
C2×#156895172
C2×#156895142
C2×#156894942
C2×#156893452
C2×#156893442
C2×#156893322
C2×#156893222
C2×#156893282
C2×#156893272
C2×#156892512
C2×#156892222
C2×#156892172
C2×C47×#4402
C2×#340047