Finite Group Databasebeta

← C2×#20256464 #27097295

Subgroups — C2×#20256464 #27097295

Order 12032.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689847C211yesmaximal, characteristic, complemented
2C2×#15689842C211yesmaximal, characteristic, complemented
3#20256464C2116yesmaximal, direct product factor
4C2×#15689516C211yesmaximal, characteristic, complemented
5C2×#15689504C211yesmaximal, characteristic
6C2×#15689347C211yesmaximal, characteristic, complemented
7C2×#15689343C211yesmaximal, characteristic, complemented
8C2×#15689331C211yesmaximal, characteristic, complemented
9C2×#15689330C211yesmaximal, characteristic, complemented
10C2×#15689340C211yesmaximal, characteristic
11C2×#15689335C211yesmaximal, characteristic
12C2×#15689251C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×#15689224C211yesmaximal, characteristic, complemented
15C2×Q16×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#497C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22#15689847—24no—
23#15689847C2218yescomplemented
24#15689842—24no—
25#15689842C2218yescomplemented
26C2×#13094022C2211yescharacteristic
27C2×#13094019—21no—
28C2×#13094019—21no—
29C2×#13094017—21no—
30C2×#13094017—21no—
31C2×#13094013C2211yescharacteristic
32C2×#13094013C2211yescharacteristic
33C2×#13094011C2211yescharacteristic
34C2×#13094004—21no—
35C2×#13094001—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×Q8×Dic47C2211yescharacteristic
38C2×Q8×Dic47C2211yescharacteristic
39C2×C4×Dic94C2211yescharacteristic
40C2×C4×Dic94C2211yescharacteristic
41C2×C4×D188C2211yescharacteristic
42C2×D4×Dic47C2211yescharacteristic
43C2×#13093982—21no—
44C2×#13093980—21no—
45#15689516C2218yescomplemented
46#15689504C2218yes—
47#15689347C2218yescomplemented
48#15689343C2218yescomplemented
49#15689340C2218yes—
50#15689335C2218yes—
51#15689331C2218yescomplemented
52#15689330C2218yescomplemented
53#15689251C2218yescomplemented
54#15689225C2218yescomplemented
55#15689224C2218yescomplemented
56Q16×Dic47C2218yescomplemented
57C2×#13093958C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C22×SD16×C47C2211yescharacteristic
72C22×SD16×C47C2211yescharacteristic
73C2×C4⋊Q8×C47C2211yescharacteristic
74C2×#124×C47C2211yescharacteristic
75C47×#497C2218yescomplemented
76C2×#97×C47C2211yescharacteristic
77C22×Dic94D411yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C23×Dic47—21no—
81C22×C4×D47—21no—
82C2×#10625337—42no—
83C2×#10625337—42no—
84C2×#10625337C2314yes—
85C2×#10625337C2314yes—
86C2×#10625325—24no—
87C2×#10625325C2314yes—
88C2×#10625336—42no—
89C2×#10625336C2314yes—
90C2×#10625334—42no—
91C2×#10625334C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94#13094022—22no—
95#13094022C2314yes—
96#13094019—28no—
97#13094019—28no—
98#13094017—28no—
99#13094017—28no—
100#13094013—22no—
101#13094013—22no—
102#13094013C2314yes—
103#13094013C2314yes—
104#13094011—22no—
105#13094011C2314yes—
106#13094004—28no—
107#13094001—28no—
108Q8×Dic47—22no—
109Q8×Dic47—22no—
110Q8×Dic47—22no—
111Q8×Dic47C2314yes—
112Q8×Dic47C2314yes—
113Q8×Dic47C2314yes—
114C4×Dic94—22no—
115C4×Dic94D414yes—
116C4×Dic94C2314yes—
117C4×Dic94C2314yes—
118C4×D188—22no—
119C4×D188C2314yes—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122#13093982—28no—
123#13093980—28no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47D411yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4D411yescharacteristic
134C2×Dic47⋊C4D411yescharacteristic
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
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×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47C2311yescharacteristic
148C2×C4×Dic47C2311yescharacteristic
149#13093958C2314yes—
150C4⋊(C47⋊C8)C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093948C2314yes—
157#13093946C2314yes—
158#13093945C2314yes—
159#13093934C2314yes—
160C8×Dic47C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×Q8×C47C2311yescharacteristic
163C22×Q8×C47C2311yescharacteristic
164C22×D4×C47C2311yescharacteristic
165C2×Q16×C47—24no—
166C2×Q16×C47—42no—
167C2×Q16×C47C2314yes—
168C2×Q16×C47C2314yes—
169C2×SD16×C47—24no—
170C2×SD16×C47—42no—
171C2×SD16×C47C2314yes—
172C2×SD16×C47C2314yes—
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2311yescharacteristic
175C4⋊Q8×C47—22no—
176C4⋊Q8×C47C2314yes—
177#124×C47—22no—
178#124×C47C2314yes—
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C42×C47C2311yescharacteristic
184#97×C47C2314yes—
185C24×C47—21no—
186C23×D47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47C2412yes—
197C2×Q8×C47C2412yes—
198C2×Q8×C47C2412yes—
199C2×D4×C47—21no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47C2412yes—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2411yescharacteristic
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—24no—
213C22×Dic47—44no—
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218C2×D188—22no—
219C2×D188—22no—
220C2×D188—21no—
221C2×D188C2412yes—
222C2×C4×D47—24no—
223C2×C4×D47—44no—
224C2×Dic94—22no—
225C2×Dic94—22no—
226C2×Dic94—21no—
227C2×Dic94—42no—
228C2×Dic94C2×D414yes—
229C2×Dic94C2412yes—
230Q16×C47—28no—
231Q16×C47—44no—
232SD16×C47—28no—
233SD16×C47—44no—
234C2×C8×C47—22no—
235C2×C8×C47#4114yes—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—24no—
240C22⋊C4×C47—24no—
241C22⋊C4×C47—24no—
242C42×C47C2×D412yes—
243C42×C47C2412yes—
244C22⋊Dic47—24no—
245C22⋊Dic47—24no—
246C22⋊Dic47—24no—
247#10625337—44no—
248#10625337—44no—
249#10625336—44no—
250#10625334—44no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—24no—
259C4⋊Dic47—24no—
260C4⋊Dic47—24no—
261C4⋊Dic47C2×D414yes—
262C4⋊Dic47C2412yes—
263C4⋊Dic47C2412yes—
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×Dic47—24no—
273C4×Dic47C2×D412yes—
274C4×Dic47C2×D412yes—
275C4×Dic47C2412yes—
276C4×Dic47C2412yes—
277C2×C47⋊C8—22no—
278C2×C47⋊C8—22no—
279C2×C47⋊C8C2412yes—
280C2×C47⋊C8C2412yes—
281#10625325—28no—
282C23×C47—22no—
283C23×C47—42no—
284C23×C47—42no—
285C23×C47—42no—
286C23×C47C22×D411yescharacteristic
287C22×D47—22no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—22no—
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47—42no—
298Q8×C47—42no—
299Q8×C47—42no—
300D4×C47—22no—
301D4×C47—22no—
302D4×C47—42no—
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×C47C22×D412yes—
312C2×C4×C47C22×D412yes—
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C2×#4112yes—
315C2×C4×C47H(5,𝔽2)12yes—
316C2×C4×C47C2511yescharacteristic
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—48no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47C22×D412yes—
329C2×Dic47C22×D412yes—
330C2×Dic47C22×D412yes—
331C2×Dic47C22×D412yes—
332D188—22no—
333D188—22no—
334D188—42no—
335C4×D47—48no—
336Dic94—22no—
337Dic94—22no—
338Dic94—44no—
339Dic94—42no—
340C8×C47—22no—
341C8×C47C2×#4114yes—
342C47⋊C8—22no—
343C47⋊C8—22no—
344C2×#3402—471nomaximal, Sylow
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—84no—
349C22×C47#55012yes—
350C22×C47#57512yes—
351C22×C47#57812yes—
352C22×C47C23×D411yescharacteristic
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—84no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47#55012yes—
363C4×C47C22×#4111yescharacteristic
364C4×C47C2×H(5,𝔽2)11yescharacteristic
365Dic47—22no—
366Dic47—22no—
367Dic47—22no—
368Dic47—22no—
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#556—471no—
373C2×#556—471no—
374#3402—4716no—
375C2×#497—471no—
376C2×#497D4711yescharacteristic, complemented
377C2×#495—471no—
378C2×#464—471no—
379C2×#464—471no—
380C2×#462—471no—
381C2×#462—471no—
382C2×#463—471no—
383C2×#463—471no—
384C2×#446—471no—
385C2×#440—471no—
386C2×#440—471no—
387C2×C4×Q16—471no—
388C2×C47—82no—
389C2×C47#340214yescomplemented
390C2×C47C2×#55011yescharacteristic
391C2×C47C2×#57511yescharacteristic
392C2×C47C2×#57811yescharacteristic
393D47—82no—
394C22×Q16—471no—
395C22×Q16—471no—
396C22×Q16C2×D4711yescharacteristic
397C22×Q16C2×D4711yescharacteristic
398C22×SD16—471no—
399C22×SD16—471no—
400C22×SD16C2×D4711yescharacteristic
401C22×SD16C2×D4711yescharacteristic
402C22×D8—471no—
403#556—478no—
404#556—478no—
405#556—944no—
406#556—944no—
407C2×C4⋊Q8—471no—
408C2×C4⋊Q8C2×D4711yescharacteristic
409C2×#126—941no—
410C2×#126—941no—
411C2×#126—941no—
412C2×#126—941no—
413C2×#124—471no—
414C2×#124—471no—
415C2×#124—471no—
416C2×#124C2×D4711yescharacteristic
417C2×C22⋊Q8—941no—
418C2×C22⋊Q8—941no—
419C2×C4×Q8—471no—
420C2×C4×Q8—471no—
421C2×C4×Q8—471no—
422C2×C4×Q8—471no—
423C2×C4×Q8—471no—
424C2×C4×D4—471no—
425C2×C4×D4—471no—
426C2×#117—941no—
427C2×#117—941no—
428#497—478no—
429#497C2×D4718yescomplemented
430#495—478no—
431#464—478no—
432#464—478no—
433#463—478no—
434#463—478no—
435#462—478no—
436#462—478no—
437#446—478no—
438#440—478no—
439#440—478no—
440C4×Q16—478no—
441C2×#107—471no—
442C2×C4⋊C8—471no—
443C2×C4⋊C8—471no—
444C2×C4⋊C8—471no—
445C2×#103—471no—
446C2×#103—471no—
447C2×#103—471no—
448C2×#103—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×#97—471no—
452C2×#97C2×D4711yescharacteristic
453C2×C4×C8—471no—
454C47C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—471no—
456C22×Q8—471no—
457C22×Q8C22×D4711yescharacteristic
458C22×Q8C22×D4711yescharacteristic
459C22×Q8C22×D4711yescharacteristic
460C22×D4—471no—
461C22×D4C22×D4711yescharacteristic
462C23×C4—941no—
463C23×C4—941no—
464C2×Q16—24no—
465C2×Q16—42no—
466C2×Q16—474no—
467C2×Q16—474no—
468C2×Q16—1882no—
469C2×Q16—1882no—
470C2×Q16C22×D4714yes—
471C2×Q16C22×D4714yes—
472C2×SD16—24no—
473C2×SD16—42no—
474C2×SD16—474no—
475C2×SD16—474no—
476C2×SD16—944no—
477C2×SD16—1882no—
478C2×SD16C22×D4714yes—
479C2×SD16C22×D4714yes—
480C2×D8—474no—
481C2×D8—1882no—
482C22×C8—471no—
483C22×C8—471no—
484C22×C8C22×D4711yescharacteristic
485C22×C8C22×D4711yescharacteristic
486C4⋊Q8—22no—
487C4⋊Q8—474no—
488C4⋊Q8—942no—
489C4⋊Q8C22×D4714yes—
490#126—948no—
491#126—948no—
492#126—948no—
493#126—948no—
494#124—22no—
495#124—474no—
496#124—474no—
497#124—474no—
498#124—942no—
499#124—942no—
500#124—942no—
501#124C22×D4714yes—
502C22⋊Q8—948no—
503C22⋊Q8—948no—
504C4×Q8—474no—
505C4×Q8—474no—
506C4×Q8—474no—
507C4×Q8—474no—
508C4×Q8—474no—
509C4×Q8—474no—
510C4×Q8—942no—
511C4×Q8—942no—
512C4×Q8—942no—
513C4×Q8—942no—
514C4×D4—474no—
515C4×D4—474no—
516C4×D4—942no—
517C4×D4—942no—
518#117—948no—
519#117—948no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4—471no—
525C2×C4⋊C4—471no—
526C2×C4⋊C4—471no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—941no—
532C2×C4⋊C4—941no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C42—471no—
544C2×C42—471no—
545C2×C42—941no—
546C2×C42—941no—
547C2×C42—941no—
548C2×C42—941no—
549C2×C42C22×D4711yescharacteristic
550#107—474no—
551C4⋊C8—474no—
552C4⋊C8—474no—
553C4⋊C8—474no—
554#103—474no—
555#103—474no—
556#103—474no—
557#103—474no—
558#102—474no—
559#102—474no—
560#97—474no—
561#97C22×D4714yes—
562C4×C8—474no—
563C24—21no—
564C24—941no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—474no—
575C2×Q8—472no—
576C2×Q8—941no—
577C2×Q8—942no—
578C2×Q8—942no—
579C2×Q8—1882no—
580C2×Q8C23×D4712yes—
581C2×Q8C23×D4712yes—
582C2×Q8C23×D4712yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—472no—
587C2×D4—941no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4C23×D4712yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—471no—
595C22×C4—471no—
596C22×C4—471no—
597C22×C4—471no—
598C22×C4—944no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—944no—
603C22×C4—1884no—
604C22×C4—1884no—
605C22×C4D4×D4711yescharacteristic
606C22×C4D4×D4711yescharacteristic
607C22×C4C23×D4711yescharacteristic
608Q16—28no—
609Q16—44no—
610Q16—1884no—
611Q16—1884no—
612SD16—28no—
613SD16—44no—
614SD16—948no—
615SD16—1884no—
616D8—1884no—
617C2×C8—22no—
618C2×C8—472no—
619C2×C8—472no—
620C2×C8—942no—
621C2×C8—942no—
622C2×C8#1062535214yes—
623C2×C8C23×D4712yes—
624C2×C8C23×D4712yes—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—474no—
628C4⋊C4—474no—
629C4⋊C4—474no—
630C4⋊C4—472no—
631C4⋊C4—472no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—944no—
635C4⋊C4—944no—
636C4⋊C4—944no—
637C4⋊C4—944no—
638C4⋊C4—941no—
639C4⋊C4—941no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C42—472no—
651C42—472no—
652C42—472no—
653C42—472no—
654C42—944no—
655C42—944no—
656C42—944no—
657C42—944no—
658C42D4×D4712yes—
659C42C23×D4712yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—942no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23C2×D4×D4711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—942no—
679Q8—942no—
680Q8—1884no—
681Q8—1882no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—942no—
686D4—942no—
687D4—1882no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—472no—
697C2×C4—472no—
698C2×C4—472no—
699C2×C4—472no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—1888no—
708C2×C4—1888no—
709C2×C4—1882no—
710C2×C4—1882no—
711C2×C4—1882no—
712C2×C4C2×D4×D4712yes—
713C2×C4C2×D4×D4712yes—
714C2×C4C2×D4×D4711yescharacteristic
715C2×C4C2×#1062535212yes—
716C2×C4#1309406912yes—
717C2×C4C24×D4711yescharacteristic
718C8—22no—
719C8—942no—
720C8—942no—
721C8C2×#1062535214yes—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—3764no—
727C22—1882no—
728C22—1882no—
729C22—1882no—
730C22#1568979312yes—
731C22#1568992212yes—
732C22#1568993912yes—
733C22C22×D4×D4711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—942no—
740C4—942no—
741C4—942no—
742C4—942no—
743C4—1882no—
744C4—1882no—
745C4—1882no—
746C4#1568979312yes—
747C4C22×#1062535211yescharacteristic
748C4C2×#1309406911yescharacteristic
749C2—82no—
750C2—3762no—
751C2#2025646414yesdirect product factor
752C2C2×#1568979311yescharacteristic
753C2C2×#1568992211yescharacteristic
754C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#497C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#497D47
hypocenterC47C2×#3402
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#15689847C2semidirect
2. C2×#15689842C2semidirect
3. #20256464C2direct (N × H)
4. C2×#15689516C2semidirect
6. C2×#15689347C2semidirect
7. C2×#15689343C2semidirect
8. C2×#15689331C2semidirect
9. C2×#15689330C2semidirect
12. C2×#15689251C2semidirect
13. C2×#15689225C2semidirect
14. C2×#15689224C2semidirect
15. C2×Q16×Dic47C2semidirect
16. C2×C47×#497C2semidirect
23. #15689847C22semidirect
25. #15689842C22semidirect
45. #15689516C22semidirect
47. #15689347C22semidirect
48. #15689343C22semidirect
51. #15689331C22semidirect
52. #15689330C22semidirect
53. #15689251C22semidirect
54. #15689225C22semidirect
55. #15689224C22semidirect
56. Q16×Dic47C22semidirect
75. C47×#497C22semidirect
376. C2×#497D47semidirect
389. C2×C47#3402semidirect
429. #497C2×D47semidirect
454. C47C2×#3402semidirect
751. C2#20256464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898472
C2×#156898422
#202564642
C2×#156895162
C2×#156895042
C2×#156893472
C2×#156893432
C2×#156893312
C2×#156893302
C2×#156893402
C2×#156893352
C2×#156892512
C2×#156892252
C2×#156892242
C2×Q16×Dic472
C2×C47×#4972
C2×#340247