Finite Group Databasebeta

← C2×#20256438 #27097267

Subgroups — C2×#20256438 #27097267

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×#15689855C211yesmaximal, characteristic
2C2×#15689848C211yesmaximal, characteristic, complemented
3#20256438C2116yesmaximal, direct product factor
4C2×#15689516C211yesmaximal, characteristic, complemented
5C2×#15689494C211yesmaximal, characteristic
6C2×#15689347C211yesmaximal, characteristic, complemented
7C2×#15689342C211yesmaximal, characteristic, complemented
8C2×#15689331C211yesmaximal, characteristic, complemented
9C2×#15689321C211yesmaximal, characteristic
10C2×#15689326C211yesmaximal, characteristic, complemented
11C2×#15689325C211yesmaximal, characteristic, complemented
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×#10625325C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22#15689855—24no—
23#15689855C2218yes—
24#15689848—24no—
25#15689848C2218yescomplemented
26C2×#13094022C2211yescharacteristic
27C2×#13094022C2211yescharacteristic
28C2×#13094020C2211yescharacteristic
29C2×#13094015—21no—
30C2×#13094014—21no—
31C2×#13094014—21no—
32C2×#13094013C2211yescharacteristic
33C2×#13094010—21no—
34C2×#13094008—21no—
35C2×#13094006—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×Q8×Dic47C2211yescharacteristic
38C2×Q8×Dic47C2211yescharacteristic
39C2×C4×Dic94C2211yescharacteristic
40C2×C4×Dic94C2211yescharacteristic
41C2×#13093989—21no—
42C2×C4×D188C2211yescharacteristic
43C2×D4×Dic47C2211yescharacteristic
44C2×(C22⋊D47)⋊C4—21no—
45#15689516C2218yescomplemented
46#15689494C2218yes—
47#15689347C2218yescomplemented
48#15689342C2218yescomplemented
49#15689331C2218yescomplemented
50#15689326C2218yescomplemented
51#15689325C2218yescomplemented
52#15689321C2218yes—
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
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C23×Dic47—21no—
83C22×C4×D47—21no—
84C2×#10625337—42no—
85C2×#10625337C2314yes—
86C2×#10625325—24no—
87C2×#10625325C2314yes—
88C2×#10625335—42no—
89C2×#10625335C2314yes—
90C2×#10625336—42no—
91C2×#10625336—42no—
92C2×#10625336C2314yes—
93C2×#10625336C2314yes—
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2311yescharacteristic
96#13094022—22no—
97#13094022—22no—
98#13094022C2314yes—
99#13094022C2314yes—
100#13094020—22no—
101#13094020C2314yes—
102#13094015—28no—
103#13094014—28no—
104#13094014—28no—
105#13094013—22no—
106#13094013C2314yes—
107#13094010—28no—
108#13094008—28no—
109#13094006—28no—
110Q8×Dic47—22no—
111Q8×Dic47—22no—
112Q8×Dic47—22no—
113Q8×Dic47C2314yes—
114Q8×Dic47C2314yes—
115Q8×Dic47C2314yes—
116C4×Dic94—22no—
117C4×Dic94D414yes—
118C4×Dic94C2314yes—
119C4×Dic94C2314yes—
120#13093989—28no—
121C4×D188—22no—
122C4×D188C2314yes—
123D4×Dic47—22no—
124D4×Dic47C2314yes—
125(C22⋊D47)⋊C4—28no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47D411yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×Dic47⋊C4D411yescharacteristic
139C2×C22⋊Dic47—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
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—44no—
212C2×C22⋊D47—82no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—24no—
217C22×Dic47—82no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221C22×Dic47C2×D411yescharacteristic
222C2×D188—22no—
223C2×D188—22no—
224C2×D188—21no—
225C2×D188C2412yes—
226C2×C4×D47—24no—
227C2×C4×D47—82no—
228C2×Dic94—24no—
229C2×Dic94—22no—
230C2×Dic94—22no—
231C2×Dic94—21no—
232C2×Dic94C2×D414yes—
233C2×Dic94C2412yes—
234Q16×C47—28no—
235Q16×C47—44no—
236SD16×C47—28no—
237SD16×C47—44no—
238C2×C8×C47—22no—
239C2×C8×C47#4114yes—
240C2×C8×C47C2412yes—
241C2×C8×C47C2412yes—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—24no—
244C22⋊C4×C47—24no—
245C22⋊C4×C47—24no—
246C42×C47C2×D412yes—
247C42×C47C2412yes—
248C22⋊Dic47—24no—
249#10625337—44no—
250#10625336—44no—
251#10625336—44no—
252#10625335—44no—
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⋊C4—24no—
268Dic47⋊C4—24no—
269Dic47⋊C4C2×D414yes—
270Dic47⋊C4C2×D414yes—
271C4×Dic47—24no—
272C4×Dic47—24no—
273C4×Dic47—24no—
274C4×Dic47—24no—
275C4×Dic47C2×D412yes—
276C4×Dic47C2×D412yes—
277C4×Dic47C2412yes—
278C4×Dic47C2412yes—
279C2×C47⋊C8—22no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8C2412yes—
282C2×C47⋊C8C2412yes—
283#10625325—28no—
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—22no—
296Q8×C47—22no—
297Q8×C47—22no—
298Q8×C47—22no—
299Q8×C47—42no—
300Q8×C47—42no—
301Q8×C47—42no—
302D4×C47—22no—
303D4×C47—22no—
304D4×C47—42no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4112yes—
317C2×C4×C47H(5,𝔽2)12yes—
318C2×C4×C47C2511yescharacteristic
319C22⋊D47—48no—
320C22⋊D47—84no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—84no—
331C2×Dic47#13714yes—
332C2×Dic47C22×D412yes—
333C2×Dic47C22×D412yes—
334C2×Dic47C22×D412yes—
335C2×Dic47C22×D412yes—
336D188—22no—
337D188—22no—
338D188—42no—
339C4×D47—84no—
340Dic94—28no—
341Dic94—22no—
342Dic94—22no—
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×#497D4711yescharacteristic, complemented
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×#440—471no—
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×Q16C2×D4711yescharacteristic
400C22×Q16C2×D4711yescharacteristic
401C22×SD16—471no—
402C22×SD16—471no—
403C22×SD16—471no—
404C22×SD16—471no—
405C22×SD16C2×D4711yescharacteristic
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⋊Q8C2×D4711yescharacteristic
414C2×#127—471no—
415C2×#125—941no—
416C2×#125—941no—
417C2×#125—941no—
418C2×#124—471no—
419C2×#124—941no—
420C2×#124C2×D4711yescharacteristic
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—471no—
428C2×C4×Q8—941no—
429C2×C4×D4—471no—
430C2×C4×D4—471no—
431C2×C4×D4—941no—
432#497—478no—
433#497C2×D4718yescomplemented
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#440—478no—
444C4×Q16—478no—
445C2×#107—471no—
446C2×C4⋊C8—471no—
447C2×C4⋊C8—471no—
448C2×C4⋊C8—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#97—471no—
456C2×#97C2×D4711yescharacteristic
457C2×C4×C8—471no—
458C47C2×#340011yescharacteristic, complemented, Sylow
459C22×Q8—471no—
460C22×Q8—471no—
461C22×Q8C22×D4711yescharacteristic
462C22×Q8C22×D4711yescharacteristic
463C22×Q8C22×D4711yescharacteristic
464C22×D4—471no—
465C22×D4—941no—
466C22×D4—941no—
467C22×D4C22×D4711yescharacteristic
468C23×C4—941no—
469C23×C4—941no—
470C2×Q16—24no—
471C2×Q16—42no—
472C2×Q16—474no—
473C2×Q16—1882no—
474C2×Q16C22×D4714yes—
475C2×Q16C22×D4714yes—
476C2×SD16—24no—
477C2×SD16—42no—
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×SD16C22×D4714yes—
487C2×SD16C22×D4714yes—
488C22×C8—471no—
489C22×C8—471no—
490C22×C8C22×D4711yescharacteristic
491C22×C8C22×D4711yescharacteristic
492C4⋊Q8—22no—
493C4⋊Q8—474no—
494C4⋊Q8—474no—
495C4⋊Q8—942no—
496C4⋊Q8—942no—
497C4⋊Q8C22×D4714yes—
498#127—474no—
499#127—942no—
500#125—948no—
501#125—948no—
502#125—948no—
503#124—22no—
504#124—474no—
505#124—942no—
506#124—948no—
507#124C22×D4714yes—
508#123—948no—
509#123—948no—
510C4×Q8—474no—
511C4×Q8—474no—
512C4×Q8—474no—
513C4×Q8—474no—
514C4×Q8—474no—
515C4×Q8—474no—
516C4×Q8—942no—
517C4×Q8—942no—
518C4×Q8—942no—
519C4×Q8—948no—
520C4×Q8—942no—
521C4×D4—474no—
522C4×D4—474no—
523C4×D4—942no—
524C4×D4—948no—
525C4×D4—942no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—471no—
529C2×C4⋊C4—471no—
530C2×C4⋊C4—471no—
531C2×C4⋊C4—471no—
532C2×C4⋊C4—471no—
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⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—941no—
544C2×C22⋊C4—941no—
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C42—471no—
548C2×C42—471no—
549C2×C42—941no—
550C2×C42—941no—
551C2×C42—941no—
552C2×C42—941no—
553C2×C42C22×D4711yescharacteristic
554#107—474no—
555C4⋊C8—474no—
556C4⋊C8—474no—
557C4⋊C8—474no—
558#103—474no—
559#103—474no—
560#103—474no—
561#103—474no—
562#102—474no—
563#102—474no—
564#97—474no—
565#97C22×D4714yes—
566C4×C8—474no—
567C24—21no—
568C24—941no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—474no—
579C2×Q8—472no—
580C2×Q8—944no—
581C2×Q8—941no—
582C2×Q8—942no—
583C2×Q8—942no—
584C2×Q8C23×D4712yes—
585C2×Q8C23×D4712yes—
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—471no—
603C22×C4—471no—
604C22×C4—471no—
605C22×C4—471no—
606C22×C4—944no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—944no—
611C22×C4—3762no—
612C22×C4—3762no—
613C22×C4D4×D4711yescharacteristic
614C22×C4D4×D4711yescharacteristic
615C22×C4C23×D4711yescharacteristic
616Q16—28no—
617Q16—44no—
618Q16—1884no—
619SD16—28no—
620SD16—44no—
621SD16—948no—
622SD16—1884no—
623SD16—1884no—
624SD16—1884no—
625C2×C8—22no—
626C2×C8—472no—
627C2×C8—472no—
628C2×C8—942no—
629C2×C8—942no—
630C2×C8#1062535214yes—
631C2×C8C23×D4712yes—
632C2×C8C23×D4712yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—474no—
636C4⋊C4—474no—
637C4⋊C4—474no—
638C4⋊C4—472no—
639C4⋊C4—472no—
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⋊C4—941no—
649C4⋊C4—941no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C42—472no—
657C42—472no—
658C42—472no—
659C42—472no—
660C42—944no—
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—22no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—948no—
685Q8—942no—
686Q8—942no—
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—474no—
705C2×C4—472no—
706C2×C4—472no—
707C2×C4—472no—
708C2×C4—472no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—3764no—
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×#1062535212yes—
724C2×C4#1309406912yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—942no—
728C8—942no—
729C8C2×#1062535214yes—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—3764no—
735C22—1882no—
736C22—1882no—
737C22—1882no—
738C22#1568979312yes—
739C22#137×D4712yes—
740C22#1568993212yes—
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#1568979312yes—
755C4C22×#1062535211yescharacteristic
756C4C2×#1309406911yescharacteristic
757C2—82no—
758C2—3762no—
759C2#2025643814yesdirect product factor
760C2C2×#1568979311yescharacteristic
761C2C2×#137×D4711yescharacteristic
762C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#497C2
socleC23×C47C22×D4
prime radicalC2×#13094020C22
hypercenterC2×#497D47
hypocenterC47C2×#3400
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
2. C2×#15689848C2semidirect
3. #20256438C2direct (N × H)
4. C2×#15689516C2semidirect
6. C2×#15689347C2semidirect
7. C2×#15689342C2semidirect
8. C2×#15689331C2semidirect
10. C2×#15689326C2semidirect
11. C2×#15689325C2semidirect
12. C2×#15689251C2semidirect
13. C2×#15689225C2semidirect
14. C2×#15689224C2semidirect
15. C2×Q16×Dic47C2semidirect
16. C2×C47×#497C2semidirect
25. #15689848C22semidirect
45. #15689516C22semidirect
47. #15689347C22semidirect
48. #15689342C22semidirect
49. #15689331C22semidirect
50. #15689326C22semidirect
51. #15689325C22semidirect
53. #15689251C22semidirect
54. #15689225C22semidirect
55. #15689224C22semidirect
56. Q16×Dic47C22semidirect
75. C47×#497C22semidirect
380. C2×#497D47semidirect
393. C2×C47#3400semidirect
433. #497C2×D47semidirect
458. C47C2×#3400semidirect
759. C2#20256438direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898552
C2×#156898482
#202564382
C2×#156895162
C2×#156894942
C2×#156893472
C2×#156893422
C2×#156893312
C2×#156893212
C2×#156893262
C2×#156893252
C2×#156892512
C2×#156892252
C2×#156892242
C2×Q16×Dic472
C2×C47×#4972
C2×#340047