Finite Group Databasebeta

← C2×#20255564 #27092905

Subgroups — C2×#20255564 #27092905

Order 12032.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689823C211yesmaximal, characteristic
2C2×Q8×D188C211yesmaximal, characteristic, complemented
3#20255564C2116yesmaximal, direct product factor
4C2×#15689492C211yesmaximal, characteristic, complemented
5C2×#15689460C211yesmaximal, characteristic, complemented
6C2×#15689466C211yesmaximal, characteristic, complemented
7C2×#15689430C211yesmaximal, characteristic, complemented
8C2×#15689368C211yesmaximal, characteristic, complemented
9C2×#15689351C211yesmaximal, characteristic, complemented
10C2×#15689328C211yesmaximal, characteristic, complemented
11C2×#15689260C211yesmaximal, characteristic, complemented
12C2×#15689260C211yesmaximal, characteristic, complemented
13C2×#15689196C211yesmaximal, characteristic, complemented
14C2×#15689130C211yesmaximal, characteristic, complemented
15C2×#103×D47C211yesmaximal, characteristic, complemented
16C2×C47×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23#15689823—24no—
24#15689823C2218yes—
25Q8×D188—24no—
26Q8×D188C2218yescomplemented
27C2×#13094024—21no—
28C2×#13094024C2211yescharacteristic
29C2×#13094017—21no—
30C2×#13094016C2211yescharacteristic
31C2×#13094007—21no—
32C2×#13094004—21no—
33C2×#13094004—21no—
34C2×#13094004C2211yescharacteristic
35C2×#13094004C2211yescharacteristic
36C2×#13093997—21no—
37C2×#13093995C2211yescharacteristic
38C2×#13093995C2211yescharacteristic
39C2×C4×D188—21no—
40C2×C4×D188C2211yescharacteristic
41C2×C4×C22⋊D47—21no—
42C2×#13093982C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44#15689492C2218yescomplemented
45#15689466C2218yescomplemented
46#15689460C2218yescomplemented
47#15689430C2218yescomplemented
48#15689368C2218yescomplemented
49#15689351C2218yescomplemented
50#15689328C2218yescomplemented
51#15689260C2218yescomplemented
52#15689260C2218yescomplemented
53#15689196C2218yescomplemented
54C2×#13093957C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×C4⋊(C47⋊C8)C2211yescharacteristic
57#15689130C2218yescomplemented
58C2×#13093949C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66#103×D47C2218yescomplemented
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
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×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C22×Dic94C2311yescharacteristic
81C2×Q8×D47—22no—
82C2×Q8×D47—22no—
83C2×Q8×D47—24no—
84C2×Q8×D47—24no—
85C2×Q8×D47—42no—
86C2×Q8×D47—42no—
87C2×Q8×D47C2314yes—
88C2×Q8×D47C2314yes—
89C22×D188D411yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47C2311yescharacteristic
96C22×C4×D47C2311yescharacteristic
97C2×#10625335—42no—
98C2×#10625335—42no—
99C2×#10625335C2314yes—
100C2×#10625335C2314yes—
101C2×#10625324—42no—
102C2×#10625324C2314yes—
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2311yescharacteristic
105C2×C8×D47—42no—
106C2×C8×D47C2314yes—
107#13094024—22no—
108#13094024—28no—
109#13094024C2314yes—
110#13094017—28no—
111#13094016—22no—
112#13094016C2314yes—
113#13094007—28no—
114#13094004—22no—
115#13094004—22no—
116#13094004—28no—
117#13094004—28no—
118#13094004C2314yes—
119#13094004C2314yes—
120#13093997—28no—
121#13093995—22no—
122#13093995—22no—
123#13093995C2314yes—
124#13093995C2314yes—
125C4×D188—28no—
126C4×D188D414yes—
127C4×D188C2314yes—
128C4×C22⋊D47—28no—
129#13093982—22no—
130#13093982C2314yes—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47—21no—
135C2×C4⋊Dic47D411yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C4⋊C4×D47—22no—
142C4⋊C4×D47C2314yes—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4D411yescharacteristic
149C2×(C2×D47)⋊C4D411yescharacteristic
150C2×C4×Dic47—21no—
151#13093957C2314yes—
152#13093955C2314yes—
153C4⋊(C47⋊C8)C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093949C2314yes—
158#13093948C2314yes—
159#13093948C2314yes—
160#13093947C2314yes—
161#13093947C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
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×D47C2×D411yescharacteristic
187C23×D47C2×D411yescharacteristic
188C2×Q8×C47—21no—
189C2×Q8×C47—22no—
190C2×Q8×C47#4114yes—
191C2×Q8×C47C2412yes—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47C2412yes—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—24no—
200C22×C4×C47—82no—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—24no—
205C2×C22⋊D47—24no—
206C2×C22⋊D47—44no—
207C2×C22⋊D47—82no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214Q8×D47—28no—
215Q8×D47—28no—
216Q8×D47—44no—
217Q8×D47—44no—
218Q8×D47—48no—
219Q8×D47—48no—
220C2×D188—24no—
221C2×D188C2×D414yes—
222C2×C4×D47—22no—
223C2×C4×D47—22no—
224C2×C4×D47—22no—
225C2×C4×D47—22no—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—24no—
229C2×C4×D47—44no—
230C2×C4×D47—44no—
231C2×C4×D47—82no—
232C2×C4×D47C2×D412yes—
233C2×C4×D47C2×D412yes—
234C2×C4×D47C2412yes—
235C2×C4×D47C2412yes—
236C2×Dic94—22no—
237C2×Dic94—22no—
238C2×Dic94—22no—
239C2×Dic94—22no—
240C2×Dic94—21no—
241C2×Dic94—21no—
242C2×Dic94—24no—
243C2×Dic94—24no—
244C2×Dic94—44no—
245C2×Dic94—44no—
246C2×Dic94C2412yes—
247C2×Dic94C2412yes—
248SD16×C47—28no—
249C2×C8×C47—22no—
250C2×C8×C47—22no—
251C2×C8×C47C2412yes—
252C2×C8×C47C2412yes—
253C4⋊C4×C47—24no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47C2412yes—
257C4⋊C4×C47C2412yes—
258C22⋊C4×C47—24no—
259C42×C47—24no—
260C42×C47C2×D412yes—
261C42×C47C2412yes—
262C22⋊Dic47—24no—
263C22⋊Dic47—24no—
264#10625335—44no—
265#10625335—44no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4C2×D414yes—
270(C2×D47)⋊C4C2×D414yes—
271C4⋊Dic47—21no—
272C4⋊Dic47—24no—
273C4⋊Dic47—24no—
274C4⋊Dic47—21no—
275C4⋊Dic47—24no—
276C4⋊Dic47—24no—
277C4⋊Dic47C2×D414yes—
278C4⋊Dic47C2412yes—
279C4⋊Dic47C2412yes—
280Dic47⋊C4—24no—
281Dic47⋊C4—24no—
282Dic47⋊C4—24no—
283C4×Dic47—24no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8C2412yes—
287C2×C47⋊C8C2412yes—
288#10625324—44no—
289C8×D47—44no—
290C23×C47—22no—
291C23×C47—42no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47C22×D411yescharacteristic
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47#13714yes—
301C22×D47C22×D412yes—
302C22×D47C22×D412yes—
303Q8×C47—24no—
304Q8×C47—22no—
305Q8×C47C2×#4114yes—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—42no—
309C2×C4×C47—24no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—84no—
318C2×C4×C47C22×D412yes—
319C2×C4×C47C22×D412yes—
320C2×C4×C47C22×D411yescharacteristic
321C2×C4×C47C2×#4112yes—
322C2×C4×C47H(5,𝔽2)12yes—
323C2×C4×C47C2511yescharacteristic
324C22⋊D47—48no—
325C22⋊D47—84no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47C22×D412yes—
337C2×Dic47C22×D412yes—
338D188—28no—
339C4×D47—24no—
340C4×D47—24no—
341C4×D47—22no—
342C4×D47—22no—
343C4×D47—22no—
344C4×D47—22no—
345C4×D47—48no—
346C4×D47—48no—
347C4×D47—84no—
348Dic94—22no—
349Dic94—22no—
350Dic94—22no—
351Dic94—22no—
352Dic94—48no—
353Dic94—48no—
354Dic94—42no—
355Dic94—42no—
356C8×C47—22no—
357C8×C47—22no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360C2×#3320—471nomaximal, Sylow
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—84no—
365C22×C47#54612yes—
366C22×C47C2×#13712yes—
367C22×C47#57712yes—
368C22×C47C23×D411yescharacteristic
369C2×D47—22no—
370C2×D47—28no—
371C2×D47—22no—
372C2×D47—22no—
373C2×D47—22no—
374C2×D47—22no—
375C2×D47—44no—
376C2×D47C2×#13714yes—
377C4×C47—24no—
378C4×C47—22no—
379C4×C47—22no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47#54612yes—
383C4×C47C22×#4111yescharacteristic
384C4×C47C2×H(5,𝔽2)11yescharacteristic
385Dic47—22no—
386Dic47—22no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390Dic47—42no—
391C2×#553—471no—
392C2×D4×Q8—471no—
393#3320—4716no—
394C2×#491—471no—
395C2×#484—471no—
396C2×#485—471no—
397C2×#479—471no—
398C2×#468—471no—
399C2×#465—471no—
400C2×#461—471no—
401C2×#448—471no—
402C2×#448—471no—
403C2×#440D4711yescharacteristic, complemented
404C2×#435—471no—
405C2×#419—471no—
406C22×#103—471no—
407C2×C47—82no—
408C2×C47#332014yescomplemented
409C2×C47C2×#54611yescharacteristic
410C2×C47C22×#13711yescharacteristic
411C2×C47C2×#57711yescharacteristic
412D47—24no—
413D47—42no—
414C23×Q8—471no—
415C23×Q8—471no—
416C22×SD16—471no—
417C22×SD16—471no—
418C22×SD16C2×D4711yescharacteristic
419C22×M16—471no—
420C23×C8—471no—
421#553—478no—
422#553—944no—
423D4×Q8—478no—
424D4×Q8—944no—
425C2×C4⋊Q8—471no—
426C2×C4⋊Q8—941no—
427C2×#126—941no—
428C2×#125—471no—
429C2×#123—941no—
430C2×C22⋊Q8—471no—
431C2×C22⋊Q8—471no—
432C2×C22⋊Q8—941no—
433C2×C22⋊Q8—941no—
434C2×#121—471no—
435C2×#121—471no—
436C2×#121—941no—
437C2×C4×Q8C2×D4711yescharacteristic
438C2×C4×D4—471no—
439C2×C4×D4—941no—
440C2×C4×D4—941no—
441C2×C4×D4C2×D4711yescharacteristic
442C2×#117—471no—
443C22×C4⋊C4—471no—
444#491—478no—
445#485—478no—
446#484—478no—
447#479—478no—
448#468—478no—
449#465—478no—
450#461—478no—
451#448—478no—
452#448—478no—
453#440C2×D4718yescomplemented
454#435—478no—
455C2×#107—471no—
456C2×#107C2×D4711yescharacteristic
457C2×#106—471no—
458C2×C4⋊C8—471no—
459#419—478no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#103—471no—
463C2×#103—471no—
464C2×#103—471no—
465C2×#103—471no—
466C2×#103—471no—
467C2×#103—471no—
468C2×#103—478no—
469C2×#103C2×D4711yescharacteristic
470C2×#102C2×D4711yescharacteristic
471C2×C22⋊C8—471no—
472C2×C22⋊C8—471no—
473C2×#97C2×D4711yescharacteristic
474C47C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—474no—
476C22×Q8—474no—
477C22×Q8—471no—
478C22×Q8—471no—
479C22×Q8—941no—
480C22×Q8—941no—
481C22×Q8—942no—
482C22×Q8—942no—
483C22×Q8—944no—
484C22×Q8—944no—
485C22×Q8—1882no—
486C22×Q8—1882no—
487C22×Q8C22×D4711yescharacteristic
488C22×D4—471no—
489C22×D4—941no—
490C22×D4—941no—
491C22×D4C22×D4711yescharacteristic
492C23×C4—21no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—941no—
496C23×C4—941no—
497C23×C4—941no—
498C2×SD16—24no—
499C2×SD16—474no—
500C2×SD16—474no—
501C2×SD16—1882no—
502C2×SD16—1882no—
503C2×SD16C22×D4714yes—
504C2×M16—474no—
505C2×M16—1882no—
506C22×C8—471no—
507C22×C8—471no—
508C22×C8—474no—
509C22×C8—1882no—
510C22×C8C22×D4711yescharacteristic
511C22×C8C22×D4711yescharacteristic
512C4⋊Q8—474no—
513C4⋊Q8—948no—
514C4⋊Q8—942no—
515#126—948no—
516#125—474no—
517#125—942no—
518#123—948no—
519C22⋊Q8—474no—
520C22⋊Q8—474no—
521C22⋊Q8—948no—
522C22⋊Q8—948no—
523C22⋊Q8—942no—
524C22⋊Q8—942no—
525#121—474no—
526#121—474no—
527#121—948no—
528#121—942no—
529#121—942no—
530C4×Q8—22no—
531C4×Q8C22×D4714yes—
532C4×D4—22no—
533C4×D4—474no—
534C4×D4—474no—
535C4×D4—948no—
536C4×D4—948no—
537C4×D4C22×D4714yes—
538#117—474no—
539#117—942no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—471no—
542C2×C4⋊C4—471no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—474no—
545C2×C4⋊C4—942no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4—941no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4—941no—
550C2×C4⋊C4—941no—
551C2×C4⋊C4—941no—
552C2×C4⋊C4—941no—
553C2×C4⋊C4C22×D4711yescharacteristic
554C2×C4⋊C4C22×D4711yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—471no—
557C2×C22⋊C4—471no—
558C2×C22⋊C4—941no—
559C2×C22⋊C4—941no—
560C2×C22⋊C4—941no—
561C2×C22⋊C4—941no—
562C2×C22⋊C4—941no—
563C2×C42—21no—
564C2×C42—941no—
565C2×C42C22×D4711yescharacteristic
566#107—474no—
567#107C22×D4714yes—
568#106—474no—
569C4⋊C8—474no—
570#103—474no—
571#103—474no—
572#103—474no—
573#103—474no—
574#103—474no—
575#103—474no—
576#103—474no—
577#103—474no—
578#103C22×D4714yes—
579#102C22×D4714yes—
580C22⋊C8—474no—
581C22⋊C8—474no—
582#97C22×D4714yes—
583C24—21no—
584C24—471no—
585C24—471no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—472no—
589C2×Q8—472no—
590C2×Q8—944no—
591C2×Q8—944no—
592C2×Q8—941no—
593C2×Q8—941no—
594C2×Q8—948no—
595C2×Q8—948no—
596C2×Q8—942no—
597C2×Q8—942no—
598C2×Q8—942no—
599C2×Q8—942no—
600C2×Q8—1884no—
601C2×Q8—1884no—
602C2×Q8—1884no—
603C2×Q8—1884no—
604C2×Q8—1888no—
605C2×Q8—1888no—
606C2×Q8#1062535014yes—
607C2×Q8C23×D4712yes—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—474no—
612C2×D4—944no—
613C2×D4—944no—
614C2×D4—944no—
615C2×D4—3762no—
616C2×D4—1884no—
617C2×D4C23×D4712yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—82no—
623C22×C4—471no—
624C22×C4—471no—
625C22×C4—472no—
626C22×C4—472no—
627C22×C4—472no—
628C22×C4—472no—
629C22×C4—944no—
630C22×C4—944no—
631C22×C4—944no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—941no—
640C22×C4—3762no—
641C22×C4—1884no—
642C22×C4—1884no—
643C22×C4D4×D4711yescharacteristic
644C22×C4D4×D4711yescharacteristic
645C22×C4C23×D4711yescharacteristic
646SD16—28no—
647SD16—1884no—
648SD16—1884no—
649M16—1884no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—472no—
653C2×C8—472no—
654C2×C8—942no—
655C2×C8—942no—
656C2×C8—1884no—
657C2×C8C23×D4712yes—
658C2×C8C23×D4712yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—474no—
663C4⋊C4—472no—
664C4⋊C4—472no—
665C4⋊C4—944no—
666C4⋊C4—944no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—941no—
671C4⋊C4—941no—
672C4⋊C4—944no—
673C4⋊C4—944no—
674C4⋊C4C23×D4712yes—
675C4⋊C4C23×D4712yes—
676C22⋊C4—24no—
677C22⋊C4—474no—
678C22⋊C4—474no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C22⋊C4—944no—
682C22⋊C4—944no—
683C22⋊C4—944no—
684C42—24no—
685C42—944no—
686C42D4×D4712yes—
687C42C23×D4712yes—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—474no—
693C23—472no—
694C23—472no—
695C23—942no—
696C23—942no—
697C23—942no—
698C23—942no—
699C23—942no—
700C23C2×D4×D4711yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—942no—
704Q8—942no—
705Q8—942no—
706Q8—942no—
707Q8—1888no—
708Q8—1888no—
709Q8—1882no—
710Q8—1882no—
711Q8C2×#1062535014yes—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—948no—
716D4—3764no—
717D4—1888no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—84no—
727C2×C4—472no—
728C2×C4—472no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—944no—
732C2×C4—944no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—3764no—
742C2×C4—1888no—
743C2×C4—1888no—
744C2×C4—1882no—
745C2×C4—1882no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4C2×D4×D4712yes—
749C2×C4C2×D4×D4712yes—
750C2×C4C2×D4×D4711yescharacteristic
751C2×C4C2×#1062535012yes—
752C2×C4#1309407012yes—
753C2×C4C24×D4711yescharacteristic
754C8—22no—
755C8—22no—
756C8—942no—
757C8—942no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—474no—
763C22—942no—
764C22—948no—
765C22—942no—
766C22—942no—
767C22—942no—
768C22—942no—
769C22—1884no—
770C22#1568976912yes—
771C22#137×D4712yes—
772C22#1568993312yes—
773C22C22×D4×D4711yescharacteristic
774C4—24no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—942no—
780C4—942no—
781C4—1882no—
782C4—1882no—
783C4—1882no—
784C4—1882no—
785C4#1568976912yes—
786C4C22×#1062535011yescharacteristic
787C4C2×#1309407011yescharacteristic
788C2—82no—
789C2—944no—
790C2—1882no—
791C2#2025556414yesdirect product factor
792C2C2×#1568976911yescharacteristic
793C2C2×#137×D4711yescharacteristic
794C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#440C2
socleC23×C47C22×D4
prime radicalC2×#15689823C2
hypercenterC2×#440D47
hypocenterC47C2×#3320
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×Q8×D188C2semidirect
3. #20255564C2direct (N × H)
4. C2×#15689492C2semidirect
5. C2×#15689460C2semidirect
6. C2×#15689466C2semidirect
7. C2×#15689430C2semidirect
8. C2×#15689368C2semidirect
9. C2×#15689351C2semidirect
10. C2×#15689328C2semidirect
11. C2×#15689260C2semidirect
12. C2×#15689260C2semidirect
13. C2×#15689196C2semidirect
14. C2×#15689130C2semidirect
15. C2×#103×D47C2semidirect
16. C2×C47×#440C2semidirect
26. Q8×D188C22semidirect
44. #15689492C22semidirect
45. #15689466C22semidirect
46. #15689460C22semidirect
47. #15689430C22semidirect
48. #15689368C22semidirect
49. #15689351C22semidirect
50. #15689328C22semidirect
51. #15689260C22semidirect
52. #15689260C22semidirect
53. #15689196C22semidirect
57. #15689130C22semidirect
66. #103×D47C22semidirect
72. C47×#440C22semidirect
403. C2×#440D47semidirect
408. C2×C47#3320semidirect
453. #440C2×D47semidirect
474. C47C2×#3320semidirect
791. C2#20255564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898232
C2×Q8×D1882
#202555642
C2×#156894922
C2×#156894602
C2×#156894662
C2×#156894302
C2×#156893682
C2×#156893512
C2×#156893282
C2×#156892602
C2×#156891962
C2×#156891302
C2×#103×D472
C2×C47×#4402
C2×#332047