Finite Group Databasebeta

← C2×#20252841 #27083096

Subgroups — C2×#20252841 #27083096

Order 12032.

2874 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094046C211yesmaximal, characteristic, complemented
2C22×#13094044C211yesmaximal, characteristic, complemented
3C2×#15689669C211yesmaximal, characteristic, complemented
4C2×#15689591C211yesmaximal, characteristic, complemented
5#20252841C2116yesmaximal, direct product factor
6C2×#15689348C211yesmaximal, characteristic, complemented
7C2×#15689344C211yesmaximal, characteristic, complemented
8C2×#15689332C211yesmaximal, characteristic, complemented
9C2×#15689322C211yesmaximal, characteristic, complemented
10C2×#15689341C211yesmaximal, characteristic, complemented
11C2×#15689337C211yesmaximal, characteristic, complemented
12C2×#15689327C211yesmaximal, characteristic, complemented
13C2×#15689317C211yesmaximal, characteristic, complemented
14C22×Dic47⋊C8C211yesmaximal, characteristic, complemented
15C2×#15689117C211yesmaximal, characteristic, complemented
16C2×C47×#416C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C2×#13094046—28no—
20C2×#13094046C2218yescomplemented
21C2×#13094044—28no—
22C2×#13094044C2218yescomplemented
23C22×Dic188C2211yescharacteristic
24C22×#10625337C2211yescharacteristic
25C22×#10625325C2211yescharacteristic
26C22×#10625325C2211yescharacteristic
27C22×#10625335C2211yescharacteristic
28C22×#10625336C2211yescharacteristic
29C22×D376C2211yescharacteristic
30C22×#10625334C2211yescharacteristic
31C23×C47⋊C8C2211yescharacteristic
32#15689669—24no—
33#15689669C2218yescomplemented
34C2×#13094022C2211yescharacteristic
35C2×#13094020C2211yescharacteristic
36C2×#13094013C2211yescharacteristic
37C2×#13094011C2211yescharacteristic
38C2×#13093996—21no—
39C2×#13093996—21no—
40#15689591—24no—
41#15689591C2218yescomplemented
42C2×#13093989C2211yescharacteristic
43C2×#13093989C2211yescharacteristic
44C2×#13093986C2211yescharacteristic
45C2×#13093986C2211yescharacteristic
46C2×C4×C22⋊D47—21no—
47C2×C4×C22⋊D47—21no—
48C2×(C22⋊D47)⋊C4—21no—
49C2×(C22⋊D47)⋊C4—21no—
50C2×#13093981—21no—
51C22×C4×Dic47C2211yescharacteristic
52C2×C42×D47—21no—
53#15689348C2218yescomplemented
54#15689344C2218yescomplemented
55#15689341C2218yescomplemented
56#15689337C2218yescomplemented
57#15689332C2218yescomplemented
58#15689327C2218yescomplemented
59#15689322C2218yescomplemented
60#15689317C2218yescomplemented
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×Dic47⋊C8C2211yescharacteristic
64C2×Dic47⋊C8C2211yescharacteristic
65C2×Dic47⋊C8C2218yescomplemented
66#15689117C2218yescomplemented
67C2×#13093947C2211yescharacteristic
68C2×#13093947C2211yescharacteristic
69C2×#13093944C2211yescharacteristic
70C2×#13093944C2211yescharacteristic
71C22×#41×C47C2211yescharacteristic
72C23×C8×C47C2211yescharacteristic
73C2×#117×C47C2211yescharacteristic
74C47×#416C2218yescomplemented
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C2×#102×C47C2211yescharacteristic
78C2×#102×C47C2211yescharacteristic
79C2×#10625350—22no—
80C2×#10625350—24no—
81C2×#10625350—22no—
82C2×#10625350—24no—
83C2×#10625350—24no—
84C2×#10625350D418yescomplemented
85C2×#10625350C2314yes—
86C2×#10625350C2314yes—
87C22×Dic94C2311yescharacteristic
88C22×Dic94C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×D188C2311yescharacteristic
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C23×Dic47D411yescharacteristic
96C23×Dic47D411yescharacteristic
97C22×C4×D47—21no—
98C22×C4×D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47—21no—
101#13094046—232no—
102#13094044—232no—
103C2×Dic188—24no—
104C2×Dic188C2314yes—
105C2×#10625337—24no—
106C2×#10625337C2314yes—
107C2×#10625325—24no—
108C2×#10625325—24no—
109C2×#10625325C2314yes—
110C2×#10625325C2314yes—
111C2×#10625335—24no—
112C2×#10625335C2314yes—
113C2×#10625336—24no—
114C2×#10625336C2314yes—
115C2×D376—24no—
116C2×D376C2314yes—
117C2×#10625334—24no—
118C2×#10625334C2314yes—
119C22×C47⋊C8—24no—
120C22×C47⋊C8C2311yescharacteristic
121C22×C47⋊C8C2311yescharacteristic
122C22×C47⋊C8C2314yes—
123#13094022—22no—
124#13094022C2314yes—
125#13094020—22no—
126#13094020C2314yes—
127#13094013—22no—
128#13094013C2314yes—
129#13094011—22no—
130#13094011C2314yes—
131#13093996—28no—
132#13093996—28no—
133#13093989—22no—
134#13093989—22no—
135#13093989C2314yes—
136#13093989C2314yes—
137#13093986—22no—
138#13093986—22no—
139#13093986C2314yes—
140#13093986C2314yes—
141C4×C22⋊D47—28no—
142C4×C22⋊D47—28no—
143(C22⋊D47)⋊C4—28no—
144(C22⋊D47)⋊C4—28no—
145#13093981—28no—
146C2×Dic47⋊C4—21no—
147C2×Dic47⋊C4—21no—
148C2×Dic47⋊C4—21no—
149C2×Dic47⋊C4—21no—
150C2×C22⋊Dic47—21no—
151C2×C22⋊Dic47—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×C4×Dic47—21no—
157C2×C4×Dic47—21no—
158C2×C4×Dic47D411yescharacteristic
159C2×C4×Dic47D411yescharacteristic
160C2×C4×Dic47D414yes—
161C2×C4×Dic47C2311yescharacteristic
162C2×C4×Dic47C2311yescharacteristic
163C2×C4×Dic47C2314yes—
164C42×D47—28no—
165Dic47⋊C8C2314yes—
166Dic47⋊C8C2314yes—
167Dic47⋊C8C2314yes—
168Dic47⋊C8C2314yes—
169#13093947C2314yes—
170#13093947C2314yes—
171#13093944C2314yes—
172#13093944C2314yes—
173C2×#41×C47—22no—
174C2×#41×C47—24no—
175C2×#41×C47—24no—
176C2×#41×C47C2314yes—
177C22×Q8×C47C2311yescharacteristic
178C22×D4×C47—21no—
179C22×D4×C47C2311yescharacteristic
180C23×C4×C47—21no—
181C23×C4×C47C2311yescharacteristic
182C22×C8×C47—24no—
183C22×C8×C47C2311yescharacteristic
184C22×C8×C47C2311yescharacteristic
185C22×C8×C47C2314yes—
186#117×C47—22no—
187#117×C47C2314yes—
188C2×C4⋊C4×C47C2311yescharacteristic
189C2×C4⋊C4×C47C2311yescharacteristic
190C2×C22⋊C4×C47—21no—
191C2×C42×C47—21no—
192#103×C47C2314yes—
193#103×C47C2314yes—
194#102×C47C2314yes—
195#102×C47C2314yes—
196C24×C47—21no—
197C24×C47C2×D411yescharacteristic
198C23×D47—21no—
199C23×D47—21no—
200#41×C47—28no—
201#41×C47—28no—
202#41×C47—48no—
203C2×Q8×C47—21no—
204C2×Q8×C47—22no—
205C2×Q8×C47—22no—
206C2×Q8×C47C2412yes—
207C2×D4×C47—24no—
208C2×D4×C47—22no—
209C2×D4×C47—21no—
210C2×D4×C47—22no—
211C2×D4×C47—44no—
212C2×D4×C47C2412yes—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—24no—
217C22×C4×C47—44no—
218C22×C4×C47C2×D412yes—
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D414yes—
221C22×C4×C47#4114yes—
222C22×C4×C47C2411yescharacteristic
223C22×C4×C47C2412yes—
224C2×C22⋊D47—28no—
225C2×C22⋊D47—24no—
226C2×C22⋊D47—24no—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—44no—
230C2×C22⋊D47—44no—
231C2×C22⋊D47—44no—
232C22×Dic47—21no—
233C22×Dic47—24no—
234C22×Dic47—21no—
235C22×Dic47—42no—
236C22×Dic47C2×D411yescharacteristic
237C22×Dic47C2×D411yescharacteristic
238C22×Dic47C2×D411yescharacteristic
239C22×Dic47C2×D414yes—
240C22×Dic47C2×D414yes—
241C22×Dic47C2×D411yescharacteristic
242#10625350—216no—
243#10625350—28no—
244#10625350—28no—
245#10625350—28no—
246#10625350—48no—
247#10625350C2×D4116yescomplemented
248C2×D188—21no—
249C2×D188—22no—
250C2×D188—22no—
251C2×D188—22no—
252C2×D188—21no—
253C2×D188C2×D414yes—
254C2×D188C2412yes—
255C2×D188C2412yes—
256C2×C4×D47—28no—
257C2×C4×D47—24no—
258C2×C4×D47—24no—
259C2×C4×D47—24no—
260C2×C4×D47—24no—
261C2×C4×D47—44no—
262C2×C4×D47—44no—
263C2×C4×D47—44no—
264C2×Dic94—21no—
265C2×Dic94—22no—
266C2×Dic94—22no—
267C2×Dic94—22no—
268C2×Dic94—21no—
269C2×Dic94C2×D414yes—
270C2×Dic94C2412yes—
271C2×Dic94C2412yes—
272C2×C8×C47—22no—
273C2×C8×C47—22no—
274C2×C8×C47—28no—
275C2×C8×C47C2412yes—
276C2×C8×C47C2412yes—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47C2412yes—
280C4⋊C4×C47C2412yes—
281C22⋊C4×C47—24no—
282C42×C47—24no—
283C22⋊Dic47—24no—
284C22⋊Dic47—24no—
285#10625337—28no—
286#10625336—28no—
287#10625335—28no—
288#10625334—28no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293Dic47⋊C4—24no—
294Dic47⋊C4—24no—
295Dic47⋊C4—24no—
296Dic47⋊C4—24no—
297C4×Dic47—24no—
298C4×Dic47—24no—
299C4×Dic47C2×D414yes—
300C4×Dic47C2×D414yes—
301C4×Dic47C2×D412yes—
302C4×Dic47C2×D412yes—
303C4×Dic47C2412yes—
304C4×Dic47C2412yes—
305C2×C47⋊C8—22no—
306C2×C47⋊C8—22no—
307C2×C47⋊C8—28no—
308C2×C47⋊C8C2412yes—
309C2×C47⋊C8C2412yes—
310Dic188—28no—
311D376—28no—
312#10625325—28no—
313#10625325—28no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—42no—
318C23×C47—42no—
319C23×C47—42no—
320C23×C47#12114yes—
321C23×C47C22×D412yes—
322C23×C47C22×D411yescharacteristic
323C22×D47—24no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—42no—
331Q8×C47—22no—
332Q8×C47—22no—
333Q8×C47—42no—
334D4×C47—22no—
335D4×C47—22no—
336D4×C47—48no—
337D4×C47—42no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—42no—
342C2×C4×C47—42no—
343C2×C4×C47—42no—
344C2×C4×C47—48no—
345C2×C4×C47#12114yes—
346C2×C4×C47#12118yes—
347C2×C4×C47C22×D412yes—
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C22×D412yes—
350C2×C4×C47C22×D414yes—
351C2×C4×C47C2×#4112yes—
352C2×C4×C47C2×#4114yes—
353C2×C4×C47C2511yescharacteristic
354C22⋊D47—216no—
355C22⋊D47—48no—
356C22⋊D47—48no—
357C22⋊D47—48no—
358C2×Dic47—24no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—28no—
364C2×Dic47—22no—
365C2×Dic47—44no—
366C2×Dic47—42no—
367C2×Dic47#13514yescomplemented
368C2×Dic47C22×D412yes—
369C2×Dic47C22×D412yes—
370C2×Dic47C22×D412yes—
371C2×Dic47C22×D412yes—
372D188—24no—
373D188—22no—
374D188—22no—
375D188—22no—
376D188—42no—
377D188C22×D414yes—
378C4×D47—216no—
379C4×D47—48no—
380C4×D47—48no—
381C4×D47—48no—
382Dic94—24no—
383Dic94—22no—
384Dic94—22no—
385Dic94—22no—
386Dic94—42no—
387Dic94C22×D414yes—
388C8×C47—22no—
389C8×C47—22no—
390C47⋊C8—22no—
391C47⋊C8—22no—
392C2×#3035—471nomaximal, Sylow
393C22×C47—28no—
394C22×C47—22no—
395C22×C47—22no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—84no—
400C22×C47C2×#12114yes—
401C22×C47C2×#12112yes—
402C22×C47C2×#13512yes—
403C22×C47#57512yes—
404C22×C47C23×D411yescharacteristic
405C2×D47—24no—
406C2×D47—48no—
407C2×D47—42no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—42no—
412C2×D47—84no—
413C4×C47—42no—
414C4×C47—42no—
415C4×C47—42no—
416C4×C47C2×#12112yes—
417C4×C47C2×#12114yes—
418C4×C47C23×D411yescharacteristic
419C4×C47C22×#4111yescharacteristic
420Dic47—24no—
421Dic47—22no—
422Dic47—22no—
423Dic47—22no—
424Dic47—42no—
425Dic47C2×#13514yescomplemented
426C22×#135—471no—
427C22×#135—471no—
428C2×#532—471no—
429C2×C4×#41—471no—
430#3035—4716no—
431C2×#464—471no—
432C2×#464—471no—
433C2×#462—471no—
434C2×#460—471no—
435C2×#463—471no—
436C2×#463—471no—
437C2×#461—471no—
438C2×#459—471no—
439C22×C4⋊C8—471no—
440C2×#416—471no—
441C2×#416D4711yescharacteristic, complemented
442C2×C47—24no—
443C2×C47—82no—
444C2×C47#303514yescomplemented
445C2×C47C22×#12111yescharacteristic
446C2×C47C22×#13511yescharacteristic
447C2×C47C2×#57511yescharacteristic
448D47—44no—
449D47—82no—
450C22×#41—471no—
451C22×#41—471no—
452C22×#41C2×D4711yescharacteristic
453C2×#135—478no—
454C2×#135—478no—
455C2×#135—948no—
456C2×#135—948no—
457C22×Q16—471no—
458C22×Q16—471no—
459C22×SD16—471no—
460C22×SD16—471no—
461C22×SD16—471no—
462C22×SD16—471no—
463C22×D8—471no—
464C22×D8—471no—
465C23×C8—471no—
466C23×C8C2×D4711yescharacteristic
467#532—478no—
468#532—944no—
469C2×C4⋊Q8—471no—
470C2×#127—471no—
471C2×#124—471no—
472C2×#124—471no—
473C2×#121—941no—
474C2×#121—941no—
475C4×#41—478no—
476C4×#41—944no—
477C2×C4×Q8—471no—
478C2×C4×Q8—471no—
479C2×C4×D4—471no—
480C2×C4×D4—471no—
481C2×C4×D4—941no—
482C2×C4×D4—941no—
483C2×C4×D4—941no—
484C2×C4×D4—941no—
485C2×#117—941no—
486C2×#117C2×D4711yescharacteristic
487C22×C42—471no—
488C22×C42—941no—
489#464—478no—
490#464—478no—
491#463—478no—
492#463—478no—
493#462—478no—
494#461—478no—
495#460—478no—
496#459—478no—
497C2×C4⋊C8—471no—
498C2×C4⋊C8—471no—
499C2×C4⋊C8—471no—
500C2×C4⋊C8—471no—
501C2×C4⋊C8—478no—
502#416—478no—
503#416C2×D4718yescomplemented
504C2×#103—471no—
505C2×#103—471no—
506C2×#103C2×D4711yescharacteristic
507C2×#103C2×D4711yescharacteristic
508C2×#102—471no—
509C2×#102—471no—
510C2×#102C2×D4711yescharacteristic
511C2×#102C2×D4711yescharacteristic
512C47C2×#303511yescharacteristic, complemented, Sylow
513C2×#41—22no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—478no—
517C2×#41—474no—
518C2×#41—474no—
519C2×#41—944no—
520C2×#41—942no—
521C2×#41—942no—
522C2×#41—944no—
523C2×#41—944no—
524C2×#41C22×D4714yes—
525C22×Q8—471no—
526C22×Q8—471no—
527C22×Q8C22×D4711yescharacteristic
528C22×D4—21no—
529C22×D4—471no—
530C22×D4—471no—
531C22×D4—941no—
532C22×D4—941no—
533C22×D4—941no—
534C22×D4—941no—
535C22×D4C22×D4711yescharacteristic
536C23×C4—21no—
537C23×C4—471no—
538C23×C4—471no—
539C23×C4—941no—
540C23×C4—941no—
541C23×C4—941no—
542C23×C4—941no—
543C23×C4C22×D4711yescharacteristic
544#135—9432no—
545#135—9432no—
546C2×Q16—474no—
547C2×Q16—474no—
548C2×Q16—944no—
549C2×Q16—944no—
550C2×SD16—474no—
551C2×SD16—474no—
552C2×SD16—474no—
553C2×SD16—474no—
554C2×SD16—944no—
555C2×SD16—944no—
556C2×SD16—944no—
557C2×SD16—944no—
558C2×D8—474no—
559C2×D8—474no—
560C2×D8—944no—
561C2×D8—944no—
562C22×C8—24no—
563C22×C8—471no—
564C22×C8—471no—
565C22×C8—474no—
566C22×C8—944no—
567C22×C8C22×D4711yescharacteristic
568C22×C8C22×D4711yescharacteristic
569C22×C8C22×D4714yes—
570C4⋊Q8—474no—
571C4⋊Q8—942no—
572#127—474no—
573#127—942no—
574#124—474no—
575#124—474no—
576#124—942no—
577#124—942no—
578#121—948no—
579#121—948no—
580C4×Q8—474no—
581C4×Q8—474no—
582C4×Q8—942no—
583C4×Q8—942no—
584C4×D4—474no—
585C4×D4—474no—
586C4×D4—942no—
587C4×D4—942no—
588C4×D4—948no—
589C4×D4—948no—
590C4×D4—948no—
591C4×D4—948no—
592#117—22no—
593#117—948no—
594#117C22×D4714yes—
595C2×C4⋊C4—941no—
596C2×C4⋊C4—941no—
597C2×C4⋊C4—941no—
598C2×C4⋊C4—941no—
599C2×C4⋊C4C22×D4711yescharacteristic
600C2×C4⋊C4C22×D4711yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—941no—
603C2×C22⋊C4—941no—
604C2×C22⋊C4—941no—
605C2×C22⋊C4—941no—
606C2×C22⋊C4—941no—
607C2×C22⋊C4—941no—
608C2×C42—21no—
609C2×C42—474no—
610C2×C42—471no—
611C2×C42—471no—
612C2×C42—471no—
613C2×C42—471no—
614C2×C42—474no—
615C2×C42—948no—
616C2×C42—941no—
617C2×C42—941no—
618C4⋊C8—474no—
619C4⋊C8—474no—
620C4⋊C8—474no—
621C4⋊C8—474no—
622#103—474no—
623#103—474no—
624#103C22×D4714yes—
625#103C22×D4714yes—
626#102—474no—
627#102—474no—
628#102C22×D4714yes—
629#102C22×D4714yes—
630C24—21no—
631C24—941no—
632C24—941no—
633C24D4×D4711yescharacteristic
634#41—28no—
635#41—28no—
636#41—48no—
637#41—4716no—
638#41—9416no—
639#41—948no—
640#41—948no—
641#41—948no—
642#41—1888no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—474no—
647C2×Q8—472no—
648C2×Q8—472no—
649C2×Q8—941no—
650C2×Q8—941no—
651C2×Q8—942no—
652C2×Q8—942no—
653C2×Q8—942no—
654C2×Q8C23×D4712yes—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—44no—
660C2×D4—474no—
661C2×D4—472no—
662C2×D4—472no—
663C2×D4—944no—
664C2×D4—944no—
665C2×D4—948no—
666C2×D4—944no—
667C2×D4—944no—
668C2×D4—941no—
669C2×D4—942no—
670C2×D4—941no—
671C2×D4—942no—
672C2×D4—942no—
673C2×D4—1884no—
674C2×D4—1884no—
675C2×D4—1884no—
676C2×D4C23×D4712yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—44no—
682C22×C4—471no—
683C22×C4—471no—
684C22×C4—471no—
685C22×C4—471no—
686C22×C4—474no—
687C22×C4—474no—
688C22×C4—944no—
689C22×C4—944no—
690C22×C4—944no—
691C22×C4—941no—
692C22×C4—948no—
693C22×C4—944no—
694C22×C4—941no—
695C22×C4—944no—
696C22×C4—1884no—
697C22×C4—1884no—
698C22×C4—1882no—
699C22×C4—1884no—
700C22×C4#1062535014yes—
701C22×C4D4×D4712yes—
702C22×C4D4×D4714yes—
703C22×C4D4×D4711yescharacteristic
704C22×C4C23×D4711yescharacteristic
705C22×C4C23×D4712yes—
706Q16—948no—
707Q16—948no—
708SD16—948no—
709SD16—948no—
710SD16—948no—
711SD16—948no—
712D8—948no—
713D8—948no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—28no—
717C2×C8—472no—
718C2×C8—472no—
719C2×C8—942no—
720C2×C8—942no—
721C2×C8—948no—
722C2×C8C23×D4712yes—
723C2×C8C23×D4712yes—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—944no—
727C4⋊C4—944no—
728C4⋊C4—944no—
729C4⋊C4—944no—
730C4⋊C4C23×D4712yes—
731C4⋊C4C23×D4712yes—
732C22⋊C4—24no—
733C22⋊C4—944no—
734C22⋊C4—944no—
735C22⋊C4—944no—
736C22⋊C4—944no—
737C22⋊C4—944no—
738C22⋊C4—944no—
739C42—24no—
740C42—474no—
741C42—474no—
742C42—472no—
743C42—472no—
744C42—472no—
745C42—472no—
746C42—944no—
747C42—944no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—944no—
755C23—942no—
756C23—942no—
757C23—1882no—
758C23—1882no—
759C23—1882no—
760C23—1882no—
761C23—1882no—
762C23#1309399714yes—
763C23C2×D4×D4712yes—
764C23C2×D4×D4711yescharacteristic
765Q8—22no—
766Q8—22no—
767Q8—42no—
768Q8—474no—
769Q8—944no—
770Q8—942no—
771Q8—942no—
772Q8—942no—
773Q8—1882no—
774D4—22no—
775D4—22no—
776D4—48no—
777D4—42no—
778D4—474no—
779D4—9416no—
780D4—944no—
781D4—942no—
782D4—942no—
783D4—942no—
784D4—1888no—
785D4—1888no—
786D4—1888no—
787D4—1882no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—48no—
795C2×C4—474no—
796C2×C4—472no—
797C2×C4—472no—
798C2×C4—472no—
799C2×C4—472no—
800C2×C4—948no—
801C2×C4—944no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—942no—
806C2×C4—9416no—
807C2×C4—942no—
808C2×C4—1888no—
809C2×C4—1888no—
810C2×C4—1884no—
811C2×C4—1882no—
812C2×C4—1888no—
813C2×C4#1309399714yes—
814C2×C4#1309399718yes—
815C2×C4C2×D4×D4712yes—
816C2×C4C2×D4×D4711yescharacteristic
817C2×C4C2×D4×D4712yes—
818C2×C4C2×D4×D4714yes—
819C2×C4C2×#1062535012yes—
820C2×C4C2×#1062535014yes—
821C2×C4C24×D4711yescharacteristic
822C8—22no—
823C8—22no—
824C8—942no—
825C8—942no—
826C22—22no—
827C22—22no—
828C22—28no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—84no—
833C22—944no—
834C22—3764no—
835C22—1882no—
836C22—1882no—
837C22—1882no—
838C22—1882no—
839C22—1882no—
840C22—1888no—
841C22C2×#1309399714yes—
842C22C2×#1309399712yes—
843C22#135×D4712yes—
844C22#1568992012yes—
845C22C22×D4×D4711yescharacteristic
846C4—42no—
847C4—42no—
848C4—42no—
849C4—474no—
850C4—942no—
851C4—942no—
852C4—942no—
853C4—944no—
854C4—1882no—
855C4C2×#1309399714yes—
856C4C2×#1309399712yes—
857C4C22×D4×D4711yescharacteristic
858C4C22×#1062535011yescharacteristic
859C2—24no—
860C2—82no—
861C2—3762no—
862C2—1884no—
863C2#2025284114yesdirect product factor
864C2C22×#1309399711yescharacteristic
865C2C2×#135×D4711yescharacteristic
866C2C2×#1568992011yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#416C2
socleC23×C47C22×D4
hypercenterC2×#416D47
hypocenterC47C2×#3035
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C22×#13094046C2semidirect
2. C22×#13094044C2semidirect
3. C2×#15689669C2semidirect
4. C2×#15689591C2semidirect
5. #20252841C2direct (N × H)
6. C2×#15689348C2semidirect
7. C2×#15689344C2semidirect
8. C2×#15689332C2semidirect
9. C2×#15689322C2semidirect
10. C2×#15689341C2semidirect
11. C2×#15689337C2semidirect
12. C2×#15689327C2semidirect
13. C2×#15689317C2semidirect
14. C22×Dic47⋊C8C2semidirect
15. C2×#15689117C2semidirect
16. C2×C47×#416C2semidirect
20. C2×#13094046C22semidirect
22. C2×#13094044C22semidirect
33. #15689669C22semidirect
41. #15689591C22semidirect
53. #15689348C22semidirect
54. #15689344C22semidirect
55. #15689341C22semidirect
56. #15689337C22semidirect
57. #15689332C22semidirect
58. #15689327C22semidirect
59. #15689322C22semidirect
60. #15689317C22semidirect
65. C2×Dic47⋊C8C22semidirect
66. #15689117C22semidirect
74. C47×#416C22semidirect
84. C2×#10625350D4semidirect
247. #10625350C2×D4semidirect
367. C2×Dic47#135semidirect
425. Dic47C2×#135semidirect
441. C2×#416D47semidirect
444. C2×C47#3035semidirect
503. #416C2×D47semidirect
512. C47C2×#3035semidirect
863. C2#20252841direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940462
C22×#130940442
C2×#156896692
C2×#156895912
#202528412
C2×#156893482
C2×#156893442
C2×#156893322
C2×#156893222
C2×#156893412
C2×#156893372
C2×#156893272
C2×#156893172
C22×Dic47⋊C82
C2×#156891172
C2×C47×#4162
C2×#303547