Finite Group Databasebeta

← C2×#20254173 #27086834

Subgroups — C2×#20254173 #27086834

Order 12032.

2374 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689635C211yesmaximal, characteristic
2C2×C22⋊Q8×D47C211yesmaximal, characteristic, complemented
3#20254173C2116yesmaximal, direct product factor
4C2×#15689464C211yesmaximal, characteristic, complemented
5C2×#15689455C211yesmaximal, characteristic, complemented
6C2×#15689438C211yesmaximal, characteristic, complemented
7C2×#15689365C211yesmaximal, characteristic, complemented
8C2×#15689363C211yesmaximal, characteristic, complemented
9C2×#15689355C211yesmaximal, characteristic, complemented
10C2×#15689353C211yesmaximal, characteristic, complemented
11C2×#15689287C211yesmaximal, characteristic, complemented
12C2×#15689283C211yesmaximal, characteristic, complemented
13C2×#15689280C211yesmaximal, characteristic, complemented
14C2×#15689263C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C22×Dic188C2211yescharacteristic, complemented
21C22×#10625337C2211yescharacteristic, complemented
22C22×#10625325C2211yescharacteristic, complemented
23C22×#10625336C2211yescharacteristic, complemented
24C22×C8×D47C2211yescharacteristic
25C22×C8×D47C2211yescharacteristic
26#15689635—24no—
27#15689635C2218yes—
28C2×#13094008—21no—
29C2×#13094004C2211yescharacteristic
30C2×#13094004C2211yescharacteristic
31C2×#13094004C2211yescharacteristic
32C2×#13094003C2211yescharacteristic
33C2×#13094002—21no—
34C2×#13094001—21no—
35C2×#13094000C2211yescharacteristic
36C22⋊Q8×D47—24no—
37C22⋊Q8×D47C2218yescomplemented
38C2×#13093999C2211yescharacteristic
39C2×#13093999C2211yescharacteristic
40C2×#13093994—21no—
41C2×C4×D188—21no—
42C2×C4×D188—21no—
43C2×C4⋊C4×D47—21no—
44C2×C4⋊C4×D47C2211yescharacteristic
45C2×C22⋊C4×D47—21no—
46#15689464C2218yescomplemented
47#15689455C2218yescomplemented
48#15689438C2218yescomplemented
49#15689365C2218yescomplemented
50#15689363C2218yescomplemented
51#15689355C2218yescomplemented
52#15689353C2218yescomplemented
53#15689287C2218yescomplemented
54#15689283C2218yescomplemented
55#15689280C2218yescomplemented
56#15689263C2218yescomplemented
57C2×#13093957C2211yescharacteristic, complemented
58C2×#13093955C2211yescharacteristic, complemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093947C2211yescharacteristic, complemented
61C2×#13093947C2211yescharacteristic, complemented
62C2×#13093947C2211yescharacteristic, complemented
63C2×#13093946C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic, complemented
65C2×C22⋊(C47⋊C8)C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C22⋊C8×D47C2218yescomplemented
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#485C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47D411yescharacteristic
78C2×#10625350—22no—
79C2×#10625350—42no—
80C2×#10625350—42no—
81C2×#10625350C2314yes—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C22×Dic94C2311yescharacteristic
85C2×Q8×D47—22no—
86C2×Q8×D47—42no—
87C2×Q8×D47—42no—
88C2×Q8×D47C2314yes—
89C22×D188—21no—
90C22×D188—21no—
91C22×D188C2311yescharacteristic
92C22×C22⋊D47—21no—
93C23×Dic47D411yescharacteristic
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—42no—
98C22×C4×D47—42no—
99C22×C4×D47D411yescharacteristic
100C22×C4×D47D411yescharacteristic
101C22×C4×D47D414yes—
102C22×C4×D47C2311yescharacteristic
103C22×C4×D47C2311yescharacteristic
104C22×C4×D47C2314yes—
105C2×Dic188—42no—
106C2×Dic188C2314yescomplemented
107C2×#10625337—42no—
108C2×#10625337C2314yescomplemented
109C2×#10625325—42no—
110C2×#10625325C2314yescomplemented
111C2×#10625336—42no—
112C2×#10625336C2314yescomplemented
113C22×C47⋊C8C2311yescharacteristic
114C22×C47⋊C8C2311yescharacteristic
115C2×C8×D47—42no—
116C2×C8×D47—42no—
117C2×C8×D47C2314yes—
118C2×C8×D47C2314yes—
119#13094008—28no—
120#13094004—22no—
121#13094004—22no—
122#13094004—22no—
123#13094004C2314yes—
124#13094004C2314yes—
125#13094004C2314yes—
126#13094003—22no—
127#13094003C2314yes—
128#13094002—28no—
129#13094001—28no—
130#13094000—22no—
131#13094000C2314yes—
132#13093999—22no—
133#13093999—22no—
134#13093999C2314yes—
135#13093999C2314yes—
136#13093994—28no—
137C4×D188—28no—
138C4×D188—28no—
139C2×C4⋊Dic47—21no—
140C2×C4⋊Dic47—21no—
141C2×C4⋊Dic47—21no—
142C2×C4⋊Dic47C2311yescharacteristic
143C2×Dic47⋊C4—21no—
144C2×Dic47⋊C4—21no—
145C2×Dic47⋊C4—21no—
146C4⋊C4×D47—28no—
147C4⋊C4×D47—22no—
148C4⋊C4×D47C2314yes—
149C2×C22⋊Dic47—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C22⋊C4×D47—28no—
157#13093957C2314yescomplemented
158#13093955C2314yescomplemented
159#13093949C2314yescomplemented
160#13093947C2314yescomplemented
161#13093947C2314yescomplemented
162#13093947C2314yescomplemented
163#13093946C2314yescomplemented
164#13093944C2314yescomplemented
165C22⋊(C47⋊C8)C2314yes—
166(C2×D47)⋊C8C2314yes—
167(C2×D47)⋊C8C2314yes—
168C22×Q8×C47C2311yescharacteristic
169C23×C4×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22⋊Q8×C47—22no—
173C22⋊Q8×C47C2314yes—
174#117×C47—22no—
175#117×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C42×C47—21no—
183#107×C47C2314yescomplemented
184#106×C47C2314yescomplemented
185#103×C47C2314yescomplemented
186#103×C47C2314yescomplemented
187C22⋊C8×C47C2314yes—
188C24×C47C2×D411yescharacteristic
189C23×D47—24no—
190C23×D47—24no—
191C23×D47—21no—
192C23×D47—42no—
193C23×D47C2×D414yes—
194C23×D47C2×D411yescharacteristic
195C23×D47C2×D411yescharacteristic
196C2×Q8×C47—21no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47C2412yes—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D412yes—
208C22×C4×C47C2412yes—
209C22×C4×C47C2411yescharacteristic
210C2×C22⋊D47—24no—
211C2×C22⋊D47—44no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—42no—
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D414yes—
219Q8×D47—44no—
220Q8×D47—44no—
221Q8×D47—48no—
222#10625350—44no—
223#10625350—44no—
224#10625350—48no—
225C2×D188—22no—
226C2×D188—22no—
227C2×D188—24no—
228C2×D188—24no—
229C2×D188—21no—
230C2×D188—44no—
231C2×D188—44no—
232C2×D188C2412yes—
233C2×C4×D47—22no—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47—22no—
237C2×C4×D47—24no—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—48no—
241C2×C4×D47—44no—
242C2×C4×D47—44no—
243C2×C4×D47—42no—
244C2×C4×D47—42no—
245C2×C4×D47—44no—
246C2×C4×D47—44no—
247C2×C4×D47—44no—
248C2×C4×D47C2×D412yes—
249C2×C4×D47C2×D412yes—
250C2×C4×D47C2×D414yes—
251C2×C4×D47C2×D414yes—
252C2×C4×D47C2412yes—
253C2×C4×D47C2412yes—
254C2×Dic94—22no—
255C2×Dic94—22no—
256C2×Dic94—22no—
257C2×Dic94—22no—
258C2×Dic94—21no—
259C2×Dic94—21no—
260C2×Dic94—24no—
261C2×Dic94—44no—
262C2×Dic94C2412yes—
263C2×Dic94C2412yes—
264C2×C8×C47—22no—
265C2×C8×C47—22no—
266C2×C8×C47C2412yes—
267C2×C8×C47C2412yes—
268C4⋊C4×C47—24no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47C2412yes—
273C4⋊C4×C47C2412yes—
274C4⋊C4×C47C2412yes—
275C22⋊C4×C47—24no—
276C22⋊C4×C47—24no—
277C42×C47—24no—
278C22⋊Dic47—24no—
279#10625337—44no—
280#10625336—44no—
281(C2×D47)⋊C4—24no—
282(C2×D47)⋊C4—24no—
283(C2×D47)⋊C4—24no—
284(C2×D47)⋊C4—24no—
285(C2×D47)⋊C4—24no—
286(C2×D47)⋊C4—24no—
287C4⋊Dic47—21no—
288C4⋊Dic47—24no—
289C4⋊Dic47—24no—
290C4⋊Dic47—24no—
291C4⋊Dic47C2412yes—
292Dic47⋊C4—24no—
293Dic47⋊C4—24no—
294Dic47⋊C4—24no—
295C2×C47⋊C8—22no—
296C2×C47⋊C8—22no—
297C2×C47⋊C8C2412yes—
298C2×C47⋊C8C2412yes—
299Dic188—44no—
300#10625325—44no—
301C8×D47—44no—
302C8×D47—44no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47C22×D412yes—
307C23×C47C22×D411yescharacteristic
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—22no—
312C22×D47—28no—
313C22×D47—28no—
314C22×D47—22no—
315C22×D47—44no—
316C22×D47—416no—
317C22×D47—42no—
318C22×D47—42no—
319C22×D47—42no—
320C22×D47#13514yes—
321C22×D47#13714yes—
322C22×D47C22×D412yes—
323C22×D47C22×D412yes—
324Q8×C47—22no—
325Q8×C47—22no—
326Q8×C47—42no—
327C2×C4×C47—22no—
328C2×C4×C47—24no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—42no—
336C2×C4×C47—42no—
337C2×C4×C47—42no—
338C2×C4×C47—42no—
339C2×C4×C47C22×D412yes—
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47H(5,𝔽2)12yes—
342C2×C4×C47H(5,𝔽2)12yes—
343C2×C4×C47C2511yescharacteristic
344C22⋊D47—48no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—44no—
351C2×Dic47—42no—
352C2×Dic47—42no—
353C2×Dic47—42no—
354C2×Dic47C22×D412yes—
355C2×Dic47C22×D412yes—
356D188—22no—
357D188—22no—
358D188—48no—
359D188—48no—
360D188—42no—
361C4×D47—24no—
362C4×D47—24no—
363C4×D47—22no—
364C4×D47—22no—
365C4×D47—22no—
366C4×D47—22no—
367C4×D47—44no—
368C4×D47—44no—
369C4×D47—48no—
370C4×D47—48no—
371C4×D47—48no—
372Dic94—22no—
373Dic94—22no—
374Dic94—22no—
375Dic94—22no—
376Dic94—48no—
377Dic94—42no—
378Dic94—42no—
379C8×C47—22no—
380C8×C47—22no—
381C47⋊C8—22no—
382C47⋊C8—22no—
383C2×#3190—471nomaximal, Sylow
384C22×C47—22no—
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—44no—
388C22×C47#53412yes—
389C22×C47C2×#13512yes—
390C22×C47C2×#13712yes—
391C22×C47C23×D411yescharacteristic
392C2×D47—22no—
393C2×D47—22no—
394C2×D47—28no—
395C2×D47—28no—
396C2×D47—22no—
397C2×D47—22no—
398C2×D47—416no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—84no—
403C2×D47C2×#13514yes—
404C2×D47C2×#13714yes—
405C4×C47—22no—
406C4×C47—42no—
407C4×C47—42no—
408C4×C47—42no—
409C4×C47—42no—
410C4×C47#53412yes—
411C4×C47C2×H(5,𝔽2)11yescharacteristic
412C4×C47C2×H(5,𝔽2)11yescharacteristic
413Dic47—22no—
414Dic47—22no—
415Dic47—42no—
416Dic47—42no—
417Dic47—42no—
418C2×#525—471no—
419C22×C22⋊Q8—471no—
420#3190—4716no—
421C2×#485—471no—
422C2×#485D4711yescharacteristic, complemented
423C2×#483—471no—
424C2×#480—471no—
425C2×#467—471no—
426C2×#467—471no—
427C2×#465—471no—
428C2×#465—471no—
429C2×#452—471no—
430C2×#452—471no—
431C2×#451—471no—
432C2×#448—471no—
433C22×C22⋊C8—471no—
434C2×C47—42no—
435C2×C47#319014yescomplemented
436C2×C47C2×#53411yescharacteristic
437C2×C47C22×#13511yescharacteristic
438C2×C47C22×#13711yescharacteristic
439D47—24no—
440D47—24no—
441D47—82no—
442C22×#41—471no—
443C23×Q8—471no—
444C24×C4—471no—
445C22×Q16—471no—
446C22×Q16—471no—
447C22×SD16—471no—
448C22×SD16—471no—
449C23×C8—471no—
450C23×C8—471no—
451#525—478no—
452#525—944no—
453C2×#123—941no—
454C2×C22⋊Q8—471no—
455C2×C22⋊Q8—471no—
456C2×C22⋊Q8—478no—
457C2×C22⋊Q8—471no—
458C2×C22⋊Q8—471no—
459C2×C22⋊Q8—471no—
460C2×C22⋊Q8—941no—
461C2×C22⋊Q8—941no—
462C2×C22⋊Q8—944no—
463C2×C22⋊Q8C2×D4711yescharacteristic
464C2×#121—471no—
465C2×#121—471no—
466C2×#120—941no—
467C2×C4×D4—941no—
468C2×C4×D4—941no—
469C2×#117C2×D4711yescharacteristic
470C22×C4⋊C4—471no—
471C22×C4⋊C4—941no—
472C22×C22⋊C4—941no—
473#485—478no—
474#485C2×D4718yescomplemented
475#483—478no—
476#480—478no—
477#467—478no—
478#467—478no—
479#465—478no—
480#465—478no—
481#452—478no—
482#452—478no—
483#451—478no—
484#448—478no—
485C2×#107—471no—
486C2×#107C2×D4711yescharacteristic, complemented
487C2×#106—471no—
488C2×#106C2×D4711yescharacteristic, complemented
489C2×#103—471no—
490C2×#103—471no—
491C2×#103—471no—
492C2×#103—471no—
493C2×#103C2×D4711yescharacteristic, complemented
494C2×#103C2×D4711yescharacteristic, complemented
495C2×#102—471no—
496C2×#102—471no—
497C2×C22⋊C8—471no—
498C2×C22⋊C8—471no—
499C2×C22⋊C8—471no—
500C2×C22⋊C8—478no—
501C2×C22⋊C8C2×D4711yescharacteristic
502C47C2×#319011yescharacteristic, complemented, Sylow
503C25—471no—
504C2×#41—474no—
505C2×#41—942no—
506C2×#41—1882no—
507C2×#41—1882no—
508C22×Q8—474no—
509C22×Q8—471no—
510C22×Q8—471no—
511C22×Q8—941no—
512C22×Q8—942no—
513C22×Q8—1882no—
514C22×Q8—1882no—
515C22×Q8C22×D4711yescharacteristic
516C22×D4—471no—
517C22×D4—941no—
518C22×D4—941no—
519C22×D4—941no—
520C23×C4—471no—
521C23×C4—471no—
522C23×C4—471no—
523C23×C4—471no—
524C23×C4—471no—
525C23×C4—474no—
526C23×C4—474no—
527C23×C4—941no—
528C23×C4—941no—
529C23×C4—941no—
530C23×C4—1882no—
531C23×C4—1882no—
532C23×C4C22×D4711yescharacteristic
533C2×Q16—474no—
534C2×Q16—474no—
535C2×Q16—1882no—
536C2×Q16—1882no—
537C2×SD16—474no—
538C2×SD16—474no—
539C2×SD16—1882no—
540C2×SD16—1882no—
541C22×C8—471no—
542C22×C8—471no—
543C22×C8—474no—
544C22×C8—474no—
545C22×C8—1882no—
546C22×C8—1882no—
547C22×C8C22×D4711yescharacteristic
548C22×C8C22×D4711yescharacteristic
549#123—948no—
550C22⋊Q8—22no—
551C22⋊Q8—474no—
552C22⋊Q8—474no—
553C22⋊Q8—474no—
554C22⋊Q8—474no—
555C22⋊Q8—474no—
556C22⋊Q8—948no—
557C22⋊Q8—948no—
558C22⋊Q8—942no—
559C22⋊Q8—942no—
560C22⋊Q8—942no—
561C22⋊Q8—942no—
562C22⋊Q8—942no—
563C22⋊Q8C22×D4714yes—
564#121—474no—
565#121—474no—
566#121—942no—
567#121—942no—
568#120—948no—
569C4×D4—948no—
570C4×D4—948no—
571#117—22no—
572#117C22×D4714yes—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—471no—
575C2×C4⋊C4—474no—
576C2×C4⋊C4—942no—
577C2×C4⋊C4—948no—
578C2×C4⋊C4—941no—
579C2×C4⋊C4—941no—
580C2×C4⋊C4—941no—
581C2×C4⋊C4—941no—
582C2×C4⋊C4—941no—
583C2×C4⋊C4—941no—
584C2×C4⋊C4C22×D4711yescharacteristic
585C2×C4⋊C4C22×D4711yescharacteristic
586C2×C4⋊C4C22×D4711yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—948no—
590C2×C22⋊C4—941no—
591C2×C22⋊C4—941no—
592C2×C22⋊C4—941no—
593C2×C22⋊C4—941no—
594C2×C22⋊C4—941no—
595C2×C22⋊C4—941no—
596C2×C22⋊C4—941no—
597C2×C42—21no—
598#107—474no—
599#107C22×D4714yescomplemented
600#106—474no—
601#106C22×D4714yescomplemented
602#103—474no—
603#103—474no—
604#103—474no—
605#103—474no—
606#103C22×D4714yescomplemented
607#103C22×D4714yescomplemented
608#102—474no—
609#102—474no—
610C22⋊C8—474no—
611C22⋊C8—474no—
612C22⋊C8—474no—
613C22⋊C8C22×D4714yes—
614C24—471no—
615C24—471no—
616C24—474no—
617C24—944no—
618C24—944no—
619C24—941no—
620C24—1882no—
621C24D4×D4711yescharacteristic
622#41—1884no—
623#41—1884no—
624#41—1888no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—472no—
629C2×Q8—472no—
630C2×Q8—944no—
631C2×Q8—941no—
632C2×Q8—941no—
633C2×Q8—942no—
634C2×Q8—942no—
635C2×Q8—942no—
636C2×Q8—942no—
637C2×Q8—1884no—
638C2×Q8—1884no—
639C2×Q8—1884no—
640C2×Q8—1888no—
641C2×Q8C23×D4712yes—
642C2×D4—472no—
643C2×D4—944no—
644C2×D4—944no—
645C2×D4—944no—
646C2×D4—941no—
647C2×D4—942no—
648C2×D4—942no—
649C2×D4—1884no—
650C2×D4—1884no—
651C2×D4—1884no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—471no—
659C22×C4—471no—
660C22×C4—474no—
661C22×C4—472no—
662C22×C4—472no—
663C22×C4—472no—
664C22×C4—472no—
665C22×C4—474no—
666C22×C4—474no—
667C22×C4—944no—
668C22×C4—944no—
669C22×C4—942no—
670C22×C4—942no—
671C22×C4—942no—
672C22×C4—942no—
673C22×C4—941no—
674C22×C4—941no—
675C22×C4—941no—
676C22×C4—944no—
677C22×C4—1888no—
678C22×C4—1884no—
679C22×C4—1884no—
680C22×C4—1882no—
681C22×C4—1882no—
682C22×C4—1884no—
683C22×C4—1884no—
684C22×C4—1884no—
685C22×C4—1882no—
686C22×C4D4×D4712yes—
687C22×C4D4×D4711yescharacteristic
688C22×C4C23×D4712yes—
689C22×C4C23×D4711yescharacteristic
690Q16—1884no—
691Q16—1884no—
692SD16—1884no—
693SD16—1884no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—472no—
697C2×C8—472no—
698C2×C8—942no—
699C2×C8—942no—
700C2×C8—1884no—
701C2×C8—1884no—
702C2×C8C23×D4712yes—
703C2×C8C23×D4712yes—
704C4⋊C4—24no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—472no—
709C4⋊C4—944no—
710C4⋊C4—944no—
711C4⋊C4—944no—
712C4⋊C4—944no—
713C4⋊C4—944no—
714C4⋊C4—944no—
715C4⋊C4—941no—
716C4⋊C4C23×D4712yes—
717C4⋊C4C23×D4712yes—
718C4⋊C4C23×D4712yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—944no—
722C22⋊C4—944no—
723C22⋊C4—944no—
724C22⋊C4—944no—
725C22⋊C4—944no—
726C22⋊C4—944no—
727C22⋊C4—944no—
728C42—24no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—474no—
733C23—474no—
734C23—472no—
735C23—472no—
736C23—948no—
737C23—948no—
738C23—942no—
739C23—942no—
740C23—942no—
741C23—942no—
742C23—942no—
743C23—1884no—
744C23—18816no—
745C23—1882no—
746C23—1882no—
747C23—1882no—
748C23C2×D4×D4712yes—
749C23C2×D4×D4711yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—42no—
753Q8—942no—
754Q8—942no—
755Q8—942no—
756Q8—942no—
757Q8—1888no—
758Q8—1882no—
759Q8—1882no—
760D4—942no—
761D4—942no—
762D4—1888no—
763D4—1888no—
764D4—1888no—
765D4—1882no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—472no—
779C2×C4—472no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—944no—
783C2×C4—944no—
784C2×C4—942no—
785C2×C4—942no—
786C2×C4—942no—
787C2×C4—942no—
788C2×C4—942no—
789C2×C4—942no—
790C2×C4—942no—
791C2×C4—1884no—
792C2×C4—1884no—
793C2×C4—1888no—
794C2×C4—1888no—
795C2×C4—1888no—
796C2×C4—1884no—
797C2×C4—1882no—
798C2×C4—1882no—
799C2×C4—1882no—
800C2×C4C2×D4×D4712yes—
801C2×C4C2×D4×D4711yescharacteristic
802C2×C4#1309407012yes—
803C2×C4#1309407012yes—
804C2×C4C24×D4711yescharacteristic
805C8—22no—
806C8—22no—
807C8—942no—
808C8—942no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—474no—
814C22—474no—
815C22—942no—
816C22—942no—
817C22—942no—
818C22—942no—
819C22—948no—
820C22—948no—
821C22—3764no—
822C22—18816no—
823C22—1882no—
824C22—1882no—
825C22—1882no—
826C22#1568968412yes—
827C22#135×D4712yes—
828C22#137×D4712yes—
829C22C22×D4×D4711yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—942no—
836C4—942no—
837C4—1882no—
838C4—1882no—
839C4—1882no—
840C4#1568968412yes—
841C4C2×#1309407011yescharacteristic
842C4C2×#1309407011yescharacteristic
843C2—42no—
844C2—944no—
845C2—944no—
846C2—3762no—
847C2#2025417314yesdirect product factor
848C2C2×#1568968411yescharacteristic
849C2C2×#135×D4711yescharacteristic
850C2C2×#137×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
prime radicalC2×#15689635C2
hypercenterC2×#485D47
hypocenterC47C2×#3190
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D47C2semidirect
3. #20254173C2direct (N × H)
4. C2×#15689464C2semidirect
5. C2×#15689455C2semidirect
6. C2×#15689438C2semidirect
7. C2×#15689365C2semidirect
8. C2×#15689363C2semidirect
9. C2×#15689355C2semidirect
10. C2×#15689353C2semidirect
11. C2×#15689287C2semidirect
12. C2×#15689283C2semidirect
13. C2×#15689280C2semidirect
14. C2×#15689263C2semidirect
15. C2×C22⋊C8×D47C2semidirect
16. C2×C47×#485C2semidirect
20. C22×Dic188C22semidirect
21. C22×#10625337C22semidirect
22. C22×#10625325C22semidirect
23. C22×#10625336C22semidirect
37. C22⋊Q8×D47C22semidirect
46. #15689464C22semidirect
47. #15689455C22semidirect
48. #15689438C22semidirect
49. #15689365C22semidirect
50. #15689363C22semidirect
51. #15689355C22semidirect
52. #15689353C22semidirect
53. #15689287C22semidirect
54. #15689283C22semidirect
55. #15689280C22semidirect
56. #15689263C22semidirect
57. C2×#13093957C22semidirect
58. C2×#13093955C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093947C22semidirect
61. C2×#13093947C22semidirect
62. C2×#13093947C22semidirect
63. C2×#13093946C22semidirect
64. C2×#13093944C22semidirect
68. C22⋊C8×D47C22semidirect
71. C47×#485C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#103×C47C22semidirect
75. C2×#103×C47C22semidirect
106. C2×Dic188C23semidirect
108. C2×#10625337C23semidirect
110. C2×#10625325C23semidirect
112. C2×#10625336C23semidirect
157. #13093957C23semidirect
158. #13093955C23semidirect
159. #13093949C23semidirect
160. #13093947C23semidirect
161. #13093947C23semidirect
162. #13093947C23semidirect
163. #13093946C23semidirect
164. #13093944C23semidirect
183. #107×C47C23semidirect
184. #106×C47C23semidirect
185. #103×C47C23semidirect
186. #103×C47C23semidirect
422. C2×#485D47semidirect
435. C2×C47#3190semidirect
474. #485C2×D47semidirect
486. C2×#107C2×D47semidirect
488. C2×#106C2×D47semidirect
493. C2×#103C2×D47semidirect
494. C2×#103C2×D47semidirect
502. C47C2×#3190semidirect
599. #107C22×D47semidirect
601. #106C22×D47semidirect
606. #103C22×D47semidirect
607. #103C22×D47semidirect
847. C2#20254173direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896352
C2×C22⋊Q8×D472
#202541732
C2×#156894642
C2×#156894552
C2×#156894382
C2×#156893652
C2×#156893632
C2×#156893552
C2×#156893532
C2×#156892872
C2×#156892832
C2×#156892802
C2×#156892632
C2×C22⋊C8×D472
C2×C47×#4852
C2×#319047