Finite Group Databasebeta

← C2×#20249135 #26382639

Subgroups — C2×#20249135 #26382639

Order 12032.

3718 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094009C211yesmaximal, characteristic, complemented
2C22×#13094006C211yesmaximal, characteristic, complemented
3C22×#13093997C211yesmaximal, characteristic
4C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
5#20249135C2116yesmaximal, direct product factor
6C2×#15689057C211yesmaximal, characteristic, complemented
7C2×#15689056C211yesmaximal, characteristic, complemented
8C2×#15689046C211yesmaximal, characteristic, complemented
9C2×#15689045C211yesmaximal, characteristic, complemented
10C2×#15689045C211yesmaximal, characteristic, complemented
11C2×#15689039C211yesmaximal, characteristic, complemented
12C2×#15689038C211yesmaximal, characteristic, complemented
13C2×#15689001C211yesmaximal, characteristic, complemented
14C2×#15688999C211yesmaximal, characteristic, complemented
15C2×#15688980C211yesmaximal, characteristic, complemented
16C2×C47×#396C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13094009—28no—
24C2×#13094009C2218yescomplemented
25C2×#13094006—28no—
26C2×#13094006C2218yescomplemented
27C2×#13093997—28no—
28C2×#13093997C2218yes—
29C22×C4⋊Dic47C2211yescharacteristic
30C22×C4⋊Dic47C2211yescharacteristic
31C22×C4⋊Dic47C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C2×C4⋊C4×D47—28no—
38C2×C4⋊C4×D47C2218yescomplemented
39C22×C22⋊Dic47C2211yescharacteristic
40C22×C22⋊Dic47C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C22×(C2×D47)⋊C4C2211yescharacteristic
48#15689057C2218yescomplemented
49#15689056C2218yescomplemented
50#15689046C2218yescomplemented
51#15689045C2218yescomplemented
52#15689045C2218yescomplemented
53#15689039C2218yescomplemented
54#15689038C2218yescomplemented
55#15689001C2218yescomplemented
56#15688999C2218yescomplemented
57#15688980C2218yescomplemented
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic
69C47×#396C2218yescomplemented
70C2×#95×C47C2211yescharacteristic
71C24×D47C2311yescharacteristic
72C24×D47C2311yescharacteristic
73C22×D188—24no—
74C22×D188—24no—
75C22×D188—24no—
76C22×D188C2314yes—
77C22×C22⋊D47—24no—
78C22×C22⋊D47—24no—
79C22×C22⋊D47—24no—
80C22×C22⋊D47—24no—
81C22×C22⋊D47—42no—
82C22×C22⋊D47—42no—
83C22×C22⋊D47C2314yes—
84C22×C22⋊D47C2314yes—
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47—24no—
94C22×C4×D47—42no—
95C22×C4×D47—42no—
96C22×C4×D47—42no—
97C22×C4×D47—42no—
98C22×C4×D47D418yes—
99C22×C4×D47D418yescomplemented
100C22×C4×D47C2314yes—
101C22×C4×D47C2314yes—
102C22×C4×D47C2314yes—
103#13094009—232no—
104#13094006—232no—
105#13093997—232no—
106C2×C4⋊Dic47—24no—
107C2×C4⋊Dic47—24no—
108C2×C4⋊Dic47—42no—
109C2×C4⋊Dic47C2314yes—
110C2×C4⋊Dic47C2314yes—
111C2×C4⋊Dic47C2314yes—
112C2×Dic47⋊C4—24no—
113C2×Dic47⋊C4—24no—
114C2×Dic47⋊C4—24no—
115C2×Dic47⋊C4—24no—
116C2×Dic47⋊C4—24no—
117C2×Dic47⋊C4C2314yes—
118C2×Dic47⋊C4C2314yes—
119C2×Dic47⋊C4C2314yes—
120C2×Dic47⋊C4C2314yes—
121C2×Dic47⋊C4C2314yes—
122C4⋊C4×D47—232no—
123C2×C22⋊Dic47—24no—
124C2×C22⋊Dic47—42no—
125C2×C22⋊Dic47C2314yes—
126C2×C22⋊Dic47C2314yes—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—24no—
129C2×(C2×D47)⋊C4—24no—
130C2×(C2×D47)⋊C4—24no—
131C2×(C2×D47)⋊C4—24no—
132C2×(C2×D47)⋊C4—42no—
133C2×(C2×D47)⋊C4—42no—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C47⋊#95C2314yes—
142C47⋊#95C2314yes—
143C47⋊#95C2314yes—
144C47⋊#95C2314yes—
145C47⋊#95C2314yes—
146C25×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C2×C4⋊C4×C47—24no—
154C2×C4⋊C4×C47—24no—
155C2×C4⋊C4×C47—42no—
156C2×C4⋊C4×C47C2314yes—
157C2×C4⋊C4×C47C2314yes—
158C2×C4⋊C4×C47C2314yes—
159C2×C22⋊C4×C47—24no—
160C2×C22⋊C4×C47—24no—
161C2×C22⋊C4×C47—42no—
162C2×C22⋊C4×C47C2314yes—
163C2×C22⋊C4×C47C2314yes—
164C2×C22⋊C4×C47C2314yes—
165#95×C47C2314yes—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47—22no—
171C24×C47—22no—
172C24×C47—22no—
173C24×C47C2412yes—
174C24×C47C2411yescharacteristic
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47C2×D414yes—
187C23×D47C2×D414yes—
188C23×D47#4114yes—
189C23×D47C2412yes—
190C23×D47C2412yes—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47C2×D414yes—
208C22×C4×C47C2×D414yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C2×C22⋊D47—28no—
216C2×C22⋊D47—28no—
217C2×C22⋊D47—28no—
218C2×C22⋊D47—28no—
219C2×C22⋊D47—44no—
220C2×C22⋊D47—44no—
221C2×C22⋊D47—416no—
222C2×C22⋊D47—416no—
223C22×Dic47—22no—
224C22×Dic47—22no—
225C22×Dic47—22no—
226C22×Dic47—22no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—22no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47C2×D414yes—
240C22×Dic47C2×D414yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C22×Dic47C2412yes—
244C22×Dic47C2412yes—
245C22×Dic47C2412yes—
246C22×Dic47C2412yes—
247C2×D188—28no—
248C2×D188—28no—
249C2×D188—28no—
250C2×D188—416no—
251C2×C4×D47—232no—
252C2×C4×D47—28no—
253C2×C4×D47—28no—
254C2×C4×D47—28no—
255C2×C4×D47—416no—
256C2×C4×D47—44no—
257C2×C4×D47—44no—
258C2×C4×D47—44no—
259C2×C4×D47—44no—
260C2×C4×D47—416no—
261C2×C4×D47C2×D4116yes—
262C2×C4×D47C2×D4116yescomplemented
263C4⋊C4×C47—28no—
264C4⋊C4×C47—28no—
265C4⋊C4×C47—44no—
266C22⋊C4×C47—28no—
267C22⋊C4×C47—28no—
268C22⋊C4×C47—44no—
269C22⋊Dic47—28no—
270C22⋊Dic47—44no—
271(C2×D47)⋊C4—28no—
272(C2×D47)⋊C4—28no—
273(C2×D47)⋊C4—28no—
274(C2×D47)⋊C4—28no—
275(C2×D47)⋊C4—28no—
276(C2×D47)⋊C4—44no—
277(C2×D47)⋊C4—44no—
278C4⋊Dic47—28no—
279C4⋊Dic47—28no—
280C4⋊Dic47—44no—
281Dic47⋊C4—28no—
282Dic47⋊C4—28no—
283Dic47⋊C4—28no—
284Dic47⋊C4—28no—
285Dic47⋊C4—28no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—44no—
294C23×C47—44no—
295C23×C47—44no—
296C23×C47—44no—
297C23×C47—44no—
298C23×C47—44no—
299C23×C47—44no—
300C23×C47C22×D412yes—
301C23×C47C22×D412yes—
302C23×C47C2×#4112yes—
303C23×C47H(5,𝔽2)12yes—
304C23×C47H(5,𝔽2)12yes—
305C23×C472−1+412yes—
306C23×C472−1+412yes—
307C23×C47C2511yescharacteristic
308C22×D47—28no—
309C22×D47—28no—
310C22×D47—28no—
311C22×D47—28no—
312C22×D47—28no—
313C22×D47—28no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—44no—
326C22×D47—44no—
327C22×D47—44no—
328C22×D47—44no—
329C22×D47—44no—
330C22×D47—44no—
331C22×D47—44no—
332C22×D47#121116yes—
333C22×D47C22×D414yes—
334C22×D47C22×D414yes—
335C22×D47C2×#4114yes—
336C2×C4×C47—28no—
337C2×C4×C47—28no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—44no—
355C2×C4×C47—44no—
356C2×C4×C47—44no—
357C2×C4×C47—44no—
358C2×C4×C47C22×D414yes—
359C2×C4×C47C22×D414yes—
360C22⋊D47—416no—
361C22⋊D47—416no—
362C2×Dic47—28no—
363C2×Dic47—28no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—44no—
381C2×Dic47—44no—
382C2×Dic47—44no—
383C2×Dic47—44no—
384C2×Dic47C22×D414yes—
385C2×Dic47C22×D414yes—
386D188—416no—
387C4×D47—232no—
388C4×D47—416no—
389C4×D47—416no—
390C2×#2618—471nomaximal, Sylow
391C22×C47—42no—
392C22×C47—42no—
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—88no—
399C22×C47C2×#12114yes—
400C22×C47#53414yes—
401C22×C47#53614yes—
402C22×C47#53714yes—
403C22×C47#53714yes—
404C22×C47#53914yes—
405C22×C47#53914yes—
406C22×C47C23×D411yescharacteristic
407C22×C47C23×D411yescharacteristic
408C22×C47C22×#4111yescharacteristic
409C22×C47C2×H(5,𝔽2)11yescharacteristic
410C22×C47C2×H(5,𝔽2)11yescharacteristic
411C22×C47C2×2−1+411yescharacteristic
412C22×C47C2×2−1+411yescharacteristic
413C2×D47—232no—
414C2×D47—24no—
415C2×D47—24no—
416C2×D47—24no—
417C2×D47—24no—
418C2×D47—24no—
419C2×D47—24no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—42no—
424C2×D47—42no—
425C2×D47—42no—
426C2×D47—42no—
427C2×D47—88no—
428C2×D47C2×#12118yes—
429C4×C47—24no—
430C4×C47—24no—
431C4×C47—42no—
432C4×C47—42no—
433C4×C47—42no—
434C4×C47—42no—
435Dic47—24no—
436Dic47—24no—
437Dic47—42no—
438Dic47—42no—
439Dic47—42no—
440Dic47—42no—
441C22×#123—471no—
442C22×#123—471no—
443C22×#121—471no—
444C23×C4⋊C4—471no—
445#2618—4716no—
446C2×#398—471no—
447C2×#398—471no—
448C2×#396—471no—
449C2×#396—471no—
450C2×#396—471no—
451C2×#396D4711yescharacteristic, complemented
452C2×#394—471no—
453C2×#394—471no—
454C2×#386—471no—
455C2×#386—471no—
456C2×#380—471no—
457C2×C47—82no—
458C2×C47#261818yescomplemented
459C2×C47C22×#12111yescharacteristic
460C2×C47C2×#53411yescharacteristic
461C2×C47C2×#53611yescharacteristic
462C2×C47C2×#53711yescharacteristic
463C2×C47C2×#53711yescharacteristic
464C2×C47C2×#53911yescharacteristic
465C2×C47C2×#53911yescharacteristic
466D47—28no—
467D47—82no—
468C23×D4—471no—
469C23×D4—471no—
470C23×D4—471no—
471C24×C4—471no—
472C24×C4—471no—
473C24×C4—471no—
474C2×#123—478no—
475C2×#123—478no—
476C2×#123—948no—
477C2×#123—948no—
478C2×#121—478no—
479C2×#121—948no—
480C22×C4⋊C4—471no—
481C22×C4⋊C4—471no—
482C22×C4⋊C4—471no—
483C22×C4⋊C4—471no—
484C22×C4⋊C4—471no—
485C22×C4⋊C4—471no—
486C22×C4⋊C4—471no—
487C22×C4⋊C4—471no—
488C22×C4⋊C4—478no—
489C22×C4⋊C4—948no—
490C22×C4⋊C4C2×D4711yescharacteristic
491C22×C4⋊C4C2×D4711yescharacteristic
492C22×C4⋊C4C2×D4711yescharacteristic
493C22×C22⋊C4—471no—
494C22×C22⋊C4—471no—
495C22×C22⋊C4—471no—
496C22×C22⋊C4—471no—
497C22×C22⋊C4—471no—
498C22×C22⋊C4—471no—
499C22×C22⋊C4—471no—
500C22×C22⋊C4—471no—
501C22×C22⋊C4—471no—
502C22×C22⋊C4C2×D4711yescharacteristic
503C22×C22⋊C4C2×D4711yescharacteristic
504C22×C22⋊C4C2×D4711yescharacteristic
505#398—478no—
506#398—478no—
507#396—478no—
508#396—478no—
509#396—478no—
510#396C2×D4718yescomplemented
511#394—478no—
512#394—478no—
513#386—478no—
514#386—478no—
515#380—478no—
516C2×#95—471no—
517C2×#95—471no—
518C2×#95—471no—
519C2×#95—471no—
520C2×#95—471no—
521C2×#95C2×D4711yescharacteristic
522C47C2×#261811yescharacteristic, complemented, Sylow
523C25—471no—
524C25—471no—
525C25C22×D4711yescharacteristic
526C22×D4—474no—
527C22×D4—474no—
528C22×D4—474no—
529C22×D4—944no—
530C22×D4—944no—
531C22×D4—944no—
532C22×D4—944no—
533C22×D4—944no—
534C22×D4—944no—
535C22×D4—944no—
536C22×D4—1882no—
537C22×D4—1882no—
538C23×C4—471no—
539C23×C4—471no—
540C23×C4—478no—
541C23×C4—474no—
542C23×C4—478no—
543C23×C4—474no—
544C23×C4—471no—
545C23×C4—471no—
546C23×C4—471no—
547C23×C4—471no—
548C23×C4—474no—
549C23×C4—944no—
550C23×C4—944no—
551C23×C4—944no—
552C23×C4—1882no—
553C23×C4—1882no—
554C23×C4—1882no—
555C23×C4—1882no—
556C23×C4C22×D4711yescharacteristic
557C23×C4C22×D4711yescharacteristic
558C23×C4C22×D4711yescharacteristic
559C23×C4C22×D4711yescharacteristic
560C23×C4C22×D4711yescharacteristic
561C23×C4C22×D4711yescharacteristic
562#123—9432no—
563#123—9432no—
564#121—9432no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—42no—
568C2×C4⋊C4—474no—
569C2×C4⋊C4—474no—
570C2×C4⋊C4—474no—
571C2×C4⋊C4—474no—
572C2×C4⋊C4—474no—
573C2×C4⋊C4—474no—
574C2×C4⋊C4—474no—
575C2×C4⋊C4—474no—
576C2×C4⋊C4—9432no—
577C2×C4⋊C4—944no—
578C2×C4⋊C4—944no—
579C2×C4⋊C4—944no—
580C2×C4⋊C4—944no—
581C2×C4⋊C4—944no—
582C2×C4⋊C4—944no—
583C2×C4⋊C4—944no—
584C2×C4⋊C4—1882no—
585C2×C4⋊C4C22×D4714yes—
586C2×C4⋊C4C22×D4714yes—
587C2×C4⋊C4C22×D4714yes—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—474no—
592C2×C22⋊C4—474no—
593C2×C22⋊C4—474no—
594C2×C22⋊C4—474no—
595C2×C22⋊C4—474no—
596C2×C22⋊C4—474no—
597C2×C22⋊C4—474no—
598C2×C22⋊C4—474no—
599C2×C22⋊C4—474no—
600C2×C22⋊C4—944no—
601C2×C22⋊C4—944no—
602C2×C22⋊C4—944no—
603C2×C22⋊C4—944no—
604C2×C22⋊C4—944no—
605C2×C22⋊C4—944no—
606C2×C22⋊C4—1882no—
607C2×C22⋊C4—1882no—
608C2×C22⋊C4—1882no—
609C2×C22⋊C4C22×D4714yes—
610C2×C22⋊C4C22×D4714yes—
611C2×C22⋊C4C22×D4714yes—
612#95—474no—
613#95—474no—
614#95—474no—
615#95—474no—
616#95—474no—
617#95C22×D4714yes—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—474no—
626C24—474no—
627C24—474no—
628C24—472no—
629C24—472no—
630C24—942no—
631C24—942no—
632C24—942no—
633C24—942no—
634C24—942no—
635C24—942no—
636C24—942no—
637C24—942no—
638C24—942no—
639C24—942no—
640C24—942no—
641C24C23×D4712yes—
642C24C23×D4711yescharacteristic
643C2×D4—948no—
644C2×D4—948no—
645C2×D4—948no—
646C2×D4—948no—
647C2×D4—948no—
648C2×D4—948no—
649C2×D4—948no—
650C2×D4—18816no—
651C2×D4—1884no—
652C2×D4—1884no—
653C2×D4—18816no—
654C2×D4—18816no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—474no—
672C22×C4—474no—
673C22×C4—472no—
674C22×C4—472no—
675C22×C4—4716no—
676C22×C4—4716no—
677C22×C4—472no—
678C22×C4—472no—
679C22×C4—472no—
680C22×C4—472no—
681C22×C4—948no—
682C22×C4—9432no—
683C22×C4—948no—
684C22×C4—948no—
685C22×C4—942no—
686C22×C4—942no—
687C22×C4—942no—
688C22×C4—942no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4—942no—
692C22×C4—942no—
693C22×C4—942no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4—942no—
697C22×C4—942no—
698C22×C4—942no—
699C22×C4—942no—
700C22×C4—942no—
701C22×C4—18816no—
702C22×C4—1884no—
703C22×C4—1884no—
704C22×C4—1884no—
705C22×C4—1884no—
706C22×C4—18816no—
707C22×C4D4×D4714yes—
708C22×C4D4×D4714yes—
709C22×C4C23×D4712yes—
710C22×C4C23×D4712yes—
711C22×C4C23×D4712yes—
712C22×C4C23×D4712yes—
713C22×C4C23×D4712yes—
714C22×C4C23×D4712yes—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—44no—
718C4⋊C4—948no—
719C4⋊C4—948no—
720C4⋊C4—948no—
721C4⋊C4—948no—
722C4⋊C4—948no—
723C4⋊C4—948no—
724C4⋊C4—948no—
725C4⋊C4—1884no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—44no—
729C22⋊C4—948no—
730C22⋊C4—948no—
731C22⋊C4—948no—
732C22⋊C4—948no—
733C22⋊C4—948no—
734C22⋊C4—948no—
735C22⋊C4—1884no—
736C22⋊C4—1884no—
737C22⋊C4—1884no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—4716no—
753C23—474no—
754C23—474no—
755C23—474no—
756C23—948no—
757C23—948no—
758C23—942no—
759C23—942no—
760C23—942no—
761C23—942no—
762C23—948no—
763C23—948no—
764C23—948no—
765C23—948no—
766C23—942no—
767C23—942no—
768C23—942no—
769C23—942no—
770C23—942no—
771C23—942no—
772C23—942no—
773C23—1884no—
774C23—1884no—
775C23—1884no—
776C23—1884no—
777C23—1884no—
778C23—1884no—
779C23—1884no—
780C23C2×D4×D4712yes—
781C23C2×D4×D4712yes—
782C23#41×D4712yes—
783C23#1309406912yes—
784C23#1309407012yes—
785C23#1309407112yes—
786C23#1309407212yes—
787C23C24×D4711yescharacteristic
788D4—18816no—
789D4—18816no—
790D4—18816no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—474no—
814C2×C4—474no—
815C2×C4—9432no—
816C2×C4—948no—
817C2×C4—948no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—942no—
832C2×C4—942no—
833C2×C4—942no—
834C2×C4—18816no—
835C2×C4—18816no—
836C2×C4—1884no—
837C2×C4—1884no—
838C2×C4—1884no—
839C2×C4—1884no—
840C2×C4C2×D4×D4714yes—
841C2×C4C2×D4×D4714yes—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—88no—
850C22—478no—
851C22—9432no—
852C22—944no—
853C22—944no—
854C22—944no—
855C22—944no—
856C22—944no—
857C22—944no—
858C22—3768no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1882no—
865C22—1882no—
866C22#121×D4714yes—
867C22#1568968114yes—
868C22#1568969614yes—
869C22#1568970214yes—
870C22#1568970314yes—
871C22#1568971414yes—
872C22#1568971914yes—
873C22C22×D4×D4711yescharacteristic
874C22C22×D4×D4711yescharacteristic
875C22C2×#41×D4711yescharacteristic
876C22C2×#1309406911yescharacteristic
877C22C2×#1309407011yescharacteristic
878C22C2×#1309407111yescharacteristic
879C22C2×#1309407211yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—944no—
887C4—944no—
888C4—1882no—
889C4—1882no—
890C4—1882no—
891C4—1882no—
892C2—82no—
893C2—948no—
894C2—3762no—
895C2#2024913518yesdirect product factor
896C2C2×#121×D4711yescharacteristic
897C2C2×#1568968111yescharacteristic
898C2C2×#1568969611yescharacteristic
899C2C2×#1568970211yescharacteristic
900C2C2×#1568970311yescharacteristic
901C2C2×#1568971411yescharacteristic
902C2C2×#1568971911yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC22×#13093997C2
hypercenterC2×#396D47
hypocenterC47C2×#2618
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13094009C2semidirect
2. C22×#13094006C2semidirect
4. C22×C4⋊C4×D47C2semidirect
5. #20249135C2direct (N × H)
6. C2×#15689057C2semidirect
7. C2×#15689056C2semidirect
8. C2×#15689046C2semidirect
9. C2×#15689045C2semidirect
10. C2×#15689045C2semidirect
11. C2×#15689039C2semidirect
12. C2×#15689038C2semidirect
13. C2×#15689001C2semidirect
14. C2×#15688999C2semidirect
15. C2×#15688980C2semidirect
16. C2×C47×#396C2semidirect
24. C2×#13094009C22semidirect
26. C2×#13094006C22semidirect
38. C2×C4⋊C4×D47C22semidirect
48. #15689057C22semidirect
49. #15689056C22semidirect
50. #15689046C22semidirect
51. #15689045C22semidirect
52. #15689045C22semidirect
53. #15689039C22semidirect
54. #15689038C22semidirect
55. #15689001C22semidirect
56. #15688999C22semidirect
57. #15688980C22semidirect
69. C47×#396C22semidirect
99. C22×C4×D47D4semidirect
262. C2×C4×D47C2×D4semidirect
451. C2×#396D47semidirect
458. C2×C47#2618semidirect
510. #396C2×D47semidirect
522. C47C2×#2618semidirect
895. C2#20249135direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940092
C22×#130940062
C22×#130939972
C22×C4⋊C4×D472
#202491352
C2×#156890572
C2×#156890562
C2×#156890462
C2×#156890452
C2×#156890392
C2×#156890382
C2×#156890012
C2×#156889992
C2×#156889802
C2×C47×#3962
C2×#261847