Finite Group Databasebeta

← C2×#20246080 #26375031

Subgroups — C2×#20246080 #26375031

Order 12032.

3934 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093997C211yesmaximal, characteristic
2C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3C22×#13093982C211yesmaximal, characteristic, complemented
4#20246080C2116yesmaximal, direct product factor
5C2×#15689024C211yesmaximal, characteristic, complemented
6C2×#15689023C211yesmaximal, characteristic, complemented
7C2×#15689023C211yesmaximal, characteristic, complemented
8C2×#15689018C211yesmaximal, characteristic, complemented
9C2×#15689016C211yesmaximal, characteristic, complemented
10C2×#15689015C211yesmaximal, characteristic, complemented
11C2×#15689002C211yesmaximal, characteristic, complemented
12C2×#15689001C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×#15688982C211yesmaximal, characteristic, complemented
15C2×#15688974C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×#13093997C4116yescomplemented
23C2×#13093997C2218yes—
24C2×C4×C22⋊D47—28no—
25C2×C4×C22⋊D47C2218yescomplemented
26C2×#13093982—28no—
27C2×#13093982C2218yescomplemented
28C22×C4⋊Dic47C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45C22×C4×Dic47C2211yescharacteristic
46C22×C4×Dic47C2211yescharacteristic
47#15689024C2218yescomplemented
48#15689023C2218yescomplemented
49#15689023C2218yescomplemented
50#15689018C2218yescomplemented
51#15689016C2218yescomplemented
52#15689015C2218yescomplemented
53#15689002C2218yescomplemented
54#15689001C2218yescomplemented
55#15688994C2218yescomplemented
56#15688982C2218yescomplemented
57#15688974C2218yescomplemented
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C24×C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#385C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C24×D47C2311yescharacteristic
72C22×D188—42no—
73C22×D188—42no—
74C22×D188C2×C418yescomplemented
75C22×D188C2314yes—
76C22×C22⋊D47—24no—
77C22×C22⋊D47—24no—
78C22×C22⋊D47—42no—
79C22×C22⋊D47—42no—
80C22×C22⋊D47C2×C418yes—
81C22×C22⋊D47C2×C418yescomplemented
82C22×C22⋊D47C2314yes—
83C22×C22⋊D47C2314yes—
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47—42no—
94C22×C4×D47—42no—
95C22×C4×D47C2×C418yescomplemented
96C22×C4×D47C2314yes—
97C22×C4×D47C2314yes—
98#13093997C2×C4164yescomplemented
99C4×C22⋊D47—232no—
100#13093982—232no—
101C2×C4⋊Dic47—24no—
102C2×C4⋊Dic47C2314yes—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—24no—
105C2×Dic47⋊C4—42no—
106C2×Dic47⋊C4C2×C418yescomplemented
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×C22⋊Dic47—24no—
112C2×C22⋊Dic47—42no—
113C2×C22⋊Dic47C2314yes—
114C2×C22⋊Dic47C2314yes—
115C2×(C2×D47)⋊C4—24no—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—42no—
119C2×(C2×D47)⋊C4—42no—
120C2×(C2×D47)⋊C4—42no—
121C2×(C2×D47)⋊C4—42no—
122C2×(C2×D47)⋊C4C2×C418yescomplemented
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×C4×Dic47—24no—
132C2×C4×Dic47—42no—
133C2×C4×Dic47—42no—
134C2×C4×Dic47D418yescomplemented
135C2×C4×Dic47C2314yes—
136C2×C4×Dic47C2314yes—
137C2×C4×Dic47C2314yes—
138C2×C4×Dic47C2314yes—
139C47⋊#95C2314yes—
140C47⋊#95C2314yes—
141C47⋊#95C2314yes—
142C47⋊#95C2314yes—
143C25×C47C2311yescharacteristic
144C23×C4×C47—24no—
145C23×C4×C47—42no—
146C23×C4×C47—42no—
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2314yes—
154C2×C4⋊C4×C47—24no—
155C2×C4⋊C4×C47—42no—
156C2×C4⋊C4×C47C2314yes—
157C2×C4⋊C4×C47C2314yes—
158C2×C22⋊C4×C47—42no—
159C2×C22⋊C4×C47C2×C418yescomplemented
160C2×C22⋊C4×C47C2314yes—
161C2×C22⋊C4×C47C2314yes—
162#95×C47C2314yes—
163#95×C47C2314yes—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47C22×C414yes—
171C24×C47C2412yes—
172C24×C47C2411yescharacteristic
173C23×D47—22no—
174C23×D47—22no—
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×D47C22×C414yes—
186C23×D47C22×C414yes—
187C23×D47C2412yes—
188C23×D47C2412yes—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
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—28no—
205C22×C4×C47—44no—
206C22×C4×C47—44no—
207C22×C4×C47—416no—
208C22×C4×C47C22×C414yes—
209C22×C4×C47C22×C414yes—
210C22×C4×C47C2×D414yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2412yes—
217C2×C22⋊D47—232no—
218C2×C22⋊D47—28no—
219C2×C22⋊D47—28no—
220C2×C22⋊D47—416no—
221C2×C22⋊D47—44no—
222C2×C22⋊D47—44no—
223C2×C22⋊D47C22×C4116yes—
224C2×C22⋊D47C22×C4116yescomplemented
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×Dic47C22×C414yes—
239C22×Dic47C22×C414yes—
240C22×Dic47C2×D414yes—
241C22×Dic47C2×D414yes—
242C22×Dic47#4114yes—
243C22×Dic47C2412yes—
244C22×Dic47C2412yes—
245C22×Dic47C2412yes—
246C22×Dic47C2412yes—
247C22×Dic47C2412yes—
248C22×Dic47C2412yes—
249C2×D188—416no—
250C2×D188—44no—
251C2×D188—44no—
252C2×D188C22×C4116yescomplemented
253C2×C4×D47—232no—
254C2×C4×D47—28no—
255C2×C4×D47—28no—
256C2×C4×D47—28no—
257C2×C4×D47—44no—
258C2×C4×D47—44no—
259C2×C4×D47—416no—
260C2×C4×D47C22×C4116yescomplemented
261C4⋊C4×C47—28no—
262C4⋊C4×C47—44no—
263C22⋊C4×C47—44no—
264C22⋊C4×C47C22×C4116yescomplemented
265C22⋊Dic47—28no—
266C22⋊Dic47—44no—
267(C2×D47)⋊C4—28no—
268(C2×D47)⋊C4—28no—
269(C2×D47)⋊C4—28no—
270(C2×D47)⋊C4—44no—
271(C2×D47)⋊C4—44no—
272(C2×D47)⋊C4—44no—
273(C2×D47)⋊C4—44no—
274(C2×D47)⋊C4C22×C4116yescomplemented
275C4⋊Dic47—28no—
276Dic47⋊C4—28no—
277Dic47⋊C4—28no—
278Dic47⋊C4—44no—
279Dic47⋊C4C22×C4116yescomplemented
280C4×Dic47—28no—
281C4×Dic47—44no—
282C4×Dic47—44no—
283C4×Dic47C2×D4116yescomplemented
284C23×C47—28no—
285C23×C47—28no—
286C23×C47—28no—
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×C47C23×C414yes—
298C23×C47C23×C412yes—
299C23×C47C22×D412yes—
300C23×C47C2×#4112yes—
301C23×C47H(5,𝔽2)12yes—
302C23×C47H(5,𝔽2)12yes—
303C23×C47H(5,𝔽2)12yes—
304C23×C472−1+412yes—
305C23×C47C2511yescharacteristic
306C22×D47—28no—
307C22×D47—28no—
308C22×D47—28no—
309C22×D47—28no—
310C22×D47—28no—
311C22×D47—28no—
312C22×D47—22no—
313C22×D47—22no—
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—44no—
325C22×D47—44no—
326C22×D47—44no—
327C22×D47—44no—
328C22×D47—44no—
329C22×D47—44no—
330C22×D47—44no—
331C22×D47—44no—
332C22×D47C23×C414yes—
333C22×D47C23×C414yes—
334C2×C4×C47—28no—
335C2×C4×C47—28no—
336C2×C4×C47—28no—
337C2×C4×C47—22no—
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—416no—
353C2×C4×C47—44no—
354C2×C4×C47—44no—
355C2×C4×C47—44no—
356C2×C4×C47C23×C414yes—
357C2×C4×C47C23×C414yes—
358C2×C4×C47C22×D414yes—
359C22⋊D47—232no—
360C22⋊D47—416no—
361C2×Dic47—28no—
362C2×Dic47—28no—
363C2×Dic47—22no—
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—44no—
377C2×Dic47—44no—
378C2×Dic47—44no—
379C2×Dic47C4×D4116yes—
380C2×Dic47C23×C414yes—
381C2×Dic47C23×C414yes—
382C2×Dic47C22×D414yes—
383C2×Dic47C22×D414yes—
384C2×Dic47C2×#4114yes—
385D188—416no—
386C4×D47—232no—
387C4×D47—416no—
388C2×#2324—471nomaximal, Sylow
389C22×C47—24no—
390C22×C47—24no—
391C22×C47—24no—
392C22×C47—416no—
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47C2×C4×D414yes—
398C22×C47#51814yes—
399C22×C47#52014yes—
400C22×C47#53514yes—
401C22×C47#53714yes—
402C22×C47#54014yes—
403C22×C47#54214yes—
404C22×C47C24×C411yescharacteristic
405C22×C47C23×D411yescharacteristic
406C22×C47C22×#4111yescharacteristic
407C22×C47C2×H(5,𝔽2)11yescharacteristic
408C22×C47C2×H(5,𝔽2)11yescharacteristic
409C22×C47C2×H(5,𝔽2)11yescharacteristic
410C22×C47C2×2−1+411yescharacteristic
411C2×D47—24no—
412C2×D47—24no—
413C2×D47—24no—
414C2×D47—24no—
415C2×D47—24no—
416C2×D47—24no—
417C2×D47—416no—
418C2×D47—416no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—42no—
424C2×D47—42no—
425C2×D47—42no—
426C2×D47—42no—
427C4×C47—24no—
428C4×C47—24no—
429C4×C47—24no—
430C4×C47—42no—
431C4×C47—42no—
432C4×C47—42no—
433Dic47—24no—
434Dic47—24no—
435Dic47—42no—
436Dic47—42no—
437Dic47—42no—
438Dic47C2×C4×D418yes—
439C22×#121—471no—
440C22×C4×D4—471no—
441C22×#117—471no—
442#2324—4716no—
443C2×#390—471no—
444C2×#390—471no—
445C2×#390—471no—
446C2×#389—471no—
447C2×#388—471no—
448C2×#388—471no—
449C2×#386—471no—
450C2×#386—471no—
451C2×#385—471no—
452C2×#385D4711yescharacteristic, complemented
453C2×#380—471no—
454C2×C4×C4⋊C4—471no—
455C2×C47—44no—
456C2×C47#232418yescomplemented
457C2×C47C22×C4×D411yescharacteristic
458C2×C47C2×#51811yescharacteristic
459C2×C47C2×#52011yescharacteristic
460C2×C47C2×#53511yescharacteristic
461C2×C47C2×#53711yescharacteristic
462C2×C47C2×#54011yescharacteristic
463C2×C47C2×#54211yescharacteristic
464D47—44no—
465D47—44no—
466C23×D4—471no—
467C23×D4—471no—
468C23×D4—471no—
469C24×C4—471no—
470C24×C4—471no—
471C24×C4C2×D4711yescharacteristic
472C2×#121—4716no—
473C2×#121—478no—
474C2×C4×D4—478no—
475C2×C4×D4—948no—
476C2×#117—478no—
477C2×#117—948no—
478C22×C4⋊C4—471no—
479C22×C4⋊C4—471no—
480C22×C4⋊C4—471no—
481C22×C4⋊C4—471no—
482C22×C4⋊C4—471no—
483C22×C4⋊C4C2×D4711yescharacteristic
484C22×C4⋊C4C2×D4711yescharacteristic
485C22×C22⋊C4—471no—
486C22×C22⋊C4—471no—
487C22×C22⋊C4—471no—
488C22×C22⋊C4—471no—
489C22×C22⋊C4—471no—
490C22×C22⋊C4—471no—
491C22×C22⋊C4—471no—
492C22×C22⋊C4—471no—
493C22×C22⋊C4—471no—
494C22×C22⋊C4—471no—
495C22×C22⋊C4C2×D4711yescharacteristic
496C22×C22⋊C4C2×D4711yescharacteristic
497C22×C42—471no—
498C22×C42—471no—
499C22×C42—471no—
500C22×C42—471no—
501#390—478no—
502#390—478no—
503#390—478no—
504#389—478no—
505#388—478no—
506#388—478no—
507#386—478no—
508#386—478no—
509#385—478no—
510#385C2×D4718yescomplemented
511#380—478no—
512C4×C4⋊C4—478no—
513C2×#95—471no—
514C2×#95—471no—
515C2×#95—471no—
516C2×#95—471no—
517C2×#95C2×D4711yescharacteristic
518C2×#95C2×D4711yescharacteristic
519C47C2×#232411yescharacteristic, complemented, Sylow
520C25—471no—
521C25—471no—
522C25C22×D4711yescharacteristic
523C22×D4—478no—
524C22×D4—474no—
525C22×D4—478no—
526C22×D4—474no—
527C22×D4—478no—
528C22×D4—474no—
529C22×D4—944no—
530C22×D4—944no—
531C22×D4—1882no—
532C22×D4—1882no—
533C22×D4—1882no—
534C22×D4—1882no—
535C23×C4—24no—
536C23×C4—42no—
537C23×C4—42no—
538C23×C4—471no—
539C23×C4—471no—
540C23×C4—471no—
541C23×C4—478no—
542C23×C4—474no—
543C23×C4—471no—
544C23×C4—471no—
545C23×C4—471no—
546C23×C4—474no—
547C23×C4—944no—
548C23×C4—944no—
549C23×C4—944no—
550C23×C4—1882no—
551C23×C4—1882no—
552C23×C4C22×D4711yescharacteristic
553C23×C4C22×D4711yescharacteristic
554C23×C4C22×D4711yescharacteristic
555C23×C4C22×D4711yescharacteristic
556C23×C4C22×D4711yescharacteristic
557C23×C4C22×D4711yescharacteristic
558C23×C4C22×D4714yes—
559#121—4764no—
560C4×D4—9432no—
561#117—9432no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—42no—
564C2×C4⋊C4—478no—
565C2×C4⋊C4—474no—
566C2×C4⋊C4—474no—
567C2×C4⋊C4—474no—
568C2×C4⋊C4—474no—
569C2×C4⋊C4—474no—
570C2×C4⋊C4—944no—
571C2×C4⋊C4—944no—
572C2×C4⋊C4—944no—
573C2×C4⋊C4—1882no—
574C2×C4⋊C4C22×D4714yes—
575C2×C4⋊C4C22×D4714yes—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—478no—
578C2×C22⋊C4—474no—
579C2×C22⋊C4—474no—
580C2×C22⋊C4—474no—
581C2×C22⋊C4—474no—
582C2×C22⋊C4—474no—
583C2×C22⋊C4—474no—
584C2×C22⋊C4—474no—
585C2×C22⋊C4—474no—
586C2×C22⋊C4—474no—
587C2×C22⋊C4—474no—
588C2×C22⋊C4—944no—
589C2×C22⋊C4—944no—
590C2×C22⋊C4—944no—
591C2×C22⋊C4—944no—
592C2×C22⋊C4—1882no—
593C2×C22⋊C4—1882no—
594C2×C22⋊C4—1882no—
595C2×C22⋊C4—1882no—
596C2×C22⋊C4—1882no—
597C2×C22⋊C4C4×D4718yescomplemented
598C2×C22⋊C4C22×D4714yes—
599C2×C22⋊C4C22×D4714yes—
600C2×C42—478no—
601C2×C42—474no—
602C2×C42—474no—
603C2×C42—474no—
604C2×C42—474no—
605C2×C42—944no—
606C2×C42—1882no—
607C2×C42—1882no—
608#95—474no—
609#95—474no—
610#95—474no—
611#95—474no—
612#95C22×D4714yes—
613#95C22×D4714yes—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—474no—
621C24—474no—
622C24—472no—
623C24—472no—
624C24—942no—
625C24—942no—
626C24—942no—
627C24—942no—
628C24—942no—
629C24—942no—
630C24—942no—
631C24—942no—
632C24—942no—
633C24—942no—
634C24—942no—
635C24—942no—
636C24C2×C4×D4714yes—
637C24C23×D4712yes—
638C24C23×D4711yescharacteristic
639C2×D4—4716no—
640C2×D4—4716no—
641C2×D4—4716no—
642C2×D4—948no—
643C2×D4—9432no—
644C2×D4—948no—
645C2×D4—18816no—
646C2×D4—1884no—
647C2×D4—1884no—
648C2×D4—18816no—
649C2×D4—1884no—
650C2×D4—1884no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
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—28no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—416no—
670C22×C4—474no—
671C22×C4—474no—
672C22×C4—474no—
673C22×C4—472no—
674C22×C4—474no—
675C22×C4—474no—
676C22×C4—472no—
677C22×C4—472no—
678C22×C4—4716no—
679C22×C4—472no—
680C22×C4—472no—
681C22×C4—472no—
682C22×C4—948no—
683C22×C4—9432no—
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—948no—
699C22×C4—1884no—
700C22×C4—1884no—
701C22×C4—18816no—
702C22×C4C2×C4×D4714yes—
703C22×C4C2×C4×D4714yes—
704C22×C4D4×D4714yes—
705C22×C4C23×D4712yes—
706C22×C4C23×D4712yes—
707C22×C4C23×D4712yes—
708C22×C4C23×D4712yes—
709C22×C4C23×D4712yes—
710C22×C4C23×D4712yes—
711C4⋊C4—28no—
712C4⋊C4—44no—
713C4⋊C4—4716no—
714C4⋊C4—948no—
715C4⋊C4—948no—
716C4⋊C4—948no—
717C4⋊C4—1884no—
718C22⋊C4—44no—
719C22⋊C4—4716no—
720C22⋊C4—948no—
721C22⋊C4—948no—
722C22⋊C4—948no—
723C22⋊C4—948no—
724C22⋊C4—1884no—
725C22⋊C4—1884no—
726C22⋊C4—1884no—
727C22⋊C4—1884no—
728C22⋊C4—1884no—
729C22⋊C4C2×C4×D47116yescomplemented
730C42—4716no—
731C42—948no—
732C42—1884no—
733C42—1884no—
734C23—28no—
735C23—28no—
736C23—28no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—474no—
748C23—474no—
749C23—948no—
750C23—948no—
751C23—948no—
752C23—948no—
753C23—948no—
754C23—948no—
755C23—942no—
756C23—942no—
757C23—942no—
758C23—942no—
759C23—942no—
760C23—942no—
761C23—942no—
762C23—942no—
763C23—942no—
764C23—942no—
765C23—942no—
766C23—942no—
767C23—1884no—
768C23—1884no—
769C23—1884no—
770C23—1884no—
771C23—1884no—
772C23—1884no—
773C23—1884no—
774C23—1884no—
775C23C22×C4×D4714yes—
776C23C22×C4×D4712yes—
777C23C2×D4×D4712yes—
778C23#41×D4712yes—
779C23#1309406912yes—
780C23#1309406912yes—
781C23#1309407012yes—
782C23#1309407212yes—
783C23C24×D4711yescharacteristic
784D4—9432no—
785D4—18816no—
786D4—18816no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—22no—
790C2×C4—28no—
791C2×C4—22no—
792C2×C4—22no—
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—416no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—4716no—
810C2×C4—474no—
811C2×C4—474no—
812C2×C4—474no—
813C2×C4—474no—
814C2×C4—474no—
815C2×C4—9432no—
816C2×C4—948no—
817C2×C4—942no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—942no—
821C2×C4—948no—
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—18816no—
832C2×C4—1884no—
833C2×C4—1884no—
834C2×C4—1884no—
835C2×C4C22×C4×D4714yes—
836C2×C4C22×C4×D4714yes—
837C2×C4C2×D4×D4714yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—416no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—944no—
847C22—944no—
848C22—944no—
849C22—944no—
850C22—944no—
851C22—944no—
852C22—18816no—
853C22—18816no—
854C22—1882no—
855C22—1882no—
856C22—1882no—
857C22—1882no—
858C22—1882no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22C4×D4×D4714yes—
863C22#1568959514yes—
864C22#1568960414yes—
865C22#1568968814yes—
866C22#1568970314yes—
867C22#1568972514yes—
868C22#1568974314yes—
869C22C23×C4×D4711yescharacteristic
870C22C22×D4×D4711yescharacteristic
871C22C2×#41×D4711yescharacteristic
872C22C2×#1309406911yescharacteristic
873C22C2×#1309406911yescharacteristic
874C22C2×#1309407011yescharacteristic
875C22C2×#1309407211yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—478no—
883C4—944no—
884C4—944no—
885C4—1882no—
886C4—1882no—
887C4—1882no—
888C2—44no—
889C2—1884no—
890C2—1884no—
891C2#2024608018yesdirect product factor
892C2C2×C4×D4×D4711yescharacteristic
893C2C2×#1568959511yescharacteristic
894C2C2×#1568960411yescharacteristic
895C2C2×#1568968811yescharacteristic
896C2C2×#1568970311yescharacteristic
897C2C2×#1568972511yescharacteristic
898C2C2×#1568974311yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC22×#13093997C2
cosocleC23×C47C25
hypercenterC2×#385D47
hypocenterC47C2×#2324
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D47C2semidirect
3. C22×#13093982C2semidirect
4. #20246080C2direct (N × H)
5. C2×#15689024C2semidirect
6. C2×#15689023C2semidirect
7. C2×#15689023C2semidirect
8. C2×#15689018C2semidirect
9. C2×#15689016C2semidirect
10. C2×#15689015C2semidirect
11. C2×#15689002C2semidirect
12. C2×#15689001C2semidirect
13. C2×#15688994C2semidirect
14. C2×#15688982C2semidirect
15. C2×#15688974C2semidirect
16. C2×C47×#385C2semidirect
22. C2×#13093997C4semidirect
25. C2×C4×C22⋊D47C22semidirect
27. C2×#13093982C22semidirect
47. #15689024C22semidirect
48. #15689023C22semidirect
49. #15689023C22semidirect
50. #15689018C22semidirect
51. #15689016C22semidirect
52. #15689015C22semidirect
53. #15689002C22semidirect
54. #15689001C22semidirect
55. #15688994C22semidirect
56. #15688982C22semidirect
57. #15688974C22semidirect
67. C47×#385C22semidirect
74. C22×D188C2×C4semidirect
81. C22×C22⋊D47C2×C4semidirect
95. C22×C4×D47C2×C4semidirect
98. #13093997C2×C4semidirect
106. C2×Dic47⋊C4C2×C4semidirect
122. C2×(C2×D47)⋊C4C2×C4semidirect
134. C2×C4×Dic47D4semidirect
159. C2×C22⋊C4×C47C2×C4semidirect
224. C2×C22⋊D47C22×C4semidirect
252. C2×D188C22×C4semidirect
260. C2×C4×D47C22×C4semidirect
264. C22⋊C4×C47C22×C4semidirect
274. (C2×D47)⋊C4C22×C4semidirect
279. Dic47⋊C4C22×C4semidirect
283. C4×Dic47C2×D4semidirect
452. C2×#385D47semidirect
456. C2×C47#2324semidirect
510. #385C2×D47semidirect
519. C47C2×#2324semidirect
597. C2×C22⋊C4C4×D47semidirect
729. C22⋊C4C2×C4×D47semidirect
891. C2#20246080direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939972
C22×C4×C22⋊D472
C22×#130939822
#202460802
C2×#156890242
C2×#156890232
C2×#156890182
C2×#156890162
C2×#156890152
C2×#156890022
C2×#156890012
C2×#156889942
C2×#156889822
C2×#156889742
C2×C47×#3852
C2×#232447