Finite Group Databasebeta

← C2×#20246544 #26378874

Subgroups — C2×#20246544 #26378874

Order 12032.

3302 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093997C211yesmaximal, characteristic
2#20246544C2116yesmaximal, direct product factor
3C2×#15689024C211yesmaximal, characteristic, complemented
4C2×#15689023C211yesmaximal, characteristic, complemented
5C2×#15689016C211yesmaximal, characteristic, complemented
6C2×#15689013C211yesmaximal, characteristic, complemented
7C2×#15689005C211yesmaximal, characteristic, complemented
8C2×#15689004C211yesmaximal, characteristic, complemented
9C2×#15689002C211yesmaximal, characteristic, complemented
10C2×#15689002C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15688999C211yesmaximal, characteristic, complemented
13C2×#15688997C211yesmaximal, characteristic, complemented
14C2×#15688985C211yesmaximal, characteristic, complemented
15C2×#15688980C211yesmaximal, 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—
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39#15689024C2218yescomplemented
40#15689023C2218yescomplemented
41#15689016C2218yescomplemented
42#15689013C2218yescomplemented
43#15689005C2218yescomplemented
44#15689004C2218yescomplemented
45#15689002C2218yescomplemented
46#15689002C2218yescomplemented
47#15689001C2218yescomplemented
48#15688999C2218yescomplemented
49#15688997C2218yescomplemented
50#15688985C2218yescomplemented
51#15688980C2218yescomplemented
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C24×C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C47×#385C2218yescomplemented
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C24×D47C2311yescharacteristic
69C24×D47C2311yescharacteristic
70C22×D188—42no—
71C22×D188—42no—
72C22×D188C2×C418yescomplemented
73C22×D188C2314yes—
74C22×C22⋊D47—42no—
75C22×C22⋊D47—42no—
76C22×C22⋊D47—42no—
77C22×C22⋊D47—42no—
78C22×C22⋊D47C2×C418yes—
79C22×C22⋊D47C2×C418yescomplemented
80C22×C22⋊D47C2314yes—
81C22×C22⋊D47C2314yes—
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C22×C4×D47—42no—
89C22×C4×D47—42no—
90C22×C4×D47—42no—
91C22×C4×D47—42no—
92C22×C4×D47—42no—
93C22×C4×D47C2×C418yescomplemented
94C22×C4×D47C2314yes—
95C22×C4×D47C2314yes—
96#13093997C2×C4164yescomplemented
97C2×C4⋊Dic47—42no—
98C2×C4⋊Dic47C2314yes—
99C2×Dic47⋊C4—42no—
100C2×Dic47⋊C4C2×C418yescomplemented
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×C22⋊Dic47—42no—
104C2×C22⋊Dic47—42no—
105C2×C22⋊Dic47C2314yes—
106C2×C22⋊Dic47C2314yes—
107C2×(C2×D47)⋊C4—42no—
108C2×(C2×D47)⋊C4—42no—
109C2×(C2×D47)⋊C4—42no—
110C2×(C2×D47)⋊C4—42no—
111C2×(C2×D47)⋊C4—42no—
112C2×(C2×D47)⋊C4—42no—
113C2×(C2×D47)⋊C4—42no—
114C2×(C2×D47)⋊C4C2×C418yescomplemented
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×C4×Dic47—42no—
124C2×C4×Dic47—42no—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C25×C47C2311yescharacteristic
136C23×C4×C47—42no—
137C23×C4×C47—42no—
138C23×C4×C47—42no—
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2314yes—
146C2×C4⋊C4×C47—42no—
147C2×C4⋊C4×C47—42no—
148C2×C4⋊C4×C47C2314yes—
149C2×C4⋊C4×C47C2314yes—
150C2×C22⋊C4×C47—42no—
151C2×C22⋊C4×C47C2×C418yescomplemented
152C2×C22⋊C4×C47C2314yes—
153C2×C22⋊C4×C47C2314yes—
154#95×C47C2314yes—
155#95×C47C2314yes—
156C24×C47—22no—
157C24×C47—22no—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47C22×C414yes—
163C24×C47C2412yes—
164C24×C47C2411yescharacteristic
165C23×D47—22no—
166C23×D47—22no—
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47—22no—
172C23×D47—22no—
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47C22×C414yes—
178C23×D47C22×C414yes—
179C23×D47C2412yes—
180C23×D47C2412yes—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
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—44no—
198C22×C4×C47—44no—
199C22×C4×C47—44no—
200C22×C4×C47—416no—
201C22×C4×C47C22×C414yes—
202C22×C4×C47C22×C414yes—
203C22×C4×C47C2412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2412yes—
206C22×C4×C47C2412yes—
207C22×C4×C47C2412yes—
208C22×C4×C47C2412yes—
209C2×C22⋊D47—416no—
210C2×C22⋊D47—416no—
211C2×C22⋊D47—44no—
212C2×C22⋊D47—44no—
213C2×C22⋊D47—44no—
214C2×C22⋊D47—44no—
215C2×C22⋊D47C22×C4116yes—
216C2×C22⋊D47C22×C4116yescomplemented
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
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×Dic47C22×C414yes—
234C22×Dic47C22×C414yes—
235C22×Dic47C2412yes—
236C22×Dic47C2412yes—
237C22×Dic47C2412yes—
238C22×Dic47C2412yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C2×D188—416no—
242C2×D188—44no—
243C2×D188—44no—
244C2×D188C22×C4116yescomplemented
245C2×C4×D47—416no—
246C2×C4×D47—44no—
247C2×C4×D47—44no—
248C2×C4×D47—44no—
249C2×C4×D47—44no—
250C2×C4×D47—44no—
251C2×C4×D47—416no—
252C2×C4×D47C22×C4116yescomplemented
253C4⋊C4×C47—44no—
254C4⋊C4×C47—44no—
255C22⋊C4×C47—44no—
256C22⋊C4×C47C22×C4116yescomplemented
257C22⋊Dic47—44no—
258C22⋊Dic47—44no—
259(C2×D47)⋊C4—44no—
260(C2×D47)⋊C4—44no—
261(C2×D47)⋊C4—44no—
262(C2×D47)⋊C4—44no—
263(C2×D47)⋊C4—44no—
264(C2×D47)⋊C4—44no—
265(C2×D47)⋊C4—44no—
266(C2×D47)⋊C4C22×C4116yescomplemented
267C4⋊Dic47—44no—
268Dic47⋊C4—44no—
269Dic47⋊C4C22×C4116yescomplemented
270C4×Dic47—44no—
271C4×Dic47—44no—
272C23×C47—28no—
273C23×C47—28no—
274C23×C47—28no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—44no—
282C23×C47—44no—
283C23×C47—44no—
284C23×C47—44no—
285C23×C47C23×C414yes—
286C23×C47C23×C412yes—
287C23×C47H(5,𝔽2)12yes—
288C23×C47H(5,𝔽2)12yes—
289C23×C47H(5,𝔽2)12yes—
290C23×C47H(5,𝔽2)12yes—
291C23×C47H(5,𝔽2)12yes—
292C23×C472−1+412yes—
293C23×C47C2511yescharacteristic
294C22×D47—28no—
295C22×D47—28no—
296C22×D47—28no—
297C22×D47—28no—
298C22×D47—28no—
299C22×D47—28no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—22no—
312C22×D47—44no—
313C22×D47—44no—
314C22×D47—44no—
315C22×D47—44no—
316C22×D47—44no—
317C22×D47—44no—
318C22×D47—44no—
319C22×D47—44no—
320C22×D47C23×C414yes—
321C22×D47C23×C414yes—
322C2×C4×C47—28no—
323C2×C4×C47—28no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
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—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—416no—
341C2×C4×C47—44no—
342C2×C4×C47—44no—
343C2×C4×C47—44no—
344C2×C4×C47—44no—
345C2×C4×C47C23×C414yes—
346C2×C4×C47C23×C414yes—
347C22⋊D47—416no—
348C22⋊D47—416no—
349C2×Dic47—28no—
350C2×Dic47—28no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—22no—
357C2×Dic47—22no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—22no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—44no—
368C2×Dic47—44no—
369C2×Dic47—44no—
370C2×Dic47—44no—
371C2×Dic47C23×C414yes—
372C2×Dic47C23×C414yes—
373D188—416no—
374C4×D47—416no—
375C4×D47—416no—
376C2×#2377—471nomaximal, Sylow
377C22×C47—24no—
378C22×C47—24no—
379C22×C47—24no—
380C22×C47—416no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—42no—
385C22×C47#51814yes—
386C22×C47#51814yes—
387C22×C47#52014yes—
388C22×C47#56014yes—
389C22×C47#56014yes—
390C22×C47#56214yes—
391C22×C47#56214yes—
392C22×C47C24×C411yescharacteristic
393C22×C47C2×H(5,𝔽2)11yescharacteristic
394C22×C47C2×H(5,𝔽2)11yescharacteristic
395C22×C47C2×H(5,𝔽2)11yescharacteristic
396C22×C47C2×H(5,𝔽2)11yescharacteristic
397C22×C47C2×H(5,𝔽2)11yescharacteristic
398C22×C47C2×2−1+411yescharacteristic
399C2×D47—24no—
400C2×D47—24no—
401C2×D47—24no—
402C2×D47—24no—
403C2×D47—24no—
404C2×D47—24no—
405C2×D47—416no—
406C2×D47—416no—
407C2×D47—42no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—42no—
412C2×D47—42no—
413C2×D47—42no—
414C2×D47—42no—
415C4×C47—24no—
416C4×C47—24no—
417C4×C47—42no—
418C4×C47—42no—
419C4×C47—42no—
420C4×C47—42no—
421Dic47—24no—
422Dic47—24no—
423Dic47—42no—
424Dic47—42no—
425Dic47—42no—
426Dic47—42no—
427C22×#121—471no—
428#2377—4716no—
429C2×#390—471no—
430C2×#390—471no—
431C2×#388—471no—
432C2×#388—471no—
433C2×#387—471no—
434C2×#387—471no—
435C2×#386—471no—
436C2×#386—471no—
437C2×#386—471no—
438C2×#386—471no—
439C2×#385—471no—
440C2×#385D4711yescharacteristic, complemented
441C2×#381—471no—
442C2×#380—471no—
443C2×C47—44no—
444C2×C47#237718yescomplemented
445C2×C47C2×#51811yescharacteristic
446C2×C47C2×#51811yescharacteristic
447C2×C47C2×#52011yescharacteristic
448C2×C47C2×#56011yescharacteristic
449C2×C47C2×#56011yescharacteristic
450C2×C47C2×#56211yescharacteristic
451C2×C47C2×#56211yescharacteristic
452D47—44no—
453D47—44no—
454C23×D4—471no—
455C23×D4—471no—
456C23×D4—471no—
457C24×C4—471no—
458C24×C4—471no—
459C24×C4C2×D4711yescharacteristic
460C2×#121—4716no—
461C2×#121—478no—
462C22×C4⋊C4—471no—
463C22×C4⋊C4—471no—
464C22×C4⋊C4—471no—
465C22×C4⋊C4C2×D4711yescharacteristic
466C22×C4⋊C4C2×D4711yescharacteristic
467C22×C22⋊C4—471no—
468C22×C22⋊C4—471no—
469C22×C22⋊C4—471no—
470C22×C22⋊C4—471no—
471C22×C22⋊C4—471no—
472C22×C22⋊C4—471no—
473C22×C22⋊C4—471no—
474C22×C22⋊C4—471no—
475C22×C22⋊C4—471no—
476C22×C22⋊C4—471no—
477C22×C22⋊C4C2×D4711yescharacteristic
478C22×C22⋊C4C2×D4711yescharacteristic
479C22×C42—471no—
480C22×C42—471no—
481#390—478no—
482#390—478no—
483#388—478no—
484#388—478no—
485#387—478no—
486#387—478no—
487#386—478no—
488#386—478no—
489#386—478no—
490#386—478no—
491#385—478no—
492#385C2×D4718yescomplemented
493#381—478no—
494#380—478no—
495C2×#95—471no—
496C2×#95—471no—
497C2×#95—471no—
498C2×#95—471no—
499C2×#95—471no—
500C2×#95—471no—
501C2×#95—471no—
502C2×#95—471no—
503C2×#95C2×D4711yescharacteristic
504C2×#95C2×D4711yescharacteristic
505C47C2×#237711yescharacteristic, complemented, Sylow
506C25—471no—
507C25—471no—
508C25C22×D4711yescharacteristic
509C22×D4—478no—
510C22×D4—478no—
511C22×D4—474no—
512C22×D4—474no—
513C22×D4—478no—
514C22×D4—474no—
515C22×D4—1882no—
516C22×D4—1882no—
517C22×D4—1882no—
518C22×D4—1882no—
519C22×D4—1882no—
520C22×D4—1882no—
521C23×C4—42no—
522C23×C4—42no—
523C23×C4—42no—
524C23×C4—471no—
525C23×C4—471no—
526C23×C4—478no—
527C23×C4—474no—
528C23×C4—471no—
529C23×C4—471no—
530C23×C4—471no—
531C23×C4—471no—
532C23×C4—474no—
533C23×C4—1882no—
534C23×C4—1882no—
535C23×C4—1882no—
536C23×C4—1882no—
537C23×C4—1882no—
538C23×C4C22×D4711yescharacteristic
539C23×C4C22×D4711yescharacteristic
540C23×C4C22×D4711yescharacteristic
541C23×C4C22×D4711yescharacteristic
542C23×C4C22×D4711yescharacteristic
543C23×C4C22×D4711yescharacteristic
544C23×C4C22×D4714yes—
545#121—4764no—
546C2×C4⋊C4—42no—
547C2×C4⋊C4—42no—
548C2×C4⋊C4—478no—
549C2×C4⋊C4—474no—
550C2×C4⋊C4—474no—
551C2×C4⋊C4—474no—
552C2×C4⋊C4—1882no—
553C2×C4⋊C4—1882no—
554C2×C4⋊C4C22×D4714yes—
555C2×C4⋊C4C22×D4714yes—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—478no—
558C2×C22⋊C4—474no—
559C2×C22⋊C4—474no—
560C2×C22⋊C4—474no—
561C2×C22⋊C4—474no—
562C2×C22⋊C4—474no—
563C2×C22⋊C4—474no—
564C2×C22⋊C4—474no—
565C2×C22⋊C4—474no—
566C2×C22⋊C4—474no—
567C2×C22⋊C4—474no—
568C2×C22⋊C4—1882no—
569C2×C22⋊C4—1882no—
570C2×C22⋊C4—1882no—
571C2×C22⋊C4—1882no—
572C2×C22⋊C4—1882no—
573C2×C22⋊C4—1882no—
574C2×C22⋊C4—1882no—
575C2×C22⋊C4—1882no—
576C2×C22⋊C4—1882no—
577C2×C22⋊C4C4×D4718yescomplemented
578C2×C22⋊C4C22×D4714yes—
579C2×C22⋊C4C22×D4714yes—
580C2×C42—474no—
581C2×C42—474no—
582C2×C42—1882no—
583C2×C42—1882no—
584#95—474no—
585#95—474no—
586#95—474no—
587#95—474no—
588#95—474no—
589#95—474no—
590#95—474no—
591#95—474no—
592#95C22×D4714yes—
593#95C22×D4714yes—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—474no—
601C24—474no—
602C24—472no—
603C24—472no—
604C24—942no—
605C24—942no—
606C24—942no—
607C24—942no—
608C24—942no—
609C24—942no—
610C24—942no—
611C24—942no—
612C24—942no—
613C24—942no—
614C24—942no—
615C24—942no—
616C24C2×C4×D4714yes—
617C24C23×D4712yes—
618C24C23×D4711yescharacteristic
619C2×D4—4716no—
620C2×D4—4716no—
621C2×D4—4716no—
622C2×D4—18816no—
623C2×D4—1884no—
624C2×D4—1884no—
625C2×D4—18816no—
626C2×D4—18816no—
627C2×D4—1884no—
628C2×D4—1884no—
629C2×D4—1884no—
630C2×D4—1884no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—416no—
651C22×C4—474no—
652C22×C4—474no—
653C22×C4—472no—
654C22×C4—472no—
655C22×C4—4716no—
656C22×C4—472no—
657C22×C4—472no—
658C22×C4—472no—
659C22×C4—472no—
660C22×C4—942no—
661C22×C4—942no—
662C22×C4—942no—
663C22×C4—942no—
664C22×C4—942no—
665C22×C4—942no—
666C22×C4—942no—
667C22×C4—942no—
668C22×C4—942no—
669C22×C4—942no—
670C22×C4—942no—
671C22×C4—942no—
672C22×C4—942no—
673C22×C4—942no—
674C22×C4—942no—
675C22×C4—942no—
676C22×C4—18816no—
677C22×C4—1884no—
678C22×C4—1884no—
679C22×C4—1884no—
680C22×C4—1884no—
681C22×C4—1884no—
682C22×C4—18816no—
683C22×C4C2×C4×D4714yes—
684C22×C4C2×C4×D4714yes—
685C22×C4C23×D4712yes—
686C22×C4C23×D4712yes—
687C22×C4C23×D4712yes—
688C22×C4C23×D4712yes—
689C22×C4C23×D4712yes—
690C22×C4C23×D4712yes—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—4716no—
694C4⋊C4—1884no—
695C4⋊C4—1884no—
696C22⋊C4—44no—
697C22⋊C4—4716no—
698C22⋊C4—1884no—
699C22⋊C4—1884no—
700C22⋊C4—1884no—
701C22⋊C4—1884no—
702C22⋊C4—1884no—
703C22⋊C4—1884no—
704C22⋊C4—1884no—
705C22⋊C4—1884no—
706C22⋊C4—1884no—
707C22⋊C4C2×C4×D47116yescomplemented
708C42—1884no—
709C42—1884no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—474no—
724C23—474no—
725C23—948no—
726C23—948no—
727C23—948no—
728C23—948no—
729C23—948no—
730C23—948no—
731C23—942no—
732C23—942no—
733C23—942no—
734C23—942no—
735C23—942no—
736C23—942no—
737C23—942no—
738C23—942no—
739C23—942no—
740C23—942no—
741C23—942no—
742C23—942no—
743C23—1884no—
744C23—1884no—
745C23—1884no—
746C23—1884no—
747C23—1884no—
748C23—1884no—
749C23—1884no—
750C23—1884no—
751C23C22×C4×D4714yes—
752C23C22×C4×D4712yes—
753C23#1309406912yes—
754C23#1309406912yes—
755C23#1309406912yes—
756C23#1309407012yes—
757C23#1309407012yes—
758C23#1309407212yes—
759C23C24×D4711yescharacteristic
760D4—18816no—
761D4—18816no—
762D4—18816no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—474no—
787C2×C4—474no—
788C2×C4—948no—
789C2×C4—948no—
790C2×C4—942no—
791C2×C4—942no—
792C2×C4—942no—
793C2×C4—942no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—942no—
797C2×C4—942no—
798C2×C4—942no—
799C2×C4—942no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—942no—
806C2×C4—18816no—
807C2×C4—18816no—
808C2×C4—1884no—
809C2×C4—1884no—
810C2×C4—1884no—
811C2×C4—1884no—
812C2×C4C22×C4×D4714yes—
813C2×C4C22×C4×D4714yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—944no—
823C22—944no—
824C22—944no—
825C22—944no—
826C22—944no—
827C22—944no—
828C22—18816no—
829C22—18816no—
830C22—1882no—
831C22—1882no—
832C22—1882no—
833C22—1882no—
834C22—1882no—
835C22—1882no—
836C22—1882no—
837C22—1882no—
838C22#1568959514yes—
839C22#1568959514yes—
840C22#1568960414yes—
841C22#1568986214yes—
842C22#1568986314yes—
843C22#1568986914yes—
844C22#1568986914yes—
845C22C23×C4×D4711yescharacteristic
846C22C2×#1309406911yescharacteristic
847C22C2×#1309406911yescharacteristic
848C22C2×#1309406911yescharacteristic
849C22C2×#1309407011yescharacteristic
850C22C2×#1309407011yescharacteristic
851C22C2×#1309407211yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—944no—
859C4—944no—
860C4—1882no—
861C4—1882no—
862C4—1882no—
863C4—1882no—
864C2—44no—
865C2—1884no—
866C2—1884no—
867C2#2024654418yesdirect product factor
868C2C2×#1568959511yescharacteristic
869C2C2×#1568959511yescharacteristic
870C2C2×#1568960411yescharacteristic
871C2C2×#1568986211yescharacteristic
872C2C2×#1568986311yescharacteristic
873C2C2×#1568986911yescharacteristic
874C2C2×#1568986911yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC22×#13093997C2
cosocleC23×C47C25
hypercenterC2×#385D47
hypocenterC47C2×#2377
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #20246544C2direct (N × H)
3. C2×#15689024C2semidirect
4. C2×#15689023C2semidirect
5. C2×#15689016C2semidirect
6. C2×#15689013C2semidirect
7. C2×#15689005C2semidirect
8. C2×#15689004C2semidirect
9. C2×#15689002C2semidirect
10. C2×#15689002C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15688999C2semidirect
13. C2×#15688997C2semidirect
14. C2×#15688985C2semidirect
15. C2×#15688980C2semidirect
16. C2×C47×#385C2semidirect
22. C2×#13093997C4semidirect
39. #15689024C22semidirect
40. #15689023C22semidirect
41. #15689016C22semidirect
42. #15689013C22semidirect
43. #15689005C22semidirect
44. #15689004C22semidirect
45. #15689002C22semidirect
46. #15689002C22semidirect
47. #15689001C22semidirect
48. #15688999C22semidirect
49. #15688997C22semidirect
50. #15688985C22semidirect
51. #15688980C22semidirect
65. C47×#385C22semidirect
72. C22×D188C2×C4semidirect
79. C22×C22⋊D47C2×C4semidirect
93. C22×C4×D47C2×C4semidirect
96. #13093997C2×C4semidirect
100. C2×Dic47⋊C4C2×C4semidirect
114. C2×(C2×D47)⋊C4C2×C4semidirect
151. C2×C22⋊C4×C47C2×C4semidirect
216. C2×C22⋊D47C22×C4semidirect
244. C2×D188C22×C4semidirect
252. C2×C4×D47C22×C4semidirect
256. C22⋊C4×C47C22×C4semidirect
266. (C2×D47)⋊C4C22×C4semidirect
269. Dic47⋊C4C22×C4semidirect
440. C2×#385D47semidirect
444. C2×C47#2377semidirect
492. #385C2×D47semidirect
505. C47C2×#2377semidirect
577. C2×C22⋊C4C4×D47semidirect
707. C22⋊C4C2×C4×D47semidirect
867. C2#20246544direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939972
#202465442
C2×#156890242
C2×#156890232
C2×#156890162
C2×#156890132
C2×#156890052
C2×#156890042
C2×#156890022
C2×#156890012
C2×#156889992
C2×#156889972
C2×#156889852
C2×#156889802
C2×C47×#3852
C2×#237747