Finite Group Databasebeta

← C2×#20246543 #26378873

Subgroups — C2×#20246543 #26378873

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×#13093999C211yesmaximal, characteristic
2#20246543C2116yesmaximal, direct product factor
3C2×#15689025C211yesmaximal, characteristic, complemented
4C2×#15689024C211yesmaximal, characteristic, complemented
5C2×#15689014C211yesmaximal, characteristic, complemented
6C2×#15689012C211yesmaximal, characteristic, complemented
7C2×#15689009C211yesmaximal, characteristic, complemented
8C2×#15689001C211yesmaximal, characteristic, complemented
9C2×#15689001C211yesmaximal, characteristic, complemented
10C2×#15689001C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15688997C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×#15688985C211yesmaximal, characteristic, complemented
15C2×#15688982C211yesmaximal, characteristic, complemented
16C2×C47×#387C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13093999C4116yescomplemented
24C2×#13093999C2218yes—
25C22×C4⋊Dic47C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
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×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41#15689025C2218yescomplemented
42#15689024C2218yescomplemented
43#15689014C2218yescomplemented
44#15689012C2218yescomplemented
45#15689009C2218yescomplemented
46#15689001C2218yescomplemented
47#15689001C2218yescomplemented
48#15689001C2218yescomplemented
49#15689001C2218yescomplemented
50#15688997C2218yescomplemented
51#15688994C2218yescomplemented
52#15688985C2218yescomplemented
53#15688982C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C42×C47C2211yescharacteristic
63C47×#387C2218yescomplemented
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C24×D47C2311yescharacteristic
69C24×D47C2311yescharacteristic
70C24×D47C2311yescharacteristic
71C22×D188—42no—
72C22×D188—42no—
73C22×D188—42no—
74C22×D188—42no—
75C22×D188—42no—
76C22×D188—42no—
77C22×D188C2×C418yes—
78C22×D188C2×C418yescomplemented
79C22×D188C2×C418yescomplemented
80C22×D188C2314yes—
81C22×D188C2314yes—
82C22×D188C2314yes—
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×D47—42no—
94C22×C4×D47—42no—
95C22×C4×D47—42no—
96C22×C4×D47C2×C418yescomplemented
97C22×C4×D47C2314yes—
98C22×C4×D47C2314yes—
99C22×C4×D47C2314yes—
100#13093999C2×C4164yescomplemented
101C2×C4⋊Dic47—42no—
102C2×C4⋊Dic47C2314yes—
103C2×Dic47⋊C4—42no—
104C2×Dic47⋊C4—42no—
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
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)⋊C4—42no—
115C2×(C2×D47)⋊C4—42no—
116C2×(C2×D47)⋊C4—42no—
117C2×(C2×D47)⋊C4C2×C418yescomplemented
118C2×(C2×D47)⋊C4C2×C418yescomplemented
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
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—42no—
132C2×C4×Dic47C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×C4⋊C4×C47—42no—
147C2×C4⋊C4×C47C2×C418yescomplemented
148C2×C4⋊C4×C47C2314yes—
149C2×C4⋊C4×C47C2314yes—
150C2×C42×C47—42no—
151C2×C42×C47C2314yes—
152#95×C47C2314yes—
153#95×C47C2314yes—
154#95×C47C2314yes—
155#95×C47C2314yes—
156C24×C47C2411yescharacteristic
157C23×D47—22no—
158C23×D47—22no—
159C23×D47—22no—
160C23×D47—22no—
161C23×D47—22no—
162C23×D47—22no—
163C23×D47—22no—
164C23×D47—22no—
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×D47C22×C414yes—
176C23×D47C22×C414yes—
177C23×D47C22×C414yes—
178C23×D47C2412yes—
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—22no—
198C22×C4×C47—22no—
199C22×C4×C47C22×C414yes—
200C22×C4×C47C22×C414yes—
201C22×C4×C47C22×C414yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2412yes—
206C22×C4×C47C2412yes—
207C22×C4×C47C2412yes—
208C22×C4×C47C2412yes—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47C22×C414yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C22×Dic47C2412yes—
228C22×Dic47C2412yes—
229C2×D188—416no—
230C2×D188—416no—
231C2×D188—416no—
232C2×D188—44no—
233C2×D188—44no—
234C2×D188—44no—
235C2×D188—44no—
236C2×D188—44no—
237C2×D188—44no—
238C2×D188C22×C4116yes—
239C2×D188C22×C4116yescomplemented
240C2×D188C22×C4116yescomplemented
241C2×C4×D47—416no—
242C2×C4×D47—44no—
243C2×C4×D47—44no—
244C2×C4×D47—44no—
245C2×C4×D47—44no—
246C2×C4×D47—44no—
247C2×C4×D47—44no—
248C2×C4×D47—44no—
249C2×C4×D47—44no—
250C2×C4×D47—416no—
251C2×C4×D47—416no—
252C2×C4×D47C22×C4116yescomplemented
253C4⋊C4×C47—44no—
254C4⋊C4×C47C22×C4116yescomplemented
255C42×C47—44no—
256(C2×D47)⋊C4—44no—
257(C2×D47)⋊C4—44no—
258(C2×D47)⋊C4—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
267(C2×D47)⋊C4C22×C4116yescomplemented
268C4⋊Dic47—44no—
269Dic47⋊C4—44no—
270Dic47⋊C4—44no—
271C4×Dic47—44no—
272C23×C47C23×C412yes—
273C23×C47H(5,𝔽2)12yes—
274C23×C47H(5,𝔽2)12yes—
275C23×C47H(5,𝔽2)12yes—
276C23×C47H(5,𝔽2)12yes—
277C23×C47H(5,𝔽2)12yes—
278C23×C472−1+412yes—
279C23×C47C2511yescharacteristic
280C22×D47—28no—
281C22×D47—28no—
282C22×D47—28no—
283C22×D47—28no—
284C22×D47—28no—
285C22×D47—28no—
286C22×D47—28no—
287C22×D47—28no—
288C22×D47—28no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—44no—
308C22×D47—44no—
309C22×D47—44no—
310C22×D47—44no—
311C22×D47—44no—
312C22×D47—44no—
313C22×D47—44no—
314C22×D47—44no—
315C22×D47—44no—
316C22×D47—44no—
317C22×D47—44no—
318C22×D47—44no—
319C22×D47C23×C414yes—
320C22×D47C23×C414yes—
321C22×D47C23×C414yes—
322C2×C4×C47—28no—
323C2×C4×C47—28no—
324C2×C4×C47—28no—
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—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—44no—
344C2×C4×C47—44no—
345C2×C4×C47—44no—
346C2×C4×C47—44no—
347C2×C4×C47C23×C414yes—
348C2×C4×C47C23×C414yes—
349C2×C4×C47C23×C414yes—
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—44no—
366C2×Dic47—44no—
367C2×Dic47—44no—
368C2×Dic47—44no—
369C2×Dic47C23×C414yes—
370D188—416no—
371D188—416no—
372D188—416no—
373C4×D47—416no—
374C4×D47—416no—
375C4×D47—416no—
376C2×#2377—471nomaximal, Sylow
377C22×C47#51814yes—
378C22×C47#51814yes—
379C22×C47#52014yes—
380C22×C47#56014yes—
381C22×C47#56014yes—
382C22×C47#56214yes—
383C22×C47#56214yes—
384C22×C47C24×C411yescharacteristic
385C22×C47C2×H(5,𝔽2)11yescharacteristic
386C22×C47C2×H(5,𝔽2)11yescharacteristic
387C22×C47C2×H(5,𝔽2)11yescharacteristic
388C22×C47C2×H(5,𝔽2)11yescharacteristic
389C22×C47C2×H(5,𝔽2)11yescharacteristic
390C22×C47C2×2−1+411yescharacteristic
391C2×D47—24no—
392C2×D47—24no—
393C2×D47—24no—
394C2×D47—24no—
395C2×D47—24no—
396C2×D47—24no—
397C2×D47—24no—
398C2×D47—24no—
399C2×D47—24no—
400C2×D47—416no—
401C2×D47—416no—
402C2×D47—416no—
403C2×D47—42no—
404C2×D47—42no—
405C2×D47—42no—
406C2×D47—42no—
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—24no—
418C4×C47—42no—
419C4×C47—42no—
420C4×C47—42no—
421C4×C47—42no—
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×#387D4711yescharacteristic, complemented
435C2×#386—471no—
436C2×#386—471no—
437C2×#386—471no—
438C2×#386—471no—
439C2×#385—471no—
440C2×#385—471no—
441C2×#381—471no—
442C2×#380—471no—
443C2×C47#237718yescomplemented
444C2×C47C2×#51811yescharacteristic
445C2×C47C2×#51811yescharacteristic
446C2×C47C2×#52011yescharacteristic
447C2×C47C2×#56011yescharacteristic
448C2×C47C2×#56011yescharacteristic
449C2×C47C2×#56211yescharacteristic
450C2×C47C2×#56211yescharacteristic
451D47—44no—
452D47—44no—
453D47—44no—
454C23×D4—471no—
455C23×D4—471no—
456C23×D4—471no—
457C24×C4—471no—
458C24×C4—471no—
459C24×C4—471no—
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⋊C4—471no—
478C22×C22⋊C4—471no—
479C22×C42—471no—
480C22×C42C2×D4711yescharacteristic
481#390—478no—
482#390—478no—
483#388—478no—
484#388—478no—
485#387—478no—
486#387C2×D4718yescomplemented
487#386—478no—
488#386—478no—
489#386—478no—
490#386—478no—
491#385—478no—
492#385—478no—
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×#95C2×D4711yescharacteristic
502C2×#95C2×D4711yescharacteristic
503C2×#95C2×D4711yescharacteristic
504C2×#95C2×D4711yescharacteristic
505C47C2×#237711yescharacteristic, complemented, Sylow
506C25—471no—
507C25—471no—
508C25—471no—
509C22×D4—478no—
510C22×D4—478no—
511C22×D4—478no—
512C22×D4—474no—
513C22×D4—474no—
514C22×D4—474no—
515C22×D4—1882no—
516C22×D4—1882no—
517C22×D4—1882no—
518C22×D4—1882no—
519C22×D4—1882no—
520C22×D4—1882no—
521C23×C4—471no—
522C23×C4—478no—
523C23×C4—474no—
524C23×C4—471no—
525C23×C4—471no—
526C23×C4—471no—
527C23×C4—471no—
528C23×C4—474no—
529C23×C4—474no—
530C23×C4—1882no—
531C23×C4—1882no—
532C23×C4—1882no—
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×D4711yescharacteristic
545#121—4764no—
546C2×C4⋊C4—42no—
547C2×C4⋊C4—474no—
548C2×C4⋊C4—474no—
549C2×C4⋊C4—474no—
550C2×C4⋊C4—1882no—
551C2×C4⋊C4—1882no—
552C2×C4⋊C4—1882no—
553C2×C4⋊C4C4×D4718yescomplemented
554C2×C4⋊C4C22×D4714yes—
555C2×C4⋊C4C22×D4714yes—
556C2×C22⋊C4—478no—
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—474no—
569C2×C22⋊C4—474no—
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⋊C4—1882no—
578C2×C22⋊C4—1882no—
579C2×C22⋊C4—1882no—
580C2×C42—42no—
581C2×C42—474no—
582C2×C42—1882no—
583C2×C42C22×D4714yes—
584#95—474no—
585#95—474no—
586#95—474no—
587#95—474no—
588#95—474no—
589#95—474no—
590#95C22×D4714yes—
591#95C22×D4714yes—
592#95C22×D4714yes—
593#95C22×D4714yes—
594C24—474no—
595C24—474no—
596C24—474no—
597C24—472no—
598C24—472no—
599C24—472no—
600C24—942no—
601C24—942no—
602C24—942no—
603C24—942no—
604C24—942no—
605C24—942no—
606C24—942no—
607C24—942no—
608C24—942no—
609C24—942no—
610C24—942no—
611C24—942no—
612C24—942no—
613C24—942no—
614C24—942no—
615C24—942no—
616C24—942no—
617C24—942no—
618C24C23×D4711yescharacteristic
619C2×D4—4716no—
620C2×D4—4716no—
621C2×D4—4716no—
622C2×D4—18816no—
623C2×D4—18816no—
624C2×D4—18816no—
625C2×D4—1884no—
626C2×D4—1884no—
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—22no—
648C22×C4—22no—
649C22×C4—474no—
650C22×C4—472no—
651C22×C4—4716no—
652C22×C4—472no—
653C22×C4—472no—
654C22×C4—472no—
655C22×C4—472no—
656C22×C4—942no—
657C22×C4—942no—
658C22×C4—942no—
659C22×C4—942no—
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—18816no—
671C22×C4—1884no—
672C22×C4—1884no—
673C22×C4—1884no—
674C22×C4—1884no—
675C22×C4—1884no—
676C22×C4—1884no—
677C22×C4—1884no—
678C22×C4—1884no—
679C22×C4—18816no—
680C22×C4—18816no—
681C22×C4C2×C4×D4714yes—
682C22×C4C2×C4×D4714yes—
683C22×C4C2×C4×D4714yes—
684C22×C4C23×D4712yes—
685C22×C4C23×D4712yes—
686C22×C4C23×D4712yes—
687C22×C4C23×D4712yes—
688C22×C4C23×D4712yes—
689C22×C4C23×D4712yes—
690C22×C4C23×D4712yes—
691C4⋊C4—44no—
692C4⋊C4—1884no—
693C4⋊C4—1884no—
694C4⋊C4—1884no—
695C4⋊C4C2×C4×D47116yescomplemented
696C22⋊C4—4716no—
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⋊C4—1884no—
708C42—44no—
709C42—1884no—
710C23—474no—
711C23—474no—
712C23—474no—
713C23—948no—
714C23—948no—
715C23—948no—
716C23—948no—
717C23—948no—
718C23—948no—
719C23—948no—
720C23—948no—
721C23—948no—
722C23—942no—
723C23—942no—
724C23—942no—
725C23—942no—
726C23—942no—
727C23—942no—
728C23—942no—
729C23—942no—
730C23—942no—
731C23—942no—
732C23—942no—
733C23—942no—
734C23—942no—
735C23—942no—
736C23—942no—
737C23—942no—
738C23—942no—
739C23—942no—
740C23—1884no—
741C23—1884no—
742C23—1884no—
743C23—1884no—
744C23—1884no—
745C23—1884no—
746C23—1884no—
747C23—1884no—
748C23—1884no—
749C23—1884no—
750C23—1884no—
751C23—1884no—
752C23C22×C4×D4712yes—
753C23#1309406912yes—
754C23#1309407012yes—
755C23#1309407012yes—
756C23#1309407012yes—
757C23#1309407012yes—
758C23#1309407212yes—
759C23C24×D4711yescharacteristic
760D4—18816no—
761D4—18816no—
762D4—18816no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
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—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—474no—
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—18816no—
805C2×C4—18816no—
806C2×C4—18816no—
807C2×C4—1884no—
808C2×C4—1884no—
809C2×C4—1884no—
810C2×C4—1884no—
811C2×C4C22×C4×D4714yes—
812C2×C4C22×C4×D4714yes—
813C2×C4C22×C4×D4714yes—
814C22—944no—
815C22—944no—
816C22—944no—
817C22—944no—
818C22—944no—
819C22—944no—
820C22—944no—
821C22—944no—
822C22—944no—
823C22—18816no—
824C22—18816no—
825C22—18816no—
826C22—1882no—
827C22—1882no—
828C22—1882no—
829C22—1882no—
830C22—1882no—
831C22—1882no—
832C22—1882no—
833C22—1882no—
834C22—1882no—
835C22—1882no—
836C22—1882no—
837C22—1882no—
838C22#1568959514yes—
839C22#1568959714yes—
840C22#1568960514yes—
841C22#1568986314yes—
842C22#1568986414yes—
843C22#1568986914yes—
844C22#1568987114yes—
845C22C23×C4×D4711yescharacteristic
846C22C2×#1309406911yescharacteristic
847C22C2×#1309407011yescharacteristic
848C22C2×#1309407011yescharacteristic
849C22C2×#1309407011yescharacteristic
850C22C2×#1309407011yescharacteristic
851C22C2×#1309407211yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—944no—
860C4—1882no—
861C4—1882no—
862C4—1882no—
863C4—1882no—
864C2—1884no—
865C2—1884no—
866C2—1884no—
867C2#2024654318yesdirect product factor
868C2C2×#1568959511yescharacteristic
869C2C2×#1568959711yescharacteristic
870C2C2×#1568960511yescharacteristic
871C2C2×#1568986311yescharacteristic
872C2C2×#1568986411yescharacteristic
873C2C2×#1568986911yescharacteristic
874C2C2×#1568987111yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#387C2
socleC24×C47C24
prime radicalC22×#13093999C2
cosocleC23×C47C25
hypercenterC2×#387D47
hypocenterC47C2×#2377
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #20246543C2direct (N × H)
3. C2×#15689025C2semidirect
4. C2×#15689024C2semidirect
5. C2×#15689014C2semidirect
6. C2×#15689012C2semidirect
7. C2×#15689009C2semidirect
8. C2×#15689001C2semidirect
9. C2×#15689001C2semidirect
10. C2×#15689001C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15688997C2semidirect
13. C2×#15688994C2semidirect
14. C2×#15688985C2semidirect
15. C2×#15688982C2semidirect
16. C2×C47×#387C2semidirect
23. C2×#13093999C4semidirect
41. #15689025C22semidirect
42. #15689024C22semidirect
43. #15689014C22semidirect
44. #15689012C22semidirect
45. #15689009C22semidirect
46. #15689001C22semidirect
47. #15689001C22semidirect
48. #15689001C22semidirect
49. #15689001C22semidirect
50. #15688997C22semidirect
51. #15688994C22semidirect
52. #15688985C22semidirect
53. #15688982C22semidirect
63. C47×#387C22semidirect
78. C22×D188C2×C4semidirect
79. C22×D188C2×C4semidirect
96. C22×C4×D47C2×C4semidirect
100. #13093999C2×C4semidirect
117. C2×(C2×D47)⋊C4C2×C4semidirect
118. C2×(C2×D47)⋊C4C2×C4semidirect
147. C2×C4⋊C4×C47C2×C4semidirect
239. C2×D188C22×C4semidirect
240. C2×D188C22×C4semidirect
252. C2×C4×D47C22×C4semidirect
254. C4⋊C4×C47C22×C4semidirect
266. (C2×D47)⋊C4C22×C4semidirect
267. (C2×D47)⋊C4C22×C4semidirect
434. C2×#387D47semidirect
443. C2×C47#2377semidirect
486. #387C2×D47semidirect
505. C47C2×#2377semidirect
553. C2×C4⋊C4C4×D47semidirect
695. C4⋊C4C2×C4×D47semidirect
867. C2#20246543direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939992
#202465432
C2×#156890252
C2×#156890242
C2×#156890142
C2×#156890122
C2×#156890092
C2×#156890012
C2×#156889972
C2×#156889942
C2×#156889852
C2×#156889822
C2×C47×#3872
C2×#237747