Finite Group Databasebeta

← C2×#20245982 #26374856

Subgroups — C2×#20245982 #26374856

Order 12032.

4142 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D47C211yesmaximal, characteristic
2#20245982C2116yesmaximal, direct product factor
3C2×#15689017C211yesmaximal, characteristic, complemented
4C2×#15689016C211yesmaximal, characteristic, complemented
5C2×#15689015C211yesmaximal, characteristic, complemented
6C2×#15689014C211yesmaximal, characteristic, complemented
7C2×#15689013C211yesmaximal, characteristic, complemented
8C2×#15689012C211yesmaximal, characteristic, complemented
9C2×#15689011C211yesmaximal, characteristic, complemented
10C2×#15688982C211yesmaximal, characteristic, complemented
11C2×#15688980C211yesmaximal, characteristic, complemented
12C2×#15688978C211yesmaximal, characteristic
13C2×#15688978C211yesmaximal, characteristic
14C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic, complemented
21C22×Dic47⋊C4C2211yescharacteristic, complemented
22C22×Dic47⋊C4C2211yescharacteristic, complemented
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊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
36C2×C22⋊C4×D47C4116yescomplemented
37C2×C22⋊C4×D47C2218yes—
38C22×C4×Dic47C2211yescharacteristic, complemented
39C22×C4×Dic47C2211yescharacteristic, complemented
40C22×C4×Dic47C2211yescharacteristic, complemented
41#15689017C2218yescomplemented
42#15689016C2218yescomplemented
43#15689015C2218yescomplemented
44#15689014C2218yescomplemented
45#15689013C2218yescomplemented
46#15689012C2218yescomplemented
47#15689011C2218yescomplemented
48#15688982C2218yescomplemented
49#15688980C2218yescomplemented
50#15688978C2218yes—
51#15688978C2218yes—
52C4×(C2×D47)⋊C4C2218yescomplemented
53#15688970C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic, complemented
55C2×C47⋊#95C2211yescharacteristic, complemented
56C2×C47⋊#95C2211yescharacteristic, complemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C22×C4⋊C4×C47C2211yescharacteristic, complemented
61C22×C22⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C42×C47C2211yescharacteristic, complemented
65C47×#388C2218yescomplemented
66C2×#95×C47C2211yescharacteristic, complemented
67C2×#95×C47C2211yescharacteristic, complemented
68C24×D47—24no—
69C24×D47—24no—
70C24×D47—42no—
71C24×D47—42no—
72C24×D47—42no—
73C24×D47—42no—
74C24×D47C2×C418yes—
75C24×D47C2311yescharacteristic
76C24×D47C2311yescharacteristic
77C24×D47C2314yes—
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C22×C4×D47—42no—
85C22×C4×D47—42no—
86C22×C4×D47—42no—
87C22×C4×D47—42no—
88C22×C4×D47C2×C418yes—
89C22×C4×D47C2×C418yes—
90C22×C4×D47C2314yes—
91C22×C4×D47C2314yes—
92C2×C4⋊Dic47—42no—
93C2×C4⋊Dic47C2314yescomplemented
94C2×Dic47⋊C4—42no—
95C2×Dic47⋊C4—42no—
96C2×Dic47⋊C4C2314yescomplemented
97C2×Dic47⋊C4C2314yescomplemented
98C2×C22⋊Dic47—42no—
99C2×C22⋊Dic47—42no—
100C2×C22⋊Dic47C2×C418yes—
101C2×C22⋊Dic47C2314yes—
102C2×C22⋊Dic47C2314yes—
103C2×C22⋊Dic47C2314yes—
104C2×(C2×D47)⋊C4—24no—
105C2×(C2×D47)⋊C4—24no—
106C2×(C2×D47)⋊C4—24no—
107C2×(C2×D47)⋊C4—24no—
108C2×(C2×D47)⋊C4—42no—
109C2×(C2×D47)⋊C4—42no—
110C2×(C2×D47)⋊C4—42no—
111C2×(C2×D47)⋊C4—42no—
112C2×(C2×D47)⋊C4C2×C418yes—
113C2×(C2×D47)⋊C4C2×C418yes—
114C2×(C2×D47)⋊C4C2314yes—
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×(C2×D47)⋊C4C2314yes—
124C22⋊C4×D47C2×C4164yescomplemented
125C2×C4×Dic47—42no—
126C2×C4×Dic47—42no—
127C2×C4×Dic47—42no—
128C2×C4×Dic47C2314yescomplemented
129C2×C4×Dic47C2314yescomplemented
130C2×C4×Dic47C2314yescomplemented
131C47⋊#95C2314yescomplemented
132C47⋊#95C2314yescomplemented
133C47⋊#95C2314yescomplemented
134C47⋊#95C2314yescomplemented
135C47⋊#95C2314yescomplemented
136C47⋊#95C2314yescomplemented
137C25×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C2×C4⋊C4×C47—42no—
145C2×C4⋊C4×C47C2314yescomplemented
146C2×C22⋊C4×C47—42no—
147C2×C22⋊C4×C47—42no—
148C2×C22⋊C4×C47C2×C418yes—
149C2×C22⋊C4×C47C2314yes—
150C2×C22⋊C4×C47C2314yes—
151C2×C22⋊C4×C47C2314yes—
152C2×C42×C47—42no—
153C2×C42×C47C2314yescomplemented
154#95×C47C2314yescomplemented
155#95×C47C2314yescomplemented
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—232no—
176C23×D47—28no—
177C23×D47—28no—
178C23×D47—416no—
179C23×D47—416no—
180C23×D47—44no—
181C23×D47—44no—
182C23×D47—44no—
183C23×D47—44no—
184C23×D47—416no—
185C23×D47—416no—
186C23×D47—416no—
187C23×D47—416no—
188C23×D47C22×C414yes—
189C23×D47C22×C414yes—
190C23×D47C22×C4116yes—
191C23×D47#4114yes—
192C23×D47#4114yes—
193C23×D47C2412yes—
194C23×D47C2412yes—
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×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47C22×C414yes—
212C22×C4×C47C22×C414yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2412yes—
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×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47C22×C414yes—
236C22×Dic47C22×C414yes—
237C22×Dic47C2412yes—
238C22×Dic47C2412yes—
239C22×Dic47C2412yes—
240C22×Dic47C2412yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C2×C4×D47—416no—
244C2×C4×D47—416no—
245C2×C4×D47—44no—
246C2×C4×D47—44no—
247C2×C4×D47—44no—
248C2×C4×D47—44no—
249C2×C4×D47C22×C4116yes—
250C2×C4×D47C22×C4116yes—
251C4⋊C4×C47—44no—
252C22⋊C4×C47—44no—
253C22⋊C4×C47—44no—
254C22⋊C4×C47C22×C4116yes—
255C42×C47—44no—
256C22⋊Dic47—44no—
257C22⋊Dic47—44no—
258C22⋊Dic47C22×C4116yes—
259(C2×D47)⋊C4—28no—
260(C2×D47)⋊C4—28no—
261(C2×D47)⋊C4—28no—
262(C2×D47)⋊C4—28no—
263(C2×D47)⋊C4—44no—
264(C2×D47)⋊C4—44no—
265(C2×D47)⋊C4—44no—
266(C2×D47)⋊C4—44no—
267(C2×D47)⋊C4C22×C4116yes—
268(C2×D47)⋊C4C22×C4116yes—
269C4⋊Dic47—44no—
270Dic47⋊C4—44no—
271Dic47⋊C4—44no—
272C4×Dic47—44no—
273C4×Dic47—44no—
274C4×Dic47—44no—
275C23×C47—28no—
276C23×C47—28no—
277C23×C47—28no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—44no—
285C23×C47—44no—
286C23×C47—44no—
287C23×C47—44no—
288C23×C47C23×C414yes—
289C23×C47C23×C412yes—
290C23×C47C2×#4112yes—
291C23×C47C2×#4112yes—
292C23×C47H(5,𝔽2)12yes—
293C23×C47H(5,𝔽2)12yes—
294C23×C47H(5,𝔽2)12yes—
295C23×C47H(5,𝔽2)12yes—
296C23×C47C2511yescharacteristic
297C22×D47—28no—
298C22×D47—28no—
299C22×D47—28no—
300C22×D47—28no—
301C22×D47—28no—
302C22×D47—28no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—28no—
308C22×D47—28no—
309C22×D47—28no—
310C22×D47—22no—
311C22×D47—22no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—232no—
317C22×D47—416no—
318C22×D47—416no—
319C22×D47—4128no—
320C22×D47—416no—
321C22×D47—416no—
322C22×D47—416no—
323C22×D47—416no—
324C22×D47—44no—
325C22×D47—44no—
326C22×D47—44no—
327C22×D47—44no—
328C22×D47#117116yes—
329C22×D47C23×C414yes—
330C22×D47C23×C414yes—
331C22×D47C2×#4114yes—
332C22×D47C2×#4114yes—
333C2×C4×C47—28no—
334C2×C4×C47—28no—
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—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—44no—
352C2×C4×C47—44no—
353C2×C4×C47—44no—
354C2×C4×C47—44no—
355C2×C4×C47C23×C414yes—
356C2×C4×C47C23×C414yes—
357C2×Dic47—28no—
358C2×Dic47—28no—
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—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—44no—
376C2×Dic47—44no—
377C2×Dic47—44no—
378C2×Dic47—44no—
379C2×Dic47C23×C414yes—
380C2×Dic47C23×C414yes—
381C4×D47—416no—
382C4×D47—416no—
383C2×#2312—471nomaximal, Sylow
384C22×C47—24no—
385C22×C47—24no—
386C22×C47—24no—
387C22×C47—416no—
388C22×C47—42no—
389C22×C47—42no—
390C22×C47—42no—
391C22×C47—42no—
392C22×C47C2×#11714yes—
393C22×C47#51814yes—
394C22×C47#51814yes—
395C22×C47#53814yes—
396C22×C47#53814yes—
397C22×C47#53814yes—
398C22×C47#53814yes—
399C22×C47C24×C411yescharacteristic
400C22×C47C22×#4111yescharacteristic
401C22×C47C22×#4111yescharacteristic
402C22×C47C2×H(5,𝔽2)11yescharacteristic
403C22×C47C2×H(5,𝔽2)11yescharacteristic
404C22×C47C2×H(5,𝔽2)11yescharacteristic
405C22×C47C2×H(5,𝔽2)11yescharacteristic
406C2×D47—232no—
407C2×D47—24no—
408C2×D47—24no—
409C2×D47—24no—
410C2×D47—24no—
411C2×D47—24no—
412C2×D47—24no—
413C2×D47—24no—
414C2×D47—24no—
415C2×D47—24no—
416C2×D47—464no—
417C2×D47—416no—
418C2×D47—42no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47C2×#11718yes—
423C4×C47—24no—
424C4×C47—24no—
425C4×C47—42no—
426C4×C47—42no—
427C4×C47—42no—
428C4×C47—42no—
429Dic47—24no—
430Dic47—24no—
431Dic47—42no—
432Dic47—42no—
433Dic47—42no—
434Dic47—42no—
435C23×C22⋊C4—471no—
436#2312—4716no—
437C2×#388—471no—
438C2×#388—471no—
439C2×#388—471no—
440C2×#388—471no—
441C2×#388—471no—
442C2×#388—471no—
443C2×#388—471no—
444C2×#388D4711yescharacteristic, complemented
445C2×#380—471no—
446C2×#380—471no—
447C2×#379—471no—
448C2×#379—471no—
449C2×C4×C22⋊C4—471no—
450C2×C4×C22⋊C4—471no—
451C2×C47—44no—
452C2×C47#231218yescomplemented
453C2×C47C22×#11711yescharacteristic
454C2×C47C2×#51811yescharacteristic
455C2×C47C2×#51811yescharacteristic
456C2×C47C2×#53811yescharacteristic
457C2×C47C2×#53811yescharacteristic
458C2×C47C2×#53811yescharacteristic
459C2×C47C2×#53811yescharacteristic
460D47—28no—
461D47—44no—
462C26—471no—
463C24×C4—471no—
464C24×C4—471no—
465C22×C4⋊C4—471no—
466C22×C4⋊C4—471no—
467C22×C4⋊C4—471no—
468C22×C4⋊C4C2×D4711yescharacteristic, complemented
469C22×C22⋊C4—471no—
470C22×C22⋊C4—471no—
471C22×C22⋊C4—471no—
472C22×C22⋊C4—4716no—
473C22×C22⋊C4—478no—
474C22×C22⋊C4—471no—
475C22×C22⋊C4—471no—
476C22×C22⋊C4—471no—
477C22×C22⋊C4—471no—
478C22×C22⋊C4—471no—
479C22×C22⋊C4—471no—
480C22×C22⋊C4—471no—
481C22×C22⋊C4—471no—
482C22×C22⋊C4—471no—
483C22×C22⋊C4—471no—
484C22×C22⋊C4C2×D4711yescharacteristic
485C22×C22⋊C4C2×D4711yescharacteristic
486C22×C22⋊C4C2×D4711yescharacteristic
487C22×C42—471no—
488C22×C42—471no—
489C22×C42—471no—
490C22×C42C2×D4711yescharacteristic, complemented
491#388—478no—
492#388—478no—
493#388—478no—
494#388—478no—
495#388—478no—
496#388—478no—
497#388—478no—
498#388C2×D4718yescomplemented
499#380—478no—
500#380—478no—
501#379—478no—
502#379—478no—
503C4×C22⋊C4—478no—
504C4×C22⋊C4—478no—
505C2×#95—471no—
506C2×#95—471no—
507C2×#95—471no—
508C2×#95—471no—
509C2×#95—471no—
510C2×#95—471no—
511C2×#95C2×D4711yescharacteristic, complemented
512C2×#95C2×D4711yescharacteristic, complemented
513C47C2×#231211yescharacteristic, complemented, Sylow
514C25—471no—
515C25—471no—
516C25—478no—
517C25—474no—
518C25—944no—
519C25—944no—
520C25—1882no—
521C25—1882no—
522C25—1882no—
523C25—1882no—
524C25C22×D4711yescharacteristic
525C23×C4—471no—
526C23×C4—471no—
527C23×C4—478no—
528C23×C4—478no—
529C23×C4—474no—
530C23×C4—474no—
531C23×C4—471no—
532C23×C4—471no—
533C23×C4—471no—
534C23×C4—471no—
535C23×C4—1882no—
536C23×C4—1882no—
537C23×C4—1882no—
538C23×C4—1882no—
539C23×C4C22×D4711yescharacteristic
540C23×C4C22×D4711yescharacteristic
541C23×C4C22×D4711yescharacteristic
542C23×C4C22×D4711yescharacteristic
543C23×C4C22×D4711yescharacteristic
544C23×C4C22×D4711yescharacteristic
545C2×C4⋊C4—42no—
546C2×C4⋊C4—474no—
547C2×C4⋊C4—474no—
548C2×C4⋊C4—474no—
549C2×C4⋊C4—1882no—
550C2×C4⋊C4—1882no—
551C2×C4⋊C4—1882no—
552C2×C4⋊C4C22×D4714yescomplemented
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—478no—
556C2×C22⋊C4—474no—
557C2×C22⋊C4—478no—
558C2×C22⋊C4—478no—
559C2×C22⋊C4—474no—
560C2×C22⋊C4—474no—
561C2×C22⋊C4—4764no—
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—474no—
571C2×C22⋊C4—474no—
572C2×C22⋊C4—944no—
573C2×C22⋊C4—944no—
574C2×C22⋊C4—944no—
575C2×C22⋊C4—944no—
576C2×C22⋊C4—1882no—
577C2×C22⋊C4—1882no—
578C2×C22⋊C4—1882no—
579C2×C22⋊C4—1882no—
580C2×C22⋊C4—1882no—
581C2×C22⋊C4—1882no—
582C2×C22⋊C4C4×D4718yes—
583C2×C22⋊C4C22×D4714yes—
584C2×C22⋊C4C22×D4714yes—
585C2×C22⋊C4C22×D4714yes—
586C2×C42—42no—
587C2×C42—474no—
588C2×C42—474no—
589C2×C42—474no—
590C2×C42—1882no—
591C2×C42—1882no—
592C2×C42—1882no—
593C2×C42C22×D4714yescomplemented
594#95—474no—
595#95—474no—
596#95—474no—
597#95—474no—
598#95—474no—
599#95—474no—
600#95C22×D4714yescomplemented
601#95C22×D4714yescomplemented
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—474no—
609C24—474no—
610C24—474no—
611C24—472no—
612C24—474no—
613C24—472no—
614C24—4716no—
615C24—9432no—
616C24—948no—
617C24—948no—
618C24—942no—
619C24—942no—
620C24—942no—
621C24—942no—
622C24—942no—
623C24—942no—
624C24—942no—
625C24—942no—
626C24—942no—
627C24—942no—
628C24—18816no—
629C24—18816no—
630C24—1884no—
631C24—1884no—
632C24—1884no—
633C24—1884no—
634C24—18816no—
635C24—18816no—
636C24—18816no—
637C24—18816no—
638C24C2×C4×D4714yes—
639C24C23×D4712yes—
640C24C23×D4711yescharacteristic
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—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—474no—
658C22×C4—474no—
659C22×C4—472no—
660C22×C4—472no—
661C22×C4—4716no—
662C22×C4—4716no—
663C22×C4—472no—
664C22×C4—472no—
665C22×C4—472no—
666C22×C4—472no—
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—942no—
677C22×C4—942no—
678C22×C4—942no—
679C22×C4—942no—
680C22×C4—942no—
681C22×C4—942no—
682C22×C4—942no—
683C22×C4—18816no—
684C22×C4—18816no—
685C22×C4—1884no—
686C22×C4—1884no—
687C22×C4—1884no—
688C22×C4—1884no—
689C22×C4C2×C4×D4714yes—
690C22×C4C2×C4×D4714yes—
691C22×C4C23×D4712yes—
692C22×C4C23×D4712yes—
693C22×C4C23×D4712yes—
694C22×C4C23×D4712yes—
695C22×C4C23×D4712yes—
696C22×C4C23×D4712yes—
697C4⋊C4—44no—
698C4⋊C4—1884no—
699C4⋊C4—1884no—
700C4⋊C4—1884no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—4716no—
704C22⋊C4—4716no—
705C22⋊C4—4716no—
706C22⋊C4—948no—
707C22⋊C4—948no—
708C22⋊C4—948no—
709C22⋊C4—948no—
710C22⋊C4—1884no—
711C22⋊C4—1884no—
712C22⋊C4—1884no—
713C22⋊C4—1884no—
714C22⋊C4—1884no—
715C22⋊C4—1884no—
716C22⋊C4C2×C4×D47116yes—
717C42—44no—
718C42—1884no—
719C42—1884no—
720C42—1884no—
721C23—28no—
722C23—28no—
723C23—28no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—4716no—
735C23—474no—
736C23—474no—
737C23—474no—
738C23—474no—
739C23—9432no—
740C23—948no—
741C23—948no—
742C23—942no—
743C23—942no—
744C23—942no—
745C23—942no—
746C23—948no—
747C23—948no—
748C23—948no—
749C23—948no—
750C23—948no—
751C23—948no—
752C23—948no—
753C23—942no—
754C23—942no—
755C23—942no—
756C23—942no—
757C23—942no—
758C23—942no—
759C23—18816no—
760C23—18816no—
761C23—18816no—
762C23—18816no—
763C23—18816no—
764C23—18816no—
765C23—188128no—
766C23—1884no—
767C23—1884no—
768C23—1884no—
769C23—1884no—
770C23C22×C4×D4714yes—
771C23C22×C4×D4712yes—
772C23#41×D4712yes—
773C23#41×D4712yes—
774C23#1309406912yes—
775C23#1309406912yes—
776C23#1309407012yes—
777C23#1309407012yes—
778C23C24×D4711yescharacteristic
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—474no—
802C2×C4—474no—
803C2×C4—948no—
804C2×C4—948no—
805C2×C4—942no—
806C2×C4—942no—
807C2×C4—942no—
808C2×C4—942no—
809C2×C4—942no—
810C2×C4—942no—
811C2×C4—942no—
812C2×C4—942no—
813C2×C4—942no—
814C2×C4—942no—
815C2×C4—942no—
816C2×C4—942no—
817C2×C4—942no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—942no—
821C2×C4—18816no—
822C2×C4—18816no—
823C2×C4—1884no—
824C2×C4—1884no—
825C2×C4—1884no—
826C2×C4—1884no—
827C2×C4C22×C4×D4714yes—
828C2×C4C22×C4×D4714yes—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—416no—
837C22—478no—
838C22—944no—
839C22—944no—
840C22—944no—
841C22—944no—
842C22—944no—
843C22—944no—
844C22—9432no—
845C22—944no—
846C22—944no—
847C22—944no—
848C22—18864no—
849C22—1882no—
850C22—1882no—
851C22—1882no—
852C22—1882no—
853C22—18816no—
854C22#117×D4714yes—
855C22#1568959514yes—
856C22#1568959514yes—
857C22#1568970514yes—
858C22#1568970714yes—
859C22#1568970914yes—
860C22#1568971214yes—
861C22C23×C4×D4711yescharacteristic
862C22C2×#41×D4711yescharacteristic
863C22C2×#41×D4711yescharacteristic
864C22C2×#1309406911yescharacteristic
865C22C2×#1309406911yescharacteristic
866C22C2×#1309407011yescharacteristic
867C22C2×#1309407011yescharacteristic
868C4—24no—
869C4—24no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—944no—
875C4—944no—
876C4—1882no—
877C4—1882no—
878C4—1882no—
879C4—1882no—
880C2—44no—
881C2—948no—
882C2—1884no—
883C2#2024598218yesdirect product factor
884C2C2×#117×D4711yescharacteristic
885C2C2×#1568959511yescharacteristic
886C2C2×#1568959511yescharacteristic
887C2C2×#1568970511yescharacteristic
888C2C2×#1568970711yescharacteristic
889C2C2×#1568970911yescharacteristic
890C2C2×#1568971211yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC25×D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2312
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #20245982C2direct (N × H)
3. C2×#15689017C2semidirect
4. C2×#15689016C2semidirect
5. C2×#15689015C2semidirect
6. C2×#15689014C2semidirect
7. C2×#15689013C2semidirect
8. C2×#15689012C2semidirect
9. C2×#15689011C2semidirect
10. C2×#15688982C2semidirect
11. C2×#15688980C2semidirect
14. C2×C4×(C2×D47)⋊C4C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#388C2semidirect
20. C22×C4⋊Dic47C22semidirect
21. C22×Dic47⋊C4C22semidirect
22. C22×Dic47⋊C4C22semidirect
36. C2×C22⋊C4×D47C4semidirect
38. C22×C4×Dic47C22semidirect
39. C22×C4×Dic47C22semidirect
40. C22×C4×Dic47C22semidirect
41. #15689017C22semidirect
42. #15689016C22semidirect
43. #15689015C22semidirect
44. #15689014C22semidirect
45. #15689013C22semidirect
46. #15689012C22semidirect
47. #15689011C22semidirect
48. #15688982C22semidirect
49. #15688980C22semidirect
52. C4×(C2×D47)⋊C4C22semidirect
53. #15688970C22semidirect
54. C2×C47⋊#95C22semidirect
55. C2×C47⋊#95C22semidirect
56. C2×C47⋊#95C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C22×C4⋊C4×C47C22semidirect
64. C22×C42×C47C22semidirect
65. C47×#388C22semidirect
66. C2×#95×C47C22semidirect
67. C2×#95×C47C22semidirect
93. C2×C4⋊Dic47C23semidirect
96. C2×Dic47⋊C4C23semidirect
97. C2×Dic47⋊C4C23semidirect
124. C22⋊C4×D47C2×C4semidirect
128. C2×C4×Dic47C23semidirect
129. C2×C4×Dic47C23semidirect
130. C2×C4×Dic47C23semidirect
131. C47⋊#95C23semidirect
132. C47⋊#95C23semidirect
133. C47⋊#95C23semidirect
134. C47⋊#95C23semidirect
135. C47⋊#95C23semidirect
136. C47⋊#95C23semidirect
145. C2×C4⋊C4×C47C23semidirect
153. C2×C42×C47C23semidirect
154. #95×C47C23semidirect
155. #95×C47C23semidirect
444. C2×#388D47semidirect
452. C2×C47#2312semidirect
468. C22×C4⋊C4C2×D47semidirect
490. C22×C42C2×D47semidirect
498. #388C2×D47semidirect
511. C2×#95C2×D47semidirect
512. C2×#95C2×D47semidirect
513. C47C2×#2312semidirect
552. C2×C4⋊C4C22×D47semidirect
593. C2×C42C22×D47semidirect
600. #95C22×D47semidirect
601. #95C22×D47semidirect
883. C2#20245982direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D472
#202459822
C2×#156890172
C2×#156890162
C2×#156890152
C2×#156890142
C2×#156890132
C2×#156890122
C2×#156890112
C2×#156889822
C2×#156889802
C2×#156889782
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×C47×#3882
C2×#231247