Finite Group Databasebeta

← C2×#20247197 #26383760

Subgroups — C2×#20247197 #26383760

Order 12032.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094003C211yesmaximal, characteristic, complemented
2C22×#13094002C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D47C211yesmaximal, characteristic
4#20247197C2116yesmaximal, direct product factor
5C2×#15689058C211yesmaximal, characteristic, complemented
6C2×#15689054C211yesmaximal, characteristic, complemented
7C2×#15689045C211yesmaximal, characteristic, complemented
8C2×#15689043C211yesmaximal, characteristic, complemented
9C2×#15689018C211yesmaximal, characteristic, complemented
10C2×#15689009C211yesmaximal, characteristic, complemented
11C2×#15689002C211yesmaximal, characteristic
12C2×#15689002C211yesmaximal, characteristic
13C2×#15688996C211yesmaximal, characteristic, complemented
14C2×#15688996C211yesmaximal, characteristic, complemented
15C2×#15688994C211yesmaximal, characteristic, complemented
16C23×C4⋊C4×C47C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13094003—28no—
21C2×#13094003C2218yescomplemented
22C2×#13094002—28no—
23C2×#13094002C2218yescomplemented
24C2×C4×C22⋊D47—28no—
25C2×C4×C22⋊D47C2218yes—
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×C22⋊Dic47C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689058C2218yescomplemented
44#15689054C2218yescomplemented
45#15689045C2218yescomplemented
46#15689043C2218yescomplemented
47#15689018C2218yescomplemented
48#15689009C2218yescomplemented
49#15689002C2218yes—
50#15689002C2218yes—
51#15688996C2218yescomplemented
52#15688996C2218yescomplemented
53#15688994C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C24×C4×C47C2211yescharacteristic
63C24×C4×C47C2211yescharacteristic
64C24×C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47—28no—
66C22×C4⋊C4×C47C2211yescharacteristic
67C22×C4⋊C4×C47C2211yescharacteristic
68C22×C4⋊C4×C47C2211yescharacteristic
69C22×C4⋊C4×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2218yescomplemented
71C24×D47C2311yescharacteristic
72C22×Dic94—24no—
73C22×Dic94—24no—
74C22×Dic94—42no—
75C22×Dic94C2314yes—
76C22×C22⋊D47—24no—
77C22×C22⋊D47—24no—
78C22×C22⋊D47Q818yescomplemented
79C22×C22⋊D47C2314yes—
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—42no—
90C22×C4×D47C2314yes—
91#13094003—232no—
92#13094002—232no—
93C4×C22⋊D47—232no—
94C2×C4⋊Dic47—24no—
95C2×C4⋊Dic47C2314yes—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—24no—
98C2×Dic47⋊C4—24no—
99C2×Dic47⋊C4—24no—
100C2×Dic47⋊C4—24no—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—42no—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×C22⋊Dic47—24no—
111C2×C22⋊Dic47—24no—
112C2×C22⋊Dic47D418yes—
113C2×C22⋊Dic47C2314yes—
114C2×C22⋊Dic47C2314yes—
115C2×C22⋊Dic47C2314yes—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4—24no—
120C2×(C2×D47)⋊C4—42no—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×C4×Dic47—24no—
127C2×C4×Dic47C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C25×C47C2311yescharacteristic
137C23×C4×C47—24no—
138C23×C4×C47—24no—
139C23×C4×C47—24no—
140C23×C4×C47—24no—
141C23×C4×C47—24no—
142C23×C4×C47—24no—
143C23×C4×C47—24no—
144C23×C4×C47—42no—
145C23×C4×C47—42no—
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2314yes—
149C23×C4×C47C2314yes—
150C23×C4×C47C2314yes—
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C2×C4⋊C4×C47—24no—
156C2×C4⋊C4×C47—24no—
157C2×C4⋊C4×C47—24no—
158C2×C4⋊C4×C47—232no—
159C2×C4⋊C4×C47D418yescomplemented
160C2×C4⋊C4×C47C2314yes—
161C2×C4⋊C4×C47C2314yes—
162C2×C4⋊C4×C47C2314yes—
163C2×C4⋊C4×C47C2314yes—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47C2×D414yes—
169C24×C47C2×Q814yes—
170C24×C47#4114yes—
171C24×C47C2412yes—
172C24×C47C2411yescharacteristic
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47C2×Q814yes—
180C23×D47C2412yes—
181C22×C4×C47—232no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—28no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—28no—
192C22×C4×C47—28no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—28no—
198C22×C4×C47—28no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—28no—
202C22×C4×C47—28no—
203C22×C4×C47—44no—
204C22×C4×C47—44no—
205C22×C4×C47—416no—
206C22×C4×C47—416no—
207C22×C4×C47C2×D414yes—
208C22×C4×C47C2×D414yes—
209C22×C4×C47C2×D414yes—
210C22×C4×C47#4114yes—
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⋊D47C2×Q8116yescomplemented
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×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47C2×D414yes—
240C22×Dic47C2×D414yes—
241C22×Dic47C2×Q814yes—
242C22×Dic47C2412yes—
243C22×Dic47C2412yes—
244C22×Dic47C2412yes—
245C22×Dic47C2412yes—
246C22×Dic47C2412yes—
247C22×Dic47C2412yes—
248C22×Dic47C2412yes—
249C2×C4×D47—28no—
250C2×C4×D47—28no—
251C2×C4×D47—44no—
252C2×C4×D47—416no—
253C2×Dic94—28no—
254C2×Dic94—28no—
255C2×Dic94—44no—
256C2×Dic94—416no—
257C4⋊C4×C47—28no—
258C4⋊C4×C47—28no—
259C4⋊C4×C47—28no—
260C4⋊C4×C47C2×D4116yescomplemented
261C22⋊Dic47—28no—
262C22⋊Dic47—28no—
263C22⋊Dic47C2×D4116yes—
264(C2×D47)⋊C4—28no—
265(C2×D47)⋊C4—28no—
266(C2×D47)⋊C4—28no—
267(C2×D47)⋊C4—28no—
268(C2×D47)⋊C4—44no—
269C4⋊Dic47—28no—
270Dic47⋊C4—28no—
271Dic47⋊C4—28no—
272Dic47⋊C4—28no—
273Dic47⋊C4—28no—
274Dic47⋊C4—28no—
275Dic47⋊C4—28no—
276Dic47⋊C4—44no—
277C4×Dic47—28no—
278C23×C47—28no—
279C23×C47—28no—
280C23×C47—28no—
281C23×C47—28no—
282C23×C47—28no—
283C23×C47—28no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47C22⋊Q8116yescomplemented
289C23×C47C22×D414yes—
290C23×C47C22×D412yes—
291C23×C47C22×D412yes—
292C23×C47C22×Q814yes—
293C23×C47C22×Q812yes—
294C23×C47C2×#4114yes—
295C23×C47C2×#4112yes—
296C23×C47C2×#4112yes—
297C23×C47H(5,𝔽2)12yes—
298C23×C472−1+412yes—
299C23×C47C2511yescharacteristic
300C22×D47—28no—
301C22×D47—28no—
302C22×D47—28no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—44no—
310C22×D47—44no—
311C22×D47—44no—
312C22×D47—44no—
313C22×D47C22×Q814yes—
314C2×C4×C47—232no—
315C2×C4×C47—28no—
316C2×C4×C47—28no—
317C2×C4×C47—28no—
318C2×C4×C47—28no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
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—416no—
334C2×C4×C47—416no—
335C2×C4×C47—44no—
336C2×C4×C47—44no—
337C2×C4×C47C22×D414yes—
338C2×C4×C47C22×D414yes—
339C2×C4×C47C22×D414yes—
340C2×C4×C47C2×#4114yes—
341C22⋊D47—232no—
342C2×Dic47—28no—
343C2×Dic47—28no—
344C2×Dic47—28no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
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—44no—
364C2×Dic47—44no—
365C2×Dic47—44no—
366C2×Dic47—44no—
367C2×Dic47C22×D414yes—
368C2×Dic47C22×D414yes—
369C2×Dic47C22×Q814yes—
370C4×D47—416no—
371Dic94—416no—
372C2×#2449—471nomaximal, Sylow
373C22×C47—24no—
374C22×C47—24no—
375C22×C47—24no—
376C22×C47—24no—
377C22×C47—24no—
378C22×C47—24no—
379C22×C47—232no—
380C22×C47C2×C22⋊Q814yes—
381C22×C47C2×C22⋊Q818yescomplemented
382C22×C47#52514yes—
383C22×C47#53914yes—
384C22×C47D4214yes—
385C22×C47#54714yes—
386C22×C47D4×Q814yes—
387C22×C47#55414yes—
388C22×C47C23×D411yescharacteristic
389C22×C47C23×D411yescharacteristic
390C22×C47C23×Q811yescharacteristic
391C22×C47C22×#4111yescharacteristic
392C22×C47C22×#4111yescharacteristic
393C22×C47C2×H(5,𝔽2)11yescharacteristic
394C22×C47C2×2−1+411yescharacteristic
395C2×D47—24no—
396C2×D47—24no—
397C2×D47—24no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—416no—
403C4×C47—24no—
404C4×C47—24no—
405C4×C47—24no—
406C4×C47—24no—
407C4×C47—42no—
408C4×C47—42no—
409Dic47—24no—
410Dic47—24no—
411Dic47—24no—
412Dic47—42no—
413Dic47—42no—
414Dic47—42no—
415Dic47—42no—
416C22×C22⋊Q8—471no—
417C22×C22⋊Q8—471no—
418C22×C4×D4—471no—
419C23×C4⋊C4D4711yescharacteristic, complemented
420#2449—4716no—
421C2×#399—471no—
422C2×#398—471no—
423C2×#396—471no—
424C2×#395—471no—
425C2×#389—471no—
426C2×#387—471no—
427C2×#386—471no—
428C2×#386—471no—
429C2×#385—471no—
430C2×#385—471no—
431C2×#385—471no—
432C2×C47—28no—
433C2×C47#244918yescomplemented
434C2×C47C22×C22⋊Q811yescharacteristic
435C2×C47C2×#52511yescharacteristic
436C2×C47C2×#53911yescharacteristic
437C2×C47C2×D4211yescharacteristic
438C2×C47C2×#54711yescharacteristic
439C2×C47C2×D4×Q811yescharacteristic
440C2×C47C2×#55411yescharacteristic
441D47—44no—
442C23×Q8—471no—
443C23×D4—471no—
444C24×C4—471no—
445C24×C4C2×D4711yescharacteristic
446C24×C4C2×D4711yescharacteristic
447C24×C4C2×D4711yescharacteristic
448C2×C22⋊Q8—478no—
449C2×C22⋊Q8—478no—
450C2×C22⋊Q8—948no—
451C2×C22⋊Q8—948no—
452C2×C4×D4—478no—
453C2×C4×D4—948no—
454C22×C4⋊C4—28no—
455C22×C4⋊C4—471no—
456C22×C4⋊C4—471no—
457C22×C4⋊C4—471no—
458C22×C4⋊C4—471no—
459C22×C4⋊C4—471no—
460C22×C4⋊C4—471no—
461C22×C4⋊C4—471no—
462C22×C4⋊C4—471no—
463C22×C4⋊C4C2×D4711yescharacteristic
464C22×C4⋊C4C2×D4711yescharacteristic
465C22×C4⋊C4C2×D4711yescharacteristic
466C22×C4⋊C4C2×D4711yescharacteristic
467C22×C4⋊C4C2×D4718yescomplemented
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×C42—471no—
477#399—478no—
478#398—478no—
479#396—478no—
480#395—478no—
481#389—478no—
482#387—478no—
483#386—478no—
484#386—478no—
485#385—478no—
486#385—478no—
487#385—478no—
488C2×#95—471no—
489C2×#95—471no—
490C2×#95—471no—
491C2×#95—471no—
492C2×#95—471no—
493C2×#95—471no—
494C2×#95—471no—
495C2×#95—471no—
496C47C2×#244911yescharacteristic, complemented, Sylow
497C25—471no—
498C25C22×D4711yescharacteristic
499C22×Q8—474no—
500C22×Q8—944no—
501C22×Q8—944no—
502C22×Q8—1882no—
503C22×D4—478no—
504C22×D4—474no—
505C22×D4—944no—
506C22×D4—944no—
507C23×C4—24no—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—42no—
515C23×C4—42no—
516C23×C4—471no—
517C23×C4—471no—
518C23×C4—471no—
519C23×C4—471no—
520C23×C4—471no—
521C23×C4—471no—
522C23×C4—471no—
523C23×C4—474no—
524C23×C4—944no—
525C23×C4—944no—
526C23×C4—1882no—
527C23×C4C22×D4714yes—
528C23×C4C22×D4711yescharacteristic
529C23×C4C22×D4711yescharacteristic
530C23×C4C22×D4714yes—
531C23×C4C22×D4714yes—
532C23×C4C22×D4711yescharacteristic
533C23×C4C22×D4711yescharacteristic
534C23×C4C22×D4711yescharacteristic
535C23×C4C22×D4711yescharacteristic
536C22⋊Q8—9432no—
537C22⋊Q8—9432no—
538C4×D4—9432no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—232no—
543C2×C4⋊C4—474no—
544C2×C4⋊C4—474no—
545C2×C4⋊C4—474no—
546C2×C4⋊C4—474no—
547C2×C4⋊C4—474no—
548C2×C4⋊C4—474no—
549C2×C4⋊C4—474no—
550C2×C4⋊C4—474no—
551C2×C4⋊C4—944no—
552C2×C4⋊C4—944no—
553C2×C4⋊C4—944no—
554C2×C4⋊C4—944no—
555C2×C4⋊C4—944no—
556C2×C4⋊C4—944no—
557C2×C4⋊C4—944no—
558C2×C4⋊C4—1882no—
559C2×C4⋊C4C22⋊D4718yescomplemented
560C2×C4⋊C4C22×D4714yes—
561C2×C4⋊C4C22×D4714yes—
562C2×C4⋊C4C22×D4714yes—
563C2×C4⋊C4C22×D4714yes—
564C2×C22⋊C4—478no—
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—474no—
573C2×C22⋊C4—944no—
574C2×C22⋊C4—944no—
575C2×C22⋊C4—944no—
576C2×C22⋊C4—944no—
577C2×C22⋊C4—944no—
578C2×C22⋊C4—944no—
579C2×C22⋊C4—1882no—
580C2×C42—474no—
581C2×C42—944no—
582#95—474no—
583#95—474no—
584#95—474no—
585#95—474no—
586#95—474no—
587#95—474no—
588#95—474no—
589#95—474no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—474no—
595C24—472no—
596C24—942no—
597C24—942no—
598C24—942no—
599C24—942no—
600C24—942no—
601C24—942no—
602C24#1062535014yes—
603C24D4×D4714yes—
604C24Q8×D4714yes—
605C24C23×D4712yes—
606C24C23×D4711yescharacteristic
607C2×Q8—948no—
608C2×Q8—948no—
609C2×Q8—1884no—
610C2×Q8—18816no—
611C2×D4—4716no—
612C2×D4—9432no—
613C2×D4—948no—
614C2×D4—948no—
615C22×C4—232no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—28no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—28no—
626C22×C4—28no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—416no—
640C22×C4—416no—
641C22×C4—474no—
642C22×C4—474no—
643C22×C4—474no—
644C22×C4—472no—
645C22×C4—472no—
646C22×C4—472no—
647C22×C4—472no—
648C22×C4—472no—
649C22×C4—472no—
650C22×C4—472no—
651C22×C4—948no—
652C22×C4—942no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4—942no—
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—948no—
671C22×C4—1884no—
672C22×C4—18816no—
673C22×C4#1062535014yes—
674C22×C4C2×C22⋊D4714yes—
675C22×C4C2×C22⋊D4714yes—
676C22×C4C2×C22⋊D4714yes—
677C22×C4C23×D4712yes—
678C22×C4C23×D4712yes—
679C22×C4C23×D4712yes—
680C22×C4C23×D4712yes—
681C22×C4C23×D4712yes—
682C22×C4C23×D4712yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—948no—
687C4⋊C4—948no—
688C4⋊C4—948no—
689C4⋊C4—948no—
690C4⋊C4—948no—
691C4⋊C4—948no—
692C4⋊C4—948no—
693C4⋊C4—1884no—
694C4⋊C4C2×C22⋊D47116yescomplemented
695C22⋊C4—4716no—
696C22⋊C4—948no—
697C22⋊C4—948no—
698C22⋊C4—948no—
699C22⋊C4—948no—
700C22⋊C4—948no—
701C22⋊C4—948no—
702C22⋊C4—1884no—
703C42—948no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—28no—
714C23—474no—
715C23—948no—
716C23—948no—
717C23—948no—
718C23—942no—
719C23—942no—
720C23—942no—
721C23—942no—
722C23—942no—
723C23—942no—
724C23—1884no—
725C23—1884no—
726C23—1884no—
727C23—1884no—
728C23#13094002116yescomplemented
729C23C2×D4×D4714yes—
730C23C2×D4×D4712yes—
731C23C22×C22⋊D4712yes—
732C23C2×Q8×D4714yes—
733C23C2×Q8×D4712yes—
734C23C2×#1062535014yes—
735C23C2×#1062535012yes—
736C23C2×#1062535012yes—
737C23#1309406912yes—
738C23#1309407212yes—
739C23C24×D4711yescharacteristic
740Q8—18816no—
741D4—9432no—
742C2×C4—232no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—416no—
762C2×C4—416no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—474no—
766C2×C4—474no—
767C2×C4—474no—
768C2×C4—948no—
769C2×C4—948no—
770C2×C4—948no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—942no—
778C2×C4—942no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—942no—
783C2×C4—942no—
784C2×C4—942no—
785C2×C4—942no—
786C2×C4—942no—
787C2×C4—942no—
788C2×C4—942no—
789C2×C4—18816no—
790C2×C4—1884no—
791C2×C4—1884no—
792C2×C4—1884no—
793C2×C4—1884no—
794C2×C4C22×C22⋊D4714yes—
795C2×C4C22×C22⋊D4714yes—
796C2×C4C22×C22⋊D4714yes—
797C2×C4C2×#1062535014yes—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—232no—
804C22—24no—
805C22—944no—
806C22—944no—
807C22—944no—
808C22—1882no—
809C22—1882no—
810C22—1882no—
811C22—18816no—
812C22—1882no—
813C22C2×#1309400214yes—
814C22C2×#1309400218yescomplemented
815C22#1568963414yes—
816C22#1568972014yes—
817C22D4×C22⋊D4714yes—
818C22#1568977414yes—
819C22Q8×C22⋊D4714yes—
820C22#1568982814yes—
821C22C22×D4×D4711yescharacteristic
822C22C23×C22⋊D4711yescharacteristic
823C22C22×Q8×D4711yescharacteristic
824C22C22×#1062535011yescharacteristic
825C22C22×#1062535011yescharacteristic
826C22C2×#1309406911yescharacteristic
827C22C2×#1309407211yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—42no—
833C4—42no—
834C4—944no—
835C4—944no—
836C4—944no—
837C4—1882no—
838C4—1882no—
839C4—1882no—
840C4—1882no—
841C2—28no—
842C2—1884no—
843C2#2024719718yesdirect product factor
844C2C22×#1309400211yescharacteristic
845C2C2×#1568963411yescharacteristic
846C2C2×#1568972011yescharacteristic
847C2C2×D4×C22⋊D4711yescharacteristic
848C2C2×#1568977411yescharacteristic
849C2C2×Q8×C22⋊D4711yescharacteristic
850C2C2×#1568982811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC23×C4⋊C4×C47C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC23×C4⋊C4D47
hypocenterC47C2×#2449
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#13094003C2semidirect
2. C22×#13094002C2semidirect
4. #20247197C2direct (N × H)
5. C2×#15689058C2semidirect
6. C2×#15689054C2semidirect
7. C2×#15689045C2semidirect
8. C2×#15689043C2semidirect
9. C2×#15689018C2semidirect
10. C2×#15689009C2semidirect
13. C2×#15688996C2semidirect
14. C2×#15688996C2semidirect
15. C2×#15688994C2semidirect
16. C23×C4⋊C4×C47C2semidirect
21. C2×#13094003C22semidirect
23. C2×#13094002C22semidirect
43. #15689058C22semidirect
44. #15689054C22semidirect
45. #15689045C22semidirect
46. #15689043C22semidirect
47. #15689018C22semidirect
48. #15689009C22semidirect
51. #15688996C22semidirect
52. #15688996C22semidirect
53. #15688994C22semidirect
70. C22×C4⋊C4×C47C22semidirect
78. C22×C22⋊D47Q8semidirect
159. C2×C4⋊C4×C47D4semidirect
220. C2×C22⋊D47C2×Q8semidirect
260. C4⋊C4×C47C2×D4semidirect
288. C23×C47C22⋊Q8semidirect
381. C22×C47C2×C22⋊Q8semidirect
419. C23×C4⋊C4D47semidirect
433. C2×C47#2449semidirect
467. C22×C4⋊C4C2×D47semidirect
496. C47C2×#2449semidirect
559. C2×C4⋊C4C22⋊D47semidirect
694. C4⋊C4C2×C22⋊D47semidirect
728. C23#13094002semidirect
814. C22C2×#13094002semidirect
843. C2#20247197direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940032
C22×#130940022
C22×C4×C22⋊D472
#202471972
C2×#156890582
C2×#156890542
C2×#156890452
C2×#156890432
C2×#156890182
C2×#156890092
C2×#156890022
C2×#156889962
C2×#156889942
C23×C4⋊C4×C472
C2×#244947