Finite Group Databasebeta

← #44510039

Subgroups — #44510039

Order 30848.

672 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D241C211yesmaximal, characteristic
2#29507611C211yesmaximal, characteristic, complemented
3#29507610C211yesmaximal, characteristic, complemented
4#29507609C211yesmaximal, characteristic, complemented
5#29507608C211yesmaximal, characteristic, complemented
6#29507607C211yesmaximal, characteristic, complemented
7#29507606C211yesmaximal, characteristic, complemented
8#29507605C211yesmaximal, characteristic, complemented
9#29507576C211yesmaximal, characteristic, complemented
10#29507574C211yesmaximal, characteristic, complemented
11#29507572C211yesmaximal, characteristic
12#29507572C211yesmaximal, characteristic
13C4×#16838747C211yesmaximal, characteristic, complemented
14#29507564C211yesmaximal, characteristic, complemented
15#388×C241C211yesmaximal, characteristic, complemented
16C24×D241C2211yescharacteristic
17C22×C4×D241C2211yescharacteristic
18C22×C4×D241C2211yescharacteristic
19C2×C4⋊Dic241C2211yescharacteristic, complemented
20C2×#16838749C2211yescharacteristic, complemented
21C2×#16838749C2211yescharacteristic, complemented
22C2×C22⋊Dic241C2211yescharacteristic
23C2×C22⋊Dic241C2211yescharacteristic
24C2×C22⋊Dic241C2211yescharacteristic
25C2×#16838747C2211yescharacteristic
26C2×#16838747C2211yescharacteristic
27C2×#16838747C2211yescharacteristic
28C2×#16838747C2211yescharacteristic
29C2×#16838747C2211yescharacteristic
30C2×#16838747C2211yescharacteristic
31C2×#16838747C2211yescharacteristic
32C2×#16838747C2211yescharacteristic
33C2×#16838747C2211yescharacteristic
34C2×#16838747C2211yescharacteristic
35C22⋊C4×D241C418yescomplemented
36C2×C4×Dic241C2211yescharacteristic, complemented
37C2×C4×Dic241C2211yescharacteristic, complemented
38C2×C4×Dic241C2211yescharacteristic, complemented
39#21440549C2211yescharacteristic, complemented
40#21440549C2211yescharacteristic, complemented
41#21440549C2211yescharacteristic, complemented
42#21440549C2211yescharacteristic, complemented
43#21440549C2211yescharacteristic, complemented
44#21440549C2211yescharacteristic, complemented
45C2×C4⋊C4×C241C2211yescharacteristic, complemented
46C2×C22⋊C4×C241C2211yescharacteristic
47C2×C22⋊C4×C241C2211yescharacteristic
48C2×C22⋊C4×C241C2211yescharacteristic
49C2×C42×C241C2211yescharacteristic, complemented
50#95×C241C2211yescharacteristic, complemented
51#95×C241C2211yescharacteristic, complemented
52C23×D241—22no—
53C23×D241—22no—
54C23×D241—41no—
55C23×D241—41no—
56C23×D241—41no—
57C23×D241—41no—
58C23×D241C2×C414yes—
59C23×D241C2311yescharacteristic
60C23×D241C2311yescharacteristic
61C22×Dic241C2311yescharacteristic
62C22×Dic241C2311yescharacteristic
63C22×Dic241C2311yescharacteristic
64C22×Dic241C2311yescharacteristic
65C22×Dic241C2311yescharacteristic
66C22×Dic241C2311yescharacteristic
67C2×C4×D241—41no—
68C2×C4×D241—41no—
69C2×C4×D241—41no—
70C2×C4×D241—41no—
71C2×C4×D241C2×C414yes—
72C2×C4×D241C2×C414yes—
73C4⋊Dic241—41no—
74#16838749—41no—
75#16838749—41no—
76C22⋊Dic241—41no—
77C22⋊Dic241—41no—
78C22⋊Dic241C2×C414yes—
79#16838747—22no—
80#16838747—22no—
81#16838747—22no—
82#16838747—22no—
83#16838747—41no—
84#16838747—41no—
85#16838747—41no—
86#16838747—41no—
87#16838747C2×C414yes—
88#16838747C2×C414yes—
89C4×Dic241—41no—
90C4×Dic241—41no—
91C4×Dic241—41no—
92C24×C241C2311yescharacteristic
93C22×C4×C241C2311yescharacteristic
94C22×C4×C241C2311yescharacteristic
95C22×C4×C241C2311yescharacteristic
96C22×C4×C241C2311yescharacteristic
97C22×C4×C241C2311yescharacteristic
98C22×C4×C241C2311yescharacteristic
99C4⋊C4×C241—41no—
100C22⋊C4×C241—41no—
101C22⋊C4×C241—41no—
102C22⋊C4×C241C2×C414yes—
103C42×C241—41no—
104C22×D241—21no—
105C22×D241—21no—
106C22×D241—21no—
107C22×D241—21no—
108C22×D241—21no—
109C22×D241—21no—
110C22×D241—21no—
111C22×D241—21no—
112C22×D241—21no—
113C22×D241—21no—
114C22×D241—28no—
115C22×D241—44no—
116C22×D241—44no—
117C22×D241—44no—
118C22×D241—44no—
119C22×D241—44no—
120C22×D241—44no—
121C22×D241C22×C412yes—
122C22×D241C22×C412yes—
123C22×D241#4112yes—
124C22×D241#4112yes—
125C2×Dic241—21no—
126C2×Dic241—21no—
127C2×Dic241—21no—
128C2×Dic241—21no—
129C2×Dic241—21no—
130C2×Dic241—21no—
131C2×Dic241—21no—
132C2×Dic241—21no—
133C2×Dic241—21no—
134C2×Dic241—21no—
135C2×Dic241—21no—
136C2×Dic241—21no—
137C2×Dic241—21no—
138C2×Dic241—21no—
139C2×Dic241—21no—
140C2×Dic241—21no—
141C2×Dic241C22×C412yes—
142C2×Dic241C22×C412yes—
143C4×D241—44no—
144C4×D241—44no—
145C23×C241—21no—
146C23×C241—21no—
147C23×C241—21no—
148C23×C241—21no—
149C23×C241—21no—
150C23×C241—21no—
151C23×C241C22×C412yes—
152C23×C241C2411yescharacteristic
153C2×C4×C241—21no—
154C2×C4×C241—21no—
155C2×C4×C241—21no—
156C2×C4×C241—21no—
157C2×C4×C241—21no—
158C2×C4×C241—21no—
159C2×C4×C241—21no—
160C2×C4×C241—21no—
161C2×C4×C241—21no—
162C2×C4×C241—21no—
163C2×C4×C241—21no—
164C2×C4×C241—21no—
165C2×C4×C241—21no—
166C2×C4×C241—21no—
167C2×C4×C241—21no—
168C2×C4×C241—21no—
169C2×C4×C241C22×C412yes—
170C2×C4×C241C22×C412yes—
171C22×C241—22no—
172C22×C241—22no—
173C22×C241—22no—
174C22×C241—41no—
175C22×C241—41no—
176C22×C241—41no—
177C22×C241—41no—
178C22×C241C23×C411yescharacteristic
179C22×C241C2×#4111yescharacteristic
180C22×C241C2×#4111yescharacteristic
181C22×C241H(5,𝔽2)11yescharacteristic
182C22×C241H(5,𝔽2)11yescharacteristic
183C22×C241H(5,𝔽2)11yescharacteristic
184C22×C241H(5,𝔽2)11yescharacteristic
185C2×D241—22no—
186C2×D241—22no—
187C2×D241—22no—
188C2×D241—22no—
189C2×D241—22no—
190C2×D241—22no—
191C2×D241—22no—
192C2×D241—22no—
193C2×D241—22no—
194C2×D241—416no—
195C2×D241—41no—
196C2×D241—41no—
197C2×D241—41no—
198C2×D241—41no—
199C2×D241#11714yes—
200C4×C241—22no—
201C4×C241—22no—
202C4×C241—41no—
203C4×C241—41no—
204C4×C241—41no—
205C4×C241—41no—
206Dic241—22no—
207Dic241—22no—
208Dic241—41no—
209Dic241—41no—
210Dic241—41no—
211Dic241—41no—
212C2×C241—42no—
213C2×C241C2×#11711yescharacteristic
214C2×C241#51811yescharacteristic
215C2×C241#51811yescharacteristic
216C2×C241#53811yescharacteristic
217C2×C241#53811yescharacteristic
218C2×C241#53811yescharacteristic
219C2×C241#53811yescharacteristic
220D241—24no—
221D241—42no—
222C241#231211yescharacteristic, complemented, Sylow
223#2312—2411nomaximal, Sylow
224C22×C22⋊C4—2411no—
225#388—2411no—
226#388—2411no—
227#388—2411no—
228#388—2411no—
229#388—2411no—
230#388—2411no—
231#388—2411no—
232#388D24111yescharacteristic, complemented
233#380—2411no—
234#380—2411no—
235#379—2411no—
236#379—2411no—
237C4×C22⋊C4—2411no—
238C4×C22⋊C4—2411no—
239C25—2411no—
240C23×C4—2411no—
241C23×C4—2411no—
242C2×C4⋊C4—2411no—
243C2×C4⋊C4—2411no—
244C2×C4⋊C4—2411no—
245C2×C4⋊C4C2×D24111yescharacteristic, complemented
246C2×C22⋊C4—2411no—
247C2×C22⋊C4—2411no—
248C2×C22⋊C4—2411no—
249C2×C22⋊C4—2411no—
250C2×C22⋊C4—2411no—
251C2×C22⋊C4—2411no—
252C2×C22⋊C4—2411no—
253C2×C22⋊C4—2411no—
254C2×C22⋊C4—2411no—
255C2×C22⋊C4—2411no—
256C2×C22⋊C4—2411no—
257C2×C22⋊C4—2411no—
258C2×C22⋊C4—2411no—
259C2×C22⋊C4—2418no—
260C2×C22⋊C4C2×D24111yescharacteristic
261C2×C22⋊C4C2×D24111yescharacteristic
262C2×C22⋊C4C2×D24111yescharacteristic
263C2×C42—2411no—
264C2×C42—2411no—
265C2×C42—2411no—
266C2×C42C2×D24111yescharacteristic, complemented
267#95—2411no—
268#95—2411no—
269#95—2411no—
270#95—2411no—
271#95—2411no—
272#95—2411no—
273#95C2×D24111yescharacteristic, complemented
274#95C2×D24111yescharacteristic, complemented
275C24—9641no—
276C24—9641no—
277C24—9641no—
278C24—9641no—
279C24—4822no—
280C24—4822no—
281C24—2414no—
282C24—2411no—
283C24—2411no—
284C24C22×D24111yescharacteristic
285C22×C4—9641no—
286C22×C4—9641no—
287C22×C4—9641no—
288C22×C4—9641no—
289C22×C4—2414no—
290C22×C4—2414no—
291C22×C4—2411no—
292C22×C4—2411no—
293C22×C4—2411no—
294C22×C4—2411no—
295C22×C4—2411no—
296C22×C4—2411no—
297C22×C4C22×D24111yescharacteristic
298C22×C4C22×D24111yescharacteristic
299C22×C4C22×D24111yescharacteristic
300C22×C4C22×D24111yescharacteristic
301C22×C4C22×D24111yescharacteristic
302C22×C4C22×D24111yescharacteristic
303C4⋊C4—41no—
304C4⋊C4—9641no—
305C4⋊C4—9641no—
306C4⋊C4—9641no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—9641no—
310C22⋊C4—9641no—
311C22⋊C4—9641no—
312C22⋊C4—9641no—
313C22⋊C4—9641no—
314C22⋊C4—9641no—
315C22⋊C4—4822no—
316C22⋊C4—4822no—
317C22⋊C4—4822no—
318C22⋊C4—4822no—
319C22⋊C4—2414no—
320C22⋊C4—2414no—
321C22⋊C4—2414no—
322C22⋊C4C4×D24114yes—
323C42—41no—
324C42—9641no—
325C42—9641no—
326C42—9641no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—9644no—
334C23—9644no—
335C23—9644no—
336C23—9644no—
337C23—9644no—
338C23—9644no—
339C23—4828no—
340C23—4821no—
341C23—4821no—
342C23—4821no—
343C23—4821no—
344C23—4821no—
345C23—4821no—
346C23—4821no—
347C23—4821no—
348C23—4821no—
349C23—4821no—
350C23—2412no—
351C23—2412no—
352C23—2412no—
353C23—2412no—
354C23C2×C4×D24112yes—
355C23C23×D24111yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—9644no—
373C2×C4—9644no—
374C2×C4—4821no—
375C2×C4—4821no—
376C2×C4—4821no—
377C2×C4—4821no—
378C2×C4—4821no—
379C2×C4—4821no—
380C2×C4—4821no—
381C2×C4—4821no—
382C2×C4—4821no—
383C2×C4—4821no—
384C2×C4—4821no—
385C2×C4—4821no—
386C2×C4—4821no—
387C2×C4—4821no—
388C2×C4—4821no—
389C2×C4—4821no—
390C2×C4—2412no—
391C2×C4—2412no—
392C2×C4C2×C4×D24112yes—
393C2×C4C2×C4×D24112yes—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—96416no—
402C22—9641no—
403C22—9641no—
404C22—9641no—
405C22—9641no—
406C22—4822no—
407C22—4822no—
408C22—4822no—
409C22—4822no—
410C22—4822no—
411C22—4822no—
412C22—4822no—
413C22—4822no—
414C22—4822no—
415C22—2414no—
416C22C22×C4×D24111yescharacteristic
417C22#41×D24111yescharacteristic
418C22#41×D24111yescharacteristic
419C22#2144068711yescharacteristic
420C22#2144068711yescharacteristic
421C22#2144068811yescharacteristic
422C22#2144068811yescharacteristic
423C4—22no—
424C4—22no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—9641no—
430C4—9641no—
431C4—9641no—
432C4—9641no—
433C4—4822no—
434C4—4822no—
435C2—42no—
436C2—9642no—
437C2—4824no—
438C2#117×D24111yescharacteristic
439C2#2950818911yescharacteristic
440C2#2950818911yescharacteristic
441C2#2950829911yescharacteristic
442C2#2950830111yescharacteristic
443C2#2950830311yescharacteristic
444C2#2950830611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#388×C241C2
socle, cosocleC23×C241C24
prime radicalC24×D241C22
hypercenter#388D241
hypocenterC241#2312
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #29507611C2semidirect
3. #29507610C2semidirect
4. #29507609C2semidirect
5. #29507608C2semidirect
6. #29507607C2semidirect
7. #29507606C2semidirect
8. #29507605C2semidirect
9. #29507576C2semidirect
10. #29507574C2semidirect
13. C4×#16838747C2semidirect
14. #29507564C2semidirect
15. #388×C241C2semidirect
19. C2×C4⋊Dic241C22semidirect
20. C2×#16838749C22semidirect
21. C2×#16838749C22semidirect
35. C22⋊C4×D241C4semidirect
36. C2×C4×Dic241C22semidirect
37. C2×C4×Dic241C22semidirect
38. C2×C4×Dic241C22semidirect
39. #21440549C22semidirect
40. #21440549C22semidirect
41. #21440549C22semidirect
42. #21440549C22semidirect
43. #21440549C22semidirect
44. #21440549C22semidirect
45. C2×C4⋊C4×C241C22semidirect
49. C2×C42×C241C22semidirect
50. #95×C241C22semidirect
51. #95×C241C22semidirect
222. C241#2312semidirect
232. #388D241semidirect
245. C2×C4⋊C4C2×D241semidirect
266. C2×C42C2×D241semidirect
273. #95C2×D241semidirect
274. #95C2×D241semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D2412
#295076112
#295076102
#295076092
#295076082
#295076072
#295076062
#295076052
#295075762
#295075742
#295075722
C4×#168387472
#295075642
#388×C2412
#2312241