Finite Group Databasebeta

← #44509885

Subgroups — #44509885

Order 30848.

696 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic241C211yesmaximal, characteristic
2C2×#21440598C211yesmaximal, characteristic, complemented
3C22×C4×Dic241C211yesmaximal, characteristic, complemented
4#29507611C211yesmaximal, characteristic, complemented
5#29507605C211yesmaximal, characteristic, complemented
6#29507602C211yesmaximal, characteristic, complemented
7#29507600C211yesmaximal, characteristic, complemented
8#29507597C211yesmaximal, characteristic
9#29507590C211yesmaximal, characteristic, complemented
10#29507589C211yesmaximal, characteristic, complemented
11#29507568C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic241C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic241C211yesmaximal, characteristic, complemented
14#29507562C211yesmaximal, characteristic, complemented
15#386×C241C211yesmaximal, characteristic
16C23×Dic241C2211yescharacteristic
17C23×Dic241C2211yescharacteristic
18C23×Dic241C2211yescharacteristic
19D4×Dic241C418yescomplemented
20#21440598—24no—
21C2×C4⋊Dic241C2211yescharacteristic
22C2×#16838749C2211yescharacteristic
23C2×#16838749C2211yescharacteristic
24C2×#16838749C2211yescharacteristic
25C2×#16838749C2211yescharacteristic
26C2×C22⋊Dic241C2211yescharacteristic
27C2×C22⋊Dic241C2211yescharacteristic
28C2×C22⋊Dic241C2211yescharacteristic
29C2×C22⋊Dic241C2211yescharacteristic
30C2×C22⋊Dic241C2211yescharacteristic
31C2×C4×Dic241—24no—
32C2×C4×Dic241C2211yescharacteristic
33C2×C4×Dic241C2211yescharacteristic
34C2×C4×Dic241C2211yescharacteristic
35C2×C4×Dic241C2211yescharacteristic
36C2×C4×Dic241C2211yescharacteristic
37C2×C4×Dic241C2211yescharacteristic
38C2×C4×Dic241C2211yescharacteristic
39#21440549C2211yescharacteristic
40#21440549C2211yescharacteristic
41#21440549C2211yescharacteristic
42#21440549C2211yescharacteristic
43#21440549C2211yescharacteristic
44#21440549C2211yescharacteristic
45#21440549C2211yescharacteristic
46#21440549C2211yescharacteristic
47C22×D4×C241C2211yescharacteristic
48C23×C4×C241C2211yescharacteristic
49C2×C22⋊C4×C241C2211yescharacteristic
50C2×C22⋊C4×C241C2211yescharacteristic
51C2×C22⋊C4×C241C2211yescharacteristic
52#95×C241C2211yescharacteristic
53#95×C241C2211yescharacteristic
54C22×Dic241—22no—
55C22×Dic241—22no—
56C22×Dic241—22no—
57C22×Dic241—22no—
58C22×Dic241—22no—
59C22×Dic241—22no—
60C22×Dic241—22no—
61C22×Dic241C2×C414yes—
62C22×Dic241C2×C414yescomplemented
63C22×Dic241C2311yescharacteristic
64C22×Dic241C2311yescharacteristic
65C22×Dic241C2311yescharacteristic
66C22×Dic241C2311yescharacteristic
67C22×Dic241C2311yescharacteristic
68C22×Dic241C2311yescharacteristic
69C22×Dic241C2311yescharacteristic
70C22×Dic241C2311yescharacteristic
71C4⋊Dic241C2×C414yescomplemented
72#16838749—22no—
73#16838749—22no—
74#16838749—22no—
75#16838749—22no—
76C22⋊Dic241—22no—
77C22⋊Dic241—22no—
78C22⋊Dic241—22no—
79C22⋊Dic241C2×C414yes—
80C22⋊Dic241C2×C414yescomplemented
81C4×Dic241—22no—
82C4×Dic241—22no—
83C4×Dic241—22no—
84C4×Dic241—22no—
85C4×Dic241—22no—
86C4×Dic241C2×C414yescomplemented
87C4×Dic241D414yescomplemented
88C24×C241C2311yescharacteristic
89C24×C241C2311yescharacteristic
90C2×D4×C241—22no—
91C2×D4×C241—22no—
92C2×D4×C241C2×C414yes—
93C22×C4×C241—22no—
94C22×C4×C241—22no—
95C22×C4×C241—22no—
96C22×C4×C241C2311yescharacteristic
97C22×C4×C241C2311yescharacteristic
98C22×C4×C241C2311yescharacteristic
99C22×C4×C241C2311yescharacteristic
100C22×C4×C241C2311yescharacteristic
101C22⋊C4×C241—22no—
102C22⋊C4×C241—22no—
103C22⋊C4×C241—22no—
104C2×Dic241—28no—
105C2×Dic241—21no—
106C2×Dic241—21no—
107C2×Dic241—21no—
108C2×Dic241—21no—
109C2×Dic241—21no—
110C2×Dic241—21no—
111C2×Dic241—21no—
112C2×Dic241—21no—
113C2×Dic241—21no—
114C2×Dic241—21no—
115C2×Dic241—28no—
116C2×Dic241—28no—
117C2×Dic241—21no—
118C2×Dic241—21no—
119C2×Dic241—21no—
120C2×Dic241—21no—
121C2×Dic241—21no—
122C2×Dic241—21no—
123C2×Dic241C22×C412yes—
124C2×Dic241C22×C412yes—
125C2×Dic241C22×C412yes—
126C2×Dic241C22×C412yes—
127C2×Dic241C2×D412yes—
128C2×Dic241C2×D412yes—
129C2×Dic241#4112yes—
130C2×Dic241#4112yes—
131C23×C241—21no—
132C23×C241—21no—
133C23×C241—21no—
134C23×C241—21no—
135C23×C241—21no—
136C23×C241—21no—
137C23×C241—21no—
138C23×C241—21no—
139C23×C241—21no—
140C23×C241—21no—
141C23×C241C22×C412yes—
142C23×C241C22×C412yes—
143C23×C241#4112yes—
144C23×C241#4112yes—
145C23×C241C2411yescharacteristic
146D4×C241—28no—
147C2×C4×C241—28no—
148C2×C4×C241—21no—
149C2×C4×C241—21no—
150C2×C4×C241—21no—
151C2×C4×C241—21no—
152C2×C4×C241—21no—
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×C241C22×C412yes—
161C2×C4×C241C2×D412yes—
162C2×C4×C241#4112yes—
163C22×C241—22no—
164C22×C241—22no—
165C22×C241—22no—
166C22×C241—22no—
167C22×C241—22no—
168C22×C241—22no—
169C22×C241—22no—
170C22×C241—22no—
171C22×C241—22no—
172C22×C241—41no—
173C22×C241—41no—
174C22×C241—41no—
175C22×C241—41no—
176C22×C241#11714yescomplemented
177C22×C241C23×C411yescharacteristic
178C22×C241C22×D411yescharacteristic
179C22×C241C2×#4111yescharacteristic
180C22×C241C2×#4111yescharacteristic
181C22×C241C2×#4111yescharacteristic
182C22×C241C2×#4111yescharacteristic
183C22×C241C2×#4111yescharacteristic
184C4×C241—22no—
185C4×C241—22no—
186C4×C241—22no—
187C4×C241—41no—
188C4×C241—41no—
189Dic241—22no—
190Dic241—22no—
191Dic241—22no—
192Dic241—22no—
193Dic241—22no—
194Dic241—41no—
195Dic241—41no—
196Dic241C4×D414yes—
197C2×C241—24no—
198C2×C241—42no—
199C2×C241C2×#11711yescharacteristic
200C2×C241C2×C4×D411yescharacteristic
201C2×C241C4×#4111yescharacteristic
202C2×C241#52511yescharacteristic
203C2×C241#52511yescharacteristic
204C2×C241#52911yescharacteristic
205C2×C241#52911yescharacteristic
206C241#229011yescharacteristic, complemented, Sylow
207#2290—2411nomaximal, Sylow
208C2×C4×D4—2411no—
209C2×#117—2411no—
210C22×C42—2411no—
211#388—2411no—
212#388—2411no—
213#387—2411no—
214#387—2411no—
215#386—2411no—
216#386D24111yescharacteristic
217#385—2411no—
218#385—2411no—
219C4×C4⋊C4—2411no—
220C4×C22⋊C4—2411no—
221C4×C22⋊C4—2411no—
222#376—2411no—
223C22×D4C2×D24111yescharacteristic
224C23×C4—2411no—
225C23×C4—2411no—
226C23×C4—2411no—
227C23×C4C2×D24111yescharacteristic
228C4×D4—2418no—
229#117—4824no—
230C2×C4⋊C4—2411no—
231C2×C4⋊C4—2411no—
232C2×C4⋊C4—2411no—
233C2×C4⋊C4—2411no—
234C2×C4⋊C4—2411no—
235C2×C22⋊C4—2411no—
236C2×C22⋊C4—2411no—
237C2×C22⋊C4—2411no—
238C2×C22⋊C4—2411no—
239C2×C22⋊C4—2411no—
240C2×C22⋊C4C2×D24111yescharacteristic
241C2×C22⋊C4C2×D24111yescharacteristic
242C2×C22⋊C4C2×D24111yescharacteristic
243C2×C42—4824no—
244C2×C42—2411no—
245C2×C42—2411no—
246C2×C42—2411no—
247C2×C42—2411no—
248C2×C42—2411no—
249C2×C42—2411no—
250C2×C42—2411no—
251#95—2411no—
252#95—2411no—
253#95—2411no—
254#95—2411no—
255#95—2411no—
256#95—2411no—
257#95—2411no—
258#95—2411no—
259#95C2×D24111yescharacteristic
260#95C2×D24111yescharacteristic
261C24C22×D24111yescharacteristic
262C24C22×D24111yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4C4×D24114yes—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—4822no—
270C22×C4—4822no—
271C22×C4—4822no—
272C22×C4—4822no—
273C22×C4—4822no—
274C22×C4—4822no—
275C22×C4—4822no—
276C22×C4—2411no—
277C22×C4—2411no—
278C22×C4—2414no—
279C22×C4—2414no—
280C22×C4—2411no—
281C22×C4—2411no—
282C22×C4—2411no—
283C22×C4—2411no—
284C22×C4—2411no—
285C22×C4—2411no—
286C22×C4C22×D24111yescharacteristic
287C22×C4C22×D24111yescharacteristic
288C22×C4C22×D24111yescharacteristic
289C22×C4C22×D24111yescharacteristic
290C22×C4C22×D24111yescharacteristic
291C4⋊C4—4822no—
292C4⋊C4—4822no—
293C4⋊C4—4822no—
294C4⋊C4—4822no—
295C4⋊C4—2414no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—4822no—
300C22⋊C4—4822no—
301C22⋊C4—4822no—
302C22⋊C4—2414no—
303C22⋊C4—2414no—
304C42—4822no—
305C42—4822no—
306C42—4822no—
307C42—4822no—
308C42—4822no—
309C42—2414no—
310C42—2414no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C4×D24112yes—
322C23C2×C4×D24112yes—
323C23#1683876912yes—
324C23#1683876912yes—
325C23C23×D24111yescharacteristic
326D4—28no—
327C2×C4—28no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—4821no—
341C2×C4—4821no—
342C2×C4—4821no—
343C2×C4—4821no—
344C2×C4—4821no—
345C2×C4—4821no—
346C2×C4—4828no—
347C2×C4—4821no—
348C2×C4—4821no—
349C2×C4—4821no—
350C2×C4—4821no—
351C2×C4—4821no—
352C2×C4—4821no—
353C2×C4—4821no—
354C2×C4—4821no—
355C2×C4—4821no—
356C2×C4—4821no—
357C2×C4—4828no—
358C2×C4—4828no—
359C2×C4—2412no—
360C2×C4—2412no—
361C2×C4—2412no—
362C2×C4—2412no—
363C2×C4—2412no—
364C2×C4—2412no—
365C2×C4—2412no—
366C2×C4—2412no—
367C2×C4C2×C4×D24112yes—
368C2×C4D4×D24112yes—
369C2×C4#1683876912yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22#2144059814yescomplemented
384C22C22×C4×D24111yescharacteristic
385C22C2×D4×D24111yescharacteristic
386C22#41×D24111yescharacteristic
387C22#41×D24111yescharacteristic
388C22C2×#1683876911yescharacteristic
389C22C2×#1683876911yescharacteristic
390C22C2×#1683876911yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—9641no—
397C4—9641no—
398C4—4822no—
399C4—4822no—
400C4—4822no—
401C4—4822no—
402C4—4822no—
403C4—2414no—
404C2—24no—
405C2—42no—
406C2C2×#2144059811yescharacteristic
407C2C4×D4×D24111yescharacteristic
408C2C4×#1683876911yescharacteristic
409C2#2950822311yescharacteristic
410C2#2950822711yescharacteristic
411C2#2950824411yescharacteristic
412C2#2950824811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#386×C241C2
socle, cosocleC23×C241C24
prime radicalC22×D4×C241C22
hypercenter#386D241
hypocenterC241#2290
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#21440598C2semidirect
3. C22×C4×Dic241C2semidirect
4. #29507611C2semidirect
5. #29507605C2semidirect
6. #29507602C2semidirect
7. #29507600C2semidirect
9. #29507590C2semidirect
10. #29507589C2semidirect
11. #29507568C2semidirect
12. C22⋊C4×Dic241C2semidirect
13. C22⋊C4×Dic241C2semidirect
14. #29507562C2semidirect
19. D4×Dic241C4semidirect
62. C22×Dic241C2×C4semidirect
71. C4⋊Dic241C2×C4semidirect
80. C22⋊Dic241C2×C4semidirect
86. C4×Dic241C2×C4semidirect
87. C4×Dic241D4semidirect
176. C22×C241#117semidirect
206. C241#2290semidirect
383. C22#21440598semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic2412
C2×#214405982
C22×C4×Dic2412
#295076112
#295076052
#295076022
#295076002
#295075972
#295075902
#295075892
#295075682
C22⋊C4×Dic2412
#295075622
#386×C2412
#2290241