Finite Group Databasebeta

← #44509986

Subgroups — #44509986

Order 30848.

652 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21440628C211yesmaximal, characteristic
2C2×#21440607C211yesmaximal, characteristic, complemented
3C2×#21440602C211yesmaximal, characteristic
4#29507621C211yesmaximal, characteristic, complemented
5#29507617C211yesmaximal, characteristic
6#29507611C211yesmaximal, characteristic, complemented
7#29507608C211yesmaximal, characteristic, complemented
8#29507607C211yesmaximal, characteristic, complemented
9#29507581C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic241C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic241C211yesmaximal, characteristic, complemented
12#29507564C211yesmaximal, characteristic, complemented
13#29507564C211yesmaximal, characteristic, complemented
14C42×Dic241C211yesmaximal, characteristic, complemented
15#388×C241C211yesmaximal, characteristic, complemented
16C22×Dic482C2211yescharacteristic
17C22×C22⋊D241C2211yescharacteristic
18C23×Dic241C2211yescharacteristic
19C22×C4×D241C2211yescharacteristic
20#21440628C418yescomplemented
21#21440607—24no—
22#21440602—24no—
23C2×#16838749C2211yescharacteristic
24C2×#16838749C2211yescharacteristic
25C2×#16838749C2211yescharacteristic
26C2×C22⋊Dic241C2211yescharacteristic
27C2×C22⋊Dic241C2211yescharacteristic
28C2×#16838747C2211yescharacteristic
29C2×#16838747C2211yescharacteristic
30C2×#16838747C2211yescharacteristic
31C2×#16838747C2211yescharacteristic
32C2×#16838747C2211yescharacteristic
33C2×C4×Dic241C2211yescharacteristic
34C2×C4×Dic241C2211yescharacteristic
35C2×C4×Dic241C2211yescharacteristic
36C2×C4×Dic241C2211yescharacteristic
37C2×C4×Dic241C2211yescharacteristic
38C2×C4×Dic241C2211yescharacteristic
39C2×C4×Dic241C2211yescharacteristic
40C2×C4×Dic241C2211yescharacteristic
41#21440549C2211yescharacteristic
42#21440549C2211yescharacteristic
43#21440549C2211yescharacteristic
44#21440549C2211yescharacteristic
45#21440549C2211yescharacteristic
46#21440549C2211yescharacteristic
47C2×C4⋊C4×C241C2211yescharacteristic
48C2×C22⋊C4×C241C2211yescharacteristic
49C2×C22⋊C4×C241C2211yescharacteristic
50C2×C22⋊C4×C241C2211yescharacteristic
51C2×C42×C241C2211yescharacteristic
52#95×C241C2211yescharacteristic
53#95×C241C2211yescharacteristic
54C23×D241C2311yescharacteristic
55C2×Dic482—22no—
56C2×Dic482—22no—
57C2×Dic482C2×C414yescomplemented
58C2×C22⋊D241—22no—
59C2×C22⋊D241—22no—
60C2×C22⋊D241C2×C414yes—
61C22×Dic241—22no—
62C22×Dic241—22no—
63C22×Dic241—22no—
64C22×Dic241C2311yescharacteristic
65C22×Dic241C2311yescharacteristic
66C22×Dic241C2311yescharacteristic
67C22×Dic241C2311yescharacteristic
68C22×Dic241C2311yescharacteristic
69C22×Dic241C2311yescharacteristic
70C22×Dic241C2311yescharacteristic
71C2×C4×D241—22no—
72C2×C4×D241—22no—
73C2×C4×D241—22no—
74#16838749—22no—
75#16838749—22no—
76#16838749—22no—
77C22⋊Dic241—22no—
78C22⋊Dic241C2×C414yescomplemented
79#16838747—22no—
80#16838747—22no—
81#16838747—22no—
82#16838747C2×C414yescomplemented
83#16838747C2×C414yescomplemented
84C4×Dic241—22no—
85C4×Dic241—22no—
86C4×Dic241—22no—
87C4×Dic241—22no—
88C4×Dic241—22no—
89C4×Dic241—22no—
90C4×Dic241C2×C414yescomplemented
91C4×Dic241D414yes—
92C24×C241C2311yescharacteristic
93C22×C4×C241C2311yescharacteristic
94C22×C4×C241C2311yescharacteristic
95C22×C4×C241C2311yescharacteristic
96C22×C4×C241C2311yescharacteristic
97C22×C4×C241C2311yescharacteristic
98C22×C4×C241C2311yescharacteristic
99C4⋊C4×C241—22no—
100C22⋊C4×C241—22no—
101C22⋊C4×C241—22no—
102C22⋊C4×C241C2×C414yescomplemented
103C42×C241—22no—
104C22×D241—21no—
105C22×D241—21no—
106C22×D241—21no—
107C22×D241—21no—
108C22×D241—21no—
109C22×D241—21no—
110C22×D241C22×C412yes—
111Dic482—28no—
112C22⋊D241—28no—
113C2×Dic241—21no—
114C2×Dic241—21no—
115C2×Dic241—21no—
116C2×Dic241—21no—
117C2×Dic241—21no—
118C2×Dic241—21no—
119C2×Dic241—21no—
120C2×Dic241—21no—
121C2×Dic241—21no—
122C2×Dic241—21no—
123C2×Dic241—21no—
124C2×Dic241—21no—
125C2×Dic241—44no—
126C2×Dic241C22×C412yes—
127C2×Dic241C22×C412yes—
128C2×Dic241C22×C412yes—
129C2×Dic241C2×D412yes—
130C2×Dic241C2×D412yes—
131C2×Dic241#4112yes—
132C2×Dic241#4112yes—
133C2×Dic241#4112yes—
134C2×Dic241#4112yes—
135C4×D241—44no—
136C23×C241—21no—
137C23×C241—21no—
138C23×C241—21no—
139C23×C241—21no—
140C23×C241—21no—
141C23×C241—21no—
142C23×C241C22×C412yes—
143C23×C241C2411yescharacteristic
144C2×C4×C241—21no—
145C2×C4×C241—21no—
146C2×C4×C241—21no—
147C2×C4×C241—21no—
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×C241C22×C412yes—
159C2×C4×C241C22×C412yes—
160C2×C4×C241C2×D412yes—
161C2×C4×C241#4112yes—
162C22×C241—22no—
163C22×C241—22no—
164C22×C241—22no—
165C22×C241—41no—
166C22×C241—41no—
167C22×C241—41no—
168C22×C241—41no—
169C22×C241C23×C411yescharacteristic
170C22×C241C22×D411yescharacteristic
171C22×C241C2×#4111yescharacteristic
172C22×C241C2×#4111yescharacteristic
173C22×C241C2×#4111yescharacteristic
174C22×C241C2×#4111yescharacteristic
175C22×C241C2×#4111yescharacteristic
176C2×D241—22no—
177C2×D241—22no—
178C2×D241—22no—
179C2×D241—41no—
180C2×D241—41no—
181C2×D241—41no—
182C2×D241—41no—
183C4×C241—22no—
184C4×C241—22no—
185C4×C241—22no—
186C4×C241—22no—
187C4×C241—41no—
188C4×C241—41no—
189Dic241—22no—
190Dic241—22no—
191Dic241—22no—
192Dic241—41no—
193Dic241—41no—
194Dic241C4×D414yes—
195Dic241#12414yescomplemented
196C2×C241—42no—
197C2×C241C2×C4×D411yescharacteristic
198C2×C241C4×#4111yescharacteristic
199C2×C241C4×#4111yescharacteristic
200C2×C241C2×#12411yescharacteristic
201C2×C241#52911yescharacteristic
202C2×C241#52911yescharacteristic
203C2×C241#53211yescharacteristic
204D241—42no—
205C241C4×#12411yescharacteristic, complemented, Sylow
206C4×#124—2411nomaximal, Sylow
207C2×#124—2411no—
208C2×C4×Q8—2411no—
209C2×C4×D4—2411no—
210#391—2411no—
211#390—2411no—
212#388—2411no—
213#388—2411no—
214#388—2411no—
215#388D24111yescharacteristic, complemented
216#382—2411no—
217C4×C22⋊C4—2411no—
218C4×C22⋊C4—2411no—
219C4×C22⋊C4—2411no—
220C4×C22⋊C4—2411no—
221C43—2411no—
222C22×Q8—2411no—
223C22×D4—2411no—
224C23×C4—2411no—
225C23×C4—2411no—
226#124—2418no—
227C4×Q8—4824no—
228C4×D4—4824no—
229C2×C4⋊C4—2411no—
230C2×C4⋊C4—2411no—
231C2×C4⋊C4—2411no—
232C2×C4⋊C4C2×D24111yescharacteristic
233C2×C22⋊C4—2411no—
234C2×C22⋊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—2411no—
244C2×C42—2411no—
245C2×C42—2411no—
246C2×C42—2411no—
247C2×C42—2411no—
248C2×C42—2411no—
249C2×C42—2411no—
250C2×C42—2411no—
251C2×C42C2×D24111yescharacteristic
252#95—2411no—
253#95—2411no—
254#95—2411no—
255#95—2411no—
256#95—2411no—
257#95—2411no—
258#95C2×D24111yescharacteristic
259#95C2×D24111yescharacteristic
260C24—2411no—
261C24C22×D24111yescharacteristic
262C2×Q8—4822no—
263C2×Q8—4822no—
264C2×Q8—2414no—
265C2×D4—4822no—
266C2×D4—4822no—
267C2×D4—2414no—
268C22×C4—4822no—
269C22×C4—4822no—
270C22×C4—4822no—
271C22×C4—4822no—
272C22×C4—4822no—
273C22×C4—4822no—
274C22×C4—2411no—
275C22×C4—2411no—
276C22×C4—2411no—
277C22×C4—2411no—
278C22×C4—2411no—
279C22×C4—2411no—
280C22×C4—2411no—
281C22×C4C22×D24111yescharacteristic
282C22×C4C22×D24111yescharacteristic
283C22×C4C22×D24111yescharacteristic
284C22×C4C22×D24111yescharacteristic
285C22×C4C22×D24111yescharacteristic
286C22×C4C22×D24111yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—4822no—
289C4⋊C4—4822no—
290C4⋊C4—4822no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—4822no—
294C22⋊C4—4822no—
295C22⋊C4—4822no—
296C22⋊C4—4822no—
297C22⋊C4—2414no—
298C22⋊C4—2414no—
299C22⋊C4—2414no—
300C22⋊C4C4×D24114yescomplemented
301C42—22no—
302C42—4822no—
303C42—4822no—
304C42—4822no—
305C42—4822no—
306C42—4822no—
307C42—4822no—
308C42—2414no—
309C42—2414no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—4821no—
317C23—4821no—
318C23—4821no—
319C23—4821no—
320C23—4821no—
321C23—4821no—
322C23—2412no—
323C23C2×C4×D24112yes—
324C23C23×D24111yescharacteristic
325Q8—4828no—
326D4—4828no—
327C2×C4—21no—
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—21no—
341C2×C4—9644no—
342C2×C4—9644no—
343C2×C4—4821no—
344C2×C4—4821no—
345C2×C4—4821no—
346C2×C4—4821no—
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—2412no—
356C2×C4—2412no—
357C2×C4—2412no—
358C2×C4—2412no—
359C2×C4—2412no—
360C2×C4—2412no—
361C2×C4—2412no—
362C2×C4—2412no—
363C2×C4—2412no—
364C2×C4C2×C4×D24112yes—
365C2×C4C2×C4×D24112yes—
366C2×C4D4×D24112yes—
367C2×C4#1683876912yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—9641no—
376C22—9641no—
377C22—9641no—
378C22—9641no—
379C22—4822no—
380C22—4822no—
381C22—4822no—
382C22C22×C4×D24111yescharacteristic
383C22C2×D4×D24111yescharacteristic
384C22#41×D24111yescharacteristic
385C22#41×D24111yescharacteristic
386C22#41×D24111yescharacteristic
387C22#41×D24111yescharacteristic
388C22C2×#1683876911yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—9641no—
396C4—9641no—
397C4—4822no—
398C4—4822no—
399C4—4822no—
400C4—2414no—
401C4—2414no—
402C2—42no—
403C2—9642no—
404C2C4×D4×D24111yescharacteristic
405C2C4×#1683876911yescharacteristic
406C2#2950818511yescharacteristic
407C2#124×D24111yescharacteristic
408C2#2950824411yescharacteristic
409C2#2950825011yescharacteristic
410C2#2950826211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#388×C241C2
socle, cosocleC23×C241C24
prime radicalC22×C22⋊D241C22
hypercenter#388D241
hypocenterC241C4×#124
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#21440607C2semidirect
4. #29507621C2semidirect
6. #29507611C2semidirect
7. #29507608C2semidirect
8. #29507607C2semidirect
9. #29507581C2semidirect
10. C22⋊C4×Dic241C2semidirect
11. C22⋊C4×Dic241C2semidirect
12. #29507564C2semidirect
13. #29507564C2semidirect
14. C42×Dic241C2semidirect
15. #388×C241C2semidirect
20. #21440628C4semidirect
57. C2×Dic482C2×C4semidirect
78. C22⋊Dic241C2×C4semidirect
82. #16838747C2×C4semidirect
83. #16838747C2×C4semidirect
90. C4×Dic241C2×C4semidirect
102. C22⋊C4×C241C2×C4semidirect
195. Dic241#124semidirect
205. C241C4×#124semidirect
215. #388D241semidirect
300. C22⋊C4C4×D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406282
C2×#214406072
C2×#214406022
#295076212
#295076172
#295076112
#295076082
#295076072
#295075812
C22⋊C4×Dic2412
#295075642
C42×Dic2412
#388×C2412
C4×#124241