Finite Group Databasebeta

← #34055947

Subgroups — #34055947

Order 19072.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750255C211yesmaximal, characteristic, complemented
2#23750231C211yesmaximal, characteristic
3#23750035C211yesmaximal, characteristic, complemented
4#23749991C211yesmaximal, characteristic, complemented
5#23749972C211yesmaximal, characteristic, complemented
6#23749952C211yesmaximal, characteristic, complemented
7#23749951C211yesmaximal, characteristic, complemented
8#23749945C211yesmaximal, characteristic, complemented
9#23749940C211yesmaximal, characteristic, complemented
10#23749928C211yesmaximal, characteristic, complemented
11#23749924C211yesmaximal, characteristic, complemented
12#23749914C211yesmaximal, characteristic, complemented
13#23749904C211yesmaximal, characteristic, complemented
14#23749684C211yesmaximal, characteristic, complemented
15#499×C149C211yesmaximal, characteristic, complemented
16#18011911C2211yescharacteristic
17#18011910—21no—
18#18011910C2211yescharacteristic
19#18011908C2211yescharacteristic
20#18011902C2211yescharacteristic
21#18011901—21no—
22#18011896—21no—
23#18011896—21no—
24#18011891—21no—
25#18011889—21no—
26#18011886—21no—
27#18011886—21no—
28#18011886C2211yescharacteristic
29#18011886C2211yescharacteristic
30#18011873C2211yescharacteristic
31#18011873C2211yescharacteristic
32#18011869C2211yescharacteristic
33#18011868C2211yescharacteristic
34C4⋊C4×D149C2211yescharacteristic
35#18011844C2211yescharacteristic
36#18011844C2211yescharacteristic
37#18011842C2211yescharacteristic
38#18011842C2211yescharacteristic
39#18011840C2211yescharacteristic
40#18011840C2211yescharacteristic
41#18011833C2211yescharacteristic
42#18011833C2211yescharacteristic
43#18011833C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011831C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011822C2211yescharacteristic
52#125×C149C2211yescharacteristic
53#125×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#106×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×D596—21no—
62C2×D596—21no—
63C2×D596—21no—
64C2×D596—21no—
65C2×D596C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715D411yescharacteristic
81#14558715D411yescharacteristic
82#14558713—21no—
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713D411yescharacteristic
88#14558713D411yescharacteristic
89C4×Dic149—21no—
90C4×Dic149C2311yescharacteristic
91C2×C8×C149C2311yescharacteristic
92C2×C8×C149C2311yescharacteristic
93C4⋊C4×C149—21no—
94C4⋊C4×C149—21no—
95C4⋊C4×C149—21no—
96C4⋊C4×C149—21no—
97C4⋊C4×C149C2311yescharacteristic
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C42×C149C2311yescharacteristic
102C22×D149—21no—
103C22×D149—21no—
104C22×D149C2×D411yescharacteristic
105Dic298—81no—
106Dic298—81no—
107D596—21no—
108D596—21no—
109D596—21no—
110D596—21no—
111D596—81no—
112D596—81no—
113D596—81no—
114D596—81no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C4×D149—21no—
121C4×D149—21no—
122C4×D149—81no—
123C4×D149—81no—
124C4×D149—81no—
125#11924746—21no—
126#11924746—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2411yescharacteristic
134C8×C149—21no—
135C8×C149—21no—
136C22×C149C22×D411yescharacteristic
137C2×D149—21no—
138C2×D149—21no—
139C2×D149—21no—
140C2×D149—41no—
141C2×D149—41no—
142C2×D149—41no—
143C2×D149—41no—
144C2×D149—41no—
145C2×D149—41no—
146C4×C149—21no—
147C4×C149—21no—
148C4×C149—41no—
149C4×C149—41no—
150C4×C149—41no—
151C4×C149—41no—
152C4×C1492−1+411yescharacteristic
153C4×C1492−1+411yescharacteristic
154Dic149—21no—
155Dic149—21no—
156Dic149—21no—
157Dic149—41no—
158Dic149—41no—
159C2×C149#53611yescharacteristic
160C2×C149#57611yescharacteristic
161C2×C149#57711yescharacteristic
162D149—41no—
163D149—81no—
164D149—81no—
165C149#324111yescharacteristic, complemented, Sylow
166#3241—1491nomaximal, Sylow
167#544—1491no—
168#540—1491no—
169#501—1491no—
170#499D14911yescharacteristic, complemented
171#490—1491no—
172#486—1491no—
173#482—1491no—
174#482—1491no—
175#481—1491no—
176#480—1491no—
177#478—1491no—
178#478—1491no—
179#476—1491no—
180#474—1491no—
181#433—1491no—
182C4⋊Q8—2981no—
183C4⋊Q8—1491no—
184C4⋊Q8—1491no—
185#127—1491no—
186#125—2981no—
187#125—1491no—
188#125C2×D14911yescharacteristic
189#125C2×D14911yescharacteristic
190#123—2981no—
191#123—2981no—
192C22⋊Q8—2981no—
193C22⋊Q8—2981no—
194#121—2981no—
195#121—2981no—
196#121—1491no—
197#121—1491no—
198C4×D4—1491no—
199C4×D4—1491no—
200#117—1491no—
201#117—1491no—
202C2×C4⋊C4—1491no—
203#107—1491no—
204#107—1491no—
205#107C2×D14911yescharacteristic
206#107C2×D14911yescharacteristic
207#106—1491no—
208#106—1491no—
209#106C2×D14911yescharacteristic
210#106C2×D14911yescharacteristic
211C4⋊C8—1491no—
212C4⋊C8—1491no—
213#102—1491no—
214#102—1491no—
215#102—1491no—
216#102—1491no—
217#102—1491no—
218#102—1491no—
219#102—1491no—
220#102—1491no—
221C22⋊C8—1491no—
222C22⋊C8—1491no—
223#97—1491no—
224C4×C8C2×D14911yescharacteristic
225C2×Q8—2981no—
226C2×Q8—2981no—
227C2×D4—2981no—
228C2×D4—2981no—
229C2×D4—2981no—
230C2×D4—2981no—
231C2×D4—1491no—
232C2×D4—1491no—
233C22×C4—2981no—
234C22×C4—2981no—
235C22×C4—2981no—
236C22×C4—1491no—
237C2×C8—1491no—
238C2×C8—1491no—
239C2×C8C22×D14911yescharacteristic
240C2×C8C22×D14911yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—2981no—
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—1491no—
251C4⋊C4—1491no—
252C4⋊C4—1491no—
253C4⋊C4—1491no—
254C4⋊C4C22×D14911yescharacteristic
255C4⋊C4C22×D14911yescharacteristic
256C4⋊C4C22×D14911yescharacteristic
257C4⋊C4C22×D14911yescharacteristic
258C22⋊C4—2981no—
259C22⋊C4—2981no—
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C22⋊C4—1491no—
264C22⋊C4—1491no—
265C42—2981no—
266C42—1491no—
267C42C22×D14911yescharacteristic
268C23—2981no—
269C23—2981no—
270C23—1491no—
271Q8—11921no—
272Q8—11921no—
273D4—2981no—
274D4—2981no—
275D4—2981no—
276D4—2981no—
277D4—11921no—
278D4—11921no—
279D4—11921no—
280D4—11921no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—2981no—
286C2×C4—2981no—
287C2×C4—2981no—
288C2×C4—2981no—
289C2×C4—1491no—
290C2×C4—1491no—
291C2×C4—1491no—
292C2×C4—11921no—
293C2×C4—11921no—
294C2×C4—11921no—
295C2×C4D4×D14911yescharacteristic
296C2×C4D4×D14911yescharacteristic
297C2×C4C23×D14911yescharacteristic
298C8—21no—
299C8—21no—
300C8—2981no—
301C8—2981no—
302C22—2981no—
303C22—2981no—
304C22—2981no—
305C22—5961no—
306C22—5961no—
307C22—5961no—
308C22—5961no—
309C22—5961no—
310C22—5961no—
311C22C2×D4×D14911yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—2981no—
319C4—2981no—
320C4—2981no—
321C4—5961no—
322C4—5961no—
323C4#1801195911yescharacteristic
324C4#1801195911yescharacteristic
325C2—5961no—
326C2—11921no—
327C2—11921no—
328C2#2375020011yescharacteristic
329C2#2375042711yescharacteristic
330C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#499×C149C2
socleC22×C149C22×D4
prime radical#23750231C2
hypercenter#499D149
hypocenterC149#3241
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #23750255C2semidirect
3. #23750035C2semidirect
4. #23749991C2semidirect
5. #23749972C2semidirect
6. #23749952C2semidirect
7. #23749951C2semidirect
8. #23749945C2semidirect
9. #23749940C2semidirect
10. #23749928C2semidirect
11. #23749924C2semidirect
12. #23749914C2semidirect
13. #23749904C2semidirect
14. #23749684C2semidirect
15. #499×C149C2semidirect
165. C149#3241semidirect
170. #499D149semidirect

Maximal subgroups

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

subgroupindex
#237502552
#237502312
#237500352
#237499912
#237499722
#237499522
#237499512
#237499452
#237499402
#237499282
#237499242
#237499142
#237499042
#237496842
#499×C1492
#3241149