Finite Group Databasebeta

← #34055938

Subgroups — #34055938

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#23750253C211yesmaximal, characteristic, complemented
2#23750035C211yesmaximal, characteristic, complemented
3#23750024C211yesmaximal, characteristic, complemented
4#23749989C211yesmaximal, characteristic, complemented
5#23749971C211yesmaximal, characteristic, complemented
6#23749946C211yesmaximal, characteristic, complemented
7#23749946C211yesmaximal, characteristic, complemented
8#23749941C211yesmaximal, characteristic, complemented
9#23749936C211yesmaximal, characteristic, complemented
10#23749925C211yesmaximal, characteristic, complemented
11#23749925C211yesmaximal, characteristic, complemented
12#23749915C211yesmaximal, characteristic, complemented
13#23749905C211yesmaximal, characteristic, complemented
14#23749686C211yesmaximal, characteristic, complemented
15#540×C149C211yesmaximal, characteristic
16#18011911C2211yescharacteristic
17#18011911C2211yescharacteristic
18#18011910—21no—
19#18011903C2211yescharacteristic
20#18011903C2211yescharacteristic
21#18011902—21no—
22#18011888—21no—
23#18011888—21no—
24#18011870C2211yescharacteristic
25C2×C4⋊Dic149C2211yescharacteristic
26#18011844C2211yescharacteristic
27#18011844C2211yescharacteristic
28#18011844C2211yescharacteristic
29#18011844C2211yescharacteristic
30#18011842C2211yescharacteristic
31#18011842C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35C4⋊#11924746C2211yescharacteristic
36#18011832C2211yescharacteristic
37#18011832C2211yescharacteristic
38#18011832C2211yescharacteristic
39#18011832C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011832C2211yescharacteristic
43#18011832C2211yescharacteristic
44C22⋊#11924746C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46#18011822C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48#127×C149C2211yescharacteristic
49#125×C149C2211yescharacteristic
50#123×C149—21no—
51#123×C149—21no—
52#121×C149—21no—
53#121×C149—21no—
54#121×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56C4×D4×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58#117×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C22×Dic149—21no—
62C2×#11924746C2311yescharacteristic
63C2×#11924746C2311yescharacteristic
64C2×#11924746C2311yescharacteristic
65C2×#11924746C2311yescharacteristic
66C4⋊Dic149—21no—
67C4⋊Dic149—21no—
68C4⋊Dic149—21no—
69C4⋊Dic149C2311yescharacteristic
70C4⋊Dic149C2311yescharacteristic
71C4⋊Dic149C2311yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73#14558715—21no—
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77C22⋊Dic149—21no—
78C4×Dic149—21no—
79C2×D4×C149—21no—
80C2×D4×C149—21no—
81C2×D4×C149—21no—
82C2×D4×C149—21no—
83C2×D4×C149C2311yescharacteristic
84C2×D4×C149C2311yescharacteristic
85C22×C4×C149—21no—
86C22×C4×C149—21no—
87C22×C4×C149C2311yescharacteristic
88C4⋊C4×C149—21no—
89C4⋊C4×C149—21no—
90C4⋊C4×C149D411yescharacteristic
91C4⋊C4×C149D411yescharacteristic
92C4⋊C4×C149C2311yescharacteristic
93C4⋊C4×C149C2311yescharacteristic
94C22⋊C4×C149—21no—
95C22⋊C4×C149—21no—
96C22⋊C4×C149—21no—
97C22⋊C4×C149—21no—
98C22⋊C4×C149D411yescharacteristic
99C22⋊C4×C149D411yescharacteristic
100C42×C149C2311yescharacteristic
101C42×C149C2311yescharacteristic
102Dic298—81no—
103Dic298—81no—
104C2×Dic149—21no—
105C2×Dic149—21no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149—81no—
109#11924746—21no—
110#11924746—21no—
111#11924746—21no—
112#11924746—21no—
113C23×C149—21no—
114C23×C149—21no—
115C23×C149C2×D411yescharacteristic
116D4×C149—21no—
117D4×C149—21no—
118D4×C149—21no—
119D4×C149—21no—
120D4×C149—81no—
121D4×C149—81no—
122D4×C149—81no—
123D4×C149—81no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—81no—
129C2×C4×C149—81no—
130C2×C4×C149C2×D411yescharacteristic
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2411yescharacteristic
136C22×C149—21no—
137C22×C149—21no—
138C22×C149—21no—
139C22×C149—41no—
140C22×C149—41no—
141C22×C149—41no—
142C22×C149—41no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149C22×D411yescharacteristic
146C4×C149—21no—
147C4×C149—21no—
148C4×C149—21no—
149C4×C149—21no—
150C4×C149—21no—
151C4×C149—41no—
152C4×C149—41no—
153C4×C1492−1+411yescharacteristic
154C4×C1492−1+411yescharacteristic
155Dic149—41no—
156Dic149—41no—
157Dic149—41no—
158Dic149—41no—
159C2×C149—41no—
160C2×C149—81no—
161C2×C149—81no—
162C2×C149#53611yescharacteristic
163C2×C149#57611yescharacteristic
164C2×C149#57711yescharacteristic
165C149#324111yescharacteristic, complemented, Sylow
166#3241—1491nomaximal, Sylow
167#544—1491no—
168#540D14911yescharacteristic
169#501—1491no—
170#499—1491no—
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#127C2×D14911yescharacteristic
186#125—2981no—
187#125—1491no—
188#125—1491no—
189#125C2×D14911yescharacteristic
190#123—21no—
191#123—21no—
192C22⋊Q8—2981no—
193C22⋊Q8—2981no—
194#121—21no—
195#121—21no—
196#121C2×D14911yescharacteristic
197#121C2×D14911yescharacteristic
198C4×D4C2×D14911yescharacteristic
199C4×D4C2×D14911yescharacteristic
200#117—1491no—
201#117C2×D14911yescharacteristic
202C2×C4⋊C4—1491no—
203#107—1491no—
204#107—1491no—
205#107—1491no—
206#107—1491no—
207#106—1491no—
208#106—1491no—
209#106—1491no—
210#106—1491no—
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×C8—1491no—
225C2×Q8—2981no—
226C2×Q8—2981no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C22×D14911yescharacteristic
232C2×D4C22×D14911yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—2981no—
236C22×C4C22×D14911yescharacteristic
237C2×C8—1491no—
238C2×C8—1491no—
239C2×C8—1491no—
240C2×C8—1491no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—2981no—
244C4⋊C4—2981no—
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—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—2981no—
263C22⋊C4C22⋊D14911yescharacteristic
264C22⋊C4C22⋊D14911yescharacteristic
265C42—2981no—
266C42C22×D14911yescharacteristic
267C42C22×D14911yescharacteristic
268C23—21no—
269C23—21no—
270C23C2×C22⋊D14911yescharacteristic
271Q8—11921no—
272Q8—11921no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—2981no—
288C2×C4—2981no—
289C2×C4—2981no—
290C2×C4—2981no—
291C2×C4—11921no—
292C2×C4C2×C22⋊D14911yescharacteristic
293C2×C4C2×C22⋊D14911yescharacteristic
294C2×C4C2×C22⋊D14911yescharacteristic
295C2×C4C2×C22⋊D14911yescharacteristic
296C2×C4C2×C22⋊D14911yescharacteristic
297C2×C4C23×D14911yescharacteristic
298C8—2981no—
299C8—2981no—
300C8—2981no—
301C8—2981no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×C22⋊D14911yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—5961no—
320C4—5961no—
321C4—5961no—
322C4—5961no—
323C4#1801195811yescharacteristic
324C4#1801195811yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2#2375019611yescharacteristic
329C2#2375042811yescharacteristic
330C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radical#540×C149C2
socleC22×C149C22×D4
hypercenter#540D149
hypocenterC149#3241
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23750253C2semidirect
2. #23750035C2semidirect
3. #23750024C2semidirect
4. #23749989C2semidirect
5. #23749971C2semidirect
6. #23749946C2semidirect
7. #23749946C2semidirect
8. #23749941C2semidirect
9. #23749936C2semidirect
10. #23749925C2semidirect
11. #23749925C2semidirect
12. #23749915C2semidirect
13. #23749905C2semidirect
14. #23749686C2semidirect
165. C149#3241semidirect

Maximal subgroups

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

subgroupindex
#237502532
#237500352
#237500242
#237499892
#237499712
#237499462
#237499412
#237499362
#237499252
#237499152
#237499052
#237496862
#540×C1492
#3241149