Finite Group Databasebeta

← #34055979

Subgroups — #34055979

Order 19072.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750252C211yesmaximal, characteristic, complemented
2#23750247C211yesmaximal, characteristic
3#23750033C211yesmaximal, characteristic, complemented
4#23750029C211yesmaximal, characteristic, complemented
5#23749986C211yesmaximal, characteristic, complemented
6#23749981C211yesmaximal, characteristic, complemented
7#23749964C211yesmaximal, characteristic, complemented
8#23749959C211yesmaximal, characteristic, complemented
9#23749952C211yesmaximal, characteristic
10#23749940C211yesmaximal, characteristic
11#23749932C211yesmaximal, characteristic, complemented
12#23749926C211yesmaximal, characteristic, complemented
13#23749902C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#477×C149C211yesmaximal, characteristic, complemented
16#18011910C2211yescharacteristic
17#18011910C2211yescharacteristic
18#18011909—21no—
19#18011905—21no—
20#18011903C2211yescharacteristic
21#18011902C2211yescharacteristic
22#18011901—21no—
23#18011900C2211yescharacteristic
24#18011899—21no—
25#18011896—21no—
26#18011889—21no—
27#18011889—21no—
28#18011887—21no—
29#18011887C2211yescharacteristic
30#18011886C2211yescharacteristic
31C4×D596C2211yescharacteristic
32#18011869C2211yescharacteristic
33#18011868C2211yescharacteristic
34C4⋊C4×D149C2211yescharacteristic
35#18011845C2211yescharacteristic
36#18011844C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011835C2211yescharacteristic
43#18011835C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C4⋊Q8×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×D596—21no—
62C2×D596C2311yescharacteristic
63C2×C4×D149—21no—
64C2×C4×D149—21no—
65C2×C4×D149C2311yescharacteristic
66C2×#11924746C2311yescharacteristic
67C2×#11924746C2311yescharacteristic
68C4⋊Dic149—21no—
69C4⋊Dic149C2311yescharacteristic
70C4⋊Dic149C2311yescharacteristic
71C4⋊Dic149C2311yescharacteristic
72#14558715—21no—
73#14558715—21no—
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715D411yescharacteristic
80#14558715D411yescharacteristic
81#14558713—21no—
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×Q8×C149—21no—
92C2×Q8×C149C2311yescharacteristic
93C2×C8×C149C2311yescharacteristic
94C2×C8×C149C2311yescharacteristic
95C4⋊C4×C149—21no—
96C4⋊C4×C149—21no—
97C4⋊C4×C149C2311yescharacteristic
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C42×C149—21no—
101C42×C149C2311yescharacteristic
102C22×D149—21no—
103C22×D149C2×D411yescharacteristic
104Dic298—81no—
105Dic298—81no—
106D596—21no—
107D596—21no—
108D596—81no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149C2×D411yescharacteristic
113C2×Dic149C2×D411yescharacteristic
114C2×Dic149C2×D411yescharacteristic
115C4×D149—21no—
116C4×D149—21no—
117C4×D149—81no—
118C4×D149—81no—
119#11924746—21no—
120#11924746—21no—
121Q8×C149—21no—
122Q8×C149—21no—
123Q8×C149—81no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149C2×D411yescharacteristic
129C2×C4×C149C2×D411yescharacteristic
130C2×C4×C149C2411yescharacteristic
131C8×C149—21no—
132C8×C149—21no—
133C22×C149C22×D411yescharacteristic
134C2×D149—21no—
135C2×D149—21no—
136C2×D149—21no—
137C2×D149—41no—
138C2×D149—41no—
139C2×D149—41no—
140C4×C149—21no—
141C4×C149—21no—
142C4×C149—41no—
143C4×C149—41no—
144C4×C149—41no—
145C4×C149—41no—
146C4×C1492−1+411yescharacteristic
147C4×C1492−1+411yescharacteristic
148Dic149—21no—
149Dic149—21no—
150Dic149—21no—
151Dic149—41no—
152Dic149—41no—
153Dic149—41no—
154C2×C149#53611yescharacteristic
155C2×C149#57611yescharacteristic
156C2×C149#57811yescharacteristic
157D149—41no—
158D149—81no—
159C149#324311yescharacteristic, complemented, Sylow
160#3243—1491nomaximal, Sylow
161#544—1491no—
162#542—1491no—
163#501—1491no—
164#500—1491no—
165#489—1491no—
166#488—1491no—
167#485—1491no—
168#484—1491no—
169#482—1491no—
170#480—1491no—
171#479—1491no—
172#478—1491no—
173#477D14911yescharacteristic, complemented
174#474—1491no—
175#433—1491no—
176C4⋊Q8—2981no—
177C4⋊Q8—1491no—
178C4⋊Q8—1491no—
179C4⋊Q8C2×D14911yescharacteristic
180#126—2981no—
181#125—2981no—
182#125—1491no—
183#125—1491no—
184#124—2981no—
185#124—1491no—
186#123—2981no—
187C22⋊Q8—2981no—
188C22⋊Q8—2981no—
189C22⋊Q8—2981no—
190C22⋊Q8—1491no—
191#121—1491no—
192C4×Q8C2×D14911yescharacteristic
193C4×D4—1491no—
194#117—1491no—
195#117—1491no—
196C2×C4⋊C4—1491no—
197#107—1491no—
198#107—1491no—
199#107—1491no—
200#107—1491no—
201#107C2×D14911yescharacteristic
202#107C2×D14911yescharacteristic
203#106—1491no—
204#106—1491no—
205C4⋊C8—1491no—
206C4⋊C8C2×D14911yescharacteristic
207#103—1491no—
208#103—1491no—
209#103C2×D14911yescharacteristic
210#103C2×D14911yescharacteristic
211#102—1491no—
212#102—1491no—
213#102—1491no—
214#102—1491no—
215C22⋊C8—1491no—
216C22⋊C8—1491no—
217#97—1491no—
218C4×C8—1491no—
219C2×Q8—21no—
220C2×Q8—2981no—
221C2×Q8—2981no—
222C2×Q8C22×D14911yescharacteristic
223C2×D4—2981no—
224C2×D4—1491no—
225C22×C4—2981no—
226C22×C4—2981no—
227C22×C4—1491no—
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8C22×D14911yescharacteristic
231C2×C8C22×D14911yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—2981no—
235C4⋊C4—2981no—
236C4⋊C4—2981no—
237C4⋊C4—2981no—
238C4⋊C4—2981no—
239C4⋊C4—2981no—
240C4⋊C4—2981no—
241C4⋊C4—2981no—
242C4⋊C4—1491no—
243C4⋊C4—1491no—
244C4⋊C4—1491no—
245C4⋊C4—1491no—
246C4⋊C4—1491no—
247C4⋊C4C22×D14911yescharacteristic
248C4⋊C4C22×D14911yescharacteristic
249C4⋊C4C22×D14911yescharacteristic
250C22⋊C4—2981no—
251C22⋊C4—2981no—
252C22⋊C4—2981no—
253C22⋊C4—2981no—
254C22⋊C4—2981no—
255C22⋊C4—2981no—
256C22⋊C4—1491no—
257C22⋊C4—1491no—
258C42—21no—
259C42—2981no—
260C42—1491no—
261C42C22×D14911yescharacteristic
262C23—2981no—
263C23—1491no—
264Q8—21no—
265Q8—21no—
266Q8—81no—
267Q8—11921no—
268Q8—11921no—
269D4—2981no—
270D4—2981no—
271D4—11921no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—2981no—
277C2×C4—2981no—
278C2×C4—2981no—
279C2×C4—2981no—
280C2×C4—2981no—
281C2×C4—1491no—
282C2×C4—1491no—
283C2×C4—1491no—
284C2×C4—11921no—
285C2×C4—11921no—
286C2×C4D4×D14911yescharacteristic
287C2×C4D4×D14911yescharacteristic
288C2×C4C23×D14911yescharacteristic
289C8—21no—
290C8—21no—
291C8—2981no—
292C8—2981no—
293C22—2981no—
294C22—2981no—
295C22—2981no—
296C22—5961no—
297C22—5961no—
298C22—5961no—
299C22C2×D4×D14911yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—2981no—
307C4—2981no—
308C4—2981no—
309C4—5961no—
310C4—5961no—
311C4—5961no—
312C4#1801195811yescharacteristic
313C4#1801195911yescharacteristic
314C2—5961no—
315C2—11921no—
316C2#2375019811yescharacteristic
317C2#2375042911yescharacteristic
318C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#477×C149C2
socleC22×C149C22×D4
prime radical#18011886C22
hypercenter#477D149
hypocenterC149#3243
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #23750252C2semidirect
3. #23750033C2semidirect
4. #23750029C2semidirect
5. #23749986C2semidirect
6. #23749981C2semidirect
7. #23749964C2semidirect
8. #23749959C2semidirect
11. #23749932C2semidirect
12. #23749926C2semidirect
13. #23749902C2semidirect
14. #23749685C2semidirect
15. #477×C149C2semidirect
159. C149#3243semidirect
173. #477D149semidirect

Maximal subgroups

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

subgroupindex
#237502522
#237502472
#237500332
#237500292
#237499862
#237499812
#237499642
#237499592
#237499522
#237499402
#237499322
#237499262
#237499022
#237496852
#477×C1492
#3243149