Finite Group Databasebeta

← #34057553

Subgroups — #34057553

Order 19072.

352 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750334C211yesmaximal, characteristic, complemented
2#23750331C211yesmaximal, characteristic, complemented
3#23750029C211yesmaximal, characteristic, complemented
4#23750025C211yesmaximal, characteristic, complemented
5#23750024C211yesmaximal, characteristic, complemented
6#23749928C211yesmaximal, characteristic, complemented
7#23749926C211yesmaximal, characteristic, complemented
8#23749923C211yesmaximal, characteristic, complemented
9#23749914C211yesmaximal, characteristic, complemented
10#23749913C211yesmaximal, characteristic, complemented
11#23749749C211yesmaximal, characteristic, complemented
12C4×#14558721C211yesmaximal, characteristic
13#23749705C211yesmaximal, characteristic
14#23749705C211yesmaximal, characteristic
15#478×C149C211yesmaximal, characteristic, complemented
16C2×#14558721C2211yescharacteristic
17#18011910C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011903C2211yescharacteristic
20#18011902C2211yescharacteristic
21#18011902C2211yescharacteristic
22#18011891—21no—
23#18011890—21no—
24#18011889—21no—
25#18011889—21no—
26#18011888—21no—
27#18011888—21no—
28C4×Dic298C2211yescharacteristic
29C4×D596C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31D4×Dic149C2211yescharacteristic
32#18011873C2211yescharacteristic
33#18011873C2211yescharacteristic
34C2×#14558715—21no—
35C4⋊C4×D149—21no—
36#18011845C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011831C2211yescharacteristic
49C4×#11924746C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298D411yescharacteristic
62C2×D596C2311yescharacteristic
63C22×Dic149—21no—
64C22×Dic149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68#14558721Q814yescomplemented
69C2×#11924746C2311yescharacteristic
70C2×#11924746C2311yescharacteristic
71C4⋊Dic149—21no—
72C4⋊Dic149—21no—
73C4⋊Dic149D411yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90C4×Dic149C2311yescharacteristic
91C4×Dic149C2311yescharacteristic
92C2×D4×C149C2311yescharacteristic
93C22×C4×C149—21no—
94C2×C8×C149C2311yescharacteristic
95C2×C8×C149C2311yescharacteristic
96C4⋊C4×C149—21no—
97C4⋊C4×C149—21no—
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C22⋊C4×C149—21no—
102C42×C149C2311yescharacteristic
103C22×D149—21no—
104Dic298—22no—
105Dic298—81no—
106Dic298—81no—
107D596—21no—
108D596C2×Q812yes—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—42no—
113C2×Dic149—81no—
114C2×Dic149C2×D411yescharacteristic
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C4×D149—42no—
119C4×D149—81no—
120C4×D149—81no—
121#11924746—21no—
122#11924746C2×Q812yes—
123C23×C149—21no—
124D4×C149—21no—
125D4×C149C2×Q812yes—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—81no—
130C2×C4×C149C2×D411yescharacteristic
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2411yescharacteristic
133C8×C149—21no—
134C8×C149—21no—
135C22×C149—22no—
136C22×C149—41no—
137C22×C149—41no—
138C22×C149C22×D411yescharacteristic
139C2×D149—22no—
140C2×D149—41no—
141C2×D149—41no—
142C4×C149—21no—
143C4×C149—21no—
144C4×C149—41no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149C22×Q811yescharacteristic
148C4×C1492−1+411yescharacteristic
149Dic149—21no—
150Dic149—21no—
151Dic149—21no—
152Dic149—41no—
153Dic149—41no—
154Dic149—41no—
155Dic149#13512yes—
156C2×C149—42no—
157C2×C149D4×Q811yescharacteristic
158C2×C149C2×#13511yescharacteristic
159C2×C149#57611yescharacteristic
160D149—42no—
161C149#338011yescharacteristic, complemented, Sylow
162#3380—1491nomaximal, Sylow
163#554—1491no—
164#554—1491no—
165#500—1491no—
166#499—1491no—
167#499—1491no—
168#478—1491no—
169#478—1491no—
170#478—1491no—
171#478D14911yescharacteristic, complemented
172#476—1491no—
173#476—1491no—
174C8×Q8—1491no—
175C4×D8—1491no—
176C4×D8—1491no—
177C4×D8—1491no—
178C2×D8—1491no—
179C4⋊Q8—1491no—
180C4⋊Q8—1491no—
181#125—1491no—
182#125—1491no—
183#125—1491no—
184#125C2×D14911yescharacteristic
185C22⋊Q8—2981no—
186C22⋊Q8—2981no—
187C22⋊Q8—2981no—
188C22⋊Q8—2981no—
189C22⋊Q8—2981no—
190C22⋊Q8—2981no—
191C4×Q8—1491no—
192C4×D4—1491no—
193C4×D4—1491no—
194C4×D4—1491no—
195C4×D4—1491no—
196C4×D4—1491no—
197C4×D4C2×D14911yescharacteristic
198C2×C4⋊C4—2981no—
199C2×C4⋊C4—2981no—
200#107—1491no—
201#107—1491no—
202#107—1491no—
203#107—1491no—
204#107C2×D14911yescharacteristic
205#106—1491no—
206#106—1491no—
207#106—1491no—
208#106C2×D14911yescharacteristic
209C4⋊C8—1491no—
210C4⋊C8—1491no—
211C4⋊C8C2×D14911yescharacteristic
212#102—1491no—
213#102—1491no—
214#102—1491no—
215#102—1491no—
216#102C2×D14911yescharacteristic
217#102C2×D14911yescharacteristic
218C4×C8—1491no—
219C4×C8—1491no—
220C4×C8—1491no—
221C2×Q8—2981no—
222C2×Q8—2981no—
223C2×Q8—1491no—
224C2×D4—1491no—
225C2×D4C22×D14911yescharacteristic
226C22×C4—21no—
227C22×C4—2981no—
228C22×C4—2981no—
229C22×C4—2981no—
230C22×C4—2981no—
231C22×C4—2981no—
232D8—1494no—
233C2×C8—1491no—
234C2×C8—1491no—
235C2×C8C22×D14911yescharacteristic
236C2×C8C22×D14911yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—2981no—
240C4⋊C4—2981no—
241C4⋊C4—2981no—
242C4⋊C4—2981no—
243C4⋊C4—2981no—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—1491no—
248C4⋊C4—1491no—
249C4⋊C4—1491no—
250C4⋊C4—1491no—
251C4⋊C4—1491no—
252C4⋊C4—1491no—
253C4⋊C4C22×D14911yescharacteristic
254C4⋊C4C22×D14911yescharacteristic
255C4⋊C4C22×D14911yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—2981no—
258C22⋊C4—2981no—
259C22⋊C4—2981no—
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C42—1491no—
263C42—1491no—
264C42C22×D14911yescharacteristic
265C23—21no—
266C23—2981no—
267Q8—2982no—
268Q8—11921no—
269Q8—11921no—
270D4—21no—
271D4—2981no—
272D4—1492no—
273D4Q8×D14912yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—81no—
278C2×C4—2981no—
279C2×C4—2981no—
280C2×C4—2981no—
281C2×C4—5962no—
282C2×C4—5962no—
283C2×C4—1491no—
284C2×C4—1491no—
285C2×C4—1491no—
286C2×C4—1491no—
287C2×C4—11921no—
288C2×C4—11921no—
289C2×C4—11921no—
290C2×C4D4×D14911yescharacteristic
291C2×C4D4×D14911yescharacteristic
292C2×C4C23×D14911yescharacteristic
293C8—21no—
294C8—21no—
295C8—2981no—
296C8—1492no—
297C22—22no—
298C22—41no—
299C22—41no—
300C22—2982no—
301C22—5961no—
302C22—5961no—
303C22C2×D4×D14911yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—2981no—
310C4—2981no—
311C4—2981no—
312C4—5961no—
313C4—5961no—
314C4—5961no—
315C4—1492no—
316C4C2×Q8×D14911yescharacteristic
317C4#1801195811yescharacteristic
318C2—42no—
319C2—5962no—
320C2#2375028811yescharacteristic
321C2#135×D14911yescharacteristic
322C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558721C22
hypercenter#478D149
hypocenterC149#3380
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23750334C2semidirect
2. #23750331C2semidirect
3. #23750029C2semidirect
4. #23750025C2semidirect
5. #23750024C2semidirect
6. #23749928C2semidirect
7. #23749926C2semidirect
8. #23749923C2semidirect
9. #23749914C2semidirect
10. #23749913C2semidirect
11. #23749749C2semidirect
15. #478×C149C2semidirect
68. #14558721Q8semidirect
161. C149#3380semidirect
171. #478D149semidirect

Maximal subgroups

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

subgroupindex
#237503342
#237503312
#237500292
#237500252
#237500242
#237499282
#237499262
#237499232
#237499142
#237499132
#237497492
C4×#145587212
#237497052
#478×C1492
#3380149