Finite Group Databasebeta

← #34057646

Subgroups — #34057646

Order 19072.

348 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#23750336C211yesmaximal, characteristic, complemented
2#23750331C211yesmaximal, characteristic, complemented
3#23750033C211yesmaximal, characteristic, complemented
4#23750025C211yesmaximal, characteristic, complemented
5#23749928C211yesmaximal, characteristic, complemented
6#23749924C211yesmaximal, characteristic, complemented
7#23749924C211yesmaximal, characteristic, complemented
8#23749922C211yesmaximal, characteristic, complemented
9#23749904C211yesmaximal, characteristic, complemented
10#23749902C211yesmaximal, characteristic, complemented
11#23749753C211yesmaximal, characteristic, complemented
12#23749738C211yesmaximal, characteristic
13#23749736C211yesmaximal, characteristic
14#23749707C211yesmaximal, characteristic
15#501×C149C211yesmaximal, characteristic, complemented
16C2×D1192C2211yescharacteristic
17#18011910C2211yescharacteristic
18#18011902C2211yescharacteristic
19#18011902C2211yescharacteristic
20#18011902C2211yescharacteristic
21#18011891—21no—
22#18011891—21no—
23#18011889—21no—
24#18011889—21no—
25#18011887—21no—
26#18011887—21no—
27C4×Dic298C2211yescharacteristic
28C4×D596C2211yescharacteristic
29C4×D596C2211yescharacteristic
30#18011873C2211yescharacteristic
31#18011873C2211yescharacteristic
32#18011873C2211yescharacteristic
33#18011873C2211yescharacteristic
34C4⋊C4×D149—21no—
35C4⋊C4×D149—21no—
36#18011844C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011833C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C4⋊Q8×C149C2211yescharacteristic
53#125×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#106×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298D411yescharacteristic
61C2×D596C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C4×D149—21no—
64C2×C4×D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69D1192Q814yescomplemented
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C4⋊Dic149—21no—
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149D411yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715D411yescharacteristic
83#14558715D411yescharacteristic
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90C4×Dic149C2311yescharacteristic
91C4×Dic149C2311yescharacteristic
92C2×Q8×C149—21no—
93C2×C8×C149C2311yescharacteristic
94C2×C8×C149C2311yescharacteristic
95C4⋊C4×C149—21no—
96C4⋊C4×C149—21no—
97C4⋊C4×C149—21no—
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C42×C149C2311yescharacteristic
103C22×D149—21no—
104C22×D149—21no—
105Dic298—41no—
106Dic298—81no—
107D596—21no—
108D596—21no—
109D596C2×Q812yes—
110D596C2×Q812yes—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149C2×D411yescharacteristic
114C2×Dic149C2×D411yescharacteristic
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117C4×D149—42no—
118C4×D149—42no—
119C4×D149—81no—
120C4×D149—81no—
121C4×D149—81no—
122C4×D149—81no—
123#11924746—21no—
124#11924746—21no—
125Q8×C149—81no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149C2×D411yescharacteristic
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2411yescharacteristic
133C8×C149—21no—
134C8×C149C2×Q812yes—
135C22×C149C22×D411yescharacteristic
136C2×D149—22no—
137C2×D149—22no—
138C2×D149—41no—
139C2×D149—41no—
140C2×D149—41no—
141C2×D149—41no—
142C4×C149—21no—
143C4×C149—21no—
144C4×C149—41no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149—41no—
148C4×C149C22×Q811yescharacteristic
149C4×C1492−1+411yescharacteristic
150Dic149—21no—
151Dic149—21no—
152Dic149—21no—
153Dic149—21no—
154Dic149—41no—
155Dic149—41no—
156C2×C149D4×Q811yescharacteristic
157C2×C149#57511yescharacteristic
158C2×C149#57611yescharacteristic
159D149—42no—
160D149—42no—
161C149#338911yescharacteristic, complemented, Sylow
162#3389—1491nomaximal, Sylow
163#554—1491no—
164#554—1491no—
165#501—1491no—
166#501D14911yescharacteristic, complemented
167#499—1491no—
168#478—1491no—
169#478—1491no—
170#478—1491no—
171#478—1491no—
172#474—1491no—
173#474—1491no—
174#446—1491no—
175#442—1491no—
176#442—1491no—
177C4×D8—1491no—
178C2×D8—1491no—
179C4⋊Q8—1491no—
180C4⋊Q8C2×D14911yescharacteristic
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×D4—1491no—
198C2×C4⋊C4—2981no—
199C2×C4⋊C4—2981no—
200#107—1491no—
201#107—1491no—
202#107—1491no—
203#107C2×D14911yescharacteristic
204#107C2×D14911yescharacteristic
205#106—1491no—
206#106—1491no—
207#106C2×D14911yescharacteristic
208#106C2×D14911yescharacteristic
209C4⋊C8—1491no—
210C4⋊C8—1491no—
211C4⋊C8—1491no—
212#102—1491no—
213#102—1491no—
214#102—1491no—
215#102—1491no—
216#102—1491no—
217#102—1491no—
218#97—1491no—
219#97C2×D14911yescharacteristic
220C4×C8—1491no—
221C2×Q8—21no—
222C2×Q8—2981no—
223C2×Q8—1491no—
224C2×D4—1491no—
225C2×D4—1491no—
226C22×C4—2981no—
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—21no—
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⋊C4C22×D14911yescharacteristic
253C4⋊C4C22×D14911yescharacteristic
254C4⋊C4C22×D14911yescharacteristic
255C4⋊C4C22×D14911yescharacteristic
256C22⋊C4—2981no—
257C22⋊C4—2981no—
258C22⋊C4—2981no—
259C22⋊C4—2981no—
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C42—1491no—
263C42—1491no—
264C42C22×D14911yescharacteristic
265C23—2981no—
266C23—2981no—
267Q8—81no—
268Q8—5961no—
269Q8—11921no—
270D4—2981no—
271D4—2981no—
272D4—1492no—
273D4—1492no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2981no—
279C2×C4—2981no—
280C2×C4—5962no—
281C2×C4—5962no—
282C2×C4—1491no—
283C2×C4—1491no—
284C2×C4—1491no—
285C2×C4—1491no—
286C2×C4—11921no—
287C2×C4—11921no—
288C2×C4—11921no—
289C2×C4—11921no—
290C2×C4D4×D14911yescharacteristic
291C2×C4D4×D14911yescharacteristic
292C2×C4C23×D14911yescharacteristic
293C8—21no—
294C8—2981no—
295C8—2981no—
296C8Q8×D14912yes—
297C22—2982no—
298C22—2982no—
299C22—5961no—
300C22—5961no—
301C22—5961no—
302C22—5961no—
303C22C2×D4×D14911yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—2981no—
311C4—2981no—
312C4—2981no—
313C4—2981no—
314C4—5961no—
315C4—5961no—
316C4C2×Q8×D14911yescharacteristic
317C4#1801195911yescharacteristic
318C2—5962no—
319C2—5962no—
320C2#2375029011yescharacteristic
321C2#2375042411yescharacteristic
322C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#501×C149C2
socleC22×C149C22×D4
prime radicalC2×D1192C22
hypercenter#501D149
hypocenterC149#3389
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #23750336C2semidirect
2. #23750331C2semidirect
3. #23750033C2semidirect
4. #23750025C2semidirect
5. #23749928C2semidirect
6. #23749924C2semidirect
7. #23749924C2semidirect
8. #23749922C2semidirect
9. #23749904C2semidirect
10. #23749902C2semidirect
11. #23749753C2semidirect
15. #501×C149C2semidirect
69. D1192Q8semidirect
161. C149#3389semidirect
166. #501D149semidirect

Maximal subgroups

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

subgroupindex
#237503362
#237503312
#237500332
#237500252
#237499282
#237499242
#237499222
#237499042
#237499022
#237497532
#237497382
#237497362
#237497072
#501×C1492
#3389149