Finite Group Databasebeta

← #34057587

Subgroups — #34057587

Order 19072.

374 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750331C211yesmaximal, characteristic, complemented
2#23750290C211yesmaximal, characteristic, complemented
3#23750033C211yesmaximal, characteristic, complemented
4#23750022C211yesmaximal, characteristic, complemented
5#23749928C211yesmaximal, characteristic, complemented
6#23749922C211yesmaximal, characteristic, complemented
7#23749914C211yesmaximal, characteristic, complemented
8#23749914C211yesmaximal, characteristic, complemented
9#23749912C211yesmaximal, characteristic, complemented
10#23749904C211yesmaximal, characteristic, complemented
11#23749753C211yesmaximal, characteristic, complemented
12#23749738C211yesmaximal, characteristic
13#23749736C211yesmaximal, characteristic
14#23749707C211yesmaximal, characteristic
15#501×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149—21no—
17C2×D1192C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011910C2211yescharacteristic
20#18011910C2211yescharacteristic
21#18011902C2211yescharacteristic
22#18011891—21no—
23#18011889—21no—
24#18011889—21no—
25#18011889—21no—
26#18011889—21no—
27#18011887—21no—
28C4×Dic298C2211yescharacteristic
29C4×D596C2211yescharacteristic
30C4×D596C2211yescharacteristic
31#18011873C2211yescharacteristic
32#18011873C2211yescharacteristic
33#18011873C2211yescharacteristic
34#18011873C2211yescharacteristic
35C4⋊C4×D149—21no—
36#18011844C2211yescharacteristic
37#18011843C2211yescharacteristic
38#18011842C2211yescharacteristic
39#18011842C2211yescharacteristic
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×Dic298—21no—
61C2×Dic298—21no—
62C2×Dic298D411yescharacteristic
63Q8×D149—44no—
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149—21no—
72D1192Q814yescomplemented
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149—21no—
76C4⋊Dic149D411yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91C4×Dic149C2311yescharacteristic
92C4×Dic149C2311yescharacteristic
93C2×Q8×C149—21no—
94C2×C8×C149C2311yescharacteristic
95C2×C8×C149C2311yescharacteristic
96C4⋊C4×C149—21no—
97C4⋊C4×C149—21no—
98C4⋊C4×C149—21no—
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C42×C149C2311yescharacteristic
104C22×D149—21no—
105C22×D149—21no—
106Dic298—22no—
107Dic298—42no—
108Dic298—42no—
109Dic298—81no—
110D596—21no—
111D596—21no—
112D596C2×Q812yes—
113D596C2×Q812yescomplemented
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C4×D149—42no—
121C4×D149—42no—
122C4×D149—42no—
123C4×D149—42no—
124C4×D149—81no—
125C4×D149—81no—
126#11924746—21no—
127#11924746—21no—
128Q8×C149—42no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2411yescharacteristic
136C8×C149—21no—
137C8×C149C2×Q812yescomplemented
138C22×C149C22×D411yescharacteristic
139C2×D149—22no—
140C2×D149—22no—
141C2×D149—41no—
142C2×D149—41no—
143C2×D149—41no—
144C2×D149—41no—
145C4×C149—21no—
146C4×C149—21no—
147C4×C149—41no—
148C4×C149—41no—
149C4×C149—41no—
150C4×C149—41no—
151C4×C149C22×Q811yescharacteristic
152C4×C1492−1+411yescharacteristic
153Dic149—21no—
154Dic149—21no—
155Dic149—21no—
156Dic149—41no—
157Dic149—41no—
158Dic149AGL(1,ℤ/8)12yes—
159C2×C149D4×Q811yescharacteristic
160C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C149#57711yescharacteristic
162D149—42no—
163D149—42no—
164C149#338411yescharacteristic, complemented, Sylow
165#3384—1491nomaximal, Sylow
166#554—1491no—
167D4×Q8—1491no—
168#501—1491no—
169#501D14911yescharacteristic, complemented
170#498—1491no—
171#478—1491no—
172#478—1491no—
173#476—1491no—
174#476—1491no—
175#476—1491no—
176#474—1491no—
177#446—1491no—
178#442—1491no—
179#442—1491no—
180C4×D8—1491no—
181C22×Q8—2981no—
182C2×D8—1491no—
183C4⋊Q8—1491no—
184C4⋊Q8—1491no—
185C4⋊Q8—1491no—
186C4⋊Q8C2×D14911yescharacteristic
187#125—1491no—
188#125C2×D14911yescharacteristic
189C22⋊Q8—2981no—
190C22⋊Q8—2981no—
191C22⋊Q8—2981no—
192C22⋊Q8—2981no—
193C22⋊Q8—2981no—
194C22⋊Q8—2981no—
195C4×Q8—1491no—
196C4×D4—1491no—
197C4×D4—1491no—
198C4×D4—1491no—
199C4×D4—1491no—
200C4×D4—1491no—
201C4×D4—1491no—
202C2×C4⋊C4—2981no—
203#107—1491no—
204#107C2×D14911yescharacteristic
205#107C2×D14911yescharacteristic
206#106—1491no—
207#106—1491no—
208#106—1491no—
209#106—1491no—
210#106C2×D14911yescharacteristic
211#106C2×D14911yescharacteristic
212C4⋊C8—1491no—
213C4⋊C8—1491no—
214C4⋊C8—1491no—
215#102—1491no—
216#102—1491no—
217#102—1491no—
218#102—1491no—
219#102—1491no—
220#102—1491no—
221#97—1491no—
222#97C2×D14911yescharacteristic
223C4×C8—1491no—
224C2×Q8—21no—
225C2×Q8—2981no—
226C2×Q8—2981no—
227C2×Q8—2981no—
228C2×Q8—5964no—
229C2×Q8—1491no—
230C2×D4—1491no—
231C2×D4—1491no—
232C22×C4—2981no—
233C22×C4—2981no—
234C22×C4—2981no—
235C22×C4—2981no—
236C22×C4—2981no—
237C22×C4—2981no—
238D8—1494no—
239C2×C8—1491no—
240C2×C8—1491no—
241C2×C8C22×D14911yescharacteristic
242C2×C8C22×D14911yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—2981no—
247C4⋊C4—2981no—
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—2981no—
251C4⋊C4—1491no—
252C4⋊C4—1491no—
253C4⋊C4—1491no—
254C4⋊C4—1491no—
255C4⋊C4—1491no—
256C4⋊C4C22×D14911yescharacteristic
257C4⋊C4C22×D14911yescharacteristic
258C4⋊C4C22×D14911yescharacteristic
259C4⋊C4C22×D14911yescharacteristic
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C22⋊C4—2981no—
264C22⋊C4—2981no—
265C22⋊C4—2981no—
266C42—1491no—
267C42—1491no—
268C42C22×D14911yescharacteristic
269C23—2981no—
270C23—2981no—
271Q8—42no—
272Q8—2982no—
273Q8—5962no—
274Q8—5962no—
275Q8—11921no—
276D4—2981no—
277D4—2981no—
278D4—1492no—
279D4—1492no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—2981no—
285C2×C4—2981no—
286C2×C4—5962no—
287C2×C4—5962no—
288C2×C4—5962no—
289C2×C4—5962no—
290C2×C4—1491no—
291C2×C4—1491no—
292C2×C4—1491no—
293C2×C4—1491no—
294C2×C4—11921no—
295C2×C4—11921no—
296C2×C4D4×D14911yescharacteristic
297C2×C4D4×D14911yescharacteristic
298C2×C4C23×D14911yescharacteristic
299C8—21no—
300C8—2981no—
301C8—2981no—
302C8Q8×D14912yescomplemented
303C22—2982no—
304C22—2982no—
305C22—5961no—
306C22—5961no—
307C22—5961no—
308C22—5961no—
309C22C2×D4×D14911yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—2981no—
317C4—2981no—
318C4—2981no—
319C4—5961no—
320C4—5961no—
321C4—1492no—
322C4C2×Q8×D14911yescharacteristic
323C4#1801195911yescharacteristic
324C2—5962no—
325C2—5962no—
326C2#2375029011yescharacteristic
327C2AGL(1,ℤ/8)×D14911yescharacteristic
328C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#501×C149C2
socleC22×C149C22×D4
prime radicalC2×D1192C22
hypercenter#501D149
hypocenterC149#3384
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. #23750331C2semidirect
2. #23750290C2semidirect
3. #23750033C2semidirect
4. #23750022C2semidirect
5. #23749928C2semidirect
6. #23749922C2semidirect
7. #23749914C2semidirect
8. #23749914C2semidirect
9. #23749912C2semidirect
10. #23749904C2semidirect
11. #23749753C2semidirect
15. #501×C149C2semidirect
72. D1192Q8semidirect
113. D596C2×Q8semidirect
137. C8×C149C2×Q8semidirect
164. C149#3384semidirect
169. #501D149semidirect
302. C8Q8×D149semidirect

Maximal subgroups

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

subgroupindex
#237503312
#237502902
#237500332
#237500222
#237499282
#237499222
#237499142
#237499122
#237499042
#237497532
#237497382
#237497362
#237497072
#501×C1492
#3384149