Finite Group Databasebeta

← #34079321

Subgroups — #34079321

Order 19328.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752823C211yesmaximal, characteristic, complemented
2#23752691C211yesmaximal, characteristic
3#23752546C211yesmaximal, characteristic, complemented
4#23752541C211yesmaximal, characteristic, complemented
5#23752520C211yesmaximal, characteristic, complemented
6#23752512C211yesmaximal, characteristic, complemented
7#23752419C211yesmaximal, characteristic, complemented
8#23752371C211yesmaximal, characteristic
9#23752371C211yesmaximal, characteristic
10#23752316C211yesmaximal, characteristic, complemented
11#23752313C211yesmaximal, characteristic, complemented
12#23752304C211yesmaximal, characteristic, complemented
13SD16×Dic151C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#461×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19#18012734—21no—
20#18012734—21no—
21#18012731C2211yescharacteristic
22#18012729—21no—
23#18012729—21no—
24#18012715C2211yescharacteristic
25#18012715C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic
27Q8×Dic151C2211yescharacteristic
28C4×Dic302C2211yescharacteristic
29#18012704C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31C4×C22⋊D151—21no—
32(C22⋊D151)⋊C4—21no—
33#18012696C2211yescharacteristic
34#18012695—21no—
35C2×Dic151⋊C4—21no—
36C4⋊C4×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C4⋊Q8×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—22no—
61C2×Dic302C2311yescharacteristic
62C2×C22⋊D151—21no—
63C22×Dic151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151C2311yescharacteristic
67#14558994—22no—
68#14558994—22no—
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C4⋊Dic151—21no—
72C4⋊Dic151—21no—
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84Dic151⋊C4D411yescharacteristic
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4D411yescharacteristic
89(C2×D151)⋊C4D411yescharacteristic
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151—21no—
99SD16×C151—22no—
100SD16×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151—21no—
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151C2×D411yescharacteristic
109Dic302—21no—
110Dic302#4112yes—
111C22⋊D151—24no—
112C2×Dic151—24no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—81no—
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C4×D151—21no—
122C4×D151—21no—
123C4×D151—81no—
124C151⋊C8—21no—
125C151⋊C8—21no—
126C23×C151—21no—
127Q8×C151—21no—
128Q8×C151—21no—
129Q8×C151—21no—
130Q8×C151—21no—
131D4×C151—21no—
132D4×C151#4112yes—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—81no—
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2411yescharacteristic
140C8×C151—21no—
141C8×C151—21no—
142C22×C151—22no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151C22×D411yescharacteristic
146C2×D151—21no—
147C2×D151—21no—
148C2×D151—21no—
149C4×C151—21no—
150C4×C151—21no—
151C4×C151—41no—
152C4×C151—41no—
153C4×C151—41no—
154C4×C151C2×#4111yescharacteristic
155C4×C151C2×#4111yescharacteristic
156Dic151—21no—
157Dic151—22no—
158Dic151—21no—
159Dic151—21no—
160Dic151—41no—
161Dic151—41no—
162Dic151—41no—
163C2×C151—42no—
164C2×C151#52511yescharacteristic
165C2×C151#57711yescharacteristic
166C2×C151#57811yescharacteristic
167D151—41no—
168C151#312011yescharacteristic, complemented, Sylow
169#3120—1511nomaximal, Sylow
170#541—1511no—
171#520—1511no—
172#484—1511no—
173#483—1511no—
174#479—1511no—
175#478—1511no—
176#462—1511no—
177#461D15111yescharacteristic, complemented
178#452—1511no—
179#452—1511no—
180#441—1511no—
181#440—1511no—
182C4×Q16—1511no—
183C4×SD16—1511no—
184#433—1511no—
185C2×#41—1511no—
186C2×Q16—1511no—
187C2×Q16—1511no—
188C2×SD16C2×D15111yescharacteristic
189C2×SD16C2×D15111yescharacteristic
190C4⋊Q8C2×D15111yescharacteristic
191#126—3021no—
192#126—3021no—
193#125—3021no—
194#125—3021no—
195#125—1511no—
196C22⋊Q8—1511no—
197C22⋊Q8—1511no—
198C4×Q8—1511no—
199C4×Q8—1511no—
200C4×Q8—1511no—
201C4×Q8—1511no—
202C4×D4—3021no—
203C4×D4—3021no—
204C4×D4—1511no—
205C4×D4C2×D15111yescharacteristic
206#117—3021no—
207#117—1511no—
208C2×C4⋊C4—3021no—
209C2×C4⋊C4—1511no—
210#107—1511no—
211#107—1511no—
212#106—1511no—
213#106—1511no—
214C4⋊C8—1511no—
215C4⋊C8C2×D15111yescharacteristic
216#103—1511no—
217#103—1511no—
218#103—1511no—
219#103—1511no—
220#103C2×D15111yescharacteristic
221#103C2×D15111yescharacteristic
222#102—1511no—
223#102—1511no—
224C22⋊C8—1511no—
225C22⋊C8—1511no—
226#97—1511no—
227C4×C8—1511no—
228#41—3022no—
229#41—3022no—
230C2×Q8—1511no—
231C2×Q8C22×D15111yescharacteristic
232C2×Q8C22×D15111yescharacteristic
233C2×D4—3021no—
234C2×D4C22×D15111yescharacteristic
235C22×C4—21no—
236C22×C4—3021no—
237C22×C4—3021no—
238C22×C4—3021no—
239C22×C4—1511no—
240Q16—3022no—
241Q16—3022no—
242SD16—22no—
243SD16—22no—
244C2×C8—1511no—
245C2×C8—1511no—
246C2×C8C22×D15111yescharacteristic
247C2×C8C22×D15111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—3021no—
251C4⋊C4—3021no—
252C4⋊C4—3021no—
253C4⋊C4—3021no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—1511no—
260C4⋊C4—1511no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4—1511no—
264C4⋊C4C22×D15111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—1511no—
270C22⋊C4—1511no—
271C42—3021no—
272C42—3021no—
273C42—3021no—
274C42—3021no—
275C42—1511no—
276C42C22×D15111yescharacteristic
277C23—21no—
278C23—1511no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—3021no—
284Q8—1512no—
285D4—21no—
286D4—3024no—
287D4#1455900312yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—3024no—
293C2×C4—3021no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—3021no—
299C2×C4—1511no—
300C2×C4—1511no—
301C2×C4—1511no—
302C2×C4—12081no—
303C2×C4—12081no—
304C2×C4D4×D15111yescharacteristic
305C2×C4D4×D15111yescharacteristic
306C2×C4C23×D15111yescharacteristic
307C8—21no—
308C8—21no—
309C8—3021no—
310C8—3021no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—3021no—
315C22—3021no—
316C22—3021no—
317C22C2×D4×D15111yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—3021no—
324C4—3022no—
325C4—3021no—
326C4—3021no—
327C4—6041no—
328C4—6041no—
329C4—6041no—
330C4#41×D15111yescharacteristic
331C4C2×#1455900311yescharacteristic
332C2—42no—
333C2—6041no—
334C2#2375272211yescharacteristic
335C2#2375301811yescharacteristic
336C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#461×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559003C22
hypercenter#461D151
hypocenterC151#3120
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #23752823C2semidirect
3. #23752546C2semidirect
4. #23752541C2semidirect
5. #23752520C2semidirect
6. #23752512C2semidirect
7. #23752419C2semidirect
10. #23752316C2semidirect
11. #23752313C2semidirect
12. #23752304C2semidirect
13. SD16×Dic151C2semidirect
14. #23752272C2semidirect
15. #461×C151C2semidirect
168. C151#3120semidirect
177. #461D151semidirect

Maximal subgroups

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

subgroupindex
#237528232
#237526912
#237525462
#237525412
#237525202
#237525122
#237524192
#237523712
#237523162
#237523132
#237523042
SD16×Dic1512
#237522722
#461×C1512
#3120151