Finite Group Databasebeta

← #34079817

Subgroups — #34079817

Order 19328.

366 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#23752766C211yesmaximal, characteristic, complemented
2#23752749C211yesmaximal, characteristic
3#23752619C211yesmaximal, characteristic, complemented
4#23752605C211yesmaximal, characteristic, complemented
5#23752579C211yesmaximal, characteristic, complemented
6#23752573C211yesmaximal, characteristic, complemented
7#23752452C211yesmaximal, characteristic, complemented
8#23752450C211yesmaximal, characteristic, complemented
9#23752444C211yesmaximal, characteristic
10#23752442C211yesmaximal, characteristic
11#23752317C211yesmaximal, characteristic, complemented
12#23752314C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#97×D151C211yesmaximal, characteristic, complemented
15#441×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558993C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012737C2211yescharacteristic
23#18012734—21no—
24#18012730C2211yescharacteristic
25#18012729—21no—
26#18012728C2211yescharacteristic
27#18012724—21no—
28#18012719C2211yescharacteristic
29#18012717—21no—
30#18012715C2211yescharacteristic
31#18012715C2211yescharacteristic
32#18012714C2211yescharacteristic
33C4×Dic302—21no—
34C4×Dic302C2211yescharacteristic
35C4×D604—21no—
36C4×D604C2211yescharacteristic
37#18012696—21no—
38#18012696—21no—
39C42×D151C2211yescharacteristic
40#18012673C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012650C2211yescharacteristic
50#18012649C2211yescharacteristic
51#18012649C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×C4×D151—21no—
64C2×C4×D151D411yescharacteristic
65C2×C4×D151D411yescharacteristic
66C2×C4×D151C2311yescharacteristic
67#14558994—22no—
68#14558993—22no—
69#14558991—22no—
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C8×D151—22no—
73C8×D151—22no—
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92C4×Dic151—21no—
93C4×Dic151D411yescharacteristic
94C4×Dic151D411yescharacteristic
95C4×Dic151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98Q16×C151—22no—
99C2×C8×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C42×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110Dic302—21no—
111Dic302—21no—
112Dic302—42no—
113D604—21no—
114D604—21no—
115D604—42no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—22no—
123C4×D151—21no—
124C4×D151—21no—
125C4×D151—41no—
126C4×D151—42no—
127C151⋊C8—21no—
128C151⋊C8#4112yes—
129Q8×C151—21no—
130Q8×C151—21no—
131Q8×C151—21no—
132Q8×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2411yescharacteristic
140C8×C151—21no—
141C8×C151#4112yes—
142C22×C151C22×D411yescharacteristic
143C2×D151—21no—
144C2×D151—21no—
145C2×D151—41no—
146C2×D151—41no—
147C2×D151—41no—
148C2×D151#13712yes—
149C4×C151—21no—
150C4×C151—21no—
151C4×C151—41no—
152C4×C151—41no—
153C4×C151—41no—
154C4×C151—41no—
155C4×C151C2×#4111yescharacteristic
156C4×C151C2×#4111yescharacteristic
157Dic151—21no—
158Dic151—21no—
159Dic151—21no—
160Dic151—41no—
161Dic151—41no—
162Dic151—41no—
163C2×C151#53211yescharacteristic
164C2×C151C2×#13711yescharacteristic
165C2×C151#57511yescharacteristic
166D151—22no—
167D151—81no—
168C151#318111yescharacteristic, complemented, Sylow
169#3181—1511nomaximal, Sylow
170#533—1511no—
171#529—1511no—
172#501—1511no—
173#497—1511no—
174#491—1511no—
175#489—1511no—
176#467—1511no—
177#467—1511no—
178#465—1511no—
179#465—1511no—
180#441—1511no—
181#441D15111yescharacteristic, complemented
182#440—1511no—
183#440—1511no—
184C2×#97—1511no—
185C2×Q16—1511no—
186C2×Q16C2×D15111yescharacteristic
187C2×SD16—1511no—
188C2×SD16—1511no—
189C22×C8—1511no—
190C22×C8—1511no—
191C4⋊Q8—1511no—
192C4⋊Q8—1511no—
193#126—3021no—
194#125—3021no—
195#125—1511no—
196#124—1511no—
197#123—3021no—
198C22⋊Q8—3021no—
199C22⋊Q8—1511no—
200C22⋊Q8—1511no—
201C22⋊Q8—1511no—
202#121—1511no—
203C4×Q8—3021no—
204C4×Q8—1511no—
205C4×Q8C2×D15111yescharacteristic
206C4×Q8C2×D15111yescharacteristic
207C4×D4—3021no—
208C4×D4—1511no—
209#117—3021no—
210#117—3021no—
211C2×C42—1511no—
212#107—1511no—
213#107—1511no—
214#106—1511no—
215#106C2×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—
224#97—1511no—
225#97—1511no—
226#97—1511no—
227#97C2×D15111yescharacteristic
228C2×Q8—3021no—
229C2×Q8—1511no—
230C2×Q8C22×D15111yescharacteristic
231C2×Q8C22×D15111yescharacteristic
232C2×D4—3021no—
233C2×D4—1511no—
234C22×C4—3021no—
235C22×C4—1511no—
236C22×C4—1511no—
237C22×C4—1511no—
238Q16—22no—
239Q16—3022no—
240SD16—3022no—
241SD16—3022no—
242C2×C8—3022no—
243C2×C8—3022no—
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⋊C4C22×D15111yescharacteristic
262C4⋊C4C22×D15111yescharacteristic
263C22⋊C4—3021no—
264C22⋊C4—3021no—
265C22⋊C4—3021no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C42—21no—
271C42—21no—
272C42—3021no—
273C42—1511no—
274C42—1511no—
275C42—1511no—
276C42C22×D15111yescharacteristic
277C23—3021no—
278C23—1511no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—3021no—
284Q8—3021no—
285Q8—6042no—
286D4—3021no—
287D4—3021no—
288D4—6042no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—3022no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—3021no—
299C2×C4—6041no—
300C2×C4—6042no—
301C2×C4—1511no—
302C2×C4—1511no—
303C2×C4—1511no—
304C2×C4D4×D15111yescharacteristic
305C2×C4D4×D15111yescharacteristic
306C2×C4C23×D15111yescharacteristic
307C8—21no—
308C8—3021no—
309C8—1512no—
310C8#1455900412yes—
311C22—3021no—
312C22—3021no—
313C22—6041no—
314C22—6041no—
315C22—6041no—
316C22—1512no—
317C22C2×D4×D15111yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3021no—
325C4—3021no—
326C4—3021no—
327C4—6041no—
328C4—6041no—
329C4—6041no—
330C4#41×D15111yescharacteristic
331C4C2×#1455900411yescharacteristic
332C2—3022no—
333C2—12081no—
334C2#2375275911yescharacteristic
335C2#137×D15111yescharacteristic
336C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#441×C151C2
socleC22×C151C22×D4
prime radical#18012714C22
hypercenter#441D151
hypocenterC151#3181
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #23752766C2semidirect
3. #23752619C2semidirect
4. #23752605C2semidirect
5. #23752579C2semidirect
6. #23752573C2semidirect
7. #23752452C2semidirect
8. #23752450C2semidirect
11. #23752317C2semidirect
12. #23752314C2semidirect
13. #23752310C2semidirect
14. #97×D151C2semidirect
15. #441×C151C2semidirect
168. C151#3181semidirect
181. #441D151semidirect

Maximal subgroups

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

subgroupindex
#237527662
#237527492
#237526192
#237526052
#237525792
#237525732
#237524522
#237524502
#237524442
#237524422
#237523172
#237523142
#237523102
#97×D1512
#441×C1512
#3181151