Finite Group Databasebeta

← #34079286

Subgroups — #34079286

Order 19328.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752747C211yesmaximal, characteristic
2C4×Q8×D151C211yesmaximal, characteristic, complemented
3#23752549C211yesmaximal, characteristic, complemented
4#23752532C211yesmaximal, characteristic
5#23752516C211yesmaximal, characteristic, complemented
6#23752435C211yesmaximal, characteristic, complemented
7#23752434C211yesmaximal, characteristic, complemented
8#23752369C211yesmaximal, characteristic, complemented
9#23752352C211yesmaximal, characteristic
10#23752318C211yesmaximal, characteristic, complemented
11#23752316C211yesmaximal, characteristic, complemented
12#23752315C211yesmaximal, characteristic, complemented
13#23752311C211yesmaximal, characteristic, complemented
14#23752268C211yesmaximal, characteristic, complemented
15#479×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×Dic604C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21#18012734—21no—
22#18012727C2211yescharacteristic
23#18012724—21no—
24#18012719C2211yescharacteristic
25#18012714C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic
27C4×Dic302—21no—
28C4×Dic302C2211yescharacteristic
29#18012704—21no—
30#18012704C2211yescharacteristic
31#18012704C2211yescharacteristic
32#18012701—21no—
33#18012701C2211yescharacteristic
34#18012697—21no—
35C4⋊C4×D151—21no—
36C4⋊C4×D151C2211yescharacteristic
37C42×D151—21no—
38C42×D151C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51#18012649C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C2×Dic302C2311yescharacteristic
62Q8×D151—22no—
63Q8×D151—22no—
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151D411yescharacteristic
70C2×C4×D151D411yescharacteristic
71C2×C4×D151C2311yescharacteristic
72Dic604—22no—
73#14558994—22no—
74#14558993—22no—
75#14558991—22no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C4⋊Dic151—21no—
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
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—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151D411yescharacteristic
95C4×Dic151D411yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110Dic302—24no—
111Dic302—21no—
112Dic302—21no—
113Dic302—21no—
114Dic302#4112yes—
115D604—21no—
116D604—21no—
117D604—42no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C4×D151—24no—
125C4×D151—22no—
126C4×D151—21no—
127C4×D151—21no—
128C4×D151—41no—
129C4×D151—42no—
130C4×D151—42no—
131C151⋊C8—21no—
132C151⋊C8—21no—
133Q8×C151—21no—
134Q8×C151#4112yes—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2411yescharacteristic
142C8×C151—21no—
143C8×C151—21no—
144C22×C151C22×D411yescharacteristic
145C2×D151—21no—
146C2×D151—21no—
147C2×D151—41no—
148C2×D151—41no—
149C2×D151—41no—
150C2×D151#13712yes—
151C4×C151—22no—
152C4×C151—21no—
153C4×C151—21no—
154C4×C151—41no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151C2×#4111yescharacteristic
158C4×C151C2×#4111yescharacteristic
159Dic151—22no—
160Dic151—21no—
161Dic151—21no—
162Dic151—21no—
163Dic151—41no—
164Dic151—41no—
165C2×C151#52511yescharacteristic
166C2×C151C2×#13711yescharacteristic
167C2×C151#57511yescharacteristic
168D151—22no—
169D151—81no—
170C151#311711yescharacteristic, complemented, Sylow
171#3117—1511nomaximal, Sylow
172#529—1511no—
173C2×C4×Q8—1511no—
174#484—1511no—
175#481—1511no—
176#479—1511no—
177#479D15111yescharacteristic, complemented
178#464—1511no—
179#464—1511no—
180#451—1511no—
181#448—1511no—
182#441—1511no—
183#441—1511no—
184#440—1511no—
185#440—1511no—
186#432—1511no—
187C22×Q8—1511no—
188C2×Q16—1511no—
189C2×Q16—1511no—
190C2×SD16—1511no—
191C2×SD16—1511no—
192#126—3021no—
193#125C2×D15111yescharacteristic
194#124—1511no—
195#123—3021no—
196C22⋊Q8—1511no—
197#121—1511no—
198C4×Q8—3021no—
199C4×Q8—3021no—
200C4×Q8—1511no—
201C4×Q8—1511no—
202C4×Q8—1511no—
203C4×Q8—1511no—
204C4×Q8C2×D15111yescharacteristic
205C4×D4—3021no—
206C4×D4—1511no—
207#117—3021no—
208C2×C4⋊C4—3021no—
209C2×C4⋊C4—1511no—
210C2×C42—3021no—
211C2×C42—1511no—
212#107—1511no—
213#107C2×D15111yescharacteristic
214#106—1511no—
215#106C2×D15111yescharacteristic
216C4⋊C8—1511no—
217C4⋊C8C2×D15111yescharacteristic
218#103—1511no—
219#103—1511no—
220#103—1511no—
221#103—1511no—
222#103C2×D15111yescharacteristic
223#103C2×D15111yescharacteristic
224#102—1511no—
225#102—1511no—
226C22⋊C8—1511no—
227C22⋊C8—1511no—
228#97—1511no—
229#97—1511no—
230C2×Q8—3021no—
231C2×Q8—3022no—
232C2×Q8—3022no—
233C2×Q8—1511no—
234C2×Q8—1511no—
235C2×Q8C22×D15111yescharacteristic
236C2×D4—3021no—
237C2×D4—1511no—
238C22×C4—3021no—
239C22×C4—3021no—
240C22×C4—3021no—
241C22×C4—1511no—
242C22×C4—1511no—
243C22×C4—1511no—
244Q16—3022no—
245Q16—3022no—
246SD16—3022no—
247SD16—3022no—
248C2×C8—1511no—
249C2×C8—1511no—
250C2×C8C22×D15111yescharacteristic
251C2×C8C22×D15111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—1511no—
262C4⋊C4C22×D15111yescharacteristic
263C4⋊C4C22×D15111yescharacteristic
264C4⋊C4C22×D15111yescharacteristic
265C22⋊C4—3021no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C42—21no—
271C42—3021no—
272C42—3021no—
273C42—3021no—
274C42—3021no—
275C42—1511no—
276C42—1511no—
277C42—1511no—
278C42C22×D15111yescharacteristic
279C23—3021no—
280C23—1511no—
281Q8—21no—
282Q8—3024no—
283Q8—3021no—
284Q8—3021no—
285Q8—3021no—
286Q8—1512no—
287Q8#1455900512yes—
288D4—3021no—
289D4—3021no—
290D4—6042no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—3024no—
296C2×C4—3022no—
297C2×C4—3021no—
298C2×C4—3021no—
299C2×C4—3021no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—6041no—
303C2×C4—6042no—
304C2×C4—6042no—
305C2×C4—1511no—
306C2×C4—1511no—
307C2×C4—1511no—
308C2×C4D4×D15111yescharacteristic
309C2×C4D4×D15111yescharacteristic
310C2×C4C23×D15111yescharacteristic
311C8—21no—
312C8—21no—
313C8—3021no—
314C8—3021no—
315C22—3021no—
316C22—3021no—
317C22—6041no—
318C22—6041no—
319C22—6041no—
320C22—1512no—
321C22C2×D4×D15111yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—3022no—
329C4—3021no—
330C4—3021no—
331C4—3021no—
332C4—6041no—
333C4—6041no—
334C4#41×D15111yescharacteristic
335C4C2×#1455900511yescharacteristic
336C2—3022no—
337C2—12081no—
338C2#2375272511yescharacteristic
339C2#137×D15111yescharacteristic
340C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#479×C151C2
socleC22×C151C22×D4
prime radical#18012714C22
hypercenter#479D151
hypocenterC151#3117
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D151C2semidirect
3. #23752549C2semidirect
5. #23752516C2semidirect
6. #23752435C2semidirect
7. #23752434C2semidirect
8. #23752369C2semidirect
10. #23752318C2semidirect
11. #23752316C2semidirect
12. #23752315C2semidirect
13. #23752311C2semidirect
14. #23752268C2semidirect
15. #479×C151C2semidirect
170. C151#3117semidirect
177. #479D151semidirect

Maximal subgroups

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

subgroupindex
#237527472
C4×Q8×D1512
#237525492
#237525322
#237525162
#237524352
#237524342
#237523692
#237523522
#237523182
#237523162
#237523152
#237523112
#237522682
#479×C1512
#3117151