Finite Group Databasebeta

← #34079280

Subgroups — #34079280

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#23752741C211yesmaximal, characteristic
2C4×Q8×D151C211yesmaximal, characteristic, complemented
3#23752546C211yesmaximal, characteristic, complemented
4#23752529C211yesmaximal, characteristic
5#23752520C211yesmaximal, characteristic, complemented
6#23752519C211yesmaximal, characteristic, complemented
7#23752431C211yesmaximal, characteristic, complemented
8#23752366C211yesmaximal, characteristic, complemented
9#23752349C211yesmaximal, characteristic
10#23752319C211yesmaximal, characteristic, complemented
11#23752316C211yesmaximal, characteristic, complemented
12#23752313C211yesmaximal, characteristic, complemented
13#23752309C211yesmaximal, characteristic, complemented
14#23752268C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19#18012732—21no—
20#18012731C2211yescharacteristic
21#18012721—21no—
22#18012715C2211yescharacteristic
23#18012710C2211yescharacteristic
24Q8×Dic151C2211yescharacteristic
25Q8×Dic151C2211yescharacteristic
26C4×Dic302—21no—
27C4×Dic302C2211yescharacteristic
28#18012704—21no—
29#18012704C2211yescharacteristic
30D4×Dic151C2211yescharacteristic
31(C22⋊D151)⋊C4—21no—
32#18012695—21no—
33C4⋊C4×D151—21no—
34C4⋊C4×D151C2211yescharacteristic
35C42×D151—21no—
36C42×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51#18012649C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61Q8×D151—22no—
62Q8×D151—22no—
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151D411yescharacteristic
68C2×C4×D151D411yescharacteristic
69C2×C4×D151C2311yescharacteristic
70#14558994—22no—
71#14558992—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87(C2×D151)⋊C4—21no—
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151D411yescharacteristic
93C4×Dic151D411yescharacteristic
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98Q16×C151—22no—
99SD16×C151—22no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151C2×D411yescharacteristic
109Dic302—24no—
110Dic302—21no—
111Dic302#4112yes—
112C22⋊D151—42no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—42no—
118C2×Dic151C2×D411yescharacteristic
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C4×D151—24no—
122C4×D151—22no—
123C4×D151—21no—
124C4×D151—21no—
125C4×D151—41no—
126C4×D151—42no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151—21no—
130Q8×C151—21no—
131Q8×C151—21no—
132Q8×C151—21no—
133Q8×C151#4112yes—
134D4×C151—21no—
135D4×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×C151—41no—
145C22×C151—41no—
146C22×C151—41no—
147C22×C151C22×D411yescharacteristic
148C2×D151—21no—
149C2×D151—21no—
150C2×D151#13712yes—
151C4×C151—22no—
152C4×C151—21no—
153C4×C151—21no—
154C4×C151—41no—
155C4×C151—41no—
156C4×C151C2×#4111yescharacteristic
157C4×C151C2×#4111yescharacteristic
158Dic151—22no—
159Dic151—21no—
160Dic151—21no—
161Dic151—21no—
162Dic151—41no—
163Dic151—41no—
164Dic151—41no—
165C2×C151—81no—
166C2×C151#52511yescharacteristic
167C2×C151C2×#13711yescharacteristic
168C2×C151#57511yescharacteristic
169D151—22no—
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#479—1511no—
178#464—1511no—
179#464D15111yescharacteristic, complemented
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×Q16C2×D15111yescharacteristic
190C2×SD16—1511no—
191C2×SD16C2×D15111yescharacteristic
192#126—3021no—
193#125—1511no—
194#124C2×D15111yescharacteristic
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#107—1511no—
214#106—1511no—
215#106—1511no—
216C4⋊C8—1511no—
217C4⋊C8C2×D15111yescharacteristic
218#103—1511no—
219#103—1511no—
220#103—1511no—
221#103—1511no—
222#103—1511no—
223#103C2×D15111yescharacteristic
224#102—1511no—
225#102C2×D15111yescharacteristic
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×Q8C22×D15111yescharacteristic
235C2×Q8C22×D15111yescharacteristic
236C2×D4—3021no—
237C2×D4C22×D15111yescharacteristic
238C22×C4—3021no—
239C22×C4—3021no—
240C22×C4—3021no—
241C22×C4—1511no—
242C22×C4—1511no—
243C22×C4—1511no—
244Q16—22no—
245Q16—3022no—
246SD16—22no—
247SD16—3022no—
248C2×C8—1511no—
249C2×C8—1511no—
250C2×C8C22×D15111yescharacteristic
251C2×C8C22×D15111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—3021no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4—1511no—
264C4⋊C4C22×D15111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
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—21no—
280C23—1511no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—3024no—
285Q8—3021no—
286Q8—1512no—
287Q8#1455900312yes—
288D4—21no—
289D4—21no—
290D4—6042no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—3024no—
295C2×C4—3022no—
296C2×C4—3021no—
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—41no—
316C22—41no—
317C22—41no—
318C22—3021no—
319C22—3021no—
320C22—1512no—
321C22C2×D4×D15111yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—3022no—
328C4—3021no—
329C4—3021no—
330C4—3021no—
331C4—6041no—
332C4—6041no—
333C4—6041no—
334C4#41×D15111yescharacteristic
335C4C2×#1455900311yescharacteristic
336C2—81no—
337C2—3022no—
338C2#2375272211yescharacteristic
339C2#137×D15111yescharacteristic
340C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radical#18012710C22
hypercenter#464D151
hypocenterC151#3117
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D151C2semidirect
3. #23752546C2semidirect
5. #23752520C2semidirect
6. #23752519C2semidirect
7. #23752431C2semidirect
8. #23752366C2semidirect
10. #23752319C2semidirect
11. #23752316C2semidirect
12. #23752313C2semidirect
13. #23752309C2semidirect
14. #23752268C2semidirect
15. #464×C151C2semidirect
170. C151#3117semidirect
179. #464D151semidirect

Maximal subgroups

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

subgroupindex
#237527412
C4×Q8×D1512
#237525462
#237525292
#237525202
#237525192
#237524312
#237523662
#237523492
#237523192
#237523162
#237523132
#237523092
#237522682
#464×C1512
#3117151