Finite Group Databasebeta

← #34079238

Subgroups — #34079238

Order 19328.

380 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752766C211yesmaximal, characteristic
2C4×Q8×D151C211yesmaximal, characteristic
3#23752544C211yesmaximal, characteristic
4#23752541C211yesmaximal, characteristic
5#23752496C211yesmaximal, characteristic, complemented
6#23752495C211yesmaximal, characteristic, complemented
7#23752421C211yesmaximal, characteristic, complemented
8#23752420C211yesmaximal, characteristic, complemented
9#23752369C211yesmaximal, characteristic
10#23752366C211yesmaximal, characteristic
11#23752320C211yesmaximal, characteristic, complemented
12#23752317C211yesmaximal, characteristic, complemented
13#23752317C211yesmaximal, characteristic, complemented
14#23752267C211yesmaximal, characteristic
15#441×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×Dic604C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20#18012738C2211yescharacteristic
21#18012737C2211yescharacteristic
22#18012729—21no—
23#18012719C2211yescharacteristic
24#18012717—21no—
25#18012715C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic
27C4×Dic302—21no—
28C4×Dic302—21no—
29C4×Dic302C2211yescharacteristic
30C4×Dic302C2211yescharacteristic
31#18012704—21no—
32#18012704C2211yescharacteristic
33#18012696—21no—
34C4⋊C4×D151—21no—
35C4⋊C4×D151C2211yescharacteristic
36C42×D151—21no—
37C42×D151C2211yescharacteristic
38#18012671C2211yescharacteristic
39#18012670C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012662C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic
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×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62C2×Dic302C2311yescharacteristic
63Q8×D151—22no—
64Q8×D151—22no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151D411yescharacteristic
68C2×C4×D151D411yescharacteristic
69C2×C4×D151C2311yescharacteristic
70Dic604—22no—
71#14558994—22no—
72#14558994—22no—
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C4⋊Dic151—21no—
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151—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×D151C2×D411yescharacteristic
109Dic302—24no—
110Dic302—21no—
111Dic302—21no—
112Dic302—21no—
113Dic302—42no—
114Dic302#4112yes—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—24no—
123C4×D151—22no—
124C4×D151—21no—
125C4×D151—21no—
126C4×D151—22no—
127C4×D151—42no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130Q8×C151—21no—
131Q8×C151—21no—
132Q8×C151—21no—
133Q8×C151#4112yes—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2411yescharacteristic
141C8×C151—21no—
142C8×C151—21no—
143C22×C151C22×D411yescharacteristic
144C2×D151—21no—
145C2×D151—21no—
146C2×D151#13712yes—
147C4×C151—22no—
148C4×C151—21no—
149C4×C151—21no—
150C4×C151—41no—
151C4×C151—41no—
152C4×C151—41no—
153C4×C151C2×#4111yescharacteristic
154C4×C151C2×#4111yescharacteristic
155Dic151—22no—
156Dic151—21no—
157Dic151—21no—
158Dic151—41no—
159Dic151—41no—
160Dic151—41no—
161Dic151#13712yes—
162C2×C151#52511yescharacteristic
163C2×C151C2×#13711yescharacteristic
164C2×C151C2×#13711yescharacteristic
165D151—22no—
166C151#311311yescharacteristic, complemented, Sylow
167#3113—1511nomaximal, Sylow
168#533—1511no—
169C2×C4×Q8—1511no—
170#483—1511no—
171#483—1511no—
172#475—1511no—
173#475—1511no—
174#462—1511no—
175#462—1511no—
176#451—1511no—
177#451—1511no—
178#441—1511no—
179#441—1511no—
180#441—1511no—
181#441D15111yescharacteristic, complemented
182#432—1511no—
183C22×Q8—1511no—
184C2×Q16—1511no—
185C2×Q16—1511no—
186C2×Q16—1511no—
187C2×Q16C2×D15111yescharacteristic
188C4⋊Q8—1511no—
189C4⋊Q8—1511no—
190#125—3021no—
191C22⋊Q8—3021no—
192C22⋊Q8—1511no—
193C22⋊Q8—1511no—
194C4×Q8—3021no—
195C4×Q8—3021no—
196C4×Q8—3021no—
197C4×Q8—1511no—
198C4×Q8—1511no—
199C4×Q8—1511no—
200C4×Q8—1511no—
201C4×Q8C2×D15111yescharacteristic
202C4×Q8C2×D15111yescharacteristic
203#117—3021no—
204C2×C4⋊C4—3021no—
205C2×C4⋊C4—1511no—
206C2×C42—3021no—
207C2×C42—1511no—
208#106—1511no—
209#106—1511no—
210#106—1511no—
211#106C2×D15111yescharacteristic
212C4⋊C8—1511no—
213C4⋊C8—1511no—
214#103—1511no—
215#103—1511no—
216#103—1511no—
217#103—1511no—
218#103—1511no—
219#103—1511no—
220#103C2×D15111yescharacteristic
221#103C2×D15111yescharacteristic
222C22⋊C8—1511no—
223C22⋊C8—1511no—
224#97—1511no—
225#97C2×D15111yescharacteristic
226C2×Q8—3021no—
227C2×Q8—3021no—
228C2×Q8—3022no—
229C2×Q8—3022no—
230C2×Q8—1511no—
231C2×Q8—1511no—
232C2×Q8C22×D15111yescharacteristic
233C2×Q8C22×D15111yescharacteristic
234C22×C4—3021no—
235C22×C4—3021no—
236C22×C4—1511no—
237C22×C4—1511no—
238C22×C4—1511no—
239Q16—22no—
240Q16—3022no—
241Q16—3022no—
242Q16—3022no—
243C2×C8—1511no—
244C2×C8—1511no—
245C2×C8C22×D15111yescharacteristic
246C2×C8C22×D15111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—3021no—
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—
265C42—21no—
266C42—21no—
267C42—3021no—
268C42—3021no—
269C42—3021no—
270C42—3021no—
271C42—1511no—
272C42—1511no—
273C42—1511no—
274C42C22×D15111yescharacteristic
275C23—1511no—
276Q8—21no—
277Q8—21no—
278Q8—21no—
279Q8—3024no—
280Q8—3021no—
281Q8—3021no—
282Q8—3021no—
283Q8—6042no—
284Q8—1512no—
285Q8#1455900412yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—3024no—
291C2×C4—3022no—
292C2×C4—3022no—
293C2×C4—3021no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—3021no—
299C2×C4—6042no—
300C2×C4—1511no—
301C2×C4—1511no—
302C2×C4—1511no—
303C2×C4D4×D15111yescharacteristic
304C2×C4D4×D15111yescharacteristic
305C2×C4C23×D15111yescharacteristic
306C8—21no—
307C8—21no—
308C8—3021no—
309C8—3021no—
310C22—3021no—
311C22—3021no—
312C22—1512no—
313C22C2×D4×D15111yescharacteristic
314C4—22no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—3022no—
321C4—3021no—
322C4—3021no—
323C4—6041no—
324C4—6041no—
325C4—6041no—
326C4—1512no—
327C4#41×D15111yescharacteristic
328C4C2×#1455900411yescharacteristic
329C2—3022no—
330C2#2375272111yescharacteristic
331C2#137×D15111yescharacteristic
332C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#441×C151C2
socleC22×C151C22×D4
prime radicalC22×D151C2×D4
hypercenter#441D151
hypocenterC151#3113
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
5. #23752496C2semidirect
6. #23752495C2semidirect
7. #23752421C2semidirect
8. #23752420C2semidirect
11. #23752320C2semidirect
12. #23752317C2semidirect
13. #23752317C2semidirect
15. #441×C151C2semidirect
166. C151#3113semidirect
181. #441D151semidirect

Maximal subgroups

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

subgroupindex
#237527662
C4×Q8×D1512
#237525442
#237525412
#237524962
#237524952
#237524212
#237524202
#237523692
#237523662
#237523202
#237523172
#237522672
#441×C1512
#3113151