Finite Group Databasebeta

← #34079637

Subgroups — #34079637

Order 19328.

340 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752842C211yesmaximal, characteristic
2#23752839C211yesmaximal, characteristic
3#23752621C211yesmaximal, characteristic, complemented
4#23752620C211yesmaximal, characteristic, complemented
5#23752619C211yesmaximal, characteristic, complemented
6#23752613C211yesmaximal, characteristic, complemented
7#23752611C211yesmaximal, characteristic, complemented
8#23752609C211yesmaximal, characteristic, complemented
9#23752608C211yesmaximal, characteristic, complemented
10#23752253C211yesmaximal, characteristic
11#23752251C211yesmaximal, characteristic
12#23752249C211yesmaximal, characteristic
13#106×D151C211yesmaximal, characteristic
14#23752169C211yesmaximal, characteristic
15#501×C151C211yesmaximal, characteristic, complemented
16C2×#14558987C2211yescharacteristic
17C2×C8×D151C2211yescharacteristic
18#18012739C2211yescharacteristic
19#18012738—21no—
20#18012738C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012737—21no—
23#18012731C2211yescharacteristic
24#18012730C2211yescharacteristic
25#18012730C2211yescharacteristic
26#18012729—21no—
27#18012729—21no—
28#18012719—21no—
29#18012717—21no—
30#18012717—21no—
31#18012715—21no—
32#18012697C2211yescharacteristic
33#18012697C2211yescharacteristic
34#18012696C2211yescharacteristic
35C4⋊C4×D151C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012671C2211yescharacteristic
43#18012670C2211yescharacteristic
44#18012670C2211yescharacteristic
45#18012670C2211yescharacteristic
46#18012670C2211yescharacteristic
47#18012670C2211yescharacteristic
48#18012670C2211yescharacteristic
49#18012649C2211yescharacteristic
50C4×C151⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53#125×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic
57#106×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302—21no—
62C2×C4×D151—21no—
63C2×C4×D151—21no—
64C2×C4×D151C2311yescharacteristic
65#14558987Q814yescomplemented
66C2×C151⋊C8C2311yescharacteristic
67C2×C151⋊C8C2311yescharacteristic
68C8×D151Q814yescomplemented
69C4⋊Dic151—21no—
70C4⋊Dic151—21no—
71C4⋊Dic151—21no—
72C4⋊Dic151C2311yescharacteristic
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⋊C4—21no—
84Dic151⋊C4D411yescharacteristic
85Dic151⋊C4D411yescharacteristic
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×Dic151C2311yescharacteristic
93C2×Q8×C151—21no—
94C2×C8×C151C2311yescharacteristic
95C2×C8×C151C2311yescharacteristic
96C4⋊C4×C151—21no—
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151C2311yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C42×C151C2311yescharacteristic
104C22×D151C2×D411yescharacteristic
105Dic302—81no—
106Dic302—81no—
107Dic302—81no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151C2×D411yescharacteristic
113C2×Dic151C2×D411yescharacteristic
114C2×Dic151C2×D411yescharacteristic
115C4×D151—81no—
116C4×D151—81no—
117C4×D151C2×Q812yes—
118C4×D151C2×Q812yes—
119C151⋊C8C2×Q812yes—
120C151⋊C8C2×Q812yes—
121Q8×C151—81no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151C2×D411yescharacteristic
127C2×C4×C151C2×D411yescharacteristic
128C2×C4×C151C2411yescharacteristic
129C8×C151C2×Q812yes—
130C8×C151C2×Q812yes—
131C22×C151C22×D411yescharacteristic
132C2×D151—21no—
133C2×D151—21no—
134C2×D151C4⋊Q812yes—
135C4×C151—21no—
136C4×C151—21no—
137C4×C151—41no—
138C4×C151—41no—
139C4×C151—41no—
140C4×C151—41no—
141C4×C151C22×Q811yescharacteristic
142C4×C151C22×Q811yescharacteristic
143Dic151—21no—
144Dic151—21no—
145Dic151—41no—
146Dic151—41no—
147Dic151—41no—
148Dic151—41no—
149Dic151C4⋊Q812yes—
150C2×C151C2×C4⋊Q811yescharacteristic
151C2×C151#57711yescharacteristic
152C2×C151#57711yescharacteristic
153D151—22no—
154C151#316311yescharacteristic, complemented, Sylow
155#3163—1511nomaximal, Sylow
156#544—1511no—
157#544—1511no—
158#501—1511no—
159#501—1511no—
160#501—1511no—
161#501D15111yescharacteristic, complemented
162#499—1511no—
163#499—1511no—
164#498—1511no—
165#498—1511no—
166#428—1511no—
167#428—1511no—
168#427—1511no—
169C2×#106—1511no—
170#405—1511no—
171C2×M16—1511no—
172C22×C8—1511no—
173C4⋊Q8—3021no—
174C4⋊Q8—3021no—
175C4⋊Q8—1511no—
176C4⋊Q8—1511no—
177C4⋊Q8—1511no—
178C4⋊Q8C2×D15111yescharacteristic
179#125—3021no—
180#125—3021no—
181#125—1511no—
182#125—1511no—
183#125—1511no—
184#125C2×D15111yescharacteristic
185C22⋊Q8—3021no—
186C22⋊Q8—3021no—
187C22⋊Q8—3021no—
188C22⋊Q8—3021no—
189#117—1511no—
190#117—1511no—
191#117—1511no—
192C2×C4⋊C4—1511no—
193C2×C4⋊C4—1511no—
194#107—1511no—
195#107—1511no—
196#107—1511no—
197#107—1511no—
198#107C2×D15111yescharacteristic
199#107C2×D15111yescharacteristic
200#106—1511no—
201#106—1511no—
202#106—1511no—
203#106—1511no—
204#106—1511no—
205#106—1511no—
206#106—1511no—
207#106—1511no—
208#106C2×D15111yescharacteristic
209#106C2×D15111yescharacteristic
210#97—1511no—
211#97C2×D15111yescharacteristic
212C4×C8—1511no—
213C4×C8—1511no—
214C2×Q8—21no—
215C2×Q8—3021no—
216C2×Q8—3021no—
217C2×Q8—3021no—
218C22×C4—3021no—
219C22×C4—3021no—
220C22×C4—1511no—
221M16—1514no—
222C2×C8—1511no—
223C2×C8—1511no—
224C2×C8—1514no—
225C2×C8C22×D15111yescharacteristic
226C2×C8C22×D15111yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—3021no—
231C4⋊C4—3021no—
232C4⋊C4—3021no—
233C4⋊C4—3021no—
234C4⋊C4—3021no—
235C4⋊C4—3021no—
236C4⋊C4—3021no—
237C4⋊C4—3021no—
238C4⋊C4—3021no—
239C4⋊C4—3021no—
240C4⋊C4—3021no—
241C4⋊C4—1511no—
242C4⋊C4—1511no—
243C4⋊C4—1511no—
244C4⋊C4—1511no—
245C4⋊C4—1511no—
246C4⋊C4—1511no—
247C4⋊C4C22×D15111yescharacteristic
248C4⋊C4C22×D15111yescharacteristic
249C4⋊C4C22×D15111yescharacteristic
250C4⋊C4C22×D15111yescharacteristic
251C22⋊C4—3021no—
252C22⋊C4—3021no—
253C22⋊C4—1511no—
254C22⋊C4—1511no—
255C42—3021no—
256C42—3021no—
257C42—1511no—
258C42C22×D15111yescharacteristic
259C23—1511no—
260Q8—81no—
261Q8—12081no—
262Q8—12081no—
263Q8—12081no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—3021no—
269C2×C4—3021no—
270C2×C4—3021no—
271C2×C4—3021no—
272C2×C4—1511no—
273C2×C4—1511no—
274C2×C4—1511no—
275C2×C4—1512no—
276C2×C4—1512no—
277C2×C4—12081no—
278C2×C4—12081no—
279C2×C4D4×D15111yescharacteristic
280C2×C4D4×D15111yescharacteristic
281C2×C4C23×D15111yescharacteristic
282C8—1512no—
283C8—1512no—
284C8Q8×D15112yes—
285C8Q8×D15112yes—
286C22—3021no—
287C22—3021no—
288C22—1512no—
289C22C2×D4×D15111yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—3021no—
297C4—3021no—
298C4—6041no—
299C4—6041no—
300C4—6041no—
301C4—6041no—
302C4—1512no—
303C4C2×Q8×D15111yescharacteristic
304C4C2×Q8×D15111yescharacteristic
305C2—3022no—
306C2C4⋊Q8×D15111yescharacteristic
307C2#2375302111yescharacteristic
308C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#501×C151C2
socleC22×C151C22×D4
prime radicalC22×D151C2×D4
hypercenter#501D151
hypocenterC151#3163
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #23752621C2semidirect
4. #23752620C2semidirect
5. #23752619C2semidirect
6. #23752613C2semidirect
7. #23752611C2semidirect
8. #23752609C2semidirect
9. #23752608C2semidirect
15. #501×C151C2semidirect
65. #14558987Q8semidirect
68. C8×D151Q8semidirect
154. C151#3163semidirect
161. #501D151semidirect

Maximal subgroups

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

subgroupindex
#237528422
#237528392
#237526212
#237526202
#237526192
#237526132
#237526112
#237526092
#237526082
#237522532
#237522512
#237522492
#106×D1512
#237521692
#501×C1512
#3163151