Finite Group Databasebeta

← #34078947

Subgroups — #34078947

Order 19328.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752839C211yesmaximal, characteristic
2#23752688C211yesmaximal, characteristic
3#23752521C211yesmaximal, characteristic, complemented
4#23752520C211yesmaximal, characteristic, complemented
5#23752519C211yesmaximal, characteristic, complemented
6#23752518C211yesmaximal, characteristic, complemented
7#23752506C211yesmaximal, characteristic, complemented
8#23752495C211yesmaximal, characteristic, complemented
9#23752494C211yesmaximal, characteristic, complemented
10#23752253C211yesmaximal, characteristic
11#23752249C211yesmaximal, characteristic
12#23752237C211yesmaximal, characteristic
13#23752219C211yesmaximal, characteristic
14#103×D151C211yesmaximal, characteristic
15#477×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×#14558987C2211yescharacteristic
18C2×C8×D151C2211yescharacteristic
19#18012738C2211yescharacteristic
20#18012737—21no—
21#18012731C2211yescharacteristic
22#18012730C2211yescharacteristic
23#18012729—21no—
24#18012717—21no—
25#18012715—21no—
26Q8×Dic151C2211yescharacteristic
27C4×Dic302—21no—
28C4×Dic302C2211yescharacteristic
29#18012704—21no—
30#18012704C2211yescharacteristic
31#18012697—21no—
32#18012697C2211yescharacteristic
33#18012697C2211yescharacteristic
34#18012696—21no—
35#18012696C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012663C2211yescharacteristic
49#18012663C2211yescharacteristic
50#18012662C2211yescharacteristic
51#18012662C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62Q8×D151—22no—
63Q8×D151Q814yescomplemented
64C2×C4×D151—21no—
65C2×C4×D151—21no—
66C2×C4×D151C2311yescharacteristic
67#14558987—22no—
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2311yescharacteristic
70C8×D151—22no—
71C4⋊Dic151—21no—
72C4⋊Dic151—21no—
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⋊C4D411yescharacteristic
84Dic151⋊C4D411yescharacteristic
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4D411yescharacteristic
88(C2×D151)⋊C4D411yescharacteristic
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151—21no—
96C2×Q8×C151C2311yescharacteristic
97C2×C8×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C42×C151—21no—
105C42×C151C2311yescharacteristic
106C22×D151C2×D411yescharacteristic
107Dic302—21no—
108Dic302—24no—
109Dic302—81no—
110Dic302C2×Q812yes—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151C2×D411yescharacteristic
116C2×Dic151C2×D411yescharacteristic
117C2×Dic151C2×D411yescharacteristic
118C4×D151—24no—
119C4×D151—81no—
120C4×D151C2×Q812yes—
121C4×D151#4112yes—
122C151⋊C8—21no—
123C151⋊C8—21no—
124Q8×C151—21no—
125Q8×C151—81no—
126Q8×C151C2×Q812yes—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151C2×D411yescharacteristic
132C2×C4×C151C2×D411yescharacteristic
133C2×C4×C151C2411yescharacteristic
134C8×C151—21no—
135C8×C151—21no—
136C22×C151C22×D411yescharacteristic
137C2×D151—21no—
138C2×D151—21no—
139C2×D151C22⋊Q812yes—
140C4×C151—22no—
141C4×C151—21no—
142C4×C151—21no—
143C4×C151—41no—
144C4×C151—41no—
145C4×C151—41no—
146C4×C151C22×Q811yescharacteristic
147C4×C151C2×#4111yescharacteristic
148Dic151—22no—
149Dic151—21no—
150Dic151—21no—
151Dic151—41no—
152Dic151—41no—
153Dic151—41no—
154Dic151C22⋊Q812yes—
155C2×C151C2×C22⋊Q811yescharacteristic
156C2×C151#57711yescharacteristic
157C2×C151#57811yescharacteristic
158D151—22no—
159C151#308211yescharacteristic, complemented, Sylow
160#3082—1511nomaximal, Sylow
161#544—1511no—
162#519—1511no—
163#479—1511no—
164#479—1511no—
165#479—1511no—
166#479—1511no—
167#477—1511no—
168#477D15111yescharacteristic, complemented
169#475—1511no—
170#475—1511no—
171#428—1511no—
172#427—1511no—
173#424—1511no—
174#419—1511no—
175C2×#103—1511no—
176C22×Q8—1511no—
177C2×M16—1511no—
178C22×C8—1511no—
179C4⋊Q8—3021no—
180C4⋊Q8—1511no—
181C4⋊Q8C2×D15111yescharacteristic
182#125—3021no—
183#125—1511no—
184#125—1511no—
185C22⋊Q8—3021no—
186C22⋊Q8—3021no—
187C4×Q8—3021no—
188C4×Q8—3021no—
189C4×Q8—1511no—
190C4×Q8—1511no—
191C4×Q8—1511no—
192C4×Q8C2×D15111yescharacteristic
193#117—3021no—
194#117—3021no—
195#117—1511no—
196#117—1511no—
197#117—1511no—
198C2×C4⋊C4—1511no—
199#107—1511no—
200#107—1511no—
201#107C2×D15111yescharacteristic
202#107C2×D15111yescharacteristic
203#106—1511no—
204#106—1511no—
205#106—1511no—
206#106—1511no—
207C4⋊C8—1511no—
208C4⋊C8—1511no—
209C4⋊C8—1511no—
210C4⋊C8C2×D15111yescharacteristic
211#103—1511no—
212#103—1511no—
213#103—1511no—
214#103—1511no—
215#103—1511no—
216#103—1511no—
217#103C2×D15111yescharacteristic
218#103C2×D15111yescharacteristic
219C2×Q8—21no—
220C2×Q8—3021no—
221C2×Q8—3021no—
222C2×Q8—3022no—
223C2×Q8—1514no—
224C2×Q8—1511no—
225C2×Q8C22×D15111yescharacteristic
226C22×C4—3021no—
227C22×C4—3021no—
228C22×C4—1511no—
229M16—3022no—
230C2×C8—3022no—
231C2×C8—1511no—
232C2×C8—1511no—
233C2×C8C22×D15111yescharacteristic
234C2×C8C22×D15111yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—3021no—
238C4⋊C4—3021no—
239C4⋊C4—3021no—
240C4⋊C4—3021no—
241C4⋊C4—3021no—
242C4⋊C4—3021no—
243C4⋊C4—3021no—
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—1511no—
247C4⋊C4—1511no—
248C4⋊C4—1511no—
249C4⋊C4—1511no—
250C4⋊C4—1511no—
251C4⋊C4C22×D15111yescharacteristic
252C4⋊C4C22×D15111yescharacteristic
253C4⋊C4C22×D15111yescharacteristic
254C22⋊C4—3021no—
255C22⋊C4—3021no—
256C22⋊C4—1511no—
257C22⋊C4—1511no—
258C42—21no—
259C42—3021no—
260C42—3021no—
261C42—3021no—
262C42—3021no—
263C42—3021no—
264C42—1511no—
265C42C22×D15111yescharacteristic
266C23—1511no—
267Q8—21no—
268Q8—81no—
269Q8—3024no—
270Q8—3021no—
271Q8—1512no—
272Q8—12081no—
273Q8Q8×D15112yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—3024no—
279C2×C4—3021no—
280C2×C4—3021no—
281C2×C4—3021no—
282C2×C4—3021no—
283C2×C4—1511no—
284C2×C4—1511no—
285C2×C4—1511no—
286C2×C4—1512no—
287C2×C4—1512no—
288C2×C4—12081no—
289C2×C4D4×D15111yescharacteristic
290C2×C4D4×D15111yescharacteristic
291C2×C4C23×D15111yescharacteristic
292C8—21no—
293C8—21no—
294C8—3021no—
295C8—3021no—
296C22—3021no—
297C22—3021no—
298C22—1512no—
299C22C2×D4×D15111yescharacteristic
300C4—22no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—3022no—
307C4—3021no—
308C4—3021no—
309C4—6041no—
310C4—6041no—
311C4—6041no—
312C4—1512no—
313C4C2×Q8×D15111yescharacteristic
314C4#41×D15111yescharacteristic
315C2—3022no—
316C2C22⋊Q8×D15111yescharacteristic
317C2#2375302211yescharacteristic
318C2#2375302511yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#477×C151C2
socleC22×C151C22×D4
prime radicalC22×D151C2×D4
hypercenter#477D151
hypocenterC151#3082
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #23752521C2semidirect
4. #23752520C2semidirect
5. #23752519C2semidirect
6. #23752518C2semidirect
7. #23752506C2semidirect
8. #23752495C2semidirect
9. #23752494C2semidirect
15. #477×C151C2semidirect
63. Q8×D151Q8semidirect
159. C151#3082semidirect
168. #477D151semidirect

Maximal subgroups

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

subgroupindex
#237528392
#237526882
#237525212
#237525202
#237525192
#237525182
#237525062
#237524952
#237524942
#237522532
#237522492
#237522372
#237522192
#103×D1512
#477×C1512
#3082151