Finite Group Databasebeta

← #34077948

Subgroups — #34077948

Order 19328.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012771C211yesmaximal, characteristic
2#23752694C211yesmaximal, characteristic
3#23752688C211yesmaximal, characteristic, complemented
4#23752319C211yesmaximal, characteristic, complemented
5#23752317C211yesmaximal, characteristic, complemented
6#23752311C211yesmaximal, characteristic, complemented
7#23752310C211yesmaximal, characteristic, complemented
8#23752304C211yesmaximal, characteristic, complemented
9C4×#14558993C211yesmaximal, characteristic, complemented
10#23752297C211yesmaximal, characteristic, complemented
11#23752253C211yesmaximal, characteristic, complemented
12#23752207C211yesmaximal, characteristic
13#103×D151C211yesmaximal, characteristic, complemented
14#23752166C211yesmaximal, characteristic, complemented
15C4×Q16×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18#18012771C418yescomplemented
19C2×#14558994C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558991C2211yescharacteristic
22C2×#14558987C2211yescharacteristic
23C2×C8×D151C2211yescharacteristic
24Q8×Dic151C2211yescharacteristic
25Q8×Dic151C2211yescharacteristic
26C4×Dic302—21no—
27C4×Dic302C2211yescharacteristic
28#18012704—21no—
29#18012704C2211yescharacteristic
30C4×D604—21no—
31C4×D604C2211yescharacteristic
32#18012701—21no—
33#18012701C2211yescharacteristic
34#18012697—21no—
35#18012697C2211yescharacteristic
36#18012696—21no—
37#18012696—21no—
38#18012696C2211yescharacteristic
39C4⋊C4×D151—21no—
40C4⋊C4×D151C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012671C2211yescharacteristic
43#18012670C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012650C2211yescharacteristic
51#18012649C2211yescharacteristic
52C8×Dic151C2211yescharacteristic
53C2×Q16×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59C4×C8×C151C2211yescharacteristic
60#14559005—22no—
61#14559005C2×C414yes—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64Q8×D151—22no—
65Q8×D151C2×C414yescomplemented
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74#14558994C2×C414yescomplemented
75#14558993C2×C414yescomplemented
76#14558991C2×C414yescomplemented
77#14558987C2×C414yescomplemented
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C8×D151—22no—
81C4⋊Dic151—21no—
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4D411yescharacteristic
89Dic151⋊C4D411yescharacteristic
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4D411yescharacteristic
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151—21no—
98C4×Dic151—21no—
99C4×Dic151—21no—
100C4×Dic151C2311yescharacteristic
101C2×Q8×C151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103Q16×C151C2×C414yescomplemented
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C42×C151—21no—
111C42×C151—21no—
112C42×C151C2311yescharacteristic
113C22×D151—21no—
114C22×D151C2×D411yescharacteristic
115Dic302—21no—
116Dic302—24no—
117Dic302C22×C412yes—
118D604—24no—
119D604—21no—
120D604C22×C412yes—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—24no—
128C4×D151—24no—
129C4×D151—81no—
130C4×D151—81no—
131C4×D151—81no—
132C4×D151C22×C412yes—
133C4×D151#4112yes—
134C151⋊C8—21no—
135C151⋊C8C22×C412yes—
136Q8×C151—21no—
137Q8×C151—21no—
138Q8×C151C22×C412yes—
139Q8×C151C22×C412yes—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2411yescharacteristic
147C8×C151—21no—
148C8×C151C22×C412yes—
149C22×C151C22×D411yescharacteristic
150C2×D151—21no—
151C2×D151—21no—
152C2×D151—22no—
153C2×D151—41no—
154C2×D151—41no—
155C2×D151C4×D412yes—
156C4×C151—22no—
157C4×C151—22no—
158C4×C151—21no—
159C4×C151—21no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151C23×C411yescharacteristic
163C4×C151C2×#4111yescharacteristic
164Dic151—22no—
165Dic151—21no—
166Dic151—21no—
167Dic151—41no—
168Dic151—41no—
169Dic151C4×D412yes—
170C2×C151C2×C4×D411yescharacteristic
171C2×C151#57711yescharacteristic
172C2×C151#57811yescharacteristic
173D151—22no—
174D151—42no—
175C151#294711yescharacteristic, complemented, Sylow
176#2947—1511nomaximal, Sylow
177C2×#137—1511no—
178#520—1511no—
179#519—1511no—
180#441—1511no—
181#441—1511no—
182#440—1511no—
183#440—1511no—
184C4×Q16—1511no—
185C4×Q16D15111yescharacteristic, complemented
186C4×SD16—1511no—
187C4×SD16—1511no—
188#428—1511no—
189#416—1511no—
190C2×#103—1511no—
191#405—1511no—
192C2×#41—1511no—
193C22×Q8—1511no—
194#137—1518no—
195C2×Q16—1511no—
196C2×Q16C2×D15111yescharacteristic
197C2×SD16—1511no—
198C2×SD16—1511no—
199C2×M16—1511no—
200C22×C8—1511no—
201C4×Q8—3021no—
202C4×Q8—3021no—
203C4×Q8—1511no—
204C4×Q8—1511no—
205C4×Q8—1511no—
206C4×Q8—1511no—
207C4×Q8C2×D15111yescharacteristic
208C4×Q8C2×D15111yescharacteristic
209C4×D4—3021no—
210C4×D4—3021no—
211C4×D4—1511no—
212C4×D4—1511no—
213#117—3021no—
214#117—3021no—
215#117—3021no—
216#117—1511no—
217#117—1511no—
218C2×C4⋊C4—3021no—
219C2×C4⋊C4—1511no—
220#107—1511no—
221#107C2×D15111yescharacteristic
222#106—1511no—
223#106—1511no—
224#103—1511no—
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103C2×D15111yescharacteristic
229#103C2×D15111yescharacteristic
230#102—1511no—
231#102—1511no—
232#97—1511no—
233#97—1511no—
234C4×C8—1511no—
235C4×C8C2×D15111yescharacteristic
236#41—3022no—
237#41—1514no—
238C2×Q8—3021no—
239C2×Q8—3022no—
240C2×Q8—1514no—
241C2×Q8—1511no—
242C2×Q8C22×D15111yescharacteristic
243C2×Q8C22×D15111yescharacteristic
244C2×D4—3021no—
245C2×D4—1511no—
246C22×C4—3021no—
247C22×C4—3021no—
248C22×C4—3021no—
249C22×C4—3021no—
250C22×C4—3021no—
251C22×C4—1511no—
252Q16—1514no—
253Q16C4×D15114yescomplemented
254SD16—1514no—
255SD16—1514no—
256M16—1514no—
257C2×C8—3022no—
258C2×C8—1511no—
259C2×C8—1511no—
260C2×C8C22×D15111yescharacteristic
261C2×C8C22×D15111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—3021no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—1511no—
270C4⋊C4—1511no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4C22×D15111yescharacteristic
274C4⋊C4C22×D15111yescharacteristic
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C22⋊C4—3021no—
278C22⋊C4—1511no—
279C22⋊C4—1511no—
280C42—21no—
281C42—21no—
282C42—3021no—
283C42—3021no—
284C42—3021no—
285C42—3021no—
286C42—3021no—
287C42—1511no—
288C42C22×D15111yescharacteristic
289C23—3021no—
290C23—1511no—
291Q8—21no—
292Q8—21no—
293Q8—3024no—
294Q8—3021no—
295Q8—1512no—
296Q8C2×C4×D15112yes—
297Q8C2×C4×D15112yes—
298D4—3024no—
299D4—3021no—
300D4—1512no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—3024no—
306C2×C4—3024no—
307C2×C4—3021no—
308C2×C4—3021no—
309C2×C4—3021no—
310C2×C4—1511no—
311C2×C4—1511no—
312C2×C4—1511no—
313C2×C4—1512no—
314C2×C4—1512no—
315C2×C4—12081no—
316C2×C4—12081no—
317C2×C4—12081no—
318C2×C4D4×D15111yescharacteristic
319C2×C4D4×D15111yescharacteristic
320C2×C4C23×D15111yescharacteristic
321C8—21no—
322C8—3021no—
323C8—1512no—
324C8C2×C4×D15112yes—
325C22—3021no—
326C22—3021no—
327C22—3022no—
328C22—6041no—
329C22—6041no—
330C22—1512no—
331C22C2×D4×D15111yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—3021no—
339C4—3021no—
340C4—3022no—
341C4—6041no—
342C4—6041no—
343C4—1512no—
344C4C22×C4×D15111yescharacteristic
345C4#41×D15111yescharacteristic
346C2—3022no—
347C2—6042no—
348C2C4×D4×D15111yescharacteristic
349C2#2375301911yescharacteristic
350C2#2375302511yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
FittingC4×Q16×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559005C22
cosocleC2×C4×C151C24
hypercenterC4×Q16D151
hypocenterC151#2947
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. #23752688C2semidirect
4. #23752319C2semidirect
5. #23752317C2semidirect
6. #23752311C2semidirect
7. #23752310C2semidirect
8. #23752304C2semidirect
9. C4×#14558993C2semidirect
10. #23752297C2semidirect
11. #23752253C2semidirect
13. #103×D151C2semidirect
14. #23752166C2semidirect
15. C4×Q16×C151C2semidirect
18. #18012771C4semidirect
65. Q8×D151C2×C4semidirect
74. #14558994C2×C4semidirect
75. #14558993C2×C4semidirect
76. #14558991C2×C4semidirect
77. #14558987C2×C4semidirect
103. Q16×C151C2×C4semidirect
175. C151#2947semidirect
185. C4×Q16D151semidirect
253. Q16C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127712
#237526942
#237526882
#237523192
#237523172
#237523112
#237523102
#237523042
C4×#145589932
#237522972
#237522532
#237522072
#103×D1512
#237521662
C4×Q16×C1512
#2947151