Finite Group Databasebeta

← #34077926

Subgroups — #34077926

Order 19328.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012771C211yesmaximal, characteristic
2C4×#14559005C211yesmaximal, characteristic
3C4×Q8×D151C211yesmaximal, characteristic, complemented
4#23752317C211yesmaximal, characteristic, complemented
5#23752314C211yesmaximal, characteristic, complemented
6#23752310C211yesmaximal, characteristic, complemented
7Q16×Dic151C211yesmaximal, characteristic, complemented
8#23752304C211yesmaximal, characteristic, complemented
9#23752299C211yesmaximal, characteristic, complemented
10#23752297C211yesmaximal, characteristic, complemented
11#23752251C211yesmaximal, characteristic, complemented
12#23752219C211yesmaximal, characteristic, complemented
13#23752212C211yesmaximal, characteristic
14#23752164C211yesmaximal, characteristic, complemented
15#441×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18#18012771C418yescomplemented
19C2×#14558994C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558991C2211yescharacteristic
22C2×#14558987C2211yescharacteristic
23C2×#14558987C2211yescharacteristic
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
36C4⋊C4×D151—21no—
37C4⋊C4×D151C2211yescharacteristic
38C42×D151—21no—
39C42×D151—21no—
40C42×D151C2211yescharacteristic
41#18012673C2211yescharacteristic
42#18012672C2211yescharacteristic
43#18012670C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012650C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C8×Dic151C2211yescharacteristic
53C2×Q16×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59#97×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×D151D411yescharacteristic
74C2×C4×D151D411yescharacteristic
75C2×C4×D151C2311yescharacteristic
76#14558994C2×C414yescomplemented
77#14558993C2×C414yescomplemented
78#14558991C2×C414yescomplemented
79#14558987—22no—
80#14558987C2×C414yescomplemented
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C4⋊Dic151—21no—
84C4⋊Dic151—21no—
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151—21no—
98C4×Dic151D411yescharacteristic
99C4×Dic151D411yescharacteristic
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—22no—
130C4×D151—41no—
131C4×D151—42no—
132C4×D151—42no—
133C4×D151—42no—
134C4×D151C22×C412yes—
135C4×D151#4112yes—
136C151⋊C8—21no—
137C151⋊C8C22×C412yes—
138Q8×C151—21no—
139Q8×C151—21no—
140Q8×C151C22×C412yes—
141Q8×C151C22×C412yes—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2411yescharacteristic
149C8×C151—21no—
150C8×C151C22×C412yes—
151C22×C151C22×D411yescharacteristic
152C2×D151—21no—
153C2×D151—21no—
154C2×D151—22no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151C4×D412yes—
158C4×C151—22no—
159C4×C151—22no—
160C4×C151—21no—
161C4×C151—21no—
162C4×C151—41no—
163C4×C151—41no—
164C4×C151C23×C411yescharacteristic
165C4×C151C2×#4111yescharacteristic
166Dic151—22no—
167Dic151—21no—
168Dic151—41no—
169Dic151—41no—
170Dic151C4×D412yes—
171Dic151#13712yescomplemented
172C2×C151C2×C4×D411yescharacteristic
173C2×C151C2×#13711yescharacteristic
174C2×C151#57511yescharacteristic
175D151—22no—
176D151—42no—
177C151C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—1511nomaximal, Sylow
179C2×#137—1511no—
180C4×#41—1511no—
181C2×C4×Q8—1511no—
182#441—1511no—
183#441D15111yescharacteristic, complemented
184#440—1511no—
185#440—1511no—
186C4×Q16—1511no—
187C4×Q16—1511no—
188C4×SD16—1511no—
189C4×SD16—1511no—
190#428—1511no—
191#419—1511no—
192#417—1511no—
193C4×M16—1511no—
194C2×#41—1511no—
195C22×Q8—1511no—
196#137—1518no—
197C2×Q16—1511no—
198C2×Q16C2×D15111yescharacteristic
199C2×SD16—1511no—
200C2×SD16—1511no—
201C2×M16—1511no—
202C2×M16—1511no—
203C4×Q8—3021no—
204C4×Q8—3021no—
205C4×Q8—1511no—
206C4×Q8—1511no—
207C4×Q8—1511no—
208C4×Q8—1511no—
209C4×Q8C2×D15111yescharacteristic
210C4×Q8C2×D15111yescharacteristic
211C4×D4—3021no—
212C4×D4—3021no—
213C4×D4—1511no—
214C4×D4—1511no—
215#117—3021no—
216#117—1511no—
217C2×C4⋊C4—3021no—
218C2×C4⋊C4—1511no—
219C2×C42—3021no—
220C2×C42—3021no—
221C2×C42—1511no—
222#107—1511no—
223#107—1511no—
224#106—1511no—
225#106C2×D15111yescharacteristic
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103—1511no—
230#103C2×D15111yescharacteristic
231#103C2×D15111yescharacteristic
232#102—1511no—
233#102—1511no—
234#97—1511no—
235#97C2×D15111yescharacteristic
236C4×C8—1511no—
237C4×C8—1511no—
238#41—3022no—
239#41—1514no—
240C2×Q8—3021no—
241C2×Q8—3022no—
242C2×Q8—1514no—
243C2×Q8—1511no—
244C2×Q8C22×D15111yescharacteristic
245C2×Q8C22×D15111yescharacteristic
246C2×D4—3021no—
247C2×D4—1511no—
248C22×C4—3021no—
249C22×C4—3021no—
250C22×C4—3021no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—1511no—
254C22×C4—1511no—
255C22×C4—1511no—
256Q16—1514no—
257Q16C4×D15114yescomplemented
258SD16—1514no—
259SD16—1514no—
260M16—3022no—
261M16—1514no—
262C2×C8—1511no—
263C2×C8—1511no—
264C2×C8C22×D15111yescharacteristic
265C2×C8C22×D15111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C42—21no—
281C42—21no—
282C42—3021no—
283C42—3021no—
284C42—3021no—
285C42—3021no—
286C42—3021no—
287C42—1511no—
288C42—1511no—
289C42—1511no—
290C42C22×D15111yescharacteristic
291C23—3021no—
292C23—1511no—
293Q8—21no—
294Q8—21no—
295Q8—3024no—
296Q8—3021no—
297Q8—1512no—
298Q8C2×C4×D15112yes—
299Q8C2×C4×D15112yes—
300D4—3024no—
301D4—3021no—
302D4—1512no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—3024no—
308C2×C4—3024no—
309C2×C4—3022no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—6041no—
314C2×C4—6042no—
315C2×C4—6042no—
316C2×C4—6042no—
317C2×C4—1511no—
318C2×C4—1511no—
319C2×C4—1511no—
320C2×C4—1512no—
321C2×C4—1512no—
322C2×C4D4×D15111yescharacteristic
323C2×C4D4×D15111yescharacteristic
324C2×C4C23×D15111yescharacteristic
325C8—21no—
326C8—3021no—
327C8—1512no—
328C8C2×C4×D15112yes—
329C22—3021no—
330C22—3021no—
331C22—3022no—
332C22—6041no—
333C22—6041no—
334C22—1512no—
335C22C2×D4×D15111yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—3021no—
343C4—3022no—
344C4—6041no—
345C4—6041no—
346C4—1512no—
347C4—1512no—
348C4C22×C4×D15111yescharacteristic
349C4#41×D15111yescharacteristic
350C2—3022no—
351C2—6042no—
352C2C4×D4×D15111yescharacteristic
353C2#137×D15111yescharacteristic
354C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#441×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559005C22
cosocleC2×C4×C151C24
hypercenter#441D151
hypocenterC151C4×#137
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D151C2semidirect
4. #23752317C2semidirect
5. #23752314C2semidirect
6. #23752310C2semidirect
7. Q16×Dic151C2semidirect
8. #23752304C2semidirect
9. #23752299C2semidirect
10. #23752297C2semidirect
11. #23752251C2semidirect
12. #23752219C2semidirect
14. #23752164C2semidirect
15. #441×C151C2semidirect
18. #18012771C4semidirect
65. Q8×D151C2×C4semidirect
76. #14558994C2×C4semidirect
77. #14558993C2×C4semidirect
78. #14558991C2×C4semidirect
80. #14558987C2×C4semidirect
103. Q16×C151C2×C4semidirect
171. Dic151#137semidirect
177. C151C4×#137semidirect
183. #441D151semidirect
257. Q16C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127712
C4×#145590052
C4×Q8×D1512
#237523172
#237523142
#237523102
Q16×Dic1512
#237523042
#237522992
#237522972
#237522512
#237522192
#237522122
#237521642
#441×C1512
C4×#137151