Finite Group Databasebeta

← #34079219

Subgroups — #34079219

Order 19328.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752746C211yesmaximal, characteristic, complemented
2#23752553C211yesmaximal, characteristic, complemented
3#23752536C211yesmaximal, characteristic, complemented
4#23752519C211yesmaximal, characteristic, complemented
5#23752512C211yesmaximal, characteristic, complemented
6#23752434C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752374C211yesmaximal, characteristic, complemented
9#23752357C211yesmaximal, characteristic
10#23752322C211yesmaximal, characteristic, complemented
11#23752317C211yesmaximal, characteristic, complemented
12#23752312C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#23752269C211yesmaximal, characteristic, complemented
15C4×#41×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20#18012733—21no—
21#18012731C2211yescharacteristic
22#18012727C2211yescharacteristic
23#18012722—21no—
24#18012718C2211yescharacteristic
25#18012713C2211yescharacteristic
26C4×Dic302C2211yescharacteristic
27C4×D604C2211yescharacteristic
28C4×C22⋊D151—21no—
29#18012696—21no—
30#18012672C2211yescharacteristic
31#18012672C2211yescharacteristic
32#18012670C2211yescharacteristic
33#18012670C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35C4⋊(C151⋊C8)C2211yescharacteristic
36#18012663C2211yescharacteristic
37#18012663C2211yescharacteristic
38#18012662C2211yescharacteristic
39#18012662C2211yescharacteristic
40#18012660C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46#18012650C2211yescharacteristic
47#18012650C2211yescharacteristic
48C2×#41×C151C2211yescharacteristic
49C4×Q8×C151C2211yescharacteristic
50C4×Q8×C151C2211yescharacteristic
51C4×D4×C151—21no—
52C4×D4×C151—21no—
53C4×D4×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#117×C151—21no—
56#117×C151C2211yescharacteristic
57C2×C42×C151—21no—
58C2×C42×C151C2211yescharacteristic
59C2×Dic302C2311yescharacteristic
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C2×C4×D151—21no—
63#14558994—22no—
64#14558992—22no—
65#14558991—22no—
66#14558989—22no—
67C2×C151⋊C8C2311yescharacteristic
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2311yescharacteristic
70C2×C151⋊C8C2311yescharacteristic
71C4⋊Dic151C2311yescharacteristic
72C4⋊Dic151C2311yescharacteristic
73Dic151⋊C4—21no—
74Dic151⋊C4—21no—
75Dic151⋊C4—21no—
76Dic151⋊C4—21no—
77C22⋊Dic151—21no—
78(C2×D151)⋊C4—21no—
79(C2×D151)⋊C4—21no—
80(C2×D151)⋊C4—21no—
81(C2×D151)⋊C4—21no—
82C4×Dic151—21no—
83#41×C151—22no—
84#41×C151—22no—
85C2×Q8×C151C2311yescharacteristic
86C2×D4×C151—21no—
87C2×D4×C151C2311yescharacteristic
88C22×C4×C151—21no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151D411yescharacteristic
92C22×C4×C151D411yescharacteristic
93C22×C4×C151C2311yescharacteristic
94C4⋊C4×C151—21no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151C2311yescharacteristic
97C4⋊C4×C151C2311yescharacteristic
98C22⋊C4×C151—21no—
99C22⋊C4×C151—21no—
100C22⋊C4×C151—21no—
101C42×C151—21no—
102C42×C151—21no—
103C42×C151—21no—
104C42×C151D411yescharacteristic
105C42×C151D411yescharacteristic
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109Dic302—21no—
110Dic302—21no—
111D604—21no—
112D604—21no—
113C22⋊D151—42no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C4×D151—42no—
118C151⋊C8—21no—
119C151⋊C8—21no—
120C151⋊C8—21no—
121C151⋊C8—21no—
122C23×C151—21no—
123C23×C151C2×D411yescharacteristic
124Q8×C151—21no—
125Q8×C151#4112yes—
126D4×C151—24no—
127D4×C151—21no—
128D4×C151#4112yes—
129C2×C4×C151—24no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—42no—
138C2×C4×C151—42no—
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2411yescharacteristic
145C22×C151—21no—
146C22×C151—22no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151C22×D411yescharacteristic
152C2×D151—41no—
153C2×D151—41no—
154C2×D151—41no—
155C4×C151—21no—
156C4×C151—22no—
157C4×C151—21no—
158C4×C151—21no—
159C4×C151—21no—
160C4×C151—21no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151C2×#4111yescharacteristic
164C4×C151C2×#4111yescharacteristic
165Dic151—41no—
166Dic151—41no—
167Dic151—41no—
168C2×C151—41no—
169C2×C151—42no—
170C2×C151#52511yescharacteristic
171C2×C151#57511yescharacteristic
172C2×C151#57511yescharacteristic
173D151—81no—
174C151#311111yescharacteristic, complemented, Sylow
175#3111—1511nomaximal, Sylow
176#529—1511no—
177C4×#41D15111yescharacteristic, complemented
178#485—1511no—
179#482—1511no—
180#479—1511no—
181#478—1511no—
182#464—1511no—
183#463—1511no—
184#452—1511no—
185#449—1511no—
186#442—1511no—
187#441—1511no—
188#440—1511no—
189#440—1511no—
190#432—1511no—
191C2×#41C2×D15111yescharacteristic
192C2×Q16—1511no—
193C2×SD16—1511no—
194C2×SD16—1511no—
195C2×D8—1511no—
196#126—3021no—
197#125—1511no—
198#124—1511no—
199#123—3021no—
200C22⋊Q8—1511no—
201#121—1511no—
202C4×Q8—1511no—
203C4×Q8C2×D15111yescharacteristic
204C4×Q8C2×D15111yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4—3021no—
208C4×D4—1511no—
209C4×D4C2×D15111yescharacteristic
210C4×D4C2×D15111yescharacteristic
211#117—21no—
212#117—3021no—
213#117C2×D15111yescharacteristic
214C2×C42—21no—
215C2×C42C2×D15111yescharacteristic
216#107—1511no—
217#107—1511no—
218#106—1511no—
219#106—1511no—
220C4⋊C8—1511no—
221C4⋊C8—1511no—
222#103—1511no—
223#103—1511no—
224#103—1511no—
225#103—1511no—
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102—1511no—
230C22⋊C8—1511no—
231C22⋊C8—1511no—
232#97—1511no—
233#97—1511no—
234#41—22no—
235#41—22no—
236C2×Q8—1511no—
237C2×Q8C22×D15111yescharacteristic
238C2×D4—21no—
239C2×D4—3021no—
240C2×D4—1511no—
241C2×D4C22×D15111yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—3021no—
246C22×C4C22⋊D15111yescharacteristic
247C22×C4C22⋊D15111yescharacteristic
248C22×C4C22×D15111yescharacteristic
249Q16—3022no—
250SD16—3022no—
251SD16—3022no—
252D8—3022no—
253C2×C8—1511no—
254C2×C8—1511no—
255C2×C8—1511no—
256C2×C8—1511no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—1511no—
264C4⋊C4—1511no—
265C4⋊C4C22×D15111yescharacteristic
266C4⋊C4C22×D15111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—3021no—
279C42C22⋊D15111yescharacteristic
280C42C22⋊D15111yescharacteristic
281C42C22×D15111yescharacteristic
282C42C22×D15111yescharacteristic
283C23—21no—
284C23—3021no—
285C23C2×C22⋊D15111yescharacteristic
286Q8—21no—
287Q8—3021no—
288Q8—3021no—
289Q8#1455900412yes—
290D4—24no—
291D4—21no—
292D4—3021no—
293D4—3021no—
294D4—6042no—
295D4#1455900412yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—3021no—
307C2×C4—3021no—
308C2×C4—3021no—
309C2×C4—6042no—
310C2×C4C2×C22⋊D15111yescharacteristic
311C2×C4C2×C22⋊D15111yescharacteristic
312C2×C4C2×C22⋊D15111yescharacteristic
313C2×C4C2×C22⋊D15111yescharacteristic
314C2×C4C2×C22⋊D15111yescharacteristic
315C2×C4C23×D15111yescharacteristic
316C8—3021no—
317C8—3021no—
318C8—3021no—
319C8—3021no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—6041no—
327C22—6041no—
328C22—6041no—
329C22C22×C22⋊D15111yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—6041no—
339C4—6041no—
340C4—6041no—
341C4C2×#1455900411yescharacteristic
342C4C2×#1455900411yescharacteristic
343C2—41no—
344C2—42no—
345C2—12081no—
346C2#2375272311yescharacteristic
347C2#2375301011yescharacteristic
348C2#2375301011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC4×#41×C151C2
socleC22×C151C22×D4
prime radical#23752357C2
hypercenterC4×#41D151
hypocenterC151#3111
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #23752746C2semidirect
2. #23752553C2semidirect
3. #23752536C2semidirect
4. #23752519C2semidirect
5. #23752512C2semidirect
6. #23752434C2semidirect
7. #23752427C2semidirect
8. #23752374C2semidirect
10. #23752322C2semidirect
11. #23752317C2semidirect
12. #23752312C2semidirect
13. #23752310C2semidirect
14. #23752269C2semidirect
15. C4×#41×C151C2semidirect
174. C151#3111semidirect
177. C4×#41D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237525532
#237525362
#237525192
#237525122
#237524342
#237524272
#237523742
#237523572
#237523222
#237523172
#237523122
#237523102
#237522692
C4×#41×C1512
#3111151