Finite Group Databasebeta

← #34079216

Subgroups — #34079216

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#23752741C211yesmaximal, characteristic, complemented
2C4×#14559003C211yesmaximal, characteristic, complemented
3#23752551C211yesmaximal, characteristic, complemented
4#23752534C211yesmaximal, characteristic, complemented
5#23752520C211yesmaximal, characteristic, complemented
6#23752512C211yesmaximal, characteristic, complemented
7#23752431C211yesmaximal, characteristic, complemented
8#23752371C211yesmaximal, characteristic, complemented
9#23752354C211yesmaximal, characteristic
10#23752324C211yesmaximal, characteristic, complemented
11#23752316C211yesmaximal, characteristic, complemented
12#23752313C211yesmaximal, characteristic, complemented
13#23752309C211yesmaximal, characteristic, complemented
14#23752268C211yesmaximal, characteristic, complemented
15#463×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19#18012732—21no—
20#18012731C2211yescharacteristic
21#18012721—21no—
22#18012715C2211yescharacteristic
23#18012710C2211yescharacteristic
24Q8×Dic151C2211yescharacteristic
25C4×Dic302C2211yescharacteristic
26#18012704C2211yescharacteristic
27D4×Dic151C2211yescharacteristic
28D4×Dic151C2211yescharacteristic
29C4×C22⋊D151—21no—
30(C22⋊D151)⋊C4—21no—
31(C22⋊D151)⋊C4—21no—
32#18012697C2211yescharacteristic
33#18012695—21no—
34#18012695—21no—
35C2×C4×Dic151—21no—
36C42×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51#18012649C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—22no—
61C2×Dic302C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C22×Dic151—21no—
66C22×Dic151—21no—
67C2×C4×D151D411yescharacteristic
68C2×C4×D151D411yescharacteristic
69C2×C4×D151C2311yescharacteristic
70#14558994—22no—
71#14558992—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C4⋊Dic151—21no—
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151D411yescharacteristic
93C4×Dic151D411yescharacteristic
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×D4×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151—21no—
99SD16×C151—22no—
100D8×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151C2×D411yescharacteristic
109Dic302—21no—
110Dic302#4112yes—
111C22⋊D151—24no—
112C22⋊D151—42no—
113C2×Dic151—24no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—42no—
119C2×Dic151—42no—
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C4×D151—21no—
124C4×D151—21no—
125C4×D151—41no—
126C4×D151—41no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151—21no—
130C23×C151—21no—
131Q8×C151—21no—
132Q8×C151—21no—
133D4×C151—21no—
134D4×C151—21no—
135D4×C151—21no—
136D4×C151#4112yes—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—42no—
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2411yescharacteristic
143C8×C151—21no—
144C8×C151—21no—
145C22×C151—22no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151—41no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151C22×D411yescharacteristic
152C2×D151—21no—
153C2×D151—21no—
154C2×D151—21no—
155C4×C151—21no—
156C4×C151—21no—
157C4×C151—41no—
158C4×C151—41no—
159C4×C151C2×#4111yescharacteristic
160C4×C151C2×#4111yescharacteristic
161Dic151—21no—
162Dic151—22no—
163Dic151—21no—
164Dic151—21no—
165Dic151—41no—
166Dic151—41no—
167Dic151—41no—
168C2×C151—42no—
169C2×C151—81no—
170C2×C151#52511yescharacteristic
171C2×C151#57511yescharacteristic
172C2×C151#57511yescharacteristic
173D151—41no—
174C151#311111yescharacteristic, complemented, Sylow
175#3111—1511nomaximal, Sylow
176#529—1511no—
177C4×#41—1511no—
178#485—1511no—
179#482—1511no—
180#479—1511no—
181#478—1511no—
182#464—1511no—
183#463D15111yescharacteristic, complemented
184#452—1511no—
185#449—1511no—
186#442—1511no—
187#441—1511no—
188#440—1511no—
189#440—1511no—
190#432—1511no—
191C2×#41—1511no—
192C2×Q16—1511no—
193C2×SD16—1511no—
194C2×SD16C2×D15111yescharacteristic
195C2×D8C2×D15111yescharacteristic
196#126—3021no—
197#125—1511no—
198#124C2×D15111yescharacteristic
199#123—3021no—
200C22⋊Q8—1511no—
201#121—1511no—
202C4×Q8—1511no—
203C4×Q8—1511no—
204C4×Q8—1511no—
205C4×D4—3021no—
206C4×D4—3021no—
207C4×D4—3021no—
208C4×D4—1511no—
209C4×D4—1511no—
210C4×D4C2×D15111yescharacteristic
211#117—3021no—
212#117—3021no—
213#117—1511no—
214C2×C42—3021no—
215C2×C42—1511no—
216#107—1511no—
217#107—1511no—
218#106—1511no—
219#106—1511no—
220C4⋊C8—1511no—
221C4⋊C8C2×D15111yescharacteristic
222#103—1511no—
223#103—1511no—
224#103—1511no—
225#103C2×D15111yescharacteristic
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102C2×D15111yescharacteristic
230C22⋊C8—1511no—
231C22⋊C8—1511no—
232#97—1511no—
233#97—1511no—
234#41—3022no—
235#41—3022no—
236C2×Q8—1511no—
237C2×Q8C22×D15111yescharacteristic
238C2×D4—3021no—
239C2×D4—3021no—
240C2×D4C22×D15111yescharacteristic
241C2×D4C22×D15111yescharacteristic
242C22×C4—21no—
243C22×C4—3021no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—1511no—
247C22×C4—1511no—
248C22×C4—1511no—
249Q16—3022no—
250SD16—22no—
251SD16—3022no—
252D8—22no—
253C2×C8—1511no—
254C2×C8—1511no—
255C2×C8C22×D15111yescharacteristic
256C2×C8C22×D15111yescharacteristic
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—1511no—
264C4⋊C4—1511no—
265C4⋊C4—1511no—
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—3021no—
276C42—3021no—
277C42—3021no—
278C42—3021no—
279C42—1511no—
280C42—1511no—
281C42—1511no—
282C42C22×D15111yescharacteristic
283C23—21no—
284C23—21no—
285C23—1511no—
286Q8—21no—
287Q8—21no—
288Q8—3021no—
289Q8—1512no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—3024no—
294D4—6042no—
295D4#1455900312yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—3024no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—6041no—
307C2×C4—6041no—
308C2×C4—6042no—
309C2×C4—6042no—
310C2×C4—1511no—
311C2×C4—1511no—
312C2×C4—1511no—
313C2×C4D4×D15111yescharacteristic
314C2×C4D4×D15111yescharacteristic
315C2×C4C23×D15111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3021no—
319C8—3021no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—3021no—
327C22—3021no—
328C22—3021no—
329C22C2×D4×D15111yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—3021no—
335C4—3022no—
336C4—3021no—
337C4—3021no—
338C4—6041no—
339C4—6041no—
340C4—6041no—
341C4#41×D15111yescharacteristic
342C4C2×#1455900311yescharacteristic
343C2—42no—
344C2—81no—
345C2—6041no—
346C2#2375272211yescharacteristic
347C2#2375300811yescharacteristic
348C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#463×C151C2
socleC22×C151C22×D4
prime radical#23752354C2
hypercenter#463D151
hypocenterC151#3111
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23752741C2semidirect
2. C4×#14559003C2semidirect
3. #23752551C2semidirect
4. #23752534C2semidirect
5. #23752520C2semidirect
6. #23752512C2semidirect
7. #23752431C2semidirect
8. #23752371C2semidirect
10. #23752324C2semidirect
11. #23752316C2semidirect
12. #23752313C2semidirect
13. #23752309C2semidirect
14. #23752268C2semidirect
15. #463×C151C2semidirect
174. C151#3111semidirect
183. #463D151semidirect

Maximal subgroups

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

subgroupindex
#237527412
C4×#145590032
#237525512
#237525342
#237525202
#237525122
#237524312
#237523712
#237523542
#237523242
#237523162
#237523132
#237523092
#237522682
#463×C1512
#3111151