Finite Group Databasebeta

← #34079072

Subgroups — #34079072

Order 19328.

386 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
1#23752785C211yesmaximal, characteristic
2#23752693C211yesmaximal, characteristic
3#23752556C211yesmaximal, characteristic, complemented
4#23752554C211yesmaximal, characteristic, complemented
5#23752551C211yesmaximal, characteristic, complemented
6#23752550C211yesmaximal, characteristic, complemented
7#23752547C211yesmaximal, characteristic, complemented
8#23752546C211yesmaximal, characteristic, complemented
9#23752544C211yesmaximal, characteristic, complemented
10#23752251C211yesmaximal, characteristic, complemented
11#23752247C211yesmaximal, characteristic, complemented
12#23752219C211yesmaximal, characteristic, complemented
13#103×D151C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic
15#483×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012738—21no—
21#18012725—21no—
22#18012724—21no—
23#18012721—21no—
24#18012719C2211yescharacteristic
25#18012718C2211yescharacteristic
26#18012715C2211yescharacteristic
27#18012704—21no—
28#18012701—21no—
29C4×C22⋊D151—21no—
30C4×C22⋊D151—21no—
31#18012698C2211yescharacteristic
32#18012697C2211yescharacteristic
33#18012697C2211yescharacteristic
34#18012697C2211yescharacteristic
35C4⋊C4×D151C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012662C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic
54#106×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—22no—
61C2×Dic302—21no—
62C2×Dic302D411yescharacteristic
63C2×Dic302C2311yescharacteristic
64Q8×D151—22no—
65Q8×D151—22no—
66C2×D604D411yescharacteristic
67C2×C22⋊D151D411yescharacteristic
68C2×C22⋊D151D411yescharacteristic
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151C2311yescharacteristic
73C2×C4×D151C2311yescharacteristic
74#14558987—22no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C8×D151—22no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊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—
97C2×Q8×C151C2311yescharacteristic
98C22×C4×C151—21no—
99C22×C4×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C22×D151C2×D411yescharacteristic
109C22×D151C2×D411yescharacteristic
110Dic302—22no—
111Dic302—21no—
112Dic302—21no—
113Dic302—42no—
114D604—22no—
115C22⋊D151—22no—
116C22⋊D151—22no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C4×D151—21no—
124C4×D151—21no—
125C4×D151—42no—
126C4×D151—81no—
127C4×D151—81no—
128C4×D151#4112yes—
129C4×D151#4112yes—
130C151⋊C8—21no—
131C151⋊C8—21no—
132C23×C151C2×D411yescharacteristic
133Q8×C151—21no—
134Q8×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—81no—
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2411yescharacteristic
144C8×C151—21no—
145C8×C151—21no—
146C22×C151—21no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151C22×D411yescharacteristic
150C2×D151—21no—
151C2×D151—21no—
152C2×D151—21no—
153C2×D151—21no—
154C2×D151—21no—
155C2×D151#12312yes—
156C4×C151—21no—
157C4×C151—41no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151—41no—
161C4×C151C2×#4111yescharacteristic
162C4×C151C2×#4111yescharacteristic
163Dic151—21no—
164Dic151—41no—
165Dic151—41no—
166Dic151—41no—
167Dic151—41no—
168Dic151#12312yes—
169C2×C151—41no—
170C2×C151C2×#12311yescharacteristic
171C2×C151#57711yescharacteristic
172C2×C151#57811yescharacteristic
173D151—22no—
174D151—41no—
175C151#309711yescharacteristic, complemented, Sylow
176#3097—1511nomaximal, Sylow
177#536—1511no—
178#520—1511no—
179#485—1511no—
180#485—1511no—
181#485—1511no—
182#485—1511no—
183#484—1511no—
184#484—1511no—
185#483—1511no—
186#483D15111yescharacteristic, complemented
187#428—1511no—
188#427—1511no—
189#419—1511no—
190C2×#103—1511no—
191#408—1511no—
192C2×#41—1511no—
193C22×Q8—1511no—
194C2×M16—1511no—
195C22×C8—1511no—
196C4⋊Q8—3021no—
197#124—3021no—
198#123—3021no—
199#123—3021no—
200C22⋊Q8—1511no—
201C22⋊Q8—1511no—
202C22⋊Q8—1511no—
203C22⋊Q8C2×D15111yescharacteristic
204C4×Q8—3021no—
205C4×D4—3021no—
206C4×D4—3021no—
207C4×D4—3021no—
208#117—1511no—
209#117—1511no—
210#117—1511no—
211#117—1511no—
212C2×C4⋊C4—1511no—
213C2×C4⋊C4—1511no—
214C2×C4⋊C4C2×D15111yescharacteristic
215#107—1511no—
216#107—1511no—
217#107—1511no—
218#107—1511no—
219#106—1511no—
220#106—1511no—
221#106C2×D15111yescharacteristic
222#106C2×D15111yescharacteristic
223#103—1511no—
224#103—1511no—
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103C2×D15111yescharacteristic
230#103C2×D15111yescharacteristic
231C22⋊C8—1511no—
232C22⋊C8—1511no—
233C22⋊C8—1511no—
234C22⋊C8C2×D15111yescharacteristic
235#41—3022no—
236#41—3022no—
237C2×Q8—3021no—
238C2×Q8—3022no—
239C2×Q8—3022no—
240C2×Q8—1511no—
241C2×Q8—1511no—
242C2×Q8C22×D15111yescharacteristic
243C2×D4—1511no—
244C2×D4—1511no—
245C2×D4—1511no—
246C22×C4—21no—
247C22×C4—3021no—
248C22×C4—3021no—
249C22×C4—3021no—
250C22×C4—1511no—
251C22×C4—1511no—
252C22×C4C22×D15111yescharacteristic
253M16—3022no—
254C2×C8—3022no—
255C2×C8—1511no—
256C2×C8—1511no—
257C2×C8C22×D15111yescharacteristic
258C2×C8C22×D15111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—3021no—
264C4⋊C4—3021no—
265C4⋊C4—3021no—
266C4⋊C4—1511no—
267C4⋊C4—1511no—
268C4⋊C4—1511no—
269C4⋊C4C22×D15111yescharacteristic
270C4⋊C4C22×D15111yescharacteristic
271C4⋊C4C22×D15111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C42—3021no—
281C42—3021no—
282C42—3021no—
283C42—3021no—
284C23—1511no—
285C23—1511no—
286C23D4×D15111yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—3022no—
290Q8—3021no—
291Q8—3021no—
292Q8—6042no—
293D4—3022no—
294D4—3022no—
295D4—3022no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—3021no—
307C2×C4—3021no—
308C2×C4—3021no—
309C2×C4—6042no—
310C2×C4—1511no—
311C2×C4—1511no—
312C2×C4—1512no—
313C2×C4—1512no—
314C2×C4—12081no—
315C2×C4—12081no—
316C2×C4D4×D15111yescharacteristic
317C2×C4C23×D15111yescharacteristic
318C8—21no—
319C8—21no—
320C8—3021no—
321C8—3021no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—3021no—
326C22—3021no—
327C22—3021no—
328C22—3021no—
329C22—3021no—
330C22—1512no—
331C22C2×D4×D15111yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3021no—
338C4—6041no—
339C4—6041no—
340C4—6041no—
341C4—6041no—
342C4—1512no—
343C4#41×D15111yescharacteristic
344C4#41×D15111yescharacteristic
345C2—41no—
346C2—3022no—
347C2—6041no—
348C2#123×D15111yescharacteristic
349C2#2375301811yescharacteristic
350C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#483×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559004C22
hypercenter#483D151
hypocenterC151#3097
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #23752556C2semidirect
4. #23752554C2semidirect
5. #23752551C2semidirect
6. #23752550C2semidirect
7. #23752547C2semidirect
8. #23752546C2semidirect
9. #23752544C2semidirect
10. #23752251C2semidirect
11. #23752247C2semidirect
12. #23752219C2semidirect
13. #103×D151C2semidirect
15. #483×C151C2semidirect
175. C151#3097semidirect
186. #483D151semidirect

Maximal subgroups

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

subgroupindex
#237527852
#237526932
#237525562
#237525542
#237525512
#237525502
#237525472
#237525462
#237525442
#237522512
#237522472
#237522192
#103×D1512
#237521772
#483×C1512
#3097151