Finite Group Databasebeta

← #34079360

Subgroups — #34079360

Order 19328.

394 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#23752823C211yesmaximal, characteristic, complemented
2#23752684C211yesmaximal, characteristic
3#23752552C211yesmaximal, characteristic, complemented
4#23752551C211yesmaximal, characteristic, complemented
5#23752513C211yesmaximal, characteristic, complemented
6#23752512C211yesmaximal, characteristic, complemented
7#23752414C211yesmaximal, characteristic, complemented
8#23752361C211yesmaximal, characteristic
9#23752361C211yesmaximal, characteristic
10#23752315C211yesmaximal, characteristic, complemented
11#23752313C211yesmaximal, characteristic, complemented
12SD16×Dic151C211yesmaximal, characteristic, complemented
13#23752297C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#461×C151C211yesmaximal, characteristic, complemented
16C2×D4×D151C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19#18012734—21no—
20#18012734—21no—
21#18012731C2211yescharacteristic, complemented
22#18012729—21no—
23#18012729—21no—
24#18012715C2211yescharacteristic
25#18012715C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic, complemented
27Q8×Dic151C2211yescharacteristic, complemented
28C4×D604C2211yescharacteristic
29D4×Dic151C2211yescharacteristic
30#18012701C2211yescharacteristic
31C4×C22⋊D151—21no—
32(C22⋊D151)⋊C4—21no—
33#18012697C2211yescharacteristic
34#18012696C2211yescharacteristic
35C2×(C2×D151)⋊C4—21no—
36C22⋊C4×D151—21no—
37#18012673C2211yescharacteristic, complemented
38#18012672C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012663C2211yescharacteristic, complemented
43#18012663C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C2×SD16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C4⋊Q8×C151C2211yescharacteristic, complemented
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic, complemented
57#103×C151C2211yescharacteristic, complemented
58#103×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62D4×D151—22no—
63D4×D151—22no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151C2311yescharacteristic
68#14558991—22no—
69#14558991—22no—
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C4⋊Dic151—21no—
73C4⋊Dic151—21no—
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4D411yescharacteristic
90(C2×D151)⋊C4D411yescharacteristic
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151—21no—
99SD16×C151—22no—
100SD16×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151—21no—
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—24no—
110C22×D151—81no—
111C22×D151—81no—
112C22×D151C2×D411yescharacteristic
113D604—21no—
114D604#4112yes—
115C22⋊D151—24no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—81no—
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C4×D151—21no—
124C4×D151—21no—
125C4×D151—81no—
126C4×D151—81no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151—21no—
130Q8×C151—21no—
131Q8×C151—21no—
132Q8×C151—21no—
133Q8×C151—21no—
134D4×C151—21no—
135D4×C151#4112yes—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—81no—
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×C151C22×D411yescharacteristic
149C2×D151—21no—
150C2×D151—22no—
151C2×D151—21no—
152C2×D151—21no—
153C2×D151—41no—
154C2×D151—41no—
155C2×D151—84no—
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151—41no—
161C4×C151C2×#4111yescharacteristic
162C4×C151C2×#4111yescharacteristic
163Dic151—21no—
164Dic151—21no—
165Dic151—21no—
166Dic151—41no—
167Dic151—41no—
168Dic151—41no—
169C2×C151—42no—
170C2×C151#52511yescharacteristic
171C2×C151#57711yescharacteristic
172C2×C151#57711yescharacteristic
173D151—41no—
174D151—42no—
175C151#312311yescharacteristic, complemented, Sylow
176#3123—1511nomaximal, Sylow
177#541—1511no—
178#518—1511no—
179#485—1511no—
180#485—1511no—
181#478—1511no—
182#478—1511no—
183#461—1511no—
184#461D15111yescharacteristic, complemented
185#450—1511no—
186#450—1511no—
187#440—1511no—
188#440—1511no—
189C4×SD16—1511no—
190C4×SD16—1511no—
191#433—1511no—
192C22×D4—1511no—
193C2×SD16—1511no—
194C2×SD16—1511no—
195C2×SD16C2×D15111yescharacteristic
196C2×SD16C2×D15111yescharacteristic
197C4⋊Q8C2×D15111yescharacteristic, complemented
198#126—3021no—
199#126—3021no—
200#125—3021no—
201#125—3021no—
202#125—1511no—
203C22⋊Q8—1511no—
204C22⋊Q8—1511no—
205C4×Q8—1511no—
206C4×Q8—1511no—
207C4×D4—3021no—
208C4×D4—3021no—
209C4×D4—1511no—
210C4×D4—1511no—
211C4×D4—1511no—
212C4×D4C2×D15111yescharacteristic
213#117—1511no—
214#117—1511no—
215C2×C22⋊C4—3021no—
216C2×C22⋊C4—3021no—
217#107—1511no—
218#107—1511no—
219#106—1511no—
220#106—1511no—
221C4⋊C8—1511no—
222C4⋊C8C2×D15111yescharacteristic, complemented
223#103—1511no—
224#103—1511no—
225#103C2×D15111yescharacteristic, complemented
226#103C2×D15111yescharacteristic, complemented
227#102—1511no—
228#102—1511no—
229#102—1511no—
230#102—1511no—
231C22⋊C8—1511no—
232C22⋊C8—1511no—
233#97—1511no—
234C4×C8—1511no—
235C24—3021no—
236C2×Q8C22×D15111yescharacteristic
237C2×Q8C22×D15111yescharacteristic
238C2×D4—3022no—
239C2×D4—3022no—
240C2×D4—3021no—
241C2×D4—1511no—
242C2×D4C22×D15111yescharacteristic
243C22×C4—21no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—3021no—
247C22×C4—1511no—
248SD16—22no—
249SD16—22no—
250SD16—3022no—
251SD16—3022no—
252C2×C8—1511no—
253C2×C8—1511no—
254C2×C8C22×D15111yescharacteristic
255C2×C8C22×D15111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—3021no—
264C4⋊C4—1511no—
265C4⋊C4—1511no—
266C4⋊C4—1511no—
267C4⋊C4—1511no—
268C4⋊C4—1511no—
269C4⋊C4C22×D15111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C22⋊C4—1511no—
278C22⋊C4—1511no—
279C42—3021no—
280C42—3021no—
281C42—3021no—
282C42—1511no—
283C42C22×D15111yescharacteristic
284C23—21no—
285C23—3024no—
286C23—3021no—
287C23—1511no—
288C23—12081no—
289C23—12081no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—3024no—
296D4—3021no—
297D4—1512no—
298D4#1455900312yes—
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—1511no—
309C2×C4—1511no—
310C2×C4—1511no—
311C2×C4—12081no—
312C2×C4—12081no—
313C2×C4—12081no—
314C2×C4D4×D15111yescharacteristic
315C2×C4D4×D15111yescharacteristic
316C2×C4C23×D15111yescharacteristic
317C8—21no—
318C8—21no—
319C8—3021no—
320C8—3021no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—3021no—
325C22—3022no—
326C22—3021no—
327C22—3021no—
328C22—6041no—
329C22—6041no—
330C22—12084no—
331C22C2×D4×D15111yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3021no—
338C4—3021no—
339C4—3021no—
340C4—6041no—
341C4—6041no—
342C4—6041no—
343C4#41×D15111yescharacteristic
344C4C2×#1455900311yescharacteristic
345C2—42no—
346C2—6041no—
347C2—6042no—
348C2#2375272211yescharacteristic
349C2#2375301811yescharacteristic
350C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#461×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
hypercenter#461D151
hypocenterC151#3123
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #23752823C2semidirect
3. #23752552C2semidirect
4. #23752551C2semidirect
5. #23752513C2semidirect
6. #23752512C2semidirect
7. #23752414C2semidirect
10. #23752315C2semidirect
11. #23752313C2semidirect
12. SD16×Dic151C2semidirect
13. #23752297C2semidirect
14. #23752272C2semidirect
15. #461×C151C2semidirect
21. #18012731C22semidirect
26. Q8×Dic151C22semidirect
27. Q8×Dic151C22semidirect
37. #18012673C22semidirect
38. #18012672C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012663C22semidirect
43. #18012663C22semidirect
50. #18012649C22semidirect
51. C8×Dic151C22semidirect
54. C4⋊Q8×C151C22semidirect
56. C4⋊C8×C151C22semidirect
57. #103×C151C22semidirect
58. #103×C151C22semidirect
175. C151#3123semidirect
184. #461D151semidirect
197. C4⋊Q8C2×D151semidirect
222. C4⋊C8C2×D151semidirect
225. #103C2×D151semidirect
226. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528232
#237526842
#237525522
#237525512
#237525132
#237525122
#237524142
#237523612
#237523152
#237523132
SD16×Dic1512
#237522972
#237522722
#461×C1512
#3123151