Finite Group Databasebeta

← #34079374

Subgroups — #34079374

Order 19328.

384 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#23752833C211yesmaximal, characteristic, complemented
2#23752692C211yesmaximal, characteristic, complemented
3#23752548C211yesmaximal, characteristic, complemented
4#23752526C211yesmaximal, characteristic, complemented
5#23752508C211yesmaximal, characteristic, complemented
6#23752493C211yesmaximal, characteristic, complemented
7#23752435C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752376C211yesmaximal, characteristic, complemented
10#23752359C211yesmaximal, characteristic
11#23752314C211yesmaximal, characteristic, complemented
12#23752314C211yesmaximal, characteristic, complemented
13C4×Dic604C211yesmaximal, characteristic, complemented
14C4×D1208C211yesmaximal, characteristic, complemented
15#433×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Dic604C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21#18012739C2211yescharacteristic
22#18012734—21no—
23#18012727C2211yescharacteristic
24#18012725—21no—
25#18012721—21no—
26#18012718C2211yescharacteristic
27#18012717—21no—
28#18012713C2211yescharacteristic
29C4×Dic302C2211yescharacteristic
30C4×Dic302C2211yescharacteristic
31C4×Dic302C2211yescharacteristic
32C4×D604C2211yescharacteristic
33C4×D604C2211yescharacteristic
34C4×D604C2211yescharacteristic
35(C22⋊D151)⋊C4—21no—
36(C22⋊D151)⋊C4—21no—
37#18012697—21no—
38C2×C4⋊Dic151C2211yescharacteristic
39C4⋊C4×D151—21no—
40#18012673C2211yescharacteristic
41#18012673C2211yescharacteristic
42#18012673C2211yescharacteristic
43#18012673C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52#117×C151C2211yescharacteristic
53C4⋊C8×C151C2211yescharacteristic
54C4⋊C8×C151C2211yescharacteristic
55C22⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57#97×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—22no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C22×Dic151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73Dic604—22no—
74#14558993—22no—
75#14558993—22no—
76D1208—22no—
77C4⋊Dic151—21no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—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—
93(C2×D151)⋊C4—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C22×C4×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151D411yescharacteristic
103C4⋊C4×C151D411yescharacteristic
104C22⋊C4×C151D411yescharacteristic
105C22⋊C4×C151D411yescharacteristic
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110Dic302—21no—
111Dic302—21no—
112Dic302—21no—
113Dic302—81no—
114Dic302#4112yes—
115D604—21no—
116D604—21no—
117D604—21no—
118D604#4112yes—
119C22⋊D151—24no—
120C22⋊D151—81no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—81no—
128C4×D151—24no—
129C4×D151—81no—
130C4×D151—81no—
131C4×D151—81no—
132C23×C151C2×D411yescharacteristic
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151C2×D411yescharacteristic
136C2×C4×C151C2×D411yescharacteristic
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2411yescharacteristic
141C8×C151—21no—
142C8×C151—21no—
143C8×C151—21no—
144C8×C151—21no—
145C22×C151—21no—
146C22×C151—21no—
147C22×C151—21no—
148C22×C151C22×D411yescharacteristic
149C2×D151—22no—
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
153C2×D151—41no—
154C2×D151—41no—
155C4×C151—21no—
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—21no—
159C4×C151—21no—
160C4×C151C2×#4111yescharacteristic
161C4×C151C2×#4111yescharacteristic
162Dic151—22no—
163Dic151—41no—
164Dic151—41no—
165Dic151—41no—
166Dic151—41no—
167Dic151—41no—
168C2×C151—41no—
169C2×C151#52511yescharacteristic
170C2×C151#57611yescharacteristic
171C2×C151#57811yescharacteristic
172D151—42no—
173D151—81no—
174C151#312411yescharacteristic, complemented, Sylow
175#3124—1511nomaximal, Sylow
176#542—1511no—
177#520—1511no—
178#484—1511no—
179#480—1511no—
180#477—1511no—
181#474—1511no—
182#464—1511no—
183#463—1511no—
184#452—1511no—
185#449—1511no—
186#440—1511no—
187#440—1511no—
188C4×Q16—1511no—
189C4×D8—1511no—
190#433D15111yescharacteristic, complemented
191C2×#41—1511no—
192C2×Q16—1511no—
193C2×SD16—1511no—
194C2×SD16—1511no—
195C2×D8—1511no—
196C4⋊Q8—1511no—
197#126—3021no—
198#124—3021no—
199#124—1511no—
200#123—3021no—
201C22⋊Q8—3021no—
202C22⋊Q8—1511no—
203#121—1511no—
204C4×Q8—1511no—
205C4×Q8—1511no—
206C4×Q8—1511no—
207C4×D4—3021no—
208C4×D4—3021no—
209C4×D4—1511no—
210C4×D4—1511no—
211C4×D4—1511no—
212#117—3021no—
213#117C2×D15111yescharacteristic
214C2×C4⋊C4—3021no—
215C2×C4⋊C4—1511no—
216#107—1511no—
217#107—1511no—
218#107—1511no—
219#107—1511no—
220C4⋊C8C2×D15111yescharacteristic
221C4⋊C8C2×D15111yescharacteristic
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⋊C8C2×D15111yescharacteristic
231C22⋊C8C2×D15111yescharacteristic
232#97C2×D15111yescharacteristic
233C4×C8C2×D15111yescharacteristic
234#41—3022no—
235#41—3022no—
236C2×Q8—3021no—
237C2×Q8—1511no—
238C2×Q8—1511no—
239C2×D4—3021no—
240C2×D4—3021no—
241C2×D4—1511no—
242C2×D4—1511no—
243C22×C4—3021no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—3021no—
247C22×C4—3021no—
248C22×C4C22×D15111yescharacteristic
249Q16—3022no—
250SD16—3022no—
251SD16—3022no—
252D8—3022no—
253C2×C8C22×D15111yescharacteristic
254C2×C8C22×D15111yescharacteristic
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⋊C4—1511no—
267C4⋊C4D60411yescharacteristic
268C4⋊C4D60411yescharacteristic
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4D60411yescharacteristic
277C22⋊C4D60411yescharacteristic
278C42—3021no—
279C42—3021no—
280C42—3021no—
281C42C22×D15111yescharacteristic
282C42C22×D15111yescharacteristic
283C23—3021no—
284C23—3021no—
285C23C2×D60411yescharacteristic
286Q8—3021no—
287Q8—3021no—
288Q8—3021no—
289Q8—1512no—
290Q8—12081no—
291D4—3024no—
292D4—3021no—
293D4—3021no—
294D4—3021no—
295D4—1512no—
296D4—12081no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—3024no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—12081no—
307C2×C4—12081no—
308C2×C4—12081no—
309C2×C4—12081no—
310C2×C4C2×D60411yescharacteristic
311C2×C4C2×D60411yescharacteristic
312C2×C4C2×D60411yescharacteristic
313C2×C4C2×D60411yescharacteristic
314C2×C4C2×D60411yescharacteristic
315C2×C4C23×D15111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—3022no—
324C22—6041no—
325C22—6041no—
326C22—6041no—
327C22—6041no—
328C22—6041no—
329C22C22×D60411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—3022no—
336C4—6041no—
337C4—6041no—
338C4—6041no—
339C4—6041no—
340C4—6041no—
341C4#41×D15111yescharacteristic
342C4#41×D15111yescharacteristic
343C2—41no—
344C2—6042no—
345C2—12081no—
346C2#2375272411yescharacteristic
347C2#2375301711yescharacteristic
348C2#2375302911yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
prime radical#23752359C2
hypercenter#433D151
hypocenterC151#3124
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23752833C2semidirect
2. #23752692C2semidirect
3. #23752548C2semidirect
4. #23752526C2semidirect
5. #23752508C2semidirect
6. #23752493C2semidirect
7. #23752435C2semidirect
8. #23752428C2semidirect
9. #23752376C2semidirect
11. #23752314C2semidirect
12. #23752314C2semidirect
13. C4×Dic604C2semidirect
14. C4×D1208C2semidirect
15. #433×C151C2semidirect
174. C151#3124semidirect
190. #433D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237526922
#237525482
#237525262
#237525082
#237524932
#237524352
#237524282
#237523762
#237523592
#237523142
C4×Dic6042
C4×D12082
#433×C1512
#3124151