Finite Group Databasebeta

← #34079326

Subgroups — #34079326

Order 19328.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752824C211yesmaximal, characteristic, complemented
2#23752692C211yesmaximal, characteristic
3#23752548C211yesmaximal, characteristic, complemented
4#23752543C211yesmaximal, characteristic, complemented
5#23752520C211yesmaximal, characteristic, complemented
6#23752513C211yesmaximal, characteristic, complemented
7#23752423C211yesmaximal, characteristic, complemented
8#23752418C211yesmaximal, characteristic, complemented
9#23752376C211yesmaximal, characteristic
10#23752376C211yesmaximal, characteristic
11#23752320C211yesmaximal, characteristic, complemented
12#23752314C211yesmaximal, characteristic, complemented
13C4×Dic604C211yesmaximal, characteristic, complemented
14C4×#14558993C211yesmaximal, characteristic, complemented
15#433×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Dic604C2211yescharacteristic
18C2×Dic604C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21#18012739C2211yescharacteristic
22#18012732—21no—
23#18012732—21no—
24#18012731C2211yescharacteristic
25#18012729—21no—
26#18012729—21no—
27#18012718C2211yescharacteristic
28#18012718C2211yescharacteristic
29C4×Dic302C2211yescharacteristic
30C4×Dic302C2211yescharacteristic
31C4×Dic302C2211yescharacteristic
32C4×Dic302C2211yescharacteristic
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#18012671C2211yescharacteristic
43#18012671C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012664C2211yescharacteristic
49#18012664C2211yescharacteristic
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×Dic302C2311yescharacteristic
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C22×Dic151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70Dic604—22no—
71Dic604—22no—
72#14558993—22no—
73#14558993—22no—
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—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—
109Dic302—21no—
110Dic302—21no—
111Dic302—21no—
112Dic302—21no—
113Dic302—21no—
114Dic302#4112yes—
115D604—21no—
116D604#4112yes—
117C22⋊D151—24no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—81no—
126C4×D151—24no—
127C4×D151—81no—
128C4×D151—81no—
129C23×C151C2×D411yescharacteristic
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151C2×D411yescharacteristic
133C2×C4×C151C2×D411yescharacteristic
134C2×C4×C151C2×D411yescharacteristic
135C2×C4×C151C2×D411yescharacteristic
136C2×C4×C151C2×D411yescharacteristic
137C2×C4×C151C2411yescharacteristic
138C8×C151—21no—
139C8×C151—21no—
140C8×C151—21no—
141C8×C151—21no—
142C22×C151—21no—
143C22×C151—21no—
144C22×C151—21no—
145C22×C151C22×D411yescharacteristic
146C2×D151—22no—
147C2×D151—41no—
148C2×D151—41no—
149C4×C151—21no—
150C4×C151—21no—
151C4×C151—21no—
152C4×C151—21no—
153C4×C151—21no—
154C4×C151C2×#4111yescharacteristic
155C4×C151C2×#4111yescharacteristic
156Dic151—22no—
157Dic151—41no—
158Dic151—41no—
159Dic151—41no—
160Dic151—41no—
161Dic151—41no—
162Dic151—41no—
163C2×C151—41no—
164C2×C151#52511yescharacteristic
165C2×C151#57711yescharacteristic
166C2×C151#57811yescharacteristic
167D151—42no—
168C151#312011yescharacteristic, complemented, Sylow
169#3120—1511nomaximal, Sylow
170#541—1511no—
171#520—1511no—
172#484—1511no—
173#483—1511no—
174#479—1511no—
175#478—1511no—
176#462—1511no—
177#461—1511no—
178#452—1511no—
179#452—1511no—
180#441—1511no—
181#440—1511no—
182C4×Q16—1511no—
183C4×SD16—1511no—
184#433D15111yescharacteristic, complemented
185C2×#41—1511no—
186C2×Q16—1511no—
187C2×Q16—1511no—
188C2×SD16—1511no—
189C2×SD16—1511no—
190C4⋊Q8—1511no—
191#126—3021no—
192#126—3021no—
193#125—3021no—
194#125—3021no—
195#125—1511no—
196C22⋊Q8—1511no—
197C22⋊Q8—1511no—
198C4×Q8—1511no—
199C4×Q8—1511no—
200C4×Q8—1511no—
201C4×Q8—1511no—
202C4×D4—3021no—
203C4×D4—3021no—
204C4×D4—1511no—
205C4×D4—1511no—
206#117—3021no—
207#117C2×D15111yescharacteristic
208C2×C4⋊C4—3021no—
209C2×C4⋊C4—1511no—
210#107—1511no—
211#107—1511no—
212#106—1511no—
213#106—1511no—
214C4⋊C8C2×D15111yescharacteristic
215C4⋊C8C2×D15111yescharacteristic
216#103—1511no—
217#103—1511no—
218#103—1511no—
219#103—1511no—
220#103—1511no—
221#103—1511no—
222#102—1511no—
223#102—1511no—
224C22⋊C8C2×D15111yescharacteristic
225C22⋊C8C2×D15111yescharacteristic
226#97C2×D15111yescharacteristic
227C4×C8C2×D15111yescharacteristic
228#41—3022no—
229#41—3022no—
230C2×Q8—1511no—
231C2×Q8—1511no—
232C2×Q8—1511no—
233C2×D4—3021no—
234C2×D4—1511no—
235C22×C4—3021no—
236C22×C4—3021no—
237C22×C4—3021no—
238C22×C4—3021no—
239C22×C4C22×D15111yescharacteristic
240Q16—3022no—
241Q16—3022no—
242SD16—3022no—
243SD16—3022no—
244C2×C8C22×D15111yescharacteristic
245C2×C8C22×D15111yescharacteristic
246C2×C8C22×D15111yescharacteristic
247C2×C8C22×D15111yescharacteristic
248C4⋊C4—3021no—
249C4⋊C4—3021no—
250C4⋊C4—3021no—
251C4⋊C4—3021no—
252C4⋊C4—3021no—
253C4⋊C4—3021no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—1511no—
260C4⋊C4—1511no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4D60411yescharacteristic
264C4⋊C4D60411yescharacteristic
265C22⋊C4—3021no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4D60411yescharacteristic
270C22⋊C4D60411yescharacteristic
271C42—3021no—
272C42—3021no—
273C42—3021no—
274C42—3021no—
275C42C22×D15111yescharacteristic
276C42C22×D15111yescharacteristic
277C23—3021no—
278C23C2×D60411yescharacteristic
279Q8—3021no—
280Q8—3021no—
281Q8—3021no—
282Q8—3021no—
283Q8—3021no—
284Q8—1512no—
285D4—3024no—
286D4—3021no—
287D4—1512no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—3024no—
291C2×C4—3021no—
292C2×C4—3021no—
293C2×C4—3021no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—12081no—
299C2×C4—12081no—
300C2×C4—12081no—
301C2×C4C2×D60411yescharacteristic
302C2×C4C2×D60411yescharacteristic
303C2×C4C2×D60411yescharacteristic
304C2×C4C2×D60411yescharacteristic
305C2×C4C2×D60411yescharacteristic
306C2×C4C23×D15111yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—3022no—
315C22—6041no—
316C22—6041no—
317C22C22×D60411yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—3022no—
324C4—6041no—
325C4—6041no—
326C4—6041no—
327C4—6041no—
328C4—6041no—
329C4—6041no—
330C4#41×D15111yescharacteristic
331C4#41×D15111yescharacteristic
332C2—41no—
333C2—6042no—
334C2#2375272411yescharacteristic
335C2#2375302411yescharacteristic
336C2#2375302911yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559004C22
hypercenter#433D151
hypocenterC151#3120
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. #23752824C2semidirect
3. #23752548C2semidirect
4. #23752543C2semidirect
5. #23752520C2semidirect
6. #23752513C2semidirect
7. #23752423C2semidirect
8. #23752418C2semidirect
11. #23752320C2semidirect
12. #23752314C2semidirect
13. C4×Dic604C2semidirect
14. C4×#14558993C2semidirect
15. #433×C151C2semidirect
168. C151#3120semidirect
184. #433D151semidirect

Maximal subgroups

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

subgroupindex
#237528242
#237526922
#237525482
#237525432
#237525202
#237525132
#237524232
#237524182
#237523762
#237523202
#237523142
C4×Dic6042
C4×#145589932
#433×C1512
#3120151