Finite Group Databasebeta

← #34079783

Subgroups — #34079783

Order 19328.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752836C211yesmaximal, characteristic
2#23752825C211yesmaximal, characteristic, complemented
3#23752606C211yesmaximal, characteristic, complemented
4#23752569C211yesmaximal, characteristic, complemented
5#23752564C211yesmaximal, characteristic, complemented
6#23752471C211yesmaximal, characteristic, complemented
7#23752459C211yesmaximal, characteristic
8#23752454C211yesmaximal, characteristic, complemented
9#23752442C211yesmaximal, characteristic
10#23752318C211yesmaximal, characteristic, complemented
11#23752311C211yesmaximal, characteristic, complemented
12#23752306C211yesmaximal, characteristic, complemented
13#23752299C211yesmaximal, characteristic, complemented
14#23752169C211yesmaximal, characteristic, complemented
15#501×C151C211yesmaximal, characteristic, complemented
16C2×Dic604C2211yescharacteristic
17C2×Dic604C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012739C2211yescharacteristic
23#18012734—21no—
24#18012734—21no—
25#18012734—21no—
26#18012730—21no—
27#18012730—21no—
28#18012728—21no—
29#18012727C2211yescharacteristic
30#18012724—21no—
31#18012719C2211yescharacteristic
32#18012719C2211yescharacteristic
33#18012719C2211yescharacteristic
34#18012715—21no—
35#18012714C2211yescharacteristic
36#18012704C2211yescharacteristic
37#18012704C2211yescharacteristic
38#18012704C2211yescharacteristic
39#18012701C2211yescharacteristic
40#18012696C2211yescharacteristic
41#18012662C2211yescharacteristic
42#18012662C2211yescharacteristic
43#18012662C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012649C2211yescharacteristic
50C4×C151⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53#125×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#106×C151C2211yescharacteristic
57#106×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59C2×Dic302C2311yescharacteristic
60C2×Dic302C2311yescharacteristic
61C2×Dic302C2311yescharacteristic
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×C4×D151—21no—
65C2×C4×D151C2311yescharacteristic
66Dic604—22no—
67Dic604—22no—
68#14558993—22no—
69#14558993—22no—
70#14558987—22no—
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C8×D151—22no—
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76C4⋊Dic151—21no—
77C4⋊Dic151—21no—
78C4⋊Dic151—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4D411yescharacteristic
83Dic151⋊C4D411yescharacteristic
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)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4D411yescharacteristic
92(C2×D151)⋊C4D411yescharacteristic
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151—21no—
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110Dic302—21no—
111Dic302—21no—
112Dic302—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—21no—
116D604—21no—
117D604—21no—
118D604—81no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C2×Dic151C2×D411yescharacteristic
125C4×D151—21no—
126C4×D151—21no—
127C4×D151—81no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130Q8×C151—81no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151C2×D411yescharacteristic
136C2×C4×C151C2×D411yescharacteristic
137C2×C4×C151C2411yescharacteristic
138C8×C151#4112yes—
139C8×C151#4112yes—
140C22×C151C22×D411yescharacteristic
141C2×D151—21no—
142C2×D151—21no—
143C2×D151—21no—
144C2×D151—41no—
145C2×D151—41no—
146C2×D151—41no—
147C4×C151—21no—
148C4×C151—21no—
149C4×C151—41no—
150C4×C151—41no—
151C4×C151—41no—
152C4×C151—41no—
153C4×C151C2×#4111yescharacteristic
154C4×C151C2×#4111yescharacteristic
155Dic151—21no—
156Dic151—21no—
157Dic151—21no—
158Dic151—41no—
159Dic151—41no—
160Dic151—41no—
161C2×C151#53211yescharacteristic
162C2×C151#57711yescharacteristic
163C2×C151#57811yescharacteristic
164D151—41no—
165D151—81no—
166C151#317811yescharacteristic, complemented, Sylow
167#3178—1511nomaximal, Sylow
168#542—1511no—
169#541—1511no—
170#501D15111yescharacteristic, complemented
171#497—1511no—
172#488—1511no—
173#487—1511no—
174#470—1511no—
175#468—1511no—
176#467—1511no—
177#465—1511no—
178#441—1511no—
179#440—1511no—
180C4×Q16—1511no—
181C4×SD16—1511no—
182#405—1511no—
183C2×Q16—1511no—
184C2×Q16—1511no—
185C2×SD16—1511no—
186C2×SD16—1511no—
187C2×M16—1511no—
188C22×C8—1511no—
189C4⋊Q8—1511no—
190C4⋊Q8C2×D15111yescharacteristic
191#126—3021no—
192#126—3021no—
193#126—3021no—
194#125—3021no—
195#125—3021no—
196#125C2×D15111yescharacteristic
197#124—3021no—
198#124—1511no—
199#123—3021no—
200C22⋊Q8—3021no—
201C22⋊Q8—1511no—
202C22⋊Q8—1511no—
203C22⋊Q8—1511no—
204#121—1511no—
205C4×Q8—1511no—
206C4×Q8—1511no—
207C4×Q8—1511no—
208C4×D4—1511no—
209#117—1511no—
210#107C2×D15111yescharacteristic
211#107C2×D15111yescharacteristic
212#106C2×D15111yescharacteristic
213#106C2×D15111yescharacteristic
214#103—1511no—
215#103—1511no—
216#103—1511no—
217#103—1511no—
218#103—1511no—
219#103—1511no—
220#102—1511no—
221#102—1511no—
222#97—1511no—
223#97C2×D15111yescharacteristic
224C4×C8—1511no—
225C4×C8—1511no—
226C2×Q8—21no—
227C2×Q8—1511no—
228C2×Q8—1511no—
229C2×Q8—1511no—
230C2×D4—3021no—
231C2×D4—1511no—
232C22×C4—3021no—
233C22×C4—1511no—
234Q16—3022no—
235Q16—3022no—
236SD16—3022no—
237SD16—3022no—
238M16—3022no—
239C2×C8—3022no—
240C2×C8—1511no—
241C2×C8—1511no—
242C2×C8C22×D15111yescharacteristic
243C2×C8C22×D15111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—3021no—
248C4⋊C4—3021no—
249C4⋊C4—3021no—
250C4⋊C4—3021no—
251C4⋊C4—3021no—
252C4⋊C4—3021no—
253C4⋊C4—3021no—
254C4⋊C4—3021no—
255C4⋊C4—1511no—
256C4⋊C4—1511no—
257C4⋊C4C22×D15111yescharacteristic
258C4⋊C4C22×D15111yescharacteristic
259C4⋊C4C22×D15111yescharacteristic
260C4⋊C4C22×D15111yescharacteristic
261C22⋊C4—3021no—
262C22⋊C4—3021no—
263C22⋊C4—3021no—
264C22⋊C4—3021no—
265C22⋊C4—3021no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—1511no—
269C22⋊C4—1511no—
270C42—3021no—
271C42—3021no—
272C42—3021no—
273C42—1511no—
274C42C22×D15111yescharacteristic
275C23—3021no—
276C23—1511no—
277Q8—81no—
278Q8—3021no—
279Q8—3021no—
280Q8—3021no—
281Q8—3021no—
282Q8—3021no—
283Q8—3021no—
284D4—3021no—
285D4—3021no—
286D4—12081no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—3021no—
292C2×C4—3021no—
293C2×C4—3021no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—1511no—
297C2×C4—1511no—
298C2×C4—1511no—
299C2×C4—12081no—
300C2×C4D4×D15111yescharacteristic
301C2×C4D4×D15111yescharacteristic
302C2×C4C23×D15111yescharacteristic
303C8—3021no—
304C8—3021no—
305C8#1455900512yes—
306C8#1455900512yes—
307C22—3021no—
308C22—3021no—
309C22—3021no—
310C22—6041no—
311C22—6041no—
312C22—6041no—
313C22C2×D4×D15111yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—3021no—
321C4—3021no—
322C4—3021no—
323C4—6041no—
324C4—6041no—
325C4—6041no—
326C4C2×#1455900511yescharacteristic
327C4C2×#1455900511yescharacteristic
328C2—6041no—
329C2—12081no—
330C2#2375276311yescharacteristic
331C2#2375302211yescharacteristic
332C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#501×C151C2
socleC22×C151C22×D4
prime radical#18012714C22
hypercenter#501D151
hypocenterC151#3178
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #23752825C2semidirect
3. #23752606C2semidirect
4. #23752569C2semidirect
5. #23752564C2semidirect
6. #23752471C2semidirect
8. #23752454C2semidirect
10. #23752318C2semidirect
11. #23752311C2semidirect
12. #23752306C2semidirect
13. #23752299C2semidirect
14. #23752169C2semidirect
15. #501×C151C2semidirect
166. C151#3178semidirect
170. #501D151semidirect

Maximal subgroups

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

subgroupindex
#237528362
#237528252
#237526062
#237525692
#237525642
#237524712
#237524592
#237524542
#237524422
#237523182
#237523112
#237523062
#237522992
#237521692
#501×C1512
#3178151