Finite Group Databasebeta

← #34079366

Subgroups — #34079366

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#23752692C211yesmaximal, characteristic, complemented
2#23752545C211yesmaximal, characteristic, complemented
3#23752523C211yesmaximal, characteristic, complemented
4#23752504C211yesmaximal, characteristic, complemented
5#23752489C211yesmaximal, characteristic, complemented
6#23752431C211yesmaximal, characteristic, complemented
7#23752424C211yesmaximal, characteristic, complemented
8#23752372C211yesmaximal, characteristic, complemented
9#23752355C211yesmaximal, characteristic
10#23752312C211yesmaximal, characteristic, complemented
11#23752310C211yesmaximal, characteristic, complemented
12C4×#14558994C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14#23752273C211yesmaximal, characteristic, complemented
15#542×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C4×Dic302C2211yescharacteristic
22C4×Dic302C2211yescharacteristic
23C4×D604C2211yescharacteristic
24C4×D604C2211yescharacteristic
25(C22⋊D151)⋊C4—21no—
26(C22⋊D151)⋊C4—21no—
27#18012697—21no—
28C2×C4⋊Dic151C2211yescharacteristic
29C4⋊C4×D151—21no—
30#18012672C2211yescharacteristic
31#18012672C2211yescharacteristic
32#18012672C2211yescharacteristic
33#18012672C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35C4⋊(C151⋊C8)C2211yescharacteristic
36#18012663C2211yescharacteristic
37#18012663C2211yescharacteristic
38#18012662C2211yescharacteristic
39#18012662C2211yescharacteristic
40#18012660C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46#18012650C2211yescharacteristic
47C4×C151⋊C8C2211yescharacteristic
48C4⋊Q8×C151C2211yescharacteristic
49#126×C151—21no—
50#124×C151—21no—
51#124×C151C2211yescharacteristic
52#123×C151—21no—
53C22⋊Q8×C151—21no—
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56C4×Q8×C151C2211yescharacteristic
57C4×D4×C151C2211yescharacteristic
58#117×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—22no—
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68#14558994—22no—
69#14558992—22no—
70#14558991—22no—
71#14558989—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81(C2×D151)⋊C4—21no—
82(C2×D151)⋊C4—21no—
83C4×Dic151—21no—
84C4×Dic151—21no—
85C2×Q8×C151—21no—
86C2×Q8×C151C2311yescharacteristic
87C2×D4×C151—21no—
88C2×D4×C151C2311yescharacteristic
89C22×C4×C151—21no—
90C22×C4×C151C2311yescharacteristic
91C4⋊C4×C151—21no—
92C4⋊C4×C151—21no—
93C4⋊C4×C151—21no—
94C4⋊C4×C151D411yescharacteristic
95C4⋊C4×C151D411yescharacteristic
96C4⋊C4×C151C2311yescharacteristic
97C4⋊C4×C151C2311yescharacteristic
98C22⋊C4×C151—21no—
99C22⋊C4×C151—21no—
100C22⋊C4×C151—21no—
101C22⋊C4×C151—21no—
102C22⋊C4×C151—21no—
103C22⋊C4×C151D411yescharacteristic
104C22⋊C4×C151D411yescharacteristic
105C42×C151—21no—
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109Dic302—21no—
110Dic302#4112yes—
111D604—21no—
112D604#4112yes—
113C22⋊D151—24no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—81no—
118C4×D151—24no—
119C4×D151—81no—
120C4×D151—81no—
121C151⋊C8—21no—
122C151⋊C8—21no—
123C151⋊C8—21no—
124C151⋊C8—21no—
125C23×C151—21no—
126C23×C151C2×D411yescharacteristic
127Q8×C151—21no—
128Q8×C151—21no—
129Q8×C151—81no—
130D4×C151—21no—
131D4×C151—21no—
132D4×C151—81no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—81no—
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2411yescharacteristic
145C22×C151—21no—
146C22×C151—21no—
147C22×C151—21no—
148C22×C151—41no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151C22×D411yescharacteristic
152C2×D151—22no—
153C2×D151—41no—
154C2×D151—41no—
155C4×C151—21no—
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—21no—
159C4×C151—21no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151C2×#4111yescharacteristic
164C4×C151C2×#4111yescharacteristic
165Dic151—22no—
166Dic151—41no—
167Dic151—41no—
168C2×C151—41no—
169C2×C151—81no—
170C2×C151#52511yescharacteristic
171C2×C151#57611yescharacteristic
172C2×C151#57811yescharacteristic
173D151—42no—
174C151#312411yescharacteristic, complemented, Sylow
175#3124—1511nomaximal, Sylow
176#542D15111yescharacteristic, complemented
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#433—1511no—
191C2×#41—1511no—
192C2×Q16—1511no—
193C2×SD16—1511no—
194C2×SD16—1511no—
195C2×D8—1511no—
196C4⋊Q8C2×D15111yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D15111yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D15111yescharacteristic
203#121C2×D15111yescharacteristic
204C4×Q8—1511no—
205C4×Q8—1511no—
206C4×Q8C2×D15111yescharacteristic
207C4×D4—3021no—
208C4×D4—3021no—
209C4×D4—1511no—
210C4×D4—1511no—
211C4×D4C2×D15111yescharacteristic
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⋊C8—1511no—
221C4⋊C8—1511no—
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⋊C8—1511no—
231C22⋊C8—1511no—
232#97—1511no—
233C4×C8—1511no—
234#41—3022no—
235#41—3022no—
236C2×Q8—21no—
237C2×Q8—1511no—
238C2×Q8C22×D15111yescharacteristic
239C2×D4—21no—
240C2×D4—3021no—
241C2×D4—1511no—
242C2×D4C22×D15111yescharacteristic
243C22×C4—21no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—3021no—
247C22×C4—3021no—
248C22×C4C22×D15111yescharacteristic
249Q16—3022no—
250SD16—3022no—
251SD16—3022no—
252D8—3022no—
253C2×C8—1511no—
254C2×C8—1511no—
255C2×C8—1511no—
256C2×C8—1511no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—1511no—
264C4⋊C4—1511no—
265C4⋊C4C22⋊D15111yescharacteristic
266C4⋊C4C22⋊D15111yescharacteristic
267C4⋊C4C22×D15111yescharacteristic
268C4⋊C4C22×D15111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4C22⋊D15111yescharacteristic
277C22⋊C4C22⋊D15111yescharacteristic
278C42—21no—
279C42—3021no—
280C42—3021no—
281C42C22×D15111yescharacteristic
282C42C22×D15111yescharacteristic
283C23—21no—
284C23—3021no—
285C23C2×C22⋊D15111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—3021no—
290Q8—1512no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—3024no—
295D4—3021no—
296D4—1512no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—3024no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—3021no—
307C2×C4—12081no—
308C2×C4—12081no—
309C2×C4—12081no—
310C2×C4C2×C22⋊D15111yescharacteristic
311C2×C4C2×C22⋊D15111yescharacteristic
312C2×C4C2×C22⋊D15111yescharacteristic
313C2×C4C2×C22⋊D15111yescharacteristic
314C2×C4C2×C22⋊D15111yescharacteristic
315C2×C4C23×D15111yescharacteristic
316C8—3021no—
317C8—3021no—
318C8—3021no—
319C8—3021no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—3022no—
327C22—6041no—
328C22—6041no—
329C22C22×C22⋊D15111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—3022no—
339C4—6041no—
340C4—6041no—
341C4#41×D15111yescharacteristic
342C4#41×D15111yescharacteristic
343C2—41no—
344C2—81no—
345C2—6042no—
346C2#2375271911yescharacteristic
347C2#2375301511yescharacteristic
348C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#542×C151C2
socleC22×C151C22×D4
prime radical#23752355C2
hypercenter#542D151
hypocenterC151#3124
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #23752692C2semidirect
2. #23752545C2semidirect
3. #23752523C2semidirect
4. #23752504C2semidirect
5. #23752489C2semidirect
6. #23752431C2semidirect
7. #23752424C2semidirect
8. #23752372C2semidirect
10. #23752312C2semidirect
11. #23752310C2semidirect
12. C4×#14558994C2semidirect
13. C4×#14558989C2semidirect
14. #23752273C2semidirect
15. #542×C151C2semidirect
174. C151#3124semidirect
176. #542D151semidirect

Maximal subgroups

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

subgroupindex
#237526922
#237525452
#237525232
#237525042
#237524892
#237524312
#237524242
#237523722
#237523552
#237523122
#237523102
C4×#145589942
C4×#145589892
#237522732
#542×C1512
#3124151