Finite Group Databasebeta

← #34082183

Subgroups — #34082183

Order 19328.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752945C211yesmaximal, characteristic, complemented
2#23752936C211yesmaximal, characteristic, complemented
3#23752604C211yesmaximal, characteristic, complemented
4#23752598C211yesmaximal, characteristic
5#23752593C211yesmaximal, characteristic, complemented
6#23752437C211yesmaximal, characteristic, complemented
7#23752432C211yesmaximal, characteristic, complemented
8#23752430C211yesmaximal, characteristic, complemented
9#23752428C211yesmaximal, characteristic, complemented
10#23752410C211yesmaximal, characteristic, complemented
11#23752341C211yesmaximal, characteristic, complemented
12#23752322C211yesmaximal, characteristic, complemented
13#23752316C211yesmaximal, characteristic, complemented
14#23752297C211yesmaximal, characteristic, complemented
15#461×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21C2×D1208C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23#18012735C2211yescharacteristic
24#18012734—21no—
25#18012734—21no—
26#18012728C2211yescharacteristic
27#18012728C2211yescharacteristic
28#18012727C2211yescharacteristic
29#18012726C2211yescharacteristic
30#18012725—21no—
31#18012722—21no—
32#18012721—21no—
33#18012719—21no—
34Q8×Dic151C2211yescharacteristic
35Q8×Dic151C2211yescharacteristic
36C4×Dic302C2211yescharacteristic
37#18012704C2211yescharacteristic
38C4×D604C2211yescharacteristic
39#18012701C2211yescharacteristic
40C4×C22⋊D151—21no—
41#18012697—21no—
42#18012670C2211yescharacteristic
43Dic151⋊C8C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012650C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C4⋊Q8×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59C2×Dic302D411yescharacteristic
60C2×Dic302C2311yescharacteristic
61C2×D604C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67#14558994—22no—
68#14558994—41no—
69#14558993—41no—
70#14558991—22no—
71#14558991—41no—
72D1208—41no—
73#14558989—22no—
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151—21no—
77C4⋊Dic151—21no—
78C4⋊Dic151D411yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84C22⋊Dic151—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)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C4×Dic151C2311yescharacteristic
98C2×Q8×C151C2311yescharacteristic
99C2×Q8×C151C2311yescharacteristic
100C2×D4×C151C2311yescharacteristic
101C22×C4×C151—21no—
102SD16×C151—41no—
103SD16×C151—41no—
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112C22×D151—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—41no—
116D604—21no—
117D604—21no—
118D604—21no—
119D604—21no—
120C22⋊D151—42no—
121C22⋊D151—81no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C4×D151—42no—
129C4×D151—81no—
130C151⋊C8—21no—
131C151⋊C8#4112yes—
132C23×C151—21no—
133Q8×C151—21no—
134Q8×C151—21no—
135Q8×C151—21no—
136Q8×C151—21no—
137D4×C151—21no—
138D4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—81no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2411yescharacteristic
146C8×C151—21no—
147C8×C151—21no—
148C22×C151—41no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151C22×D411yescharacteristic
152C2×D151—41no—
153C2×D151—41no—
154C2×D151—41no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C4×C151—21no—
159C4×C151—21no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151C2×#4111yescharacteristic
164C4×C151H(5,𝔽2)11yescharacteristic
165Dic151—21no—
166Dic151—21no—
167Dic151—21no—
168Dic151—21no—
169Dic151—41no—
170Dic151—41no—
171C2×C151—81no—
172C2×C151#55011yescharacteristic
173C2×C151#57511yescharacteristic
174C2×C151#57711yescharacteristic
175D151—81no—
176D151—81no—
177C151#340111yescharacteristic, complemented, Sylow
178#3401—1511nomaximal, Sylow
179#559—1511no—
180#556—1511no—
181#497—1511no—
182#496—1511no—
183#495—1511no—
184#464—1511no—
185#464—1511no—
186#463—1511no—
187#463—1511no—
188#461D15111yescharacteristic, complemented
189#460—1511no—
190#446—1511no—
191#442—1511no—
192#441—1511no—
193C4×SD16—1511no—
194C2×Q16—1511no—
195C2×Q16—1511no—
196C2×SD16—1511no—
197C2×SD16—1511no—
198C2×SD16—1511no—
199C2×SD16C2×D15111yescharacteristic
200C2×SD16C2×D15111yescharacteristic
201C2×D8—1511no—
202C2×D8—1511no—
203C4⋊Q8C2×D15111yescharacteristic
204#127—1511no—
205#126—3021no—
206#126—3021no—
207#124—3021no—
208#124—1511no—
209#124—1511no—
210#124—1511no—
211#124—1511no—
212#123—3021no—
213#123—3021no—
214C22⋊Q8—3021no—
215C4×Q8—1511no—
216C4×Q8—1511no—
217C4×Q8—1511no—
218C4×Q8—1511no—
219C4×D4—3021no—
220C4×D4—1511no—
221C4×D4—1511no—
222C4×D4C2×D15111yescharacteristic
223#117—3021no—
224#106—1511no—
225C4⋊C8—1511no—
226C4⋊C8—1511no—
227C4⋊C8C2×D15111yescharacteristic
228#103—1511no—
229#103C2×D15111yescharacteristic
230#103C2×D15111yescharacteristic
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#97—1511no—
235#97—1511no—
236C4×C8—1511no—
237C2×Q8—1511no—
238C2×Q8—1511no—
239C2×Q8C22×D15111yescharacteristic
240C2×Q8C22×D15111yescharacteristic
241C2×D4—3021no—
242C2×D4—3021no—
243C2×D4—1511no—
244C2×D4—1511no—
245C2×D4C22×D15111yescharacteristic
246C22×C4—21no—
247C22×C4—3021no—
248C22×C4—3021no—
249Q16—3022no—
250Q16—6041no—
251SD16—41no—
252SD16—41no—
253SD16—3022no—
254SD16—6041no—
255SD16—6041no—
256D8—3022no—
257D8—6041no—
258C2×C8—1511no—
259C2×C8—1511no—
260C2×C8C22×D15111yescharacteristic
261C2×C8C22×D15111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—3021no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—1511no—
268C4⋊C4—1511no—
269C4⋊C4—1511no—
270C4⋊C4—1511no—
271C4⋊C4C22×D15111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C42—3021no—
284C42—3021no—
285C42—3021no—
286C42—1511no—
287C42—1511no—
288C42C22×D15111yescharacteristic
289C23—21no—
290C23—3021no—
291C23—3021no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—3021no—
297Q8—3021no—
298Q8—6041no—
299D4—21no—
300D4—21no—
301D4—3021no—
302D4—3021no—
303D4—3021no—
304D4—3021no—
305D4—6042no—
306D4—12081no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—6042no—
314C2×C4—1511no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—1511no—
318C2×C4—12081no—
319C2×C4D4×D15111yescharacteristic
320C2×C4D4×D15111yescharacteristic
321C2×C4C23×D15111yescharacteristic
322C8—21no—
323C8—21no—
324C8—3021no—
325C8—1512no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—6041no—
330C22—6041no—
331C22—6041no—
332C22—6041no—
333C22—6041no—
334C22—6041no—
335C22C2×D4×D15111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—3021no—
342C4—3021no—
343C4—3021no—
344C4—3021no—
345C4—6041no—
346C4—6041no—
347C4#41×D15111yescharacteristic
348C4#1801278411yescharacteristic
349C2—81no—
350C2—12081no—
351C2—12081no—
352C2#2375288011yescharacteristic
353C2#2375301111yescharacteristic
354C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#461×C151C2
socleC22×C151C22×D4
prime radical#23752598C2
hypercenter#461D151
hypocenterC151#3401
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. #23752945C2semidirect
2. #23752936C2semidirect
3. #23752604C2semidirect
5. #23752593C2semidirect
6. #23752437C2semidirect
7. #23752432C2semidirect
8. #23752430C2semidirect
9. #23752428C2semidirect
10. #23752410C2semidirect
11. #23752341C2semidirect
12. #23752322C2semidirect
13. #23752316C2semidirect
14. #23752297C2semidirect
15. #461×C151C2semidirect
177. C151#3401semidirect
188. #461D151semidirect

Maximal subgroups

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

subgroupindex
#237529452
#237529362
#237526042
#237525982
#237525932
#237524372
#237524322
#237524302
#237524282
#237524102
#237523412
#237523222
#237523162
#237522972
#461×C1512
#3401151