Finite Group Databasebeta

← #34079225

Subgroups — #34079225

Order 19328.

392 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#23752749C211yesmaximal, characteristic, complemented
2C4×#14559005C211yesmaximal, characteristic, complemented
3#23752551C211yesmaximal, characteristic, complemented
4#23752538C211yesmaximal, characteristic, complemented
5#23752517C211yesmaximal, characteristic, complemented
6#23752511C211yesmaximal, characteristic, complemented
7#23752436C211yesmaximal, characteristic, complemented
8#23752430C211yesmaximal, characteristic, complemented
9#23752373C211yesmaximal, characteristic, complemented
10#23752360C211yesmaximal, characteristic
11#23752325C211yesmaximal, characteristic, complemented
12#23752310C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#23752267C211yesmaximal, characteristic, complemented
15#441×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20#18012734—21no—
21#18012730C2211yescharacteristic
22#18012728C2211yescharacteristic
23#18012724—21no—
24#18012715C2211yescharacteristic
25#18012714C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic
27C4×D604—21no—
28C4×D604—21no—
29C4×D604C2211yescharacteristic
30C4×D604C2211yescharacteristic
31#18012701—21no—
32#18012701C2211yescharacteristic
33#18012697—21no—
34#18012697C2211yescharacteristic
35#18012696—21no—
36C42×D151—21no—
37C42×D151C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012671C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012650C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—22no—
61C2×D604—21no—
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151D411yescharacteristic
70C2×C4×D151D411yescharacteristic
71C2×C4×D151C2311yescharacteristic
72#14558991—22no—
73#14558991—22no—
74D1208—22no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C4⋊Dic151—21no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83(C2×D151)⋊C4—21no—
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—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151D411yescharacteristic
94C4×Dic151D411yescharacteristic
95C4×Dic151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98Q16×C151—22no—
99C2×C8×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C42×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110C22×D151C2×D411yescharacteristic
111D604—24no—
112D604—21no—
113D604—21no—
114D604—21no—
115D604—42no—
116D604#4112yes—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—24no—
123C4×D151—21no—
124C4×D151—21no—
125C4×D151—41no—
126C4×D151—41no—
127C4×D151—42no—
128C4×D151—42no—
129C4×D151—42no—
130C151⋊C8—21no—
131C151⋊C8—21no—
132Q8×C151—21no—
133Q8×C151—21no—
134Q8×C151—21no—
135Q8×C151#4112yes—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2411yescharacteristic
143C8×C151—21no—
144C8×C151—21no—
145C22×C151C22×D411yescharacteristic
146C2×D151—21no—
147C2×D151—22no—
148C2×D151—21no—
149C2×D151—21no—
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
153C2×D151—41no—
154C2×D151—41no—
155C4×C151—22no—
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151—41no—
161C4×C151C2×#4111yescharacteristic
162C4×C151C2×#4111yescharacteristic
163Dic151—21no—
164Dic151—21no—
165Dic151—21no—
166Dic151—41no—
167Dic151—41no—
168C2×C151#52511yescharacteristic
169C2×C151#57511yescharacteristic
170C2×C151#57511yescharacteristic
171D151—41no—
172D151—42no—
173D151—81no—
174C151#311111yescharacteristic, complemented, Sylow
175#3111—1511nomaximal, Sylow
176#529—1511no—
177C4×#41—1511no—
178#485—1511no—
179#482—1511no—
180#479—1511no—
181#478—1511no—
182#464—1511no—
183#463—1511no—
184#452—1511no—
185#449—1511no—
186#442—1511no—
187#441D15111yescharacteristic, complemented
188#440—1511no—
189#440—1511no—
190#432—1511no—
191C2×#41—1511no—
192C2×Q16C2×D15111yescharacteristic
193C2×SD16—1511no—
194C2×SD16—1511no—
195C2×D8—1511no—
196#126—3021no—
197#125—1511no—
198#124—1511no—
199#123—3021no—
200C22⋊Q8—1511no—
201#121—1511no—
202C4×Q8—1511no—
203C4×Q8C2×D15111yescharacteristic
204C4×Q8C2×D15111yescharacteristic
205C4×D4—3021no—
206C4×D4—3021no—
207C4×D4—3021no—
208C4×D4—1511no—
209C4×D4—1511no—
210C4×D4—1511no—
211#117—3021no—
212#117—3021no—
213#117—1511no—
214C2×C42—3021no—
215C2×C42—1511no—
216#107—1511no—
217#107—1511no—
218#106—1511no—
219#106C2×D15111yescharacteristic
220C4⋊C8—1511no—
221C4⋊C8—1511no—
222#103—1511no—
223#103—1511no—
224#103C2×D15111yescharacteristic
225#103C2×D15111yescharacteristic
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102—1511no—
230C22⋊C8—1511no—
231C22⋊C8—1511no—
232#97—1511no—
233#97C2×D15111yescharacteristic
234#41—3022no—
235#41—3022no—
236C2×Q8C22×D15111yescharacteristic
237C2×Q8C22×D15111yescharacteristic
238C2×D4—3021no—
239C2×D4—3021no—
240C2×D4—1511no—
241C2×D4—1511no—
242C22×C4—3021no—
243C22×C4—3021no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—1511no—
247C22×C4—1511no—
248C22×C4—1511no—
249Q16—22no—
250SD16—3022no—
251SD16—3022no—
252D8—3022no—
253C2×C8—1511no—
254C2×C8—1511no—
255C2×C8C22×D15111yescharacteristic
256C2×C8C22×D15111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—1511no—
264C4⋊C4—1511no—
265C4⋊C4C22×D15111yescharacteristic
266C4⋊C4C22×D15111yescharacteristic
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C42—21no—
276C42—21no—
277C42—3021no—
278C42—3021no—
279C42—1511no—
280C42—1511no—
281C42—1511no—
282C42C22×D15111yescharacteristic
283C23—3021no—
284C23—3021no—
285C23—1511no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#1455900412yes—
290D4—3024no—
291D4—3021no—
292D4—3021no—
293D4—3021no—
294D4—6042no—
295D4—1512no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—3024no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—6041no—
306C2×C4—6041no—
307C2×C4—6042no—
308C2×C4—6042no—
309C2×C4—6042no—
310C2×C4—1511no—
311C2×C4—1511no—
312C2×C4—1511no—
313C2×C4D4×D15111yescharacteristic
314C2×C4D4×D15111yescharacteristic
315C2×C4C23×D15111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3021no—
319C8—3021no—
320C22—3021no—
321C22—3022no—
322C22—3021no—
323C22—3021no—
324C22—6041no—
325C22—6041no—
326C22—6041no—
327C22—6041no—
328C22—6041no—
329C22C2×D4×D15111yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—3021no—
337C4—3021no—
338C4—3021no—
339C4—6041no—
340C4—6041no—
341C4#41×D15111yescharacteristic
342C4C2×#1455900411yescharacteristic
343C2—6041no—
344C2—6042no—
345C2—12081no—
346C2#2375272111yescharacteristic
347C2#2375301111yescharacteristic
348C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#441×C151C2
socleC22×C151C22×D4
prime radical#23752360C2
hypercenter#441D151
hypocenterC151#3111
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #23752749C2semidirect
2. C4×#14559005C2semidirect
3. #23752551C2semidirect
4. #23752538C2semidirect
5. #23752517C2semidirect
6. #23752511C2semidirect
7. #23752436C2semidirect
8. #23752430C2semidirect
9. #23752373C2semidirect
11. #23752325C2semidirect
12. #23752310C2semidirect
13. #23752310C2semidirect
14. #23752267C2semidirect
15. #441×C151C2semidirect
174. C151#3111semidirect
187. #441D151semidirect

Maximal subgroups

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

subgroupindex
#237527492
C4×#145590052
#237525512
#237525382
#237525172
#237525112
#237524362
#237524302
#237523732
#237523602
#237523252
#237523102
#237522672
#441×C1512
#3111151