Finite Group Databasebeta

← #34079376

Subgroups — #34079376

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#23752834C211yesmaximal, characteristic, complemented
2#23752691C211yesmaximal, characteristic, complemented
3#23752546C211yesmaximal, characteristic, complemented
4#23752527C211yesmaximal, characteristic, complemented
5#23752506C211yesmaximal, characteristic, complemented
6#23752490C211yesmaximal, characteristic, complemented
7#23752437C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752371C211yesmaximal, characteristic, complemented
10#23752358C211yesmaximal, characteristic
11#23752314C211yesmaximal, characteristic, complemented
12C4×#14558994C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14#23752274C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20#18012738C2211yescharacteristic
21#18012733—21no—
22#18012728C2211yescharacteristic
23#18012727—21no—
24#18012724—21no—
25#18012717—21no—
26#18012715C2211yescharacteristic
27#18012714C2211yescharacteristic
28C4×Dic302C2211yescharacteristic
29#18012704C2211yescharacteristic
30C4×D604C2211yescharacteristic
31D4×Dic151C2211yescharacteristic
32C4×C22⋊D151—21no—
33(C22⋊D151)⋊C4—21no—
34#18012696C2211yescharacteristic
35#18012695—21no—
36C2×Dic151⋊C4—21no—
37C4⋊C4×D151C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—22no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C22×Dic151—21no—
67C22×Dic151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151C2311yescharacteristic
71#14558994—22no—
72#14558993—22no—
73#14558989—22no—
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84Dic151⋊C4D411yescharacteristic
85C22⋊Dic151—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×Dic151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151—21no—
99SD16×C151—22no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110Dic302—21no—
111Dic302—81no—
112Dic302#4112yes—
113D604—21no—
114D604—21no—
115D604—81no—
116C22⋊D151—24no—
117C2×Dic151—24no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—81no—
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C2×Dic151C2×D411yescharacteristic
125C4×D151—21no—
126C4×D151—21no—
127C4×D151—81no—
128C4×D151—81no—
129C151⋊C8—21no—
130C151⋊C8—21no—
131C23×C151—21no—
132Q8×C151—21no—
133Q8×C151—21no—
134D4×C151—21no—
135D4×C151#4112yes—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—81no—
140C2×C4×C151C2×D411yescharacteristic
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2411yescharacteristic
143C8×C151—21no—
144C8×C151—21no—
145C22×C151—22no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151C22×D411yescharacteristic
149C2×D151—21no—
150C2×D151—21no—
151C2×D151—21no—
152C2×D151—41no—
153C2×D151—41no—
154C2×D151—41no—
155C4×C151—21no—
156C4×C151—21no—
157C4×C151—41no—
158C4×C151—41no—
159C4×C151—41no—
160C4×C151C2×#4111yescharacteristic
161C4×C151C2×#4111yescharacteristic
162Dic151—21no—
163Dic151—22no—
164Dic151—21no—
165Dic151—21no—
166Dic151—41no—
167Dic151—41no—
168C2×C151—42no—
169C2×C151#52511yescharacteristic
170C2×C151#57611yescharacteristic
171C2×C151#57811yescharacteristic
172D151—41no—
173D151—81no—
174C151#312411yescharacteristic, complemented, Sylow
175#3124—1511nomaximal, Sylow
176#542—1511no—
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#440D15111yescharacteristic, complemented
188C4×Q16—1511no—
189C4×D8—1511no—
190#433—1511no—
191C2×#41—1511no—
192C2×Q16—1511no—
193C2×SD16—1511no—
194C2×SD16C2×D15111yescharacteristic
195C2×D8—1511no—
196C4⋊Q8—1511no—
197#126—3021no—
198#124—3021no—
199#124—1511no—
200#123—3021no—
201C22⋊Q8—3021no—
202C22⋊Q8—1511no—
203#121—1511no—
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#117—1511no—
214C2×C4⋊C4—3021no—
215C2×C4⋊C4—1511no—
216#107—1511no—
217#107—1511no—
218#107—1511no—
219#107C2×D15111yescharacteristic
220C4⋊C8—1511no—
221C4⋊C8—1511no—
222#103—1511no—
223#103—1511no—
224#103—1511no—
225#103C2×D15111yescharacteristic
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102C2×D15111yescharacteristic
230C22⋊C8—1511no—
231C22⋊C8—1511no—
232#97C2×D15111yescharacteristic
233C4×C8—1511no—
234#41—3022no—
235#41—3022no—
236C2×Q8—3021no—
237C2×Q8—1511no—
238C2×Q8C22×D15111yescharacteristic
239C2×D4—3021no—
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×C4—1511no—
249Q16—3022no—
250SD16—22no—
251SD16—3022no—
252D8—3022no—
253C2×C8—1511no—
254C2×C8—1511no—
255C2×C8C22×D15111yescharacteristic
256C2×C8C22×D15111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—1511no—
264C4⋊C4—1511no—
265C4⋊C4—1511no—
266C4⋊C4—1511no—
267C4⋊C4C22×D15111yescharacteristic
268C4⋊C4C22×D15111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4—1511no—
277C22⋊C4—1511no—
278C42—21no—
279C42—3021no—
280C42—3021no—
281C42—1511no—
282C42C22×D15111yescharacteristic
283C23—21no—
284C23—3021no—
285C23—1511no—
286Q8—21no—
287Q8—21no—
288Q8—3021no—
289Q8—1512no—
290Q8—12081no—
291D4—21no—
292D4—3024no—
293D4—3021no—
294D4—3021no—
295D4—12081no—
296D4#1455900412yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—3024no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—3021no—
307C2×C4—1511no—
308C2×C4—1511no—
309C2×C4—1511no—
310C2×C4—12081no—
311C2×C4—12081no—
312C2×C4—12081no—
313C2×C4D4×D15111yescharacteristic
314C2×C4D4×D15111yescharacteristic
315C2×C4C23×D15111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3021no—
319C8—3021no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—3021no—
324C22—3021no—
325C22—3021no—
326C22—6041no—
327C22—6041no—
328C22—6041no—
329C22C2×D4×D15111yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—3021no—
336C4—3022no—
337C4—3021no—
338C4—3021no—
339C4—6041no—
340C4—6041no—
341C4#41×D15111yescharacteristic
342C4C2×#1455900411yescharacteristic
343C2—42no—
344C2—6041no—
345C2—12081no—
346C2#2375272111yescharacteristic
347C2#2375301611yescharacteristic
348C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
prime radical#23752358C2
hypercenter#440D151
hypocenterC151#3124
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23752834C2semidirect
2. #23752691C2semidirect
3. #23752546C2semidirect
4. #23752527C2semidirect
5. #23752506C2semidirect
6. #23752490C2semidirect
7. #23752437C2semidirect
8. #23752429C2semidirect
9. #23752371C2semidirect
11. #23752314C2semidirect
12. C4×#14558994C2semidirect
13. C4×#14558989C2semidirect
14. #23752274C2semidirect
15. #440×C151C2semidirect
174. C151#3124semidirect
187. #440D151semidirect

Maximal subgroups

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

subgroupindex
#237528342
#237526912
#237525462
#237525272
#237525062
#237524902
#237524372
#237524292
#237523712
#237523582
#237523142
C4×#145589942
C4×#145589892
#237522742
#440×C1512
#3124151