Finite Group Databasebeta

← #34081712

Subgroups — #34081712

Order 19328.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752910C211yesmaximal, characteristic, complemented
2#23752906C211yesmaximal, characteristic, complemented
3#23752612C211yesmaximal, characteristic, complemented
4#23752538C211yesmaximal, characteristic, complemented
5#23752536C211yesmaximal, characteristic, complemented
6#23752527C211yesmaximal, characteristic, complemented
7#23752525C211yesmaximal, characteristic, complemented
8#23752515C211yesmaximal, characteristic, complemented
9#23752511C211yesmaximal, characteristic, complemented
10#23752466C211yesmaximal, characteristic, complemented
11#23752465C211yesmaximal, characteristic, complemented
12#23752294C211yesmaximal, characteristic, complemented
13#23752288C211yesmaximal, characteristic, complemented
14#23752253C211yesmaximal, characteristic, complemented
15#428×C151C211yesmaximal, characteristic, complemented
16C2×D1208C2211yescharacteristic
17C2×#14558987C2211yescharacteristic
18#18012734—21no—
19#18012733—21no—
20#18012730C2211yescharacteristic
21#18012730C2211yescharacteristic
22#18012724—21no—
23#18012721—21no—
24#18012714C2211yescharacteristic
25#18012714C2211yescharacteristic
26#18012713—21no—
27#18012713C2211yescharacteristic
28#18012713C2211yescharacteristic
29#18012712—21no—
30C4×D604—21no—
31#18012701C2211yescharacteristic
32#18012701C2211yescharacteristic
33C4×C22⋊D151—21no—
34C4×C22⋊D151C2211yescharacteristic
35#18012697C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic
37#18012672C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012671C2211yescharacteristic
41#18012670C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012661C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012659C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×M16×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54C2×C4⋊C4×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#107×C151C2211yescharacteristic
57#106×C151C2211yescharacteristic
58#106×C151C2211yescharacteristic
59C2×D604—21no—
60C2×D604—21no—
61C2×D604C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151D411yescharacteristic
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151C2311yescharacteristic
70D1208—22no—
71#14558987—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82C22⋊Dic151D411yescharacteristic
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)⋊C4D411yescharacteristic
91C4×Dic151—21no—
92C4×Dic151C2311yescharacteristic
93C22×C4×C151—21no—
94C22×C4×C151C2311yescharacteristic
95M16×C151—22no—
96C2×C8×C151C2311yescharacteristic
97C2×C8×C151C2311yescharacteristic
98C4⋊C4×C151—21no—
99C4⋊C4×C151C2311yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C22⋊C4×C151—21no—
104C42×C151—21no—
105C22×D151—21no—
106C22×D151—21no—
107C22×D151C2×D411yescharacteristic
108D604—21no—
109D604—21no—
110D604—21no—
111D604—21no—
112D604—42no—
113D604—81no—
114C22⋊D151—41no—
115C22⋊D151—42no—
116C22⋊D151—81no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—21no—
123C4×D151—21no—
124C4×D151—81no—
125C4×D151—81no—
126C4×D151—81no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151C2×D411yescharacteristic
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—81no—
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2411yescharacteristic
139C8×C151—21no—
140C8×C151#4112yes—
141C22×C151—21no—
142C22×C151—21no—
143C22×C151—21no—
144C22×C151C22×D411yescharacteristic
145C2×D151—21no—
146C2×D151—21no—
147C2×D151—21no—
148C2×D151—41no—
149C2×D151—41no—
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
153C2×D151—41no—
154C4×C151—21no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151—41no—
158C4×C151—41no—
159C4×C151C2×#4111yescharacteristic
160C4×C1512−1+411yescharacteristic
161Dic151—21no—
162Dic151—21no—
163Dic151—21no—
164Dic151—41no—
165Dic151—41no—
166C2×C151—41no—
167C2×C151#54711yescharacteristic
168C2×C151#57511yescharacteristic
169C2×C151#57611yescharacteristic
170D151—41no—
171D151—81no—
172D151—81no—
173C151#335511yescharacteristic, complemented, Sylow
174#3355—1511nomaximal, Sylow
175#553—1511no—
176#553—1511no—
177#499—1511no—
178#482—1511no—
179#482—1511no—
180#480—1511no—
181#480—1511no—
182#478—1511no—
183#478—1511no—
184#469—1511no—
185#469—1511no—
186C4×D8—1511no—
187#436—1511no—
188#428—1511no—
189#428D15111yescharacteristic, complemented
190C2×D8—1511no—
191C2×M16—1511no—
192C2×M16C2×D15111yescharacteristic
193#126—3021no—
194#126—3021no—
195#125—1511no—
196#125—1511no—
197#123—3021no—
198#123—3021no—
199#121—3021no—
200#121—3021no—
201#121—1511no—
202#121—1511no—
203#121—1511no—
204#121—1511no—
205C4×D4—3021no—
206C4×D4—3021no—
207C4×D4—1511no—
208C4×D4—1511no—
209C4×D4—1511no—
210#117—1511no—
211#117C2×D15111yescharacteristic
212C2×C4⋊C4—1511no—
213C2×C4⋊C4C2×D15111yescharacteristic
214#107—1511no—
215#107—1511no—
216#107—1511no—
217#107C2×D15111yescharacteristic
218#107C2×D15111yescharacteristic
219#106—1511no—
220#106—1511no—
221#106C2×D15111yescharacteristic
222#106C2×D15111yescharacteristic
223C4⋊C8—1511no—
224#102—1511no—
225#102—1511no—
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102—1511no—
230C22⋊C8—1511no—
231C22⋊C8—1511no—
232C4×C8—1511no—
233C2×D4—3021no—
234C2×D4—3021no—
235C2×D4—3021no—
236C2×D4—3021no—
237C2×D4—1511no—
238C2×D4—1511no—
239C2×D4—1511no—
240C22×C4—21no—
241C22×C4—3021no—
242C22×C4—3021no—
243C22×C4—3021no—
244C22×C4—1511no—
245C22×C4C22×D15111yescharacteristic
246D8—3022no—
247M16—22no—
248M16—3022no—
249C2×C8—1511no—
250C2×C8—1511no—
251C2×C8C22×D15111yescharacteristic
252C2×C8C22×D15111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—1511no—
260C4⋊C4—1511no—
261C4⋊C4—1511no—
262C4⋊C4C22×D15111yescharacteristic
263C4⋊C4C22×D15111yescharacteristic
264C4⋊C4C22×D15111yescharacteristic
265C4⋊C4C22×D15111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—1511no—
275C22⋊C4—1511no—
276C42—21no—
277C42—3021no—
278C42—1511no—
279C23—3021no—
280C23—3021no—
281C23—1511no—
282C23D4×D15111yescharacteristic
283D4—3021no—
284D4—3021no—
285D4—3021no—
286D4—3021no—
287D4—6042no—
288D4—6041no—
289D4—6042no—
290D4—12081no—
291D4—12081no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—81no—
299C2×C4—3021no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—1511no—
304C2×C4—1511no—
305C2×C4—1511no—
306C2×C4—12081no—
307C2×C4—12081no—
308C2×C4—12081no—
309C2×C4D4×D15111yescharacteristic
310C2×C4C23×D15111yescharacteristic
311C8—21no—
312C8—3021no—
313C8—3021no—
314C8#1455900412yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—3021no—
319C22—3021no—
320C22—3021no—
321C22—6041no—
322C22—6041no—
323C22—6041no—
324C22—6041no—
325C22—6041no—
326C22—6041no—
327C22C2×D4×D15111yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—3021no—
334C4—3021no—
335C4—3021no—
336C4—6041no—
337C4—6041no—
338C4C2×#1455900411yescharacteristic
339C4#1801278711yescharacteristic
340C2—41no—
341C2—6041no—
342C2—12081no—
343C2—12081no—
344C2#2375286311yescharacteristic
345C2#2375301111yescharacteristic
346C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#428×C151C2
socleC22×C151C22×D4
hypercenter#428D151
hypocenterC151#3355
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #23752910C2semidirect
2. #23752906C2semidirect
3. #23752612C2semidirect
4. #23752538C2semidirect
5. #23752536C2semidirect
6. #23752527C2semidirect
7. #23752525C2semidirect
8. #23752515C2semidirect
9. #23752511C2semidirect
10. #23752466C2semidirect
11. #23752465C2semidirect
12. #23752294C2semidirect
13. #23752288C2semidirect
14. #23752253C2semidirect
15. #428×C151C2semidirect
173. C151#3355semidirect
189. #428D151semidirect

Maximal subgroups

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

subgroupindex
#237529102
#237529062
#237526122
#237525382
#237525362
#237525272
#237525252
#237525152
#237525112
#237524662
#237524652
#237522942
#237522882
#237522532
#428×C1512
#3355151