Finite Group Databasebeta

← #34081732

Subgroups — #34081732

Order 19328.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752925C211yesmaximal, characteristic
2#23752917C211yesmaximal, characteristic, complemented
3#23752616C211yesmaximal, characteristic, complemented
4#23752556C211yesmaximal, characteristic, complemented
5#23752553C211yesmaximal, characteristic, complemented
6#23752527C211yesmaximal, characteristic, complemented
7#23752525C211yesmaximal, characteristic, complemented
8#23752506C211yesmaximal, characteristic, complemented
9#23752501C211yesmaximal, characteristic, complemented
10#23752459C211yesmaximal, characteristic, complemented
11#23752458C211yesmaximal, characteristic, complemented
12#23752299C211yesmaximal, characteristic, complemented
13#23752288C211yesmaximal, characteristic, complemented
14#23752251C211yesmaximal, characteristic, complemented
15#428×C151C211yesmaximal, characteristic, complemented
16C2×#14558993C2211yescharacteristic
17C2×#14558987C2211yescharacteristic
18#18012738C2211yescharacteristic
19#18012738C2211yescharacteristic
20#18012729—21no—
21#18012727—21no—
22#18012725—21no—
23#18012719C2211yescharacteristic
24#18012718—21no—
25#18012718C2211yescharacteristic
26#18012717—21no—
27#18012714C2211yescharacteristic
28#18012713C2211yescharacteristic
29#18012712—21no—
30#18012704C2211yescharacteristic
31#18012701C2211yescharacteristic
32C4×C22⋊D151—21no—
33C4×C22⋊D151C2211yescharacteristic
34#18012697C2211yescharacteristic
35#18012696—21no—
36C4⋊C4×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012670C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
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×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151D411yescharacteristic
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68C2×C4×D151C2311yescharacteristic
69#14558993—22no—
70#14558987—22no—
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C4⋊Dic151—21no—
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76Dic151⋊C4—21no—
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82C22⋊Dic151—21no—
83C22⋊Dic151D411yescharacteristic
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)⋊C4D411yescharacteristic
90C4×Dic151—21no—
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×D151C2×D411yescharacteristic
107Dic302—21no—
108Dic302—21no—
109Dic302—81no—
110Dic302—81no—
111D604—21no—
112D604—21no—
113D604—81no—
114C22⋊D151—22no—
115C22⋊D151—81no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—21no—
123C4×D151—21no—
124C4×D151—42no—
125C4×D151—81no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C23×C151C2×D411yescharacteristic
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—81no—
136C2×C4×C151C2×D411yescharacteristic
137C2×C4×C151C2411yescharacteristic
138C8×C151—21no—
139C8×C151#4112yes—
140C22×C151—21no—
141C22×C151—21no—
142C22×C151—21no—
143C22×C151C22×D411yescharacteristic
144C2×D151—21no—
145C2×D151—21no—
146C2×D151—21no—
147C2×D151—41no—
148C2×D151—41no—
149C2×D151—41no—
150C4×C151—21no—
151C4×C151—41no—
152C4×C151—41no—
153C4×C151—41no—
154C4×C151—41no—
155C4×C151C2×#4111yescharacteristic
156C4×C1512−1+411yescharacteristic
157Dic151—21no—
158Dic151—21no—
159Dic151—41no—
160Dic151—41no—
161Dic151—41no—
162Dic151#13712yes—
163C2×C151—41no—
164C2×C151#54711yescharacteristic
165C2×C151C2×#13711yescharacteristic
166C2×C151#57611yescharacteristic
167D151—41no—
168D151—81no—
169C151#335711yescharacteristic, complemented, Sylow
170#3357—1511nomaximal, Sylow
171#555—1511no—
172#554—1511no—
173#500—1511no—
174#485—1511no—
175#485—1511no—
176#480—1511no—
177#480—1511no—
178#477—1511no—
179#476—1511no—
180#468—1511no—
181#468—1511no—
182C4×SD16—1511no—
183#436—1511no—
184#428—1511no—
185#428D15111yescharacteristic, complemented
186C2×SD16—1511no—
187C2×M16—1511no—
188C2×M16C2×D15111yescharacteristic
189C4⋊Q8—1511no—
190C4⋊Q8—1511no—
191#125—3021no—
192#124—3021no—
193#124—3021no—
194C22⋊Q8—3021no—
195C22⋊Q8—3021no—
196C22⋊Q8—1511no—
197C22⋊Q8—1511no—
198#121—3021no—
199#121—1511no—
200#121—1511no—
201C4×Q8—1511no—
202C4×D4—3021no—
203C4×D4—1511no—
204C4×D4—1511no—
205#117—3021no—
206#117—1511no—
207#117C2×D15111yescharacteristic
208C2×C4⋊C4—1511no—
209C2×C4⋊C4C2×D15111yescharacteristic
210#107—1511no—
211#107—1511no—
212#107—1511no—
213#107—1511no—
214#107C2×D15111yescharacteristic
215#107C2×D15111yescharacteristic
216#106—1511no—
217#106C2×D15111yescharacteristic
218#106C2×D15111yescharacteristic
219C4⋊C8—1511no—
220#103—1511no—
221#103—1511no—
222#103—1511no—
223#102—1511no—
224#102—1511no—
225#102—1511no—
226C22⋊C8—1511no—
227C22⋊C8—1511no—
228C4×C8—1511no—
229C2×Q8—3021no—
230C2×Q8—3021no—
231C2×Q8—1511no—
232C2×D4—3021no—
233C2×D4—3021no—
234C2×D4—1511no—
235C2×D4—1511no—
236C22×C4—21no—
237C22×C4—3021no—
238C22×C4—3021no—
239C22×C4—1511no—
240C22×C4C22×D15111yescharacteristic
241SD16—3022no—
242M16—22no—
243M16—3022no—
244C2×C8—1511no—
245C2×C8—1511no—
246C2×C8C22×D15111yescharacteristic
247C2×C8C22×D15111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—3021no—
250C4⋊C4—3021no—
251C4⋊C4—3021no—
252C4⋊C4—3021no—
253C4⋊C4—3021no—
254C4⋊C4—3021no—
255C4⋊C4—1511no—
256C4⋊C4—1511no—
257C4⋊C4—1511no—
258C4⋊C4C22×D15111yescharacteristic
259C4⋊C4C22×D15111yescharacteristic
260C4⋊C4C22×D15111yescharacteristic
261C4⋊C4C22×D15111yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—3021no—
264C22⋊C4—3021no—
265C22⋊C4—3021no—
266C22⋊C4—3021no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—1511no—
270C22⋊C4—1511no—
271C42—21no—
272C42—3021no—
273C42—3021no—
274C42—1511no—
275C23—3021no—
276C23—1511no—
277C23D4×D15111yescharacteristic
278Q8—3021no—
279Q8—3021no—
280Q8—12081no—
281Q8—12081no—
282D4—3022no—
283D4—3021no—
284D4—3021no—
285D4—12081no—
286D4—12081no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—3021no—
299C2×C4—6042no—
300C2×C4—1511no—
301C2×C4—1511no—
302C2×C4—1511no—
303C2×C4—12081no—
304C2×C4D4×D15111yescharacteristic
305C2×C4C23×D15111yescharacteristic
306C8—21no—
307C8—3021no—
308C8—3021no—
309C8#1455900412yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—3021no—
314C22—3021no—
315C22—3021no—
316C22—6041no—
317C22—6041no—
318C22—6041no—
319C22C2×D4×D15111yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—3021no—
326C4—3021no—
327C4—6041no—
328C4—6041no—
329C4—6041no—
330C4—1512no—
331C4C2×#1455900411yescharacteristic
332C4#1801278711yescharacteristic
333C2—41no—
334C2—6041no—
335C2—12081no—
336C2#2375286311yescharacteristic
337C2#137×D15111yescharacteristic
338C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#428×C151C2
socleC22×C151C22×D4
prime radical#23752925C2
hypercenter#428D151
hypocenterC151#3357
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
2. #23752917C2semidirect
3. #23752616C2semidirect
4. #23752556C2semidirect
5. #23752553C2semidirect
6. #23752527C2semidirect
7. #23752525C2semidirect
8. #23752506C2semidirect
9. #23752501C2semidirect
10. #23752459C2semidirect
11. #23752458C2semidirect
12. #23752299C2semidirect
13. #23752288C2semidirect
14. #23752251C2semidirect
15. #428×C151C2semidirect
169. C151#3357semidirect
185. #428D151semidirect

Maximal subgroups

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

subgroupindex
#237529252
#237529172
#237526162
#237525562
#237525532
#237525272
#237525252
#237525062
#237525012
#237524592
#237524582
#237522992
#237522882
#237522512
#428×C1512
#3357151