Finite Group Databasebeta

← #34079338

Subgroups — #34079338

Order 19328.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752831C211yesmaximal, characteristic
2#23752688C211yesmaximal, characteristic, complemented
3#23752552C211yesmaximal, characteristic, complemented
4#23752534C211yesmaximal, characteristic
5#23752508C211yesmaximal, characteristic, complemented
6#23752497C211yesmaximal, characteristic, complemented
7#23752431C211yesmaximal, characteristic, complemented
8#23752366C211yesmaximal, characteristic, complemented
9#23752349C211yesmaximal, characteristic
10#23752316C211yesmaximal, characteristic, complemented
11#23752313C211yesmaximal, characteristic, complemented
12Q16×Dic151C211yesmaximal, characteristic, complemented
13#23752303C211yesmaximal, characteristic, complemented
14#23752272C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19#18012739C2211yescharacteristic
20#18012732—21no—
21#18012725—21no—
22#18012723—21no—
23#18012716—21no—
24#18012715C2211yescharacteristic
25#18012710C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic
27Q8×Dic151C2211yescharacteristic
28C4×Dic302—21no—
29C4×Dic302C2211yescharacteristic
30#18012704—21no—
31#18012704C2211yescharacteristic
32D4×Dic151C2211yescharacteristic
33#18012697—21no—
34#18012697C2211yescharacteristic
35#18012696—21no—
36#18012696C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012670C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012660C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62Q8×D151—22no—
63Q8×D151—22no—
64C2×C22⋊D151—21no—
65C22×Dic151—21no—
66C2×C4×D151—21no—
67C2×C4×D151C2311yescharacteristic
68#14558994—22no—
69#14558992—22no—
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C4⋊Dic151—21no—
73C4⋊Dic151—21no—
74C4⋊Dic151—21no—
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
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)⋊C4D411yescharacteristic
88(C2×D151)⋊C4D411yescharacteristic
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×Q8×C151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98Q16×C151—22no—
99SD16×C151—22no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151C2×D411yescharacteristic
109Dic302—24no—
110Dic302—21no—
111Dic302—81no—
112Dic302#4112yes—
113C22⋊D151—81no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—81no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C4×D151—24no—
123C4×D151—21no—
124C4×D151—21no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127C23×C151—21no—
128Q8×C151—21no—
129Q8×C151—21no—
130Q8×C151—21no—
131Q8×C151#4112yes—
132D4×C151—21no—
133D4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151C2×D411yescharacteristic
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2411yescharacteristic
140C8×C151—21no—
141C8×C151—21no—
142C22×C151—41no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151C22×D411yescharacteristic
146C2×D151—21no—
147C2×D151—21no—
148C2×D151—21no—
149C4×C151—22no—
150C4×C151—21no—
151C4×C151—21no—
152C4×C151—41no—
153C4×C151—41no—
154C4×C151C2×#4111yescharacteristic
155C4×C151C2×#4111yescharacteristic
156Dic151—22no—
157Dic151—21no—
158Dic151—21no—
159Dic151—21no—
160Dic151—41no—
161Dic151—41no—
162Dic151—41no—
163C2×C151—81no—
164C2×C151#52511yescharacteristic
165C2×C151#57711yescharacteristic
166C2×C151#57811yescharacteristic
167D151—41no—
168C151#312111yescharacteristic, complemented, Sylow
169#3121—1511nomaximal, Sylow
170#542—1511no—
171#519—1511no—
172#485—1511no—
173#482—1511no—
174#477—1511no—
175#475—1511no—
176#464—1511no—
177#464D15111yescharacteristic, complemented
178#451—1511no—
179#448—1511no—
180#441—1511no—
181#440—1511no—
182C4×Q16—1511no—
183C4×SD16—1511no—
184#433—1511no—
185C22×Q8—1511no—
186C2×Q16—1511no—
187C2×Q16C2×D15111yescharacteristic
188C2×SD16—1511no—
189C2×SD16C2×D15111yescharacteristic
190C4⋊Q8—1511no—
191#126—3021no—
192#124—3021no—
193#124C2×D15111yescharacteristic
194#123—3021no—
195C22⋊Q8—3021no—
196C22⋊Q8—1511no—
197#121—1511no—
198C4×Q8—3021no—
199C4×Q8—3021no—
200C4×Q8—1511no—
201C4×Q8—1511no—
202C4×Q8—1511no—
203C4×Q8—1511no—
204C4×Q8C2×D15111yescharacteristic
205C4×D4—1511no—
206#117—3021no—
207#117—3021no—
208#117—1511no—
209#117—1511no—
210#107—1511no—
211#107—1511no—
212#106—1511no—
213#106—1511no—
214C4⋊C8—1511no—
215C4⋊C8C2×D15111yescharacteristic
216#103—1511no—
217#103—1511no—
218#103—1511no—
219#103—1511no—
220#103—1511no—
221#103C2×D15111yescharacteristic
222#102—1511no—
223#102C2×D15111yescharacteristic
224C22⋊C8—1511no—
225C22⋊C8—1511no—
226#97—1511no—
227C4×C8—1511no—
228C2×Q8—3021no—
229C2×Q8—3022no—
230C2×Q8—3022no—
231C2×Q8—3021no—
232C2×Q8—1511no—
233C2×Q8C22×D15111yescharacteristic
234C2×Q8C22×D15111yescharacteristic
235C2×D4—3021no—
236C2×D4C22×D15111yescharacteristic
237C22×C4—3021no—
238C22×C4—3021no—
239C22×C4—1511no—
240Q16—22no—
241Q16—3022no—
242SD16—22no—
243SD16—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⋊C4—1511no—
259C4⋊C4—1511no—
260C4⋊C4C22×D15111yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—3021no—
264C22⋊C4—3021no—
265C22⋊C4—3021no—
266C22⋊C4—3021no—
267C22⋊C4—1511no—
268C22⋊C4—1511no—
269C42—21no—
270C42—3021no—
271C42—3021no—
272C42—3021no—
273C42—3021no—
274C42—3021no—
275C42—1511no—
276C42C22×D15111yescharacteristic
277C23—21no—
278C23—1511no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—3024no—
283Q8—3021no—
284Q8—1512no—
285Q8—12081no—
286Q8#1455900312yes—
287D4—21no—
288D4—21no—
289D4—12081no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—3024no—
294C2×C4—3021no—
295C2×C4—3021no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—3021no—
299C2×C4—3021no—
300C2×C4—1511no—
301C2×C4—1511no—
302C2×C4—1511no—
303C2×C4—12081no—
304C2×C4D4×D15111yescharacteristic
305C2×C4D4×D15111yescharacteristic
306C2×C4C23×D15111yescharacteristic
307C8—21no—
308C8—21no—
309C8—3021no—
310C8—3021no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—3021no—
315C22—3021no—
316C22—3021no—
317C22C2×D4×D15111yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—3022no—
324C4—3021no—
325C4—3021no—
326C4—3021no—
327C4—6041no—
328C4—6041no—
329C4—6041no—
330C4#41×D15111yescharacteristic
331C4C2×#1455900311yescharacteristic
332C2—81no—
333C2—6041no—
334C2#2375272211yescharacteristic
335C2#2375302111yescharacteristic
336C2#2375302611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radical#18012710C22
hypercenter#464D151
hypocenterC151#3121
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #23752688C2semidirect
3. #23752552C2semidirect
5. #23752508C2semidirect
6. #23752497C2semidirect
7. #23752431C2semidirect
8. #23752366C2semidirect
10. #23752316C2semidirect
11. #23752313C2semidirect
12. Q16×Dic151C2semidirect
13. #23752303C2semidirect
14. #23752272C2semidirect
15. #464×C151C2semidirect
168. C151#3121semidirect
177. #464D151semidirect

Maximal subgroups

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

subgroupindex
#237528312
#237526882
#237525522
#237525342
#237525082
#237524972
#237524312
#237523662
#237523492
#237523162
#237523132
Q16×Dic1512
#237523032
#237522722
#464×C1512
#3121151