Finite Group Databasebeta

← #34079334

Subgroups — #34079334

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#23752829C211yesmaximal, characteristic
2#23752689C211yesmaximal, characteristic, complemented
3#23752553C211yesmaximal, characteristic, complemented
4#23752506C211yesmaximal, characteristic, complemented
5#23752496C211yesmaximal, characteristic, complemented
6#23752433C211yesmaximal, characteristic, complemented
7#23752433C211yesmaximal, characteristic, complemented
8#23752370C211yesmaximal, characteristic, complemented
9#23752350C211yesmaximal, characteristic
10#23752318C211yesmaximal, characteristic, complemented
11#23752309C211yesmaximal, characteristic, complemented
12#23752306C211yesmaximal, characteristic, complemented
13#23752303C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#482×C151C211yesmaximal, characteristic
16C22×Dic302C2211yescharacteristic
17C2×Dic604C2211yescharacteristic
18C2×Dic604C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012732—21no—
23#18012726—21no—
24#18012726C2211yescharacteristic
25#18012720—21no—
26#18012718C2211yescharacteristic
27#18012716—21no—
28C4×Dic302—21no—
29C4×Dic302—21no—
30#18012704C2211yescharacteristic
31#18012704C2211yescharacteristic
32#18012704C2211yescharacteristic
33#18012704C2211yescharacteristic
34#18012704C2211yescharacteristic
35D4×Dic151C2211yescharacteristic
36#18012698C2211yescharacteristic
37#18012695—21no—
38#18012695—21no—
39#18012672C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012662C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52#121×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×Dic302—22no—
60C2×Dic302—22no—
61C2×Dic302—21no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66C22×Dic151—21no—
67C22×Dic151—21no—
68Dic604—22no—
69Dic604—22no—
70#14558992—22no—
71#14558992—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C4⋊Dic151D411yescharacteristic
75C4⋊Dic151D411yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151D411yescharacteristic
89C22⋊Dic151D411yescharacteristic
90C4×Dic151—21no—
91C4×Dic151—21no—
92C4×Dic151—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151C2311yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C42×C151—21no—
108Dic302—24no—
109Dic302—21no—
110Dic302—21no—
111Dic302—21no—
112Dic302—21no—
113Dic302—81no—
114Dic302#4112yes—
115Dic302#4112yes—
116C2×Dic151—24no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—81no—
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C151⋊C8—21no—
127C151⋊C8—21no—
128C23×C151—21no—
129C23×C151C2×D411yescharacteristic
130D4×C151—21no—
131D4×C151—21no—
132D4×C151—81no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2411yescharacteristic
140C8×C151—21no—
141C8×C151—21no—
142C22×C151—21no—
143C22×C151—21no—
144C22×C151—21no—
145C22×C151—41no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151C22×D411yescharacteristic
149C4×C151—21no—
150C4×C151—41no—
151C4×C151—41no—
152C4×C151—41no—
153C4×C151C2×#4111yescharacteristic
154C4×C151C2×#4111yescharacteristic
155Dic151—22no—
156Dic151—22no—
157Dic151—21no—
158Dic151—21no—
159Dic151—21no—
160Dic151—21no—
161Dic151—41no—
162Dic151—41no—
163C2×C151—41no—
164C2×C151—81no—
165C2×C151#52511yescharacteristic
166C2×C151#57711yescharacteristic
167C2×C151#57811yescharacteristic
168C151#312111yescharacteristic, complemented, Sylow
169#3121—1511nomaximal, Sylow
170#542—1511no—
171#519—1511no—
172#485—1511no—
173#482D15111yescharacteristic
174#477—1511no—
175#475—1511no—
176#464—1511no—
177#464—1511no—
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×Q16—1511no—
188C2×SD16—1511no—
189C2×SD16—1511no—
190C4⋊Q8—1511no—
191#126—3021no—
192#124—3021no—
193#124—1511no—
194#123—3021no—
195C22⋊Q8—3021no—
196C22⋊Q8—1511no—
197#121C2×D15111yescharacteristic
198C4×Q8—3021no—
199C4×Q8—3021no—
200C4×Q8—1511no—
201C4×Q8—1511no—
202C4×Q8—1511no—
203C4×Q8—1511no—
204C4×Q8—1511no—
205C4×D4—1511no—
206#117—3021no—
207#117—3021no—
208#117—1511no—
209#117C2×D15111yescharacteristic
210#107—1511no—
211#107C2×D15111yescharacteristic
212#106—1511no—
213#106C2×D15111yescharacteristic
214C4⋊C8—1511no—
215C4⋊C8—1511no—
216#103—1511no—
217#103—1511no—
218#103—1511no—
219#103—1511no—
220#103—1511no—
221#103—1511no—
222#102C2×D15111yescharacteristic
223#102C2×D15111yescharacteristic
224C22⋊C8—1511no—
225C22⋊C8C2×D15111yescharacteristic
226#97—1511no—
227C4×C8—1511no—
228C2×Q8—3022no—
229C2×Q8—3022no—
230C2×Q8—3021no—
231C2×Q8—3021no—
232C2×Q8—1511no—
233C2×Q8—1511no—
234C2×Q8—1511no—
235C2×D4—21no—
236C2×D4C22×D15111yescharacteristic
237C22×C4—3021no—
238C22×C4—3021no—
239C22×C4C22×D15111yescharacteristic
240Q16—3022no—
241Q16—3022no—
242SD16—3022no—
243SD16—3022no—
244C2×C8—1511no—
245C2×C8—1511no—
246C2×C8C22×D15111yescharacteristic
247C2×C8C22×D15111yescharacteristic
248C4⋊C4—3021no—
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
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—
276C42—1511no—
277C23—21no—
278C23D4×D15111yescharacteristic
279Q8—3024no—
280Q8—3021no—
281Q8—3021no—
282Q8—3021no—
283Q8—3021no—
284Q8—1512no—
285Q8—1512no—
286Q8—12081no—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—3024no—
296C2×C4—3021no—
297C2×C4—3021no—
298C2×C4—3021no—
299C2×C4—3021no—
300C2×C4—1511no—
301C2×C4—1511no—
302C2×C4—1511no—
303C2×C4—1511no—
304C2×C4—12081no—
305C2×C4D4×D15111yescharacteristic
306C2×C4C23×D15111yescharacteristic
307C8—21no—
308C8—21no—
309C8—3021no—
310C8—3021no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×D4×D15111yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—3022no—
323C4—3022no—
324C4—3021no—
325C4—3021no—
326C4—3021no—
327C4—3021no—
328C4—6041no—
329C4—6041no—
330C4#41×D15111yescharacteristic
331C4#41×D15111yescharacteristic
332C2—41no—
333C2—81no—
334C2#2375272011yescharacteristic
335C2#2375302211yescharacteristic
336C2#2375302611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#482×C151C2
socleC22×C151C22×D4
prime radical#121×C151C22
hypercenter#482D151
hypocenterC151#3121
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #23752689C2semidirect
3. #23752553C2semidirect
4. #23752506C2semidirect
5. #23752496C2semidirect
6. #23752433C2semidirect
7. #23752433C2semidirect
8. #23752370C2semidirect
10. #23752318C2semidirect
11. #23752309C2semidirect
12. #23752306C2semidirect
13. #23752303C2semidirect
14. #23752270C2semidirect
168. C151#3121semidirect

Maximal subgroups

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

subgroupindex
#237528292
#237526892
#237525532
#237525062
#237524962
#237524332
#237523702
#237523502
#237523182
#237523092
#237523062
#237523032
#237522702
#482×C1512
#3121151