Finite Group Databasebeta

← #34080968

Subgroups — #34080968

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D151C211yesmaximal, characteristic, complemented
2#23752862C211yesmaximal, characteristic
3#23752561C211yesmaximal, characteristic, complemented
4#23752543C211yesmaximal, characteristic, complemented
5#23752541C211yesmaximal, characteristic, complemented
6#23752495C211yesmaximal, characteristic, complemented
7#23752439C211yesmaximal, characteristic, complemented
8#23752438C211yesmaximal, characteristic, complemented
9#23752415C211yesmaximal, characteristic, complemented
10#23752349C211yesmaximal, characteristic, complemented
11SD16×Dic151C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13C2×#18012663C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#448×C151C211yesmaximal, characteristic, complemented
16C2×#14559003—21no—
17C2×Q8×D151C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C22×C151⋊C8C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012737—21no—
23#18012737C2211yescharacteristic
24#18012721—21no—
25#18012720—21no—
26#18012718—21no—
27#18012718C2211yescharacteristic
28#18012716—21no—
29#18012715—21no—
30#18012715C2211yescharacteristic
31#18012710C2211yescharacteristic
32Q8×Dic151C2211yescharacteristic
33D4×Dic151C2211yescharacteristic
34C4×C22⋊D151—21no—
35C4×C22⋊D151C2211yescharacteristic
36C2×C4⋊Dic151C2211yescharacteristic
37C4⋊C4×D151C2211yescharacteristic
38#18012671C2211yescharacteristic
39#18012671C2211yescharacteristic
40#18012670C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012663C2211yescharacteristic
48#18012662C2211yescharacteristic
49#18012660C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C22×Q8×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559003—44no—
60C2×Dic302—21no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63Q8×D151—22no—
64Q8×D151—41no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151D411yescharacteristic
67C22×Dic151—21no—
68C22×Dic151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151C2311yescharacteristic
72#14558992—41no—
73C2×C151⋊C8—41no—
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C8×D151—41no—
77C4⋊Dic151—21no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4D411yescharacteristic
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151D411yescharacteristic
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151—21no—
98C2×Q8×C151—22no—
99C2×Q8×C151—41no—
100C2×Q8×C151C2311yescharacteristic
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151C2311yescharacteristic
104C22×C4×C151—21no—
105C22×C4×C151C2311yescharacteristic
106SD16×C151—22no—
107SD16×C151—41no—
108C2×C8×C151C2311yescharacteristic
109C2×C8×C151C2311yescharacteristic
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22×D151C2×D411yescharacteristic
113Dic302—21no—
114Dic302—21no—
115Dic302—42no—
116Dic302—42no—
117C22⋊D151—42no—
118C22⋊D151SD1614yescomplemented
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—42no—
124C2×Dic151—42no—
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—42no—
131C4×D151—42no—
132C151⋊C8—21no—
133C151⋊C8—21no—
134C23×C151—21no—
135C23×C151C2×D411yescharacteristic
136Q8×C151—21no—
137Q8×C151—21no—
138Q8×C151—21no—
139Q8×C151—42no—
140Q8×C151#4112yescomplemented
141D4×C151—21no—
142D4×C151—21no—
143D4×C151—42no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—42no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2411yescharacteristic
152C8×C151—21no—
153C8×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151C2×SD1612yes—
160C22×C151C22×D411yescharacteristic
161C2×D151—21no—
162C2×D151—21no—
163C2×D151C2×SD1612yes—
164C4×C151—21no—
165C4×C151—22no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151C2×#4111yescharacteristic
169C4×C151H(5,𝔽2)11yescharacteristic
170Dic151—21no—
171Dic151—21no—
172Dic151—41no—
173Dic151—41no—
174Dic151—41no—
175Dic151—41no—
176Dic151C2×SD1612yes—
177C2×C151—22no—
178C2×C151—81no—
179C2×C151#54611yescharacteristic
180C2×C151C22×SD1611yescharacteristic
181C2×C151#57811yescharacteristic
182D151—22no—
183C151#329811yescharacteristic, complemented, Sylow
184#3298—1511nomaximal, Sylow
185D4×Q8—1511no—
186#547—1511no—
187#487—1511no—
188#483—1511no—
189#483—1511no—
190#475—1511no—
191#465—1511no—
192#465—1511no—
193#461—1511no—
194#448—1511no—
195#448D15111yescharacteristic, complemented
196C4×SD16—1511no—
197C8×D4—1511no—
198C2×#103—1511no—
199C2×#103—1511no—
200C2×#41—3021no—
201C22×Q8—1511no—
202C22×Q8C2×D15111yescharacteristic
203C2×SD16—1511no—
204C2×SD16C2×D15111yescharacteristic
205C2×SD16C2×D15111yescharacteristic
206C22×C8—1511no—
207C22×C8—1511no—
208C4⋊Q8—3021no—
209C4⋊Q8—1511no—
210C4⋊Q8—1511no—
211#123—3021no—
212#123—3021no—
213C22⋊Q8—3021no—
214C22⋊Q8—3021no—
215C22⋊Q8—3021no—
216C22⋊Q8—1511no—
217C22⋊Q8—1511no—
218#121—1511no—
219#121C2×D15111yescharacteristic
220C4×Q8—1511no—
221C4×D4—3021no—
222C4×D4—1511no—
223C4×D4—1511no—
224C2×C4⋊C4—1511no—
225C2×C4⋊C4—1511no—
226#106—1511no—
227#106—1511no—
228#106—1511no—
229C4⋊C8—1511no—
230#103—1511no—
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#103C2×D15111yescharacteristic
238#103C2×D15111yescharacteristic
239#102—1511no—
240C22⋊C8—1511no—
241C22⋊C8C2×D15111yescharacteristic
242C4×C8—1511no—
243#41—6044no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—3021no—
248C2×Q8—3021no—
249C2×Q8—3022no—
250C2×Q8—6041no—
251C2×Q8—1511no—
252C2×Q8C22×D15111yescharacteristic
253C2×Q8C22×D15111yescharacteristic
254C2×D4—21no—
255C2×D4—3021no—
256C2×D4—1511no—
257C2×D4C22×D15111yescharacteristic
258C22×C4—21no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—3021no—
263C22×C4—1511no—
264C22×C4C22×D15111yescharacteristic
265SD16—22no—
266SD16—41no—
267SD16—6041no—
268C2×C8—6041no—
269C2×C8—6041no—
270C2×C8—1511no—
271C2×C8—1511no—
272C2×C8C22×D15111yescharacteristic
273C2×C8C22×D15111yescharacteristic
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—3021no—
279C4⋊C4—3021no—
280C4⋊C4—3021no—
281C4⋊C4—3021no—
282C4⋊C4—1511no—
283C4⋊C4—1511no—
284C4⋊C4—1511no—
285C4⋊C4—1511no—
286C4⋊C4C22×D15111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—1511no—
293C22⋊C4—1511no—
294C42—3021no—
295C42—1511no—
296C23—21no—
297C23—1511no—
298C23D4×D15111yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—42no—
303Q8—3021no—
304Q8—3021no—
305Q8—6042no—
306Q8—6042no—
307Q8#1455900312yescomplemented
308D4—21no—
309D4—21no—
310D4—42no—
311D4—6042no—
312D4—1514no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—6042no—
326C2×C4—6042no—
327C2×C4—6042no—
328C2×C4—6042no—
329C2×C4—1511no—
330C2×C4—1511no—
331C2×C4—1511no—
332C2×C4D4×D15111yescharacteristic
333C2×C4C23×D15111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3021no—
337C8—3021no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—3021no—
344C22—3021no—
345C22—1512no—
346C22SD16×D15112yes—
347C22C2×D4×D15111yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—3021no—
353C4—3021no—
354C4—6041no—
355C4—6041no—
356C4—6041no—
357C4—6041no—
358C4—1512no—
359C4C2×#1455900311yescharacteristic
360C4#1801278411yescharacteristic
361C2—22no—
362C2—81no—
363C2—3022no—
364C2#2375284911yescharacteristic
365C2C2×SD16×D15111yescharacteristic
366C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#448×C151C2
socleC22×C151C22×D4
prime radical#23752862C2
hypercenter#448D151
hypocenterC151#3298
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D151C2semidirect
3. #23752561C2semidirect
4. #23752543C2semidirect
5. #23752541C2semidirect
6. #23752495C2semidirect
7. #23752439C2semidirect
8. #23752438C2semidirect
9. #23752415C2semidirect
10. #23752349C2semidirect
11. SD16×Dic151C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. C2×#18012663C2semidirect
14. #103×D151C2semidirect
15. #448×C151C2semidirect
118. C22⋊D151SD16semidirect
140. Q8×C151#41semidirect
183. C151#3298semidirect
195. #448D151semidirect
307. Q8#14559003semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D1512
#237528622
#237525612
#237525432
#237525412
#237524952
#237524392
#237524382
#237524152
#237523492
SD16×Dic1512
(C22⋊D151)⋊C82
C2×#180126632
#103×D1512
#448×C1512
#3298151