Finite Group Databasebeta

← #34079804

Subgroups — #34079804

Order 19328.

410 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752759C211yesmaximal, characteristic, complemented
2#23752749C211yesmaximal, characteristic, complemented
3#23752620C211yesmaximal, characteristic, complemented
4#23752598C211yesmaximal, characteristic, complemented
5#23752575C211yesmaximal, characteristic, complemented
6#23752573C211yesmaximal, characteristic, complemented
7#23752449C211yesmaximal, characteristic, complemented
8#23752447C211yesmaximal, characteristic, complemented
9#23752444C211yesmaximal, characteristic, complemented
10#23752438C211yesmaximal, characteristic, complemented
11#23752325C211yesmaximal, characteristic, complemented
12#23752322C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#97×D151C211yesmaximal, characteristic, complemented
15#440×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×#14558991C2211yescharacteristic
18C2×D1208C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012738C2211yescharacteristic
23#18012735C2211yescharacteristic
24#18012734—21no—
25#18012730C2211yescharacteristic
26#18012728C2211yescharacteristic
27#18012725—21no—
28#18012724—21no—
29#18012715C2211yescharacteristic
30#18012714C2211yescharacteristic
31#18012714C2211yescharacteristic
32#18012712—21no—
33#18012710C2211yescharacteristic
34C4×D604—21no—
35C4×D604C2211yescharacteristic
36C4×D604C2211yescharacteristic
37C4×C22⋊D151—21no—
38#18012696—21no—
39C42×D151C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012650C2211yescharacteristic
50#18012649C2211yescharacteristic
51#18012649C2211yescharacteristic
52C2×SD16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59#14559004—44no—
60C2×Dic302—21no—
61C2×D604—21no—
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151D411yescharacteristic
71C2×C4×D151D411yescharacteristic
72C2×C4×D151C2311yescharacteristic
73#14558991—22no—
74D1208—22no—
75#14558989—22no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C8×D151—22no—
79C8×D151—22no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94C4×Dic151D411yescharacteristic
95C4×Dic151D411yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100SD16×C151—22no—
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151—21no—
108C42×C151C2311yescharacteristic
109C22×D151—21no—
110C22×D151—21no—
111C22×D151C2×D411yescharacteristic
112Dic302—42no—
113D604—21no—
114D604—21no—
115D604—21no—
116D604—21no—
117D604—42no—
118D604—42no—
119C22⋊D151—42no—
120C22⋊D151—42no—
121C22⋊D151—42no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—22no—
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—41no—
131C4×D151—42no—
132C4×D151—42no—
133C151⋊C8—21no—
134C151⋊C8#4112yescomplemented
135C23×C151—21no—
136Q8×C151—21no—
137Q8×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—42no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2411yescharacteristic
147C8×C151—21no—
148C8×C151#4112yescomplemented
149C22×C151—41no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151C22×D411yescharacteristic
153C2×D151—21no—
154C2×D151—21no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151AGL(1,ℤ/8)12yes—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151C2×#4111yescharacteristic
168C4×C151C2×#4111yescharacteristic
169Dic151—21no—
170Dic151—21no—
171Dic151—21no—
172Dic151—41no—
173Dic151—41no—
174C2×C151—81no—
175C2×C151#53211yescharacteristic
176C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C151#57511yescharacteristic
178D151—22no—
179D151—81no—
180D151—81no—
181C151#318011yescharacteristic, complemented, Sylow
182#3180—1511nomaximal, Sylow
183#532—1511no—
184#529—1511no—
185#501—1511no—
186#496—1511no—
187#490—1511no—
188#489—1511no—
189#466—1511no—
190#466—1511no—
191#465—1511no—
192#465—1511no—
193#442—1511no—
194#442—1511no—
195#440—1511no—
196#440D15111yescharacteristic, complemented
197C2×#97—1511no—
198C2×#41—3021no—
199C2×SD16—1511no—
200C2×SD16C2×D15111yescharacteristic
201C2×D8—1511no—
202C2×D8—1511no—
203C22×C8—1511no—
204C22×C8—1511no—
205C4⋊Q8—1511no—
206#127—1511no—
207#126—3021no—
208#125—1511no—
209#124—3021no—
210#124—1511no—
211#123—3021no—
212C22⋊Q8—1511no—
213#121—3021no—
214#121—1511no—
215#121—1511no—
216#121—1511no—
217C4×Q8C2×D15111yescharacteristic
218C4×D4—3021no—
219C4×D4—3021no—
220C4×D4—1511no—
221C4×D4—1511no—
222C4×D4C2×D15111yescharacteristic
223#117—3021no—
224C2×C42—1511no—
225#107—1511no—
226#107C2×D15111yescharacteristic
227#106—1511no—
228#106—1511no—
229#103—1511no—
230#103C2×D15111yescharacteristic
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236#102C2×D15111yescharacteristic
237#97—1511no—
238#97—1511no—
239#97—1511no—
240#97C2×D15111yescharacteristic
241#41—6044no—
242C2×Q8—3021no—
243C2×Q8C22×D15111yescharacteristic
244C2×D4—3021no—
245C2×D4—3021no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—3021no—
249C2×D4—1511no—
250C2×D4—1511no—
251C2×D4C22×D15111yescharacteristic
252C22×C4—21no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—1511no—
256C22×C4—1511no—
257C22×C4—1511no—
258SD16—22no—
259SD16—3022no—
260D8—3022no—
261D8—3022no—
262C2×C8—3022no—
263C2×C8—3022no—
264C2×C8—1511no—
265C2×C8—1511no—
266C2×C8C22×D15111yescharacteristic
267C2×C8C22×D15111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C42—21no—
287C42—1511no—
288C42—1511no—
289C42—1511no—
290C42C22×D15111yescharacteristic
291C23—21no—
292C23—3021no—
293C23—3021no—
294C23—1511no—
295Q8—21no—
296Q8—21no—
297Q8—6042no—
298D4—21no—
299D4—21no—
300D4—3021no—
301D4—3021no—
302D4—3021no—
303D4—3021no—
304D4—6042no—
305D4—6042no—
306D4—6042no—
307D4—6042no—
308D4—6042no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—3022no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—3021no—
318C2×C4—6041no—
319C2×C4—6042no—
320C2×C4—6042no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4D4×D15111yescharacteristic
325C2×C4D4×D15111yescharacteristic
326C2×C4C23×D15111yescharacteristic
327C8—21no—
328C8—3021no—
329C8—1512no—
330C8#1455900412yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—3021no—
335C22—3021no—
336C22—6041no—
337C22—6041no—
338C22—6041no—
339C22—6041no—
340C22—6041no—
341C22—6041no—
342C22—1512no—
343C22C2×D4×D15111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3021no—
350C4—3021no—
351C4—3021no—
352C4—6041no—
353C4—6041no—
354C4#41×D15111yescharacteristic
355C4C2×#1455900411yescharacteristic
356C2—81no—
357C2—3022no—
358C2—12081no—
359C2—12081no—
360C2#2375275911yescharacteristic
361C2AGL(1,ℤ/8)×D15111yescharacteristic
362C2#2375301111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#440×C151C2
socleC22×C151C22×D4
hypercenter#440D151
hypocenterC151#3180
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23752759C2semidirect
2. #23752749C2semidirect
3. #23752620C2semidirect
4. #23752598C2semidirect
5. #23752575C2semidirect
6. #23752573C2semidirect
7. #23752449C2semidirect
8. #23752447C2semidirect
9. #23752444C2semidirect
10. #23752438C2semidirect
11. #23752325C2semidirect
12. #23752322C2semidirect
13. #23752310C2semidirect
14. #97×D151C2semidirect
15. #440×C151C2semidirect
134. C151⋊C8#41semidirect
148. C8×C151#41semidirect
181. C151#3180semidirect
196. #440D151semidirect
330. C8#14559004semidirect

Maximal subgroups

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

subgroupindex
#237527592
#237527492
#237526202
#237525982
#237525752
#237525732
#237524492
#237524472
#237524442
#237524382
#237523252
#237523222
#237523102
#97×D1512
#440×C1512
#3180151