Finite Group Databasebeta

← #34080435

Subgroups — #34080435

Order 19328.

398 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#23752747C211yesmaximal, characteristic, complemented
3#23752509C211yesmaximal, characteristic, complemented
4#23752506C211yesmaximal, characteristic, complemented
5#23752501C211yesmaximal, characteristic, complemented
6#23752449C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752442C211yesmaximal, characteristic, complemented
9#23752440C211yesmaximal, characteristic, complemented
10#23752428C211yesmaximal, characteristic, complemented
11#23752427C211yesmaximal, characteristic, complemented
12#23752411C211yesmaximal, characteristic, complemented
13#23752406C211yesmaximal, characteristic, complemented
14C4⋊C8×D151C211yesmaximal, characteristic, complemented
15#478×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×#14558993C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22C2×C8×D151C2211yescharacteristic
23#18012738C2211yescharacteristic
24#18012735C2211yescharacteristic
25#18012734—21no—
26#18012727C2211yescharacteristic
27#18012725—21no—
28#18012724—21no—
29#18012719C2211yescharacteristic
30#18012714C2211yescharacteristic
31#18012714C2211yescharacteristic
32#18012712—21no—
33#18012710C2211yescharacteristic
34#18012704C2211yescharacteristic
35C4×D604C2211yescharacteristic
36#18012701—21no—
37#18012701C2211yescharacteristic
38C4×C22⋊D151—21no—
39#18012697—21no—
40C42×D151C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012659C2211yescharacteristic
51#18012659C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559004—44no—
60C2×Dic302—21no—
61C2×Dic302C2311yescharacteristic
62C2×D604—21no—
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151D411yescharacteristic
72C2×C4×D151D411yescharacteristic
73C2×C4×D151C2311yescharacteristic
74#14558993—41no—
75#14558992—41no—
76D1208—41no—
77#14558989—41no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C8×D151—41no—
81C8×D151—41no—
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
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×Dic151—21no—
95C4×Dic151D411yescharacteristic
96C4×Dic151D411yescharacteristic
97C4×Dic151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C42×C151C2311yescharacteristic
109C22×D151—21no—
110C22×D151—21no—
111C22×D151C2×D411yescharacteristic
112Dic302—21no—
113Dic302—21no—
114Dic302—42no—
115D604—21no—
116D604—21no—
117D604—21no—
118D604—21no—
119D604—42no—
120D604—42no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C22⋊D151—42no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—22no—
130C4×D151—21no—
131C4×D151—21no—
132C4×D151—22no—
133C4×D151—42no—
134C4×D151—42no—
135C151⋊C8—21no—
136C151⋊C8—21no—
137C23×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—21no—
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×C151H(5,𝔽2)11yescharacteristic
168C4×C1512−1+411yescharacteristic
169Dic151—21no—
170Dic151—21no—
171Dic151—41no—
172Dic151—41no—
173Dic151#13512yes—
174C2×C151—81no—
175C2×C151#53711yescharacteristic
176C2×C151C2×#13511yescharacteristic
177C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
178D151—22no—
179D151—81no—
180D151—81no—
181C151#324711yescharacteristic, complemented, Sylow
182#3247—1511nomaximal, Sylow
183#532—1511no—
184#529—1511no—
185#478—1511no—
186#478D15111yescharacteristic, complemented
187#477—1511no—
188#476—1511no—
189#466—1511no—
190#466—1511no—
191#465—1511no—
192#465—1511no—
193#463—1511no—
194#463—1511no—
195#460—1511no—
196#459—1511no—
197C2×C4⋊C8—1511no—
198C2×#41—3021no—
199C2×SD16—1511no—
200C2×SD16—1511no—
201C2×D8—1511no—
202C2×D8—1511no—
203C22×C8—1511no—
204C22×C8—1511no—
205C4⋊Q8—1511no—
206#127—1511no—
207#126—3021no—
208#125C2×D15111yescharacteristic
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×Q8—1511no—
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#106C2×D15111yescharacteristic
229C4⋊C8—1511no—
230C4⋊C8—1511no—
231C4⋊C8—1511no—
232C4⋊C8C2×D15111yescharacteristic
233#103—1511no—
234#103—1511no—
235#102—1511no—
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102C2×D15111yescharacteristic
240#102C2×D15111yescharacteristic
241#41—6044no—
242C2×Q8—3021no—
243C2×Q8—1511no—
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—6041no—
259SD16—6041no—
260D8—6041no—
261D8—6041no—
262C2×C8—6041no—
263C2×C8—6041no—
264C2×C8—1511no—
265C2×C8—1511no—
266C2×C8C22×D15111yescharacteristic
267C2×C8C22×D15111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—1511no—
274C4⋊C4C22×D15111yescharacteristic
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—3021no—
287C42—1511no—
288C42—1511no—
289C42—1511no—
290C42C22×D15111yescharacteristic
291C23—21no—
292C23—3021no—
293C23—3021no—
294C23—1511no—
295Q8—3021no—
296Q8—3021no—
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—3022no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—3021no—
318C2×C4—3021no—
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—21no—
329C8—3021no—
330C8—3021no—
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—6041no—
352C4—6041no—
353C4—1512no—
354C4#1801278511yescharacteristic
355C4#1801278711yescharacteristic
356C2—81no—
357C2—3022no—
358C2—12081no—
359C2—12081no—
360C2#2375279211yescharacteristic
361C2#135×D15111yescharacteristic
362C2AGL(1,ℤ/8)×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#478×C151C2
socleC22×C151C22×D4
hypercenter#478D151
hypocenterC151#3247
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23752759C2semidirect
2. #23752747C2semidirect
3. #23752509C2semidirect
4. #23752506C2semidirect
5. #23752501C2semidirect
6. #23752449C2semidirect
7. #23752447C2semidirect
8. #23752442C2semidirect
9. #23752440C2semidirect
10. #23752428C2semidirect
11. #23752427C2semidirect
12. #23752411C2semidirect
13. #23752406C2semidirect
14. C4⋊C8×D151C2semidirect
15. #478×C151C2semidirect
181. C151#3247semidirect
186. #478D151semidirect

Maximal subgroups

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

subgroupindex
#237527592
#237527472
#237525092
#237525062
#237525012
#237524492
#237524472
#237524422
#237524402
#237524282
#237524272
#237524112
#237524062
C4⋊C8×D1512
#478×C1512
#3247151