Finite Group Databasebeta

← #34080996

Subgroups — #34080996

Order 19328.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752900C211yesmaximal, characteristic, complemented
2#23752870C211yesmaximal, characteristic
3#23752552C211yesmaximal, characteristic, complemented
4#23752524C211yesmaximal, characteristic, complemented
5#23752516C211yesmaximal, characteristic, complemented
6#23752452C211yesmaximal, characteristic, complemented
7#23752440C211yesmaximal, characteristic, complemented
8#23752431C211yesmaximal, characteristic, complemented
9#23752375C211yesmaximal, characteristic, complemented
10#23752369C211yesmaximal, characteristic, complemented
11C4×Dic604C211yesmaximal, characteristic, complemented
12C8×D604C211yesmaximal, characteristic, complemented
13#23752205C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#488×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×Dic604C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22C2×C8×D151C2211yescharacteristic
23#18012734—21no—
24#18012730—21no—
25#18012725—21no—
26#18012724—21no—
27#18012719C2211yescharacteristic
28#18012719C2211yescharacteristic
29#18012716—21no—
30#18012715C2211yescharacteristic
31#18012712—21no—
32#18012710C2211yescharacteristic
33C4×Dic302C2211yescharacteristic
34C4×Dic302C2211yescharacteristic
35C4×D604C2211yescharacteristic
36(C22⋊D151)⋊C4—21no—
37#18012697—21no—
38#18012697C2211yescharacteristic
39C4⋊C4×D151C2211yescharacteristic
40#18012673C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012662C2211yescharacteristic
49#18012660C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52#125×C151C2211yescharacteristic
53#124×C151C2211yescharacteristic
54#103×C151C2211yescharacteristic
55#103×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59#14559003—22no—
60#14559003—41no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64Q8×D151—22no—
65Q8×D151—41no—
66C2×D604D411yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151C2311yescharacteristic
73C2×C4×D151C2311yescharacteristic
74Dic604—22no—
75#14558994—41no—
76#14558992—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C8×D151—41no—
80C8×D151—41no—
81C4⋊Dic151—21no—
82C4⋊Dic151—21no—
83C4⋊Dic151D411yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90C22⋊Dic151—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4D411yescharacteristic
96(C2×D151)⋊C4D411yescharacteristic
97C4×Dic151—21no—
98C4×Dic151—21no—
99C4×Dic151—21no—
100C2×Q8×C151C2311yescharacteristic
101C2×D4×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C2×C8×C151C2311yescharacteristic
104C4⋊C4×C151—21no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C22⋊C4×C151—21no—
109C22⋊C4×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151C2×D411yescharacteristic
112C22×D151C2×D411yescharacteristic
113Dic302—21no—
114Dic302—21no—
115Dic302—21no—
116Dic302—42no—
117Dic302#4112yes—
118D604—22no—
119C22⋊D151—42no—
120C22⋊D151—42no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—42no—
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—21no—
132C4×D151—42no—
133C4×D151—42no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151—21no—
137Q8×C151—21no—
138Q8×C151—21no—
139D4×C151—21no—
140D4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
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—21no—
156C2×D151—21no—
157C2×D151—21no—
158C2×D151#13512yes—
159C4×C151—21no—
160C4×C151—21no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151—41no—
164C4×C151C2×#4111yescharacteristic
165C4×C151H(5,𝔽2)11yescharacteristic
166Dic151—21no—
167Dic151—21no—
168Dic151—22no—
169Dic151—41no—
170Dic151—41no—
171Dic151—41no—
172C2×C151—81no—
173C2×C151#54611yescharacteristic
174C2×C151C2×#13511yescharacteristic
175C2×C151#57811yescharacteristic
176D151—22no—
177D151—41no—
178C151#330011yescharacteristic, complemented, Sylow
179#3300—1511nomaximal, Sylow
180#552—1511no—
181#548—1511no—
182#488D15111yescharacteristic, complemented
183#485—1511no—
184#480—1511no—
185#479—1511no—
186#467—1511no—
187#465—1511no—
188#464—1511no—
189#452—1511no—
190#451—1511no—
191C4×Q16—1511no—
192C8×D4—1511no—
193#416—1511no—
194C2×#103—1511no—
195C2×#41—1511no—
196C22×Q8—1511no—
197C2×Q16—1511no—
198C2×Q16—1511no—
199C2×SD16—1511no—
200C22×C8—1511no—
201C22×C8—1511no—
202#126—3021no—
203#125—3021no—
204#125C2×D15111yescharacteristic
205#124—3021no—
206#124C2×D15111yescharacteristic
207#123—3021no—
208C22⋊Q8—3021no—
209C22⋊Q8—1511no—
210C22⋊Q8—1511no—
211C22⋊Q8—1511no—
212#121—3021no—
213#121—1511no—
214C4×Q8—1511no—
215C4×Q8—1511no—
216C4×D4—3021no—
217C4×D4—1511no—
218#117—3021no—
219#117—1511no—
220C2×C4⋊C4—1511no—
221#107—1511no—
222#107—1511no—
223#106—1511no—
224C4⋊C8—1511no—
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103—1511no—
230#103C2×D15111yescharacteristic
231#103C2×D15111yescharacteristic
232#102—1511no—
233#102C2×D15111yescharacteristic
234#102C2×D15111yescharacteristic
235C22⋊C8—1511no—
236C22⋊C8—1511no—
237C4×C8C2×D15111yescharacteristic
238#41—3022no—
239#41—6041no—
240C2×Q8—3021no—
241C2×Q8—3022no—
242C2×Q8—6041no—
243C2×Q8—1511no—
244C2×Q8—1511no—
245C2×Q8C22×D15111yescharacteristic
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4C22×D15111yescharacteristic
250C22×C4—3021no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—1511no—
254C22×C4—1511no—
255Q16—3022no—
256Q16—6041no—
257SD16—6041no—
258C2×C8—6041no—
259C2×C8—6041no—
260C2×C8—1511no—
261C2×C8—1511no—
262C2×C8C22×D15111yescharacteristic
263C2×C8C22×D15111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—1511no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—1511no—
285C22⋊C4—1511no—
286C42—3021no—
287C42—3021no—
288C42—3021no—
289C42C22×D15111yescharacteristic
290C23—21no—
291C23—1511no—
292C23—1511no—
293Q8—21no—
294Q8—21no—
295Q8—3021no—
296Q8—3021no—
297Q8—3021no—
298Q8—6042no—
299Q8—1512no—
300D4—21no—
301D4—21no—
302D4—3022no—
303D4—6042no—
304D4—6042no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—3021no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—6042no—
317C2×C4—6042no—
318C2×C4—6042no—
319C2×C4—1511no—
320C2×C4—1511no—
321C2×C4D4×D15111yescharacteristic
322C2×C4D4×D15111yescharacteristic
323C2×C4C23×D15111yescharacteristic
324C8—21no—
325C8—21no—
326C8—3021no—
327C8—3021no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—3021no—
332C22—3021no—
333C22—3021no—
334C22—3021no—
335C22—3021no—
336C22—1512no—
337C22C2×D4×D15111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3021no—
344C4—3021no—
345C4—3022no—
346C4—6041no—
347C4—6041no—
348C4—6041no—
349C4#41×D15111yescharacteristic
350C4#1801278511yescharacteristic
351C2—81no—
352C2—3022no—
353C2—6041no—
354C2#2375285511yescharacteristic
355C2#135×D15111yescharacteristic
356C2#2375302611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#488×C151C2
socleC22×C151C22×D4
prime radical#23752870C2
hypercenter#488D151
hypocenterC151#3300
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #23752900C2semidirect
3. #23752552C2semidirect
4. #23752524C2semidirect
5. #23752516C2semidirect
6. #23752452C2semidirect
7. #23752440C2semidirect
8. #23752431C2semidirect
9. #23752375C2semidirect
10. #23752369C2semidirect
11. C4×Dic604C2semidirect
12. C8×D604C2semidirect
13. #23752205C2semidirect
14. #103×D151C2semidirect
15. #488×C151C2semidirect
178. C151#3300semidirect
182. #488D151semidirect

Maximal subgroups

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

subgroupindex
#237529002
#237528702
#237525522
#237525242
#237525162
#237524522
#237524402
#237524312
#237523752
#237523692
C4×Dic6042
C8×D6042
#237522052
#103×D1512
#488×C1512
#3300151