Finite Group Databasebeta

← #34083222

Subgroups — #34083222

Order 19328.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752947C213yesmaximal, complemented
2#23752928C213yesmaximal, complemented
3#23752915C213yesmaximal, complemented
4#23752900C213yesmaximal, complemented
5#23752884C211yesmaximal, characteristic, complemented
6#23752874C211yesmaximal, characteristic, complemented
7#23752874C211yesmaximal, characteristic, complemented
8#23752836C213yesmaximal, complemented
9#23752818C213yesmaximal, complemented
10#23752749C213yesmaximal, complemented
11#23752747C213yesmaximal, complemented
12#23752694C211yesmaximal, characteristic, complemented
13#23752688C211yesmaximal, characteristic, complemented
14C4×#14559005C211yesmaximal, characteristic, complemented
15#557×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559005C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19#18012736C2213yes—
20#18012734C2213yes—
21#18012734C2211yescharacteristic
22#18012734C2216yes—
23#18012730C2213yes—
24#18012728C2213yes—
25#18012728C2216yes—
26#18012727C2213yes—
27#18012727C2213yes—
28#18012724C2216yes—
29#18012724C2213yes—
30#18012724C2213yes—
31#18012724C2216yes—
32#18012719C2213yes—
33#18012719C2213yes—
34#18012715C2213yes—
35#18012714C2213yes—
36#18012714C2213yes—
37#18012714C2213yes—
38#18012714C2213yes—
39#18012714C2216yes—
40#18012714C2213yes—
41Q8×Dic151C2211yescharacteristic
42C4×Dic302C2213yes—
43#18012704C2213yes—
44C4×D604C2213yes—
45C4×D604C2213yes—
46C4×D604C2213yes—
47C4×D604C2213yes—
48C4×D604C2213yes—
49#18012701C2213yes—
50#18012701C2216yes—
51#18012701C2213yes—
52#18012697C2216yes—
53#18012697C2213yes—
54#18012697C2213yes—
55#18012696C2213yes—
56#18012696C2213yes—
57C4⋊C4×D151C2213yes—
58C42×D151C2213yes—
59C4⋊Q8×C151C2213yes—
60#125×C151C2213yes—
61#125×C151C2213yes—
62C4×Q8×C151C2213yes—
63C4×Q8×C151C2211yescharacteristic
64C4×Q8×C151C2211yescharacteristic
65C4×Q8×C151C2211yescharacteristic
66#14559005—24no—
67#14559005—24no—
68C2×Dic302C2313yes—
69Q8×D151—24no—
70C2×D604C2313yes—
71C2×D604C2313yes—
72C2×D604C2316yes—
73C2×D604C2313yes—
74C2×D604C2313yes—
75C2×D604C2313yes—
76C2×C4×D151C2313yes—
77C2×C4×D151C2313yes—
78C2×C4×D151C2313yes—
79C2×C4×D151C2313yes—
80C2×C4×D151C2313yes—
81C2×C4×D151C2316yes—
82C4⋊Dic151C2313yes—
83C4⋊Dic151C2313yes—
84C4⋊Dic151C2311yescharacteristic
85C4⋊Dic151C2313yes—
86Dic151⋊C4C2313yes—
87Dic151⋊C4C2311yescharacteristic
88Dic151⋊C4C2313yes—
89Dic151⋊C4C2313yes—
90(C2×D151)⋊C4C2311yescharacteristic
91(C2×D151)⋊C4C2313yes—
92(C2×D151)⋊C4C2313yes—
93(C2×D151)⋊C4C2313yes—
94(C2×D151)⋊C4C2313yes—
95(C2×D151)⋊C4C2316yes—
96(C2×D151)⋊C4C2316yes—
97(C2×D151)⋊C4C2313yes—
98(C2×D151)⋊C4C2316yes—
99(C2×D151)⋊C4C2311yescharacteristic
100(C2×D151)⋊C4C2311yescharacteristic
101(C2×D151)⋊C4C2313yes—
102(C2×D151)⋊C4C2313yes—
103C4×Dic151C2311yescharacteristic
104C4×Dic151C2313yes—
105C4×Dic151C2313yes—
106C4×Dic151C2316yes—
107C2×Q8×C151C2313yes—
108C2×Q8×C151C2311yescharacteristic
109C4⋊C4×C151C2313yes—
110C4⋊C4×C151C2313yes—
111C4⋊C4×C151C2313yes—
112C4⋊C4×C151C2316yes—
113C4⋊C4×C151C2313yes—
114C4⋊C4×C151C2313yes—
115C4⋊C4×C151C2311yescharacteristic
116C42×C151C2313yes—
117C42×C151C2313yes—
118C42×C151C2313yes—
119C22×D151C2411yescharacteristic
120C22×D151C2413yes—
121C22×D151C2413yes—
122Dic302—26no—
123D604—26no—
124D604—26no—
125D604—43no—
126D604—46no—
127D604—43no—
128D604—43no—
129C2×Dic151C2411yescharacteristic
130C2×Dic151C2413yes—
131C2×Dic151C2411yescharacteristic
132C2×Dic151C2413yes—
133C2×Dic151C2411yescharacteristic
134C4×D151—26no—
135C4×D151—26no—
136C4×D151—26no—
137C4×D151—43no—
138C4×D151—43no—
139C4×D151—46no—
140Q8×C151—43no—
141Q8×C151#4114yes—
142C2×C4×C151C2411yescharacteristic
143C2×C4×C151C2413yes—
144C2×C4×C151C2413yes—
145C2×C4×C151C2411yescharacteristic
146C2×C4×C151C2413yes—
147C2×C4×C151C2411yescharacteristic
148C2×C4×C151C2413yes—
149C22×C151C2511yescharacteristic
150C2×D151—21no—
151C2×D151—23no—
152C2×D151—23no—
153C2×D151—23no—
154C2×D151—23no—
155C2×D151—23no—
156C2×D151—21no—
157C2×D151—23no—
158C2×D151—21no—
159C4×C151—21no—
160C4×C151—23no—
161C4×C151—23no—
162C4×C151—21no—
163C4×C151—23no—
164C4×C151—21no—
165C4×C151C2×#4116yes—
166Dic151—21no—
167Dic151—21no—
168Dic151—23no—
169Dic151—21no—
170Dic151—23no—
171C2×C151C22×#4111yescharacteristic
172C2×C151#58511yescharacteristic
173C2×C151#58511yescharacteristic
174D151—41no—
175D151—43no—
176D151—43no—
177C151#352411yescharacteristic, complemented, Sylow
178#3524—1511nomaximal, Sylow
179#559—1513no—
180#557D15111yescharacteristic, complemented
181#555—1513no—
182#553—1513no—
183#552—1513no—
184#550—1511no—
185#548—1511no—
186#548—1511no—
187#542—1513no—
188#540—1513no—
189#529—1513no—
190#529—1513no—
191#520—1511no—
192#519—1511no—
193C4×#41—1511no—
194C2×#41—1511no—
195C2×#41—1511no—
196C22×Q8—1511no—
197C4⋊Q8C2×D15113yes—
198#127—1513no—
199#126—1511no—
200#126—1513no—
201#126—1516no—
202#125—1513no—
203#125C2×D15113yes—
204#125C2×D15113yes—
205#124—1513no—
206#124—1516no—
207#124—1513no—
208#124—1513no—
209#123—1516no—
210#123—1513no—
211#123—1513no—
212#123—1516no—
213C22⋊Q8—1513no—
214C22⋊Q8—1513no—
215C22⋊Q8—1513no—
216#121—1513no—
217#121—1513no—
218#121—1513no—
219#121—1513no—
220#121—1516no—
221#121—1513no—
222C4×Q8—1511no—
223C4×Q8—1513no—
224C4×Q8—1513no—
225C4×Q8C2×D15111yescharacteristic
226C4×Q8C2×D15111yescharacteristic
227C4×Q8C2×D15111yescharacteristic
228C4×Q8C2×D15113yes—
229C4×D4—1513no—
230C4×D4—1513no—
231C4×D4—1516no—
232C4×D4—1513no—
233C4×D4—1513no—
234C4×D4—1513no—
235C4×D4—1513no—
236C4×D4—1513no—
237#117—1513no—
238#117—1513no—
239#117—1516no—
240#117—1513no—
241#117—1513no—
242C2×C4⋊C4—1513no—
243C2×C42—1513no—
244#41—3024no—
245#41—3024no—
246C2×Q8—3024no—
247C2×Q8—1513no—
248C2×Q8C22×D15113yes—
249C2×Q8C22×D15111yescharacteristic
250C2×D4—1513no—
251C2×D4—1513no—
252C2×D4—1513no—
253C2×D4—1513no—
254C2×D4—1516no—
255C2×D4—1513no—
256C22×C4—1513no—
257C22×C4—1513no—
258C22×C4—1513no—
259C22×C4—1513no—
260C22×C4—1513no—
261C22×C4—1516no—
262C4⋊C4—1513no—
263C4⋊C4—1511no—
264C4⋊C4—1513no—
265C4⋊C4—1513no—
266C4⋊C4—1513no—
267C4⋊C4—1513no—
268C4⋊C4—1511no—
269C4⋊C4—1513no—
270C4⋊C4C22×D15113yes—
271C4⋊C4C22×D15113yes—
272C4⋊C4C22×D15113yes—
273C4⋊C4C22×D15116yes—
274C4⋊C4C22×D15113yes—
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15113yes—
277C22⋊C4—1511no—
278C22⋊C4—1513no—
279C22⋊C4—1513no—
280C22⋊C4—1513no—
281C22⋊C4—1516no—
282C22⋊C4—1513no—
283C22⋊C4—1516no—
284C22⋊C4—1511no—
285C22⋊C4—1513no—
286C22⋊C4—1511no—
287C22⋊C4—1513no—
288C22⋊C4—1516no—
289C22⋊C4—1513no—
290C42—1511no—
291C42—1513no—
292C42—1513no—
293C42—1516no—
294C42C22×D15113yes—
295C42C22×D15113yes—
296C42C22×D15113yes—
297C23—1511no—
298C23—1513no—
299C23—1513no—
300Q8—43no—
301Q8—3026no—
302Q8#1455900514yes—
303D4—3026no—
304D4—3026no—
305D4—6043no—
306D4—6046no—
307D4—6043no—
308D4—6043no—
309C2×C4—3026no—
310C2×C4—3026no—
311C2×C4—3026no—
312C2×C4—6043no—
313C2×C4—6043no—
314C2×C4—6046no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—1513no—
318C2×C4—1513no—
319C2×C4—1511no—
320C2×C4C23×D15113yes—
321C2×C4C23×D15111yescharacteristic
322C2×C4C23×D15113yes—
323C2×C4C23×D15111yescharacteristic
324C2×C4C23×D15111yescharacteristic
325C2×C4C23×D15113yes—
326C2×C4C23×D15113yes—
327C22—3021no—
328C22—3023no—
329C22—3023no—
330C22—3023no—
331C22—3021no—
332C22—3023no—
333C22—3023no—
334C22—3023no—
335C22—3021no—
336C22C24×D15111yescharacteristic
337C4—23no—
338C4—23no—
339C4—21no—
340C4—21no—
341C4—23no—
342C4—21no—
343C4—3021no—
344C4—3021no—
345C4—3023no—
346C4—3021no—
347C4—3023no—
348C4C2×#1455900516yes—
349C2—6041no—
350C2—6043no—
351C2—6043no—
352C2C22×#1455900511yescharacteristic
353C2#2375304811yescharacteristic
354C2#2375304911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D151
commutator, socle, cosocleC22×C151C25
Fitting#557×C151C2
hypercenter#557D151
hypocenterC151#3524
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #23752947C2semidirect
2. #23752928C2semidirect
3. #23752915C2semidirect
4. #23752900C2semidirect
5. #23752884C2semidirect
6. #23752874C2semidirect
7. #23752874C2semidirect
8. #23752836C2semidirect
9. #23752818C2semidirect
10. #23752749C2semidirect
11. #23752747C2semidirect
12. #23752694C2semidirect
13. #23752688C2semidirect
14. C4×#14559005C2semidirect
15. #557×C151C2semidirect
177. C151#3524semidirect
180. #557D151semidirect

Maximal subgroups

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

subgroupindex
#237529472
#237529282
#237529152
#237529002
#237528842
#237528742
#237528362
#237528182
#237527492
#237527472
#237526942
#237526882
C4×#145590052
#557×C1512
#3524151