Finite Group Databasebeta

← #34082708

Subgroups — #34082708

Order 19328.

1112 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#23752945C213yesmaximal, complemented
2#23752938C211yesmaximal, characteristic, complemented
3#23752930C213yesmaximal, complemented
4#23752912C213yesmaximal, complemented
5#23752906C213yesmaximal, complemented
6#23752881C211yesmaximal, characteristic, complemented
7#23752874C211yesmaximal, characteristic, complemented
8#23752869C211yesmaximal, characteristic, complemented
9#23752759C213yesmaximal, complemented
10#23752746C213yesmaximal, complemented
11#23752744C213yesmaximal, complemented
12C4×#14559005C211yesmaximal, characteristic, complemented
13C4×#14559004C213yesmaximal, complemented
14C4×Q8×D151C211yesmaximal, characteristic, complemented
15C4×#41×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2213yes—
18C2×Q8×D151C2211yescharacteristic
19#18012738C2213yes—
20#18012735C2213yes—
21#18012733C2216yes—
22#18012732C2216yes—
23#18012731C2213yes—
24#18012730C2213yes—
25#18012727C2213yes—
26#18012726C2213yes—
27#18012725C2216yes—
28#18012722C2216yes—
29#18012721C2216yes—
30#18012719C2213yes—
31#18012718C2213yes—
32#18012714C2213yes—
33#18012713C2213yes—
34#18012712C2216yes—
35#18012710C2213yes—
36#18012710C2213yes—
37Q8×Dic151C2211yescharacteristic
38Q8×Dic151C2211yescharacteristic
39C4×Dic302C2213yes—
40C4×Dic302C2213yes—
41C4×Dic302C2213yes—
42#18012704C2213yes—
43C4×D604C2213yes—
44C4×D604C2213yes—
45C4×D604C2213yes—
46#18012701C2213yes—
47C4×C22⋊D151C2216yes—
48C4×C22⋊D151C2213yes—
49C4×C22⋊D151C2213yes—
50C4×C22⋊D151C2213yes—
51C4×C22⋊D151C2213yes—
52#18012698C2213yes—
53#18012697C2213yes—
54#18012696C2213yes—
55#18012696C2211yescharacteristic
56C4⋊C4×D151C2213yes—
57C42×D151C2213yes—
58C42×D151C2213yes—
59C2×#41×C151C2211yescharacteristic
60C4×Q8×C151C2211yescharacteristic
61C4×Q8×C151C2211yescharacteristic
62C4×D4×C151C2213yes—
63C4×D4×C151C2213yes—
64#117×C151C2213yes—
65C2×C42×C151C2213yes—
66#14559005—24no—
67#14559004—212no—
68C2×Dic302C2313yes—
69C2×Dic302C2313yes—
70Q8×D151—24no—
71C2×D604C2313yes—
72C2×D604C2313yes—
73C2×C22⋊D151C2313yes—
74C2×C22⋊D151C2313yes—
75C2×C22⋊D151C2316yes—
76C2×C4×D151C2313yes—
77C2×C4×D151C2313yes—
78C2×C4×D151C2313yes—
79C2×C4×D151C2313yes—
80C2×C4×D151C2313yes—
81C2×C4×D151C2311yescharacteristic
82C4⋊Dic151C2313yes—
83C4⋊Dic151C2313yes—
84C4⋊Dic151C2313yes—
85C4⋊Dic151C2313yes—
86Dic151⋊C4C2316yes—
87Dic151⋊C4C2311yescharacteristic
88Dic151⋊C4C2311yescharacteristic
89Dic151⋊C4C2313yes—
90Dic151⋊C4C2313yes—
91Dic151⋊C4C2316yes—
92C22⋊Dic151C2313yes—
93C22⋊Dic151C2313yes—
94C22⋊Dic151C2316yes—
95(C2×D151)⋊C4C2311yescharacteristic
96(C2×D151)⋊C4C2311yescharacteristic
97(C2×D151)⋊C4C2313yes—
98(C2×D151)⋊C4C2313yes—
99(C2×D151)⋊C4C2316yes—
100(C2×D151)⋊C4C2316yes—
101C4×Dic151C2311yescharacteristic
102C4×Dic151C2313yes—
103C4×Dic151C2313yes—
104C4×Dic151C2313yes—
105C4×Dic151C2313yes—
106C4×Dic151C2313yes—
107#41×C151—24no—
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151C2313yes—
110C22×C4×C151C2313yes—
111C22×C4×C151C2313yes—
112C22×C4×C151C2313yes—
113C4⋊C4×C151C2313yes—
114C4⋊C4×C151C2313yes—
115C22⋊C4×C151C2316yes—
116C42×C151C2313yes—
117C42×C151C2311yescharacteristic
118C42×C151C2313yes—
119C42×C151C2313yes—
120C22×D151C2413yes—
121C22×D151C2411yescharacteristic
122Dic302—26no—
123Dic302—26no—
124D604—26no—
125D604—26no—
126C22⋊D151—26no—
127C22⋊D151—26no—
128C22⋊D151—46no—
129C2×Dic151C2411yescharacteristic
130C2×Dic151C2411yescharacteristic
131C2×Dic151C2413yes—
132C2×Dic151C2413yes—
133C2×Dic151C2413yes—
134C2×Dic151C2411yescharacteristic
135C4×D151—26no—
136C4×D151—26no—
137C4×D151—26no—
138C4×D151—43no—
139C4×D151—43no—
140C4×D151#4114yescomplemented
141C23×C151C2413yes—
142Q8×C151#4114yescomplemented
143D4×C151—26no—
144C2×C4×C151—26no—
145C2×C4×C151—26no—
146C2×C4×C151—43no—
147C2×C4×C151C2413yes—
148C2×C4×C151C2411yescharacteristic
149C2×C4×C151C2411yescharacteristic
150C2×C4×C151C2413yes—
151C2×C4×C151C2413yes—
152C2×C4×C151C2411yescharacteristic
153C22×C151—23no—
154C22×C151—23no—
155C22×C151—23no—
156C22×C151C2511yescharacteristic
157C2×D151—21no—
158C2×D151—21no—
159C2×D151—23no—
160C2×D151—23no—
161C2×D151—23no—
162C2×D151C2×#4112yes—
163C4×C151—21no—
164C4×C151—23no—
165C4×C151—21no—
166C4×C151—23no—
167C4×C151C2×#4112yes—
168C4×C151C2×#4116yes—
169Dic151—21no—
170Dic151—23no—
171Dic151—23no—
172Dic151—21no—
173Dic151—23no—
174Dic151C2×#4112yes—
175C2×C151—43no—
176C2×C151C22×#4111yescharacteristic
177C2×C151C22×#4111yescharacteristic
178C2×C151#58511yescharacteristic
179D151—22no—
180D151—43no—
181C151#348011yescharacteristic, complemented, Sylow
182#3480—1511nomaximal, Sylow
183#559—1513no—
184#557—1511no—
185#556—1513no—
186#553—1513no—
187#553—1513no—
188#550—1511no—
189#548—1511no—
190#548—1511no—
191#532—1513no—
192#529—1513no—
193#529—1513no—
194C4×#41—1511no—
195C4×#41—1513no—
196C4×#41D15111yescharacteristic, complemented
197C2×C4×Q8—1511no—
198C2×#41—1511no—
199C2×#41—1513no—
200C2×#41C2×D15111yescharacteristic
201C22×Q8—1511no—
202C4⋊Q8—1513no—
203#127—1513no—
204#126—1516no—
205#126—1516no—
206#125—1513no—
207#125—1513no—
208#124—1513no—
209#124—1516no—
210#124—1513no—
211#123—1516no—
212#123—1516no—
213C22⋊Q8—1513no—
214C22⋊Q8—1513no—
215#121—1513no—
216#121—1513no—
217#121—1513no—
218#121—1513no—
219#121—1516no—
220C4×Q8—1511no—
221C4×Q8—1511no—
222C4×Q8—1513no—
223C4×Q8—1513no—
224C4×Q8—1513no—
225C4×Q8—1513no—
226C4×Q8C2×D15111yescharacteristic
227C4×Q8C2×D15111yescharacteristic
228C4×D4—1513no—
229C4×D4—1513no—
230C4×D4—1513no—
231C4×D4—1513no—
232C4×D4—1516no—
233C4×D4—1513no—
234C4×D4—1513no—
235C4×D4—1513no—
236C4×D4—1513no—
237C4×D4C2×D15113yes—
238C4×D4C2×D15113yes—
239#117—1513no—
240#117—1513no—
241#117—1511no—
242#117—1513no—
243#117C2×D15113yes—
244C2×C4⋊C4—1513no—
245C2×C42—1513no—
246C2×C42—1513no—
247C2×C42C2×D15113yes—
248#41—24no—
249#41—30212no—
250#41—3024no—
251C2×Q8—3024no—
252C2×Q8—1513no—
253C2×Q8—1513no—
254C2×Q8C22×D15111yescharacteristic
255C2×D4—1513no—
256C2×D4—1513no—
257C2×D4—1516no—
258C2×D4—1513no—
259C2×D4—1513no—
260C2×D4C22×D15113yes—
261C22×C4—1513no—
262C22×C4—1513no—
263C22×C4—1513no—
264C22×C4—1513no—
265C22×C4—1513no—
266C22×C4—1511no—
267C22×C4C22×D15113yes—
268C22×C4C22×D15113yes—
269C22×C4C22×D15113yes—
270C4⋊C4—1516no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4—1513no—
274C4⋊C4—1513no—
275C4⋊C4—1516no—
276C4⋊C4—1513no—
277C4⋊C4—1513no—
278C4⋊C4—1513no—
279C4⋊C4—1513no—
280C4⋊C4C22×D15113yes—
281C4⋊C4C22×D15113yes—
282C22⋊C4—1513no—
283C22⋊C4—1513no—
284C22⋊C4—1516no—
285C22⋊C4—1511no—
286C22⋊C4—1511no—
287C22⋊C4—1513no—
288C22⋊C4—1516no—
289C22⋊C4—1513no—
290C22⋊C4—1516no—
291C22⋊C4C22×D15116yes—
292C42—1513no—
293C42—1513no—
294C42—1513no—
295C42—1513no—
296C42—1511no—
297C42—1513no—
298C42C22×D15113yes—
299C42C22×D15113yes—
300C42C22×D15113yes—
301C42C22×D15111yescharacteristic
302C23—1513no—
303C23—1511no—
304C23C23×D15113yes—
305Q8—3026no—
306Q8—3026no—
307Q8#1455900414yescomplemented
308D4—26no—
309D4—3026no—
310D4—3026no—
311D4—3026no—
312D4—3026no—
313D4—6046no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—3026no—
318C2×C4—3026no—
319C2×C4—3026no—
320C2×C4—6043no—
321C2×C4—6043no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4—1513no—
325C2×C4—1513no—
326C2×C4—1513no—
327C2×C4—1511no—
328C2×C4—1514no—
329C2×C4C23×D15113yes—
330C2×C4C23×D15111yescharacteristic
331C2×C4C23×D15111yescharacteristic
332C2×C4C23×D15113yes—
333C2×C4C23×D15113yes—
334C2×C4C23×D15111yescharacteristic
335C22—23no—
336C22—23no—
337C22—23no—
338C22—3021no—
339C22—3021no—
340C22—3023no—
341C22—3023no—
342C22—3023no—
343C22—1512no—
344C22C24×D15111yescharacteristic
345C4—23no—
346C4—21no—
347C4—21no—
348C4—23no—
349C4—3023no—
350C4—3021no—
351C4—3023no—
352C4—3021no—
353C4—3023no—
354C4—1512no—
355C4#41×D15112yes—
356C4C2×#1455900416yes—
357C2—43no—
358C2—3022no—
359C2—6043no—
360C2C2×#41×D15111yescharacteristic
361C2C22×#1455900411yescharacteristic
362C2#2375304811yescharacteristic
subgroupG/H
centerC2×C4C23×D151
commutator, socle, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC4×#41×C151C2
hypercenterC4×#41D151
hypocenterC151#3480
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #23752945C2semidirect
2. #23752938C2semidirect
3. #23752930C2semidirect
4. #23752912C2semidirect
5. #23752906C2semidirect
6. #23752881C2semidirect
7. #23752874C2semidirect
8. #23752869C2semidirect
9. #23752759C2semidirect
10. #23752746C2semidirect
11. #23752744C2semidirect
12. C4×#14559005C2semidirect
13. C4×#14559004C2semidirect
14. C4×Q8×D151C2semidirect
15. C4×#41×C151C2semidirect
140. C4×D151#41semidirect
142. Q8×C151#41semidirect
181. C151#3480semidirect
196. C4×#41D151semidirect
307. Q8#14559004semidirect

Maximal subgroups

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

subgroupindex
#237529452
#237529382
#237529302
#237529122
#237529062
#237528812
#237528742
#237528692
#237527592
#237527462
#237527442
C4×#145590052
C4×#145590042
C4×Q8×D1512
C4×#41×C1512
#3480151