Finite Group Databasebeta

← #34083212

Subgroups — #34083212

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#23752944C213yesmaximal, complemented
2#23752938C211yesmaximal, characteristic, complemented
3#23752926C213yesmaximal, complemented
4#23752908C213yesmaximal, complemented
5#23752904C213yesmaximal, complemented
6#23752881C211yesmaximal, characteristic, complemented
7#23752873C211yesmaximal, characteristic, complemented
8#23752835C213yesmaximal, complemented
9#23752815C213yesmaximal, complemented
10#23752744C213yesmaximal, complemented
11#23752741C213yesmaximal, complemented
12#23752695C211yesmaximal, characteristic, complemented
13#23752690C211yesmaximal, characteristic, complemented
14C4×#14559005C211yesmaximal, characteristic, complemented
15#548×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17#18012738C2213yes—
18#18012735C2213yes—
19#18012734C2216yes—
20#18012732C2213yes—
21#18012732C2211yescharacteristic
22#18012731C2213yes—
23#18012730C2213yes—
24#18012730C2213yes—
25#18012728C2213yes—
26#18012726C2213yes—
27#18012725C2216yes—
28#18012723C2216yes—
29#18012721C2216yes—
30#18012721C2213yes—
31#18012721C2213yes—
32#18012719C2213yes—
33#18012715C2213yes—
34#18012713C2213yes—
35#18012713C2213yes—
36#18012711C2216yes—
37#18012710C2213yes—
38#18012710C2213yes—
39Q8×Dic151C2213yes—
40Q8×Dic151C2211yescharacteristic
41Q8×Dic151C2211yescharacteristic
42Q8×Dic151C2213yes—
43Q8×Dic151C2211yescharacteristic
44C4×Dic302C2213yes—
45C4×D604C2213yes—
46D4×Dic151C2213yes—
47D4×Dic151C2213yes—
48#18012701C2213yes—
49C4×C22⋊D151C2213yes—
50C4×C22⋊D151C2213yes—
51(C22⋊D151)⋊C4C2216yes—
52#18012698C2213yes—
53#18012698C2213yes—
54#18012698C2213yes—
55#18012697C2213yes—
56#18012695C2216yes—
57C2×C4⋊Dic151C2213yes—
58C42×D151C2213yes—
59C2×#41×C151C2211yescharacteristic
60C22×Q8×C151C2211yescharacteristic
61#124×C151C2213yes—
62C22⋊Q8×C151C2213yes—
63#121×C151C2213yes—
64C4×Q8×C151C2211yescharacteristic
65C4×D4×C151C2213yes—
66#14559005—24no—
67C2×Dic302C2313yes—
68C2×D604C2313yes—
69C2×C22⋊D151C2316yes—
70C2×C22⋊D151C2313yes—
71C2×C22⋊D151C2313yes—
72C22×Dic151C2316yes—
73C2×C4×D151C2313yes—
74C2×C4×D151C2313yes—
75C2×C4×D151C2313yes—
76C4⋊Dic151C2313yes—
77C4⋊Dic151C2313yes—
78C4⋊Dic151C2313yes—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2313yes—
81C4⋊Dic151C2313yes—
82C4⋊Dic151C2313yes—
83C4⋊Dic151C2313yes—
84Dic151⋊C4C2313yes—
85Dic151⋊C4C2316yes—
86Dic151⋊C4C2313yes—
87Dic151⋊C4C2311yescharacteristic
88Dic151⋊C4C2311yescharacteristic
89C22⋊Dic151C2313yes—
90C22⋊Dic151C2311yescharacteristic
91C22⋊Dic151C2313yes—
92C22⋊Dic151C2313yes—
93C22⋊Dic151C2313yes—
94C22⋊Dic151C2311yescharacteristic
95(C2×D151)⋊C4C2316yes—
96(C2×D151)⋊C4C2316yes—
97(C2×D151)⋊C4C2313yes—
98(C2×D151)⋊C4C2313yes—
99C4×Dic151C2311yescharacteristic
100C4×Dic151C2313yes—
101C4×Dic151C2313yes—
102C4×Dic151C2316yes—
103C4×Dic151C2313yes—
104C4×Dic151C2313yes—
105#41×C151—24no—
106C2×Q8×C151—24no—
107C2×Q8×C151C2313yes—
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151C2313yes—
110C2×D4×C151C2313yes—
111C22×C4×C151C2313yes—
112C22×C4×C151C2313yes—
113C4⋊C4×C151C2313yes—
114C4⋊C4×C151C2313yes—
115C22⋊C4×C151C2316yes—
116C22⋊C4×C151C2313yes—
117C22⋊C4×C151C2311yescharacteristic
118C42×C151C2313yes—
119C22×D151C2413yes—
120Dic302—43no—
121D604—26no—
122C22⋊D151—43no—
123C22⋊D151—43no—
124C22⋊D151—46no—
125C2×Dic151—46no—
126C2×Dic151C2413yes—
127C2×Dic151C2411yescharacteristic
128C2×Dic151C2411yescharacteristic
129C2×Dic151C2411yescharacteristic
130C2×Dic151C2413yes—
131C2×Dic151C2411yescharacteristic
132C2×Dic151C2413yes—
133C4×D151—26no—
134C4×D151—43no—
135C4×D151—43no—
136C23×C151C2411yescharacteristic
137C23×C151C2413yes—
138Q8×C151—26no—
139Q8×C151#4114yes—
140D4×C151—26no—
141D4×C151—43no—
142C2×C4×C151—26no—
143C2×C4×C151—26no—
144C2×C4×C151C2413yes—
145C2×C4×C151C2413yes—
146C2×C4×C151C2411yescharacteristic
147C2×C4×C151C2411yescharacteristic
148C2×C4×C151C2413yes—
149C22×C151—21no—
150C22×C151—23no—
151C22×C151—21no—
152C22×C151—23no—
153C22×C151—23no—
154C22×C151—21no—
155C22×C151C2511yescharacteristic
156C2×D151—23no—
157C2×D151—23no—
158C2×D151—23no—
159C4×C151—21no—
160C4×C151—23no—
161C4×C151—23no—
162C4×C151—21no—
163C4×C151C2×#4116yes—
164Dic151—21no—
165Dic151—21no—
166Dic151—23no—
167Dic151—23no—
168Dic151—21no—
169Dic151—23no—
170Dic151—21no—
171C2×C151—41no—
172C2×C151—43no—
173C2×C151C22×#4111yescharacteristic
174C2×C151#58511yescharacteristic
175C2×C151#58511yescharacteristic
176D151—43no—
177C151#352411yescharacteristic, complemented, Sylow
178#3524—1511nomaximal, Sylow
179#559—1513no—
180#557—1511no—
181#555—1513no—
182#553—1513no—
183#552—1513no—
184#550—1511no—
185#548—1511no—
186#548D15111yescharacteristic, complemented
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×#41C2×D15111yescharacteristic
196C22×Q8C2×D15111yescharacteristic
197C4⋊Q8—1513no—
198#127—1513no—
199#126—1516no—
200#126—1511no—
201#126—1513no—
202#125—1513no—
203#125—1513no—
204#125—1513no—
205#124—1513no—
206#124—1513no—
207#124—1516no—
208#124C2×D15113yes—
209#123—1516no—
210#123—1513no—
211#123—1513no—
212#123—1516no—
213C22⋊Q8—1513no—
214C22⋊Q8—1513no—
215C22⋊Q8C2×D15113yes—
216#121—1513no—
217#121—1513no—
218#121—1516no—
219#121—1513no—
220#121—1513no—
221#121C2×D15113yes—
222C4×Q8—1511no—
223C4×Q8—1513no—
224C4×Q8—1511no—
225C4×Q8—1513no—
226C4×Q8—1511no—
227C4×Q8—1513no—
228C4×Q8C2×D15111yescharacteristic
229C4×D4—1513no—
230C4×D4—1513no—
231C4×D4—1513no—
232C4×D4—1513no—
233C4×D4—1513no—
234C4×D4—1516no—
235C4×D4—1513no—
236C4×D4C2×D15113yes—
237#117—1513no—
238#117—1513no—
239#117—1513no—
240#117—1513no—
241#117—1516no—
242C2×C4⋊C4—1513no—
243C2×C42—1513no—
244#41—24no—
245#41—3024no—
246C2×Q8—24no—
247C2×Q8—1513no—
248C2×Q8C22×D15113yes—
249C2×Q8C22×D15111yescharacteristic
250C2×D4—1513no—
251C2×D4—1516no—
252C2×D4—1513no—
253C2×D4—1513no—
254C2×D4C22×D15113yes—
255C2×D4C22×D15113yes—
256C22×C4—1513no—
257C22×C4—1516no—
258C22×C4—1513no—
259C22×C4—1513no—
260C22×C4C22×D15113yes—
261C22×C4C22×D15113yes—
262C4⋊C4—1513no—
263C4⋊C4—1516no—
264C4⋊C4—1511no—
265C4⋊C4—1513no—
266C4⋊C4—1511no—
267C4⋊C4—1513no—
268C4⋊C4—1513no—
269C4⋊C4—1513no—
270C4⋊C4—1511no—
271C4⋊C4—1513no—
272C4⋊C4—1513no—
273C4⋊C4—1513no—
274C4⋊C4—1513no—
275C4⋊C4C22×D15113yes—
276C4⋊C4C22×D15113yes—
277C22⋊C4—1511no—
278C22⋊C4—1513no—
279C22⋊C4—1513no—
280C22⋊C4—1513no—
281C22⋊C4—1513no—
282C22⋊C4—1511no—
283C22⋊C4—1516no—
284C22⋊C4—1513no—
285C22⋊C4—1516no—
286C22⋊C4—1513no—
287C22⋊C4C22×D15116yes—
288C22⋊C4C22×D15113yes—
289C22⋊C4C22×D15111yescharacteristic
290C42—1511no—
291C42—1513no—
292C42—1513no—
293C42—1516no—
294C42—1513no—
295C42—1513no—
296C42C22×D15113yes—
297C23—1513no—
298C23C23×D15111yescharacteristic
299C23C23×D15113yes—
300Q8—26no—
301Q8—6043no—
302Q8#1455900314yes—
303D4—26no—
304D4—43no—
305D4—3026no—
306D4—6046no—
307D4—6043no—
308D4—6043no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—3026no—
312C2×C4—6043no—
313C2×C4—6043no—
314C2×C4—6046no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—1513no—
318C2×C4—1511no—
319C2×C4—1513no—
320C2×C4—1511no—
321C2×C4—1513no—
322C2×C4C23×D15113yes—
323C2×C4C23×D15111yescharacteristic
324C2×C4C23×D15113yes—
325C2×C4C23×D15111yescharacteristic
326C2×C4C23×D15113yes—
327C22—21no—
328C22—23no—
329C22—21no—
330C22—23no—
331C22—23no—
332C22—21no—
333C22—3023no—
334C22—3023no—
335C22—3023no—
336C22C24×D15111yescharacteristic
337C4—21no—
338C4—23no—
339C4—23no—
340C4—21no—
341C4—3021no—
342C4—3021no—
343C4—3023no—
344C4—3021no—
345C4—3023no—
346C4—3023no—
347C4—3021no—
348C4C2×#1455900316yes—
349C2—41no—
350C2—43no—
351C2—6043no—
352C2C22×#1455900311yescharacteristic
353C2#2375304811yescharacteristic
354C2#2375304911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D151
commutator, socle, cosocleC22×C151C25
Fitting#548×C151C2
hypercenter#548D151
hypocenterC151#3524
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #23752944C2semidirect
2. #23752938C2semidirect
3. #23752926C2semidirect
4. #23752908C2semidirect
5. #23752904C2semidirect
6. #23752881C2semidirect
7. #23752873C2semidirect
8. #23752835C2semidirect
9. #23752815C2semidirect
10. #23752744C2semidirect
11. #23752741C2semidirect
12. #23752695C2semidirect
13. #23752690C2semidirect
14. C4×#14559005C2semidirect
15. #548×C151C2semidirect
177. C151#3524semidirect
186. #548D151semidirect

Maximal subgroups

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

subgroupindex
#237529442
#237529382
#237529262
#237529082
#237529042
#237528812
#237528732
#237528352
#237528152
#237527442
#237527412
#237526952
#237526902
C4×#145590052
#548×C1512
#3524151