Finite Group Databasebeta

← #34080660

Subgroups — #34080660

Order 19328.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012771C211yesmaximal, characteristic, complemented
2C2×#18012762C211yesmaximal, characteristic, complemented
3#23752874C211yesmaximal, characteristic, complemented
4#23752865C211yesmaximal, characteristic, complemented
5#23752604C211yesmaximal, characteristic, complemented
6#23752461C211yesmaximal, characteristic, complemented
7#23752452C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752377C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11#23752366C211yesmaximal, characteristic, complemented
12#23752360C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#23752282C211yesmaximal, characteristic, complemented
15#462×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559005C2211yescharacteristic
18C2×#14559005C2211yescharacteristic
19C2×Q8×D151C2211yescharacteristic
20#18012771—24no—
21#18012762—24no—
22C2×#14558994C2211yescharacteristic
23C2×#14558994C2211yescharacteristic
24C2×#14558993C2211yescharacteristic
25C2×#14558991C2211yescharacteristic
26C2×#14558991C2211yescharacteristic
27C2×#14558991C2211yescharacteristic
28C2×D1208C2211yescharacteristic
29C2×#14558987C2211yescharacteristic
30C2×C8×D151C2211yescharacteristic
31#18012727—21no—
32#18012727C2211yescharacteristic
33#18012724—21no—
34#18012724—21no—
35#18012719—21no—
36#18012719C2211yescharacteristic
37#18012715C2211yescharacteristic
38#18012715C2211yescharacteristic
39#18012714—21no—
40#18012714—21no—
41#18012714C2211yescharacteristic
42C4×D604—21no—
43C4×D604C2211yescharacteristic
44C4×D604C2211yescharacteristic
45C4⋊C4×D151—21no—
46#18012672C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012663C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012659C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic
53#18012650C2211yescharacteristic
54C2×Q16×C151C2211yescharacteristic
55C2×Q16×C151C2211yescharacteristic
56C4⋊Q8×C151C2211yescharacteristic
57C4×Q8×C151C2211yescharacteristic
58C4⋊C8×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#103×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—22no—
63#14559005—22no—
64#14559005—41no—
65#14559005—41no—
66#14559005—41no—
67C2×Dic302—21no—
68C2×Dic302C2311yescharacteristic
69Q8×D151—22no—
70Q8×D151—41no—
71C2×D604—21no—
72C2×D604—21no—
73C2×D604—21no—
74C2×D604—21no—
75C2×D604D411yescharacteristic
76C2×D604C2311yescharacteristic
77C2×D604C2311yescharacteristic
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151—21no—
82C2×C4×D151—21no—
83C2×C4×D151C2311yescharacteristic
84C2×C4×D151C2311yescharacteristic
85#14558994—22no—
86#14558994—41no—
87#14558993—22no—
88#14558991—22no—
89#14558991—41no—
90#14558991D414yescomplemented
91D1208—22no—
92#14558987—22no—
93C2×C151⋊C8C2311yescharacteristic
94C2×C151⋊C8C2311yescharacteristic
95C8×D151—22no—
96C4⋊Dic151—21no—
97C4⋊Dic151D411yescharacteristic
98C4⋊Dic151C2311yescharacteristic
99Dic151⋊C4—21no—
100Dic151⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4—21no—
108(C2×D151)⋊C4D411yescharacteristic
109(C2×D151)⋊C4D411yescharacteristic
110C2×Q8×C151C2311yescharacteristic
111C2×Q8×C151C2311yescharacteristic
112C2×Q8×C151C2311yescharacteristic
113Q16×C151—22no—
114Q16×C151—22no—
115C2×C8×C151C2311yescharacteristic
116C2×C8×C151C2311yescharacteristic
117C4⋊C4×C151—21no—
118C4⋊C4×C151—21no—
119C4⋊C4×C151—21no—
120C4⋊C4×C151C2311yescharacteristic
121C42×C151—21no—
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151—21no—
125C22×D151C2×D411yescharacteristic
126C22×D151C2×D411yescharacteristic
127Dic302—21no—
128Dic302—21no—
129Dic302—42no—
130D604—21no—
131D604—21no—
132D604—21no—
133D604—41no—
134D604—42no—
135D604—42no—
136D604—42no—
137D604—42no—
138D604C2×D412yes—
139C2×Dic151—21no—
140C2×Dic151—21no—
141C2×Dic151C2×D411yescharacteristic
142C2×Dic151C2×D411yescharacteristic
143C4×D151—21no—
144C4×D151—21no—
145C4×D151—21no—
146C4×D151—21no—
147C4×D151—42no—
148C4×D151—42no—
149C4×D151—42no—
150C4×D151—42no—
151C4×D151—42no—
152C151⋊C8—21no—
153C151⋊C8C2×D412yes—
154Q8×C151—21no—
155Q8×C151—21no—
156Q8×C151—21no—
157Q8×C151—21no—
158Q8×C151—21no—
159Q8×C151C2×D412yes—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151C2×D411yescharacteristic
165C2×C4×C151C2×D411yescharacteristic
166C2×C4×C151C2411yescharacteristic
167C8×C151—21no—
168C8×C151—21no—
169C22×C151C22×D411yescharacteristic
170C2×D151—21no—
171C2×D151—21no—
172C2×D151—22no—
173C2×D151—21no—
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—41no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C4×C151—22no—
183C4×C151—21no—
184C4×C151—21no—
185C4×C151—41no—
186C4×C151—41no—
187C4×C151—41no—
188C4×C151C22×D411yescharacteristic
189C4×C151H(5,𝔽2)11yescharacteristic
190Dic151—21no—
191Dic151—21no—
192Dic151—41no—
193Dic151—41no—
194C2×C151D4211yescharacteristic
195C2×C151#57511yescharacteristic
196C2×C151#57811yescharacteristic
197D151—41no—
198D151—41no—
199D151—42no—
200D151—81no—
201C151#326911yescharacteristic, complemented, Sylow
202#3269—1511nomaximal, Sylow
203C2×#137—1511no—
204C2×#135—1511no—
205#548—1511no—
206#547—1511no—
207#497—1511no—
208#468—1511no—
209#467—1511no—
210#463—1511no—
211#462D15111yescharacteristic, complemented
212#452—1511no—
213#452—1511no—
214#451—1511no—
215#449—1511no—
216#440—1511no—
217#435—1511no—
218C2×#41—1511no—
219C2×#41—1511no—
220C2×#41—1511no—
221C22×Q8—1511no—
222#137—3024no—
223#135—3024no—
224C2×Q16—1511no—
225C2×Q16—1511no—
226C2×Q16C2×D15111yescharacteristic
227C2×Q16C2×D15111yescharacteristic
228C2×SD16—1511no—
229C2×SD16—1511no—
230C2×SD16—1511no—
231C2×SD16—1511no—
232C2×D8—1511no—
233C2×M16—1511no—
234C22×C8—1511no—
235C4⋊Q8C2×D15111yescharacteristic
236#124—3021no—
237#124—1511no—
238#123—3021no—
239#123—3021no—
240C22⋊Q8—3021no—
241C22⋊Q8—1511no—
242C22⋊Q8—1511no—
243C22⋊Q8—1511no—
244#121—3021no—
245#121—3021no—
246#121—1511no—
247C4×Q8C2×D15111yescharacteristic
248C4×D4—3021no—
249C4×D4—1511no—
250C4×D4—1511no—
251C2×C4⋊C4—3021no—
252#107—1511no—
253C4⋊C8C2×D15111yescharacteristic
254#103—1511no—
255#103—1511no—
256#103C2×D15111yescharacteristic
257#103C2×D15111yescharacteristic
258#102—1511no—
259#102—1511no—
260C22⋊C8—1511no—
261C22⋊C8—1511no—
262#97—1511no—
263#41—3022no—
264#41—3022no—
265#41—3022no—
266#41—6041no—
267#41—6041no—
268#41—6041no—
269C2×Q8—3021no—
270C2×Q8—3022no—
271C2×Q8—6041no—
272C2×Q8—1511no—
273C2×Q8C22×D15111yescharacteristic
274C2×Q8C22×D15111yescharacteristic
275C2×Q8C22×D15111yescharacteristic
276C2×D4—3021no—
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—3021no—
280C2×D4—1511no—
281C2×D4—1511no—
282C2×D4—1511no—
283C22×C4—3021no—
284C22×C4—3021no—
285C22×C4—3021no—
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—1511no—
289C22×C4—1511no—
290Q16—22no—
291Q16—22no—
292Q16—3022no—
293Q16—6041no—
294SD16—3022no—
295SD16—3022no—
296SD16—6041no—
297SD16—1514no—
298D8—3022no—
299M16—3022no—
300C2×C8—3022no—
301C2×C8—1511no—
302C2×C8—1511no—
303C2×C8C22×D15111yescharacteristic
304C2×C8C22×D15111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—3021no—
309C4⋊C4—3021no—
310C4⋊C4—3021no—
311C4⋊C4—1511no—
312C4⋊C4—1511no—
313C4⋊C4C22×D15111yescharacteristic
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—1511no—
322C22⋊C4—1511no—
323C42—21no—
324C42C22×D15111yescharacteristic
325C23—3021no—
326C23—3021no—
327C23—1511no—
328C23—1511no—
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—3021no—
335Q8—3021no—
336Q8—6042no—
337Q8D4×D15112yes—
338D4—3021no—
339D4—3021no—
340D4—3021no—
341D4—6041no—
342D4—6042no—
343D4—6042no—
344D4—6042no—
345D4—6042no—
346D4—1512no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—3021no—
354C2×C4—3021no—
355C2×C4—3021no—
356C2×C4—3021no—
357C2×C4—6042no—
358C2×C4—6042no—
359C2×C4—6042no—
360C2×C4—6042no—
361C2×C4—6042no—
362C2×C4—1511no—
363C2×C4—1511no—
364C2×C4D4×D15111yescharacteristic
365C2×C4D4×D15111yescharacteristic
366C2×C4C23×D15111yescharacteristic
367C8—21no—
368C8—21no—
369C8—3021no—
370C8—1512no—
371C22—3021no—
372C22—3021no—
373C22—3021no—
374C22—3021no—
375C22—3021no—
376C22—3021no—
377C22—3022no—
378C22—6041no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22C2×D4×D15111yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—3021no—
391C4—3021no—
392C4—6041no—
393C4—6041no—
394C4C2×D4×D15111yescharacteristic
395C4#1801278511yescharacteristic
396C2—6041no—
397C2—6041no—
398C2—6042no—
399C2—12081no—
400C2#2375284611yescharacteristic
401C2#2375301111yescharacteristic
402C2#2375302511yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#462×C151C2
socleC22×C151C22×D4
hypercenter#462D151
hypocenterC151#3269
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×#18012771C2semidirect
2. C2×#18012762C2semidirect
3. #23752874C2semidirect
4. #23752865C2semidirect
5. #23752604C2semidirect
6. #23752461C2semidirect
7. #23752452C2semidirect
8. #23752428C2semidirect
9. #23752377C2semidirect
10. #23752373C2semidirect
11. #23752366C2semidirect
12. #23752360C2semidirect
13. #23752310C2semidirect
14. #23752282C2semidirect
15. #462×C151C2semidirect
90. #14558991D4semidirect
201. C151#3269semidirect
211. #462D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127712
C2×#180127622
#237528742
#237528652
#237526042
#237524612
#237524522
#237524282
#237523772
#237523732
#237523662
#237523602
#237523102
#237522822
#462×C1512
#3269151