Finite Group Databasebeta

← #34080846

Subgroups — #34080846

Order 19328.

482 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×#18012760C211yesmaximal, characteristic, complemented
2C2×Q16×D151C211yesmaximal, characteristic, complemented
3#23752874C211yesmaximal, characteristic, complemented
4#23752870C211yesmaximal, characteristic, complemented
5#23752594C211yesmaximal, characteristic, complemented
6#23752452C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752435C211yesmaximal, characteristic, complemented
9#23752375C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11#23752352C211yesmaximal, characteristic, complemented
12#23752349C211yesmaximal, characteristic, complemented
13C4×#14558994C211yesmaximal, characteristic, complemented
14#23752277C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19C2×Q8×D151C2211yescharacteristic
20#18012760—24no—
21C2×Dic604C2211yescharacteristic
22C2×#14558994C2211yescharacteristic
23C2×#14558994C2211yescharacteristic
24Q16×D151—24no—
25C2×#14558993C2211yescharacteristic
26C2×#14558992C2211yescharacteristic
27C2×#14558991C2211yescharacteristic
28C2×#14558989C2211yescharacteristic
29C2×C8×D151C2211yescharacteristic
30C2×C8×D151C2211yescharacteristic
31#18012727—21no—
32#18012727C2211yescharacteristic
33#18012725—21no—
34#18012719—21no—
35#18012719C2211yescharacteristic
36#18012716—21no—
37#18012715C2211yescharacteristic
38#18012714—21no—
39#18012714C2211yescharacteristic
40#18012712—21no—
41#18012710C2211yescharacteristic
42C4×Dic302C2211yescharacteristic
43C4×D604—21no—
44C4×D604C2211yescharacteristic
45(C22⋊D151)⋊C4—21no—
46#18012672C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012663C2211yescharacteristic
49#18012662C2211yescharacteristic
50#18012661C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52(C2×D151)⋊C8C2211yescharacteristic
53C4×C151⋊C8C2211yescharacteristic
54C2×Q16×C151C2211yescharacteristic
55C2×SD16×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57C4×Q8×C151C2211yescharacteristic
58C4⋊C8×C151C2211yescharacteristic
59#103×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—41no—
63#14559003—22no—
64#14559003—41no—
65C2×Dic302—21no—
66C2×Dic302—21no—
67C2×Dic302C2311yescharacteristic
68C2×Dic302C2311yescharacteristic
69Q8×D151—22no—
70Q8×D151—22no—
71Q8×D151—41no—
72Q8×D151—41no—
73C2×D604—21no—
74C2×D604—21no—
75C2×D604D411yescharacteristic
76C2×D604C2311yescharacteristic
77C2×C22⋊D151—21no—
78C2×C22⋊D151—21no—
79C22×Dic151—21no—
80C2×C4×D151—21no—
81C2×C4×D151—21no—
82C2×C4×D151—21no—
83C2×C4×D151C2311yescharacteristic
84C2×C4×D151C2311yescharacteristic
85Dic604—22no—
86#14558994—22no—
87#14558994D414yescomplemented
88#14558993—22no—
89#14558992—41no—
90#14558991—41no—
91#14558989—22no—
92C2×C151⋊C8C2311yescharacteristic
93C2×C151⋊C8C2311yescharacteristic
94C8×D151—22no—
95C8×D151—22no—
96C4⋊Dic151—21no—
97C4⋊Dic151D411yescharacteristic
98C4⋊Dic151C2311yescharacteristic
99Dic151⋊C4—21no—
100Dic151⋊C4—21no—
101C22⋊Dic151—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)⋊C4D411yescharacteristic
108(C2×D151)⋊C4D411yescharacteristic
109C4×Dic151—21no—
110C2×Q8×C151C2311yescharacteristic
111C2×Q8×C151C2311yescharacteristic
112C2×D4×C151C2311yescharacteristic
113Q16×C151—22no—
114SD16×C151—22no—
115C2×C8×C151C2311yescharacteristic
116C2×C8×C151C2311yescharacteristic
117C4⋊C4×C151—21no—
118C4⋊C4×C151C2311yescharacteristic
119C22⋊C4×C151—21no—
120C22⋊C4×C151—21no—
121C42×C151—21no—
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151C2×D411yescharacteristic
125C22×D151C2×D411yescharacteristic
126Dic302—21no—
127Dic302—21no—
128Dic302—21no—
129Dic302—42no—
130Dic302—42no—
131Dic302C2×D412yes—
132D604—22no—
133D604—21no—
134D604—21no—
135D604—42no—
136D604—42no—
137C22⋊D151—42no—
138C22⋊D151—42no—
139C2×Dic151—21no—
140C2×Dic151—21no—
141C2×Dic151—21no—
142C2×Dic151—42no—
143C2×Dic151C2×D411yescharacteristic
144C2×Dic151C2×D411yescharacteristic
145C4×D151—21no—
146C4×D151—21no—
147C4×D151—21no—
148C4×D151—21no—
149C4×D151—42no—
150C4×D151—42no—
151C4×D151—42no—
152C151⋊C8—21no—
153C151⋊C8C2×D412yes—
154C23×C151—21no—
155Q8×C151—21no—
156Q8×C151—21no—
157Q8×C151—21no—
158Q8×C151C2×D412yes—
159D4×C151—21no—
160D4×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×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151C22×D411yescharacteristic
173C2×D151—21no—
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151#13512yescomplemented
182C4×C151—22no—
183C4×C151—21no—
184C4×C151—21no—
185C4×C151—41no—
186C4×C151—41no—
187C4×C151C22×D411yescharacteristic
188C4×C151H(5,𝔽2)11yescharacteristic
189Dic151—21no—
190Dic151—21no—
191Dic151—22no—
192Dic151—41no—
193Dic151—41no—
194C2×C151—81no—
195C2×C151D4211yescharacteristic
196C2×C151C2×#13511yescharacteristic
197C2×C151#57811yescharacteristic
198D151—22no—
199D151—41no—
200D151—81no—
201C151#328511yescharacteristic, complemented, Sylow
202#3285—1511nomaximal, Sylow
203C2×#135—1511no—
204C22×Q16—1511no—
205#548—1511no—
206#548—1511no—
207#495—1511no—
208#467—1511no—
209#466—1511no—
210#464—1511no—
211#464D15111yescharacteristic, complemented
212#452—1511no—
213#452—1511no—
214#448—1511no—
215#448—1511no—
216C4×Q16—1511no—
217C8×D4—1511no—
218C2×#41—1511no—
219C2×#41—1511no—
220C22×Q8—1511no—
221C22×Q8—1511no—
222#135—3024no—
223C2×Q16—3024no—
224C2×Q16—1511no—
225C2×Q16—1511no—
226C2×Q16—1511no—
227C2×Q16C2×D15111yescharacteristic
228C2×SD16—1511no—
229C2×SD16—1511no—
230C2×SD16—1511no—
231C2×SD16C2×D15111yescharacteristic
232C2×D8—1511no—
233C22×C8—1511no—
234C22×C8—1511no—
235#124—3021no—
236#124—3021no—
237#124—1511no—
238#124C2×D15111yescharacteristic
239C22⋊Q8—3021no—
240C22⋊Q8—3021no—
241C22⋊Q8—1511no—
242C22⋊Q8—1511no—
243#121—3021no—
244#121—3021no—
245#121—1511no—
246#121—1511no—
247C4×Q8—1511no—
248C4×Q8C2×D15111yescharacteristic
249C4×D4—3021no—
250C4×D4—3021no—
251C4×D4—1511no—
252#107—1511no—
253C4⋊C8C2×D15111yescharacteristic
254#103—1511no—
255#103—1511no—
256#103—1511no—
257#103C2×D15111yescharacteristic
258#102—1511no—
259#102C2×D15111yescharacteristic
260C22⋊C8—1511no—
261C22⋊C8—1511no—
262C4×C8—1511no—
263#41—3022no—
264#41—3022no—
265#41—6041no—
266#41—6041no—
267C2×Q8—3021no—
268C2×Q8—3021no—
269C2×Q8—3022no—
270C2×Q8—3022no—
271C2×Q8—6041no—
272C2×Q8—6041no—
273C2×Q8—1511no—
274C2×Q8—1511no—
275C2×Q8C22×D15111yescharacteristic
276C2×Q8C22×D15111yescharacteristic
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—3021no—
280C2×D4—3021no—
281C2×D4—1511no—
282C2×D4—1511no—
283C2×D4C22×D15111yescharacteristic
284C22×C4—3021no—
285C22×C4—3021no—
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—1511no—
289C22×C4—1511no—
290Q16—22no—
291Q16—3022no—
292Q16—3022no—
293Q16—1514no—
294SD16—22no—
295SD16—3022no—
296SD16—6041no—
297SD16—6041no—
298D8—3022no—
299C2×C8—3022no—
300C2×C8—3022no—
301C2×C8—1511no—
302C2×C8—1511no—
303C2×C8C22×D15111yescharacteristic
304C2×C8C22×D15111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—3021no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—1511no—
310C4⋊C4—1511no—
311C4⋊C4C22×D15111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—3021no—
320C22⋊C4—1511no—
321C22⋊C4—1511no—
322C42—21no—
323C42—3021no—
324C42C22×D15111yescharacteristic
325C23—21no—
326C23—3021no—
327C23—1511no—
328C23—1511no—
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—3021no—
333Q8—3021no—
334Q8—3021no—
335Q8—6042no—
336Q8—6042no—
337Q8—1512no—
338Q8D4×D15112yes—
339D4—21no—
340D4—21no—
341D4—3022no—
342D4—3021no—
343D4—3021no—
344D4—6042no—
345D4—6042no—
346D4—6042no—
347D4—6042no—
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—3021no—
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—41no—
372C22—41no—
373C22—41no—
374C22—3021no—
375C22—3021no—
376C22—3021no—
377C22—3021no—
378C22—3021no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—1512no—
383C22C2×D4×D15111yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—41no—
388C4—41no—
389C4—3021no—
390C4—3021no—
391C4—3022no—
392C4—6041no—
393C4—6041no—
394C4C2×D4×D15111yescharacteristic
395C4#1801278511yescharacteristic
396C2—81no—
397C2—3022no—
398C2—6041no—
399C2—12081no—
400C2#2375284611yescharacteristic
401C2#135×D15111yescharacteristic
402C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
hypercenter#464D151
hypocenterC151#3285
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#18012760C2semidirect
2. C2×Q16×D151C2semidirect
3. #23752874C2semidirect
4. #23752870C2semidirect
5. #23752594C2semidirect
6. #23752452C2semidirect
7. #23752447C2semidirect
8. #23752435C2semidirect
9. #23752375C2semidirect
10. #23752373C2semidirect
11. #23752352C2semidirect
12. #23752349C2semidirect
13. C4×#14558994C2semidirect
14. #23752277C2semidirect
15. #464×C151C2semidirect
87. #14558994D4semidirect
181. C2×D151#135semidirect
201. C151#3285semidirect
211. #464D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127602
C2×Q16×D1512
#237528742
#237528702
#237525942
#237524522
#237524472
#237524352
#237523752
#237523732
#237523522
#237523492
C4×#145589942
#237522772
#464×C1512
#3285151