Finite Group Databasebeta

← #34080020

Subgroups — #34080020

Order 19328.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752793C211yesmaximal, characteristic, complemented
2#23752792C211yesmaximal, characteristic, complemented
3#23752544C211yesmaximal, characteristic, complemented
4#23752532C211yesmaximal, characteristic, complemented
5#23752530C211yesmaximal, characteristic, complemented
6#23752469C211yesmaximal, characteristic, complemented
7#23752466C211yesmaximal, characteristic, complemented
8#23752444C211yesmaximal, characteristic, complemented
9#23752442C211yesmaximal, characteristic, complemented
10#23752377C211yesmaximal, characteristic, complemented
11#23752372C211yesmaximal, characteristic, complemented
12#23752360C211yesmaximal, characteristic, complemented
13#23752359C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#483×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14559004C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558991C2211yescharacteristic
22C2×D1208C2211yescharacteristic
23C2×#14558987C2211yescharacteristic
24C2×C8×D151C2211yescharacteristic
25#18012719—21no—
26#18012719C2211yescharacteristic
27#18012719C2211yescharacteristic
28#18012717—21no—
29#18012715C2211yescharacteristic
30#18012714—21no—
31#18012714—21no—
32#18012714C2211yescharacteristic
33#18012714C2211yescharacteristic
34#18012714C2211yescharacteristic
35#18012713—21no—
36#18012713—21no—
37#18012713C2211yescharacteristic
38#18012712—21no—
39#18012712—21no—
40C4⋊C4×D151C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic
54#106×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559005—41no—
60#14559005—41no—
61#14559004—41no—
62#14559004—41no—
63#14559004—41no—
64#14559004—41no—
65C2×Dic302D411yescharacteristic
66C2×Dic302C2311yescharacteristic
67C2×D604—21no—
68C2×D604—21no—
69C2×D604—21no—
70C2×D604—21no—
71C2×D604D411yescharacteristic
72C2×D604C2311yescharacteristic
73C2×D604C2311yescharacteristic
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151D411yescharacteristic
77C2×C22⋊D151D411yescharacteristic
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151C2311yescharacteristic
82C2×C4×D151C2311yescharacteristic
83#14558994—41no—
84#14558993—41no—
85#14558991—41no—
86D1208—41no—
87#14558987—41no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C8×D151—41no—
91C4⋊Dic151—21no—
92C4⋊Dic151—21no—
93C4⋊Dic151C2311yescharacteristic
94Dic151⋊C4—21no—
95Dic151⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103C2×Q8×C151C2311yescharacteristic
104C22×C4×C151—21no—
105C22×C4×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151—21no—
109C4⋊C4×C151—21no—
110C4⋊C4×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115C22×D151—21no—
116C22×D151C2×D411yescharacteristic
117C22×D151C2×D411yescharacteristic
118Dic302—21no—
119Dic302—21no—
120Dic302—41no—
121D604—21no—
122D604—21no—
123D604—21no—
124D604—21no—
125D604—41no—
126D604—42no—
127D604—81no—
128D604—81no—
129D604—81no—
130C22⋊D151—41no—
131C22⋊D151—41no—
132C22⋊D151—42no—
133C22⋊D151—81no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151C2×D411yescharacteristic
137C2×Dic151C2×D411yescharacteristic
138C4×D151—21no—
139C4×D151—21no—
140C4×D151—21no—
141C4×D151—21no—
142C4×D151—42no—
143C4×D151—42no—
144C4×D151—81no—
145C151⋊C8—21no—
146C151⋊C8—21no—
147C23×C151C2×D411yescharacteristic
148Q8×C151—21no—
149Q8×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—81no—
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2411yescharacteristic
159C8×C151—21no—
160C8×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151C22×D411yescharacteristic
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—21no—
168C2×D151—21no—
169C2×D151—21no—
170C2×D151—21no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C4×C151—21no—
178C4×C151—41no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151H(5,𝔽2)11yescharacteristic
183C4×C151H(5,𝔽2)11yescharacteristic
184Dic151—21no—
185Dic151—21no—
186Dic151—41no—
187Dic151—41no—
188C2×C151—41no—
189C2×C151#53411yescharacteristic
190C2×C151#57711yescharacteristic
191C2×C151#57711yescharacteristic
192D151—41no—
193D151—41no—
194D151—81no—
195D151—81no—
196C151#320411yescharacteristic, complemented, Sylow
197#3204—1511nomaximal, Sylow
198#537—1511no—
199#537—1511no—
200#483—1511no—
201#483D15111yescharacteristic, complemented
202#481—1511no—
203#481—1511no—
204#470—1511no—
205#469—1511no—
206#465—1511no—
207#465—1511no—
208#452—1511no—
209#452—1511no—
210#449—1511no—
211#449—1511no—
212#408—1511no—
213C2×#41—1511no—
214C2×#41—1511no—
215C2×#41—1511no—
216C2×Q16—1511no—
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×D8—1511no—
220C2×M16—1511no—
221C22×C8—1511no—
222C22⋊Q8—3021no—
223C22⋊Q8—3021no—
224C22⋊Q8—1511no—
225C22⋊Q8—1511no—
226C22⋊Q8—1511no—
227C22⋊Q8C2×D15111yescharacteristic
228#121—3021no—
229#121—3021no—
230#121—3021no—
231#121—3021no—
232#121—3021no—
233#121—3021no—
234#121—1511no—
235#121—1511no—
236#121—1511no—
237#121—1511no—
238C2×C4⋊C4—1511no—
239C2×C4⋊C4C2×D15111yescharacteristic
240#106—1511no—
241#106—1511no—
242#106C2×D15111yescharacteristic
243#106C2×D15111yescharacteristic
244#103—1511no—
245#103—1511no—
246#103C2×D15111yescharacteristic
247#103C2×D15111yescharacteristic
248#102—1511no—
249#102—1511no—
250#102—1511no—
251#102—1511no—
252C22⋊C8—1511no—
253C22⋊C8—1511no—
254C22⋊C8—1511no—
255C22⋊C8C2×D15111yescharacteristic
256#41—6041no—
257#41—6041no—
258#41—6041no—
259#41—6041no—
260#41—6041no—
261#41—6041no—
262C2×Q8—1511no—
263C2×Q8—1511no—
264C2×Q8C22×D15111yescharacteristic
265C2×D4—3021no—
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—1511no—
272C2×D4—1511no—
273C2×D4—1511no—
274C2×D4—1511no—
275C2×D4—1511no—
276C22×C4—21no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—3021no—
280C22×C4—1511no—
281C22×C4—1511no—
282C22×C4C22×D15111yescharacteristic
283Q16—6041no—
284SD16—6041no—
285SD16—6041no—
286D8—6041no—
287M16—6041no—
288C2×C8—6041no—
289C2×C8—1511no—
290C2×C8—1511no—
291C2×C8C22×D15111yescharacteristic
292C2×C8C22×D15111yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—3021no—
296C4⋊C4—3021no—
297C4⋊C4—3021no—
298C4⋊C4—3021no—
299C4⋊C4—1511no—
300C4⋊C4C22×D15111yescharacteristic
301C4⋊C4C22×D15111yescharacteristic
302C4⋊C4C22×D15111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C23—3021no—
312C23—3021no—
313C23—1511no—
314C23—1511no—
315C23D4×D15111yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—3021no—
319Q8—3021no—
320Q8—6041no—
321D4—3021no—
322D4—3021no—
323D4—3021no—
324D4—3021no—
325D4—6041no—
326D4—6042no—
327D4—6041no—
328D4—6041no—
329D4—6042no—
330D4—12081no—
331D4—12081no—
332D4—12081no—
333D4—12081no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—81no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—6042no—
348C2×C4—6042no—
349C2×C4—1511no—
350C2×C4—1511no—
351C2×C4—12081no—
352C2×C4D4×D15111yescharacteristic
353C2×C4C23×D15111yescharacteristic
354C8—21no—
355C8—21no—
356C8—3021no—
357C8—3021no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—3021no—
362C22—3021no—
363C22—3021no—
364C22—3021no—
365C22—3021no—
366C22—3021no—
367C22—6041no—
368C22—6041no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—6041no—
373C22C2×D4×D15111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—3021no—
380C4—3021no—
381C4—6041no—
382C4—6041no—
383C4#1801278511yescharacteristic
384C4#1801278511yescharacteristic
385C2—41no—
386C2—6041no—
387C2—6041no—
388C2—12081no—
389C2—12081no—
390C2#2375277311yescharacteristic
391C2#2375301811yescharacteristic
392C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#483×C151C2
socleC22×C151C22×D4
hypercenter#483D151
hypocenterC151#3204
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #23752793C2semidirect
2. #23752792C2semidirect
3. #23752544C2semidirect
4. #23752532C2semidirect
5. #23752530C2semidirect
6. #23752469C2semidirect
7. #23752466C2semidirect
8. #23752444C2semidirect
9. #23752442C2semidirect
10. #23752377C2semidirect
11. #23752372C2semidirect
12. #23752360C2semidirect
13. #23752359C2semidirect
14. #23752177C2semidirect
15. #483×C151C2semidirect
196. C151#3204semidirect
201. #483D151semidirect

Maximal subgroups

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

subgroupindex
#237527932
#237527922
#237525442
#237525322
#237525302
#237524692
#237524662
#237524442
#237524422
#237523772
#237523722
#237523602
#237523592
#237521772
#483×C1512
#3204151