Finite Group Databasebeta

← #34080083

Subgroups — #34080083

Order 19328.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752758C211yesmaximal, characteristic, complemented
2#23752743C211yesmaximal, characteristic, complemented
3#23752595C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752568C211yesmaximal, characteristic, complemented
6#23752565C211yesmaximal, characteristic, complemented
7#23752421C211yesmaximal, characteristic, complemented
8#23752415C211yesmaximal, characteristic, complemented
9#23752411C211yesmaximal, characteristic, complemented
10#23752405C211yesmaximal, characteristic, complemented
11#23752376C211yesmaximal, characteristic, complemented
12#23752374C211yesmaximal, characteristic, complemented
13#23752355C211yesmaximal, characteristic, complemented
14#23752262C211yesmaximal, characteristic, complemented
15#449×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Dic604C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21C2×#14558992C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23#18012737C2211yescharacteristic
24#18012735C2211yescharacteristic
25#18012732—21no—
26#18012730C2211yescharacteristic
27#18012728C2211yescharacteristic
28#18012726C2211yescharacteristic
29#18012726C2211yescharacteristic
30#18012720—21no—
31#18012718C2211yescharacteristic
32#18012711—21no—
33#18012711—21no—
34#18012704C2211yescharacteristic
35D4×Dic151—21no—
36D4×Dic151C2211yescharacteristic
37C4×C22⋊D151—21no—
38C4×C22⋊D151—21no—
39#18012695—21no—
40C2×C4×Dic151C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302C2311yescharacteristic
62C2×Dic302C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C22×Dic151—21no—
68C22×Dic151D411yescharacteristic
69C22×Dic151D411yescharacteristic
70C2×C4×D151—21no—
71Dic604—41no—
72#14558994—41no—
73#14558993—41no—
74#14558992—41no—
75#14558992—41no—
76#14558989—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94C4×Dic151—21no—
95C4×Dic151D411yescharacteristic
96C4×Dic151D411yescharacteristic
97C4×Dic151C2311yescharacteristic
98C4×Dic151C2311yescharacteristic
99#41×C151—41no—
100#41×C151—41no—
101C2×Q8×C151C2311yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C2×D4×C151C2311yescharacteristic
106C22×C4×C151—21no—
107C22×C4×C151C2311yescharacteristic
108SD16×C151—41no—
109D8×C151—41no—
110C2×C8×C151C2311yescharacteristic
111C2×C8×C151C2311yescharacteristic
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119D604—21no—
120D604—21no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C22⋊D151—42no—
124C2×Dic151—22no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—41no—
129C2×Dic151—42no—
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—42no—
135C151⋊C8—21no—
136C151⋊C8—21no—
137C23×C151—21no—
138C23×C151—21no—
139C23×C151C2×D411yescharacteristic
140Q8×C151—21no—
141Q8×C151—21no—
142D4×C151—21no—
143D4×C151—21no—
144D4×C151—21no—
145D4×C151—21no—
146D4×C151—42no—
147D4×C151—42no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—42no—
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C8×C151—21no—
156C8×C151—21no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151C22×D411yescharacteristic
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C4×C151—21no—
171C4×C151—41no—
172C4×C151—41no—
173C4×C151H(5,𝔽2)11yescharacteristic
174C4×C151H(5,𝔽2)11yescharacteristic
175Dic151—21no—
176Dic151—21no—
177Dic151—21no—
178Dic151—41no—
179Dic151—41no—
180Dic151—41no—
181Dic151#13512yes—
182C2×C151—41no—
183C2×C151—81no—
184C2×C151—81no—
185C2×C151#53511yescharacteristic
186C2×C151C2×#13511yescharacteristic
187C2×C151#57511yescharacteristic
188D151—81no—
189C151#321211yescharacteristic, complemented, Sylow
190#3212—1511nomaximal, Sylow
191#532—1511no—
192#529—1511no—
193#495—1511no—
194#495—1511no—
195#488—1511no—
196#488—1511no—
197#462—1511no—
198#461—1511no—
199#460—1511no—
200#459—1511no—
201#452—1511no—
202#452—1511no—
203#449—1511no—
204#449D15111yescharacteristic, complemented
205#431—1511no—
206C2×#41—1511no—
207C2×#41C2×D15111yescharacteristic
208C2×Q16—1511no—
209C2×Q16—1511no—
210C2×SD16—1511no—
211C2×SD16—1511no—
212C2×SD16—1511no—
213C2×SD16C2×D15111yescharacteristic
214C2×D8—1511no—
215C2×D8C2×D15111yescharacteristic
216C4⋊Q8—1511no—
217#127—1511no—
218#126—3021no—
219#125—1511no—
220#124—1511no—
221#124—1511no—
222#124—1511no—
223#123—3021no—
224C22⋊Q8—1511no—
225#121—3021no—
226#121—3021no—
227#121C2×D15111yescharacteristic
228C4×Q8—1511no—
229C4×D4—3021no—
230C4×D4—3021no—
231C4×D4—3021no—
232C4×D4—1511no—
233#117—3021no—
234C2×C42—1511no—
235C4⋊C8—1511no—
236C4⋊C8—1511no—
237#103—1511no—
238#103—1511no—
239#103—1511no—
240#103C2×D15111yescharacteristic
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102C2×D15111yescharacteristic
245C22⋊C8—1511no—
246C22⋊C8C2×D15111yescharacteristic
247C4×C8—1511no—
248C4×C8—1511no—
249#41—41no—
250#41—41no—
251#41—6041no—
252#41—6041no—
253C2×Q8—1511no—
254C2×Q8—1511no—
255C2×Q8C22×D15111yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—1511no—
262C2×D4C22×D15111yescharacteristic
263C2×D4C22×D15111yescharacteristic
264C22×C4—21no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—1511no—
268C22×C4—1511no—
269C22×C4C22×D15111yescharacteristic
270Q16—6041no—
271Q16—6041no—
272SD16—41no—
273SD16—6041no—
274SD16—6041no—
275SD16—6041no—
276D8—41no—
277D8—6041no—
278C2×C8—1511no—
279C2×C8—1511no—
280C2×C8C22×D15111yescharacteristic
281C2×C8C22×D15111yescharacteristic
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—3021no—
286C4⋊C4—3021no—
287C4⋊C4—3021no—
288C4⋊C4—1511no—
289C4⋊C4C22×D15111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C42—3021no—
300C42—1511no—
301C42—1511no—
302C42—1511no—
303C42—1511no—
304C23—21no—
305C23—21no—
306C23—3021no—
307C23D4×D15111yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—3021no—
311Q8—3021no—
312Q8—3021no—
313Q8—3021no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—3021no—
321D4—3021no—
322D4—6042no—
323D4—6042no—
324D4—6042no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—3022no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—6042no—
335C2×C4—6041no—
336C2×C4—6042no—
337C2×C4—1511no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4—1511no—
341C2×C4D4×D15111yescharacteristic
342C2×C4C23×D15111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3021no—
346C8—3021no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22C2×D4×D15111yescharacteristic
360C4—21no—
361C4—41no—
362C4—41no—
363C4—3021no—
364C4—3021no—
365C4—3021no—
366C4—6041no—
367C4—6041no—
368C4—6041no—
369C4—1512no—
370C4#1801278411yescharacteristic
371C4#1801278411yescharacteristic
372C2—41no—
373C2—81no—
374C2—81no—
375C2—12081no—
376C2#2375277711yescharacteristic
377C2#135×D15111yescharacteristic
378C2#2375300811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#449×C151C2
socleC22×C151C22×D4
hypercenter#449D151
hypocenterC151#3212
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #23752758C2semidirect
2. #23752743C2semidirect
3. #23752595C2semidirect
4. #23752593C2semidirect
5. #23752568C2semidirect
6. #23752565C2semidirect
7. #23752421C2semidirect
8. #23752415C2semidirect
9. #23752411C2semidirect
10. #23752405C2semidirect
11. #23752376C2semidirect
12. #23752374C2semidirect
13. #23752355C2semidirect
14. #23752262C2semidirect
15. #449×C151C2semidirect
189. C151#3212semidirect
204. #449D151semidirect

Maximal subgroups

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

subgroupindex
#237527582
#237527432
#237525952
#237525932
#237525682
#237525652
#237524212
#237524152
#237524112
#237524052
#237523762
#237523742
#237523552
#237522622
#449×C1512
#3212151