Finite Group Databasebeta

← #34080081

Subgroups — #34080081

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#23752761C211yesmaximal, characteristic, complemented
2#23752741C211yesmaximal, characteristic, complemented
3#23752594C211yesmaximal, characteristic, complemented
4#23752567C211yesmaximal, characteristic, complemented
5#23752566C211yesmaximal, characteristic, complemented
6#23752420C211yesmaximal, characteristic, complemented
7#23752415C211yesmaximal, characteristic, complemented
8#23752410C211yesmaximal, characteristic, complemented
9#23752405C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11#23752371C211yesmaximal, characteristic, complemented
12#23752356C211yesmaximal, characteristic, complemented
13#23752354C211yesmaximal, characteristic, complemented
14#23752263C211yesmaximal, characteristic, complemented
15#495×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22#18012737C2211yescharacteristic
23#18012735C2211yescharacteristic
24#18012732—21no—
25#18012731C2211yescharacteristic
26#18012727C2211yescharacteristic
27#18012721—21no—
28#18012715C2211yescharacteristic
29#18012712—21no—
30#18012712—21no—
31#18012710C2211yescharacteristic
32Q8×Dic151C2211yescharacteristic
33D4×Dic151C2211yescharacteristic
34(C22⋊D151)⋊C4—21no—
35(C22⋊D151)⋊C4—21no—
36(C22⋊D151)⋊C4—21no—
37#18012695—21no—
38C42×D151C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012664C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C4×C151⋊C8C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C2×D8×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57#124×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59#14559005—41no—
60#14559005—41no—
61#14559003—41no—
62#14559003—41no—
63C2×Dic302C2311yescharacteristic
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C22×Dic151—21no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73C2×C4×D151D411yescharacteristic
74C2×C4×D151D411yescharacteristic
75C2×C4×D151C2311yescharacteristic
76#14558994—41no—
77#14558992—41no—
78#14558991—41no—
79#14558989—41no—
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151—21no—
96C4×Dic151D411yescharacteristic
97C4×Dic151D411yescharacteristic
98C4×Dic151C2311yescharacteristic
99C2×Q8×C151C2311yescharacteristic
100C2×Q8×C151C2311yescharacteristic
101C2×D4×C151C2311yescharacteristic
102C2×D4×C151C2311yescharacteristic
103Q16×C151—41no—
104SD16×C151—41no—
105SD16×C151—41no—
106D8×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151C2×D411yescharacteristic
116Dic302—21no—
117Dic302—21no—
118D604—21no—
119D604—21no—
120D604—42no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C22⋊D151—42no—
124C22⋊D151—42no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—42no—
129C2×Dic151—42no—
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—22no—
136C4×D151—41no—
137C4×D151—42no—
138C151⋊C8—21no—
139C151⋊C8—21no—
140C23×C151—21no—
141C23×C151—21no—
142Q8×C151—21no—
143Q8×C151—21no—
144Q8×C151—21no—
145Q8×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2411yescharacteristic
155C8×C151—21no—
156C8×C151—21no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151C22×D411yescharacteristic
164C2×D151—21no—
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151H(5,𝔽2)11yescharacteristic
175C4×C151H(5,𝔽2)11yescharacteristic
176Dic151—21no—
177Dic151—21no—
178Dic151—41no—
179Dic151—41no—
180Dic151—41no—
181Dic151#13512yes—
182C2×C151—81no—
183C2×C151—81no—
184C2×C151#53511yescharacteristic
185C2×C151C2×#13511yescharacteristic
186C2×C151#57511yescharacteristic
187D151—41no—
188D151—81no—
189C151#321211yescharacteristic, complemented, Sylow
190#3212—1511nomaximal, Sylow
191#532—1511no—
192#529—1511no—
193#495—1511no—
194#495D15111yescharacteristic, complemented
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#449—1511no—
205#431—1511no—
206C2×#41—1511no—
207C2×#41—1511no—
208C2×Q16—1511no—
209C2×Q16C2×D15111yescharacteristic
210C2×SD16—1511no—
211C2×SD16—1511no—
212C2×SD16C2×D15111yescharacteristic
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#124C2×D15111yescharacteristic
222#124C2×D15111yescharacteristic
223#123—3021no—
224C22⋊Q8—1511no—
225#121—3021no—
226#121—3021no—
227#121—1511no—
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#103—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245C22⋊C8—1511no—
246C22⋊C8—1511no—
247C4×C8—1511no—
248C4×C8C2×D15111yescharacteristic
249#41—6041no—
250#41—6041no—
251#41—6041no—
252#41—6041no—
253C2×Q8—1511no—
254C2×Q8C22×D15111yescharacteristic
255C2×Q8C22×D15111yescharacteristic
256C2×D4—3021no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—1511no—
262C2×D4C22×D15111yescharacteristic
263C2×D4C22×D15111yescharacteristic
264C22×C4—3021no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—1511no—
268C22×C4—1511no—
269C22×C4—1511no—
270Q16—41no—
271Q16—6041no—
272SD16—41no—
273SD16—41no—
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⋊C4—1511no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C42—3021no—
300C42—1511no—
301C42—1511no—
302C42—1511no—
303C42C22×D15111yescharacteristic
304C23—21no—
305C23—21no—
306C23—3021no—
307C23—1511no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—3021no—
313Q8—3021no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—3021no—
319D4—3021no—
320D4—6042no—
321D4—6042no—
322D4—6042no—
323D4—6042no—
324D4—6042no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—3022no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—6041no—
334C2×C4—6042no—
335C2×C4—6042no—
336C2×C4—6042no—
337C2×C4—1511no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4D4×D15111yescharacteristic
341C2×C4D4×D15111yescharacteristic
342C2×C4C23×D15111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3021no—
346C8—3021no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—3021no—
354C22—3021no—
355C22—3021no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22C2×D4×D15111yescharacteristic
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—3021no—
365C4—3021no—
366C4—6041no—
367C4—6041no—
368C4—6041no—
369C4—1512no—
370C4#1801278411yescharacteristic
371C4#1801278411yescharacteristic
372C2—81no—
373C2—81no—
374C2—6041no—
375C2—12081no—
376C2#2375277511yescharacteristic
377C2#135×D15111yescharacteristic
378C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#495×C151C2
socleC22×C151C22×D4
hypercenter#495D151
hypocenterC151#3212
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #23752761C2semidirect
2. #23752741C2semidirect
3. #23752594C2semidirect
4. #23752567C2semidirect
5. #23752566C2semidirect
6. #23752420C2semidirect
7. #23752415C2semidirect
8. #23752410C2semidirect
9. #23752405C2semidirect
10. #23752373C2semidirect
11. #23752371C2semidirect
12. #23752356C2semidirect
13. #23752354C2semidirect
14. #23752263C2semidirect
15. #495×C151C2semidirect
189. C151#3212semidirect
194. #495D151semidirect

Maximal subgroups

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

subgroupindex
#237527612
#237527412
#237525942
#237525672
#237525662
#237524202
#237524152
#237524102
#237524052
#237523732
#237523712
#237523562
#237523542
#237522632
#495×C1512
#3212151