Finite Group Databasebeta

← #34079083

Subgroups — #34079083

Order 19328.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752791C211yesmaximal, characteristic
2#23752693C211yesmaximal, characteristic, complemented
3#23752555C211yesmaximal, characteristic, complemented
4#23752554C211yesmaximal, characteristic, complemented
5#23752549C211yesmaximal, characteristic, complemented
6#23752547C211yesmaximal, characteristic, complemented
7#23752535C211yesmaximal, characteristic, complemented
8#23752533C211yesmaximal, characteristic, complemented
9#23752524C211yesmaximal, characteristic, complemented
10#23752253C211yesmaximal, characteristic, complemented
11#107×D151C211yesmaximal, characteristic, complemented
12#23752210C211yesmaximal, characteristic, complemented
13#23752205C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#480×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012719C2211yescharacteristic
21#18012718C2211yescharacteristic
22#18012716—21no—
23#18012712—21no—
24#18012711—21no—
25#18012710—21no—
26#18012710C2211yescharacteristic
27#18012704—21no—
28#18012701—21no—
29C4×C22⋊D151—21no—
30C4×C22⋊D151—21no—
31#18012698C2211yescharacteristic
32#18012697C2211yescharacteristic
33#18012697C2211yescharacteristic
34C4⋊C4×D151C2211yescharacteristic
35C4⋊C4×D151C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012672C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52#121×C151C2211yescharacteristic
53C2×C4⋊C4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—22no—
61#14559003—22no—
62#14559003—22no—
63C2×Dic302D411yescharacteristic
64C2×Dic302C2311yescharacteristic
65C2×D604D411yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151D411yescharacteristic
69C2×C22⋊D151D411yescharacteristic
70C22×Dic151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151C2311yescharacteristic
75C2×C4×D151C2311yescharacteristic
76#14558987—22no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C8×D151—22no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100C22×C4×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C2×C8×C151C2311yescharacteristic
103C4⋊C4×C151—21no—
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C22×D151C2×D411yescharacteristic
109C22×D151C2×D411yescharacteristic
110Dic302—22no—
111Dic302—21no—
112Dic302—21no—
113D604—22no—
114C22⋊D151—22no—
115C22⋊D151—22no—
116C22⋊D151—42no—
117C22⋊D151—81no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—42no—
123C2×Dic151C2×D411yescharacteristic
124C2×Dic151C2×D411yescharacteristic
125C4×D151—21no—
126C4×D151—21no—
127C4×D151—81no—
128C4×D151—81no—
129C4×D151—81no—
130C4×D151#4112yes—
131C4×D151#4112yes—
132C151⋊C8—21no—
133C151⋊C8—21no—
134C23×C151—21no—
135C23×C151C2×D411yescharacteristic
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—81no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—81no—
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2411yescharacteristic
147C8×C151—21no—
148C8×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151C22×D411yescharacteristic
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—21no—
159C2×D151—21no—
160C2×D151—21no—
161C2×D151#12312yes—
162C4×C151—21no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151C2×#4111yescharacteristic
167C4×C151C2×#4111yescharacteristic
168Dic151—21no—
169Dic151—41no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173Dic151#12312yes—
174C2×C151—41no—
175C2×C151—81no—
176C2×C151C2×#12311yescharacteristic
177C2×C151#57611yescharacteristic
178C2×C151#57811yescharacteristic
179D151—22no—
180D151—41no—
181C151#309811yescharacteristic, complemented, Sylow
182#3098—1511nomaximal, Sylow
183#537—1511no—
184#520—1511no—
185#485—1511no—
186#485—1511no—
187#484—1511no—
188#484—1511no—
189#482—1511no—
190#482—1511no—
191#480—1511no—
192#480D15111yescharacteristic, complemented
193#428—1511no—
194C2×#107—1511no—
195#417—1511no—
196#416—1511no—
197#408—1511no—
198C2×#41—1511no—
199C2×#41—1511no—
200C2×M16—1511no—
201C22×C8—1511no—
202C22⋊Q8—3021no—
203C22⋊Q8—1511no—
204C22⋊Q8—1511no—
205#121—3021no—
206#121—3021no—
207#121—3021no—
208#121—1511no—
209#121C2×D15111yescharacteristic
210C4×Q8—3021no—
211C4×D4—3021no—
212C4×D4—3021no—
213C4×D4—3021no—
214#117—1511no—
215#117—1511no—
216#117—1511no—
217C2×C4⋊C4—1511no—
218C2×C4⋊C4—1511no—
219C2×C4⋊C4—1511no—
220C2×C4⋊C4C2×D15111yescharacteristic
221#107—1511no—
222#107—1511no—
223#107—1511no—
224#107—1511no—
225#107C2×D15111yescharacteristic
226#107C2×D15111yescharacteristic
227#106—1511no—
228#106—1511no—
229#103—1511no—
230#103—1511no—
231#103—1511no—
232#103—1511no—
233#102—1511no—
234#102—1511no—
235#102C2×D15111yescharacteristic
236#102C2×D15111yescharacteristic
237C22⋊C8—1511no—
238C22⋊C8—1511no—
239C22⋊C8—1511no—
240C22⋊C8C2×D15111yescharacteristic
241#41—3022no—
242#41—3022no—
243#41—3022no—
244#41—3022no—
245C2×Q8—1511no—
246C2×Q8—1511no—
247C2×D4—21no—
248C2×D4—3021no—
249C2×D4—3021no—
250C2×D4—1511no—
251C2×D4—1511no—
252C2×D4—1511no—
253C2×D4C22×D15111yescharacteristic
254C22×C4—21no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4—3021no—
258C22×C4—3021no—
259C22×C4—1511no—
260C22×C4—1511no—
261C22×C4C22×D15111yescharacteristic
262M16—3022no—
263C2×C8—3022no—
264C2×C8—1511no—
265C2×C8—1511no—
266C2×C8C22×D15111yescharacteristic
267C2×C8C22×D15111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—3021no—
274C4⋊C4—1511no—
275C4⋊C4—1511no—
276C4⋊C4—1511no—
277C4⋊C4C22×D15111yescharacteristic
278C4⋊C4C22×D15111yescharacteristic
279C4⋊C4C22×D15111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C42—3021no—
288C42—3021no—
289C42—3021no—
290C23—21no—
291C23—1511no—
292C23—1511no—
293C23D4×D15111yescharacteristic
294Q8—3022no—
295Q8—3021no—
296Q8—3021no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—3022no—
301D4—3022no—
302D4—3022no—
303D4—6042no—
304D4—12081no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—6042no—
318C2×C4—1511no—
319C2×C4—1511no—
320C2×C4—1512no—
321C2×C4—1512no—
322C2×C4—12081no—
323C2×C4—12081no—
324C2×C4—12081no—
325C2×C4D4×D15111yescharacteristic
326C2×C4C23×D15111yescharacteristic
327C8—21no—
328C8—21no—
329C8—3021no—
330C8—3021no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3021no—
338C22—3021no—
339C22—3021no—
340C22—3021no—
341C22—3021no—
342C22—1512no—
343C22C2×D4×D15111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3021no—
349C4—6041no—
350C4—6041no—
351C4—6041no—
352C4—6041no—
353C4—1512no—
354C4#41×D15111yescharacteristic
355C4#41×D15111yescharacteristic
356C2—41no—
357C2—81no—
358C2—3022no—
359C2—6041no—
360C2#123×D15111yescharacteristic
361C2#2375301311yescharacteristic
362C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#480×C151C2
socleC22×C151C22×D4
prime radical#23752791C2
hypercenter#480D151
hypocenterC151#3098
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #23752693C2semidirect
3. #23752555C2semidirect
4. #23752554C2semidirect
5. #23752549C2semidirect
6. #23752547C2semidirect
7. #23752535C2semidirect
8. #23752533C2semidirect
9. #23752524C2semidirect
10. #23752253C2semidirect
11. #107×D151C2semidirect
12. #23752210C2semidirect
13. #23752205C2semidirect
14. #23752177C2semidirect
15. #480×C151C2semidirect
181. C151#3098semidirect
192. #480D151semidirect

Maximal subgroups

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

subgroupindex
#237527912
#237526932
#237525552
#237525542
#237525492
#237525472
#237525352
#237525332
#237525242
#237522532
#107×D1512
#237522102
#237522052
#237521772
#480×C1512
#3098151