Finite Group Databasebeta

← #34079091

Subgroups — #34079091

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#23752792C211yesmaximal, characteristic
2#23752692C211yesmaximal, characteristic, complemented
3#23752552C211yesmaximal, characteristic, complemented
4#23752546C211yesmaximal, characteristic, complemented
5#23752545C211yesmaximal, characteristic, complemented
6#23752538C211yesmaximal, characteristic, complemented
7#23752536C211yesmaximal, characteristic, complemented
8#23752527C211yesmaximal, characteristic, complemented
9#23752526C211yesmaximal, characteristic, complemented
10#23752251C211yesmaximal, characteristic, complemented
11#107×D151C211yesmaximal, characteristic, complemented
12#23752212C211yesmaximal, characteristic, complemented
13#23752207C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#485×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012717—21no—
21#18012715C2211yescharacteristic
22#18012714—21no—
23#18012714C2211yescharacteristic
24#18012713C2211yescharacteristic
25#18012712—21no—
26#18012712—21no—
27C4×Dic302—21no—
28C4×D604—21no—
29(C22⋊D151)⋊C4—21no—
30(C22⋊D151)⋊C4—21no—
31#18012697C2211yescharacteristic
32#18012697C2211yescharacteristic
33C2×C4⋊Dic151C2211yescharacteristic
34C4⋊C4×D151C2211yescharacteristic
35C4⋊C4×D151C2211yescharacteristic
36C4⋊C4×D151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53#117×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—22no—
61#14559004—22no—
62#14559004—22no—
63C2×Dic302D411yescharacteristic
64C2×D604—21no—
65C2×D604—21no—
66C2×D604D411yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151D411yescharacteristic
70C2×C22⋊D151D411yescharacteristic
71C22×Dic151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151C2311yescharacteristic
77C2×C4×D151C2311yescharacteristic
78#14558987—22no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C8×D151—22no—
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C2×Q8×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C4⋊C4×C151—21no—
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C42×C151—21no—
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110C22×D151C2×D411yescharacteristic
111Dic302—22no—
112D604—22no—
113D604—21no—
114D604—21no—
115D604—42no—
116D604—81no—
117C22⋊D151—22no—
118C22⋊D151—22no—
119C22⋊D151—81no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—81no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C4×D151—21no—
127C4×D151—21no—
128C4×D151—42no—
129C4×D151—81no—
130C4×D151—81no—
131C4×D151—81no—
132C4×D151#4112yes—
133C4×D151#4112yes—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151C2×D411yescharacteristic
137Q8×C151—21no—
138Q8×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2411yescharacteristic
147C8×C151—21no—
148C8×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151C22×D411yescharacteristic
153C2×D151—21no—
154C2×D151—21no—
155C2×D151—21no—
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151#12312yes—
162C4×C151—21no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166C4×C151—41no—
167C4×C151C2×#4111yescharacteristic
168C4×C151C2×#4111yescharacteristic
169Dic151—21no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173Dic151#12312yes—
174C2×C151—41no—
175C2×C151C2×#12311yescharacteristic
176C2×C151#57611yescharacteristic
177C2×C151#57811yescharacteristic
178D151—22no—
179D151—41no—
180D151—81no—
181C151#309811yescharacteristic, complemented, Sylow
182#3098—1511nomaximal, Sylow
183#537—1511no—
184#520—1511no—
185#485—1511no—
186#485D15111yescharacteristic, complemented
187#484—1511no—
188#484—1511no—
189#482—1511no—
190#482—1511no—
191#480—1511no—
192#480—1511no—
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⋊Q8C2×D15111yescharacteristic
205#121—3021no—
206#121—3021no—
207#121—3021no—
208#121—1511no—
209#121—1511no—
210C4×Q8—3021no—
211C4×D4—3021no—
212C4×D4—3021no—
213C4×D4—3021no—
214#117—1511no—
215#117—1511no—
216#117C2×D15111yescharacteristic
217C2×C4⋊C4—1511no—
218C2×C4⋊C4—1511no—
219C2×C4⋊C4—1511no—
220C2×C4⋊C4—1511no—
221#107—1511no—
222#107—1511no—
223#107—1511no—
224#107—1511no—
225#107—1511no—
226#107C2×D15111yescharacteristic
227#106—1511no—
228#106C2×D15111yescharacteristic
229#103—1511no—
230#103—1511no—
231#103C2×D15111yescharacteristic
232#103C2×D15111yescharacteristic
233#102—1511no—
234#102—1511no—
235#102—1511no—
236#102—1511no—
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×Q8C22×D15111yescharacteristic
247C2×D4—3021no—
248C2×D4—3021no—
249C2×D4—3021no—
250C2×D4—1511no—
251C2×D4—1511no—
252C2×D4—1511no—
253C2×D4—1511no—
254C22×C4—3021no—
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—21no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C42—21no—
288C42—3021no—
289C42—3021no—
290C23—3021no—
291C23—1511no—
292C23—1511no—
293C23D4×D15111yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—3022no—
297D4—3022no—
298D4—3022no—
299D4—3022no—
300D4—3021no—
301D4—3021no—
302D4—6042no—
303D4—12081no—
304D4—12081no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—6042no—
317C2×C4—1511no—
318C2×C4—1511no—
319C2×C4—1512no—
320C2×C4—1512no—
321C2×C4—12081no—
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—3021no—
335C22—3021no—
336C22—3021no—
337C22—3021no—
338C22—3021no—
339C22—6041no—
340C22—6041no—
341C22—6041no—
342C22—1512no—
343C22C2×D4×D15111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3021no—
350C4—6041no—
351C4—6041no—
352C4—6041no—
353C4—1512no—
354C4#41×D15111yescharacteristic
355C4#41×D15111yescharacteristic
356C2—41no—
357C2—3022no—
358C2—6041no—
359C2—12081no—
360C2#123×D15111yescharacteristic
361C2#2375301411yescharacteristic
362C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#485×C151C2
socleC22×C151C22×D4
prime radical#23752792C2
hypercenter#485D151
hypocenterC151#3098
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #23752692C2semidirect
3. #23752552C2semidirect
4. #23752546C2semidirect
5. #23752545C2semidirect
6. #23752538C2semidirect
7. #23752536C2semidirect
8. #23752527C2semidirect
9. #23752526C2semidirect
10. #23752251C2semidirect
11. #107×D151C2semidirect
12. #23752212C2semidirect
13. #23752207C2semidirect
14. #23752177C2semidirect
15. #485×C151C2semidirect
181. C151#3098semidirect
186. #485D151semidirect

Maximal subgroups

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

subgroupindex
#237527922
#237526922
#237525522
#237525462
#237525452
#237525382
#237525362
#237525272
#237525262
#237522512
#107×D1512
#237522122
#237522072
#237521772
#485×C1512
#3098151