Finite Group Databasebeta

← #34079996

Subgroups — #34079996

Order 19328.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752792C211yesmaximal, characteristic
2#23752786C211yesmaximal, characteristic, complemented
3#23752550C211yesmaximal, characteristic, complemented
4#23752546C211yesmaximal, characteristic, complemented
5#23752541C211yesmaximal, characteristic, complemented
6#23752537C211yesmaximal, characteristic, complemented
7#23752467C211yesmaximal, characteristic, complemented
8#23752461C211yesmaximal, characteristic, complemented
9#23752450C211yesmaximal, characteristic, complemented
10#23752444C211yesmaximal, characteristic, complemented
11#23752373C211yesmaximal, characteristic, complemented
12#23752373C211yesmaximal, characteristic, complemented
13#23752351C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic, complemented
15#451×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012737—21no—
23#18012728—21no—
24#18012722—21no—
25#18012722—21no—
26#18012717—21no—
27#18012715C2211yescharacteristic
28#18012715C2211yescharacteristic
29#18012715C2211yescharacteristic
30#18012715C2211yescharacteristic
31#18012715C2211yescharacteristic
32#18012714—21no—
33#18012714C2211yescharacteristic
34#18012713C2211yescharacteristic
35#18012712—21no—
36#18012712—21no—
37#18012698C2211yescharacteristic
38C4⋊C4×D151C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C22×Q8×C151C2211yescharacteristic
53C2×Q16×C151C2211yescharacteristic
54C2×Q16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559005—41no—
60#14559005—41no—
61#14559004—41no—
62#14559004—41no—
63C2×Dic302D411yescharacteristic
64C2×D604—21no—
65C2×D604—21no—
66C2×D604D411yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151D411yescharacteristic
70C2×C22⋊D151D411yescharacteristic
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74C2×C4×D151C2311yescharacteristic
75#14558991—41no—
76#14558991—41no—
77#14558987—41no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C8×D151—41no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90C22⋊Dic151—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98C4×Dic151—21no—
99C2×Q8×C151—21no—
100C2×Q8×C151—41no—
101C2×Q8×C151—41no—
102C2×Q8×C151C2311yescharacteristic
103C2×Q8×C151C2311yescharacteristic
104C2×Q8×C151C2311yescharacteristic
105C22×C4×C151—21no—
106C22×C4×C151C2311yescharacteristic
107Q16×C151—41no—
108Q16×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151—21no—
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115C22×D151C2×D411yescharacteristic
116C22×D151C2×D411yescharacteristic
117Dic302—41no—
118D604—21no—
119D604—21no—
120D604—41no—
121D604—42no—
122D604—81no—
123C22⋊D151—41no—
124C22⋊D151—41no—
125C22⋊D151—81no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C4×D151—21no—
132C4×D151—21no—
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—42no—
136C4×D151—81no—
137C151⋊C8—21no—
138C151⋊C8—21no—
139C23×C151C2×D411yescharacteristic
140Q8×C151—21no—
141Q8×C151—21no—
142Q8×C151—21no—
143Q8×C151—21no—
144Q8×C151—21no—
145Q8×C151—21no—
146Q8×C151—42no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—42no—
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2411yescharacteristic
156C8×C151—21no—
157C8×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151C22×D411yescharacteristic
162C2×D151—21no—
163C2×D151—21no—
164C2×D151—21no—
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—21no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—21no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151H(5,𝔽2)11yescharacteristic
177C4×C151H(5,𝔽2)11yescharacteristic
178Dic151—21no—
179Dic151—21no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—41no—
184C2×C151#53411yescharacteristic
185C2×C151#57711yescharacteristic
186C2×C151#57811yescharacteristic
187D151—41no—
188D151—41no—
189D151—81no—
190C151#320111yescharacteristic, complemented, Sylow
191#3201—1511nomaximal, Sylow
192#537—1511no—
193#536—1511no—
194#485—1511no—
195#484—1511no—
196#483—1511no—
197#482—1511no—
198#470—1511no—
199#468—1511no—
200#467—1511no—
201#465—1511no—
202#452—1511no—
203#452—1511no—
204#451D15111yescharacteristic, complemented
205#448—1511no—
206#408—1511no—
207C2×#41—1511no—
208C2×#41—1511no—
209C22×Q8C2×D15111yescharacteristic
210C2×Q16C2×D15111yescharacteristic
211C2×Q16C2×D15111yescharacteristic
212C2×SD16—1511no—
213C2×SD16—1511no—
214C2×M16—1511no—
215C22×C8—1511no—
216C4⋊Q8—3021no—
217#124—3021no—
218#123—3021no—
219#123—3021no—
220C22⋊Q8—3021no—
221C22⋊Q8—1511no—
222C22⋊Q8—1511no—
223C22⋊Q8—1511no—
224C22⋊Q8—1511no—
225C22⋊Q8—1511no—
226C22⋊Q8C2×D15111yescharacteristic
227#121—3021no—
228#121—3021no—
229#121—3021no—
230#121—1511no—
231#121—1511no—
232#117—1511no—
233C2×C4⋊C4—1511no—
234#107—1511no—
235#107—1511no—
236#106—1511no—
237#106—1511no—
238#103—1511no—
239#103—1511no—
240#103—1511no—
241#103—1511no—
242#103C2×D15111yescharacteristic
243#103C2×D15111yescharacteristic
244#102—1511no—
245#102—1511no—
246C22⋊C8—1511no—
247C22⋊C8—1511no—
248C22⋊C8—1511no—
249C22⋊C8C2×D15111yescharacteristic
250#41—6041no—
251#41—6041no—
252#41—6041no—
253#41—6041no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—1511no—
258C2×Q8C22×D15111yescharacteristic
259C2×Q8C22×D15111yescharacteristic
260C2×Q8C22×D15111yescharacteristic
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—3021no—
264C2×D4—1511no—
265C2×D4—1511no—
266C2×D4—1511no—
267C2×D4—1511no—
268C22×C4—21no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4—1511no—
272C22×C4—1511no—
273C22×C4C22×D15111yescharacteristic
274Q16—41no—
275Q16—41no—
276SD16—6041no—
277SD16—6041no—
278M16—6041no—
279C2×C8—6041no—
280C2×C8—1511no—
281C2×C8—1511no—
282C2×C8C22×D15111yescharacteristic
283C2×C8C22×D15111yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—3021no—
286C4⋊C4—3021no—
287C4⋊C4—3021no—
288C4⋊C4—3021no—
289C4⋊C4—3021no—
290C4⋊C4—3021no—
291C4⋊C4—1511no—
292C4⋊C4—1511no—
293C4⋊C4—1511no—
294C4⋊C4C22×D15111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C42—3021no—
305C23—3021no—
306C23—1511no—
307C23—1511no—
308C23D4×D15111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—42no—
316Q8—6041no—
317D4—3021no—
318D4—3021no—
319D4—6041no—
320D4—6042no—
321D4—6041no—
322D4—6041no—
323D4—12081no—
324D4—12081no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—6042no—
340C2×C4—1511no—
341C2×C4—1511no—
342C2×C4—12081no—
343C2×C4D4×D15111yescharacteristic
344C2×C4C23×D15111yescharacteristic
345C8—21no—
346C8—21no—
347C8—3021no—
348C8—3021no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—3021no—
353C22—3021no—
354C22—3021no—
355C22—3021no—
356C22—3021no—
357C22—3021no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—3021no—
368C4—3021no—
369C4—6041no—
370C4—6041no—
371C4—6041no—
372C4#1801278411yescharacteristic
373C4#1801278411yescharacteristic
374C2—41no—
375C2—6041no—
376C2—6041no—
377C2—12081no—
378C2#2375277211yescharacteristic
379C2#2375302111yescharacteristic
380C2#2375302511yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#451×C151C2
socleC22×C151C22×D4
prime radical#23752792C2
hypercenter#451D151
hypocenterC151#3201
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #23752786C2semidirect
3. #23752550C2semidirect
4. #23752546C2semidirect
5. #23752541C2semidirect
6. #23752537C2semidirect
7. #23752467C2semidirect
8. #23752461C2semidirect
9. #23752450C2semidirect
10. #23752444C2semidirect
11. #23752373C2semidirect
12. #23752373C2semidirect
13. #23752351C2semidirect
14. #23752177C2semidirect
15. #451×C151C2semidirect
190. C151#3201semidirect
204. #451D151semidirect

Maximal subgroups

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

subgroupindex
#237527922
#237527862
#237525502
#237525462
#237525412
#237525372
#237524672
#237524612
#237524502
#237524442
#237523732
#237523512
#237521772
#451×C1512
#3201151