Finite Group Databasebeta

← #34079986

Subgroups — #34079986

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#23752783C211yesmaximal, characteristic, complemented
2#23752550C211yesmaximal, characteristic, complemented
3#23752547C211yesmaximal, characteristic, complemented
4#23752542C211yesmaximal, characteristic, complemented
5#23752533C211yesmaximal, characteristic, complemented
6#23752468C211yesmaximal, characteristic, complemented
7#23752456C211yesmaximal, characteristic, complemented
8#23752451C211yesmaximal, characteristic, complemented
9#23752439C211yesmaximal, characteristic, complemented
10#23752374C211yesmaximal, characteristic, complemented
11#23752374C211yesmaximal, characteristic, complemented
12#23752367C211yesmaximal, characteristic, complemented
13#23752350C211yesmaximal, characteristic, complemented
14#23752179C211yesmaximal, characteristic, complemented
15#537×C151C211yesmaximal, characteristic
16C22×Dic302C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558992C2211yescharacteristic
21C2×#14558988C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012737—21no—
24#18012726—21no—
25#18012720—21no—
26#18012720—21no—
27#18012718C2211yescharacteristic
28#18012718C2211yescharacteristic
29#18012718C2211yescharacteristic
30#18012718C2211yescharacteristic
31#18012698C2211yescharacteristic
32#18012672C2211yescharacteristic
33#18012672C2211yescharacteristic
34#18012670C2211yescharacteristic
35#18012670C2211yescharacteristic
36#18012663C2211yescharacteristic
37#18012663C2211yescharacteristic
38#18012662C2211yescharacteristic
39#18012662C2211yescharacteristic
40#18012662C2211yescharacteristic
41#18012662C2211yescharacteristic
42#18012660C2211yescharacteristic
43#18012660C2211yescharacteristic
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic
47C22⋊(C151⋊C8)C2211yescharacteristic
48C2×#41×C151C2211yescharacteristic
49C2×#41×C151C2211yescharacteristic
50C22⋊Q8×C151—21no—
51C22⋊Q8×C151C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53#121×C151—21no—
54#121×C151—21no—
55#121×C151—21no—
56#121×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58C2×C4⋊C4×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—41no—
61C2×Dic302—41no—
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64C22×Dic151—21no—
65#14558994—41no—
66#14558994—41no—
67#14558992—41no—
68#14558992—41no—
69#14558988—41no—
70C2×C151⋊C8—41no—
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C4×Dic151—21no—
87#41×C151—41no—
88#41×C151—41no—
89#41×C151—41no—
90#41×C151—41no—
91C2×Q8×C151D411yescharacteristic
92C2×Q8×C151C2311yescharacteristic
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—21no—
96C2×D4×C151D411yescharacteristic
97C2×D4×C151D411yescharacteristic
98C2×D4×C151D411yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151C2311yescharacteristic
103C22×C4×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C22⋊C4×C151—21no—
114Dic302—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—21no—
118Dic302—42no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—42no—
124C151⋊C8—21no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C23×C151—21no—
129C23×C151C2×D411yescharacteristic
130C23×C151C2×D411yescharacteristic
131C23×C151C2×D411yescharacteristic
132Q8×C151—21no—
133Q8×C151—21no—
134Q8×C151—41no—
135D4×C151—21no—
136D4×C151—21no—
137D4×C151—41no—
138D4×C151—41no—
139D4×C151—41no—
140D4×C151—42no—
141D4×C151—81no—
142D4×C151—81no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—42no—
153C2×C4×C151—81no—
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2×D411yescharacteristic
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2411yescharacteristic
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151C22×D411yescharacteristic
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151H(5,𝔽2)11yescharacteristic
178C4×C151H(5,𝔽2)11yescharacteristic
179Dic151—41no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—41no—
184C2×C151—41no—
185C2×C151—41no—
186C2×C151—81no—
187C2×C151#53411yescharacteristic
188C2×C151#57711yescharacteristic
189C2×C151#57811yescharacteristic
190C151#320111yescharacteristic, complemented, Sylow
191#3201—1511nomaximal, Sylow
192#537D15111yescharacteristic
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#451—1511no—
205#448—1511no—
206#408—1511no—
207C2×#41C2×D15111yescharacteristic
208C2×#41C2×D15111yescharacteristic
209C22×Q8—1511no—
210C2×Q16—1511no—
211C2×Q16—1511no—
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—21no—
221C22⋊Q8—1511no—
222C22⋊Q8—1511no—
223C22⋊Q8—1511no—
224C22⋊Q8—1511no—
225C22⋊Q8C2×D15111yescharacteristic
226C22⋊Q8C2×D15111yescharacteristic
227#121—21no—
228#121—21no—
229#121—21no—
230#121C2×D15111yescharacteristic
231#121C2×D15111yescharacteristic
232#117—1511no—
233C2×C4⋊C4C2×D15111yescharacteristic
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#103—1511no—
243#103—1511no—
244#102—1511no—
245#102—1511no—
246C22⋊C8—1511no—
247C22⋊C8—1511no—
248C22⋊C8—1511no—
249C22⋊C8—1511no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—3021no—
255C2×Q8—6041no—
256C2×Q8—6041no—
257C2×Q8—1511no—
258C2×Q8—1511no—
259C2×Q8C22⋊D15111yescharacteristic
260C2×Q8C22×D15111yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C22⋊D15111yescharacteristic
265C2×D4C22⋊D15111yescharacteristic
266C2×D4C22⋊D15111yescharacteristic
267C2×D4C22×D15111yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—3021no—
271C22×C4C22×D15111yescharacteristic
272C22×C4C22×D15111yescharacteristic
273C22×C4C22×D15111yescharacteristic
274Q16—6041no—
275Q16—6041no—
276SD16—6041no—
277SD16—6041no—
278M16—6041no—
279C2×C8—6041no—
280C2×C8—1511no—
281C2×C8—1511no—
282C2×C8—1511no—
283C2×C8—1511no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—3021no—
288C4⋊C4—3021no—
289C4⋊C4—3021no—
290C4⋊C4—3021no—
291C4⋊C4—1511no—
292C4⋊C4—1511no—
293C4⋊C4C22×D15111yescharacteristic
294C4⋊C4C22×D15111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—3021no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C42—3021no—
305C23—21no—
306C23C2×C22⋊D15111yescharacteristic
307C23C2×C22⋊D15111yescharacteristic
308C23C2×C22⋊D15111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—41no—
312Q8—3021no—
313Q8—3021no—
314Q8—3021no—
315Q8—3021no—
316Q8—6042no—
317D4—21no—
318D4—21no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—3021no—
340C2×C4—6042no—
341C2×C4C2×C22⋊D15111yescharacteristic
342C2×C4C2×C22⋊D15111yescharacteristic
343C2×C4C2×C22⋊D15111yescharacteristic
344C2×C4C23×D15111yescharacteristic
345C8—3021no—
346C8—3021no—
347C8—3021no—
348C8—3021no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×C22⋊D15111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—6041no—
369C4—6041no—
370C4—6041no—
371C4—6041no—
372C4#1801278411yescharacteristic
373C4#1801278411yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—81no—
378C2#2375277111yescharacteristic
379C2#2375302311yescharacteristic
380C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting, prime radical#537×C151C2
socleC22×C151C22×D4
hypercenter#537D151
hypocenterC151#3201
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #23752783C2semidirect
2. #23752550C2semidirect
3. #23752547C2semidirect
4. #23752542C2semidirect
5. #23752533C2semidirect
6. #23752468C2semidirect
7. #23752456C2semidirect
8. #23752451C2semidirect
9. #23752439C2semidirect
10. #23752374C2semidirect
11. #23752374C2semidirect
12. #23752367C2semidirect
13. #23752350C2semidirect
14. #23752179C2semidirect
190. C151#3201semidirect

Maximal subgroups

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

subgroupindex
#237527832
#237525502
#237525472
#237525422
#237525332
#237524682
#237524562
#237524512
#237524392
#237523742
#237523672
#237523502
#237521792
#537×C1512
#3201151