Finite Group Databasebeta

← #34079992

Subgroups — #34079992

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#23752790C211yesmaximal, characteristic
2#23752553C211yesmaximal, characteristic, complemented
3#23752545C211yesmaximal, characteristic, complemented
4#23752540C211yesmaximal, characteristic, complemented
5#23752536C211yesmaximal, characteristic, complemented
6#23752468C211yesmaximal, characteristic, complemented
7#23752460C211yesmaximal, characteristic, complemented
8#23752451C211yesmaximal, characteristic, complemented
9#23752443C211yesmaximal, characteristic, complemented
10#23752372C211yesmaximal, characteristic, complemented
11#23752372C211yesmaximal, characteristic, complemented
12#23752368C211yesmaximal, characteristic, complemented
13#23752351C211yesmaximal, characteristic, complemented
14#23752179C211yesmaximal, characteristic, complemented
15#536×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21C2×#14558988C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012718C2211yescharacteristic
24#18012718C2211yescharacteristic
25#18012715—21no—
26#18012713C2211yescharacteristic
27#18012713C2211yescharacteristic
28#18012711—21no—
29#18012711—21no—
30#18012710—21no—
31C2×C4⋊Dic151C2211yescharacteristic
32#18012672C2211yescharacteristic
33#18012672C2211yescharacteristic
34#18012670C2211yescharacteristic
35#18012670C2211yescharacteristic
36#18012663C2211yescharacteristic
37#18012663C2211yescharacteristic
38#18012663C2211yescharacteristic
39#18012663C2211yescharacteristic
40#18012662C2211yescharacteristic
41#18012662C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic
47C22⋊(C151⋊C8)C2211yescharacteristic
48C2×#41×C151C2211yescharacteristic
49C22×Q8×C151C2211yescharacteristic
50C4⋊Q8×C151—21no—
51#124×C151—21no—
52#123×C151—21no—
53#123×C151—21no—
54C22⋊Q8×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56C22⋊Q8×C151C2211yescharacteristic
57C22⋊Q8×C151C2211yescharacteristic
58#117×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C22×Dic151—21no—
67C2×C4×D151—21no—
68#14558994—41no—
69#14558994—41no—
70#14558991—41no—
71#14558991—41no—
72#14558988—41no—
73C2×C151⋊C8—41no—
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87#41×C151—41no—
88#41×C151—41no—
89C2×Q8×C151—21no—
90C2×Q8×C151—41no—
91C2×Q8×C151—41no—
92C2×Q8×C151D411yescharacteristic
93C2×Q8×C151C2311yescharacteristic
94C2×Q8×C151C2311yescharacteristic
95C2×D4×C151D411yescharacteristic
96C2×D4×C151D411yescharacteristic
97C2×D4×C151D411yescharacteristic
98C22×C4×C151—21no—
99C22×C4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151—21no—
104C4⋊C4×C151—21no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C22⋊C4×C151—21no—
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C42×C151—21no—
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117D604—21no—
118D604—21no—
119C22⋊D151—42no—
120C22⋊D151—81no—
121C22⋊D151—81no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—81no—
126C4×D151—42no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130C151⋊C8—21no—
131C23×C151C2×D411yescharacteristic
132C23×C151C2×D411yescharacteristic
133C23×C151C2×D411yescharacteristic
134Q8×C151—21no—
135Q8×C151—21no—
136Q8×C151—21no—
137Q8×C151—21no—
138Q8×C151—41no—
139Q8×C151—42no—
140D4×C151—41no—
141D4×C151—41no—
142D4×C151—41no—
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—21no—
153C2×C4×C151—42no—
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×C151C22×D411yescharacteristic
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—21no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151H(5,𝔽2)11yescharacteristic
179C4×C151H(5,𝔽2)11yescharacteristic
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—41no—
184C2×C151—41no—
185C2×C151—41no—
186C2×C151#53411yescharacteristic
187C2×C151#57711yescharacteristic
188C2×C151#57811yescharacteristic
189D151—81no—
190C151#320111yescharacteristic, complemented, Sylow
191#3201—1511nomaximal, Sylow
192#537—1511no—
193#536D15111yescharacteristic, complemented
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×#41—1511no—
208C2×#41C2×D15111yescharacteristic
209C22×Q8C2×D15111yescharacteristic
210C2×Q16—1511no—
211C2×Q16—1511no—
212C2×SD16—1511no—
213C2×SD16—1511no—
214C2×M16—1511no—
215C22×C8—1511no—
216C4⋊Q8—21no—
217#124—21no—
218#123—21no—
219#123—21no—
220C22⋊Q8—3021no—
221C22⋊Q8—1511no—
222C22⋊Q8—1511no—
223C22⋊Q8C2×D15111yescharacteristic
224C22⋊Q8C2×D15111yescharacteristic
225C22⋊Q8C2×D15111yescharacteristic
226C22⋊Q8C2×D15111yescharacteristic
227#121—3021no—
228#121—3021no—
229#121—3021no—
230#121—1511no—
231#121—1511no—
232#117C2×D15111yescharacteristic
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#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—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×D4C22⋊D15111yescharacteristic
266C2×D4C22⋊D15111yescharacteristic
267C2×D4C22⋊D15111yescharacteristic
268C22×C4—21no—
269C22×C4—3021no—
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—21no—
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—21no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C42—21no—
305C23—3021no—
306C23C2×C22⋊D15111yescharacteristic
307C23C2×C22⋊D15111yescharacteristic
308C23C2×C22⋊D15111yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—41no—
314Q8—42no—
315Q8—3021no—
316Q8—3021no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—3021no—
321D4—3021no—
322D4—6042no—
323D4—12081no—
324D4—12081no—
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—21no—
335C2×C4—42no—
336C2×C4—3021no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—6042no—
340C2×C4—12081no—
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—6041no—
359C22—6041no—
360C22—6041no—
361C22C22×C22⋊D15111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—6041no—
370C4—6041no—
371C4—6041no—
372C4#1801278411yescharacteristic
373C4#1801278411yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—12081no—
378C2#2375277111yescharacteristic
379C2#2375302011yescharacteristic
380C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#536×C151C2
socleC22×C151C22×D4
prime radical#23752790C2
hypercenter#536D151
hypocenterC151#3201
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #23752553C2semidirect
3. #23752545C2semidirect
4. #23752540C2semidirect
5. #23752536C2semidirect
6. #23752468C2semidirect
7. #23752460C2semidirect
8. #23752451C2semidirect
9. #23752443C2semidirect
10. #23752372C2semidirect
11. #23752372C2semidirect
12. #23752368C2semidirect
13. #23752351C2semidirect
14. #23752179C2semidirect
15. #536×C151C2semidirect
190. C151#3201semidirect
193. #536D151semidirect

Maximal subgroups

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

subgroupindex
#237527902
#237525532
#237525452
#237525402
#237525362
#237524682
#237524602
#237524512
#237524432
#237523722
#237523682
#237523512
#237521792
#536×C1512
#3201151