Finite Group Databasebeta

← #34080962

Subgroups — #34080962

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752908C211yesmaximal, characteristic, complemented
2#23752858C211yesmaximal, characteristic, complemented
3#23752567C211yesmaximal, characteristic, complemented
4#23752548C211yesmaximal, characteristic, complemented
5#23752537C211yesmaximal, characteristic, complemented
6#23752513C211yesmaximal, characteristic, complemented
7#23752448C211yesmaximal, characteristic, complemented
8#23752441C211yesmaximal, characteristic, complemented
9#23752428C211yesmaximal, characteristic, complemented
10#23752359C211yesmaximal, characteristic, complemented
11#23752348C211yesmaximal, characteristic, complemented
12C4×D1208C211yesmaximal, characteristic, complemented
13#23752209C211yesmaximal, characteristic, complemented
14C2×#18012661C211yesmaximal, characteristic, complemented
15C8×D4×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C2×#14558993C2211yescharacteristic, complemented
19C2×D1208C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21#18012734—21no—
22#18012731C2211yescharacteristic, complemented
23#18012727C2211yescharacteristic
24#18012724—21no—
25#18012721—21no—
26#18012718C2211yescharacteristic
27#18012713C2211yescharacteristic
28#18012713C2211yescharacteristic
29#18012713C2211yescharacteristic, complemented
30#18012712—21no—
31#18012711—21no—
32#18012707—21no—
33C4×D604C2211yescharacteristic
34C4×D604C2211yescharacteristic, complemented
35(C22⋊D151)⋊C4—21no—
36#18012698C2211yescharacteristic, complemented
37C2×C4⋊Dic151C2211yescharacteristic
38C22⋊C4×D151—21no—
39#18012673C2211yescharacteristic, complemented
40#18012673C2211yescharacteristic, complemented
41#18012671C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic, complemented
52C22×C8×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic, complemented
54C4×D4×C151C2211yescharacteristic
55C4⋊C8×C151C2211yescharacteristic, complemented
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—22no—
61#14559004—41no—
62C2×Dic302C2311yescharacteristic
63C2×D604—22no—
64C2×D604—21no—
65C2×D604—41no—
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C22×Dic151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77#14558993—41no—
78D1208—22no—
79D1208—41no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—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—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97C4×Dic151—21no—
98C2×D4×C151D411yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C2×C8×C151—41no—
102C2×C8×C151—41no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151D411yescharacteristic
108C22⋊C4×C151D411yescharacteristic
109C22⋊C4×C151D411yescharacteristic
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—42no—
115C22×D151—42no—
116C22×D151—81no—
117Dic302—21no—
118Dic302—21no—
119D604—21no—
120D604—21no—
121D604—21no—
122D604—21no—
123D604—21no—
124D604—42no—
125D604#4112yes—
126C22⋊D151—42no—
127C22⋊D151—42no—
128C22⋊D151—81no—
129C22⋊D151—81no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—81no—
136C4×D151—42no—
137C4×D151—81no—
138C4×D151—81no—
139C23×C151C2×D411yescharacteristic
140C23×C151C2×D411yescharacteristic
141D4×C151—22no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2×D411yescharacteristic
150C2×C4×C151C2411yescharacteristic
151C8×C151—21no—
152C8×C151—21no—
153C8×C151—21no—
154C8×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151#13512yes—
161C22×C151C22×D411yescharacteristic
162C2×D151—22no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—84no—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—21no—
175C4×C151—21no—
176C4×C151C2×#4111yescharacteristic
177C4×C151H(5,𝔽2)11yescharacteristic
178Dic151—41no—
179Dic151—41no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—22no—
184C2×C151—41no—
185C2×C151#54611yescharacteristic
186C2×C151C2×#13511yescharacteristic
187C2×C151#57611yescharacteristic
188D151—42no—
189D151—81no—
190D151—81no—
191C151#329711yescharacteristic, complemented, Sylow
192#3297—1511nomaximal, Sylow
193#553—1511no—
194#546—1511no—
195#488—1511no—
196#484—1511no—
197#482—1511no—
198#478—1511no—
199#466—1511no—
200#465—1511no—
201#463—1511no—
202#449—1511no—
203#447—1511no—
204C4×D8—1511no—
205C8×D4D15111yescharacteristic, complemented
206#416—1511no—
207C2×#102—1511no—
208C2×#41—1511no—
209C22×D4—1511no—
210C2×SD16—1511no—
211C2×D8—1511no—
212C2×D8—1511no—
213C22×C8C2×D15111yescharacteristic
214C22×C8C2×D15111yescharacteristic, complemented
215#126—3021no—
216#125—1511no—
217#124—1511no—
218#123—3021no—
219#123—3021no—
220C22⋊Q8—1511no—
221#121—3021no—
222#121—3021no—
223#121—1511no—
224#121—1511no—
225#121—1511no—
226#120—3021no—
227C4×D4—3021no—
228C4×D4—1511no—
229C4×D4—1511no—
230C4×D4C2×D15111yescharacteristic
231#117—1511no—
232C2×C4⋊C4—1511no—
233C2×C22⋊C4—3021no—
234#107—1511no—
235#107—1511no—
236#106—1511no—
237C4⋊C8C2×D15111yescharacteristic, complemented
238#103—1511no—
239#103—1511no—
240#103—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102—1511no—
246#102—1511no—
247#102—1511no—
248C22⋊C8C2×D15111yescharacteristic
249C22⋊C8C2×D15111yescharacteristic, complemented
250C4×C8C2×D15111yescharacteristic, complemented
251C24—3021no—
252#41—3022no—
253#41—6041no—
254C2×Q8—1511no—
255C2×D4—3022no—
256C2×D4—3021no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—6041no—
262C2×D4—1511no—
263C2×D4—1511no—
264C2×D4—1511no—
265C2×D4D60411yescharacteristic
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4C22×D15111yescharacteristic
271C22×C4C22×D15111yescharacteristic
272SD16—6041no—
273D8—3022no—
274D8—6041no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D15111yescharacteristic
278C2×C8C22×D15111yescharacteristic
279C2×C8C22×D15111yescharacteristic
280C2×C8C22×D15111yescharacteristic
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C4⋊C4—1511no—
288C4⋊C4—1511no—
289C4⋊C4D60411yescharacteristic
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4D60411yescharacteristic
300C22⋊C4D60411yescharacteristic
301C42—3021no—
302C42C22×D15111yescharacteristic
303C23—3021no—
304C23—3021no—
305C23—3021no—
306C23—6042no—
307C23—6042no—
308C23—12081no—
309C23C2×D60411yescharacteristic
310C23C2×D60411yescharacteristic
311Q8—3021no—
312Q8—3021no—
313D4—22no—
314D4—3021no—
315D4—3021no—
316D4—3021no—
317D4—3021no—
318D4—3021no—
319D4—6042no—
320D4—6042no—
321D4—6042no—
322D4—1512no—
323D4—12081no—
324D4—12081no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—6042no—
335C2×C4—12081no—
336C2×C4—12081no—
337C2×C4—12081no—
338C2×C4C2×D60411yescharacteristic
339C2×C4C2×D60411yescharacteristic
340C2×C4C2×D60411yescharacteristic
341C2×C4C2×D60411yescharacteristic
342C2×C4C23×D15111yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—3022no—
353C22—6041no—
354C22—6041no—
355C22—6041no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22—12084no—
362C22#1801276112yes—
363C22C22×D60411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—6041no—
369C4—6041no—
370C4—6041no—
371C4—6041no—
372C4—6041no—
373C4#41×D15111yescharacteristic
374C4#1801278411yescharacteristic
375C2—22no—
376C2—41no—
377C2—6042no—
378C2—12081no—
379C2—12081no—
380C2#2375285711yescharacteristic
381C2C2×#1801276111yescharacteristic
382C2#2375301711yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC8×D4×C151C2
socleC22×C151C22×D4
hypercenterC8×D4D151
hypocenterC151#3297
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #23752908C2semidirect
2. #23752858C2semidirect
3. #23752567C2semidirect
4. #23752548C2semidirect
5. #23752537C2semidirect
6. #23752513C2semidirect
7. #23752448C2semidirect
8. #23752441C2semidirect
9. #23752428C2semidirect
10. #23752359C2semidirect
11. #23752348C2semidirect
12. C4×D1208C2semidirect
13. #23752209C2semidirect
14. C2×#18012661C2semidirect
15. C8×D4×C151C2semidirect
18. C2×#14558993C22semidirect
22. #18012731C22semidirect
29. #18012713C22semidirect
34. C4×D604C22semidirect
36. #18012698C22semidirect
39. #18012673C22semidirect
40. #18012673C22semidirect
41. #18012671C22semidirect
42. #18012664C22semidirect
43. #18012664C22semidirect
44. #18012664C22semidirect
51. #18012661C22semidirect
53. C22×C8×C151C22semidirect
55. C4⋊C8×C151C22semidirect
57. C22⋊C8×C151C22semidirect
58. C4×C8×C151C22semidirect
191. C151#3297semidirect
205. C8×D4D151semidirect
214. C22×C8C2×D151semidirect
237. C4⋊C8C2×D151semidirect
249. C22⋊C8C2×D151semidirect
250. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237529082
#237528582
#237525672
#237525482
#237525372
#237525132
#237524482
#237524412
#237524282
#237523592
#237523482
C4×D12082
#237522092
C2×#180126612
C8×D4×C1512
#3297151