Finite Group Databasebeta

← #34080965

Subgroups — #34080965

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#23752912C211yesmaximal, characteristic, complemented
2#23752857C211yesmaximal, characteristic, complemented
3#23752567C211yesmaximal, characteristic, complemented
4#23752549C211yesmaximal, characteristic, complemented
5#23752539C211yesmaximal, characteristic, complemented
6#23752512C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752440C211yesmaximal, characteristic, complemented
9#23752427C211yesmaximal, characteristic, complemented
10#23752354C211yesmaximal, characteristic, complemented
11#23752344C211yesmaximal, characteristic, complemented
12C8×D604C211yesmaximal, characteristic, complemented
13#23752205C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15C4×D8×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18C2×#14558992C2211yescharacteristic, complemented
19C2×#14558989C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic, complemented
22#18012732—21no—
23#18012731C2211yescharacteristic, complemented
24#18012727C2211yescharacteristic
25#18012723—21no—
26#18012722—21no—
27#18012719C2211yescharacteristic
28#18012714C2211yescharacteristic
29#18012713—21no—
30#18012712—21no—
31#18012710C2211yescharacteristic
32#18012710C2211yescharacteristic, complemented
33#18012709—21no—
34C4×D604C2211yescharacteristic
35C4×C22⋊D151—21no—
36#18012697C2211yescharacteristic, complemented
37C4⋊C4×D151C2211yescharacteristic
38C2×(C2×D151)⋊C4—21no—
39#18012672C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41C4⋊(C151⋊C8)C2211yescharacteristic, complemented
42#18012664C2211yescharacteristic, complemented
43#18012664C2211yescharacteristic, complemented
44#18012662C2211yescharacteristic, complemented
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012659C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C2×D8×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic, complemented
55#107×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559003—22no—
61#14559003—41no—
62C2×Dic302C2311yescharacteristic
63C2×D604—21no—
64C2×D604D411yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70D4×D151—22no—
71D4×D151—41no—
72C22×Dic151—21no—
73C2×C4×D151—21no—
74C2×C4×D151C2311yescharacteristic
75C2×C4×D151C2311yescharacteristic
76#14558992—41no—
77#14558989—41no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C8×D151—41no—
81C8×D151—41no—
82C4⋊Dic151—21no—
83C4⋊Dic151D411yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85C4⋊Dic151C2311yescharacteristic
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89C22⋊Dic151—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)⋊C4D411yescharacteristic
97(C2×D151)⋊C4D411yescharacteristic
98C4×Dic151—21no—
99C2×D4×C151C2311yescharacteristic
100C2×D4×C151C2311yescharacteristic
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103D8×C151—22no—
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C4⋊C4×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C22⋊C4×C151—21no—
109C22⋊C4×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112C22×D151—42no—
113C22×D151—42no—
114C22×D151—81no—
115C22×D151C2×D411yescharacteristic
116C22×D151C2×D411yescharacteristic
117Dic302—21no—
118Dic302—21no—
119D604—22no—
120D604—21no—
121D604—21no—
122D604—81no—
123C22⋊D151—42no—
124C22⋊D151—42no—
125C22⋊D151—42no—
126C22⋊D151—81no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—42no—
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—21no—
137C4×D151—81no—
138C151⋊C8—21no—
139C151⋊C8—21no—
140C23×C151—21no—
141C23×C151—21no—
142D4×C151—21no—
143D4×C151—21no—
144D4×C151—21no—
145D4×C151#4112yes—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—81no—
149C2×C4×C151—81no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151—21no—
155C22×C151—22no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151C22×D411yescharacteristic
162C2×D151—21no—
163C2×D151—21no—
164C2×D151—21no—
165C2×D151—21no—
166C2×D151—21no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—84no—
171C2×D151#13512yes—
172C4×C151—21no—
173C4×C151—21no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151C2×#4111yescharacteristic
177C4×C151H(5,𝔽2)11yescharacteristic
178Dic151—21no—
179Dic151—21no—
180Dic151—41no—
181Dic151—41no—
182Dic151—41no—
183C2×C151—42no—
184C2×C151—81no—
185C2×C151#54611yescharacteristic
186C2×C151C2×#13511yescharacteristic
187C2×C151#57611yescharacteristic
188D151—22no—
189D151—41no—
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×D8D15111yescharacteristic, complemented
205C8×D4—1511no—
206#416—1511no—
207C2×#102—1511no—
208C2×#41—1511no—
209C22×D4—1511no—
210C2×SD16—1511no—
211C2×D8—1511no—
212C2×D8C2×D15111yescharacteristic
213C22×C8—1511no—
214C22×C8—1511no—
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×D4C2×D15111yescharacteristic
230C4×D4C2×D15111yescharacteristic, complemented
231#117—1511no—
232C2×C4⋊C4—1511no—
233C2×C22⋊C4—3021no—
234#107—1511no—
235#107C2×D15111yescharacteristic, complemented
236#106—1511no—
237C4⋊C8—1511no—
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#102C2×D15111yescharacteristic
247#102C2×D15111yescharacteristic, complemented
248C22⋊C8—1511no—
249C22⋊C8—1511no—
250C4×C8C2×D15111yescharacteristic, complemented
251C24—3021no—
252#41—3022no—
253#41—6041no—
254C2×Q8—1511no—
255C2×D4—3021no—
256C2×D4—3022no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—6041no—
262C2×D4—1511no—
263C2×D4—1511no—
264C2×D4C22×D15111yescharacteristic
265C2×D4C22×D15111yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—3021no—
269C22×C4—3021no—
270C22×C4—1511no—
271C22×C4—1511no—
272SD16—6041no—
273D8—22no—
274D8—6041no—
275C2×C8—6041no—
276C2×C8—6041no—
277C2×C8—1511no—
278C2×C8—1511no—
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⋊C4C22×D15111yescharacteristic
289C4⋊C4C22×D15111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—1511no—
300C22⋊C4—1511no—
301C42—3021no—
302C42C22×D15111yescharacteristic
303C23—21no—
304C23—21no—
305C23—3021no—
306C23—6042no—
307C23—6042no—
308C23—1511no—
309C23—1511no—
310C23—12081no—
311Q8—3021no—
312Q8—3021no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—3022no—
317D4—3021no—
318D4—3021no—
319D4—6042no—
320D4—6042no—
321D4—6042no—
322D4—12081no—
323D4—12081no—
324D4#1455900412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—3021no—
336C2×C4—6042no—
337C2×C4—1511no—
338C2×C4—1511no—
339C2×C4—12081no—
340C2×C4D4×D15111yescharacteristic
341C2×C4D4×D15111yescharacteristic
342C2×C4C23×D15111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3021no—
346C8—3021no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—3021no—
354C22—3021no—
355C22—3021no—
356C22—3021no—
357C22—3021no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22—1512no—
362C22—12084no—
363C22C2×D4×D15111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—3021no—
369C4—3021no—
370C4—6041no—
371C4—6041no—
372C4—6041no—
373C4C2×#1455900411yescharacteristic
374C4#1801278511yescharacteristic
375C2—42no—
376C2—81no—
377C2—3022no—
378C2—6041no—
379C2—12081no—
380C2#2375285811yescharacteristic
381C2#135×D15111yescharacteristic
382C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC4×D8×C151C2
socleC22×C151C22×D4
hypercenterC4×D8D151
hypocenterC151#3297
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23752912C2semidirect
2. #23752857C2semidirect
3. #23752567C2semidirect
4. #23752549C2semidirect
5. #23752539C2semidirect
6. #23752512C2semidirect
7. #23752447C2semidirect
8. #23752440C2semidirect
9. #23752427C2semidirect
10. #23752354C2semidirect
11. #23752344C2semidirect
12. C8×D604C2semidirect
13. #23752205C2semidirect
14. #102×D151C2semidirect
15. C4×D8×C151C2semidirect
18. C2×#14558992C22semidirect
21. C2×C8×D151C22semidirect
23. #18012731C22semidirect
32. #18012710C22semidirect
36. #18012697C22semidirect
39. #18012672C22semidirect
40. #18012670C22semidirect
41. C4⋊(C151⋊C8)C22semidirect
42. #18012664C22semidirect
43. #18012664C22semidirect
44. #18012662C22semidirect
51. (C2×D151)⋊C8C22semidirect
54. C4×D4×C151C22semidirect
55. #107×C151C22semidirect
57. #102×C151C22semidirect
58. C4×C8×C151C22semidirect
191. C151#3297semidirect
204. C4×D8D151semidirect
230. C4×D4C2×D151semidirect
235. #107C2×D151semidirect
247. #102C2×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
#237529122
#237528572
#237525672
#237525492
#237525392
#237525122
#237524472
#237524402
#237524272
#237523542
#237523442
C8×D6042
#237522052
#102×D1512
C4×D8×C1512
#3297151