Finite Group Databasebeta

← #34081056

Subgroups — #34081056

Order 19328.

408 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#23752925C211yesmaximal, characteristic, complemented
2#23752881C211yesmaximal, characteristic, complemented
3#23752557C211yesmaximal, characteristic, complemented
4#23752536C211yesmaximal, characteristic, complemented
5#23752534C211yesmaximal, characteristic, complemented
6#23752505C211yesmaximal, characteristic, complemented
7#23752448C211yesmaximal, characteristic, complemented
8#23752447C211yesmaximal, characteristic, complemented
9#23752406C211yesmaximal, characteristic, complemented
10#23752360C211yesmaximal, characteristic, complemented
11#23752357C211yesmaximal, characteristic, complemented
12#23752297C211yesmaximal, characteristic, complemented
13C8×C22⋊D151C211yesmaximal, characteristic, complemented
14#23752207C211yesmaximal, characteristic, complemented
15#416×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×D1208C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21#18012738C2211yescharacteristic
22#18012735—21no—
23#18012735C2211yescharacteristic
24#18012727—21no—
25#18012725—21no—
26#18012714C2211yescharacteristic
27#18012713—21no—
28#18012713C2211yescharacteristic
29#18012713C2211yescharacteristic
30#18012712—21no—
31#18012710—21no—
32#18012710C2211yescharacteristic
33Q8×Dic151C2211yescharacteristic
34#18012701C2211yescharacteristic
35C4×C22⋊D151—21no—
36C4×C22⋊D151C2211yescharacteristic
37#18012697C2211yescharacteristic
38#18012696—21no—
39#18012673C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012670C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54#117×C151C2211yescharacteristic
55#103×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—41no—
61C2×Dic302—21no—
62C2×D604—21no—
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151D411yescharacteristic
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151C2311yescharacteristic
75#14558991—22no—
76D1208—41no—
77#14558989—41no—
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C8×D151—41no—
81C4⋊Dic151—21no—
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4D411yescharacteristic
86C22⋊Dic151—21no—
87C22⋊Dic151D411yescharacteristic
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4D411yescharacteristic
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97#41×C151—22no—
98#41×C151—41no—
99C2×Q8×C151C2311yescharacteristic
100C2×D4×C151—21no—
101C2×D4×C151C2311yescharacteristic
102C22×C4×C151—21no—
103C22×C4×C151C2311yescharacteristic
104C2×C8×C151—41no—
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C42×C151—21no—
111C22×D151—21no—
112C22×D151—21no—
113C22×D151C2×D411yescharacteristic
114Dic302—81no—
115D604—21no—
116D604—21no—
117D604—21no—
118D604—21no—
119D604—42no—
120D604—81no—
121C22⋊D151—22no—
122C22⋊D151—42no—
123C22⋊D151—81no—
124C22⋊D151—81no—
125C22⋊D151—81no—
126C22⋊D151—81no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C4×D151—21no—
133C4×D151—21no—
134C4×D151—42no—
135C4×D151—42no—
136C151⋊C8—21no—
137C151⋊C8—21no—
138C23×C151—21no—
139C23×C151C2×D411yescharacteristic
140Q8×C151—21no—
141Q8×C151#4112yes—
142D4×C151—21no—
143D4×C151—21no—
144D4×C151—42no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—42no—
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151C22×D411yescharacteristic
162C2×D151—21no—
163C2×D151—21no—
164C2×D151—21no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C4×C151—21no—
172C4×C151—22no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151C2×#4111yescharacteristic
176C4×C151H(5,𝔽2)11yescharacteristic
177Dic151—21no—
178Dic151—21no—
179Dic151—41no—
180Dic151—41no—
181Dic151#13512yes—
182C2×C151—41no—
183C2×C151—81no—
184C2×C151#54611yescharacteristic
185C2×C151C2×#13511yescharacteristic
186C2×C151#57611yescharacteristic
187D151—41no—
188D151—81no—
189D151—81no—
190C151#330511yescharacteristic, complemented, Sylow
191#3305—1511nomaximal, Sylow
192#555—1511no—
193#550—1511no—
194#486—1511no—
195#482—1511no—
196#482—1511no—
197#477—1511no—
198#466—1511no—
199#466—1511no—
200#459—1511no—
201#449—1511no—
202#449—1511no—
203C4×SD16—1511no—
204C8×D4—1511no—
205#416—1511no—
206#416D15111yescharacteristic, complemented
207C2×#41—1511no—
208C2×#41C2×D15111yescharacteristic
209C2×SD16—1511no—
210C2×D8—1511no—
211C2×D8—1511no—
212C22×C8—1511no—
213C22×C8C2×D15111yescharacteristic
214C4⋊Q8—1511no—
215#127—3021no—
216#127—1511no—
217#124—3021no—
218#124—3021no—
219#121—3021no—
220#121—3021no—
221#121—3021no—
222#121—1511no—
223#121—1511no—
224#121—1511no—
225#121—1511no—
226C4×Q8—1511no—
227C4×D4—3021no—
228C4×D4—1511no—
229C4×D4—1511no—
230#117—3021no—
231#117—1511no—
232#117C2×D15111yescharacteristic
233#107—1511no—
234#107—1511no—
235#106—1511no—
236C4⋊C8—1511no—
237#103—1511no—
238#103C2×D15111yescharacteristic
239#103C2×D15111yescharacteristic
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244#102—1511no—
245#102C2×D15111yescharacteristic
246#102C2×D15111yescharacteristic
247C22⋊C8—1511no—
248C22⋊C8—1511no—
249C4×C8—1511no—
250#41—22no—
251#41—41no—
252#41—3022no—
253#41—6041no—
254C2×Q8—3021no—
255C2×Q8C22×D15111yescharacteristic
256C2×D4—21no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—3021no—
261C2×D4—3021no—
262C2×D4—3021no—
263C2×D4—3021no—
264C2×D4—1511no—
265C2×D4—1511no—
266C2×D4—1511no—
267C2×D4C22×D15111yescharacteristic
268C22×C4—21no—
269C22×C4—3021no—
270C22×C4—3021no—
271C22×C4—1511no—
272C22×C4C22×D15111yescharacteristic
273SD16—3022no—
274D8—6041no—
275D8—6041no—
276C2×C8—41no—
277C2×C8—6041no—
278C2×C8—1511no—
279C2×C8—1511no—
280C2×C8C22×D15111yescharacteristic
281C2×C8C22×D15111yescharacteristic
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—1511no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C4⋊C4C22×D15111yescharacteristic
288C4⋊C4C22×D15111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—1511no—
297C22⋊C4—1511no—
298C42—21no—
299C42—3021no—
300C42—3021no—
301C42—1511no—
302C23—21no—
303C23—3021no—
304C23—3021no—
305C23—1511no—
306C23D4×D15111yescharacteristic
307Q8—21no—
308Q8—12081no—
309Q8#1455900412yes—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—3022no—
314D4—3021no—
315D4—3021no—
316D4—3021no—
317D4—3021no—
318D4—6042no—
319D4—6042no—
320D4—12081no—
321D4—12081no—
322D4—12081no—
323D4—12081no—
324D4—12081no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—3021no—
332C2×C4—3021no—
333C2×C4—3021no—
334C2×C4—3021no—
335C2×C4—6042no—
336C2×C4—6042no—
337C2×C4—1511no—
338C2×C4—1511no—
339C2×C4—1511no—
340C2×C4D4×D15111yescharacteristic
341C2×C4C23×D15111yescharacteristic
342C8—21no—
343C8—21no—
344C8—3021no—
345C8—3021no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—3021no—
353C22—3021no—
354C22—3021no—
355C22—6041no—
356C22—6041no—
357C22—6041no—
358C22—6041no—
359C22—6041no—
360C22—6041no—
361C22C2×D4×D15111yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—3021no—
367C4—3021no—
368C4—6041no—
369C4—6041no—
370C4—1512no—
371C4C2×#1455900411yescharacteristic
372C4#1801278411yescharacteristic
373C2—41no—
374C2—81no—
375C2—6041no—
376C2—12081no—
377C2—12081no—
378C2#2375285211yescharacteristic
379C2#135×D15111yescharacteristic
380C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#416×C151C2
socleC22×C151C22×D4
hypercenter#416D151
hypocenterC151#3305
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #23752925C2semidirect
2. #23752881C2semidirect
3. #23752557C2semidirect
4. #23752536C2semidirect
5. #23752534C2semidirect
6. #23752505C2semidirect
7. #23752448C2semidirect
8. #23752447C2semidirect
9. #23752406C2semidirect
10. #23752360C2semidirect
11. #23752357C2semidirect
12. #23752297C2semidirect
13. C8×C22⋊D151C2semidirect
14. #23752207C2semidirect
15. #416×C151C2semidirect
190. C151#3305semidirect
206. #416D151semidirect

Maximal subgroups

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

subgroupindex
#237529252
#237528812
#237525572
#237525362
#237525342
#237525052
#237524482
#237524472
#237524062
#237523602
#237523572
#237522972
C8×C22⋊D1512
#237522072
#416×C1512
#3305151