Finite Group Databasebeta

← #34081102

Subgroups — #34081102

Order 19328.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752869C211yesmaximal, characteristic, complemented
2#23752863C211yesmaximal, characteristic, complemented
3#23752570C211yesmaximal, characteristic, complemented
4#23752547C211yesmaximal, characteristic, complemented
5#23752524C211yesmaximal, characteristic, complemented
6#23752505C211yesmaximal, characteristic, complemented
7#23752458C211yesmaximal, characteristic, complemented
8#23752447C211yesmaximal, characteristic, complemented
9#23752426C211yesmaximal, characteristic, complemented
10#23752357C211yesmaximal, characteristic, complemented
11#23752352C211yesmaximal, characteristic, complemented
12#23752315C211yesmaximal, characteristic, complemented
13#23752281C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#417×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×Q8×D151C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012738C2211yescharacteristic
23#18012726—21no—
24#18012726C2211yescharacteristic
25#18012724—21no—
26#18012722—21no—
27#18012718—21no—
28#18012718C2211yescharacteristic
29#18012717—21no—
30#18012714C2211yescharacteristic
31#18012713C2211yescharacteristic
32#18012710—21no—
33#18012710C2211yescharacteristic
34Q8×Dic151C2211yescharacteristic
35#18012701C2211yescharacteristic
36C4×C22⋊D151—21no—
37C4×C22⋊D151C2211yescharacteristic
38C4⋊C4×D151C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012672C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51#18012649C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×M16×C151C2211yescharacteristic
54C2×C4⋊C4×C151C2211yescharacteristic
55#103×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559004—44no—
60C2×Dic302—21no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63Q8×D151—22no—
64Q8×D151—41no—
65C2×D604—21no—
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151D411yescharacteristic
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74#14558993—41no—
75#14558991—22no—
76#14558989—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C8×D151—41no—
80C4⋊Dic151—21no—
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151D411yescharacteristic
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4D411yescharacteristic
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98#41×C151—22no—
99#41×C151—41no—
100C2×Q8×C151C2311yescharacteristic
101C2×D4×C151—21no—
102C2×D4×C151C2311yescharacteristic
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151C2311yescharacteristic
106M16×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151—21no—
110C4⋊C4×C151C2311yescharacteristic
111C4⋊C4×C151C2311yescharacteristic
112C22×D151—21no—
113C22×D151C2×D411yescharacteristic
114Dic302—21no—
115Dic302—21no—
116Dic302—42no—
117Dic302—42no—
118D604—21no—
119D604—21no—
120D604—42no—
121C22⋊D151—22no—
122C22⋊D151—42no—
123C22⋊D151—42no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C4×D151—21no—
131C4×D151—21no—
132C4×D151—42no—
133C4×D151—42no—
134C4×D151—42no—
135C151⋊C8—21no—
136C151⋊C8—21no—
137C23×C151—21no—
138C23×C151C2×D411yescharacteristic
139Q8×C151—21no—
140Q8×C151#4112yescomplemented
141D4×C151—21no—
142D4×C151—21no—
143D4×C151—42no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—42no—
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—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151AGL(1,ℤ/8)12yes—
168C4×C151—21no—
169C4×C151—22no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151C2×#4111yescharacteristic
173C4×C151H(5,𝔽2)11yescharacteristic
174Dic151—21no—
175Dic151—21no—
176Dic151—21no—
177Dic151—41no—
178Dic151—41no—
179Dic151—41no—
180C2×C151—41no—
181C2×C151—81no—
182C2×C151#54611yescharacteristic
183C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C151#57811yescharacteristic
185D151—22no—
186D151—81no—
187C151#330811yescharacteristic, complemented, Sylow
188#3308—1511nomaximal, Sylow
189#548—1511no—
190#547—1511no—
191#489—1511no—
192#484—1511no—
193#480—1511no—
194#477—1511no—
195#468—1511no—
196#466—1511no—
197#463—1511no—
198#449—1511no—
199#448—1511no—
200#440—1511no—
201#435—1511no—
202#417D15111yescharacteristic, complemented
203C2×#103—1511no—
204C2×#41—3021no—
205C2×#41C2×D15111yescharacteristic
206C22×Q8—1511no—
207C2×SD16—1511no—
208C2×SD16—1511no—
209C2×D8—1511no—
210C2×M16C2×D15111yescharacteristic
211C22×C8—1511no—
212C4⋊Q8—1511no—
213#124—3021no—
214#124—1511no—
215#123—3021no—
216#123—3021no—
217C22⋊Q8—3021no—
218C22⋊Q8—3021no—
219C22⋊Q8—1511no—
220#121—3021no—
221#121—1511no—
222#121—1511no—
223#121—1511no—
224C4×Q8—1511no—
225C4×D4—3021no—
226C4×D4—1511no—
227C4×D4—1511no—
228C2×C4⋊C4—1511no—
229C2×C4⋊C4C2×D15111yescharacteristic
230#107—1511no—
231#107—1511no—
232#107—1511no—
233C4⋊C8—1511no—
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#103—1511no—
238#103C2×D15111yescharacteristic
239#103C2×D15111yescharacteristic
240#102—1511no—
241#102—1511no—
242#102C2×D15111yescharacteristic
243#102C2×D15111yescharacteristic
244C22⋊C8—1511no—
245C22⋊C8—1511no—
246#97—1511no—
247#41—22no—
248#41—41no—
249#41—6044no—
250C2×Q8—3021no—
251C2×Q8—3021no—
252C2×Q8—3022no—
253C2×Q8—6041no—
254C2×Q8—1511no—
255C2×Q8C22×D15111yescharacteristic
256C2×D4—21no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—1511no—
261C2×D4—1511no—
262C2×D4C22×D15111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4—1511no—
269C22×C4C22×D15111yescharacteristic
270SD16—3022no—
271SD16—6041no—
272D8—6041no—
273M16—41no—
274C2×C8—6041no—
275C2×C8—1511no—
276C2×C8—1511no—
277C2×C8C22×D15111yescharacteristic
278C2×C8C22×D15111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—3021no—
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—1511no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C4⋊C4C22×D15111yescharacteristic
288C4⋊C4C22×D15111yescharacteristic
289C22⋊C4—3021no—
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—3021no—
299C42—1511no—
300C23—21no—
301C23—3021no—
302C23—1511no—
303C23D4×D15111yescharacteristic
304Q8—21no—
305Q8—3021no—
306Q8—3021no—
307Q8—6042no—
308Q8—6042no—
309Q8#1455900412yescomplemented
310D4—21no—
311D4—21no—
312D4—42no—
313D4—3022no—
314D4—3021no—
315D4—3021no—
316D4—6042no—
317D4—6042no—
318D4—6042no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—3021no—
327C2×C4—3021no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—6042no—
332C2×C4—6042no—
333C2×C4—6042no—
334C2×C4—1511no—
335C2×C4—1511no—
336C2×C4—1511no—
337C2×C4D4×D15111yescharacteristic
338C2×C4C23×D15111yescharacteristic
339C8—21no—
340C8—21no—
341C8—3021no—
342C8—3021no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—3021no—
350C22—3021no—
351C22—6041no—
352C22—6041no—
353C22—6041no—
354C22—1512no—
355C22C2×D4×D15111yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—3021no—
361C4—3021no—
362C4—3021no—
363C4—6041no—
364C4—6041no—
365C4—6041no—
366C4C2×#1455900411yescharacteristic
367C4#1801278411yescharacteristic
368C2—41no—
369C2—81no—
370C2—3022no—
371C2—12081no—
372C2#2375285211yescharacteristic
373C2AGL(1,ℤ/8)×D15111yescharacteristic
374C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#417×C151C2
socleC22×C151C22×D4
hypercenter#417D151
hypocenterC151#3308
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #23752869C2semidirect
2. #23752863C2semidirect
3. #23752570C2semidirect
4. #23752547C2semidirect
5. #23752524C2semidirect
6. #23752505C2semidirect
7. #23752458C2semidirect
8. #23752447C2semidirect
9. #23752426C2semidirect
10. #23752357C2semidirect
11. #23752352C2semidirect
12. #23752315C2semidirect
13. #23752281C2semidirect
14. #103×D151C2semidirect
15. #417×C151C2semidirect
140. Q8×C151#41semidirect
187. C151#3308semidirect
202. #417D151semidirect
309. Q8#14559004semidirect

Maximal subgroups

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

subgroupindex
#237528692
#237528632
#237525702
#237525472
#237525242
#237525052
#237524582
#237524472
#237524262
#237523572
#237523522
#237523152
#237522812
#103×D1512
#417×C1512
#3308151