Finite Group Databasebeta

← #34081100

Subgroups — #34081100

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#23752870C211yesmaximal, characteristic, complemented
2#23752865C211yesmaximal, characteristic, complemented
3#23752546C211yesmaximal, characteristic, complemented
4#23752524C211yesmaximal, characteristic, complemented
5#23752504C211yesmaximal, characteristic, complemented
6#23752461C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752424C211yesmaximal, characteristic, complemented
9#23752358C211yesmaximal, characteristic, complemented
10#23752352C211yesmaximal, characteristic, complemented
11#23752314C211yesmaximal, characteristic, complemented
12#23752285C211yesmaximal, characteristic, complemented
13#23752210C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15#489×C151C211yesmaximal, characteristic, complemented
16C2×#14559005—21no—
17C2×#14559003C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×#14558987C2211yescharacteristic
23C2×C8×D151C2211yescharacteristic
24#18012725—21no—
25#18012724—21no—
26#18012724—21no—
27#18012716—21no—
28#18012715—21no—
29#18012715C2211yescharacteristic
30#18012714C2211yescharacteristic
31#18012714C2211yescharacteristic
32#18012712—21no—
33#18012710C2211yescharacteristic
34C4×Dic302C2211yescharacteristic
35C4×D604C2211yescharacteristic
36C4×D604C2211yescharacteristic
37(C22⋊D151)⋊C4—21no—
38C4⋊C4×D151C2211yescharacteristic
39C4⋊C4×D151C2211yescharacteristic
40#18012673C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012672C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012660C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53#124×C151C2211yescharacteristic
54#103×C151C2211yescharacteristic
55#103×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59#14559005—44no—
60#14559003—22no—
61#14559003—41no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64Q8×D151—22no—
65Q8×D151—41no—
66C2×D604—21no—
67C2×D604—21no—
68C2×D604D411yescharacteristic
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C22×Dic151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151C2311yescharacteristic
78C2×C4×D151C2311yescharacteristic
79#14558993—22no—
80#14558991—41no—
81#14558989—41no—
82#14558987—41no—
83C2×C151⋊C8C2311yescharacteristic
84C2×C151⋊C8C2311yescharacteristic
85C8×D151—41no—
86C4⋊Dic151D411yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93C22⋊Dic151—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4D411yescharacteristic
99(C2×D151)⋊C4D411yescharacteristic
100C4×Dic151—21no—
101C2×Q8×C151—21no—
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C4⋊C4×C151—21no—
107C4⋊C4×C151C2311yescharacteristic
108C4⋊C4×C151C2311yescharacteristic
109C22⋊C4×C151—21no—
110C22⋊C4×C151—21no—
111C42×C151C2311yescharacteristic
112C22×D151—21no—
113C22×D151C2×D411yescharacteristic
114C22×D151C2×D411yescharacteristic
115Dic302—21no—
116Dic302—42no—
117Dic302#4112yescomplemented
118D604—22no—
119D604—21no—
120D604—21no—
121D604—42no—
122D604—42no—
123C22⋊D151—42no—
124C22⋊D151—42no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—42no—
129C2×Dic151C2×D411yescharacteristic
130C2×Dic151C2×D411yescharacteristic
131C4×D151—21no—
132C4×D151—21no—
133C4×D151—21no—
134C4×D151—21no—
135C4×D151—42no—
136C4×D151—42no—
137C4×D151—42no—
138C4×D151—42no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C23×C151—21no—
142Q8×C151—21no—
143Q8×C151—21no—
144Q8×C151—42no—
145D4×C151—21no—
146D4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151—21no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—21no—
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—21no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151—41no—
173C4×C151C2×#4111yescharacteristic
174C4×C151H(5,𝔽2)11yescharacteristic
175Dic151—21no—
176Dic151—21no—
177Dic151—22no—
178Dic151—41no—
179Dic151—41no—
180C2×C151—81no—
181C2×C151#54611yescharacteristic
182C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C151#57811yescharacteristic
184D151—22no—
185D151—41no—
186D151—81no—
187C151#330811yescharacteristic, complemented, Sylow
188#3308—1511nomaximal, Sylow
189#548—1511no—
190#547—1511no—
191#489D15111yescharacteristic, complemented
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#417—1511no—
203C2×#103—1511no—
204C2×#41—3021no—
205C2×#41—1511no—
206C22×Q8—1511no—
207C2×SD16—1511no—
208C2×SD16—1511no—
209C2×D8—1511no—
210C2×M16—1511no—
211C22×C8—1511no—
212C4⋊Q8C2×D15111yescharacteristic
213#124—3021no—
214#124C2×D15111yescharacteristic
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⋊C4—1511no—
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#97C2×D15111yescharacteristic
247#41—3022no—
248#41—6041no—
249#41—6044no—
250C2×Q8—21no—
251C2×Q8—3021no—
252C2×Q8—3022no—
253C2×Q8—6041no—
254C2×Q8—1511no—
255C2×Q8C22×D15111yescharacteristic
256C2×D4—3021no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—1511no—
261C2×D4—1511no—
262C2×D4C22×D15111yescharacteristic
263C22×C4—3021no—
264C22×C4—3021no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4—1511no—
269C22×C4—1511no—
270SD16—3022no—
271SD16—6041no—
272D8—6041no—
273M16—6041no—
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—21no—
290C22⋊C4—21no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—1511no—
297C22⋊C4—1511no—
298C42—3021no—
299C42C22×D15111yescharacteristic
300C23—21no—
301C23—3021no—
302C23—1511no—
303C23—1511no—
304Q8—21no—
305Q8—21no—
306Q8—42no—
307Q8—3021no—
308Q8—6042no—
309Q8—1512no—
310D4—21no—
311D4—21no—
312D4—3022no—
313D4—3021no—
314D4—3021no—
315D4—6042no—
316D4—6042no—
317D4—6042no—
318D4—6042no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—3021no—
328C2×C4—3021no—
329C2×C4—6042no—
330C2×C4—6042no—
331C2×C4—6042no—
332C2×C4—6042no—
333C2×C4—6042no—
334C2×C4—1511no—
335C2×C4—1511no—
336C2×C4D4×D15111yescharacteristic
337C2×C4D4×D15111yescharacteristic
338C2×C4C23×D15111yescharacteristic
339C8—21no—
340C8—21no—
341C8—3021no—
342C8—3021no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3021no—
347C22—3021no—
348C22—3021no—
349C22—3021no—
350C22—3021no—
351C22—6041no—
352C22—6041no—
353C22—6041no—
354C22—1512no—
355C22C2×D4×D15111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—3021no—
362C4—3021no—
363C4—3022no—
364C4—6041no—
365C4—6041no—
366C4#41×D15111yescharacteristic
367C4#1801278511yescharacteristic
368C2—81no—
369C2—3022no—
370C2—6041no—
371C2—12081no—
372C2#2375285511yescharacteristic
373C2AGL(1,ℤ/8)×D15111yescharacteristic
374C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#489×C151C2
socleC22×C151C22×D4
hypercenter#489D151
hypocenterC151#3308
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #23752870C2semidirect
2. #23752865C2semidirect
3. #23752546C2semidirect
4. #23752524C2semidirect
5. #23752504C2semidirect
6. #23752461C2semidirect
7. #23752447C2semidirect
8. #23752424C2semidirect
9. #23752358C2semidirect
10. #23752352C2semidirect
11. #23752314C2semidirect
12. #23752285C2semidirect
13. #23752210C2semidirect
14. #103×D151C2semidirect
15. #489×C151C2semidirect
117. Dic302#41semidirect
187. C151#3308semidirect
191. #489D151semidirect

Maximal subgroups

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

subgroupindex
#237528702
#237528652
#237525462
#237525242
#237525042
#237524612
#237524472
#237524242
#237523582
#237523522
#237523142
#237522852
#237522102
#103×D1512
#489×C1512
#3308151