Finite Group Databasebeta

← #34081103

Subgroups — #34081103

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#23752871C211yesmaximal, characteristic, complemented
2#23752866C211yesmaximal, characteristic, complemented
3#23752572C211yesmaximal, characteristic, complemented
4#23752548C211yesmaximal, characteristic, complemented
5#23752526C211yesmaximal, characteristic, complemented
6#23752508C211yesmaximal, characteristic, complemented
7#23752458C211yesmaximal, characteristic, complemented
8#23752448C211yesmaximal, characteristic, complemented
9#23752428C211yesmaximal, characteristic, complemented
10#23752359C211yesmaximal, characteristic, complemented
11#23752353C211yesmaximal, characteristic, complemented
12#23752314C211yesmaximal, characteristic, complemented
13#23752214C211yesmaximal, characteristic, complemented
14C2×#18012664C211yesmaximal, characteristic, complemented
15#435×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559003—21no—
18C22×Dic302C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×D1208C2211yescharacteristic
22#18012739C2211yescharacteristic
23#18012727C2211yescharacteristic
24#18012725—21no—
25#18012723—21no—
26#18012723—21no—
27#18012719—21no—
28#18012718C2211yescharacteristic
29#18012717—21no—
30#18012713C2211yescharacteristic
31#18012713C2211yescharacteristic
32#18012713C2211yescharacteristic
33#18012711—21no—
34C4×Dic302C2211yescharacteristic
35C4×D604C2211yescharacteristic
36(C22⋊D151)⋊C4—21no—
37C2×C4⋊Dic151C2211yescharacteristic
38C2×C4⋊Dic151C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012673C2211yescharacteristic
41#18012673C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52C2×M16×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55C4⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—41no—
61#14559003—44no—
62C2×Dic302—22no—
63C2×Dic302—21no—
64C2×Dic302—21no—
65C2×Dic302—41no—
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C22×Dic151—21no—
75C22×Dic151—21no—
76C22×Dic151—21no—
77C2×C4×D151—21no—
78C2×C4×D151—21no—
79#14558993—22no—
80#14558993—41no—
81D1208—41no—
82C4⋊Dic151—21no—
83C4⋊Dic151—21no—
84C4⋊Dic151—21no—
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87C4⋊Dic151C2311yescharacteristic
88C4⋊Dic151C2311yescharacteristic
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91C22⋊Dic151—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—
97(C2×D151)⋊C4—21no—
98C4×Dic151—21no—
99C2×D4×C151D411yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102M16×C151—41no—
103C2×C8×C151—41no—
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151D411yescharacteristic
109C22⋊C4×C151D411yescharacteristic
110C22⋊C4×C151D411yescharacteristic
111C42×C151C2311yescharacteristic
112C22×D151—21no—
113C22×D151—21no—
114Dic302—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—42no—
118Dic302—42no—
119Dic302#4112yescomplemented
120D604—21no—
121D604—21no—
122D604—21no—
123D604—21no—
124C22⋊D151—42no—
125C22⋊D151—42no—
126C22⋊D151—42no—
127C22⋊D151—42no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—42no—
135C2×Dic151—42no—
136C2×Dic151—42no—
137C4×D151—42no—
138C4×D151—42no—
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×C151AGL(1,ℤ/8)12yes—
161C22×C151C22×D411yescharacteristic
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—21no—
172C4×C151C2×#4111yescharacteristic
173C4×C151H(5,𝔽2)11yescharacteristic
174Dic151—22no—
175Dic151—41no—
176Dic151—41no—
177Dic151—41no—
178Dic151—41no—
179Dic151—41no—
180C2×C151—22no—
181C2×C151—41no—
182C2×C151#54611yescharacteristic
183C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C151#57811yescharacteristic
185D151—81no—
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#435D15111yescharacteristic, complemented
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×M16C2×D15111yescharacteristic
211C22×C8C2×D15111yescharacteristic
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×D4C2×D15111yescharacteristic
228C2×C4⋊C4—1511no—
229C2×C4⋊C4—1511no—
230#107—1511no—
231#107—1511no—
232#107—1511no—
233C4⋊C8C2×D15111yescharacteristic
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#103—1511no—
238#103—1511no—
239#103—1511no—
240#102—1511no—
241#102—1511no—
242#102—1511no—
243#102—1511no—
244C22⋊C8C2×D15111yescharacteristic
245C22⋊C8C2×D15111yescharacteristic
246#97C2×D15111yescharacteristic
247#41—3022no—
248#41—6041no—
249#41—6044no—
250C2×Q8—3022no—
251C2×Q8—3021no—
252C2×Q8—3021no—
253C2×Q8—6041no—
254C2×Q8—1511no—
255C2×Q8—1511no—
256C2×D4—3021no—
257C2×D4—3021no—
258C2×D4—3021no—
259C2×D4—3021no—
260C2×D4—1511no—
261C2×D4—1511no—
262C2×D4D60411yescharacteristic
263C22×C4—3021no—
264C22×C4—3021no—
265C22×C4—3021no—
266C22×C4—3021no—
267C22×C4—3021no—
268C22×C4C22×D15111yescharacteristic
269C22×C4C22×D15111yescharacteristic
270SD16—3022no—
271SD16—6041no—
272D8—6041no—
273M16—41no—
274C2×C8—41no—
275C2×C8C22×D15111yescharacteristic
276C2×C8C22×D15111yescharacteristic
277C2×C8C22×D15111yescharacteristic
278C2×C8C22×D15111yescharacteristic
279C4⋊C4—3021no—
280C4⋊C4—3021no—
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—1511no—
285C4⋊C4—1511no—
286C4⋊C4—1511no—
287C4⋊C4—1511no—
288C4⋊C4D60411yescharacteristic
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4D60411yescharacteristic
297C22⋊C4D60411yescharacteristic
298C42—3021no—
299C42C22×D15111yescharacteristic
300C23—3021no—
301C23—3021no—
302C23C2×D60411yescharacteristic
303C23C2×D60411yescharacteristic
304Q8—3021no—
305Q8—3021no—
306Q8—3021no—
307Q8—6042no—
308Q8—6042no—
309Q8—1512no—
310D4—22no—
311D4—3021no—
312D4—3021no—
313D4—3021no—
314D4—3021no—
315D4—6042no—
316D4—6042no—
317D4—6042no—
318D4—6042no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
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×C4C2×D60411yescharacteristic
335C2×C4C2×D60411yescharacteristic
336C2×C4C2×D60411yescharacteristic
337C2×C4C2×D60411yescharacteristic
338C2×C4C23×D15111yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—6041no—
349C22—6041no—
350C22—6041no—
351C22—6041no—
352C22—6041no—
353C22—6041no—
354C22#1801276712yes—
355C22C22×D60411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—3022no—
361C4—6041no—
362C4—6041no—
363C4—6041no—
364C4—6041no—
365C4—6041no—
366C4#41×D15111yescharacteristic
367C4#1801278411yescharacteristic
368C2—22no—
369C2—41no—
370C2—12081no—
371C2—12081no—
372C2#2375285711yescharacteristic
373C2C2×#1801276711yescharacteristic
374C2#2375302911yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#435×C151C2
socleC22×C151C22×D4
hypercenter#435D151
hypocenterC151#3308
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #23752871C2semidirect
2. #23752866C2semidirect
3. #23752572C2semidirect
4. #23752548C2semidirect
5. #23752526C2semidirect
6. #23752508C2semidirect
7. #23752458C2semidirect
8. #23752448C2semidirect
9. #23752428C2semidirect
10. #23752359C2semidirect
11. #23752353C2semidirect
12. #23752314C2semidirect
13. #23752214C2semidirect
14. C2×#18012664C2semidirect
15. #435×C151C2semidirect
119. Dic302#41semidirect
187. C151#3308semidirect
201. #435D151semidirect

Maximal subgroups

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

subgroupindex
#237528712
#237528662
#237525722
#237525482
#237525262
#237525082
#237524582
#237524482
#237524282
#237523592
#237523532
#237523142
#237522142
C2×#180126642
#435×C1512
#3308151