Finite Group Databasebeta

← #34081014

Subgroups — #34081014

Order 19328.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752908C211yesmaximal, characteristic, complemented
2#23752871C211yesmaximal, characteristic, complemented
3#23752567C211yesmaximal, characteristic, complemented
4#23752554C211yesmaximal, characteristic, complemented
5#23752531C211yesmaximal, characteristic, complemented
6#23752520C211yesmaximal, characteristic, complemented
7#23752448C211yesmaximal, characteristic, complemented
8#23752441C211yesmaximal, characteristic, complemented
9#23752428C211yesmaximal, characteristic, complemented
10#23752359C211yesmaximal, characteristic, complemented
11#23752353C211yesmaximal, characteristic, complemented
12C4×#14558993C211yesmaximal, characteristic, complemented
13#23752209C211yesmaximal, characteristic, complemented
14C2×#18012664C211yesmaximal, characteristic, complemented
15C8×D4×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×#14558993C2211yescharacteristic
19C2×#14558993C2211yescharacteristic
20C2×D1208C2211yescharacteristic
21#18012734—21no—
22#18012731C2211yescharacteristic
23#18012727C2211yescharacteristic
24#18012725—21no—
25#18012721—21no—
26#18012718C2211yescharacteristic
27#18012717—21no—
28#18012713C2211yescharacteristic
29#18012713C2211yescharacteristic
30#18012713C2211yescharacteristic
31#18012711—21no—
32#18012711—21no—
33C4×Dic302C2211yescharacteristic
34C4×D604C2211yescharacteristic
35(C22⋊D151)⋊C4—21no—
36(C22⋊D151)⋊C4—21no—
37#18012698C2211yescharacteristic
38C2×C4⋊Dic151C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012671C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52C22×C8×C151C2211yescharacteristic
53C22×C8×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55C4⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57C22⋊C8×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—41no—
61C2×Dic302—22no—
62C2×Dic302—21no—
63C2×Dic302—41no—
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C22×Dic151—21no—
73C22×Dic151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76#14558993—22no—
77#14558993—41no—
78D1208—41no—
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90(C2×D151)⋊C4—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—
96C4×Dic151—21no—
97C4×Dic151—21no—
98C2×D4×C151D411yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C2×C8×C151—41no—
102C2×C8×C151—41no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C4⋊C4×C151D411yescharacteristic
108C22⋊C4×C151D411yescharacteristic
109C22⋊C4×C151D411yescharacteristic
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112C22×D151—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—21no—
116Dic302—42no—
117Dic302#4112yes—
118D604—21no—
119D604—21no—
120D604—21no—
121D604—21no—
122C22⋊D151—42no—
123C22⋊D151—42no—
124C22⋊D151—42no—
125C22⋊D151—81no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—42no—
133C2×Dic151—81no—
134C4×D151—42no—
135C4×D151—81no—
136C23×C151C2×D411yescharacteristic
137C23×C151C2×D411yescharacteristic
138D4×C151—22no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2411yescharacteristic
148C8×C151—21no—
149C8×C151—21no—
150C8×C151—21no—
151C8×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151#13512yes—
158C22×C151C22×D411yescharacteristic
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151C2×#4111yescharacteristic
170C4×C151H(5,𝔽2)11yescharacteristic
171Dic151—22no—
172Dic151—41no—
173Dic151—41no—
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177C2×C151—22no—
178C2×C151—41no—
179C2×C151#54611yescharacteristic
180C2×C151C2×#13511yescharacteristic
181C2×C151#57711yescharacteristic
182D151—81no—
183D151—81no—
184C151#330111yescharacteristic, complemented, Sylow
185#3301—1511nomaximal, Sylow
186#553—1511no—
187#548—1511no—
188#488—1511no—
189#485—1511no—
190#481—1511no—
191#479—1511no—
192#466—1511no—
193#465—1511no—
194#463—1511no—
195#449—1511no—
196#448—1511no—
197C4×SD16—1511no—
198C8×D4D15111yescharacteristic, complemented
199#416—1511no—
200C2×#103—1511no—
201C2×#41—1511no—
202C22×Q8—1511no—
203C2×SD16—1511no—
204C2×SD16—1511no—
205C2×D8—1511no—
206C22×C8C2×D15111yescharacteristic
207C22×C8C2×D15111yescharacteristic
208#126—3021no—
209#125—1511no—
210#124—3021no—
211#124—1511no—
212#123—3021no—
213C22⋊Q8—3021no—
214C22⋊Q8—1511no—
215#121—3021no—
216#121—3021no—
217#121—1511no—
218#121—1511no—
219#121—1511no—
220C4×Q8—1511no—
221C4×D4—3021no—
222C4×D4—3021no—
223C4×D4—1511no—
224C4×D4C2×D15111yescharacteristic
225#117—1511no—
226C2×C4⋊C4—1511no—
227#107—1511no—
228#106—1511no—
229#106—1511no—
230C4⋊C8C2×D15111yescharacteristic
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241C22⋊C8C2×D15111yescharacteristic
242C22⋊C8C2×D15111yescharacteristic
243C4×C8C2×D15111yescharacteristic
244#41—3022no—
245#41—6041no—
246C2×Q8—3022no—
247C2×Q8—3021no—
248C2×Q8—6041no—
249C2×Q8—1511no—
250C2×Q8—1511no—
251C2×D4—3021no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4—1511no—
257C2×D4D60411yescharacteristic
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4C22×D15111yescharacteristic
263C22×C4C22×D15111yescharacteristic
264SD16—3022no—
265SD16—6041no—
266D8—6041no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D15111yescharacteristic
270C2×C8C22×D15111yescharacteristic
271C2×C8C22×D15111yescharacteristic
272C2×C8C22×D15111yescharacteristic
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—1511no—
279C4⋊C4—1511no—
280C4⋊C4—1511no—
281C4⋊C4—1511no—
282C4⋊C4D60411yescharacteristic
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4D60411yescharacteristic
292C22⋊C4D60411yescharacteristic
293C42—3021no—
294C42—3021no—
295C42C22×D15111yescharacteristic
296C23—3021no—
297C23—3021no—
298C23C2×D60411yescharacteristic
299C23C2×D60411yescharacteristic
300Q8—3021no—
301Q8—3021no—
302Q8—3021no—
303Q8—6042no—
304Q8—1512no—
305D4—22no—
306D4—3021no—
307D4—3021no—
308D4—3021no—
309D4—3021no—
310D4—6042no—
311D4—6042no—
312D4—6042no—
313D4—12081no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—3021no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—6042no—
325C2×C4—6042no—
326C2×C4—12081no—
327C2×C4—12081no—
328C2×C4C2×D60411yescharacteristic
329C2×C4C2×D60411yescharacteristic
330C2×C4C2×D60411yescharacteristic
331C2×C4C2×D60411yescharacteristic
332C2×C4C23×D15111yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—6041no—
343C22—6041no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22—6041no—
348C22#1801276112yes—
349C22C22×D60411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—3022no—
355C4—6041no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4—6041no—
360C4#41×D15111yescharacteristic
361C4#1801278411yescharacteristic
362C2—22no—
363C2—41no—
364C2—12081no—
365C2—12081no—
366C2#2375285711yescharacteristic
367C2C2×#1801276111yescharacteristic
368C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC8×D4×C151C2
socleC22×C151C22×D4
hypercenterC8×D4D151
hypocenterC151#3301
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #23752908C2semidirect
2. #23752871C2semidirect
3. #23752567C2semidirect
4. #23752554C2semidirect
5. #23752531C2semidirect
6. #23752520C2semidirect
7. #23752448C2semidirect
8. #23752441C2semidirect
9. #23752428C2semidirect
10. #23752359C2semidirect
11. #23752353C2semidirect
12. C4×#14558993C2semidirect
13. #23752209C2semidirect
14. C2×#18012664C2semidirect
15. C8×D4×C151C2semidirect
184. C151#3301semidirect
198. C8×D4D151semidirect

Maximal subgroups

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

subgroupindex
#237529082
#237528712
#237525672
#237525542
#237525312
#237525202
#237524482
#237524412
#237524282
#237523592
#237523532
C4×#145589932
#237522092
C2×#180126642
C8×D4×C1512
#3301151