Finite Group Databasebeta

← #34080118

Subgroups — #34080118

Order 19328.

390 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752764C211yesmaximal, characteristic, complemented
2#23752758C211yesmaximal, characteristic
3#23752605C211yesmaximal, characteristic, complemented
4#23752603C211yesmaximal, characteristic, complemented
5#23752573C211yesmaximal, characteristic, complemented
6#23752570C211yesmaximal, characteristic, complemented
7#23752421C211yesmaximal, characteristic, complemented
8#23752420C211yesmaximal, characteristic, complemented
9#23752411C211yesmaximal, characteristic, complemented
10#23752410C211yesmaximal, characteristic, complemented
11#23752376C211yesmaximal, characteristic, complemented
12#23752374C211yesmaximal, characteristic, complemented
13#23752372C211yesmaximal, characteristic, complemented
14#23752266C211yesmaximal, characteristic, complemented
15#452×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Dic604C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558992C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23#18012738C2211yescharacteristic
24#18012737C2211yescharacteristic
25#18012737C2211yescharacteristic
26#18012735C2211yescharacteristic
27#18012729—21no—
28#18012728C2211yescharacteristic
29#18012726C2211yescharacteristic
30#18012718C2211yescharacteristic
31#18012716—21no—
32#18012711—21no—
33#18012711—21no—
34Q8×Dic151C2211yescharacteristic
35#18012704—21no—
36#18012704C2211yescharacteristic
37C4×C22⋊D151—21no—
38C4×C22⋊D151—21no—
39#18012695—21no—
40C2×C4×Dic151C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012662C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012660C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic
51#18012649C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×Q16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63C2×Dic302C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C22×Dic151D411yescharacteristic
69C22×Dic151D411yescharacteristic
70C2×C4×D151—21no—
71Dic604—41no—
72#14558994—41no—
73#14558994—41no—
74#14558993—41no—
75#14558992—41no—
76#14558991—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151—21no—
94C4×Dic151—21no—
95C4×Dic151D411yescharacteristic
96C4×Dic151D411yescharacteristic
97C4×Dic151C2311yescharacteristic
98C4×Dic151C2311yescharacteristic
99#41×C151—41no—
100#41×C151—41no—
101C2×Q8×C151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151—21no—
104C2×D4×C151C2311yescharacteristic
105C22×C4×C151—21no—
106C22×C4×C151C2311yescharacteristic
107Q16×C151—41no—
108SD16×C151—41no—
109C2×C8×C151C2311yescharacteristic
110C2×C8×C151C2311yescharacteristic
111C4⋊C4×C151—21no—
112C4⋊C4×C151C2311yescharacteristic
113C22⋊C4×C151—21no—
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119Dic302—42no—
120D604—21no—
121D604—21no—
122C22⋊D151—42no—
123C22⋊D151—42no—
124C22⋊D151—42no—
125C2×Dic151—22no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—41no—
130C2×Dic151C2×D411yescharacteristic
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—42no—
135C151⋊C8—21no—
136C151⋊C8—21no—
137C23×C151—21no—
138C23×C151C2×D411yescharacteristic
139Q8×C151—21no—
140Q8×C151—21no—
141Q8×C151—21no—
142Q8×C151—21no—
143D4×C151—21no—
144D4×C151—21no—
145D4×C151—42no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—42no—
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2411yescharacteristic
154C8×C151—21no—
155C8×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151—41no—
162C22×C151C22×D411yescharacteristic
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151H(5,𝔽2)11yescharacteristic
171C4×C151H(5,𝔽2)11yescharacteristic
172Dic151—21no—
173Dic151—21no—
174Dic151—21no—
175Dic151—41no—
176Dic151—41no—
177Dic151—41no—
178Dic151#13712yes—
179C2×C151—41no—
180C2×C151—81no—
181C2×C151#53511yescharacteristic
182C2×C151C2×#13711yescharacteristic
183C2×C151#57511yescharacteristic
184D151—81no—
185C151#321611yescharacteristic, complemented, Sylow
186#3216—1511nomaximal, Sylow
187#533—1511no—
188#532—1511no—
189#497—1511no—
190#497—1511no—
191#489—1511no—
192#489—1511no—
193#462—1511no—
194#462—1511no—
195#460—1511no—
196#460—1511no—
197#452—1511no—
198#452—1511no—
199#452—1511no—
200#452D15111yescharacteristic, complemented
201#432—1511no—
202C2×#41—1511no—
203C2×#41C2×D15111yescharacteristic
204C2×Q16—1511no—
205C2×Q16—1511no—
206C2×Q16—1511no—
207C2×Q16C2×D15111yescharacteristic
208C2×SD16—1511no—
209C2×SD16—1511no—
210C2×SD16—1511no—
211C2×SD16C2×D15111yescharacteristic
212C4⋊Q8—1511no—
213C4⋊Q8—1511no—
214C4⋊Q8—1511no—
215#127—1511no—
216#125—3021no—
217#124—1511no—
218#124—1511no—
219C22⋊Q8—3021no—
220C22⋊Q8—1511no—
221C22⋊Q8C2×D15111yescharacteristic
222#121—3021no—
223#121—3021no—
224C4×Q8—3021no—
225C4×Q8—1511no—
226C4×Q8—1511no—
227C4×D4—3021no—
228C4×D4—3021no—
229#117—3021no—
230C2×C42—1511no—
231C4⋊C8—1511no—
232C4⋊C8—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#103C2×D15111yescharacteristic
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102C2×D15111yescharacteristic
241C22⋊C8—1511no—
242C22⋊C8C2×D15111yescharacteristic
243#97—1511no—
244#97—1511no—
245#41—41no—
246#41—41no—
247#41—6041no—
248#41—6041no—
249C2×Q8—3021no—
250C2×Q8—1511no—
251C2×Q8—1511no—
252C2×Q8C22×D15111yescharacteristic
253C2×Q8C22×D15111yescharacteristic
254C2×D4—21no—
255C2×D4—3021no—
256C2×D4—3021no—
257C2×D4—3021no—
258C2×D4—1511no—
259C2×D4C22×D15111yescharacteristic
260C22×C4—21no—
261C22×C4—3021no—
262C22×C4—1511no—
263C22×C4—1511no—
264C22×C4C22×D15111yescharacteristic
265Q16—41no—
266Q16—6041no—
267Q16—6041no—
268Q16—6041no—
269SD16—41no—
270SD16—6041no—
271SD16—6041no—
272SD16—6041no—
273C2×C8—1511no—
274C2×C8—1511no—
275C2×C8C22×D15111yescharacteristic
276C2×C8C22×D15111yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—3021no—
279C4⋊C4—3021no—
280C4⋊C4—3021no—
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—3021no—
284C4⋊C4—3021no—
285C4⋊C4—3021no—
286C4⋊C4—1511no—
287C4⋊C4C22×D15111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C42—3021no—
295C42—3021no—
296C42—1511no—
297C42—1511no—
298C42—1511no—
299C42—1511no—
300C23—21no—
301C23—3021no—
302C23D4×D15111yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—3021no—
308Q8—3021no—
309Q8—3021no—
310Q8—3021no—
311Q8—6042no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—3021no—
316D4—3021no—
317D4—6042no—
318D4—6042no—
319D4—6042no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—3022no—
327C2×C4—3021no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—6042no—
331C2×C4—6041no—
332C2×C4—1511no—
333C2×C4—1511no—
334C2×C4—1511no—
335C2×C4—1511no—
336C2×C4D4×D15111yescharacteristic
337C2×C4C23×D15111yescharacteristic
338C8—21no—
339C8—21no—
340C8—3021no—
341C8—3021no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—6041no—
349C22—6041no—
350C22—6041no—
351C22C2×D4×D15111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3021no—
357C4—3021no—
358C4—3021no—
359C4—6041no—
360C4—6041no—
361C4—6041no—
362C4—1512no—
363C4#1801278411yescharacteristic
364C4#1801278411yescharacteristic
365C2—41no—
366C2—81no—
367C2—12081no—
368C2#2375277711yescharacteristic
369C2#137×D15111yescharacteristic
370C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#452×C151C2
socleC22×C151C22×D4
prime radical#23752758C2
hypercenter#452D151
hypocenterC151#3216
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #23752764C2semidirect
3. #23752605C2semidirect
4. #23752603C2semidirect
5. #23752573C2semidirect
6. #23752570C2semidirect
7. #23752421C2semidirect
8. #23752420C2semidirect
9. #23752411C2semidirect
10. #23752410C2semidirect
11. #23752376C2semidirect
12. #23752374C2semidirect
13. #23752372C2semidirect
14. #23752266C2semidirect
15. #452×C151C2semidirect
185. C151#3216semidirect
200. #452D151semidirect

Maximal subgroups

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

subgroupindex
#237527642
#237527582
#237526052
#237526032
#237525732
#237525702
#237524212
#237524202
#237524112
#237524102
#237523762
#237523742
#237523722
#237522662
#452×C1512
#3216151