Finite Group Databasebeta

← #34080065

Subgroups — #34080065

Order 19328.

394 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#23752766C211yesmaximal, characteristic, complemented
2#23752761C211yesmaximal, characteristic
3#23752590C211yesmaximal, characteristic, complemented
4#23752583C211yesmaximal, characteristic, complemented
5#23752561C211yesmaximal, characteristic, complemented
6#23752557C211yesmaximal, characteristic, complemented
7#23752435C211yesmaximal, characteristic, complemented
8#23752434C211yesmaximal, characteristic, complemented
9#23752431C211yesmaximal, characteristic, complemented
10#23752377C211yesmaximal, characteristic, complemented
11#23752375C211yesmaximal, characteristic, complemented
12#23752373C211yesmaximal, characteristic, complemented
13#23752371C211yesmaximal, characteristic, complemented
14#23752264C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×Dic604C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×#14558994C2211yescharacteristic
21C2×#14558993C2211yescharacteristic
22C2×#14558992C2211yescharacteristic
23C2×#14558991C2211yescharacteristic
24#18012738C2211yescharacteristic
25#18012737C2211yescharacteristic
26#18012737C2211yescharacteristic
27#18012735C2211yescharacteristic
28#18012729—21no—
29#18012727C2211yescharacteristic
30#18012719C2211yescharacteristic
31#18012717—21no—
32#18012715C2211yescharacteristic
33#18012712—21no—
34#18012712—21no—
35C4×Dic302—21no—
36C4×Dic302C2211yescharacteristic
37(C22⋊D151)⋊C4—21no—
38(C22⋊D151)⋊C4—21no—
39#18012696—21no—
40C42×D151C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012662C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012659C2211yescharacteristic
48(C2×D151)⋊C8C2211yescharacteristic
49(C2×D151)⋊C8C2211yescharacteristic
50C8×Dic151C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54#124×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559005—41no—
60#14559005—41no—
61#14559003—41no—
62#14559003—41no—
63C2×Dic302—21no—
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C22×Dic151—21no—
72C2×C4×D151—21no—
73C2×C4×D151D411yescharacteristic
74C2×C4×D151D411yescharacteristic
75C2×C4×D151C2311yescharacteristic
76Dic604—41no—
77#14558994—41no—
78#14558994—41no—
79#14558993—41no—
80#14558992—41no—
81#14558991—41no—
82C2×C151⋊C8C2311yescharacteristic
83C2×C151⋊C8C2311yescharacteristic
84C4⋊Dic151—21no—
85C4⋊Dic151C2311yescharacteristic
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4—21no—
90Dic151⋊C4—21no—
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97C4×Dic151—21no—
98C4×Dic151D411yescharacteristic
99C4×Dic151D411yescharacteristic
100C4×Dic151C2311yescharacteristic
101C2×Q8×C151C2311yescharacteristic
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104Q16×C151—41no—
105SD16×C151—41no—
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151—21no—
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C42×C151—21no—
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151C2×D411yescharacteristic
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119Dic302—21no—
120Dic302—42no—
121D604—21no—
122D604—21no—
123D604—42no—
124C22⋊D151—42no—
125C22⋊D151—42no—
126C22⋊D151—42no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—42no—
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—22no—
137C4×D151—22no—
138C4×D151—42no—
139C151⋊C8—21no—
140C151⋊C8—21no—
141C23×C151—21no—
142Q8×C151—21no—
143Q8×C151—21no—
144Q8×C151—21no—
145Q8×C151—21no—
146D4×C151—21no—
147D4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2411yescharacteristic
154C8×C151—21no—
155C8×C151—21no—
156C22×C151—41no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151C22×D411yescharacteristic
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—21no—
163C2×D151—41no—
164C2×D151—41no—
165C2×D151—41no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151H(5,𝔽2)11yescharacteristic
172C4×C151H(5,𝔽2)11yescharacteristic
173Dic151—21no—
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177Dic151#13512yes—
178Dic151#13712yes—
179C2×C151—81no—
180C2×C151#53511yescharacteristic
181C2×C151C2×#13511yescharacteristic
182C2×C151C2×#13711yescharacteristic
183D151—41no—
184D151—81no—
185C151#321011yescharacteristic, complemented, Sylow
186#3210—1511nomaximal, Sylow
187#533—1511no—
188#532—1511no—
189#494—1511no—
190#492—1511no—
191#487—1511no—
192#486—1511no—
193#464—1511no—
194#464—1511no—
195#464—1511no—
196#464D15111yescharacteristic, complemented
197#452—1511no—
198#452—1511no—
199#452—1511no—
200#452—1511no—
201#431—1511no—
202C2×#41—1511no—
203C2×#41—1511no—
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#124C2×D15111yescharacteristic
219C22⋊Q8—3021no—
220C22⋊Q8—1511no—
221C22⋊Q8—1511no—
222#121—3021no—
223#121—3021no—
224C4×Q8—3021no—
225C4×Q8—1511no—
226C4×Q8C2×D15111yescharacteristic
227C4×D4—3021no—
228C4×D4—3021no—
229#117—3021no—
230C2×C42—1511no—
231C4⋊C8—1511no—
232C4⋊C8C2×D15111yescharacteristic
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⋊C8—1511no—
243C4×C8—1511no—
244C4×C8—1511no—
245#41—6041no—
246#41—6041no—
247#41—6041no—
248#41—6041no—
249C2×Q8—3021no—
250C2×Q8—1511no—
251C2×Q8—1511no—
252C2×Q8C22×D15111yescharacteristic
253C2×Q8C22×D15111yescharacteristic
254C2×D4—3021no—
255C2×D4—3021no—
256C2×D4—3021no—
257C2×D4—3021no—
258C2×D4—1511no—
259C2×D4C22×D15111yescharacteristic
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4—1511no—
263C22×C4—1511no—
264C22×C4—1511no—
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—21no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C42—21no—
295C42—3021no—
296C42—1511no—
297C42—1511no—
298C42—1511no—
299C42C22×D15111yescharacteristic
300C23—21no—
301C23—3021no—
302C23—1511no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—3021no—
308Q8—3021no—
309Q8—3021no—
310Q8—3021no—
311Q8—6042no—
312D4—21no—
313D4—21no—
314D4—3021no—
315D4—3021no—
316D4—6042no—
317D4—6042no—
318D4—6042no—
319D4—6042no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—3022no—
324C2×C4—3022no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—3021no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—6042no—
331C2×C4—6042no—
332C2×C4—1511no—
333C2×C4—1511no—
334C2×C4—1511no—
335C2×C4D4×D15111yescharacteristic
336C2×C4D4×D15111yescharacteristic
337C2×C4C23×D15111yescharacteristic
338C8—21no—
339C8—21no—
340C8—3021no—
341C8—3021no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—3021no—
346C22—3021no—
347C22—3021no—
348C22—6041no—
349C22—6041no—
350C22—6041no—
351C22C2×D4×D15111yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3021no—
358C4—6041no—
359C4—6041no—
360C4—6041no—
361C4—1512no—
362C4—1512no—
363C4#1801278411yescharacteristic
364C4#1801278511yescharacteristic
365C2—81no—
366C2—6041no—
367C2—12081no—
368C2#2375277811yescharacteristic
369C2#135×D15111yescharacteristic
370C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
prime radical#23752761C2
hypercenter#464D151
hypocenterC151#3210
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23752766C2semidirect
3. #23752590C2semidirect
4. #23752583C2semidirect
5. #23752561C2semidirect
6. #23752557C2semidirect
7. #23752435C2semidirect
8. #23752434C2semidirect
9. #23752431C2semidirect
10. #23752377C2semidirect
11. #23752375C2semidirect
12. #23752373C2semidirect
13. #23752371C2semidirect
14. #23752264C2semidirect
15. #464×C151C2semidirect
185. C151#3210semidirect
196. #464D151semidirect

Maximal subgroups

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

subgroupindex
#237527662
#237527612
#237525902
#237525832
#237525612
#237525572
#237524352
#237524342
#237524312
#237523772
#237523752
#237523732
#237523712
#237522642
#464×C1512
#3210151