Finite Group Databasebeta

← #34080189

Subgroups — #34080189

Order 19328.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752822C211yesmaximal, characteristic, complemented
2#23752786C211yesmaximal, characteristic
3#23752605C211yesmaximal, characteristic, complemented
4#23752590C211yesmaximal, characteristic, complemented
5#23752579C211yesmaximal, characteristic, complemented
6#23752568C211yesmaximal, characteristic, complemented
7#23752437C211yesmaximal, characteristic, complemented
8#23752436C211yesmaximal, characteristic, complemented
9#23752421C211yesmaximal, characteristic, complemented
10#23752420C211yesmaximal, characteristic, complemented
11#23752376C211yesmaximal, characteristic
12#23752372C211yesmaximal, characteristic
13#23752368C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#451×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Dic604C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×#14558994C2211yescharacteristic
21C2×#14558993C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23#18012737C2211yescharacteristic
24#18012737C2211yescharacteristic
25#18012737C2211yescharacteristic
26#18012732—21no—
27#18012732—21no—
28#18012730—21no—
29#18012730C2211yescharacteristic
30#18012729—21no—
31#18012728C2211yescharacteristic
32#18012728C2211yescharacteristic
33#18012722—21no—
34#18012722—21no—
35#18012718C2211yescharacteristic
36#18012715—21no—
37#18012715—21no—
38Q8×Dic151C2211yescharacteristic
39#18012704C2211yescharacteristic
40#18012698C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012659C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C22×Q8×C151C2211yescharacteristic
53C2×Q16×C151C2211yescharacteristic
54C2×Q16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302C2311yescharacteristic
62C2×Dic302C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C4×D151—21no—
66Dic604—41no—
67#14558994—41no—
68#14558994—41no—
69#14558994—41no—
70#14558993—41no—
71#14558991—41no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C4⋊Dic151—21no—
75C4⋊Dic151—21no—
76C4⋊Dic151D411yescharacteristic
77C4⋊Dic151D411yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
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⋊Dic151D411yescharacteristic
90C22⋊Dic151D411yescharacteristic
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4—21no—
95C4×Dic151—21no—
96C4×Dic151—21no—
97C4×Dic151C2311yescharacteristic
98C4×Dic151C2311yescharacteristic
99C2×Q8×C151—21no—
100C2×Q8×C151—41no—
101C2×Q8×C151—41no—
102C2×Q8×C151C2311yescharacteristic
103C2×Q8×C151C2311yescharacteristic
104C2×Q8×C151C2311yescharacteristic
105C22×C4×C151—21no—
106C22×C4×C151C2311yescharacteristic
107Q16×C151—41no—
108Q16×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—
119D604—21no—
120D604—21no—
121C22⋊D151—42no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—42no—
130C151⋊C8—21no—
131C151⋊C8—21no—
132C23×C151C2×D411yescharacteristic
133Q8×C151—21no—
134Q8×C151—21no—
135Q8×C151—21no—
136Q8×C151—21no—
137Q8×C151—21no—
138Q8×C151—21no—
139Q8×C151—42no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—42no—
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2411yescharacteristic
149C8×C151—21no—
150C8×C151—21no—
151C22×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151C22×D411yescharacteristic
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C4×C151—21no—
159C4×C151—41no—
160C4×C151—41no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151H(5,𝔽2)11yescharacteristic
164C4×C151H(5,𝔽2)11yescharacteristic
165Dic151—21no—
166Dic151—21no—
167Dic151—21no—
168Dic151—21no—
169Dic151—41no—
170Dic151—41no—
171Dic151—41no—
172C2×C151—41no—
173C2×C151#53511yescharacteristic
174C2×C151#57811yescharacteristic
175C2×C151#57811yescharacteristic
176D151—81no—
177C151#322311yescharacteristic, complemented, Sylow
178#3223—1511nomaximal, Sylow
179#541—1511no—
180#536—1511no—
181#497—1511no—
182#494—1511no—
183#491—1511no—
184#488—1511no—
185#464—1511no—
186#464—1511no—
187#462—1511no—
188#462—1511no—
189#452—1511no—
190#452—1511no—
191#451—1511no—
192#451D15111yescharacteristic, complemented
193#433—1511no—
194C2×#41—1511no—
195C22×Q8C2×D15111yescharacteristic
196C2×Q16—1511no—
197C2×Q16—1511no—
198C2×Q16—1511no—
199C2×Q16—1511no—
200C2×Q16C2×D15111yescharacteristic
201C2×Q16C2×D15111yescharacteristic
202C2×SD16—1511no—
203C2×SD16—1511no—
204C4⋊Q8—1511no—
205C4⋊Q8—1511no—
206C4⋊Q8—1511no—
207#126—3021no—
208#126—3021no—
209#125—3021no—
210#125—3021no—
211#125—1511no—
212#124—1511no—
213#124—1511no—
214#123—3021no—
215#123—3021no—
216C22⋊Q8—3021no—
217C22⋊Q8—3021no—
218C22⋊Q8—1511no—
219C22⋊Q8C2×D15111yescharacteristic
220C4×Q8—1511no—
221C4×Q8—1511no—
222#117—1511no—
223C4⋊C8—1511no—
224C4⋊C8—1511no—
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103C2×D15111yescharacteristic
230#103C2×D15111yescharacteristic
231#102—1511no—
232#102—1511no—
233C22⋊C8—1511no—
234C22⋊C8C2×D15111yescharacteristic
235#97—1511no—
236C4×C8—1511no—
237#41—6041no—
238#41—6041no—
239C2×Q8—21no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—1511no—
243C2×Q8—1511no—
244C2×Q8C22×D15111yescharacteristic
245C2×Q8C22×D15111yescharacteristic
246C2×Q8C22×D15111yescharacteristic
247C2×D4—3021no—
248C2×D4—1511no—
249C22×C4—21no—
250C22×C4—3021no—
251C22×C4C22×D15111yescharacteristic
252Q16—41no—
253Q16—41no—
254Q16—6041no—
255Q16—6041no—
256Q16—6041no—
257Q16—6041no—
258SD16—6041no—
259SD16—6041no—
260C2×C8—1511no—
261C2×C8—1511no—
262C2×C8C22×D15111yescharacteristic
263C2×C8C22×D15111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—3021no—
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—3021no—
276C4⋊C4—1511no—
277C4⋊C4—1511no—
278C4⋊C4—1511no—
279C4⋊C4C22×D15111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—1511no—
287C22⋊C4—1511no—
288C42—3021no—
289C42—3021no—
290C42—1511no—
291C42—1511no—
292C23—3021no—
293C23D4×D15111yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—3021no—
302Q8—3021no—
303Q8—3021no—
304Q8—3021no—
305D4—3021no—
306D4—3021no—
307D4—6042no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—3021no—
318C2×C4—6042no—
319C2×C4—1511no—
320C2×C4—1511no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4D4×D15111yescharacteristic
324C2×C4C23×D15111yescharacteristic
325C8—21no—
326C8—21no—
327C8—3021no—
328C8—3021no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—6041no—
333C22—6041no—
334C22—6041no—
335C22C2×D4×D15111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—3021no—
342C4—3021no—
343C4—3021no—
344C4—3021no—
345C4—6041no—
346C4—6041no—
347C4—6041no—
348C4#1801278411yescharacteristic
349C4#1801278411yescharacteristic
350C2—41no—
351C2—12081no—
352C2#2375277711yescharacteristic
353C2#2375302511yescharacteristic
354C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#451×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559004C22
hypercenter#451D151
hypocenterC151#3223
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #23752822C2semidirect
3. #23752605C2semidirect
4. #23752590C2semidirect
5. #23752579C2semidirect
6. #23752568C2semidirect
7. #23752437C2semidirect
8. #23752436C2semidirect
9. #23752421C2semidirect
10. #23752420C2semidirect
13. #23752368C2semidirect
14. #23752270C2semidirect
15. #451×C151C2semidirect
177. C151#3223semidirect
192. #451D151semidirect

Maximal subgroups

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

subgroupindex
#237528222
#237527862
#237526052
#237525902
#237525792
#237525682
#237524372
#237524362
#237524212
#237524202
#237523762
#237523722
#237523682
#237522702
#451×C1512
#3223151