Finite Group Databasebeta

← #34080003

Subgroups — #34080003

Order 19328.

378 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#23752786C211yesmaximal, characteristic
2#23752785C211yesmaximal, characteristic
3#23752554C211yesmaximal, characteristic, complemented
4#23752552C211yesmaximal, characteristic, complemented
5#23752551C211yesmaximal, characteristic, complemented
6#23752550C211yesmaximal, characteristic, complemented
7#23752469C211yesmaximal, characteristic, complemented
8#23752467C211yesmaximal, characteristic, complemented
9#23752452C211yesmaximal, characteristic, complemented
10#23752450C211yesmaximal, characteristic, complemented
11#23752368C211yesmaximal, characteristic, complemented
12#23752366C211yesmaximal, characteristic, complemented
13#23752366C211yesmaximal, characteristic, complemented
14#23752177C211yesmaximal, characteristic
15#451×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012738—21no—
23#18012737—21no—
24#18012728—21no—
25#18012725—21no—
26#18012724—21no—
27#18012722—21no—
28#18012722—21no—
29#18012721—21no—
30#18012719C2211yescharacteristic
31#18012718C2211yescharacteristic
32#18012715C2211yescharacteristic
33#18012715C2211yescharacteristic
34#18012715C2211yescharacteristic
35#18012715C2211yescharacteristic
36#18012715C2211yescharacteristic
37#18012698C2211yescharacteristic
38#18012697C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012664C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012663C2211yescharacteristic
47#18012663C2211yescharacteristic
48#18012663C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
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×Dic302—21no—
62C2×Dic302D411yescharacteristic
63C2×Dic302C2311yescharacteristic
64Q8×D151—41no—
65Q8×D151—41no—
66C2×D604D411yescharacteristic
67C2×C22⋊D151D411yescharacteristic
68C2×C22⋊D151D411yescharacteristic
69C2×C4×D151—21no—
70C2×C4×D151C2311yescharacteristic
71C2×C4×D151C2311yescharacteristic
72#14558994—41no—
73#14558994—41no—
74#14558987—41no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C8×D151—41no—
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81C4⋊Dic151C2311yescharacteristic
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
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—
96(C2×D151)⋊C4—21no—
97C4×Dic151—21no—
98C4×Dic151—21no—
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×D151C2×D411yescharacteristic
115C22×D151C2×D411yescharacteristic
116Dic302—21no—
117Dic302—21no—
118Dic302—41no—
119Dic302—42no—
120D604—41no—
121C22⋊D151—41no—
122C22⋊D151—41no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—21no—
132C4×D151—21no—
133C4×D151—42no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136C23×C151C2×D411yescharacteristic
137Q8×C151—21no—
138Q8×C151—21no—
139Q8×C151—21no—
140Q8×C151—21no—
141Q8×C151—21no—
142Q8×C151—21no—
143Q8×C151—42no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—42no—
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2411yescharacteristic
153C8×C151—21no—
154C8×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151C22×D411yescharacteristic
159C2×D151—21no—
160C2×D151—21no—
161C2×D151—21no—
162C2×D151—21no—
163C2×D151—21no—
164C2×D151—21no—
165C4×C151—21no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151H(5,𝔽2)11yescharacteristic
171C4×C151H(5,𝔽2)11yescharacteristic
172Dic151—21no—
173Dic151—21no—
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177Dic151—41no—
178C2×C151—41no—
179C2×C151#53411yescharacteristic
180C2×C151#57811yescharacteristic
181C2×C151#57811yescharacteristic
182D151—41no—
183D151—41no—
184C151#320211yescharacteristic, complemented, Sylow
185#3202—1511nomaximal, Sylow
186#536—1511no—
187#536—1511no—
188#485—1511no—
189#485—1511no—
190#485—1511no—
191#485—1511no—
192#470—1511no—
193#470—1511no—
194#467—1511no—
195#467—1511no—
196#451—1511no—
197#451—1511no—
198#451—1511no—
199#451D15111yescharacteristic, complemented
200#408—1511no—
201C2×#41—1511no—
202C22×Q8—1511no—
203C22×Q8C2×D15111yescharacteristic
204C2×Q16—1511no—
205C2×Q16—1511no—
206C2×Q16C2×D15111yescharacteristic
207C2×Q16C2×D15111yescharacteristic
208C2×M16—1511no—
209C22×C8—1511no—
210C4⋊Q8—3021no—
211C4⋊Q8—3021no—
212#124—3021no—
213#124—3021no—
214#123—3021no—
215#123—3021no—
216#123—3021no—
217#123—3021no—
218C22⋊Q8—1511no—
219C22⋊Q8—1511no—
220C22⋊Q8—1511no—
221C22⋊Q8—1511no—
222C22⋊Q8—1511no—
223C22⋊Q8—1511no—
224C22⋊Q8—1511no—
225C22⋊Q8C2×D15111yescharacteristic
226#117—1511no—
227#117—1511no—
228#107—1511no—
229#107—1511no—
230#106—1511no—
231#106—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#103—1511no—
238#103C2×D15111yescharacteristic
239#103C2×D15111yescharacteristic
240C22⋊C8—1511no—
241C22⋊C8—1511no—
242C22⋊C8—1511no—
243C22⋊C8C2×D15111yescharacteristic
244#41—6041no—
245#41—6041no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—3021no—
250C2×Q8—6041no—
251C2×Q8—6041no—
252C2×Q8—1511no—
253C2×Q8—1511no—
254C2×Q8C22×D15111yescharacteristic
255C2×Q8C22×D15111yescharacteristic
256C2×Q8C22×D15111yescharacteristic
257C2×D4—1511no—
258C2×D4—1511no—
259C2×D4—1511no—
260C22×C4—21no—
261C22×C4—3021no—
262C22×C4—1511no—
263C22×C4—1511no—
264C22×C4C22×D15111yescharacteristic
265Q16—41no—
266Q16—41no—
267Q16—6041no—
268Q16—6041no—
269M16—6041no—
270C2×C8—6041no—
271C2×C8—1511no—
272C2×C8—1511no—
273C2×C8C22×D15111yescharacteristic
274C2×C8C22×D15111yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—3021no—
277C4⋊C4—3021no—
278C4⋊C4—3021no—
279C4⋊C4—3021no—
280C4⋊C4—3021no—
281C4⋊C4—3021no—
282C4⋊C4—3021no—
283C4⋊C4—1511no—
284C4⋊C4—1511no—
285C4⋊C4—1511no—
286C4⋊C4C22×D15111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4—3021no—
294C22⋊C4—3021no—
295C22⋊C4—3021no—
296C22⋊C4—3021no—
297C42—3021no—
298C42—3021no—
299C23—1511no—
300C23—1511no—
301C23D4×D15111yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309Q8—3021no—
310Q8—3021no—
311Q8—6041no—
312Q8—6042no—
313D4—6041no—
314D4—6041no—
315D4—6041no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—3021no—
328C2×C4—3021no—
329C2×C4—3021no—
330C2×C4—3021no—
331C2×C4—6042no—
332C2×C4—1511no—
333C2×C4—1511no—
334C2×C4D4×D15111yescharacteristic
335C2×C4C23×D15111yescharacteristic
336C8—21no—
337C8—21no—
338C8—3021no—
339C8—3021no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—3021no—
344C22—3021no—
345C22—3021no—
346C22—3021no—
347C22—3021no—
348C22—3021no—
349C22C2×D4×D15111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3021no—
356C4—3021no—
357C4—6041no—
358C4—6041no—
359C4—6041no—
360C4—6041no—
361C4#1801278411yescharacteristic
362C4#1801278411yescharacteristic
363C2—41no—
364C2—6041no—
365C2—6041no—
366C2#2375277211yescharacteristic
367C2#2375302511yescharacteristic
368C2#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#3202
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
3. #23752554C2semidirect
4. #23752552C2semidirect
5. #23752551C2semidirect
6. #23752550C2semidirect
7. #23752469C2semidirect
8. #23752467C2semidirect
9. #23752452C2semidirect
10. #23752450C2semidirect
11. #23752368C2semidirect
12. #23752366C2semidirect
13. #23752366C2semidirect
15. #451×C151C2semidirect
184. C151#3202semidirect
199. #451D151semidirect

Maximal subgroups

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

subgroupindex
#237527862
#237527852
#237525542
#237525522
#237525512
#237525502
#237524692
#237524672
#237524522
#237524502
#237523682
#237523662
#237521772
#451×C1512
#3202151