Finite Group Databasebeta

← #34080219

Subgroups — #34080219

Order 19328.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752833C211yesmaximal, characteristic, complemented
2#23752604C211yesmaximal, characteristic, complemented
3#23752594C211yesmaximal, characteristic, complemented
4#23752571C211yesmaximal, characteristic, complemented
5#23752562C211yesmaximal, characteristic, complemented
6#23752431C211yesmaximal, characteristic, complemented
7#23752424C211yesmaximal, characteristic, complemented
8#23752419C211yesmaximal, characteristic, complemented
9#23752414C211yesmaximal, characteristic, complemented
10#23752374C211yesmaximal, characteristic, complemented
11#23752368C211yesmaximal, characteristic, complemented
12#23752357C211yesmaximal, characteristic
13#23752351C211yesmaximal, characteristic, complemented
14#23752273C211yesmaximal, characteristic, complemented
15#536×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21C2×#14558991C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24#18012739C2211yescharacteristic
25#18012734—21no—
26#18012727C2211yescharacteristic
27#18012725—21no—
28#18012721—21no—
29#18012718C2211yescharacteristic
30#18012717—21no—
31#18012713C2211yescharacteristic
32C4×Dic302C2211yescharacteristic
33C4×D604C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35C4⋊(C151⋊C8)C2211yescharacteristic
36#18012663C2211yescharacteristic
37#18012663C2211yescharacteristic
38#18012663C2211yescharacteristic
39#18012663C2211yescharacteristic
40#18012663C2211yescharacteristic
41#18012663C2211yescharacteristic
42#18012660C2211yescharacteristic
43#18012660C2211yescharacteristic
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46#18012650C2211yescharacteristic
47C4×C151⋊C8C2211yescharacteristic
48C2×#41×C151C2211yescharacteristic
49C22×Q8×C151C2211yescharacteristic
50C4⋊Q8×C151C2211yescharacteristic
51C4⋊Q8×C151C2211yescharacteristic
52#124×C151C2211yescharacteristic
53#124×C151C2211yescharacteristic
54#123×C151—21no—
55#123×C151—21no—
56C22⋊Q8×C151—21no—
57C22⋊Q8×C151—21no—
58#117×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C4×D151—21no—
64#14558994—41no—
65#14558994—41no—
66#14558994—41no—
67#14558992—41no—
68#14558991—41no—
69#14558991—41no—
70#14558991—41no—
71#14558989—41no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81C22⋊Dic151—21no—
82(C2×D151)⋊C4—21no—
83(C2×D151)⋊C4—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86C4×Dic151—21no—
87#41×C151—41no—
88#41×C151—41no—
89C2×Q8×C151—21no—
90C2×Q8×C151—41no—
91C2×Q8×C151—41no—
92C2×Q8×C151C2311yescharacteristic
93C2×Q8×C151C2311yescharacteristic
94C2×Q8×C151C2311yescharacteristic
95C2×D4×C151—21no—
96C2×D4×C151C2311yescharacteristic
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151—21no—
104C4⋊C4×C151D411yescharacteristic
105C4⋊C4×C151D411yescharacteristic
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22⋊C4×C151—21no—
110C22⋊C4×C151D411yescharacteristic
111C22⋊C4×C151D411yescharacteristic
112C42×C151C2311yescharacteristic
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—81no—
118D604—21no—
119D604—21no—
120C22⋊D151—81no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C4×D151—81no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C23×C151—21no—
130C23×C151C2×D411yescharacteristic
131Q8×C151—21no—
132Q8×C151—21no—
133Q8×C151—21no—
134Q8×C151—21no—
135Q8×C151—21no—
136Q8×C151—21no—
137Q8×C151—42no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—42no—
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×C151—42no—
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2×D411yescharacteristic
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2411yescharacteristic
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—41no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151C22×D411yescharacteristic
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151H(5,𝔽2)11yescharacteristic
173C4×C151H(5,𝔽2)11yescharacteristic
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177C2×C151—41no—
178C2×C151—81no—
179C2×C151#53511yescharacteristic
180C2×C151#57711yescharacteristic
181C2×C151#57811yescharacteristic
182D151—81no—
183C151#322511yescharacteristic, complemented, Sylow
184#3225—1511nomaximal, Sylow
185#542—1511no—
186#536D15111yescharacteristic, complemented
187#497—1511no—
188#495—1511no—
189#489—1511no—
190#487—1511no—
191#464—1511no—
192#463—1511no—
193#462—1511no—
194#461—1511no—
195#452—1511no—
196#451—1511no—
197#449—1511no—
198#448—1511no—
199#433—1511no—
200C2×#41C2×D15111yescharacteristic
201C22×Q8C2×D15111yescharacteristic
202C2×Q16—1511no—
203C2×Q16—1511no—
204C2×Q16—1511no—
205C2×SD16—1511no—
206C2×SD16—1511no—
207C2×SD16—1511no—
208C2×SD16—1511no—
209C2×D8—1511no—
210C4⋊Q8—1511no—
211C4⋊Q8C2×D15111yescharacteristic
212C4⋊Q8C2×D15111yescharacteristic
213#126—3021no—
214#124—3021no—
215#124—1511no—
216#124C2×D15111yescharacteristic
217#124C2×D15111yescharacteristic
218#123—21no—
219#123—21no—
220#123—3021no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—3021no—
224C22⋊Q8—1511no—
225#121—1511no—
226C4×Q8—1511no—
227C4×D4—1511no—
228#117C2×D15111yescharacteristic
229C4⋊C8—1511no—
230C4⋊C8—1511no—
231#103—1511no—
232#103—1511no—
233#103—1511no—
234#103—1511no—
235#103—1511no—
236#103—1511no—
237#102—1511no—
238#102—1511no—
239C22⋊C8—1511no—
240C22⋊C8—1511no—
241#97—1511no—
242C4×C8—1511no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—3021no—
249C2×Q8—1511no—
250C2×Q8C22×D15111yescharacteristic
251C2×Q8C22×D15111yescharacteristic
252C2×Q8C22×D15111yescharacteristic
253C2×D4—21no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4C22×D15111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—3021no—
260C22×C4C22×D15111yescharacteristic
261Q16—6041no—
262Q16—6041no—
263Q16—6041no—
264SD16—6041no—
265SD16—6041no—
266SD16—6041no—
267SD16—6041no—
268D8—6041no—
269C2×C8—1511no—
270C2×C8—1511no—
271C2×C8—1511no—
272C2×C8—1511no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—3021no—
278C4⋊C4—3021no—
279C4⋊C4—3021no—
280C4⋊C4—1511no—
281C4⋊C4—1511no—
282C4⋊C4C22⋊D15111yescharacteristic
283C4⋊C4C22⋊D15111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4C22⋊D15111yescharacteristic
294C22⋊C4C22⋊D15111yescharacteristic
295C42—3021no—
296C42C22×D15111yescharacteristic
297C42C22×D15111yescharacteristic
298C23—21no—
299C23—3021no—
300C23C2×C22⋊D15111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—3021no—
309Q8—3021no—
310Q8—12081no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—3021no—
315D4—3021no—
316D4—12081no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—3021no—
327C2×C4—12081no—
328C2×C4C2×C22⋊D15111yescharacteristic
329C2×C4C2×C22⋊D15111yescharacteristic
330C2×C4C2×C22⋊D15111yescharacteristic
331C2×C4C2×C22⋊D15111yescharacteristic
332C2×C4C2×C22⋊D15111yescharacteristic
333C2×C4C23×D15111yescharacteristic
334C8—3021no—
335C8—3021no—
336C8—3021no—
337C8—3021no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22C22×C22⋊D15111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—6041no—
357C4—6041no—
358C4—6041no—
359C4#1801278411yescharacteristic
360C4#1801278411yescharacteristic
361C2—41no—
362C2—81no—
363C2—12081no—
364C2#2375277911yescharacteristic
365C2#2375302011yescharacteristic
366C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#536×C151C2
socleC22×C151C22×D4
prime radical#23752357C2
hypercenter#536D151
hypocenterC151#3225
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #23752833C2semidirect
2. #23752604C2semidirect
3. #23752594C2semidirect
4. #23752571C2semidirect
5. #23752562C2semidirect
6. #23752431C2semidirect
7. #23752424C2semidirect
8. #23752419C2semidirect
9. #23752414C2semidirect
10. #23752374C2semidirect
11. #23752368C2semidirect
13. #23752351C2semidirect
14. #23752273C2semidirect
15. #536×C151C2semidirect
183. C151#3225semidirect
186. #536D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237526042
#237525942
#237525712
#237525622
#237524312
#237524242
#237524192
#237524142
#237523742
#237523682
#237523572
#237523512
#237522732
#536×C1512
#3225151