Finite Group Databasebeta

← #34080213

Subgroups — #34080213

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#23752788C211yesmaximal, characteristic, complemented
2#23752607C211yesmaximal, characteristic, complemented
3#23752594C211yesmaximal, characteristic, complemented
4#23752574C211yesmaximal, characteristic, complemented
5#23752564C211yesmaximal, characteristic, complemented
6#23752434C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752422C211yesmaximal, characteristic, complemented
9#23752417C211yesmaximal, characteristic, complemented
10#23752372C211yesmaximal, characteristic, complemented
11#23752367C211yesmaximal, characteristic, complemented
12#23752355C211yesmaximal, characteristic
13#23752350C211yesmaximal, characteristic, complemented
14#23752273C211yesmaximal, characteristic, complemented
15#542×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×Dic302C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558994C2211yescharacteristic
20C2×#14558994C2211yescharacteristic
21C2×#14558992C2211yescharacteristic
22C2×#14558992C2211yescharacteristic
23C2×#14558992C2211yescharacteristic
24C2×#14558991C2211yescharacteristic
25C2×#14558989C2211yescharacteristic
26#18012739C2211yescharacteristic
27#18012739C2211yescharacteristic
28#18012727C2211yescharacteristic
29#18012727C2211yescharacteristic
30#18012723—21no—
31#18012723—21no—
32#18012719—21no—
33#18012719—21no—
34C4⋊(C151⋊C8)C2211yescharacteristic
35C4⋊(C151⋊C8)C2211yescharacteristic
36#18012662C2211yescharacteristic
37#18012662C2211yescharacteristic
38#18012662C2211yescharacteristic
39#18012662C2211yescharacteristic
40#18012662C2211yescharacteristic
41#18012662C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46#18012650C2211yescharacteristic
47C4×C151⋊C8C2211yescharacteristic
48C4⋊Q8×C151C2211yescharacteristic
49#126×C151—21no—
50#124×C151—21no—
51#124×C151C2211yescharacteristic
52#123×C151—21no—
53C22⋊Q8×C151—21no—
54C22⋊Q8×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56C4×Q8×C151C2211yescharacteristic
57C4×D4×C151C2211yescharacteristic
58#117×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302—21no—
62C2×Dic302—41no—
63C2×Dic302—41no—
64C2×Dic302C2311yescharacteristic
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C22×Dic151—21no—
70C2×C4×D151—21no—
71#14558994—41no—
72#14558994—41no—
73#14558994—41no—
74#14558992—41no—
75#14558992—41no—
76#14558992—41no—
77#14558991—41no—
78#14558989—41no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C4⋊Dic151—21no—
84C4⋊Dic151—21no—
85C4⋊Dic151—21no—
86C4⋊Dic151—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91C2×Q8×C151—21no—
92C2×Q8×C151C2311yescharacteristic
93C2×D4×C151—21no—
94C2×D4×C151C2311yescharacteristic
95C22×C4×C151—21no—
96C22×C4×C151C2311yescharacteristic
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151D411yescharacteristic
101C4⋊C4×C151D411yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151—21no—
108C22⋊C4×C151—21no—
109C22⋊C4×C151D411yescharacteristic
110C22⋊C4×C151D411yescharacteristic
111C42×C151—21no—
112C42×C151C2311yescharacteristic
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117Dic302—21no—
118Dic302—21no—
119Dic302—21no—
120Dic302—21no—
121Dic302—42no—
122D604—21no—
123D604—21no—
124C22⋊D151—42no—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—42no—
129C4×D151—42no—
130C151⋊C8—21no—
131C151⋊C8—21no—
132C151⋊C8—21no—
133C151⋊C8—21no—
134C23×C151—21no—
135C23×C151C2×D411yescharacteristic
136Q8×C151—21no—
137Q8×C151—21no—
138Q8×C151—81no—
139D4×C151—21no—
140D4×C151—21no—
141D4×C151—81no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—81no—
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#542D15111yescharacteristic, complemented
186#536—1511no—
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×#41—1511no—
201C22×Q8—1511no—
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⋊Q8—1511no—
212C4⋊Q8C2×D15111yescharacteristic
213#126—21no—
214#124—21no—
215#124—1511no—
216#124—1511no—
217#124C2×D15111yescharacteristic
218#123—21no—
219#123—3021no—
220#123—3021no—
221C22⋊Q8—21no—
222C22⋊Q8—3021no—
223C22⋊Q8—3021no—
224C22⋊Q8C2×D15111yescharacteristic
225#121C2×D15111yescharacteristic
226C4×Q8C2×D15111yescharacteristic
227C4×D4C2×D15111yescharacteristic
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—6041no—
244#41—6041no—
245C2×Q8—21no—
246C2×Q8—3021no—
247C2×Q8—6041no—
248C2×Q8—6041no—
249C2×Q8—1511no—
250C2×Q8—1511no—
251C2×Q8—1511no—
252C2×Q8C22×D15111yescharacteristic
253C2×D4—21no—
254C2×D4—3021no—
255C2×D4—1511no—
256C2×D4C22×D15111yescharacteristic
257C22×C4—21no—
258C22×C4—3021no—
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—3021no—
277C4⋊C4—3021no—
278C4⋊C4—3021no—
279C4⋊C4—3021no—
280C4⋊C4C22⋊D15111yescharacteristic
281C4⋊C4C22⋊D15111yescharacteristic
282C4⋊C4C22×D15111yescharacteristic
283C4⋊C4C22×D15111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4—3021no—
293C22⋊C4C22⋊D15111yescharacteristic
294C22⋊C4C22⋊D15111yescharacteristic
295C42—21no—
296C42C22×D15111yescharacteristic
297C42C22×D15111yescharacteristic
298C23—21no—
299C23—3021no—
300C23C2×C22⋊D15111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—81no—
304Q8—3021no—
305Q8—3021no—
306Q8—3021no—
307Q8—3021no—
308Q8—3021no—
309Q8—3021no—
310Q8—6042no—
311D4—21no—
312D4—21no—
313D4—81no—
314D4—3021no—
315D4—3021no—
316D4—6042no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—6042no—
327C2×C4—6042no—
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#1801278511yescharacteristic
360C4#1801278511yescharacteristic
361C2—41no—
362C2—81no—
363C2—12081no—
364C2#2375277611yescharacteristic
365C2#2375302311yescharacteristic
366C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#542×C151C2
socleC22×C151C22×D4
prime radical#23752355C2
hypercenter#542D151
hypocenterC151#3225
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #23752788C2semidirect
2. #23752607C2semidirect
3. #23752594C2semidirect
4. #23752574C2semidirect
5. #23752564C2semidirect
6. #23752434C2semidirect
7. #23752427C2semidirect
8. #23752422C2semidirect
9. #23752417C2semidirect
10. #23752372C2semidirect
11. #23752367C2semidirect
13. #23752350C2semidirect
14. #23752273C2semidirect
15. #542×C151C2semidirect
183. C151#3225semidirect
185. #542D151semidirect

Maximal subgroups

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

subgroupindex
#237527882
#237526072
#237525942
#237525742
#237525642
#237524342
#237524272
#237524222
#237524172
#237523722
#237523672
#237523552
#237523502
#237522732
#542×C1512
#3225151