Finite Group Databasebeta

← #34081080

Subgroups — #34081080

Order 19328.

394 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#23752867C211yesmaximal, characteristic, complemented
2#23752582C211yesmaximal, characteristic, complemented
3#23752553C211yesmaximal, characteristic, complemented
4#23752542C211yesmaximal, characteristic, complemented
5#23752509C211yesmaximal, characteristic, complemented
6#23752456C211yesmaximal, characteristic, complemented
7#23752439C211yesmaximal, characteristic, complemented
8#23752417C211yesmaximal, characteristic, complemented
9#23752355C211yesmaximal, characteristic, complemented
10#23752355C211yesmaximal, characteristic, complemented
11#23752322C211yesmaximal, characteristic, complemented
12#23752284C211yesmaximal, characteristic, complemented
13#23752211C211yesmaximal, characteristic, complemented
14#23752206C211yesmaximal, characteristic, complemented
15#553×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14559004C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558992C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×#14558988C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012739C2211yescharacteristic
24#18012721—21no—
25#18012721—21no—
26#18012718C2211yescharacteristic
27#18012718C2211yescharacteristic
28#18012710—21no—
29C4×D604C2211yescharacteristic
30C4⋊C4×D151—21no—
31#18012672C2211yescharacteristic
32#18012670C2211yescharacteristic
33#18012670C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35#18012662C2211yescharacteristic
36#18012662C2211yescharacteristic
37#18012662C2211yescharacteristic
38#18012662C2211yescharacteristic
39#18012662C2211yescharacteristic
40#18012662C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44#18012659C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic
47#18012650C2211yescharacteristic
48#126×C151—21no—
49#125×C151C2211yescharacteristic
50#123×C151—21no—
51#121×C151—21no—
52#121×C151C2211yescharacteristic
53#121×C151C2211yescharacteristic
54C4×D4×C151—21no—
55C4×D4×C151C2211yescharacteristic
56C4×D4×C151C2211yescharacteristic
57#117×C151C2211yescharacteristic
58C2×C4⋊C4×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—22no—
61#14559004—41no—
62#14559004—41no—
63C2×Dic302C2311yescharacteristic
64C2×Dic302C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×C22⋊D151—21no—
67C2×C22⋊D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71#14558992—41no—
72#14558992—41no—
73#14558989—22no—
74#14558988—41no—
75C2×C151⋊C8—41no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C2×C151⋊C8C2311yescharacteristic
80C4⋊Dic151—21no—
81C4⋊Dic151—21no—
82C4⋊Dic151C2311yescharacteristic
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87(C2×D151)⋊C4—21no—
88C2×D4×C151—21no—
89C2×D4×C151—21no—
90C2×D4×C151D411yescharacteristic
91C2×D4×C151C2311yescharacteristic
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151C2311yescharacteristic
95C22×C4×C151C2311yescharacteristic
96C4⋊C4×C151—21no—
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151D411yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C22⋊C4×C151—21no—
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C22⋊C4×C151D411yescharacteristic
108C22⋊C4×C151D411yescharacteristic
109C42×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112Dic302—21no—
113Dic302—21no—
114Dic302—21no—
115Dic302—21no—
116D604—21no—
117D604#4112yes—
118C22⋊D151—42no—
119C22⋊D151—42no—
120C2×Dic151—21no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C4×D151—42no—
124C4×D151—42no—
125C4×D151—42no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130C23×C151—21no—
131C23×C151C2×D411yescharacteristic
132C23×C151C2×D411yescharacteristic
133D4×C151—21no—
134D4×C151—21no—
135D4×C151—41no—
136D4×C151—42no—
137D4×C151—81no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—81no—
146C2×C4×C151—81no—
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2×D411yescharacteristic
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2411yescharacteristic
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151C22×D411yescharacteristic
162C2×D151—22no—
163C2×D151—41no—
164C2×D151—41no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151C2×#4111yescharacteristic
173C4×C151H(5,𝔽2)11yescharacteristic
174Dic151—41no—
175Dic151—41no—
176Dic151—41no—
177C2×C151—41no—
178C2×C151—41no—
179C2×C151—81no—
180C2×C151#54611yescharacteristic
181C2×C151#57511yescharacteristic
182C2×C151#57711yescharacteristic
183D151—42no—
184C151#330711yescharacteristic, complemented, Sylow
185#3307—1511nomaximal, Sylow
186#553D15111yescharacteristic, complemented
187#547—1511no—
188#491—1511no—
189#485—1511no—
190#483—1511no—
191#478—1511no—
192#468—1511no—
193#465—1511no—
194#461—1511no—
195#449—1511no—
196#449—1511no—
197#442—1511no—
198#435—1511no—
199#417—1511no—
200#416—1511no—
201C2×#41—1511no—
202C2×#41—1511no—
203C2×SD16—1511no—
204C2×SD16—1511no—
205C2×D8—1511no—
206C2×M16—1511no—
207C22×C8—1511no—
208C4⋊Q8—1511no—
209#126—21no—
210#125C2×D15111yescharacteristic
211#123—21no—
212#123—3021no—
213#123—3021no—
214C22⋊Q8—1511no—
215C22⋊Q8—1511no—
216#121—21no—
217#121—3021no—
218#121C2×D15111yescharacteristic
219#121C2×D15111yescharacteristic
220C4×D4—21no—
221C4×D4—1511no—
222C4×D4C2×D15111yescharacteristic
223C4×D4C2×D15111yescharacteristic
224#117C2×D15111yescharacteristic
225C2×C4⋊C4—3021no—
226C2×C4⋊C4C2×D15111yescharacteristic
227#107—1511no—
228#106—1511no—
229#106—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—
239#102—1511no—
240#102—1511no—
241C22⋊C8—1511no—
242C22⋊C8—1511no—
243#97—1511no—
244#41—3022no—
245#41—3022no—
246#41—6041no—
247#41—6041no—
248C2×Q8—1511no—
249C2×Q8—1511no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—3021no—
253C2×D4—3021no—
254C2×D4—1511no—
255C2×D4C22⋊D15111yescharacteristic
256C2×D4C22×D15111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—3021no—
260C22×C4—3021no—
261C22×C4—3021no—
262C22×C4C22×D15111yescharacteristic
263C22×C4C22×D15111yescharacteristic
264SD16—6041no—
265SD16—6041no—
266D8—3022no—
267M16—6041no—
268C2×C8—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⋊C4—1511no—
281C4⋊C4C22⋊D15111yescharacteristic
282C4⋊C4C22×D15111yescharacteristic
283C4⋊C4C22×D15111yescharacteristic
284C4⋊C4C22×D15111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—3021no—
290C22⋊C4—3021no—
291C22⋊C4—3021no—
292C22⋊C4C22⋊D15111yescharacteristic
293C22⋊C4C22⋊D15111yescharacteristic
294C42—21no—
295C42C22×D15111yescharacteristic
296C23—21no—
297C23—3021no—
298C23C2×C22⋊D15111yescharacteristic
299C23C2×C22⋊D15111yescharacteristic
300Q8—3021no—
301Q8—3021no—
302Q8—3021no—
303Q8—3021no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—42no—
308D4—81no—
309D4—3021no—
310D4—6042no—
311D4—6042no—
312D4—1512no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—6042no—
326C2×C4—6042no—
327C2×C4—6042no—
328C2×C4C2×C22⋊D15111yescharacteristic
329C2×C4C2×C22⋊D15111yescharacteristic
330C2×C4C2×C22⋊D15111yescharacteristic
331C2×C4C2×C22⋊D15111yescharacteristic
332C2×C4C23×D15111yescharacteristic
333C8—3021no—
334C8—3021no—
335C8—3021no—
336C8—3021no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3022no—
347C22—6041no—
348C22—6041no—
349C22C22×C22⋊D15111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—6041no—
358C4—6041no—
359C4—6041no—
360C4#41×D15111yescharacteristic
361C4#1801278511yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—6042no—
366C2#2375285011yescharacteristic
367C2#2375301011yescharacteristic
368C2#2375302311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#553×C151C2
socleC22×C151C22×D4
hypercenter#553D151
hypocenterC151#3307
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #23752867C2semidirect
2. #23752582C2semidirect
3. #23752553C2semidirect
4. #23752542C2semidirect
5. #23752509C2semidirect
6. #23752456C2semidirect
7. #23752439C2semidirect
8. #23752417C2semidirect
9. #23752355C2semidirect
10. #23752355C2semidirect
11. #23752322C2semidirect
12. #23752284C2semidirect
13. #23752211C2semidirect
14. #23752206C2semidirect
15. #553×C151C2semidirect
184. C151#3307semidirect
186. #553D151semidirect

Maximal subgroups

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

subgroupindex
#237528672
#237525822
#237525532
#237525422
#237525092
#237524562
#237524392
#237524172
#237523552
#237523222
#237522842
#237522112
#237522062
#553×C1512
#3307151