Finite Group Databasebeta

← #34079373

Subgroups — #34079373

Order 19328.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752835C211yesmaximal, characteristic, complemented
2#23752695C211yesmaximal, characteristic, complemented
3#23752545C211yesmaximal, characteristic, complemented
4#23752526C211yesmaximal, characteristic, complemented
5#23752505C211yesmaximal, characteristic, complemented
6#23752490C211yesmaximal, characteristic, complemented
7#23752436C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752357C211yesmaximal, characteristic
10#23752315C211yesmaximal, characteristic, complemented
11#23752313C211yesmaximal, characteristic, complemented
12Q16×Dic151C211yesmaximal, characteristic, complemented
13#23752292C211yesmaximal, characteristic, complemented
14#23752270C211yesmaximal, characteristic, complemented
15#452×C151C211yesmaximal, characteristic, complemented
16C2×#14558991C2211yescharacteristic
17C2×#14558989C2211yescharacteristic
18#18012738C2211yescharacteristic
19#18012734—21no—
20#18012728C2211yescharacteristic
21#18012725—21no—
22#18012721—21no—
23#18012719—21no—
24#18012713C2211yescharacteristic
25Q8×Dic151C2211yescharacteristic
26Q8×Dic151C2211yescharacteristic
27Q8×Dic151C2211yescharacteristic
28D4×Dic151—21no—
29D4×Dic151—21no—
30D4×Dic151C2211yescharacteristic
31D4×Dic151C2211yescharacteristic
32#18012701C2211yescharacteristic
33#18012698—21no—
34#18012698C2211yescharacteristic
35C2×C4⋊Dic151—21no—
36C2×C4⋊Dic151C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012672C2211yescharacteristic
41Dic151⋊C8C2211yescharacteristic
42Dic151⋊C8C2211yescharacteristic
43#18012663C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012660C2211yescharacteristic
49C22⋊(C151⋊C8)C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C2×#41×C151C2211yescharacteristic
53C2×Q16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C22⋊Q8×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58C22⋊C8×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C22×Dic151—21no—
63C22×Dic151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66#14558991—22no—
67#14558989—22no—
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2311yescharacteristic
70C4⋊Dic151—21no—
71C4⋊Dic151—21no—
72C4⋊Dic151—21no—
73C4⋊Dic151—21no—
74C4⋊Dic151D411yescharacteristic
75C4⋊Dic151D411yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80C22⋊Dic151—21no—
81C22⋊Dic151—21no—
82C22⋊Dic151D411yescharacteristic
83C22⋊Dic151D411yescharacteristic
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88C4×Dic151—21no—
89C4×Dic151—21no—
90C4×Dic151—21no—
91C4×Dic151C2311yescharacteristic
92C4×Dic151C2311yescharacteristic
93#41×C151—22no—
94#41×C151—22no—
95C2×Q8×C151C2311yescharacteristic
96C2×Q8×C151C2311yescharacteristic
97C2×D4×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100C22×C4×C151C2311yescharacteristic
101Q16×C151—22no—
102SD16×C151—22no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151—21no—
106C4⋊C4×C151C2311yescharacteristic
107C22⋊C4×C151—21no—
108C22×D151—21no—
109Dic302—81no—
110D604—21no—
111D604—21no—
112C22⋊D151—81no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—81no—
117C2×Dic151—81no—
118C2×Dic151—81no—
119C2×Dic151C2×D411yescharacteristic
120C2×Dic151C2×D411yescharacteristic
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C4×D151—81no—
124C151⋊C8—21no—
125C151⋊C8—21no—
126C23×C151—21no—
127C23×C151C2×D411yescharacteristic
128Q8×C151—21no—
129Q8×C151—21no—
130Q8×C151—21no—
131Q8×C151#4112yes—
132D4×C151—24no—
133D4×C151—21no—
134D4×C151#4112yes—
135C2×C4×C151—24no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2411yescharacteristic
143C8×C151—21no—
144C8×C151—21no—
145C22×C151—21no—
146C22×C151—22no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151C22×D411yescharacteristic
152C2×D151—41no—
153C2×D151—41no—
154C2×D151—41no—
155C4×C151—21no—
156C4×C151—22no—
157C4×C151—41no—
158C4×C151—41no—
159C4×C151C2×#4111yescharacteristic
160C4×C151C2×#4111yescharacteristic
161Dic151—21no—
162Dic151—21no—
163Dic151—21no—
164Dic151—21no—
165Dic151—41no—
166Dic151—41no—
167Dic151—41no—
168C2×C151—41no—
169C2×C151—42no—
170C2×C151#52511yescharacteristic
171C2×C151#57611yescharacteristic
172C2×C151#57811yescharacteristic
173D151—81no—
174C151#312411yescharacteristic, complemented, Sylow
175#3124—1511nomaximal, Sylow
176#542—1511no—
177#520—1511no—
178#484—1511no—
179#480—1511no—
180#477—1511no—
181#474—1511no—
182#464—1511no—
183#463—1511no—
184#452D15111yescharacteristic, complemented
185#449—1511no—
186#440—1511no—
187#440—1511no—
188C4×Q16—1511no—
189C4×D8—1511no—
190#433—1511no—
191C2×#41C2×D15111yescharacteristic
192C2×Q16C2×D15111yescharacteristic
193C2×SD16—1511no—
194C2×SD16C2×D15111yescharacteristic
195C2×D8—1511no—
196C4⋊Q8—1511no—
197#126—3021no—
198#124—3021no—
199#124—1511no—
200#123—3021no—
201C22⋊Q8—3021no—
202C22⋊Q8C2×D15111yescharacteristic
203#121—1511no—
204C4×Q8—1511no—
205C4×Q8—1511no—
206C4×Q8—1511no—
207C4×D4—3021no—
208C4×D4—3021no—
209C4×D4—1511no—
210C4×D4—1511no—
211C4×D4—1511no—
212#117—3021no—
213#117—1511no—
214C2×C4⋊C4—3021no—
215C2×C4⋊C4—1511no—
216#107—1511no—
217#107—1511no—
218#107—1511no—
219#107—1511no—
220C4⋊C8—1511no—
221C4⋊C8—1511no—
222#103—1511no—
223#103—1511no—
224#103—1511no—
225#103C2×D15111yescharacteristic
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102C2×D15111yescharacteristic
230C22⋊C8—1511no—
231C22⋊C8C2×D15111yescharacteristic
232#97—1511no—
233C4×C8—1511no—
234#41—22no—
235#41—22no—
236C2×Q8—3021no—
237C2×Q8C22×D15111yescharacteristic
238C2×Q8C22×D15111yescharacteristic
239C2×D4—21no—
240C2×D4—3021no—
241C2×D4—1511no—
242C2×D4C22×D15111yescharacteristic
243C22×C4—21no—
244C22×C4—3021no—
245C22×C4—3021no—
246C22×C4—3021no—
247C22×C4—3021no—
248C22×C4C22×D15111yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—3022no—
252D8—3022no—
253C2×C8—1511no—
254C2×C8—1511no—
255C2×C8C22×D15111yescharacteristic
256C2×C8C22×D15111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—3021no—
259C4⋊C4—3021no—
260C4⋊C4—3021no—
261C4⋊C4—3021no—
262C4⋊C4—3021no—
263C4⋊C4—1511no—
264C4⋊C4—1511no—
265C4⋊C4—1511no—
266C4⋊C4—1511no—
267C4⋊C4—1511no—
268C4⋊C4C22×D15111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4—1511no—
277C22⋊C4—1511no—
278C42—3021no—
279C42—3021no—
280C42—3021no—
281C42—1511no—
282C42—1511no—
283C23—21no—
284C23—3021no—
285C23D4×D15111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—12081no—
290Q8#1455900312yes—
291D4—24no—
292D4—21no—
293D4—3021no—
294D4—3021no—
295D4—12081no—
296D4#1455900312yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—1511no—
307C2×C4—1511no—
308C2×C4—1511no—
309C2×C4—1511no—
310C2×C4—12081no—
311C2×C4—12081no—
312C2×C4—12081no—
313C2×C4—12081no—
314C2×C4D4×D15111yescharacteristic
315C2×C4C23×D15111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3021no—
319C8—3021no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—6041no—
327C22—6041no—
328C22—6041no—
329C22C2×D4×D15111yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—3021no—
335C4—3021no—
336C4—3021no—
337C4—3021no—
338C4—6041no—
339C4—6041no—
340C4—6041no—
341C4C2×#1455900311yescharacteristic
342C4C2×#1455900311yescharacteristic
343C2—41no—
344C2—42no—
345C2—12081no—
346C2#2375271811yescharacteristic
347C2#2375301411yescharacteristic
348C2#2375302811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#452×C151C2
socleC22×C151C22×D4
prime radical#23752357C2
hypercenter#452D151
hypocenterC151#3124
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #23752835C2semidirect
2. #23752695C2semidirect
3. #23752545C2semidirect
4. #23752526C2semidirect
5. #23752505C2semidirect
6. #23752490C2semidirect
7. #23752436C2semidirect
8. #23752429C2semidirect
10. #23752315C2semidirect
11. #23752313C2semidirect
12. Q16×Dic151C2semidirect
13. #23752292C2semidirect
14. #23752270C2semidirect
15. #452×C151C2semidirect
174. C151#3124semidirect
184. #452D151semidirect

Maximal subgroups

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

subgroupindex
#237528352
#237526952
#237525452
#237525262
#237525052
#237524902
#237524362
#237524292
#237523572
#237523152
#237523132
Q16×Dic1512
#237522922
#237522702
#452×C1512
#3124151