Finite Group Databasebeta

← #34079726

Subgroups — #34079726

Order 19328.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752836C211yesmaximal, characteristic, complemented
2#23752831C211yesmaximal, characteristic, complemented
3#23752608C211yesmaximal, characteristic, complemented
4#23752594C211yesmaximal, characteristic, complemented
5#23752572C211yesmaximal, characteristic, complemented
6#23752469C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic
8#23752444C211yesmaximal, characteristic, complemented
9#23752440C211yesmaximal, characteristic, complemented
10#23752321C211yesmaximal, characteristic, complemented
11#23752316C211yesmaximal, characteristic, complemented
12#23752303C211yesmaximal, characteristic, complemented
13#23752297C211yesmaximal, characteristic, complemented
14#23752169C211yesmaximal, characteristic, complemented
15#489×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×#14558991C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012739C2211yescharacteristic
23#18012734—21no—
24#18012732—21no—
25#18012728—21no—
26#18012727C2211yescharacteristic
27#18012725—21no—
28#18012724—21no—
29#18012723—21no—
30#18012719C2211yescharacteristic
31#18012716—21no—
32#18012715—21no—
33#18012715C2211yescharacteristic
34#18012714C2211yescharacteristic
35#18012710C2211yescharacteristic
36Q8×Dic151C2211yescharacteristic
37#18012704C2211yescharacteristic
38D4×Dic151C2211yescharacteristic
39#18012701C2211yescharacteristic
40#18012696C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012670C2211yescharacteristic
43#18012670C2211yescharacteristic
44#18012670C2211yescharacteristic
45#18012664C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012649C2211yescharacteristic
50C4×C151⋊C8C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53#124×C151C2211yescharacteristic
54#103×C151C2211yescharacteristic
55#103×C151C2211yescharacteristic
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#97×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151C2311yescharacteristic
67#14558994—22no—
68#14558992—22no—
69#14558991—22no—
70#14558989—22no—
71#14558987—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C8×D151—22no—
75C4⋊Dic151—21no—
76C4⋊Dic151—21no—
77C4⋊Dic151—21no—
78C4⋊Dic151C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4D411yescharacteristic
83Dic151⋊C4D411yescharacteristic
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4D411yescharacteristic
93(C2×D151)⋊C4D411yescharacteristic
94C4×Dic151—21no—
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151—21no—
98C2×Q8×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151C2×D411yescharacteristic
110Dic302—21no—
111Dic302—21no—
112Dic302—81no—
113D604—21no—
114D604—21no—
115D604—81no—
116C22⋊D151—81no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—81no—
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C4×D151—21no—
125C4×D151—21no—
126C4×D151—81no—
127C151⋊C8#4112yes—
128C151⋊C8#4112yes—
129C23×C151—21no—
130Q8×C151—21no—
131Q8×C151—21no—
132Q8×C151—81no—
133D4×C151—21no—
134D4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151C2×D411yescharacteristic
139C2×C4×C151C2×D411yescharacteristic
140C2×C4×C151C2411yescharacteristic
141C8×C151—21no—
142C8×C151—21no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151—41no—
146C22×C151C22×D411yescharacteristic
147C2×D151—21no—
148C2×D151—21no—
149C2×D151—21no—
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
153C4×C151—21no—
154C4×C151—21no—
155C4×C151—41no—
156C4×C151—41no—
157C4×C151—41no—
158C4×C151C2×#4111yescharacteristic
159C4×C151C2×#4111yescharacteristic
160Dic151—21no—
161Dic151—21no—
162Dic151—21no—
163Dic151—41no—
164Dic151—41no—
165Dic151—41no—
166C2×C151—81no—
167C2×C151#53211yescharacteristic
168C2×C151#57711yescharacteristic
169C2×C151#57711yescharacteristic
170D151—41no—
171D151—81no—
172C151#317311yescharacteristic, complemented, Sylow
173#3173—1511nomaximal, Sylow
174#542—1511no—
175#542—1511no—
176#498—1511no—
177#495—1511no—
178#489—1511no—
179#489D15111yescharacteristic, complemented
180#470—1511no—
181#469—1511no—
182#465—1511no—
183#465—1511no—
184#442—1511no—
185#441—1511no—
186C4×SD16—1511no—
187C4×SD16—1511no—
188#405—1511no—
189C2×Q16—1511no—
190C2×SD16—1511no—
191C2×SD16—1511no—
192C2×D8—1511no—
193C2×M16—1511no—
194C22×C8—1511no—
195C4⋊Q8—1511no—
196C4⋊Q8C2×D15111yescharacteristic
197#126—3021no—
198#126—3021no—
199#124—3021no—
200#124—3021no—
201#124—1511no—
202#124C2×D15111yescharacteristic
203#123—3021no—
204#123—3021no—
205C22⋊Q8—3021no—
206C22⋊Q8—3021no—
207C22⋊Q8—1511no—
208C22⋊Q8—1511no—
209#121—1511no—
210#121—1511no—
211C4×Q8—1511no—
212C4×Q8—1511no—
213C4×D4—1511no—
214C4×D4—1511no—
215#117—1511no—
216#106—1511no—
217#106—1511no—
218#106—1511no—
219#106—1511no—
220#103—1511no—
221#103—1511no—
222#103C2×D15111yescharacteristic
223#103C2×D15111yescharacteristic
224#102—1511no—
225#102—1511no—
226#102C2×D15111yescharacteristic
227#102C2×D15111yescharacteristic
228#97—1511no—
229#97C2×D15111yescharacteristic
230C4×C8—1511no—
231C4×C8—1511no—
232C2×Q8—21no—
233C2×Q8—3021no—
234C2×Q8—1511no—
235C2×Q8C22×D15111yescharacteristic
236C2×D4—3021no—
237C2×D4—3021no—
238C2×D4—1511no—
239C2×D4C22×D15111yescharacteristic
240C22×C4—3021no—
241C22×C4—3021no—
242C22×C4—1511no—
243Q16—3022no—
244SD16—3022no—
245SD16—3022no—
246D8—3022no—
247M16—3022no—
248C2×C8—3022no—
249C2×C8—1511no—
250C2×C8—1511no—
251C2×C8C22×D15111yescharacteristic
252C2×C8C22×D15111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—3021no—
255C4⋊C4—3021no—
256C4⋊C4—3021no—
257C4⋊C4—3021no—
258C4⋊C4—3021no—
259C4⋊C4—1511no—
260C4⋊C4—1511no—
261C4⋊C4—1511no—
262C4⋊C4—1511no—
263C4⋊C4C22×D15111yescharacteristic
264C4⋊C4C22×D15111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—3021no—
268C22⋊C4—3021no—
269C22⋊C4—3021no—
270C22⋊C4—3021no—
271C22⋊C4—3021no—
272C22⋊C4—3021no—
273C22⋊C4—3021no—
274C22⋊C4—3021no—
275C22⋊C4—1511no—
276C22⋊C4—1511no—
277C42—3021no—
278C42—3021no—
279C42—1511no—
280C42C22×D15111yescharacteristic
281C23—21no—
282C23—3021no—
283C23—1511no—
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—3021no—
288Q8—3021no—
289Q8—12081no—
290D4—21no—
291D4—21no—
292D4—3021no—
293D4—3021no—
294D4—12081no—
295D4—12081no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—3021no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—1511no—
305C2×C4—1511no—
306C2×C4—1511no—
307C2×C4—12081no—
308C2×C4—12081no—
309C2×C4D4×D15111yescharacteristic
310C2×C4D4×D15111yescharacteristic
311C2×C4C23×D15111yescharacteristic
312C8—21no—
313C8—21no—
314C8—1512no—
315C8—1512no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—3021no—
320C22—3021no—
321C22—3021no—
322C22—6041no—
323C22—6041no—
324C22—6041no—
325C22C2×D4×D15111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3021no—
332C4—3021no—
333C4—3021no—
334C4—6041no—
335C4—6041no—
336C4—6041no—
337C4#41×D15111yescharacteristic
338C4#41×D15111yescharacteristic
339C2—81no—
340C2—6041no—
341C2—12081no—
342C2#2375276111yescharacteristic
343C2#2375302111yescharacteristic
344C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#489×C151C2
socleC22×C151C22×D4
prime radical#23752464C2
hypercenter#489D151
hypocenterC151#3173
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #23752836C2semidirect
2. #23752831C2semidirect
3. #23752608C2semidirect
4. #23752594C2semidirect
5. #23752572C2semidirect
6. #23752469C2semidirect
8. #23752444C2semidirect
9. #23752440C2semidirect
10. #23752321C2semidirect
11. #23752316C2semidirect
12. #23752303C2semidirect
13. #23752297C2semidirect
14. #23752169C2semidirect
15. #489×C151C2semidirect
172. C151#3173semidirect
179. #489D151semidirect

Maximal subgroups

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

subgroupindex
#237528362
#237528312
#237526082
#237525942
#237525722
#237524692
#237524642
#237524442
#237524402
#237523212
#237523162
#237523032
#237522972
#237521692
#489×C1512
#3173151