Finite Group Databasebeta

← #34081820

Subgroups — #34081820

Order 19328.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752918C211yesmaximal, characteristic, complemented
2#23752883C211yesmaximal, characteristic, complemented
3#23752578C211yesmaximal, characteristic, complemented
4#23752575C211yesmaximal, characteristic, complemented
5#23752557C211yesmaximal, characteristic, complemented
6#23752515C211yesmaximal, characteristic, complemented
7#23752501C211yesmaximal, characteristic, complemented
8#23752408C211yesmaximal, characteristic, complemented
9#23752406C211yesmaximal, characteristic, complemented
10#23752406C211yesmaximal, characteristic, complemented
11#23752341C211yesmaximal, characteristic, complemented
12#23752323C211yesmaximal, characteristic, complemented
13#23752322C211yesmaximal, characteristic, complemented
14#23752294C211yesmaximal, characteristic, complemented
15#478×C151C211yesmaximal, characteristic, complemented
16C2×#14559004—21no—
17C2×D1208C2211yescharacteristic
18C2×D1208C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20#18012738C2211yescharacteristic
21#18012736C2211yescharacteristic
22#18012735C2211yescharacteristic
23#18012735C2211yescharacteristic
24#18012730C2211yescharacteristic
25#18012719—21no—
26#18012717—21no—
27#18012717—21no—
28#18012713—21no—
29#18012712—21no—
30#18012712—21no—
31C4×Dic302C2211yescharacteristic
32C4×D604C2211yescharacteristic
33#18012701C2211yescharacteristic
34#18012701C2211yescharacteristic
35#18012701C2211yescharacteristic
36#18012701C2211yescharacteristic
37C4⋊C4×D151—21no—
38#18012670C2211yescharacteristic
39Dic151⋊C8C2211yescharacteristic
40Dic151⋊C8C2211yescharacteristic
41#18012661C2211yescharacteristic
42#18012661C2211yescharacteristic
43#18012660C2211yescharacteristic
44#18012659C2211yescharacteristic
45#18012659C2211yescharacteristic
46#18012659C2211yescharacteristic
47#18012659C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012650C2211yescharacteristic
50#18012649C2211yescharacteristic
51C8×Dic151C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59#14559004—44no—
60C2×Dic302—21no—
61C2×Dic302D411yescharacteristic
62C2×D604—21no—
63C2×D604—21no—
64C2×D604C2311yescharacteristic
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151—21no—
74C2×C4×D151—21no—
75C2×C4×D151—21no—
76D1208—22no—
77D1208—22no—
78#14558989—22no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C4⋊Dic151—21no—
82C4⋊Dic151D411yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4D411yescharacteristic
87Dic151⋊C4D411yescharacteristic
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93C4×Dic151C2311yescharacteristic
94C4×Dic151C2311yescharacteristic
95C2×D4×C151C2311yescharacteristic
96C22×C4×C151—21no—
97C2×C8×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C4⋊C4×C151—21no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151C2311yescharacteristic
102C4⋊C4×C151C2311yescharacteristic
103C4⋊C4×C151C2311yescharacteristic
104C22⋊C4×C151—21no—
105C42×C151C2311yescharacteristic
106C22×D151—21no—
107C22×D151—21no—
108C22×D151—21no—
109Dic302—22no—
110Dic302—81no—
111D604—21no—
112D604—21no—
113D604—21no—
114D604—21no—
115D604—21no—
116D604—42no—
117D604—81no—
118D604#4112yescomplemented
119C22⋊D151—42no—
120C22⋊D151—42no—
121C22⋊D151—81no—
122C22⋊D151—81no—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C4×D151—42no—
129C4×D151—42no—
130C4×D151—42no—
131C4×D151—81no—
132C4×D151—81no—
133C151⋊C8—21no—
134C151⋊C8—21no—
135C23×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—42no—
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2411yescharacteristic
145C8×C151—21no—
146C8×C151—21no—
147C22×C151—41no—
148C22×C151—41no—
149C22×C151—41no—
150C22×C151C22×D411yescharacteristic
151C2×D151—22no—
152C2×D151—41no—
153C2×D151—41no—
154C2×D151—41no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C4×C151—21no—
161C4×C151—21no—
162C4×C151—41no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151C2×#4111yescharacteristic
166C4×C1512−1+411yescharacteristic
167Dic151—21no—
168Dic151—21no—
169Dic151—21no—
170Dic151—41no—
171Dic151AGL(1,ℤ/8)12yes—
172C2×C151—81no—
173C2×C151#54811yescharacteristic
174C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C151#57611yescharacteristic
176D151—42no—
177D151—81no—
178D151—81no—
179C151#336611yescharacteristic, complemented, Sylow
180#3366—1511nomaximal, Sylow
181#554—1511no—
182#550—1511no—
183#490—1511no—
184#490—1511no—
185#486—1511no—
186#478—1511no—
187#478D15111yescharacteristic, complemented
188#476—1511no—
189#459—1511no—
190#459—1511no—
191#459—1511no—
192#446—1511no—
193#442—1511no—
194#442—1511no—
195C4×D8—1511no—
196C2×#41—3021no—
197C2×D8—1511no—
198C2×D8—1511no—
199C2×D8—1511no—
200C4⋊Q8—1511no—
201#127—1511no—
202#127—1511no—
203#127—1511no—
204#125—1511no—
205#125C2×D15111yescharacteristic
206C22⋊Q8—3021no—
207C22⋊Q8—3021no—
208C22⋊Q8—3021no—
209#121—3021no—
210#121—3021no—
211#121—3021no—
212C4×Q8—1511no—
213C4×D4—1511no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4—1511no—
217C4×D4—1511no—
218C4×D4C2×D15111yescharacteristic
219C2×C4⋊C4—3021no—
220#107C2×D15111yescharacteristic
221#106—1511no—
222#106C2×D15111yescharacteristic
223C4⋊C8—1511no—
224C4⋊C8—1511no—
225C4⋊C8C2×D15111yescharacteristic
226#102—1511no—
227#102—1511no—
228#102—1511no—
229#102—1511no—
230#102—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102C2×D15111yescharacteristic
235#102C2×D15111yescharacteristic
236#97—1511no—
237#97—1511no—
238C4×C8—1511no—
239#41—6044no—
240C2×Q8—3021no—
241C2×Q8—1511no—
242C2×D4—3021no—
243C2×D4—3021no—
244C2×D4—3021no—
245C2×D4—3021no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4—1511no—
250C2×D4—1511no—
251C2×D4C22×D15111yescharacteristic
252C22×C4—21no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4—3021no—
258D8—3022no—
259D8—3022no—
260D8—3022no—
261C2×C8—1511no—
262C2×C8—1511no—
263C2×C8C22×D15111yescharacteristic
264C2×C8C22×D15111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—1511no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4—1511no—
274C4⋊C4C22×D15111yescharacteristic
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C42—1511no—
284C42—1511no—
285C42C22×D15111yescharacteristic
286C23—21no—
287C23—3021no—
288C23—3021no—
289C23—3021no—
290Q8—3022no—
291Q8—12081no—
292D4—21no—
293D4—21no—
294D4—3021no—
295D4—3021no—
296D4—3021no—
297D4—3021no—
298D4—3021no—
299D4—6042no—
300D4—6042no—
301D4—6042no—
302D4—1512no—
303D4—12081no—
304D4—12081no—
305D4—12081no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—3021no—
311C2×C4—6042no—
312C2×C4—6042no—
313C2×C4—6042no—
314C2×C4—1511no—
315C2×C4—1511no—
316C2×C4—1511no—
317C2×C4—1511no—
318C2×C4—12081no—
319C2×C4—12081no—
320C2×C4D4×D15111yescharacteristic
321C2×C4D4×D15111yescharacteristic
322C2×C4C23×D15111yescharacteristic
323C8—21no—
324C8—21no—
325C8—3021no—
326C8—3021no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—3022no—
331C22—6041no—
332C22—6041no—
333C22—6041no—
334C22—6041no—
335C22—6041no—
336C22—6041no—
337C22—6041no—
338C22—6041no—
339C22C2×D4×D15111yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—3021no—
346C4—3021no—
347C4—3021no—
348C4—6041no—
349C4—1512no—
350C4#41×D15111yescharacteristic
351C4#1801278711yescharacteristic
352C2—81no—
353C2—6042no—
354C2—12081no—
355C2—12081no—
356C2#2375287211yescharacteristic
357C2AGL(1,ℤ/8)×D15111yescharacteristic
358C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#478×C151C2
socleC22×C151C22×D4
hypercenter#478D151
hypocenterC151#3366
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23752918C2semidirect
2. #23752883C2semidirect
3. #23752578C2semidirect
4. #23752575C2semidirect
5. #23752557C2semidirect
6. #23752515C2semidirect
7. #23752501C2semidirect
8. #23752408C2semidirect
9. #23752406C2semidirect
10. #23752406C2semidirect
11. #23752341C2semidirect
12. #23752323C2semidirect
13. #23752322C2semidirect
14. #23752294C2semidirect
15. #478×C151C2semidirect
118. D604#41semidirect
179. C151#3366semidirect
187. #478D151semidirect

Maximal subgroups

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

subgroupindex
#237529182
#237528832
#237525782
#237525752
#237525572
#237525152
#237525012
#237524082
#237524062
#237523412
#237523232
#237523222
#237522942
#478×C1512
#3366151