Finite Group Databasebeta

← #34079309

Subgroups — #34079309

Order 19328.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752817C211yesmaximal, characteristic, complemented
2#23752530C211yesmaximal, characteristic, complemented
3#23752525C211yesmaximal, characteristic, complemented
4#23752519C211yesmaximal, characteristic, complemented
5#23752512C211yesmaximal, characteristic, complemented
6#23752412C211yesmaximal, characteristic, complemented
7#23752407C211yesmaximal, characteristic, complemented
8#23752357C211yesmaximal, characteristic, complemented
9#23752357C211yesmaximal, characteristic, complemented
10#23752322C211yesmaximal, characteristic, complemented
11#23752310C211yesmaximal, characteristic, complemented
12C4×#14558991C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14#23752273C211yesmaximal, characteristic, complemented
15#520×C151C211yesmaximal, characteristic, complemented
16C2×#14558991C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20#18012736C2211yescharacteristic
21#18012731C2211yescharacteristic
22#18012724—21no—
23#18012724—21no—
24#18012713C2211yescharacteristic
25#18012713C2211yescharacteristic
26#18012712—21no—
27#18012712—21no—
28C4×D604C2211yescharacteristic
29C4×D604C2211yescharacteristic
30#18012672C2211yescharacteristic
31#18012672C2211yescharacteristic
32#18012670C2211yescharacteristic
33#18012670C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35C4⋊(C151⋊C8)C2211yescharacteristic
36#18012663C2211yescharacteristic
37#18012663C2211yescharacteristic
38#18012660C2211yescharacteristic
39#18012660C2211yescharacteristic
40#18012659C2211yescharacteristic
41#18012659C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46#18012650C2211yescharacteristic
47C4×C151⋊C8C2211yescharacteristic
48C2×#41×C151C2211yescharacteristic
49C4×Q8×C151C2211yescharacteristic
50C4×Q8×C151C2211yescharacteristic
51C4×D4×C151—21no—
52C4×D4×C151—21no—
53C4×D4×C151C2211yescharacteristic
54C4×D4×C151C2211yescharacteristic
55#117×C151—21no—
56#117×C151C2211yescharacteristic
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151C2211yescharacteristic
59C2×D604—21no—
60C2×D604—21no—
61C2×D604C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67#14558991—22no—
68#14558991—22no—
69#14558989—22no—
70#14558989—22no—
71C2×C151⋊C8C2311yescharacteristic
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79(C2×D151)⋊C4—21no—
80(C2×D151)⋊C4—21no—
81(C2×D151)⋊C4—21no—
82(C2×D151)⋊C4—21no—
83#41×C151—22no—
84#41×C151—22no—
85C2×Q8×C151C2311yescharacteristic
86C2×D4×C151—21no—
87C2×D4×C151C2311yescharacteristic
88C22×C4×C151—21no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151—21no—
92C22×C4×C151C2311yescharacteristic
93C4⋊C4×C151—21no—
94C4⋊C4×C151—21no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151D411yescharacteristic
97C4⋊C4×C151D411yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C22⋊C4×C151—21no—
101C22⋊C4×C151—21no—
102C22⋊C4×C151D411yescharacteristic
103C22⋊C4×C151D411yescharacteristic
104C42×C151—21no—
105C42×C151—21no—
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110D604—21no—
111D604—21no—
112D604—21no—
113D604—21no—
114D604—81no—
115D604—81no—
116C22⋊D151—81no—
117C22⋊D151—81no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C4×D151—81no—
121C4×D151—81no—
122C151⋊C8—21no—
123C151⋊C8—21no—
124C151⋊C8—21no—
125C151⋊C8—21no—
126C23×C151—21no—
127C23×C151C2×D411yescharacteristic
128Q8×C151—21no—
129Q8×C151#4112yes—
130D4×C151—24no—
131D4×C151—21no—
132D4×C151#4112yes—
133C2×C4×C151—24no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—81no—
140C2×C4×C151—81no—
141C2×C4×C151—81no—
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2411yescharacteristic
148C22×C151—21no—
149C22×C151—22no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151C22×D411yescharacteristic
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C4×C151—21no—
162C4×C151—22no—
163C4×C151—21no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151C2×#4111yescharacteristic
170C4×C151C2×#4111yescharacteristic
171Dic151—41no—
172Dic151—41no—
173C2×C151—41no—
174C2×C151—42no—
175C2×C151#52511yescharacteristic
176C2×C151#57611yescharacteristic
177C2×C151#57711yescharacteristic
178D151—81no—
179D151—81no—
180C151#311911yescharacteristic, complemented, Sylow
181#3119—1511nomaximal, Sylow
182#540—1511no—
183#520D15111yescharacteristic, complemented
184#481—1511no—
185#480—1511no—
186#479—1511no—
187#478—1511no—
188#460—1511no—
189#459—1511no—
190#449—1511no—
191#449—1511no—
192#442—1511no—
193#440—1511no—
194C4×SD16—1511no—
195C4×D8—1511no—
196#433—1511no—
197C2×#41C2×D15111yescharacteristic
198C2×SD16—1511no—
199C2×SD16—1511no—
200C2×D8—1511no—
201C2×D8—1511no—
202#127—1511no—
203#125—1511no—
204#123—3021no—
205#123—3021no—
206#121—3021no—
207#121—3021no—
208#121—1511no—
209#121—1511no—
210C4×Q8C2×D15111yescharacteristic
211C4×Q8C2×D15111yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4C2×D15111yescharacteristic
217C4×D4C2×D15111yescharacteristic
218#117—21no—
219#117C2×D15111yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D15111yescharacteristic
222#107—1511no—
223#107—1511no—
224#106—1511no—
225#106—1511no—
226C4⋊C8—1511no—
227C4⋊C8—1511no—
228#103—1511no—
229#103—1511no—
230#102—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236C22⋊C8—1511no—
237C22⋊C8—1511no—
238#97—1511no—
239C4×C8—1511no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D15111yescharacteristic
243C2×D4—21no—
244C2×D4—3021no—
245C2×D4—3021no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4—1511no—
250C2×D4C22×D15111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4C22×D15111yescharacteristic
258SD16—3022no—
259SD16—3022no—
260D8—3022no—
261D8—3022no—
262C2×C8—1511no—
263C2×C8—1511no—
264C2×C8—1511no—
265C2×C8—1511no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4C22⋊D15111yescharacteristic
274C4⋊C4C22⋊D15111yescharacteristic
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4C22⋊D15111yescharacteristic
284C22⋊C4C22⋊D15111yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D15111yescharacteristic
288C42C22×D15111yescharacteristic
289C23—21no—
290C23—3021no—
291C23—3021no—
292C23C2×C22⋊D15111yescharacteristic
293Q8—21no—
294Q8#1455900412yes—
295D4—24no—
296D4—21no—
297D4—3021no—
298D4—3021no—
299D4—3021no—
300D4—3021no—
301D4—12081no—
302D4—12081no—
303D4—12081no—
304D4—12081no—
305D4#1455900412yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—12081no—
318C2×C4—12081no—
319C2×C4C2×C22⋊D15111yescharacteristic
320C2×C4C2×C22⋊D15111yescharacteristic
321C2×C4C2×C22⋊D15111yescharacteristic
322C2×C4C2×C22⋊D15111yescharacteristic
323C2×C4C2×C22⋊D15111yescharacteristic
324C2×C4C23×D15111yescharacteristic
325C8—3021no—
326C8—3021no—
327C8—3021no—
328C8—3021no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—6041no—
336C22—6041no—
337C22—6041no—
338C22—6041no—
339C22—6041no—
340C22—6041no—
341C22C22×C22⋊D15111yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—6041no—
351C4—6041no—
352C4C2×#1455900411yescharacteristic
353C4C2×#1455900411yescharacteristic
354C2—41no—
355C2—42no—
356C2—12081no—
357C2—12081no—
358C2#2375272311yescharacteristic
359C2#2375301511yescharacteristic
360C2#2375302011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#520×C151C2
socleC22×C151C22×D4
hypercenter#520D151
hypocenterC151#3119
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #23752817C2semidirect
2. #23752530C2semidirect
3. #23752525C2semidirect
4. #23752519C2semidirect
5. #23752512C2semidirect
6. #23752412C2semidirect
7. #23752407C2semidirect
8. #23752357C2semidirect
9. #23752357C2semidirect
10. #23752322C2semidirect
11. #23752310C2semidirect
12. C4×#14558991C2semidirect
13. C4×#14558989C2semidirect
14. #23752273C2semidirect
15. #520×C151C2semidirect
180. C151#3119semidirect
183. #520D151semidirect

Maximal subgroups

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

subgroupindex
#237528172
#237525302
#237525252
#237525192
#237525122
#237524122
#237524072
#237523572
#237523222
#237523102
C4×#145589912
C4×#145589892
#237522732
#520×C1512
#3119151