Finite Group Databasebeta

← #34080548

Subgroups — #34080548

Order 19328.

370 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#23752818C211yesmaximal, characteristic, complemented
2#23752813C211yesmaximal, characteristic, complemented
3#23752515C211yesmaximal, characteristic, complemented
4#23752511C211yesmaximal, characteristic, complemented
5#23752509C211yesmaximal, characteristic, complemented
6#23752466C211yesmaximal, characteristic, complemented
7#23752464C211yesmaximal, characteristic, complemented
8#23752449C211yesmaximal, characteristic, complemented
9#23752447C211yesmaximal, characteristic, complemented
10#23752408C211yesmaximal, characteristic, complemented
11#23752407C211yesmaximal, characteristic, complemented
12#23752406C211yesmaximal, characteristic, complemented
13#23752406C211yesmaximal, characteristic, complemented
14#23752237C211yesmaximal, characteristic, complemented
15#478×C151C211yesmaximal, characteristic, complemented
16C2×D1208C2211yescharacteristic
17C2×D1208C2211yescharacteristic
18C2×#14558989C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012736C2211yescharacteristic
23#18012735C2211yescharacteristic
24#18012730C2211yescharacteristic
25#18012724—21no—
26#18012724—21no—
27#18012722—21no—
28#18012721—21no—
29#18012714—21no—
30#18012714—21no—
31#18012714C2211yescharacteristic
32#18012714C2211yescharacteristic
33#18012714C2211yescharacteristic
34#18012713—21no—
35#18012712—21no—
36#18012710C2211yescharacteristic
37C4×D604C2211yescharacteristic
38#18012701C2211yescharacteristic
39#18012701C2211yescharacteristic
40#18012696C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012659C2211yescharacteristic
51#18012659C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×D604—21no—
60C2×D604—21no—
61C2×D604—21no—
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×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151—21no—
73C2×C4×D151C2311yescharacteristic
74D1208—41no—
75D1208—41no—
76#14558989—41no—
77#14558989—41no—
78#14558987—41no—
79C2×C151⋊C8C2311yescharacteristic
80C2×C151⋊C8C2311yescharacteristic
81C8×D151—41no—
82C4⋊Dic151—21no—
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4D411yescharacteristic
86Dic151⋊C4D411yescharacteristic
87C22⋊Dic151—21no—
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—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4D411yescharacteristic
95(C2×D151)⋊C4D411yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×D4×C151C2311yescharacteristic
98C22×C4×C151—21no—
99C2×C8×C151C2311yescharacteristic
100C2×C8×C151C2311yescharacteristic
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—21no—
111C22×D151C2×D411yescharacteristic
112D604—21no—
113D604—21no—
114D604—21no—
115D604—21no—
116D604—21no—
117D604—21no—
118D604—81no—
119D604—81no—
120D604—81no—
121D604—81no—
122D604—81no—
123C22⋊D151—81no—
124C22⋊D151—81no—
125C22⋊D151—81no—
126C2×Dic151—21no—
127C2×Dic151C2×D411yescharacteristic
128C2×Dic151C2×D411yescharacteristic
129C2×Dic151C2×D411yescharacteristic
130C4×D151—21no—
131C4×D151—21no—
132C4×D151—81no—
133C4×D151—81no—
134C4×D151—81no—
135C151⋊C8—21no—
136C151⋊C8—21no—
137C23×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—81no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2411yescharacteristic
147C8×C151—21no—
148C8×C151—21no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151C22×D411yescharacteristic
153C2×D151—21no—
154C2×D151—21no—
155C2×D151—21no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C2×D151—41no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151H(5,𝔽2)11yescharacteristic
171C4×C1512−1+411yescharacteristic
172Dic151—21no—
173Dic151—21no—
174Dic151—21no—
175Dic151—41no—
176C2×C151—81no—
177C2×C151#53711yescharacteristic
178C2×C151#57611yescharacteristic
179C2×C151#57611yescharacteristic
180D151—41no—
181D151—81no—
182D151—81no—
183D151—81no—
184C151#325911yescharacteristic, complemented, Sylow
185#3259—1511nomaximal, Sylow
186#540—1511no—
187#540—1511no—
188#478—1511no—
189#478—1511no—
190#478—1511no—
191#478D15111yescharacteristic, complemented
192#469—1511no—
193#469—1511no—
194#466—1511no—
195#466—1511no—
196#459—1511no—
197#459—1511no—
198#459—1511no—
199#459—1511no—
200#424—1511no—
201C2×D8—1511no—
202C2×D8—1511no—
203C2×D8—1511no—
204C2×D8—1511no—
205C2×M16—1511no—
206C22×C8—1511no—
207#127—1511no—
208#127—1511no—
209#125—1511no—
210#125C2×D15111yescharacteristic
211#123—3021no—
212#123—3021no—
213#123—3021no—
214#123—3021no—
215#121—3021no—
216#121—3021no—
217#121—3021no—
218#121—3021no—
219#121—1511no—
220#121—1511no—
221#121—1511no—
222#121—1511no—
223C4×D4—1511no—
224C4×D4—1511no—
225C4×D4—1511no—
226C4×D4C2×D15111yescharacteristic
227#117—1511no—
228#107—1511no—
229#107C2×D15111yescharacteristic
230#106—1511no—
231#106C2×D15111yescharacteristic
232C4⋊C8—1511no—
233C4⋊C8—1511no—
234C4⋊C8—1511no—
235C4⋊C8C2×D15111yescharacteristic
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#102—1511no—
241#102—1511no—
242#102C2×D15111yescharacteristic
243#102C2×D15111yescharacteristic
244C2×D4—3021no—
245C2×D4—3021no—
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—3021no—
249C2×D4—3021no—
250C2×D4—3021no—
251C2×D4—3021no—
252C2×D4—1511no—
253C2×D4—1511no—
254C2×D4—1511no—
255C2×D4C22×D15111yescharacteristic
256C22×C4—21no—
257C22×C4—3021no—
258C22×C4—3021no—
259C22×C4—3021no—
260C22×C4—1511no—
261D8—6041no—
262D8—6041no—
263D8—6041no—
264D8—6041no—
265M16—6041no—
266C2×C8—6041no—
267C2×C8—1511no—
268C2×C8—1511no—
269C2×C8C22×D15111yescharacteristic
270C2×C8C22×D15111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—3021no—
274C4⋊C4—3021no—
275C4⋊C4—1511no—
276C4⋊C4—1511no—
277C4⋊C4—1511no—
278C4⋊C4C22×D15111yescharacteristic
279C4⋊C4C22×D15111yescharacteristic
280C4⋊C4C22×D15111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—1511no—
290C22⋊C4—1511no—
291C42—1511no—
292C42C22×D15111yescharacteristic
293C23—21no—
294C23—3021no—
295C23—3021no—
296C23—3021no—
297C23—1511no—
298D4—21no—
299D4—21no—
300D4—3021no—
301D4—3021no—
302D4—3021no—
303D4—3021no—
304D4—3021no—
305D4—3021no—
306D4—12081no—
307D4—12081no—
308D4—12081no—
309D4—12081no—
310D4—12081no—
311D4—12081no—
312D4—12081no—
313D4—12081no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—81no—
318C2×C4—3021no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—1511no—
322C2×C4—1511no—
323C2×C4—1511no—
324C2×C4—12081no—
325C2×C4—12081no—
326C2×C4—12081no—
327C2×C4D4×D15111yescharacteristic
328C2×C4D4×D15111yescharacteristic
329C2×C4C23×D15111yescharacteristic
330C8—21no—
331C8—21no—
332C8—3021no—
333C8—3021no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3021no—
338C22—3021no—
339C22—3021no—
340C22—6041no—
341C22—6041no—
342C22—6041no—
343C22—6041no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22—6041no—
348C22—6041no—
349C22C2×D4×D15111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3021no—
356C4—3021no—
357C4—3021no—
358C4—6041no—
359C4#1801278511yescharacteristic
360C4#1801278711yescharacteristic
361C2—81no—
362C2—6041no—
363C2—12081no—
364C2—12081no—
365C2—12081no—
366C2#2375279211yescharacteristic
367C2#2375301411yescharacteristic
368C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#478×C151C2
socleC22×C151C22×D4
hypercenter#478D151
hypocenterC151#3259
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. #23752818C2semidirect
2. #23752813C2semidirect
3. #23752515C2semidirect
4. #23752511C2semidirect
5. #23752509C2semidirect
6. #23752466C2semidirect
7. #23752464C2semidirect
8. #23752449C2semidirect
9. #23752447C2semidirect
10. #23752408C2semidirect
11. #23752407C2semidirect
12. #23752406C2semidirect
13. #23752406C2semidirect
14. #23752237C2semidirect
15. #478×C151C2semidirect
184. C151#3259semidirect
191. #478D151semidirect

Maximal subgroups

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

subgroupindex
#237528182
#237528132
#237525152
#237525112
#237525092
#237524662
#237524642
#237524492
#237524472
#237524082
#237524072
#237524062
#237522372
#478×C1512
#3259151