Finite Group Databasebeta

← #34081002

Subgroups — #34081002

Order 19328.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752903C211yesmaximal, characteristic, complemented
2#23752874C211yesmaximal, characteristic
3#23752567C211yesmaximal, characteristic, complemented
4#23752555C211yesmaximal, characteristic, complemented
5#23752527C211yesmaximal, characteristic, complemented
6#23752519C211yesmaximal, characteristic, complemented
7#23752452C211yesmaximal, characteristic, complemented
8#23752444C211yesmaximal, characteristic, complemented
9#23752434C211yesmaximal, characteristic, complemented
10#23752373C211yesmaximal, characteristic, complemented
11#23752366C211yesmaximal, characteristic, complemented
12C8×D604C211yesmaximal, characteristic, complemented
13#23752207C211yesmaximal, characteristic, complemented
14#103×D151C211yesmaximal, characteristic, complemented
15C4×Q16×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×#14558994C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×C8×D151C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012733—21no—
23#18012731C2211yescharacteristic
24#18012729—21no—
25#18012727—21no—
26#18012727C2211yescharacteristic
27#18012724—21no—
28#18012719—21no—
29#18012719C2211yescharacteristic
30#18012715C2211yescharacteristic
31#18012715C2211yescharacteristic
32#18012714—21no—
33#18012714C2211yescharacteristic
34C4×D604—21no—
35C4×D604C2211yescharacteristic
36#18012697C2211yescharacteristic
37#18012696—21no—
38C4⋊C4×D151C2211yescharacteristic
39#18012672C2211yescharacteristic
40#18012670C2211yescharacteristic
41C4⋊(C151⋊C8)C2211yescharacteristic
42#18012664C2211yescharacteristic
43#18012664C2211yescharacteristic
44#18012663C2211yescharacteristic
45#18012663C2211yescharacteristic
46#18012662C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012659C2211yescharacteristic
50(C2×D151)⋊C8C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic
52C2×Q16×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54C4×Q8×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56#103×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59#14559005—22no—
60#14559005—41no—
61C2×Dic302—21no—
62C2×Dic302C2311yescharacteristic
63Q8×D151—22no—
64Q8×D151—41no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604D411yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151—21no—
72C2×C4×D151C2311yescharacteristic
73C2×C4×D151C2311yescharacteristic
74#14558994—41no—
75#14558991—41no—
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C8×D151—41no—
79C8×D151—41no—
80C4⋊Dic151—21no—
81C4⋊Dic151D411yescharacteristic
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84Dic151⋊C4—21no—
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊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)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4D411yescharacteristic
97(C2×D151)⋊C4D411yescharacteristic
98C4×Dic151—21no—
99C2×Q8×C151C2311yescharacteristic
100C2×Q8×C151C2311yescharacteristic
101Q16×C151—22no—
102C2×C8×C151C2311yescharacteristic
103C2×C8×C151C2311yescharacteristic
104C4⋊C4×C151—21no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151C2311yescharacteristic
107C4⋊C4×C151C2311yescharacteristic
108C42×C151—21no—
109C42×C151—21no—
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112C22×D151C2×D411yescharacteristic
113C22×D151C2×D411yescharacteristic
114Dic302—21no—
115Dic302—21no—
116Dic302—42no—
117D604—22no—
118D604—21no—
119D604—21no—
120D604—42no—
121D604—42no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—21no—
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—21no—
131C4×D151—42no—
132C4×D151—42no—
133C4×D151—42no—
134C151⋊C8—21no—
135C151⋊C8—21no—
136Q8×C151—21no—
137Q8×C151—21no—
138Q8×C151—21no—
139Q8×C151#4112yes—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2411yescharacteristic
147C8×C151—21no—
148C8×C151—21no—
149C22×C151C22×D411yescharacteristic
150C2×D151—21no—
151C2×D151—21no—
152C2×D151—21no—
153C2×D151—21no—
154C2×D151—21no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151#13512yes—
159C4×C151—22no—
160C4×C151—21no—
161C4×C151—21no—
162C4×C151—41no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151C2×#4111yescharacteristic
166C4×C151H(5,𝔽2)11yescharacteristic
167Dic151—21no—
168Dic151—21no—
169Dic151—41no—
170Dic151—41no—
171Dic151—41no—
172C2×C151#54611yescharacteristic
173C2×C151C2×#13511yescharacteristic
174C2×C151#57811yescharacteristic
175D151—22no—
176D151—41no—
177D151—81no—
178C151#330011yescharacteristic, complemented, Sylow
179#3300—1511nomaximal, Sylow
180#552—1511no—
181#548—1511no—
182#488—1511no—
183#485—1511no—
184#480—1511no—
185#479—1511no—
186#467—1511no—
187#465—1511no—
188#464—1511no—
189#452—1511no—
190#451—1511no—
191C4×Q16D15111yescharacteristic, complemented
192C8×D4—1511no—
193#416—1511no—
194C2×#103—1511no—
195C2×#41—1511no—
196C22×Q8—1511no—
197C2×Q16—1511no—
198C2×Q16C2×D15111yescharacteristic
199C2×SD16—1511no—
200C22×C8—1511no—
201C22×C8—1511no—
202#126—3021no—
203#125—3021no—
204#125—1511no—
205#124—3021no—
206#124—1511no—
207#123—3021no—
208C22⋊Q8—3021no—
209C22⋊Q8—1511no—
210C22⋊Q8—1511no—
211C22⋊Q8—1511no—
212#121—3021no—
213#121—1511no—
214C4×Q8C2×D15111yescharacteristic
215C4×Q8C2×D15111yescharacteristic
216C4×D4—3021no—
217C4×D4—1511no—
218#117—3021no—
219#117—1511no—
220C2×C4⋊C4—1511no—
221#107—1511no—
222#107C2×D15111yescharacteristic
223#106—1511no—
224C4⋊C8—1511no—
225#103—1511no—
226#103—1511no—
227#103—1511no—
228#103—1511no—
229#103—1511no—
230#103C2×D15111yescharacteristic
231#103C2×D15111yescharacteristic
232#102—1511no—
233#102—1511no—
234#102—1511no—
235C22⋊C8—1511no—
236C22⋊C8—1511no—
237C4×C8C2×D15111yescharacteristic
238#41—3022no—
239#41—6041no—
240C2×Q8—3021no—
241C2×Q8—3022no—
242C2×Q8—6041no—
243C2×Q8—1511no—
244C2×Q8C22×D15111yescharacteristic
245C2×Q8C22×D15111yescharacteristic
246C2×D4—3021no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4—1511no—
250C22×C4—3021no—
251C22×C4—3021no—
252C22×C4—3021no—
253C22×C4—1511no—
254C22×C4—1511no—
255Q16—22no—
256Q16—6041no—
257SD16—6041no—
258C2×C8—6041no—
259C2×C8—6041no—
260C2×C8—1511no—
261C2×C8—1511no—
262C2×C8C22×D15111yescharacteristic
263C2×C8C22×D15111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—3021no—
267C4⋊C4—3021no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—3021no—
272C4⋊C4—1511no—
273C4⋊C4—1511no—
274C4⋊C4—1511no—
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4—3021no—
284C22⋊C4—1511no—
285C22⋊C4—1511no—
286C42—21no—
287C42—21no—
288C42—3021no—
289C42C22×D15111yescharacteristic
290C23—3021no—
291C23—1511no—
292C23—1511no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—3021no—
297Q8—3021no—
298Q8—6042no—
299Q8#1455900412yes—
300D4—3022no—
301D4—3021no—
302D4—3021no—
303D4—6042no—
304D4—6042no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—6042no—
317C2×C4—6042no—
318C2×C4—6042no—
319C2×C4—1511no—
320C2×C4—1511no—
321C2×C4D4×D15111yescharacteristic
322C2×C4D4×D15111yescharacteristic
323C2×C4C23×D15111yescharacteristic
324C8—21no—
325C8—21no—
326C8—3021no—
327C8—3021no—
328C22—3021no—
329C22—3021no—
330C22—3021no—
331C22—3021no—
332C22—3021no—
333C22—6041no—
334C22—6041no—
335C22—6041no—
336C22—1512no—
337C22C2×D4×D15111yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—3021no—
345C4—3021no—
346C4—6041no—
347C4—6041no—
348C4—6041no—
349C4C2×#1455900411yescharacteristic
350C4#1801278511yescharacteristic
351C2—3022no—
352C2—6041no—
353C2—12081no—
354C2#2375285811yescharacteristic
355C2#135×D15111yescharacteristic
356C2#2375302511yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC4×Q16×C151C2
socleC22×C151C22×D4
prime radical#23752874C2
hypercenterC4×Q16D151
hypocenterC151#3300
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #23752903C2semidirect
3. #23752567C2semidirect
4. #23752555C2semidirect
5. #23752527C2semidirect
6. #23752519C2semidirect
7. #23752452C2semidirect
8. #23752444C2semidirect
9. #23752434C2semidirect
10. #23752373C2semidirect
11. #23752366C2semidirect
12. C8×D604C2semidirect
13. #23752207C2semidirect
14. #103×D151C2semidirect
15. C4×Q16×C151C2semidirect
178. C151#3300semidirect
191. C4×Q16D151semidirect

Maximal subgroups

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

subgroupindex
#237529032
#237528742
#237525672
#237525552
#237525272
#237525192
#237524522
#237524442
#237524342
#237523732
#237523662
C8×D6042
#237522072
#103×D1512
C4×Q16×C1512
#3300151