Finite Group Databasebeta

← #25095214

Subgroups — #25095214

Order 11008.

886 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583030C211yesmaximal, characteristic
2C2×Q8×C43⋊C8C211yesmaximal, characteristic
3#19134470C212yesmaximal
4#19134464C211yesmaximal, characteristic
5C4⋊C4×C43⋊C8C212yesmaximal
6C4⋊C4×C43⋊C8C211yesmaximal, characteristic
7#19134452C212yesmaximal
8#19134448C211yesmaximal, characteristic
9#19134282C212yesmaximal
10C42×C43⋊C8C211yesmaximal, characteristic
11C43×#2295C211yesmaximal, characteristic
12#14583030C418yescomplemented
13Q8×C43⋊C8C418yescomplemented
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15C2×C4⋊(C43⋊C8)C2212yes—
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×C4⋊(C43⋊C8)C2212yes—
18C2×#13063236C2212yes—
19C2×#13063236C2212yes—
20C2×#13063236C2212yes—
21C2×C4×C43⋊C8C2211yescharacteristic
22C2×C4×C43⋊C8C2211yescharacteristic
23C2×C4×C43⋊C8C2211yescharacteristic
24C2×C4×C43⋊C8C2212yes—
25C2×C4×C43⋊C8C2211yescharacteristic
26C2×C4×C43⋊C8C2211yescharacteristic
27C2×C4×C43⋊C8C2212yes—
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582654C2212yes—
30#14582654C2212yes—
31#14582654C2212yes—
32C2×C4×Q8×C43C2211yescharacteristic
33C43×#391C412yes—
34C43×#389C412yes—
35C43×#387C414yes—
36C4×C4⋊C4×C43C2211yescharacteristic
37C4×C4⋊C4×C43C2212yes—
38C43×#376C2212yes—
39C43×C43C2211yescharacteristic
40C22×C43⋊C8C2311yescharacteristic
41C22×C43⋊C8C2311yescharacteristic
42C22×C43⋊C8C2312yes—
43C22×C43⋊C8C2312yes—
44C22×C43⋊C8C2311yescharacteristic
45C22×C43⋊C8C2311yescharacteristic
46C4⋊(C43⋊C8)C2×C414yes—
47C4⋊(C43⋊C8)C2×C418yes—
48C4⋊(C43⋊C8)C2×C418yes—
49C4⋊(C43⋊C8)C2×C414yes—
50#13063236—24no—
51#13063236—24no—
52#13063236C2×C418yes—
53C4×C43⋊C8—22no—
54C4×C43⋊C8—22no—
55C4×C43⋊C8—24no—
56C4×C43⋊C8—22no—
57C4×C43⋊C8C2×C414yes—
58C4×C43⋊C8C2×C418yes—
59C4×C43⋊C8C2×C414yes—
60C4×C43⋊C8Q814yescomplemented
61C22×Q8×C43C2×C411yescharacteristic
62C4×Q8×C43C2×C414yes—
63C4×Q8×C43C2×C414yes—
64C2×C4⋊C4×C43C2×C414yes—
65C2×C4⋊C4×C43C2×C412yes—
66C2×C4⋊C4×C43C2×C412yes—
67C2×C4⋊C4×C43C2×C411yescharacteristic
68C2×C42×C43C2×C412yes—
69C2×C42×C43C2×C412yes—
70C2×C42×C43C2311yescharacteristic
71C2×C42×C43C2312yes—
72C2×C42×C43C2311yescharacteristic
73C2×C42×C43C2312yes—
74C2×C42×C43C2311yescharacteristic
75#95×C43C2×C414yes—
76#95×C43C2×C414yes—
77#95×C43C2×C412yes—
78#95×C43C2×C414yes—
79C2×Q8×C43—24no—
80C2×Q8×C43C4214yes—
81C22×C4×C43C22×C414yes—
82C22×C4×C43C22×C412yes—
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C22×C412yes—
85C22×C4×C43C22×C412yes—
86C22×C4×C43C22×C412yes—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2411yescharacteristic
89C4⋊C4×C43—28no—
90C4⋊C4×C43—24no—
91C4⋊C4×C43C4218yes—
92C4⋊C4×C43C4214yes—
93C42×C43—24no—
94C42×C43—24no—
95C42×C43—21no—
96C42×C43—21no—
97C42×C43—22no—
98C42×C43—22no—
99C42×C43C22×C414yes—
100C42×C43C22×C412yes—
101C42×C43C22×C412yes—
102C42×C43C22×C414yes—
103C42×C43C2×Q812yes—
104C42×C43#4112yes—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—21no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8C22×C412yes—
114C2×C43⋊C8C22×C414yes—
115C2×C43⋊C8C22×C412yes—
116C2×C43⋊C8C22×C414yes—
117C2×C43⋊C8C22×C412yes—
118C2×C43⋊C8C22×C412yes—
119C2×C43⋊C8C2×Q812yes—
120C2×C43⋊C8C2×Q812yes—
121C2×C43⋊C8#4112yes—
122C2×C43⋊C8#4112yes—
123C23×C43C23×C411yescharacteristic
124Q8×C43—28no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—24no—
131C2×C4×C43—24no—
132C2×C4×C43—24no—
133C2×C4×C43—24no—
134C2×C4×C43—24no—
135C2×C4×C43C2×C4212yes—
136C2×C4×C43C2×C4214yes—
137C2×C4×C43C2×C4214yes—
138C2×C4×C43C2×C4212yes—
139C2×C4×C43C4×Q814yes—
140C2×C4×C43#13114yes—
141C2×C4×C43#13114yes—
142C2×C4×C43C23×C411yescharacteristic
143C2×C4×C43C23×C411yescharacteristic
144C2×C4×C43C22×Q811yescharacteristic
145C2×C4×C43C2×#4111yescharacteristic
146C2×C4×C43C2×#4111yescharacteristic
147C2×C4×C43C2×#4111yescharacteristic
148C43⋊C8—22no—
149C43⋊C8—22no—
150C43⋊C8—24no—
151C43⋊C8—24no—
152C43⋊C8C4×Q814yes—
153C43⋊C8C4×Q814yes—
154#20516—431nomaximal, Sylow
155C22×C43C22×C4211yescharacteristic
156C22×C43C2×C4×Q811yescharacteristic
157C22×C43C4×#4111yescharacteristic
158C22×C43C2×#13112yes—
159C22×C43C2×#13112yes—
160C4×C43—24no—
161C4×C43—22no—
162C4×C43—24no—
163C4×C43—24no—
164C4×C43—24no—
165C4×C43—44no—
166C4×C43#40514yes—
167C4×C43C2×C4×Q811yescharacteristic
168C4×C43C2×C4×Q811yescharacteristic
169C4×C43C4×#4111yescharacteristic
170C4×C43C4×#4111yescharacteristic
171C2×#446—431no—
172C2×C8×Q8—431no—
173#2295D4311yescharacteristic
174#1771—432no—
175#1770—431no—
176C8×C4⋊C4—432no—
177C8×C4⋊C4—431no—
178#1768—432no—
179#1767—431no—
180#1726—432no—
181C42×C8—431no—
182C2×C43C42×Q811yescharacteristic
183C2×C43C2×#40511yescharacteristic
184C2×C43C4×#13111yescharacteristic
185C2×C43#296012yes—
186C2×C43#296612yes—
187C2×C4×Q8C2×D4311yescharacteristic
188#446—438no—
189C8×Q8—438no—
190C2×C4⋊C8—431no—
191C2×C4⋊C8—432no—
192C2×C4⋊C8—431no—
193C2×C4⋊C8—432no—
194C2×#97—432no—
195C2×#97—432no—
196C2×#97—432no—
197C2×C4×C8—431no—
198C2×C4×C8—432no—
199C2×C4×C8—431no—
200C2×C4×C8—431no—
201C2×C4×C8—431no—
202C2×C4×C8—431no—
203C2×C4×C8—431no—
204C2×C4×C8—432no—
205#391Dic4312yes—
206#389Dic4312yes—
207#387Dic4314yes—
208C4×C4⋊C4C2×D4311yescharacteristic
209C4×C4⋊C4C2×D4312yes—
210#376C2×D4312yes—
211C43C2×D4311yescharacteristic
212#336—432no—
213#336—432no—
214#336—432no—
215C43#2051611yescharacteristic, complemented, Sylow
216C22×Q8C2×Dic4311yescharacteristic
217C22×C8—431no—
218C22×C8—431no—
219C22×C8—431no—
220C22×C8—431no—
221C22×C8—432no—
222C22×C8—432no—
223C4×Q8C4×D4314yes—
224C4×Q8C4×D4314yes—
225C2×C4⋊C4C2×Dic4314yes—
226C2×C4⋊C4C2×Dic4312yes—
227C2×C4⋊C4C2×Dic4312yes—
228C2×C4⋊C4C2×Dic4311yescharacteristic
229C2×C42C2×Dic4312yes—
230C2×C42C2×Dic4312yes—
231C2×C42C22×D4311yescharacteristic
232C2×C42C22×D4312yes—
233C2×C42C22×D4311yescharacteristic
234C2×C42C22×D4312yes—
235C2×C42C22×D4311yescharacteristic
236C4⋊C8—434no—
237C4⋊C8—438no—
238C4⋊C8—434no—
239C4⋊C8—438no—
240#97—438no—
241#97—864no—
242#97—864no—
243C4×C8—434no—
244C4×C8—438no—
245C4×C8—434no—
246C4×C8—434no—
247C4×C8—862no—
248C4×C8—864no—
249C4×C8—862no—
250C4×C8—862no—
251#95C2×Dic4314yes—
252#95C2×Dic4314yes—
253#95C2×Dic4312yes—
254#95C2×Dic4314yes—
255C2×Q8—24no—
256C2×Q8C4×Dic4314yes—
257C22×C4C22×Dic4314yes—
258C22×C4C22×Dic4312yes—
259C22×C4C22×Dic4311yescharacteristic
260C22×C4C22×Dic4312yes—
261C22×C4C22×Dic4312yes—
262C22×C4C22×Dic4312yes—
263C22×C4C22×Dic4311yescharacteristic
264C22×C4C23×D4311yescharacteristic
265C2×C8—432no—
266C2×C8—432no—
267C2×C8—432no—
268C2×C8—432no—
269C2×C8—432no—
270C2×C8—432no—
271C2×C8—432no—
272C2×C8—434no—
273C2×C8—432no—
274C2×C8—434no—
275C2×C8—861no—
276C2×C8—861no—
277C2×C8—862no—
278C2×C8—862no—
279C2×C8—861no—
280C2×C8—861no—
281C2×C8—862no—
282C2×C8—862no—
283C4⋊C4—28no—
284C4⋊C4—24no—
285C4⋊C4C4×Dic4318yes—
286C4⋊C4C4×Dic4314yes—
287C42—24no—
288C42—24no—
289C42—21no—
290C42—21no—
291C42—22no—
292C42—22no—
293C42C2×C4×D4314yes—
294C42C2×C4×D4312yes—
295C42C2×C4×D4312yes—
296C42C2×C4×D4314yes—
297C42Q8×D4312yes—
298C42#1062190212yes—
299C23C23×Dic4311yescharacteristic
300Q8—28no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4C2×C4×Dic4312yes—
312C2×C4C2×C4×Dic4314yes—
313C2×C4C2×C4×Dic4314yes—
314C2×C4C2×C4×Dic4312yes—
315C2×C4Q8×Dic4314yes—
316C2×C4#1306333214yes—
317C2×C4#1306333214yes—
318C2×C4C22×C4×D4311yescharacteristic
319C2×C4C22×C4×D4311yescharacteristic
320C2×C4C2×Q8×D4311yescharacteristic
321C2×C4#41×D4311yescharacteristic
322C2×C4#41×D4311yescharacteristic
323C2×C4C2×#1062190211yescharacteristic
324C8—434no—
325C8—434no—
326C8—862no—
327C8—862no—
328C8—864no—
329C8—864no—
330C22C22×C4×Dic4311yescharacteristic
331C22C2×Q8×Dic4311yescharacteristic
332C22#41×Dic4311yescharacteristic
333C22C2×#1306333212yes—
334C22C2×#1306333212yes—
335C4—24no—
336C4—22no—
337C4—24no—
338C4—24no—
339C4—24no—
340C4—44no—
341C4#1458285514yes—
342C4C4×Q8×D4311yescharacteristic
343C4C4×Q8×D4311yescharacteristic
344C4C4×#1062190211yescharacteristic
345C4C4×#1062190211yescharacteristic
346C2C4×Q8×Dic4311yescharacteristic
347C2C2×#1458285511yescharacteristic
348C2C4×#1306333211yescharacteristic
349C2#1914353012yes—
350C2#1914357112yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C22×C42
FittingC43×#2295C2
socle, prime radicalC23×C43C23×C4
cosocleC22×C4×C43C24
hypercenter#2295D43
hypocenterC43#20516
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #2295

Complements

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

NH ≅ G/Ntype
12. #14583030C4semidirect
13. Q8×C43⋊C8C4semidirect
60. C4×C43⋊C8Q8semidirect
215. C43#20516semidirect

Maximal subgroups

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

subgroupindex
C2×#145830302
C2×Q8×C43⋊C82
#191344702
#191344642
C4⋊C4×C43⋊C82
#191344522
#191344482
#191342822
C42×C43⋊C82
C43×#22952
#2051643