Finite Group Databasebeta

← #25095248

Subgroups — #25095248

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583027C212yesmaximal
2C42×Dic86C211yesmaximal, characteristic
3#19134469C212yesmaximal
4#19134467C212yesmaximal
5C8×Dic43⋊C4C212yesmaximal
6#19134449C211yesmaximal, characteristic
7#19134449C211yesmaximal, characteristic
8#19134448C211yesmaximal, characteristic
9#97×Dic43C211yesmaximal, characteristic
10#97×Dic43C211yesmaximal, characteristic
11C4×#97×C43C211yesmaximal, characteristic
12C2×C4×Dic86C412yes—
13C2×C4×Dic86C2211yescharacteristic
14#14583027C4116yescomplemented
15C2×C4⋊(C43⋊C8)C2212yes—
16C2×Dic43⋊C8C2212yes—
17C2×Dic43⋊C8C2212yes—
18C2×#13063236C2211yescharacteristic
19C2×#13063236C2211yescharacteristic
20C2×#13063235C2212yes—
21C2×#13063235C2212yes—
22C2×C8×Dic43C2212yes—
23C2×C8×Dic43C2212yes—
24C4×Dic43⋊C4C412yes—
25C4×Dic43⋊C4C412yes—
26C4×Dic43⋊C4C2211yescharacteristic
27C4×Dic43⋊C4C2211yescharacteristic
28C4×C4⋊Dic43C412yes—
29C4×C4⋊Dic43C2211yescharacteristic
30C42×Dic43C2211yescharacteristic
31C42×Dic43C2211yescharacteristic
32#14582654C2212yes—
33#14582653C2212yes—
34#14582653C2212yes—
35C2×#97×C43C2211yescharacteristic
36C2×#97×C43C2212yes—
37C2×#97×C43C2211yescharacteristic
38C2×C4×C8×C43C2212yes—
39C43×C43C2211yescharacteristic
40C22×Dic86C2×C411yescharacteristic
41C22×C43⋊C8C2312yes—
42C22×C43⋊C8C2312yes—
43C4×Dic86—28no—
44C4×Dic86C2×C418yes—
45C2×C4⋊Dic43C2×C412yes—
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×Dic43⋊C4C2×C412yes—
48C2×Dic43⋊C4C2×C411yescharacteristic
49C2×Dic43⋊C4C2×C411yescharacteristic
50C2×Dic43⋊C4C2×C412yes—
51C2×C4×Dic43C2×C412yes—
52C2×C4×Dic43C2×C412yes—
53C2×C4×Dic43C2×C412yes—
54C2×C4×Dic43C2×C412yes—
55C2×C4×Dic43C2311yescharacteristic
56C2×C4×Dic43C2311yescharacteristic
57C2×C4×Dic43C2311yescharacteristic
58C2×C4×Dic43C2311yescharacteristic
59C4⋊(C43⋊C8)C2×C418yes—
60Dic43⋊C8C2×C418yes—
61Dic43⋊C8C2×C418yes—
62#13063236—22no—
63#13063236—22no—
64#13063235—24no—
65#13063235C2×C418yes—
66C8×Dic43—24no—
67C8×Dic43C2×C418yes—
68C43⋊#95C2×C412yes—
69C43⋊#95C2×C412yes—
70C43⋊#95C2×C412yes—
71C22×C8×C43C2312yes—
72C22×C8×C43C2312yes—
73C2×C42×C43C2×C412yes—
74C2×C42×C43C2×C412yes—
75C2×C42×C43C2311yescharacteristic
76C2×C42×C43C2311yescharacteristic
77C2×C42×C43C2311yescharacteristic
78#97×C43—22no—
79#97×C43C2×C418yes—
80#97×C43Q814yescomplemented
81C4×C8×C43—24no—
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C22×C412yes—
85C22×C4×C43C22×C412yes—
86C22×C4×C43C2411yescharacteristic
87C22×Dic43C22×C412yes—
88C22×Dic43C22×C411yescharacteristic
89C22×Dic43C22×C411yescharacteristic
90C22×Dic43C22×C411yescharacteristic
91C22×Dic43C22×C412yes—
92C22×Dic43C22×C411yescharacteristic
93C2×Dic86—24no—
94C2×Dic86C4214yes—
95C2×C8×C43—22no—
96C2×C8×C43—22no—
97C2×C8×C43C22×C414yes—
98C2×C8×C43C22×C414yes—
99C2×C8×C43C2×Q814yes—
100C2×C8×C43#4114yes—
101C42×C43—24no—
102C42×C43—22no—
103C42×C43—42no—
104C42×C43C22×C414yes—
105C42×C43C2×Q812yes—
106C42×C43#4112yes—
107C4⋊Dic43—24no—
108C4⋊Dic43C4214yes—
109Dic43⋊C4—24no—
110Dic43⋊C4C4214yes—
111Dic43⋊C4C4214yes—
112Dic43⋊C4M1618yes—
113C4×Dic43—22no—
114C4×Dic43—22no—
115C4×Dic43—24no—
116C4×Dic43—24no—
117C4×Dic43—42no—
118C4×Dic43—42no—
119C4×Dic43C22×C414yes—
120C4×Dic43C22×C414yes—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8C22×C414yes—
126C2×C43⋊C8C22×C414yes—
127C23×C43C23×C411yescharacteristic
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43C2×C4212yes—
135C2×C4×C43C2×C4212yes—
136C2×C4×C43C4×Q814yes—
137C2×C4×C43C2×M1614yes—
138C2×C4×C43C23×C412yes—
139C2×C4×C43C22×Q811yescharacteristic
140C2×C4×C43C2×#4112yes—
141C2×C4×C43C2×#4111yescharacteristic
142C2×Dic43—22no—
143C2×Dic43—22no—
144C2×Dic43—22no—
145C2×Dic43—22no—
146C2×Dic43—22no—
147C2×Dic43—22no—
148C2×Dic43—22no—
149C2×Dic43—22no—
150C2×Dic43C2×C4212yes—
151C2×Dic43C2×C4212yes—
152C2×Dic43C2×C4212yes—
153C2×Dic43C2×C4212yes—
154C2×Dic43C2×M1614yes—
155C2×Dic43C2×M1614yes—
156Dic86—28no—
157C8×C43—24no—
158C8×C43C4×Q818yescomplemented
159C43⋊C8—24no—
160C43⋊C8—24no—
161#20520—431nomaximal, Sylow
162C22×C43C22×C4211yescharacteristic
163C22×C43C2×C4×Q811yescharacteristic
164C22×C43C4×#4111yescharacteristic
165C22×C43C22×M1612yes—
166C22×C43#56812yes—
167C4×C43—22no—
168C4×C43—22no—
169C4×C43—24no—
170C4×C43—24no—
171C4×C43C2×C4×Q812yes—
172C4×C43C4×#4112yes—
173Dic43—22no—
174Dic43—22no—
175Dic43—22no—
176Dic43—24no—
177Dic43—42no—
178Dic43C4×M1614yes—
179C2×#446—432no—
180C42×Q8—431no—
181#1771—432no—
182#1771—432no—
183C8×C4⋊C4—432no—
184#1767—431no—
185#1767—431no—
186#1767—431no—
187C4×#97—431no—
188C4×#97—431no—
189C4×#97D4311yescharacteristic
190C2×C43C42×Q811yescharacteristic
191C2×C43C2×C4×M1611yescharacteristic
192C2×C43#287511yescharacteristic
193C2×C43Q8×M1612yes—
194C2×C43#297012yes—
195C2×C4×Q8—431no—
196C2×C4×Q8—432no—
197#446—4316no—
198C2×C4⋊C8—432no—
199C2×C4⋊C8—432no—
200C2×C4⋊C8—432no—
201C2×#97—432no—
202C2×#97—432no—
203C2×#97—431no—
204C2×#97—431no—
205C2×#97C2×D4311yescharacteristic
206C2×#97C2×D4311yescharacteristic
207C2×#97C2×D4312yes—
208C2×C4×C8—432no—
209C2×C4×C8—432no—
210C2×C4×C8C2×D4312yes—
211C4×C4⋊C4—431no—
212C4×C4⋊C4—431no—
213C4×C4⋊C4—431no—
214C4×C4⋊C4—432no—
215C4×C4⋊C4—432no—
216C4×C4⋊C4—432no—
217C43—431no—
218C43—431no—
219C43C2×D4311yescharacteristic
220#336—432no—
221#336—432no—
222#336—432no—
223C43#2052011yescharacteristic, complemented, Sylow
224C22×Q8—431no—
225C22×C8—432no—
226C22×C8—432no—
227C22×C8C22×D4312yes—
228C22×C8C22×D4312yes—
229C4×Q8—438no—
230C4×Q8—868no—
231C2×C4⋊C4—431no—
232C2×C4⋊C4—431no—
233C2×C4⋊C4—432no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—432no—
236C2×C4⋊C4—432no—
237C2×C42—431no—
238C2×C42—431no—
239C2×C42—432no—
240C2×C42—432no—
241C2×C42—431no—
242C2×C42—431no—
243C2×C42—432no—
244C2×C42—432no—
245C2×C42C4×D4312yes—
246C2×C42C4×D4312yes—
247C2×C42C22×D4311yescharacteristic
248C2×C42C22×D4311yescharacteristic
249C2×C42C22×D4311yescharacteristic
250C4⋊C8—438no—
251C4⋊C8—438no—
252C4⋊C8—438no—
253#97—22no—
254#97—438no—
255#97—864no—
256#97—862no—
257#97—862no—
258#97Dic8614yescomplemented
259#97C4×D4318yes—
260C4×C8—24no—
261C4×C8—438no—
262C4×C8—864no—
263#95—432no—
264#95—432no—
265#95—432no—
266C2×Q8—434no—
267C2×Q8—864no—
268C22×C4—431no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—432no—
272C22×C4—431no—
273C22×C4—432no—
274C22×C4C2×C4×D4311yescharacteristic
275C22×C4C2×C4×D4311yescharacteristic
276C22×C4C2×C4×D4312yes—
277C22×C4C2×C4×D4312yes—
278C22×C4C23×D4311yescharacteristic
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—434no—
282C2×C8—434no—
283C2×C8—862no—
284C2×C8—862no—
285C2×C8—862no—
286C2×C8—862no—
287C2×C8C2×Dic8614yes—
288C2×C8C2×C4×D4314yes—
289C2×C8C2×C4×D4314yes—
290C2×C8#1062189814yes—
291C4⋊C4—434no—
292C4⋊C4—434no—
293C4⋊C4—434no—
294C4⋊C4—438no—
295C4⋊C4—864no—
296C4⋊C4—864no—
297C42—24no—
298C42—22no—
299C42—42no—
300C42—434no—
301C42—434no—
302C42—864no—
303C42—864no—
304C42—862no—
305C42—862no—
306C42—1722no—
307C42—1722no—
308C42C2×Dic8612yes—
309C42C2×C4×D4314yes—
310C42#1062189812yes—
311C23C22×C4×D4311yescharacteristic
312Q8—868no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—432no—
320C2×C4—434no—
321C2×C4—432no—
322C2×C4—432no—
323C2×C4—432no—
324C2×C4—434no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—862no—
328C2×C4—862no—
329C2×C4—862no—
330C2×C4—862no—
331C2×C4—862no—
332C2×C4—862no—
333C2×C4C42×D4312yes—
334C2×C4C42×D4312yes—
335C2×C4C4×Dic8614yes—
336C2×C4M16×D4314yes—
337C2×C4C22×C4×D4312yes—
338C2×C4C22×Dic8611yescharacteristic
339C2×C4C2×#1062189812yes—
340C2×C4C2×#1062189811yescharacteristic
341C8—24no—
342C8—864no—
343C8—864no—
344C8C4×Dic8618yescomplemented
345C22C2×C42×D4311yescharacteristic
346C22C2×C4×Dic8611yescharacteristic
347C22C4×#1062189811yescharacteristic
348C22C2×M16×D4312yes—
349C22#1458366512yes—
350C4—22no—
351C4—22no—
352C4—24no—
353C4—24no—
354C4—434no—
355C4—862no—
356C4—862no—
357C4—862no—
358C4—864no—
359C4—1722no—
360C4C2×C4×Dic8612yes—
361C4C4×#1062189812yes—
362C2C42×Dic8611yescharacteristic
363C2C4×M16×D4311yescharacteristic
364C2#1914302411yescharacteristic
365C2M16×Dic8612yes—
366C2#1914360612yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C22×C42
FittingC4×#97×C43C2
socle, prime radicalC23×C43C23×C4
cosocleC22×C4×C43C24
hypercenterC4×#97D43
hypocenterC43#20520
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
14. #14583027C4semidirect
80. #97×C43Q8semidirect
158. C8×C43C4×Q8semidirect
223. C43#20520semidirect
258. #97Dic86semidirect
344. C8C4×Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145830272
C42×Dic862
#191344692
#191344672
C8×Dic43⋊C42
#191344492
#191344482
#97×Dic432
C4×#97×C432
#2052043