Finite Group Databasebeta

← #25097101

Subgroups — #25097101

Order 11008.

854 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582961C212yesmaximal
2C4×#13063282C211yesmaximal, characteristic
3#19134746C212yesmaximal, complemented
4#19134713C212yesmaximal, complemented
5#19134578C212yesmaximal
6#19134572C212yesmaximal
7#19134455C212yesmaximal, complemented
8C4×C4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
9C43×#1767C211yesmaximal, characteristic, complemented
10C2×#13063282C2211yescharacteristic
11C2×#13063282C2211yescharacteristic
12C2×C42×D43C2211yescharacteristic
13#14582961—28no—
14C2×C4⋊(C43⋊C8)C2212yes—
15C2×Dic43⋊C8C2214yes—
16C2×Dic43⋊C8C2214yes—
17C2×(C2×D43)⋊C8C2214yes—
18C2×C4×C43⋊C8C2212yes—
19C4×Dic43⋊C4C412yes—
20C4×Dic43⋊C4C412yes—
21C4×(C2×D43)⋊C4C412yes—
22C4×(C2×D43)⋊C4C412yes—
23#14582745C2211yescharacteristic
24#14582745C2211yescharacteristic
25C42×Dic43C2211yescharacteristic
26#14582654C2212yes—
27#14582653C2214yes—
28C2×C4⋊C8×C43C2212yes—
29C2×#97×C43C2212yes—
30C43×C43C2211yescharacteristic
31C43×#336C2212yes—
32C22×C4×D43C2×C411yescharacteristic
33C22×C4×D43C2×C411yescharacteristic
34C22×C4×D43C2311yescharacteristic
35C22×C43⋊C8C2314yes—
36#13063282—24no—
37#13063282D414yes—
38#13063282Q814yes—
39C2×Dic43⋊C4C2×C412yes—
40C2×Dic43⋊C4C2×C412yes—
41C2×(C2×D43)⋊C4C2×C412yes—
42C2×(C2×D43)⋊C4C2×C412yes—
43C2×C4×Dic43C2×C411yescharacteristic
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43C2×C412yes—
46C2×C4×Dic43C2×C412yes—
47C2×C4×Dic43C2311yescharacteristic
48C2×C4×Dic43C2311yescharacteristic
49C2×C4×Dic43C2311yescharacteristic
50C42×D43—24no—
51C4⋊(C43⋊C8)—24no—
52Dic43⋊C8—28no—
53Dic43⋊C8—28no—
54(C2×D43)⋊C8—28no—
55C4×C43⋊C8—24no—
56C43⋊#95C2×C412yes—
57C43⋊#95C2×C412yes—
58C43⋊#95C2×C412yes—
59C43⋊#95C2×C412yes—
60C22×C8×C43C2314yes—
61C2×C42×C43C2×C412yes—
62C2×C42×C43C2×C412yes—
63C2×C42×C43C2311yescharacteristic
64C2×C42×C43C2311yescharacteristic
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—24no—
67#97×C43—24no—
68C23×D43C22×C411yescharacteristic
69C22×C4×C43C22×C412yes—
70C22×C4×C43C22×C412yes—
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2411yescharacteristic
74C22×Dic43C22×C411yescharacteristic
75C22×Dic43C22×C411yescharacteristic
76C22×Dic43C22×C412yes—
77C22×Dic43C22×C411yescharacteristic
78C22×Dic43C22×C412yes—
79C2×C4×D43—22no—
80C2×C4×D43—22no—
81C2×C4×D43—22no—
82C2×C4×D43—22no—
83C2×C4×D43—24no—
84C2×C4×D43—42no—
85C2×C4×D43C2×D412yes—
86C2×C4×D43C2×Q812yes—
87C2×C8×C43—24no—
88C2×C8×C43—24no—
89C2×C8×C43—24no—
90C42×C43—24no—
91C42×C43—22no—
92C42×C43—42no—
93C42×C43C2×D412yes—
94C42×C43C2×Q812yes—
95C42×C43#4114yes—
96(C2×D43)⋊C4—24no—
97(C2×D43)⋊C4C4⋊C418yes—
98Dic43⋊C4—24no—
99Dic43⋊C4C4⋊C418yes—
100C4×Dic43—22no—
101C4×Dic43—22no—
102C4×Dic43—24no—
103C4×Dic43—22no—
104C4×Dic43—42no—
105C4×Dic43C2×D412yes—
106C4×Dic43C2×Q812yes—
107C4×Dic43#4114yes—
108C2×C43⋊C8—24no—
109C2×C43⋊C8—24no—
110C2×C43⋊C8—24no—
111C23×C43C23×C411yescharacteristic
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—22no—
115C22×D43—22no—
116C22×D43C2×C4⋊C412yes—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43C2×C4⋊C414yes—
124C2×C4×C43#11712yes—
125C2×C4×C43#11712yes—
126C2×C4×C43#13114yes—
127C2×C4×C43C22×D411yescharacteristic
128C2×C4×C43C22×Q811yescharacteristic
129C2×C4×C43C2×#4112yes—
130C2×C4×C43C2×#4112yes—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—22no—
134C2×Dic43—22no—
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—22no—
140C2×Dic43—22no—
141C2×Dic43C2×C4⋊C414yes—
142C2×Dic43C2×C4⋊C412yes—
143C2×Dic43#11714yes—
144C4×D43—24no—
145C4×D43—24no—
146C4×D43—44no—
147C4×D43—44no—
148C8×C43—44no—
149C43⋊C8—44no—
150#20812—431nomaximal, Sylow
151C22×C43C22×C4⋊C411yescharacteristic
152C22×C43C2×#11711yescharacteristic
153C22×C43C2×#11711yescharacteristic
154C22×C43C2×#13112yes—
155C22×C43#56812yes—
156C2×D43—24no—
157C2×D43—22no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—42no—
161C4×C43—24no—
162C4×C43—22no—
163C4×C43—42no—
164C4×C43#43314yescomplemented
165C4×C43#53212yes—
166C4×C43#53312yes—
167Dic43—24no—
168Dic43—24no—
169Dic43—22no—
170Dic43—41no—
171Dic43—41no—
172C2×#433—432no—
173C4×#117—431no—
174#1842—432no—
175#1832—432no—
176#1798—432no—
177#1797—432no—
178#1768—432no—
179#1767D4311yescharacteristic, complemented
180C4×C4⋊C8—431no—
181C2×C43#228511yescharacteristic
182C2×C43#290612yes—
183C2×C43C2×#43311yescharacteristic
184C2×C43#292111yescharacteristic
185C2×C43#292512yes—
186D43—42no—
187C2×#117—431no—
188C2×#117—431no—
189C22×C42—431no—
190#433—868no—
191C2×C4⋊C8—434no—
192C2×C4⋊C8—434no—
193C2×C4⋊C8—432no—
194C2×C4⋊C8C2×D4312yes—
195C2×C22⋊C8—434no—
196C2×#97C2×D4312yes—
197C2×C4×C8—432no—
198C4×C4⋊C4—432no—
199C4×C4⋊C4—432no—
200C4×C22⋊C4—432no—
201C4×C22⋊C4—432no—
202#376—431no—
203#376—431no—
204C43—431no—
205C43C2×D4311yescharacteristic
206#336—434no—
207#336—432no—
208#336C2×D4312yes—
209C43#2081211yescharacteristic, complemented, Sylow
210C23×C4—431no—
211C23×C4—431no—
212C23×C4—431no—
213C22×C8—434no—
214C22×C8C22×D4314yes—
215#117—434no—
216#117—434no—
217#117—864no—
218C2×C4⋊C4—432no—
219C2×C4⋊C4—432no—
220C2×C22⋊C4—432no—
221C2×C22⋊C4—432no—
222C2×C42—431no—
223C2×C42—431no—
224C2×C42—432no—
225C2×C42—431no—
226C2×C42—431no—
227C2×C42—431no—
228C2×C42—432no—
229C2×C42—864no—
230C2×C42C4×D4312yes—
231C2×C42C4×D4312yes—
232C2×C42C22×D4311yescharacteristic
233C2×C42C22×D4311yescharacteristic
234C2×C42C22×D4311yescharacteristic
235C4⋊C8—24no—
236C4⋊C8—868no—
237C4⋊C8—868no—
238C4⋊C8—864no—
239C22⋊C8—868no—
240#97—24no—
241C4×C8—864no—
242#95—432no—
243#95—432no—
244#95—432no—
245#95—432no—
246C24—431no—
247C22×C4—432no—
248C22×C4—432no—
249C22×C4—431no—
250C22×C4—432no—
251C22×C4—432no—
252C22×C4—431no—
253C22×C4—431no—
254C22×C4—862no—
255C22×C4—862no—
256C22×C4—862no—
257C22×C4—862no—
258C22×C4—864no—
259C22×C4—1722no—
260C22×C4C2×C4×D4312yes—
261C22×C4C2×C4×D4312yes—
262C22×C4C2×C4×D4311yescharacteristic
263C22×C4C2×C4×D4311yescharacteristic
264C22×C4C23×D4311yescharacteristic
265C2×C8—24no—
266C2×C8—24no—
267C2×C8—24no—
268C2×C8—864no—
269C2×C8—864no—
270C2×C8—864no—
271C4⋊C4—438no—
272C4⋊C4—864no—
273C22⋊C4—438no—
274C22⋊C4—864no—
275C42—24no—
276C42—22no—
277C42—42no—
278C42—432no—
279C42—432no—
280C42—434no—
281C42—862no—
282C42—862no—
283C42—864no—
284C42—862no—
285C42—1722no—
286C42#1062189814yes—
287C42D4×D4312yes—
288C42Q8×D4312yes—
289C23—432no—
290C23—861no—
291C23—861no—
292C23—862no—
293C23—862no—
294C23C22×C4×D4311yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—434no—
302C2×C4—432no—
303C2×C4—434no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—862no—
307C2×C4—862no—
308C2×C4—862no—
309C2×C4—862no—
310C2×C4—864no—
311C2×C4—864no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—862no—
315C2×C4—862no—
316C2×C4—1724no—
317C2×C4—1724no—
318C2×C4C4⋊C4×D4314yes—
319C2×C4#1306328212yes—
320C2×C4#1306328212yes—
321C2×C4#1306333314yes—
322C2×C4C2×D4×D4311yescharacteristic
323C2×C4C2×Q8×D4311yescharacteristic
324C2×C4#41×D4312yes—
325C2×C4C2×#1062189812yes—
326C8—44no—
327C8—1724no—
328C22—862no—
329C22—864no—
330C22—1721no—
331C22—1721no—
332C22—1722no—
333C22C2×C4⋊C4×D4311yescharacteristic
334C22#117×D4311yescharacteristic
335C22C2×#1306328211yescharacteristic
336C22C2×#1306333312yes—
337C22#1458366512yes—
338C4—22no—
339C4—24no—
340C4—42no—
341C4—864no—
342C4—862no—
343C4—864no—
344C4—1721no—
345C4—1721no—
346C4#1458296114yescomplemented
347C4#1458344612yes—
348C4#1458345312yes—
349C2—1722no—
350C2#1913699911yescharacteristic
351C2#1914316412yes—
352C2C2×#1458296111yescharacteristic
353C2#1914323111yescharacteristic
354C2#1914326212yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1767C2
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenter#1767D43
hypocenterC43#20812
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1767

Complements

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

NH ≅ G/Ntype
3. #19134746C2semidirect
4. #19134713C2semidirect
7. #19134455C2semidirect
8. C4×C4⋊(C43⋊C8)C2semidirect
9. C43×#1767C2semidirect
164. C4×C43#433semidirect
179. #1767D43semidirect
209. C43#20812semidirect
346. C4#14582961semidirect

Maximal subgroups

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

subgroupindex
C2×#145829612
C4×#130632822
#191347462
#191347132
#191345782
#191345722
#191344552
C4×C4⋊(C43⋊C8)2
C43×#17672
#2081243