Finite Group Databasebeta

← #25097180

Subgroups — #25097180

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582853C211yesmaximal, characteristic
2#19137200C212yesmaximal
3#19134762C212yesmaximal, complemented
4#19134724C211yesmaximal, characteristic, complemented
5#19134721C211yesmaximal, characteristic, complemented
6#19134629C212yesmaximal
7#19134623C211yesmaximal, characteristic
8#19134619C211yesmaximal, characteristic
9#19134493C212yesmaximal, complemented
10C4×#13063257C211yesmaximal, characteristic, complemented
11C4×#107×C43C211yesmaximal, characteristic, complemented
12C22×#10621872C2211yescharacteristic
13C22×C8×D43C2211yescharacteristic
14C2×#13063282C2211yescharacteristic
15C2×#13063258C2212yes—
16C2×#13063257C2212yes—
17C2×#13063256C2212yes—
18#14582853C418yescomplemented
19C2×#13063236C2211yescharacteristic
20C2×#13063235C2211yescharacteristic
21C2×C8×Dic43C2211yescharacteristic
22#14582790—22no—
23#14582788—22no—
24#14582783—22no—
25#14582781—22no—
26#14582768C2212yes—
27#14582764C2212yes—
28#14582756C2212yes—
29#14582756C2212yes—
30C4×C4⋊Dic43C2212yes—
31#14582662C2211yescharacteristic
32#14582662C2211yescharacteristic
33#14582661C2212yes—
34#14582661C2212yes—
35C2×#107×C43C2212yes—
36C2×C4×C8×C43C2211yescharacteristic
37C4×C4⋊C4×C43C2212yes—
38C43×#340C2211yescharacteristic
39C43×#340C2211yescharacteristic
40C22×C4×D43C2311yescharacteristic
41C2×#10621872—24no—
42C2×#10621872C2×C414yes—
43C22×C43⋊C8C2311yescharacteristic
44C22×C43⋊C8C2311yescharacteristic
45C2×C8×D43—24no—
46C2×C8×D43C2×C414yes—
47#13063282C2×C414yes—
48#13063282Q814yes—
49C2×C4⋊Dic43C2312yes—
50C2×C4⋊Dic43C2312yes—
51C2×Dic43⋊C4—22no—
52C2×Dic43⋊C4—22no—
53C2×Dic43⋊C4D411yescharacteristic
54C2×Dic43⋊C4D411yescharacteristic
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
57C2×(C2×D43)⋊C4D411yescharacteristic
58C2×(C2×D43)⋊C4D411yescharacteristic
59C2×C4×Dic43—22no—
60C2×C4×Dic43C2311yescharacteristic
61#13063258—24no—
62#13063257—24no—
63#13063256—24no—
64#13063236C2×C414yes—
65#13063235C2×C414yes—
66C8×Dic43C2×C414yes—
67C43⋊#95—22no—
68C43⋊#95—22no—
69C43⋊#95—22no—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C22×C8×C43C2311yescharacteristic
73C22×C8×C43C2311yescharacteristic
74C2×C4⋊C4×C43C2312yes—
75C2×C4⋊C4×C43C2312yes—
76C2×C42×C43—22no—
77C2×C42×C43C2311yescharacteristic
78#107×C43—24no—
79C4×C8×C43C2×C414yes—
80#95×C43—22no—
81C23×D43C2×D411yescharacteristic
82C22×C4×C43—22no—
83C22×C4×C43—22no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2411yescharacteristic
87C22×Dic43—22no—
88C22×Dic43—22no—
89C22×Dic43C2×D411yescharacteristic
90C22×Dic43C2×D411yescharacteristic
91C22×Dic43C2×D411yescharacteristic
92C2×C4×D43—22no—
93C2×C4×D43—22no—
94C2×C4×D43C22×C412yes—
95C2×C4×D43C2×Q812yes—
96C2×C8×C43—22no—
97C2×C8×C43C22×C412yes—
98C2×C8×C43C22×C412yes—
99C2×C8×C43#4114yes—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C42×C43—82no—
105C42×C43C22×C412yes—
106C42×C43C2×Q812yes—
107(C2×D43)⋊C4—82no—
108(C2×D43)⋊C4—82no—
109(C2×D43)⋊C4C4⋊C414yes—
110(C2×D43)⋊C4C4⋊C414yes—
111C4⋊Dic43—22no—
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115Dic43⋊C4—82no—
116Dic43⋊C4—82no—
117Dic43⋊C4C4⋊C414yes—
118Dic43⋊C4C4⋊C414yes—
119C4×Dic43—82no—
120C4×Dic43C22×C412yes—
121C4×Dic43C2×Q812yes—
122C2×C43⋊C8—22no—
123C2×C43⋊C8C22×C412yes—
124C2×C43⋊C8C22×C412yes—
125C2×C43⋊C8#4114yes—
126#10621872—28no—
127C8×D43—28no—
128C23×C43C22×D411yescharacteristic
129C22×D43—22no—
130C22×D43—21no—
131C22×D43—22no—
132C22×D43—21no—
133C22×D43C2×C4⋊C412yes—
134C2×C4×C43—21no—
135C2×C4×C43—22no—
136C2×C4×C43—21no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43C2×C4⋊C412yes—
144C2×C4×C43C2×C4⋊C412yes—
145C2×C4×C43C23×C411yescharacteristic
146C2×C4×C43C22×Q811yescharacteristic
147C2×C4×C43C2×#4112yes—
148C2×C4×C43C2×#4112yes—
149C2×Dic43—22no—
150C2×Dic43—21no—
151C2×Dic43—22no—
152C2×Dic43—21no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43C2×C4⋊C412yes—
160C2×Dic43C2×C4⋊C412yes—
161C2×Dic43C2×C4⋊C412yes—
162C4×D43—22no—
163C4×D43—22no—
164C4×D43—24no—
165C8×C43—22no—
166C8×C43#11714yes—
167C43⋊C8—22no—
168C43⋊C8#11714yes—
169#20822—431nomaximal, Sylow
170C22×C43C22×C4⋊C411yescharacteristic
171C22×C43#53212yes—
172C22×C43#57611yescharacteristic
173C22×C43#57712yes—
174C22×C43#57811yescharacteristic
175C2×D43—22no—
176C2×D43—22no—
177C2×D43—22no—
178C2×D43—42no—
179C2×D43—42no—
180C4×C43—22no—
181C4×C43—22no—
182C4×C43—82no—
183C4×C43—82no—
184C4×C43C2×#11711yescharacteristic
185C4×C43C2×#11711yescharacteristic
186C4×C43#53312yes—
187Dic43—22no—
188Dic43—22no—
189Dic43—22no—
190Dic43—82no—
191Dic43—82no—
192C2×#405—431no—
193#2314—432no—
194#1847—432no—
195#1835—431no—
196#1834—431no—
197#1809—432no—
198#1808—431no—
199#1807—431no—
200#1776—432no—
201C4×#107D4311yescharacteristic, complemented
202C4×#106—431no—
203C2×C43#228511yescharacteristic
204C2×C43#291211yescharacteristic
205C2×C43#291311yescharacteristic
206C2×C43#317812yes—
207C2×C43#317912yes—
208D43—42no—
209C22×M16—431no—
210C23×C8—431no—
211C2×#117—431no—
212C2×#107—432no—
213C2×#107C2×D4312yes—
214C2×#106—432no—
215C2×#106—432no—
216#405—438no—
217C2×#97—431no—
218C2×#97—431no—
219C2×C4×C8—431no—
220C2×C4×C8C2×D4311yescharacteristic
221#388—862no—
222#388—862no—
223#387—862no—
224#387—862no—
225#384—432no—
226#382—432no—
227#380—432no—
228#380—432no—
229C4×C4⋊C4—432no—
230C4×C4⋊C4C2×D4312yes—
231#340—431no—
232#340—431no—
233#340—432no—
234#340—432no—
235#340C2×D4311yescharacteristic
236#340C2×D4311yescharacteristic
237C43#2082211yescharacteristic, complemented, Sylow
238C23×C4—431no—
239C2×M16—434no—
240C2×M16—864no—
241C22×C8—431no—
242C22×C8—431no—
243C22×C8—434no—
244C22×C8—864no—
245C22×C8C22×D4311yescharacteristic
246C22×C8C22×D4311yescharacteristic
247#117—434no—
248#117—434no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—432no—
252C2×C4⋊C4—432no—
253C2×C4⋊C4—862no—
254C2×C4⋊C4—862no—
255C2×C4⋊C4C22×D4312yes—
256C2×C4⋊C4C22×D4312yes—
257C2×C22⋊C4—431no—
258C2×C22⋊C4—431no—
259C2×C22⋊C4—862no—
260C2×C22⋊C4—862no—
261C2×C42—22no—
262C2×C42—431no—
263C2×C42—862no—
264C2×C42C22×D4311yescharacteristic
265#107—24no—
266#107—864no—
267#106—864no—
268#106—864no—
269#97—434no—
270#97—434no—
271C4×C8—434no—
272C4×C8C4×D4314yes—
273#95—22no—
274#95—862no—
275#95—862no—
276#95—862no—
277#95—862no—
278#95—862no—
279C24—431no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—432no—
286C22×C4—432no—
287C22×C4—862no—
288C22×C4—862no—
289C22×C4—862no—
290C22×C4—862no—
291C22×C4D4×D4311yescharacteristic
292C22×C4D4×D4311yescharacteristic
293C22×C4C23×D4311yescharacteristic
294M16—868no—
295C2×C8—22no—
296C2×C8—432no—
297C2×C8—434no—
298C2×C8—432no—
299C2×C8—868no—
300C2×C8—862no—
301C2×C8C2×C4×D4312yes—
302C2×C8C2×C4×D4312yes—
303C2×C8#1062189814yes—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—434no—
309C4⋊C4—434no—
310C4⋊C4—862no—
311C4⋊C4—862no—
312C4⋊C4—862no—
313C4⋊C4—862no—
314C4⋊C4—3442no—
315C4⋊C4—3442no—
316C22⋊C4—434no—
317C22⋊C4—434no—
318C22⋊C4—3442no—
319C22⋊C4—3442no—
320C42—82no—
321C42—432no—
322C42—432no—
323C42—3442no—
324C42C2×C4×D4312yes—
325C42Q8×D4312yes—
326C23—432no—
327C23—861no—
328C23—862no—
329C23—862no—
330C23—861no—
331C23C2×D4×D4311yescharacteristic
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—432no—
342C2×C4—432no—
343C2×C4—432no—
344C2×C4—861no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—861no—
348C2×C4—862no—
349C2×C4—862no—
350C2×C4—864no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4C4⋊C4×D4312yes—
358C2×C4C4⋊C4×D4312yes—
359C2×C4C22×C4×D4311yescharacteristic
360C2×C4C2×Q8×D4311yescharacteristic
361C2×C4#41×D4312yes—
362C2×C4C2×#1062189812yes—
363C8—22no—
364C8—434no—
365C8—862no—
366C8#1306328214yes—
367C22—862no—
368C22—862no—
369C22—862no—
370C22—1722no—
371C22—1722no—
372C22C2×C4⋊C4×D4311yescharacteristic
373C22#1458344612yes—
374C22#1458370011yescharacteristic
375C22#1458370612yes—
376C22#1458371211yescharacteristic
377C4—22no—
378C4—22no—
379C4—82no—
380C4—82no—
381C4—862no—
382C4—862no—
383C4—862no—
384C4—3442no—
385C4—3442no—
386C4#117×D4311yescharacteristic
387C4C2×#1306328211yescharacteristic
388C4#1458345312yes—
389C2—1722no—
390C2#1913699911yescharacteristic
391C2#1914318711yescharacteristic
392C2#1914319111yescharacteristic
393C2#1914526712yes—
394C2#1914528212yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#107×C43C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenterC4×#107D43
hypocenterC43#20822
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
3. #19134762C2semidirect
4. #19134724C2semidirect
5. #19134721C2semidirect
9. #19134493C2semidirect
10. C4×#13063257C2semidirect
11. C4×#107×C43C2semidirect
18. #14582853C4semidirect
201. C4×#107D43semidirect
237. C43#20822semidirect

Maximal subgroups

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

subgroupindex
C2×#145828532
#191372002
#191347622
#191347242
#191347212
#191346292
#191346232
#191346192
#191344932
C4×#130632572
C4×#107×C432
#2082243