Finite Group Databasebeta

← #25096755

Subgroups — #25096755

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582924C212yesmaximal
2#19136934C211yesmaximal, characteristic
3#19134715C211yesmaximal, characteristic, complemented
4#19134713C211yesmaximal, characteristic, complemented
5#19134713C211yesmaximal, characteristic, complemented
6#19134711C212yesmaximal, complemented
7#19134710C212yesmaximal, complemented
8#19134290C212yesmaximal
9#19134287C211yesmaximal, characteristic
10#336×D43C211yesmaximal, characteristic
11C43×#1832C211yesmaximal, characteristic, complemented
12C22×#10621872C2212yes—
13C22×C8×D43C2212yes—
14C2×#13063282C2211yescharacteristic
15C2×#13063282C2211yescharacteristic
16C2×C42×D43C2211yescharacteristic
17#14582924—28no—
18C2×C4⋊(C43⋊C8)C2212yes—
19C2×Dic43⋊C8C2212yes—
20C2×Dic43⋊C8C2212yes—
21#14582750C412yes—
22#14582750C412yes—
23#14582746C412yes—
24#14582746C412yes—
25#14582745C2211yescharacteristic
26C42×Dic43C2211yescharacteristic
27C42×Dic43C2211yescharacteristic
28#14582654C2211yescharacteristic
29#14582654C2211yescharacteristic
30#14582654C2212yes—
31#14582653C2212yes—
32#14582653C2212yes—
33#14582653C2212yes—
34#14582653C2212yes—
35C2×C4⋊C8×C43C2212yes—
36C43×#376C2211yescharacteristic
37C43×#336C2211yescharacteristic
38C43×#336C2211yescharacteristic
39C43×#336C2212yes—
40C22×C4×D43C2×C412yes—
41C22×C4×D43C2311yescharacteristic
42C2×#10621872—24no—
43C2×#10621872—24no—
44C2×#10621872—24no—
45C22×C43⋊C8C2312yes—
46C22×C43⋊C8C2312yes—
47C2×C8×D43—24no—
48C2×C8×D43—24no—
49C2×C8×D43—24no—
50#13063282—24no—
51#13063282D414yes—
52#13063282Q814yes—
53C2×Dic43⋊C4C2×C411yescharacteristic
54C2×Dic43⋊C4C2×C411yescharacteristic
55C2×Dic43⋊C4C2×C412yes—
56C2×(C2×D43)⋊C4C2×C411yescharacteristic
57C2×(C2×D43)⋊C4C2×C411yescharacteristic
58C2×(C2×D43)⋊C4C2×C412yes—
59C2×C4×Dic43C2×C412yes—
60C2×C4×Dic43C2×C412yes—
61C2×C4×Dic43C2×C412yes—
62C2×C4×Dic43C2×C412yes—
63C2×C4×Dic43C2×C412yes—
64C2×C4×Dic43C2311yescharacteristic
65C2×C4×Dic43C2311yescharacteristic
66C2×C4×Dic43C2311yescharacteristic
67C42×D43—24no—
68C4⋊(C43⋊C8)—24no—
69Dic43⋊C8—24no—
70Dic43⋊C8—24no—
71C43⋊#95C2×C412yes—
72C43⋊#95C2×C412yes—
73C22×C8×C43C2312yes—
74C22×C8×C43C2312yes—
75C2×C42×C43C2311yescharacteristic
76C2×C42×C43C2311yescharacteristic
77C2×C42×C43C2311yescharacteristic
78C4⋊C8×C43—24no—
79#95×C43C2×C412yes—
80#95×C43C2×C412yes—
81C23×D43C22×C411yescharacteristic
82C22×C4×C43C22×C412yes—
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C22×C412yes—
86C22×C4×C43C2411yescharacteristic
87C22×Dic43C22×C411yescharacteristic
88C22×Dic43C22×C411yescharacteristic
89C22×Dic43C22×C412yes—
90C22×Dic43C22×C412yes—
91C22×Dic43C22×C411yescharacteristic
92C2×C4×D43—24no—
93C2×C4×D43—24no—
94C2×C4×D43—42no—
95C2×C4×D43C2×D412yes—
96C2×C4×D43C2×Q812yes—
97C2×C4×D43#4114yes—
98C2×C4×D43#4114yes—
99C2×C8×C43—22no—
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C2×C8×C43—22no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C42×C43—22no—
106C42×C43—22no—
107C42×C43C2×D412yes—
108C42×C43C2×Q812yes—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4C4⋊C418yes—
112Dic43⋊C4—22no—
113Dic43⋊C4—22no—
114Dic43⋊C4C4⋊C418yes—
115C4×Dic43—22no—
116C4×Dic43—22no—
117C4×Dic43—24no—
118C4×Dic43—24no—
119C4×Dic43—24no—
120C4×Dic43—42no—
121C4×Dic43—42no—
122C4×Dic43C2×D412yes—
123C4×Dic43C2×Q812yes—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130#10621872—48no—
131C8×D43—48no—
132C23×C43C23×C411yescharacteristic
133C22×D43—22no—
134C22×D43—22no—
135C22×D43C2×C4⋊C412yes—
136C22×D43#11712yes—
137C22×D43#11712yes—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43C2×C4⋊C414yes—
148C2×C4×C43C22×D411yescharacteristic
149C2×C4×C43C22×Q811yescharacteristic
150C2×C4×C43C2×#4112yes—
151C2×C4×C43C2×#4112yes—
152C2×Dic43—22no—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—22no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—22no—
159C2×Dic43—22no—
160C2×Dic43C2×C4⋊C414yes—
161C2×Dic43C2×C4⋊C412yes—
162C2×Dic43#11712yes—
163C2×Dic43#11712yes—
164C2×Dic43#13114yes—
165C4×D43—48no—
166C4×D43#12418yes—
167C4×D43#12518yes—
168C8×C43—42no—
169C8×C43—42no—
170C43⋊C8—42no—
171C43⋊C8—42no—
172#20754—431nomaximal, Sylow
173C22×C43C22×C4⋊C411yescharacteristic
174C22×C43C2×#11711yescharacteristic
175C22×C43C2×#11711yescharacteristic
176C22×C43C2×#13112yes—
177C22×C43#56812yes—
178C2×D43—24no—
179C2×D43—22no—
180C2×D43—22no—
181C2×D43—24no—
182C2×D43#38214yes—
183C4×C43—24no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—42no—
187C4×C43C2×#12412yes—
188C4×C43C2×#12512yes—
189Dic43—24no—
190Dic43—24no—
191Dic43—41no—
192Dic43—41no—
193Dic43#38214yes—
194C2×#424—432no—
195C4×#117—431no—
196#1832—431no—
197#1832—431no—
198#1832—431no—
199#1832D4311yescharacteristic, complemented
200#1831—432no—
201#1831—432no—
202#1729—432no—
203#1728—431no—
204C2×#336—431no—
205C2×C43C2×#38211yescharacteristic
206C2×C43#290612yes—
207C2×C43#292211yescharacteristic
208C2×C43#292311yescharacteristic
209C2×C43#292412yes—
210D43—24no—
211C22×M16—432no—
212C23×C8—432no—
213C2×#117—431no—
214C2×#117—431no—
215C22×C42—431no—
216#424—868no—
217C2×C4⋊C8—432no—
218C2×C4⋊C8—432no—
219C2×C4⋊C8—432no—
220C2×C4⋊C8C2×D4312yes—
221C4×C4⋊C4—432no—
222C4×C4⋊C4—432no—
223C4×C22⋊C4—432no—
224C4×C22⋊C4—432no—
225#376—431no—
226#376C2×D4311yescharacteristic
227C43—431no—
228C43—431no—
229#336—432no—
230#336—432no—
231#336—432no—
232#336—432no—
233#336—432no—
234#336—431no—
235#336—431no—
236#336C2×D4312yes—
237#336C2×D4311yescharacteristic
238#336C2×D4311yescharacteristic
239C43#2075411yescharacteristic, complemented, Sylow
240C23×C4—431no—
241C23×C4—432no—
242C2×M16—864no—
243C2×M16—864no—
244C2×M16—864no—
245C22×C8—432no—
246C22×C8—432no—
247C22×C8—864no—
248C22×C8—864no—
249C22×C8—864no—
250C22×C8C22×D4312yes—
251C22×C8C22×D4312yes—
252#117—434no—
253#117—434no—
254#117—864no—
255C2×C4⋊C4—432no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—431no—
258C2×C22⋊C4—432no—
259C2×C22⋊C4—431no—
260C2×C22⋊C4—431no—
261C2×C42—431no—
262C2×C42—432no—
263C2×C42—432no—
264C2×C42—432no—
265C2×C42—431no—
266C2×C42—431no—
267C2×C42—432no—
268C2×C42—432no—
269C2×C42—864no—
270C2×C42C22×D4311yescharacteristic
271C2×C42C22×D4311yescharacteristic
272C2×C42C22×D4311yescharacteristic
273C4⋊C8—24no—
274C4⋊C8—864no—
275C4⋊C8—864no—
276C4⋊C8—864no—
277#95—432no—
278#95—432no—
279#95C4×D4312yes—
280#95C4×D4312yes—
281C24—431no—
282C22×C4—431no—
283C22×C4—432no—
284C22×C4—432no—
285C22×C4—434no—
286C22×C4—434no—
287C22×C4—432no—
288C22×C4—432no—
289C22×C4—431no—
290C22×C4—431no—
291C22×C4—864no—
292C22×C4—864no—
293C22×C4—1722no—
294C22×C4C2×C4×D4312yes—
295C22×C4C2×C4×D4311yescharacteristic
296C22×C4C2×C4×D4311yescharacteristic
297C22×C4C2×C4×D4312yes—
298C22×C4C23×D4311yescharacteristic
299M16—1728no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—862no—
307C2×C8—862no—
308C2×C8—862no—
309C2×C8—862no—
310C2×C8—862no—
311C2×C8—862no—
312C2×C8—1728no—
313C4⋊C4—438no—
314C4⋊C4—862no—
315C4⋊C4—862no—
316C22⋊C4—438no—
317C22⋊C4—862no—
318C22⋊C4—862no—
319C42—22no—
320C42—22no—
321C42—432no—
322C42—432no—
323C42—864no—
324C42—864no—
325C42—864no—
326C42—862no—
327C42—862no—
328C42—1722no—
329C42—1722no—
330C42D4×D4312yes—
331C42Q8×D4312yes—
332C23—432no—
333C23—432no—
334C23—432no—
335C23—862no—
336C23—862no—
337C23C22×C4×D4311yescharacteristic
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—432no—
348C2×C4—432no—
349C2×C4—432no—
350C2×C4—438no—
351C2×C4—438no—
352C2×C4—434no—
353C2×C4—434no—
354C2×C4—862no—
355C2×C4—862no—
356C2×C4—862no—
357C2×C4—862no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—862no—
361C2×C4—862no—
362C2×C4—1728no—
363C2×C4C4⋊C4×D4314yes—
364C2×C4C2×D4×D4311yescharacteristic
365C2×C4C2×Q8×D4311yescharacteristic
366C2×C4#41×D4312yes—
367C2×C4#41×D4312yes—
368C8—42no—
369C8—42no—
370C8—1722no—
371C8—1722no—
372C22—434no—
373C22—862no—
374C22—862no—
375C22—864no—
376C22—864no—
377C22C2×C4⋊C4×D4311yescharacteristic
378C22#117×D4311yescharacteristic
379C22#117×D4311yescharacteristic
380C22#131×D4312yes—
381C22#1458366412yes—
382C4—24no—
383C4—41no—
384C4—41no—
385C4—42no—
386C4—434no—
387C4—864no—
388C4—864no—
389C4—1721no—
390C4—1721no—
391C4#124×D4312yes—
392C4#125×D4312yes—
393C2—864no—
394C2#382×D4311yescharacteristic
395C2#1914316212yes—
396C2#1914323611yescharacteristic
397C2#1914324311yescharacteristic
398C2#1914325112yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1832C2
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenter#1832D43
hypocenterC43#20754
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1832

Complements

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

NH ≅ G/Ntype
3. #19134715C2semidirect
4. #19134713C2semidirect
5. #19134713C2semidirect
6. #19134711C2semidirect
7. #19134710C2semidirect
11. C43×#1832C2semidirect
199. #1832D43semidirect
239. C43#20754semidirect

Maximal subgroups

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

subgroupindex
C2×#145829242
#191369342
#191347152
#191347132
#191347112
#191347102
#191342902
#191342872
#336×D432
C43×#18322
#2075443