Finite Group Databasebeta

← #25100745

Subgroups — #25100745

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582959C212yesmaximal, complemented
2#19137056C211yesmaximal, characteristic
3#19135393C211yesmaximal, characteristic
4#19135392C211yesmaximal, characteristic
5#19135319C211yesmaximal, characteristic, complemented
6#19135202C212yesmaximal, complemented
7#19135200C212yesmaximal, complemented
8C4⋊C8×Dic43C211yesmaximal, characteristic, complemented
9#19134360C212yesmaximal, complemented
10#97×Dic43C211yesmaximal, characteristic, complemented
11C43×#1940C211yesmaximal, characteristic, complemented
12C2×C4×D172C2211yescharacteristic
13C2×#13063282C2212yes—
14#14582959—28no—
15C2×C4⋊(C43⋊C8)C2212yes—
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×(C2×D43)⋊C8C2212yes—
18C2×(C2×D43)⋊C8C2212yes—
19C2×(C2×D43)⋊C8C2212yes—
20C2×(C2×D43)⋊C8C2212yes—
21C2×#13063236C2211yescharacteristic
22C2×#13063235C2211yescharacteristic
23C2×#13063235C2211yescharacteristic
24C2×C8×Dic43C2212yes—
25C2×C8×Dic43C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582800C412yes—
28#14582795C412yes—
29#14582788C414yes—
30C4×(C2×D43)⋊C4C2212yes—
31C42×Dic43C2211yescharacteristic
32#14582654C2212yes—
33#14582653C2212yes—
34C2×C4⋊C8×C43C2212yes—
35C2×C4⋊C8×C43C2211yescharacteristic
36C2×#97×C43C2211yescharacteristic
37C4×C4⋊C4×C43C2211yescharacteristic
38C43×#336C2212yes—
39C22×D172C2×C411yescharacteristic
40C22×C4×D43C2312yes—
41C22×C43⋊C8C2312yes—
42C22×C43⋊C8C2311yescharacteristic
43C22×C43⋊C8C2311yescharacteristic
44C4×D172—22no—
45C4×D172—22no—
46#13063282—24no—
47#13063282—24no—
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×Dic43⋊C4C2×C414yes—
50C2×(C2×D43)⋊C4C2×C412yes—
51C2×(C2×D43)⋊C4C2×C414yes—
52C2×(C2×D43)⋊C4C2×C414yes—
53C2×C4×Dic43C2×C412yes—
54C2×C4×Dic43C2×C412yes—
55C2×C4×Dic43C2311yescharacteristic
56C2×C4×Dic43C2311yescharacteristic
57C4⋊(C43⋊C8)—22no—
58C4⋊(C43⋊C8)—24no—
59(C2×D43)⋊C8—24no—
60(C2×D43)⋊C8—24no—
61(C2×D43)⋊C8—24no—
62(C2×D43)⋊C8—24no—
63#13063236—22no—
64#13063235—22no—
65#13063235D414yescomplemented
66C8×Dic43—22no—
67C8×Dic43—24no—
68C8×Dic43—22no—
69C43⋊#95C2×C414yes—
70C22×C8×C43C2312yes—
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C2×C4⋊C4×C43C2×C412yes—
74C2×C42×C43C2312yes—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—24no—
77C4⋊C8×C43—22no—
78#97×C43—22no—
79#95×C43C2×C412yes—
80C23×D43C22×C412yes—
81C22×C4×C43C22×C414yes—
82C22×C4×C43C22×C411yescharacteristic
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2411yescharacteristic
85C22×Dic43C22×C412yes—
86C22×Dic43C22×C412yes—
87C22×Dic43C22×C412yes—
88C2×D172—22no—
89C2×D172—42no—
90C2×C4×D43—22no—
91C2×C4×D43—22no—
92C2×C4×D43—22no—
93C2×C4×D43—22no—
94C2×C4×D43—22no—
95C2×C4×D43—22no—
96C2×C8×C43—21no—
97C2×C8×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C2×C8×C43—22no—
103C2×C8×C43C2×D412yes—
104C2×C8×C43#4112yes—
105C4⋊C4×C43—42no—
106C42×C43—22no—
107C42×C43—22no—
108C42×C43#4112yes—
109C42×C43#4112yes—
110(C2×D43)⋊C4—24no—
111(C2×D43)⋊C4—28no—
112(C2×D43)⋊C4—28no—
113C4⋊Dic43—22no—
114Dic43⋊C4—28no—
115C4×Dic43—21no—
116C4×Dic43—21no—
117C4×Dic43—24no—
118C4×Dic43—42no—
119C4×Dic43C2×D412yes—
120C4×Dic43#4112yes—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8C2×D412yes—
129C2×C43⋊C8#4112yes—
130C23×C43C23×C411yescharacteristic
131C22×D43—22no—
132C22×D43—22no—
133C22×D43—22no—
134C22×D43—24no—
135C22×D43—24no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—24no—
139C2×C4×C43—24no—
140C2×C4×C43—24no—
141C2×C4×C43#11712yes—
142C2×C4×C43#11712yes—
143C2×C4×C43C22×D411yescharacteristic
144C2×C4×C43C2×#4111yescharacteristic
145C2×C4×C43C2×#4111yescharacteristic
146C2×C4×C43C2×#4111yescharacteristic
147C2×C4×C43C2×#4111yescharacteristic
148C2×C4×C43C2×#4111yescharacteristic
149C2×Dic43—22no—
150C2×Dic43—22no—
151C2×Dic43—22no—
152C2×Dic43—22no—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—22no—
156C2×Dic43C4×D414yes—
157C2×Dic43#13114yes—
158D172—44no—
159C4×D43—42no—
160C4×D43—42no—
161C4×D43—42no—
162C4×D43—42no—
163C8×C43—22no—
164C8×C43—22no—
165C8×C43—42no—
166C43⋊C8—22no—
167C43⋊C8—22no—
168C43⋊C8—42no—
169#21269—431nomaximal, Sylow
170C22×C43C2×#11711yescharacteristic
171C22×C43C2×C4×D411yescharacteristic
172C22×C43C4×#4111yescharacteristic
173C22×C43C2×#13112yes—
174C22×C43#56812yes—
175C2×D43—42no—
176C2×D43—42no—
177C2×D43—44no—
178C2×D43—44no—
179C2×D43—42no—
180C4×C43—22no—
181C4×C43—22no—
182C4×C43—44no—
183C4×C43#52911yescharacteristic
184C4×C43#52911yescharacteristic
185C4×C43#53211yescharacteristic
186C4×C43#53211yescharacteristic
187Dic43—24no—
188Dic43—24no—
189Dic43—42no—
190C2×#433—432no—
191#2293—431no—
192#1955—431no—
193#1955—431no—
194#1940—431no—
195#1940D4311yescharacteristic, complemented
196#1923—432no—
197#1923—432no—
198C4×C4⋊C8—431no—
199#1750—432no—
200C4×#97—431no—
201C2×C43#229311yescharacteristic
202C2×C43#292111yescharacteristic
203C2×C43#292211yescharacteristic
204C2×C43#293512yes—
205C2×C43#296812yes—
206D43—82no—
207C2×C4×D4—431no—
208C2×#117—432no—
209#433—868no—
210C2×C4⋊C8—432no—
211C2×C4⋊C8—431no—
212C2×C4⋊C8C2×D4312yes—
213C2×C4⋊C8C2×D4311yescharacteristic
214C2×C22⋊C8—432no—
215C2×C22⋊C8—432no—
216C2×C22⋊C8—432no—
217C2×C22⋊C8—432no—
218C2×#97—431no—
219C2×#97—431no—
220C2×#97—431no—
221C2×#97C2×D4311yescharacteristic
222C2×C4×C8—432no—
223C2×C4×C8—431no—
224C2×C4×C8—431no—
225#390—432no—
226#389—432no—
227#388—434no—
228C4×C4⋊C4C2×D4311yescharacteristic
229C4×C22⋊C4—432no—
230C43—431no—
231#336—432no—
232#336—432no—
233#336C2×D4312yes—
234C43#2126911yescharacteristic, complemented, Sylow
235C22×D4—431no—
236C23×C4—432no—
237C22×C8—431no—
238C22×C8—431no—
239C22×C8—432no—
240C22×C8C22×D4312yes—
241C22×C8C22×D4311yescharacteristic
242C22×C8C22×D4311yescharacteristic
243C4×D4—862no—
244C4×D4—862no—
245#117—864no—
246#117—864no—
247C2×C4⋊C4—434no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4C4×D4312yes—
250C2×C22⋊C4—434no—
251C2×C22⋊C4—432no—
252C2×C22⋊C4—434no—
253C2×C42—431no—
254C2×C42—432no—
255C2×C42—431no—
256C2×C42—432no—
257C2×C42C22×D4312yes—
258C2×C42C22×D4311yescharacteristic
259C4⋊C8—24no—
260C4⋊C8—22no—
261C4⋊C8—864no—
262C4⋊C8—862no—
263C22⋊C8—864no—
264C22⋊C8—864no—
265C22⋊C8—864no—
266C22⋊C8—864no—
267#97—22no—
268#97—434no—
269#97—862no—
270#97—862no—
271C4×C8—864no—
272C4×C8—862no—
273C4×C8—862no—
274#95—434no—
275#95C4×D4312yes—
276C24—432no—
277C2×D4—862no—
278C2×D4—1722no—
279C22×C4—432no—
280C22×C4—432no—
281C22×C4—432no—
282C22×C4—862no—
283C22×C4—862no—
284C22×C4—862no—
285C22×C4—862no—
286C22×C4—862no—
287C22×C4—862no—
288C22×C4C2×C4×D4314yes—
289C22×C4C2×C4×D4311yescharacteristic
290C22×C4C2×C4×D4311yescharacteristic
291C22×C4C23×D4311yescharacteristic
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—432no—
300C2×C8—432no—
301C2×C8—861no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8—861no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8—862no—
308C2×C8D4×D4312yes—
309C2×C8#1062190212yes—
310C4⋊C4—42no—
311C4⋊C4—868no—
312C4⋊C4—862no—
313C22⋊C4—868no—
314C22⋊C4—868no—
315C22⋊C4—864no—
316C42—22no—
317C42—22no—
318C42—432no—
319C42—432no—
320C42—864no—
321C42—861no—
322C42—861no—
323C42—1722no—
324C42#1062190012yes—
325C42#1062190212yes—
326C23—862no—
327C23—862no—
328C23—862no—
329C23—864no—
330C23—864no—
331C23C22×C4×D4311yescharacteristic
332D4—1724no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—434no—
339C2×C4—434no—
340C2×C4—862no—
341C2×C4—862no—
342C2×C4—862no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—1722no—
348C2×C4—1722no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4#1306328312yes—
352C2×C4#1306328312yes—
353C2×C4C2×D4×D4311yescharacteristic
354C2×C4#41×D4311yescharacteristic
355C2×C4#41×D4311yescharacteristic
356C2×C4C2×#1062190011yescharacteristic
357C2×C4C2×#1062190211yescharacteristic
358C2×C4C2×#1062190211yescharacteristic
359C8—22no—
360C8—22no—
361C8—42no—
362C8—862no—
363C8—862no—
364C8—1722no—
365C22—1722no—
366C22—1722no—
367C22—1722no—
368C22—1724no—
369C22—1724no—
370C22C2×#1306328311yescharacteristic
371C22C4×D4×D4311yescharacteristic
372C22C4×#1062190211yescharacteristic
373C22#131×D4312yes—
374C22#1458366512yes—
375C4—22no—
376C4—22no—
377C4—44no—
378C4—864no—
379C4—864no—
380C4—1722no—
381C4#1458343411yescharacteristic
382C4#1458343511yescharacteristic
383C4#1458344411yescharacteristic
384C4#1458345011yescharacteristic
385C2—3442no—
386C2#1913705311yescharacteristic
387C2#1914323211yescharacteristic
388C2#1914323811yescharacteristic
389C2#1914333612yes—
390C2#1914358812yes—
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1940C2
prime radicalC22×D172C2×C4
cosocleC22×C4×C43C24
hypercenter#1940D43
hypocenterC43#21269
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. C2×#14582959C2semidirect
5. #19135319C2semidirect
6. #19135202C2semidirect
7. #19135200C2semidirect
8. C4⋊C8×Dic43C2semidirect
9. #19134360C2semidirect
10. #97×Dic43C2semidirect
11. C43×#1940C2semidirect
65. #13063235D4semidirect
195. #1940D43semidirect
234. C43#21269semidirect

Maximal subgroups

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

subgroupindex
C2×#145829592
#191370562
#191353932
#191353922
#191353192
#191352022
#191352002
C4⋊C8×Dic432
#191343602
#97×Dic432
C43×#19402
#2126943