Finite Group Databasebeta

← #25196533

Subgroups — #25196533

Order 11008.

798 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
1#19137320C211yesmaximal, characteristic
2#19135738C212yesmaximal, complemented
3#19135728C212yesmaximal, complemented
4#19135418C211yesmaximal, characteristic
5#19135400C211yesmaximal, characteristic
6#19134730C211yesmaximal, characteristic, complemented
7#19134725C211yesmaximal, characteristic, complemented
8#19134602C212yesmaximal, complemented
9#19134592C212yesmaximal, complemented
10#19134452C211yesmaximal, characteristic, complemented
11C43×#2660C211yesmaximal, characteristic, complemented
12C2×#13063322C2211yescharacteristic
13C2×C4×D172C2212yes—
14C2×C4⋊(C43⋊C8)C2212yes—
15C2×#13063245C2212yes—
16C2×#13063245C2212yes—
17C2×#13063245C2212yes—
18C2×#13063245C2212yes—
19C2×#13063236C2211yescharacteristic
20C2×C4×C43⋊C8C2211yescharacteristic
21#14582801C2212yes—
22#14582777—22no—
23#14582777—22no—
24#14582765C2211yescharacteristic
25#14582661C2212yes—
26#14582661C2212yes—
27#14582661C2212yes—
28#14582661C2212yes—
29#14582654C2212yes—
30C2×C4⋊Q8×C43C2211yescharacteristic
31C2×#125×C43C2211yescharacteristic
32C43×#398—22no—
33C43×#395—22no—
34C43×#384C2211yescharacteristic
35C43×#384C2211yescharacteristic
36C43×#382C2211yescharacteristic
37C43×#382C2211yescharacteristic
38C43×#376C2211yescharacteristic
39C22×D172—22no—
40C22×D172C2312yes—
41C22×C4×D43—22no—
42C22×C43⋊C8C2312yes—
43C22×C43⋊C8C2312yes—
44#13063322—22no—
45#13063322Q814yescomplemented
46C4×D172—24no—
47C4×D172—24no—
48C2×C4⋊Dic43C2312yes—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4—22no—
51C2×(C2×D43)⋊C4—22no—
52C4⋊(C43⋊C8)—24no—
53#13063245—42no—
54#13063245—42no—
55#13063245—42no—
56#13063245—42no—
57#13063236—22no—
58C4×C43⋊C8—22no—
59C43⋊#95—22no—
60C22×Q8×C43—21no—
61C4⋊Q8×C43—42no—
62#125×C43—42no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—22no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43C2311yescharacteristic
69C2×C4⋊C4×C43C2311yescharacteristic
70C2×C4⋊C4×C43C2311yescharacteristic
71C2×C4⋊C4×C43C2311yescharacteristic
72C2×C42×C43C2311yescharacteristic
73C2×C42×C43C2311yescharacteristic
74C2×C42×C43C2311yescharacteristic
75#95×C43—22no—
76#95×C43—22no—
77#95×C43D412yes—
78#95×C43D412yes—
79C23×D43—22no—
80C2×Q8×C43—42no—
81C2×Q8×C43—82no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2411yescharacteristic
91C22×Dic43—22no—
92C2×D172—22no—
93C2×D172—28no—
94C2×D172—22no—
95C2×D172—22no—
96C2×D172—22no—
97C2×D172—22no—
98C2×D172—82no—
99C2×D172—82no—
100C2×D172C2×Q814yes—
101C2×C4×D43—44no—
102C2×C4×D43—82no—
103C2×C4×D43—82no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—42no—
109C4⋊C4×C43—42no—
110C4⋊C4×C43—42no—
111C4⋊C4×C43—82no—
112C4⋊C4×C43—82no—
113C42×C43—22no—
114C42×C43C2×Q812yes—
115C42×C43#4112yes—
116C42×C43#4114yes—
117(C2×D43)⋊C4—44no—
118(C2×D43)⋊C4—82no—
119(C2×D43)⋊C4—82no—
120C4⋊Dic43—22no—
121C4⋊Dic43—22no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—22no—
128C23×C43C22×D411yescharacteristic
129C22×D43—24no—
130C22×D43—42no—
131C22×D43—42no—
132C22×D43—42no—
133C22×D43—42no—
134C22×D43—42no—
135C22×D43—42no—
136Q8×C43—84no—
137C2×C4×C43—22no—
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—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43C22⋊Q814yes—
154C2×C4×C43#12414yes—
155C2×C4×C43C22×Q811yescharacteristic
156C2×C4×C43C2×#4112yes—
157C2×C4×C43C2×#4111yescharacteristic
158C2×C4×C43H(5,𝔽2)12yes—
159C2×Dic43—42no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162D172—24no—
163D172—24no—
164D172—42no—
165D172—42no—
166D172—88no—
167C4×D43—88no—
168C43⋊C8—42no—
169C43⋊C8—42no—
170#29152—431nomaximal, Sylow
171C22×C43C2×C22⋊Q811yescharacteristic
172C22×C43C2×#12411yescharacteristic
173C22×C43#53511yescharacteristic
174C22×C43#57612yes—
175C22×C43#57712yes—
176C2×D43—44no—
177C2×D43—44no—
178C2×D43—44no—
179C2×D43—82no—
180C2×D43—82no—
181C2×D43—82no—
182C2×D43—82no—
183C4×C43—24no—
184C4×C43—24no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—81no—
188C4×C43—81no—
189C4×C43—81no—
190C4×C43—81no—
191C4×C43#55412yes—
192C4×C43#55512yes—
193Dic43—82no—
194#2660D4311yescharacteristic, complemented
195#2328—431no—
196#2025—432no—
197#2023—432no—
198#1961—431no—
199#1957—431no—
200#1836—431no—
201#1835—431no—
202#1804—432no—
203#1802—432no—
204#1768—431no—
205C2×C43#256311yescharacteristic
206C2×C43#308112yes—
207C2×C43#313612yes—
208C2×C43#322011yescharacteristic
209C2×C43#322111yescharacteristic
210D43—84no—
211C2×C4⋊Q8C2×D4311yescharacteristic
212C2×#127—431no—
213C2×#125C2×D4311yescharacteristic
214C2×C4×D4—432no—
215C2×C4⋊C8—432no—
216C2×#102—432no—
217C2×#102—432no—
218C2×#102—432no—
219C2×#102—432no—
220C2×#97—431no—
221C2×C4×C8—431no—
222#398—22no—
223#395—22no—
224#390—432no—
225#386—862no—
226#386—862no—
227#384C2×D4311yescharacteristic
228#384C2×D4311yescharacteristic
229#382—431no—
230#382C2×D4311yescharacteristic
231#382C2×D4311yescharacteristic
232#376C2×D4311yescharacteristic
233#340—432no—
234#340—432no—
235#340—432no—
236#340—432no—
237#336—432no—
238C43#2915211yescharacteristic, complemented, Sylow
239C22×Q8—21no—
240C22×D4—432no—
241C22×D4—862no—
242C23×C4—862no—
243C22×C8—432no—
244C22×C8—432no—
245C4⋊Q8—42no—
246#127—434no—
247#127—862no—
248#125—42no—
249C4×D4—864no—
250C4×D4—864no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—432no—
257C2×C4⋊C4C22×D4311yescharacteristic
258C2×C4⋊C4C22×D4311yescharacteristic
259C2×C4⋊C4C22×D4311yescharacteristic
260C2×C4⋊C4C22×D4311yescharacteristic
261C2×C22⋊C4—862no—
262C2×C22⋊C4—862no—
263C2×C22⋊C4—862no—
264C2×C42C22×D4311yescharacteristic
265C2×C42C22×D4311yescharacteristic
266C2×C42C22×D4311yescharacteristic
267C4⋊C8—864no—
268#102—1722no—
269#102—1722no—
270#102—1722no—
271#102—1722no—
272#97—862no—
273C4×C8—862no—
274#95—22no—
275#95—22no—
276#95—862no—
277#95C22⋊D4312yes—
278#95C22⋊D4312yes—
279C24—862no—
280C2×Q8—42no—
281C2×Q8—82no—
282C2×D4—434no—
283C2×D4—868no—
284C2×D4—862no—
285C2×D4—862no—
286C2×D4—862no—
287C2×D4—862no—
288C2×D4—862no—
289C2×D4—3442no—
290C2×D4—3442no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—862no—
296C22×C4—3442no—
297C22×C4—3442no—
298C22×C4—1724no—
299C22×C4C2×C22⋊D4311yescharacteristic
300C22×C4C2×C22⋊D4311yescharacteristic
301C22×C4C2×C22⋊D4312yes—
302C22×C4C2×C22⋊D4312yes—
303C22×C4C23×D4311yescharacteristic
304C2×C8—862no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8—862no—
308C2×C8—862no—
309C2×C8—862no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—82no—
318C4⋊C4—82no—
319C4⋊C4—862no—
320C4⋊C4—862no—
321C22⋊C4—3442no—
322C22⋊C4—3442no—
323C22⋊C4—1724no—
324C42—22no—
325C42Q8×D4312yes—
326C42#1062190212yes—
327C42#1062190214yes—
328C23—864no—
329C23—1722no—
330C23—1722no—
331C23—1722no—
332C23—1722no—
333C23—1722no—
334C23—1722no—
335C23C22×C22⋊D4311yescharacteristic
336Q8—84no—
337D4—864no—
338D4—864no—
339D4—3448no—
340D4—1722no—
341D4—1722no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—3448no—
359C2×C4—1722no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4#1306330114yes—
363C2×C4#1306331414yes—
364C2×C4C2×Q8×D4311yescharacteristic
365C2×C4C2×#1062190212yes—
366C2×C4C2×#1062190211yescharacteristic
367C2×C4#1306337012yes—
368C8—1722no—
369C8—1722no—
370C22—3442no—
371C22—3442no—
372C22—3442no—
373C22—3442no—
374C22—1724no—
375C22—1724no—
376C22—1724no—
377C22C2×#1306330111yescharacteristic
378C22C2×#1306331411yescharacteristic
379C22#1458346611yescharacteristic
380C22#1458370212yes—
381C22#1458370712yes—
382C4—24no—
383C4—24no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—3442no—
391C4#1458361012yes—
392C4#1458361512yes—
393C2—3444no—
394C2#1913976911yescharacteristic
395C2#1914442012yes—
396C2#1914495412yes—
397C2#1914564511yescharacteristic
398C2#1914565611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2660C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#2660D43
hypocenterC43#29152
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #2660

Complements

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

NH ≅ G/Ntype
2. #19135738C2semidirect
3. #19135728C2semidirect
6. #19134730C2semidirect
7. #19134725C2semidirect
8. #19134602C2semidirect
9. #19134592C2semidirect
10. #19134452C2semidirect
11. C43×#2660C2semidirect
45. #13063322Q8semidirect
194. #2660D43semidirect
238. C43#29152semidirect

Maximal subgroups

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

subgroupindex
#191373202
#191357382
#191357282
#191354182
#191354002
#191347302
#191347252
#191346022
#191345922
#191344522
C43×#26602
#2915243