Finite Group Databasebeta

← #25009141

Subgroups — #25009141

Order 11008.

486 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135846C211yesmaximal, characteristic
2#19133614C211yesmaximal, characteristic
3#19133546C211yesmaximal, characteristic
4#19132619C211yesmaximal, characteristic, complemented
5#19132616C211yesmaximal, characteristic, complemented
6#19132543C211yesmaximal, characteristic, complemented
7C43×#2677C211yesmaximal, characteristic, complemented
8#14583461C2211yescharacteristic
9#14583217—21no—
10#14583038—21no—
11C2×#13063239—21no—
12#14582778—21no—
13#14582666C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C2×C4⋊Q8×C43—21no—
19C2×C22⋊Q8×C43—21no—
20C43×#399C2211yescharacteristic
21C43×#398—21no—
22C43×#395—21no—
23C43×#393C2211yescharacteristic
24C43×#388—21no—
25C43×#387—21no—
26C43×#385C2211yescharacteristic
27C22×C22⋊D43—21no—
28C2×#10621884—41no—
29#13063309—41no—
30#13063299—21no—
31#13063299—21no—
32#13063295—41no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—41no—
35#13063256—41no—
36#13063249—41no—
37#13063245—41no—
38#13063239—42no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C43⋊#95—41no—
42C22×Q8×C43—21no—
43C22×Q8×C43D411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C4⋊Q8×C43—44no—
46C22⋊Q8×C43—44no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43C2311yescharacteristic
58C2×C42×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43D411yescharacteristic
64#95×C43D411yescharacteristic
65C24×C43C2×D411yescharacteristic
66C23×D43—21no—
67C2×Q8×C43—42no—
68C2×Q8×C43—42no—
69C2×Q8×C43—42no—
70C2×Q8×C43—41no—
71C2×Q8×C43—81no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—41no—
79C22×C4×C43—42no—
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C22×Dic43—21no—
89C22×Dic43—41no—
90C2×D172—21no—
91C2×D172—21no—
92C4⋊C4×C43—24no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—42no—
95C4⋊C4×C43—42no—
96C4⋊C4×C43—42no—
97C4⋊C4×C43—42no—
98C4⋊C4×C43—42no—
99C22⋊C4×C43—21no—
100C22⋊C4×C43—41no—
101C22⋊C4×C43—42no—
102C22⋊C4×C43—42no—
103C22⋊C4×C43SD1612yescomplemented
104C42×C43—42no—
105C22⋊Dic43—41no—
106C22⋊Dic43—41no—
107#10621884—82no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110(C2×D43)⋊C4—82no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43#12011yescharacteristic
120C23×C43C2×SD1611yescharacteristic
121C23×C43#13711yescharacteristic
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—81no—
126C22×D43—81no—
127Q8×C43—42no—
128Q8×C43—81no—
129Q8×C43—84no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—81no—
154C22⋊D43—81no—
155C22⋊D43—81no—
156C22⋊D43—81no—
157C22⋊D43—81no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—81no—
162C2×Dic43—81no—
163C2×Dic43—81no—
164D172—81no—
165D172—81no—
166C43⋊C8—81no—
167C43⋊C8—81no—
168#12176—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—81no—
178C22×C43#44811yescharacteristic
179C22×C43#45411yescharacteristic
180C22×C43B(4,𝔽2)11yescharacteristic
181C2×D43—82no—
182C2×D43—81no—
183C2×D43—81no—
184C2×D43—81no—
185C2×D43—161no—
186C4×C43—42no—
187C4×C43—42no—
188C4×C43—41no—
189C4×C43—42no—
190C4×C43—42no—
191C4×C43—41no—
192C4×C43—81no—
193C4×C43—81no—
194Dic43—81no—
195Dic43—161no—
196#2677D4311yescharacteristic, complemented
197#2044—431no—
198#1613—431no—
199#1601—431no—
200#1352—431no—
201#1351—431no—
202#1326—431no—
203C2×C43—21no—
204C2×C43—21no—
205C2×C43—41no—
206C2×C43—41no—
207C2×C43#159911yescharacteristic
208C2×C43#219611yescharacteristic
209C2×C43#220111yescharacteristic
210D43—161no—
211#534—431no—
212C2×C4⋊Q8—21no—
213C2×C22⋊Q8—21no—
214#481—861no—
215#448—861no—
216C2×#99—861no—
217#399C2×D4311yescharacteristic
218#398—21no—
219#395—21no—
220#393C2×D4311yescharacteristic
221#388—21no—
222#387—21no—
223#386—861no—
224#385C2×D4311yescharacteristic
225#342—431no—
226#327—861no—
227#327—861no—
228#323—431no—
229#323—431no—
230C43#1217611yescharacteristic, complemented, Sylow
231C22×Q8—21no—
232C22×Q8C22⋊D4311yescharacteristic
233C22×D4—861no—
234C23×C4C22⋊D4311yescharacteristic
235C2×SD16—1721no—
236C4⋊Q8—44no—
237#123—1721no—
238C22⋊Q8—44no—
239#121—861no—
240#121—861no—
241#120—1721no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C22⋊D4311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4—1721no—
253C2×C22⋊C4C22⋊D4311yescharacteristic
254C2×C22⋊C4C22×D4311yescharacteristic
255C2×C42—21no—
256#106—1721no—
257#103—1721no—
258#102—1721no—
259#99—1722no—
260C22⋊C8—861no—
261C22⋊C8—861no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—1721no—
267#95C22⋊D4311yescharacteristic
268#95C22⋊D4311yescharacteristic
269C24—861no—
270C24C2×C22⋊D4311yescharacteristic
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—41no—
275C2×Q8—81no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—1721no—
279C2×D4—1721no—
280C2×D4—1721no—
281C2×D4—1721no—
282C2×D4—1721no—
283C2×D4—1721no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—861no—
293C22×C4—1721no—
294C22×C4C2×C22⋊D4311yescharacteristic
295C22×C4C2×C22⋊D4311yescharacteristic
296SD16—3442no—
297C2×C8—1721no—
298C2×C8—1721no—
299C4⋊C4—24no—
300C4⋊C4—41no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C22⋊C4—21no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—3442no—
313C22⋊C4—1721no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C22⋊C4#1062188412yescomplemented
318C42—42no—
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—3441no—
324C23—3441no—
325C23—1721no—
326C23—1721no—
327C23—1721no—
328C23#1306329411yescharacteristic
329C23C2×#1062188411yescharacteristic
330C23#1306335611yescharacteristic
331Q8—42no—
332Q8—81no—
333Q8—84no—
334D4—3441no—
335D4—3441no—
336D4—3441no—
337D4—3441no—
338D4—3441no—
339D4—3441no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—3441no—
365C2×C4—3441no—
366C2×C4—3441no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C8—3441no—
371C8—3441no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—3442no—
382C22—3441no—
383C22—3441no—
384C22—3441no—
385C22—6881no—
386C22#1458303811yescharacteristic
387C22#1458307211yescharacteristic
388C22#1458308611yescharacteristic
389C4—42no—
390C4—42no—
391C4—41no—
392C4—42no—
393C4—42no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—3441no—
398C4—6881no—
399C2—21no—
400C2—21no—
401C2—41no—
402C2—41no—
403C2—6881no—
404C2#1913353511yescharacteristic
405C2#1913657911yescharacteristic
406C2#1913660811yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2677C2
socleC22×C43B(4,𝔽2)
prime radical#14583461C22
hypercenter#2677D43
hypocenterC43#12176
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2677

Complements

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

NH ≅ G/Ntype
4. #19132619C2semidirect
5. #19132616C2semidirect
6. #19132543C2semidirect
7. C43×#2677C2semidirect
103. C22⋊C4×C43SD16semidirect
196. #2677D43semidirect
230. C43#12176semidirect
317. C22⋊C4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191358462
#191336142
#191335462
#191326192
#191326162
#191325432
C43×#26772
#1217643