Finite Group Databasebeta

← #25011565

Subgroups — #25011565

Order 11008.

854 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#14582871C212yesmaximal
2#19137082C211yesmaximal, characteristic
3#19132720C211yesmaximal, characteristic, complemented
4#19132719C212yesmaximal, complemented
5C43×#1393C211yesmaximal, characteristic, complemented
6C22×#10621900C2211yescharacteristic
7C2×#13063283C411yescharacteristic, complemented
8C2×#13063281—22no—
9C2×C42×D43C411yescharacteristic, complemented
10#14582871—24no—
11#14582871C418yescomplemented
12C2×#13063240C2212yes—
13C2×#13063239—22no—
14#14582805C411yescharacteristic, complemented
15#14582804C411yescharacteristic, complemented
16#14582802C2211yescharacteristic
17#14582775—22no—
18C22⋊C4×Dic43—22no—
19C2×#99×C43C2212yes—
20C43×#390C2211yescharacteristic
21C2×#10621900—42no—
22C2×#10621900—41no—
23C2×#10621900—41no—
24C2×#10621900C2×C414yes—
25C2×#10621900D412yes—
26C2×#10621900Q812yes—
27C22×Dic86C2×C411yescharacteristic
28C22×C22⋊D43D412yes—
29C23×Dic43D412yes—
30C22×C4×D43—21no—
31C22×C4×D43C2×C411yescharacteristic
32#13063283—41no—
33#13063283—41no—
34#13063281—28no—
35#13063281—44no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×Dic43⋊C4—42no—
38C2×C22⋊Dic43—22no—
39C2×C22⋊Dic43—22no—
40C2×(C2×D43)⋊C4—21no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—42no—
44C2×C4×Dic43C2×C411yescharacteristic
45C42×D43—42no—
46#13063240—22no—
47#13063240C2×C414yescomplemented
48#13063239—28no—
49C43⋊#95—22no—
50C43⋊#95—22no—
51C22×D4×C43C2311yescharacteristic
52C2×C4⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43—22no—
54C2×C22⋊C4×C43—22no—
55C2×C42×C43C2×C411yescharacteristic
56#99×C43—22no—
57#99×C43C2×C414yescomplemented
58C24×C43C2×D412yes—
59C23×D43C22⋊C411yescharacteristic
60C2×D4×C43—41no—
61C2×D4×C43—41no—
62C2×D4×C43C22×C412yes—
63C2×D4×C43C2×D411yescharacteristic
64C2×D4×C43C2×Q811yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—42no—
68C22×C4×C43C22×C411yescharacteristic
69C2×C22⋊D43—42no—
70C2×C22⋊D43—42no—
71C2×C22⋊D43C22⋊C414yes—
72C2×C22⋊D43C4⋊C414yes—
73C22×Dic43—22no—
74C22×Dic43—22no—
75C22×Dic43—24no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—42no—
79C22×Dic43C22⋊C412yes—
80C22×Dic43C22⋊C414yes—
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C4⋊C414yes—
83#10621900—44no—
84#10621900—44no—
85#10621900—42no—
86#10621900—42no—
87#10621900—42no—
88#10621900—42no—
89C2×C4×D43—22no—
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—42no—
93C2×C4×D43—42no—
94C2×C4×D43—42no—
95C2×C4×D43C4212yes—
96C2×C4×D43C4⋊C412yes—
97C2×Dic86—41no—
98C2×Dic86—41no—
99C2×Dic86C4212yes—
100C2×Dic86C4⋊C412yes—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—24no—
103C22⋊C4×C43—42no—
104C22⋊C4×C43—44no—
105C42×C43—41no—
106C22⋊Dic43—24no—
107C22⋊Dic43—42no—
108C22⋊Dic43—44no—
109(C2×D43)⋊C4—42no—
110C4⋊Dic43—41no—
111Dic43⋊C4—48no—
112C4×Dic43—48no—
113C4×Dic43—42no—
114C4×Dic43—41no—
115C4×Dic43—41no—
116C4×Dic43—41no—
117C23×C43—22no—
118C23×C43—22no—
119C23×C43—42no—
120C23×C43—42no—
121C23×C43C2×C22⋊C412yes—
122C23×C43C2×C22⋊C411yescharacteristic
123C23×C43C2×C4⋊C412yes—
124C22×D43—21no—
125C22×D43—21no—
126C22×D43—41no—
127C22×D43—41no—
128C22×D43#9512yes—
129D4×C43—42no—
130D4×C43—41no—
131D4×C43—41no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—44no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43—82no—
141C2×C4×C43—82no—
142C2×C4×C43C2×C4211yescharacteristic
143C2×C4×C43C2×C4⋊C411yescharacteristic
144C22⋊D43—44no—
145C22⋊D43—44no—
146C2×Dic43—22no—
147C2×Dic43—22no—
148C2×Dic43—24no—
149C2×Dic43—24no—
150C2×Dic43—24no—
151C2×Dic43—24no—
152C2×Dic43—22no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—44no—
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—82no—
159C2×Dic43—82no—
160C2×Dic43#9514yes—
161C2×Dic43#9512yes—
162C2×Dic43#9912yes—
163C2×Dic43#9911yescharacteristic
164C2×Dic43#9911yescharacteristic
165C4×D43—22no—
166C4×D43—22no—
167C4×D43—22no—
168C4×D43—22no—
169C4×D43—48no—
170Dic86—42no—
171Dic86—42no—
172#12581—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—22no—
176C22×C43—22no—
177C22×C43—42no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43—82no—
182C22×C43C2×#9511yescharacteristic
183C22×C43C2×#9911yescharacteristic
184C22×C43C2×#9911yescharacteristic
185C2×D43—22no—
186C2×D43—42no—
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—42no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—42no—
193C4×C43—84no—
194C4×C43—81no—
195Dic43—24no—
196Dic43—42no—
197Dic43—84no—
198Dic43—81no—
199Dic43#34212yes—
200Dic43#34212yes—
201C2×#410—432no—
202#2297—431no—
203#1393—432no—
204#1393—431no—
205#1393D4311yescharacteristic, complemented
206C2×C43—21no—
207C2×C43—21no—
208C2×C43—42no—
209C2×C43—42no—
210C2×C43C2×#34211yescharacteristic
211C2×C43#212611yescharacteristic
212C2×C43#212611yescharacteristic
213D43—42no—
214C22×#41—431no—
215C2×#117—431no—
216C2×#117—862no—
217C22×C42—431no—
218#410—438no—
219#410—864no—
220C2×#99—432no—
221C2×#99—862no—
222C2×#99C2×D4312yes—
223#391—431no—
224#391—431no—
225#390—431no—
226#390C2×D4311yescharacteristic
227#386—862no—
228C4×C22⋊C4—862no—
229C43#1258111yescharacteristic, complemented, Sylow
230C2×#41—434no—
231C2×#41—432no—
232C2×#41—432no—
233C2×#41—1722no—
234C2×#41—1721no—
235C2×#41—1721no—
236C22×Q8—431no—
237C22×D4—432no—
238C22×D4C22×D4311yescharacteristic
239C23×C4—432no—
240C23×C4—431no—
241C23×C4—861no—
242#117—868no—
243#117—1724no—
244#117—1721no—
245#117—1721no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—1722no—
248C2×C4⋊C4C4×D4311yescharacteristic
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—862no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—862no—
254C2×C42—431no—
255C2×C42—861no—
256C2×C42—861no—
257C2×C42—1722no—
258C2×C42—1722no—
259C2×C42C4×D4311yescharacteristic
260#99—22no—
261#99—434no—
262#99—868no—
263#99—862no—
264#99C4×D4314yescomplemented
265#95—862no—
266#95—862no—
267C24—431no—
268C24D4×D4312yes—
269#41—1722no—
270#41—1724no—
271#41—1722no—
272#41—1724no—
273#41—1722no—
274#41—1722no—
275C2×Q8—432no—
276C2×Q8—432no—
277C2×Q8—1721no—
278C2×Q8—1721no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—434no—
282C2×D4—434no—
283C2×D4—1722no—
284C2×D4—1722no—
285C2×D4C2×C4×D4312yes—
286C2×D4D4×D4311yescharacteristic
287C2×D4Q8×D4311yescharacteristic
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—431no—
292C22×C4—434no—
293C22×C4—432no—
294C22×C4—434no—
295C22×C4—432no—
296C22×C4—432no—
297C22×C4—862no—
298C22×C4—861no—
299C22×C4—861no—
300C22×C4—862no—
301C22×C4—862no—
302C22×C4—864no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—1722no—
306C22×C4—1722no—
307C22×C4—1722no—
308C22×C4—1722no—
309C22×C4C2×C4×D4311yescharacteristic
310C4⋊C4—41no—
311C4⋊C4—1721no—
312C4⋊C4—1728no—
313C22⋊C4—24no—
314C22⋊C4—44no—
315C22⋊C4—42no—
316C22⋊C4—864no—
317C22⋊C4—1722no—
318C22⋊C4—1724no—
319C22⋊C4—1722no—
320C42—41no—
321C42—1721no—
322C42—1722no—
323C42—1721no—
324C42—1721no—
325C42—1728no—
326C23—22no—
327C23—22no—
328C23—42no—
329C23—42no—
330C23—432no—
331C23—861no—
332C23—861no—
333C23—1721no—
334C23—1721no—
335C23C22⋊C4×D4312yes—
336C23C22⋊C4×D4311yescharacteristic
337C23C4⋊C4×D4312yes—
338Q8—1722no—
339Q8—1722no—
340D4—42no—
341D4—41no—
342D4—41no—
343D4—1724no—
344D4—1724no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—432no—
356C2×C4—431no—
357C2×C4—431no—
358C2×C4—432no—
359C2×C4—434no—
360C2×C4—862no—
361C2×C4—862no—
362C2×C4—862no—
363C2×C4—862no—
364C2×C4—864no—
365C2×C4—864no—
366C2×C4—864no—
367C2×C4—864no—
368C2×C4—862no—
369C2×C4—862no—
370C2×C4—862no—
371C2×C4—3442no—
372C2×C4—3442no—
373C2×C4—1728no—
374C2×C4—1724no—
375C2×C4—1722no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4C42×D4311yescharacteristic
380C2×C4C4⋊C4×D4311yescharacteristic
381C22—21no—
382C22—21no—
383C22—22no—
384C22—22no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—82no—
390C22—862no—
391C22—1722no—
392C22—1722no—
393C22—1721no—
394C22—1721no—
395C22#95×D4311yescharacteristic
396C22#99×D4311yescharacteristic
397C22#99×D4311yescharacteristic
398C4—21no—
399C4—21no—
400C4—42no—
401C4—84no—
402C4—81no—
403C4—432no—
404C4—432no—
405C4—864no—
406C4—3444no—
407C4—3441no—
408C4—1722no—
409C2—21no—
410C2—21no—
411C2—42no—
412C2—42no—
413C2—1722no—
414C2#342×D4311yescharacteristic
415C2#1913625711yescharacteristic
416C2#1913625911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C2×C42
FrattiniC22×D4C22×D43
FittingC43×#1393C2
socleC22×C43C2×#99
prime radicalC22×#10621900C22
cosocleC22×D4×C43C23
hypercenter#1393D43
hypocenterC43#12581
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #19132720C2semidirect
4. #19132719C2semidirect
5. C43×#1393C2semidirect
7. C2×#13063283C4semidirect
9. C2×C42×D43C4semidirect
11. #14582871C4semidirect
14. #14582805C4semidirect
15. #14582804C4semidirect
47. #13063240C2×C4semidirect
57. #99×C43C2×C4semidirect
205. #1393D43semidirect
229. C43#12581semidirect
264. #99C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828712
#191370822
#191327202
#191327192
C43×#13932
#1258143