Finite Group Databasebeta

← #25007085

Subgroups — #25007085

Order 11008.

436 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 71 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#19140294C211yesmaximal, characteristic
2#19134326C211yesmaximal, characteristic
3#19132926C211yesmaximal, characteristic
4#19132620C211yesmaximal, characteristic
5#19132618C211yesmaximal, characteristic
6#19132595C211yesmaximal, characteristic
7C43×#1344C211yesmaximal, characteristic
8C2×#13063316C411yescharacteristic, complemented
9C2×#13063281—21no—
10C2×#13063281C2211yescharacteristic
11#14582953—21no—
12#14582839C411yescharacteristic, complemented
13#14582835C2211yescharacteristic
14#14582830C411yescharacteristic, complemented
15#14582796—21no—
16#14582792—21no—
17#14582781—21no—
18#14582771—21no—
19#14582744C411yescharacteristic, complemented
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#397C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C23×Dic43D411yescharacteristic
28#13063316—41no—
29#13063316—41no—
30#13063281—24no—
31#13063281—41no—
32#13063281—41no—
33#13063281—42no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—41no—
40C2×Dic43⋊C4C2×C411yescharacteristic
41C2×Dic43⋊C4D411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43D411yescharacteristic
45C2×C4×Dic43—21no—
46C2×C4×Dic43—41no—
47C2×C4×Dic43C2×C411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49Dic43⋊C8—41no—
50C22⋊(C43⋊C8)—21no—
51#13063235—41no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C24×C43C2×D411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—22no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—41no—
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C22⋊C411yescharacteristic
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C2×C8×C43—41no—
83C4⋊C4×C43—41no—
84C22⋊C4×C43—22no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊Dic43—22no—
90C22⋊Dic43—41no—
91C22⋊Dic43—42no—
92C22⋊Dic43—41no—
93C4⋊Dic43—42no—
94C4⋊Dic43—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—42no—
98Dic43⋊C4—44no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—42no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—42no—
107C4×Dic43—44no—
108C2×C43⋊C8—41no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43C2×C22⋊C411yescharacteristic
114C23×C43AGL(1,ℤ/8)11yescharacteristic
115C23×C43#13711yescharacteristic
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—42no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131C2×Dic43—22no—
132C2×Dic43—22no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—22no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150C2×Dic43#9911yescharacteristic
151C2×Dic43#9911yescharacteristic
152C2×Dic43#10412yes—
153C8×C43—81no—
154C43⋊C8—81no—
155#11760—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—81no—
165C22×C43C2×#9911yescharacteristic
166C22×C43#41711yescharacteristic
167C22×C43C2×#10411yescharacteristic
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—81no—
171C4×C43—82no—
172C4×C43—81no—
173Dic43—21no—
174Dic43—21no—
175Dic43—22no—
176Dic43—42no—
177Dic43—41no—
178Dic43—41no—
179Dic43—82no—
180Dic43—81no—
181#2611—431no—
182#1740—431no—
183#1464—431no—
184#1352—431no—
185#1352—431no—
186#1344—431no—
187#1344D4311yescharacteristic
188C2×C43—21no—
189C2×C43—21no—
190C2×C43—41no—
191C2×C43—41no—
192C2×C43#150411yescharacteristic
193C2×C43#212311yescharacteristic
194C2×C43#212611yescharacteristic
195C2×#125—431no—
196C2×#117—431no—
197C2×#117—861no—
198#432—861no—
199#400—431no—
200#399—431no—
201#398—431no—
202#397C2×D4311yescharacteristic
203#389—861no—
204#388—861no—
205#387—861no—
206#385—861no—
207#376—431no—
208#342—431no—
209#342—861no—
210#342C2×D4311yescharacteristic
211#324—861no—
212#323—431no—
213#323C2×D4311yescharacteristic
214C43#1176011yescharacteristic, complemented, Sylow
215C23×C4—431no—
216#125—1721no—
217#125—1721no—
218#117—864no—
219#117—1721no—
220#117—1721no—
221#117—1722no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—1721no—
230C2×C4⋊C4C4×D4311yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—431no—
234C2×C22⋊C4—861no—
235C2×C22⋊C4—861no—
236C2×C22⋊C4C22×D4311yescharacteristic
237C2×C42—431no—
238C2×C42—431no—
239C2×C42—861no—
240C2×C42—1721no—
241C4⋊C8—1721no—
242C22⋊C8—21no—
243C22⋊C8—861no—
244#97—1721no—
245#95—21no—
246#95—431no—
247#95—861no—
248#95—861no—
249#95—861no—
250#95—861no—
251#95C4×D4311yescharacteristic
252C24D4×D4311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—431no—
257C22×C4—431no—
258C22×C4—431no—
259C22×C4—431no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—862no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—1721no—
268C22×C4C2×C4×D4311yescharacteristic
269C22×C4D4×D4311yescharacteristic
270C2×C8—41no—
271C2×C8—1721no—
272C4⋊C4—41no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4—1721no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C4⋊C4—1722no—
279C4⋊C4—1722no—
280C4⋊C4—1722no—
281C4⋊C4—1724no—
282C22⋊C4—22no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—862no—
288C22⋊C4—1721no—
289C22⋊C4—1722no—
290C22⋊C4—1721no—
291C42—861no—
292C42—861no—
293C42—861no—
294C42—861no—
295C42—1722no—
296C42—1724no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23C22⋊C4×D4311yescharacteristic
302C23#1306334911yescharacteristic
303C23#1306335411yescharacteristic
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—431no—
318C2×C4—431no—
319C2×C4—432no—
320C2×C4—862no—
321C2×C4—862no—
322C2×C4—862no—
323C2×C4—862no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—862no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—3441no—
332C2×C4—3441no—
333C2×C4—1722no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C8—81no—
342C8—3441no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22#99×D4311yescharacteristic
353C22#1458289711yescharacteristic
354C22#104×D4311yescharacteristic
355C4—41no—
356C4—41no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4—861no—
361C4—861no—
362C4—862no—
363C4—3442no—
364C4—3441no—
365C4—1722no—
366C4—1721no—
367C4—1721no—
368C2—21no—
369C2—21no—
370C2—41no—
371C2—41no—
372C2#1913309611yescharacteristic
373C2#1913624711yescharacteristic
374C2#1913625911yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1344C2
socleC22×C43C2×#99
prime radicalC24×C43C2×D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1344D43
hypocenterC43#11760
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
8. C2×#13063316C4semidirect
12. #14582839C4semidirect
14. #14582830C4semidirect
19. #14582744C4semidirect
214. C43#11760semidirect

Maximal subgroups

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

subgroupindex
#191402942
#191343262
#191329262
#191326202
#191326182
#191325952
C43×#13442
#1176043