Finite Group Databasebeta

← #25007273

Subgroups — #25007273

Order 11008.

402 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 69 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#19140360C211yesmaximal, characteristic
2#19134671C211yesmaximal, characteristic
3#19132926C211yesmaximal, characteristic
4#19132596C211yesmaximal, characteristic
5#19132595C211yesmaximal, characteristic
6#19132594C211yesmaximal, characteristic
7C43×#1344C211yesmaximal, characteristic
8C2×#13063324C411yescharacteristic, complemented
9C2×#13063302—21no—
10C2×#13063281C2211yescharacteristic
11#14582953—21no—
12#14582833—21no—
13#14582831C411yescharacteristic, complemented
14#14582830C411yescharacteristic, complemented
15#14582827—21no—
16#14582824C2211yescharacteristic
17#14582803—21no—
18#14582763C411yescharacteristic, complemented
19#14582760—21no—
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#397C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×Dic86—21no—
28C23×Dic43D411yescharacteristic
29#13063324—41no—
30#13063324—41no—
31#13063302—42no—
32#13063302—42no—
33#13063281—41no—
34#13063281—41no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4C2×C411yescharacteristic
41C2×Dic43⋊C4D411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43D411yescharacteristic
45C2×C4×Dic43C2×C411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47Dic43⋊C8—41no—
48C22⋊(C43⋊C8)—21no—
49#13063235—41no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—41no—
55C43⋊#95—41no—
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—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—41no—
77C22×Dic43—41no—
78C22×Dic43C22⋊C411yescharacteristic
79C22×Dic43C22⋊C411yescharacteristic
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C2×Dic86—42no—
83C2×Dic86—42no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×C8×C43—41no—
87C4⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊Dic43—41no—
94C22⋊Dic43—41no—
95C22⋊Dic43—41no—
96C22⋊Dic43—41no—
97C22⋊Dic43—41no—
98C4⋊Dic43—42no—
99C4⋊Dic43—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—42no—
103Dic43⋊C4—42no—
104Dic43⋊C4—42no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C4×Dic43—21no—
109C2×C43⋊C8—41no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43C2×C22⋊C411yescharacteristic
115C23×C43AGL(1,ℤ/8)11yescharacteristic
116C23×C43AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
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×C4×C43—81no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C2×Dic43#9911yescharacteristic
153C2×Dic43#9911yescharacteristic
154Dic86—82no—
155Dic86—82no—
156C8×C43—81no—
157C43⋊C8—81no—
158#11801—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—81no—
168C22×C43C2×#9911yescharacteristic
169C22×C43#41811yescharacteristic
170C22×C43#42111yescharacteristic
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—81no—
174C4×C43—81no—
175C4×C43—161no—
176Dic43—21no—
177Dic43—21no—
178Dic43—41no—
179Dic43—41no—
180Dic43—41no—
181Dic43—81no—
182Dic43—81no—
183Dic43—161no—
184#2621—431no—
185#1820—431no—
186#1464—431no—
187#1344—431no—
188#1344—431no—
189#1344—431no—
190#1344D4311yescharacteristic
191C2×C43—21no—
192C2×C43—21no—
193C2×C43—41no—
194C2×C43—41no—
195C2×C43#151011yescharacteristic
196C2×C43#212311yescharacteristic
197C2×C43#212911yescharacteristic
198C2×C4⋊Q8—431no—
199C2×C22⋊Q8—861no—
200C2×#117—431no—
201#432—861no—
202#398—431no—
203#398—431no—
204#398—861no—
205#397—431no—
206#397—861no—
207#397C2×D4311yescharacteristic
208#391—861no—
209#382—431no—
210#381—861no—
211#342—431no—
212#342—861no—
213#342C2×D4311yescharacteristic
214#324—861no—
215#323—431no—
216#323C2×D4311yescharacteristic
217C43#1180111yescharacteristic, complemented, Sylow
218C22×Q8—861no—
219C23×C4—431no—
220C4⋊Q8—1721no—
221C4⋊Q8—1721no—
222C22⋊Q8—1722no—
223C22⋊Q8—1722no—
224#117—1721no—
225#117—1721no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4C4×D4311yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—431no—
237C2×C22⋊C4—861no—
238C2×C22⋊C4—861no—
239C2×C22⋊C4C22×D4311yescharacteristic
240C2×C42—431no—
241C2×C42—431no—
242C4⋊C8—1721no—
243C22⋊C8—21no—
244C22⋊C8—861no—
245#97—1721no—
246#95—21no—
247#95—431no—
248#95—861no—
249#95—861no—
250#95—861no—
251#95—861no—
252#95—1721no—
253#95—1721no—
254#95C4×D4311yescharacteristic
255C24D4×D4311yescharacteristic
256C2×Q8—1721no—
257C2×Q8—1721no—
258C2×Q8—1722no—
259C2×Q8—1722no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—431no—
264C22×C4—431no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—1721no—
274C22×C4—1721no—
275C22×C4C2×C4×D4311yescharacteristic
276C22×C4D4×D4311yescharacteristic
277C2×C8—41no—
278C2×C8—1721no—
279C4⋊C4—41no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C4⋊C4—1721no—
283C4⋊C4—1722no—
284C4⋊C4—1722no—
285C4⋊C4—1722no—
286C4⋊C4—1722no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C22⋊C4—1721no—
295C22⋊C4—1721no—
296C22⋊C4—1721no—
297C42—861no—
298C42—861no—
299C42—861no—
300C42—861no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23C22⋊C4×D4311yescharacteristic
306C23#1306334911yescharacteristic
307C23#1306335211yescharacteristic
308Q8—3442no—
309Q8—3442no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C8—81no—
348C8—3441no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—81no—
358C22#99×D4311yescharacteristic
359C22#1458290211yescharacteristic
360C22#1458291411yescharacteristic
361C4—41no—
362C4—41no—
363C4—81no—
364C4—81no—
365C4—161no—
366C4—861no—
367C4—861no—
368C4—3441no—
369C4—3441no—
370C4—1721no—
371C4—1721no—
372C4—1721no—
373C4—6881no—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1913312211yescharacteristic
379C2#1913624711yescharacteristic
380C2#1913626811yescharacteristic
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#11801
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×#13063324C4semidirect
13. #14582831C4semidirect
14. #14582830C4semidirect
18. #14582763C4semidirect
217. C43#11801semidirect

Maximal subgroups

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

subgroupindex
#191403602
#191346712
#191329262
#191325962
#191325952
#191325942
C43×#13442
#1180143