Finite Group Databasebeta

← #24999822

Subgroups — #24999822

Order 11008.

396 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 75 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#19140792C211yesmaximal, characteristic
2#19133128C211yesmaximal, characteristic
3#19133115C211yesmaximal, characteristic
4#19132501C211yesmaximal, characteristic
5#19132481C211yesmaximal, characteristic
6#19132448C211yesmaximal, characteristic
7C43×#1996C211yesmaximal, characteristic
8#14582863C2211yescharacteristic
9#14582863C2211yescharacteristic
10#14582835—21no—
11#14582832—21no—
12#14582832—21no—
13#14582822—21no—
14#14582796—21no—
15#14582782—21no—
16#14582762C2211yescharacteristic
17C4×C22⋊Dic43C2211yescharacteristic
18#14582636—21no—
19#14582636—21no—
20#14582636—21no—
21#14582636—21no—
22C2×C22⋊Q8×C43C2211yescharacteristic
23C43×#380C2211yescharacteristic
24C4×C22⋊C4×C43C2211yescharacteristic
25C43×#342—21no—
26C43×#342—21no—
27C2×#10621877—21no—
28C2×#10621877—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C4×Dic43—21no—
38C22⋊(C43⋊C8)—21no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C22⋊(C43⋊C8)—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95D411yescharacteristic
46C43⋊#95D411yescharacteristic
47C43⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C22×Q8×C43Q811yescharacteristic
50C23×C4×C43C2311yescharacteristic
51C22⋊Q8×C43—21no—
52C22⋊Q8×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43Q811yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43D411yescharacteristic
61C2×C22⋊C4×C43D411yescharacteristic
62C2×C42×C43—21no—
63#95×C43—21no—
64#95×C43—21no—
65C24×C43C2×D411yescharacteristic
66C2×Q8×C43—21no—
67C2×Q8×C43—21no—
68C2×Q8×C43—81no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—41no—
74C22×C4×C43—81no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×Q811yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—81no—
90C22⋊C4×C43—22no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C42×C43—81no—
97C22⋊Dic43—42no—
98C22⋊Dic43—81no—
99C4⋊Dic43—42no—
100C4⋊Dic43—81no—
101Dic43⋊C4—42no—
102Dic43⋊C4—81no—
103Dic43⋊C4—81no—
104Dic43⋊C4—81no—
105C4×Dic43—81no—
106#10621877—81no—
107#10621877—81no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43#12011yescharacteristic
115C23×C43C22⋊Q811yescharacteristic
116C23×C43#12411yescharacteristic
117Q8×C43—81no—
118Q8×C43—81no—
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—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43C22⋊Q811yescharacteristic
139C2×C4×C43C22⋊Q811yescharacteristic
140C2×C4×C43#12411yescharacteristic
141C2×C4×C43#12411yescharacteristic
142C2×Dic43—22no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C43⋊C8—81no—
155C43⋊C8—81no—
156#10385—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—81no—
166C22×C43—81no—
167C22×C43#39311yescharacteristic
168C22×C43#45511yescharacteristic
169C22×C43#45611yescharacteristic
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—81no—
175C4×C43—81no—
176C4×C43—82no—
177C4×C43—81no—
178C4×C43—81no—
179Dic43—42no—
180Dic43—81no—
181Dic43—81no—
182Dic43—81no—
183#2667—431no—
184#1996D4311yescharacteristic
185#1511—431no—
186#1508—431no—
187#1305—431no—
188#1297—431no—
189#1284—431no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—41no—
193C2×C43—41no—
194C2×C43#202811yescharacteristic
195C2×C43#203111yescharacteristic
196C2×C43#203211yescharacteristic
197C2×C22⋊Q8C2×D4311yescharacteristic
198#407—431no—
199#407—431no—
200#399—861no—
201#398—861no—
202#398—861no—
203#396—861no—
204#389—861no—
205#387—861no—
206#381—431no—
207#380C2×D4311yescharacteristic
208C4×C22⋊C4—431no—
209C4×C22⋊C4C2×D4311yescharacteristic
210#342—21no—
211#342—21no—
212#328—861no—
213#328—861no—
214#328—861no—
215#328—861no—
216C43#1038511yescharacteristic, complemented, Sylow
217C22×Q8Dic8611yescharacteristic
218C23×C4C22×D4311yescharacteristic
219C2×M16—861no—
220C2×M16—861no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4Dic8611yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4—861no—
238C2×C22⋊C4C22⋊D4311yescharacteristic
239C2×C22⋊C4C22⋊D4311yescharacteristic
240C2×C42—21no—
241C2×C42—861no—
242C22⋊C8—861no—
243C22⋊C8—861no—
244C22⋊C8—861no—
245C22⋊C8—861no—
246#95—21no—
247#95—21no—
248#95—431no—
249#95—431no—
250#95—431no—
251#95—431no—
252#95—861no—
253#95—861no—
254#95—861no—
255C24C2×C22⋊D4311yescharacteristic
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—81no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—81no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4C2×Dic8611yescharacteristic
270C22×C4#1062189811yescharacteristic
271C22×C4D4×D4311yescharacteristic
272C22×C4D4×D4311yescharacteristic
273C22×C4#1062190011yescharacteristic
274C22×C4#1062190011yescharacteristic
275M16—3441no—
276M16—3441no—
277C2×C8—1721no—
278C2×C8—1721no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—81no—
284C4⋊C4—3441no—
285C4⋊C4—3441no—
286C4⋊C4—3441no—
287C4⋊C4—3441no—
288C4⋊C4—1722no—
289C4⋊C4—1722no—
290C22⋊C4—22no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—3441no—
297C22⋊C4—1722no—
298C42—81no—
299C42—3441no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23#1306329311yescharacteristic
305C23#1306330411yescharacteristic
306C23#1306331211yescharacteristic
307Q8—81no—
308Q8—81no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—862no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4#1306330211yescharacteristic
341C2×C4#1306330211yescharacteristic
342C2×C4#1306331111yescharacteristic
343C2×C4#1306331111yescharacteristic
344C8—3441no—
345C8—3441no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22#1458281111yescharacteristic
357C22#1458307611yescharacteristic
358C22#1458308111yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—81no—
364C4—81no—
365C4—82no—
366C4—81no—
367C4—81no—
368C4—3441no—
369C4—3441no—
370C4—3441no—
371C4—1722no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2#1913575611yescharacteristic
377C2#1913576911yescharacteristic
378C2#1913577211yescharacteristic
subgroupG/H
centerC22#14582811
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1996C2
socleC22×C43#393
prime radicalC24×C43C2×D4
hypercenter#1996D43
hypocenterC43#10385
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
216. C43#10385semidirect

Maximal subgroups

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

subgroupindex
#191407922
#191331282
#191331152
#191325012
#191324812
#191324482
C43×#19962
#1038543