Finite Group Databasebeta

← #24997913

Subgroups — #24997913

Order 11008.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14583267C211yesmaximal, characteristic
2#19142662C211yesmaximal, characteristic
3#19135569C211yesmaximal, characteristic
4C2×#14582641C211yesmaximal, characteristic
5C2×#14582640C211yesmaximal, characteristic
6#19132477C211yesmaximal, characteristic
7C2×C43×#501C211yesmaximal, characteristic
8C2×#13063317C2211yescharacteristic
9#14583267—22no—
10#14583267—22no—
11C2×#13063249—21no—
12C2×#13063249—21no—
13C2×#13063236C2211yescharacteristic
14C2×#13063236C2211yescharacteristic
15#14582838—21no—
16#14582837—21no—
17#14582832—22no—
18#14582830—21no—
19#14582829—21no—
20#14582765C2211yescharacteristic
21#14582661—22no—
22#14582641—22no—
23#14582640—22no—
24C2×C4⋊Q8×C43C2211yescharacteristic
25C2×#125×C43C2211yescharacteristic
26C43×#501—22no—
27C43×#501—22no—
28C2×#107×C43—21no—
29C2×#106×C43—21no—
30C2×#97×C43C2211yescharacteristic
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33#13063317—21no—
34#13063317—21no—
35#13063317—21no—
36#13063317—21no—
37C2×C4⋊Dic43D411yescharacteristic
38C2×C4⋊Dic43D411yescharacteristic
39C2×C4⋊Dic43D412yes—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—22no—
43#13063249—24no—
44#13063249—24no—
45#13063236—21no—
46#13063236—21no—
47#13063236—21no—
48#13063236D412yes—
49C43⋊#95—22no—
50C43⋊#95—22no—
51C43⋊#95—22no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C22×Q8×C43—21no—
55C22×C8×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43D412yes—
60#125×C43—21no—
61#125×C43—21no—
62#125×C43—21no—
63#125×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C42×C43C2311yescharacteristic
71#107×C43—24no—
72#106×C43—24no—
73#97×C43—21no—
74#97×C43D412yes—
75C2×Q8×C43—22no—
76C2×Q8×C43—44no—
77C2×Q8×C43—41no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—41no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×Dic43—22no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C2×C8×C43—24no—
88C2×C8×C43—22no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43#4111yescharacteristic
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—42no—
110Dic43⋊C4—41no—
111Dic43⋊C4—41no—
112Dic43⋊C4—41no—
113Dic43⋊C4—41no—
114Dic43⋊C4—82no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—22no—
117C2×C43⋊C8—42no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C23×C43#12011yescharacteristic
121Q8×C43—44no—
122Q8×C43—82no—
123C2×C4×C43—22no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—22no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—82no—
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12011yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43#12711yescharacteristic
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—42no—
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C8×C43—24no—
149C43⋊C8—42no—
150C43⋊C8—42no—
151#10084—431nomaximal, Sylow
152C22×C43#39211yescharacteristic
153C22×C43#45412yes—
154C22×C43#45511yescharacteristic
155C22×C43#45611yescharacteristic
156C22×C43#45612yes—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—81no—
164C4×C43—82no—
165C4×C43—81no—
166Dic43—82no—
167Dic43—81no—
168Dic43—81no—
169C2×#501D4311yescharacteristic
170C2×#491—431no—
171#2822—431no—
172#1993—431no—
173C2×#330—431no—
174C2×#330—431no—
175#1295—431no—
176C2×C43#166312yes—
177C2×C43#166412yes—
178C2×C43#200311yescharacteristic
179C2×C43#200511yescharacteristic
180C2×C43#200711yescharacteristic
181C2×C4⋊Q8C2×D4311yescharacteristic
182C2×#125—431no—
183C2×#125C2×D4311yescharacteristic
184#501—22no—
185#501—22no—
186#491—862no—
187#491—862no—
188C2×#107—21no—
189C2×#106—21no—
190C2×#103—861no—
191C2×#103—861no—
192C2×#97—431no—
193C2×#97—431no—
194C2×#97C2×D4311yescharacteristic
195#400—861no—
196#400—861no—
197#398—861no—
198#398—862no—
199#398—861no—
200#382—431no—
201#340—862no—
202#330—862no—
203#330—862no—
204C43#1008411yescharacteristic, complemented, Sylow
205C22×Q8—21no—
206C22×C8—21no—
207C22×C8—861no—
208C22×C8—861no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8C22⋊D4312yes—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—861no—
218#125—861no—
219#125—861no—
220#125—861no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—432no—
228C2×C4⋊C4—862no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4C22⋊D4311yescharacteristic
232C2×C4⋊C4C22⋊D4311yescharacteristic
233C2×C42C22×D4311yescharacteristic
234#107—24no—
235#106—24no—
236#103—864no—
237#103—864no—
238#97—21no—
239#97—432no—
240#97—861no—
241#97—861no—
242#97—861no—
243#97C22⋊D4312yes—
244#95—862no—
245#95—862no—
246#95—862no—
247#95—861no—
248#95—861no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—862no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4D4×D4311yescharacteristic
259C22×C4D4×D4311yescharacteristic
260C22×C4C2×C22⋊D4311yescharacteristic
261C2×C8—24no—
262C2×C8—22no—
263C2×C8—862no—
264C2×C8—862no—
265C2×C8—1722no—
266C2×C8—1721no—
267C2×C8—1721no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—3442no—
285C4⋊C4—1722no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C42D4×D4311yescharacteristic
291C42#1062190011yescharacteristic
292C42C2×C22⋊D4311yescharacteristic
293C42C2×C22⋊D4311yescharacteristic
294C23#1306329311yescharacteristic
295Q8—44no—
296Q8—82no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—82no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1722no—
311C2×C4—1721no—
312C2×C4—1722no—
313C2×C4—1721no—
314C2×C4—1722no—
315C2×C4—1722no—
316C2×C4#1306329311yescharacteristic
317C2×C4#1306329411yescharacteristic
318C2×C4#1306329611yescharacteristic
319C2×C4#1306329711yescharacteristic
320C2×C4#1306329711yescharacteristic
321C2×C4#1306332111yescharacteristic
322C8—24no—
323C8—1722no—
324C8—1722no—
325C22#1458280711yescharacteristic
326C22#1458307012yes—
327C22#1458307511yescharacteristic
328C22#1458308011yescharacteristic
329C22#1458308112yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—82no—
338C4—81no—
339C4—3441no—
340C4—3441no—
341C4—3442no—
342C2#1913392212yes—
343C2#1913392712yes—
344C2#1913561411yescharacteristic
345C2#1913563111yescharacteristic
346C2#1913564011yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#501C2
socle, prime radicalC23×C43#120
hypercenterC2×#501D43
hypocenterC43#10084
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
204. C43#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#145832672
#191426622
#191355692
C2×#145826412
C2×#145826402
#191324772
C2×C43×#5012
#1008443