Finite Group Databasebeta

← #25009707

Subgroups — #25009707

Order 11008.

362 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 55 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#19142115C211yesmaximal, characteristic
2#19135761C211yesmaximal, characteristic
3#19133586C211yesmaximal, characteristic
4#19132619C211yesmaximal, characteristic
5#19132596C211yesmaximal, characteristic
6#19132524C211yesmaximal, characteristic
7C43×#1614C211yesmaximal, characteristic
8#14583227—21no—
9#14582838—21no—
10#14582837—21no—
11#14582824C2211yescharacteristic
12#14582798—21no—
13#14582793—21no—
14#14582786—21no—
15#14582774—21no—
16#14582760—21no—
17#14582760C2211yescharacteristic
18#14582666—21no—
19#14582666C2211yescharacteristic
20#14582636—21no—
21#14582623C2211yescharacteristic
22C43×#543C2211yescharacteristic
23C43×#484—21no—
24C43×#399C2211yescharacteristic
25C43×#328—21no—
26C43×#323C2211yescharacteristic
27C23×Dic43D411yescharacteristic
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43D411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43D411yescharacteristic
35C2×C4×Dic43—21no—
36#13063256—41no—
37#13063249—41no—
38C22⋊(C43⋊C8)—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—41no—
47C43⋊#95—41no—
48C43⋊#95D411yescharacteristic
49C22⋊Q8×C43—21no—
50C22⋊Q8×C43—21no—
51C22⋊Q8×C43—41no—
52C22⋊Q8×C43—41no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43C2311yescharacteristic
58#107×C43—41no—
59#103×C43—41no—
60C22⋊C8×C43—21no—
61#95×C43D411yescharacteristic
62C24×C43C2×D411yescharacteristic
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—41no—
78C22×Dic43—41no—
79C22×Dic43—41no—
80C2×C8×C43—41no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—42no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—42no—
90C22⋊C4×C43—41no—
91C22⋊Dic43—41no—
92C22⋊Dic43—41no—
93C22⋊Dic43—41no—
94C22⋊Dic43—41no—
95C22⋊Dic43—41no—
96C4⋊Dic43—41no—
97C4⋊Dic43—81no—
98C4⋊Dic43—81no—
99Dic43⋊C4—42no—
100C4×Dic43—81no—
101C2×C43⋊C8—41no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—41no—
105C23×C43—41no—
106C23×C43#12011yescharacteristic
107C23×C43#13511yescharacteristic
108C23×C43#13711yescharacteristic
109Q8×C43—81no—
110Q8×C43—81no—
111C2×C4×C43—22no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—42no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142C8×C43—81no—
143C43⋊C8—81no—
144#12265—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—81no—
154C22×C43#45211yescharacteristic
155C22×C43#45511yescharacteristic
156C22×C43B(4,𝔽2)11yescharacteristic
157C4×C43—42no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—81no—
161C4×C43—81no—
162C4×C43—81no—
163Dic43—81no—
164Dic43—81no—
165Dic43—81no—
166Dic43—81no—
167Dic43—161no—
168#2771—431no—
169#2030—431no—
170#1614D4311yescharacteristic
171#1608—431no—
172#1352—431no—
173#1344—431no—
174#1317—431no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43—41no—
178C2×C43—41no—
179C2×C43#160611yescharacteristic
180C2×C43#219811yescharacteristic
181C2×C43#220111yescharacteristic
182#543C2×D4311yescharacteristic
183#484—21no—
184#483—861no—
185#400—861no—
186#400—861no—
187#399C2×D4311yescharacteristic
188#397—431no—
189#389—861no—
190#388—861no—
191#387—861no—
192#385—861no—
193#381—431no—
194#381—861no—
195#342—431no—
196#342—861no—
197#328—21no—
198#328—861no—
199#323—431no—
200#323C2×D4311yescharacteristic
201C43#1226511yescharacteristic, complemented, Sylow
202C23×C4—431no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C22⋊Q8—41no—
206C22⋊Q8—41no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4C22⋊D4311yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—431no—
216C2×C22⋊C4—861no—
217C2×C22⋊C4—861no—
218C2×C22⋊C4C22×D4311yescharacteristic
219C2×C42—861no—
220#107—41no—
221#106—1721no—
222#103—41no—
223#103—1721no—
224C22⋊C8—21no—
225C22⋊C8—861no—
226#95—431no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95—1721no—
235#95—1721no—
236#95C22⋊D4311yescharacteristic
237C24D4×D4311yescharacteristic
238C2×Q8—21no—
239C2×Q8—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—1721no—
251C22×C4—1721no—
252C22×C4—1721no—
253C22×C4D4×D4311yescharacteristic
254C22×C4C2×C22⋊D4311yescharacteristic
255C2×C8—41no—
256C2×C8—1721no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—3441no—
264C4⋊C4—3441no—
265C4⋊C4—1721no—
266C4⋊C4—1722no—
267C22⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—1721no—
272C22⋊C4—1721no—
273C22⋊C4—1721no—
274C22⋊C4—1721no—
275C22⋊C4—1721no—
276C42—3441no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23#1306329311yescharacteristic
282C23#1306334811yescharacteristic
283C23#1306335711yescharacteristic
284Q8—81no—
285Q8—81no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—3441no—
301C2×C4—3441no—
302C2×C4—3441no—
303C2×C4—3441no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1722no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C8—81no—
318C8—3441no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22#1458306011yescharacteristic
329C22#1458307511yescharacteristic
330C22#1458308511yescharacteristic
331C4—42no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—3441no—
338C4—3441no—
339C4—3441no—
340C4—3441no—
341C4—6881no—
342C2—21no—
343C2—21no—
344C2—41no—
345C2—41no—
346C2#1913357411yescharacteristic
347C2#1913659011yescharacteristic
348C2#1913660611yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1614C2
socleC22×C43B(4,𝔽2)
prime radicalC24×C43C2×D4
hypercenter#1614D43
hypocenterC43#12265
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1614

Complements

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

NH ≅ G/Ntype
201. C43#12265semidirect

Maximal subgroups

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

subgroupindex
#191421152
#191357612
#191335862
#191326192
#191325962
#191325242
C43×#16142
#1226543