Finite Group Databasebeta

← #25009392

Subgroups — #25009392

Order 11008.

388 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 57 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#19140257C211yesmaximal, characteristic
2#19135761C211yesmaximal, characteristic
3#19133620C211yesmaximal, characteristic
4#19132620C211yesmaximal, characteristic
5#19132619C211yesmaximal, characteristic
6#19132524C211yesmaximal, characteristic
7C43×#1614C211yesmaximal, characteristic
8#14583232—21no—
9#14582835C2211yescharacteristic
10#14582811—21no—
11#14582804—21no—
12#14582803—21no—
13#14582785—21no—
14#14582780—21no—
15#14582760—21no—
16#14582760C2211yescharacteristic
17C22⋊C4×Dic43—21no—
18#14582666—21no—
19#14582666C2211yescharacteristic
20#14582636—21no—
21#14582623C2211yescharacteristic
22C43×#543C2211yescharacteristic
23C43×#484—21no—
24C43×#399C2211yescharacteristic
25C43×#328—21no—
26C43×#323C2211yescharacteristic
27C22×Dic86—21no—
28C23×Dic43D411yescharacteristic
29C2×C4⋊Dic43D411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43D411yescharacteristic
34C2×C4×Dic43—21no—
35C2×C4×Dic43—21no—
36#13063258—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—41no—
77C22×Dic43—41no—
78C22×Dic43—41no—
79C22×Dic43Q1612yes—
80C2×Dic86—42no—
81C2×Dic86—42no—
82C2×Dic86—81no—
83C2×C8×C43—41no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—42no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—42no—
93C22⋊C4×C43—41no—
94C22⋊Dic43—41no—
95C22⋊Dic43—41no—
96C22⋊Dic43—42no—
97C22⋊Dic43—41no—
98C4⋊Dic43—41no—
99Dic43⋊C4—42no—
100C4×Dic43—81no—
101C4×Dic43—81no—
102C2×C43⋊C8—41no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43#12011yescharacteristic
108C23×C43C2×Q1611yescharacteristic
109C23×C43#13711yescharacteristic
110Q8×C43—81no—
111Q8×C43—81no—
112C2×C4×C43—22no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
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—41no—
124C2×C4×C43—81no—
125C2×C4×C43—81no—
126C2×Dic43—22no—
127C2×Dic43—22no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—42no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142C2×Dic43—81no—
143Dic86—84no—
144C8×C43—81no—
145C43⋊C8—81no—
146#12216—431nomaximal, Sylow
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—81no—
156C22×C43#45111yescharacteristic
157C22×C43#45511yescharacteristic
158C22×C43B(4,𝔽2)11yescharacteristic
159C4×C43—42no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—81no—
163C4×C43—81no—
164C4×C43—81no—
165Dic43—42no—
166Dic43—42no—
167Dic43—81no—
168Dic43—81no—
169Dic43—161no—
170#2607—431no—
171#2030—431no—
172#1614—431no—
173#1614D4311yescharacteristic
174#1352—431no—
175#1352—431no—
176#1317—431no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—41no—
180C2×C43—41no—
181C2×C43#160211yescharacteristic
182C2×C43#219811yescharacteristic
183C2×C43#219811yescharacteristic
184#543C2×D4311yescharacteristic
185#484—21no—
186#484—861no—
187#399—431no—
188#399C2×D4311yescharacteristic
189#393—861no—
190#391—861no—
191#391—861no—
192#387—861no—
193#387—861no—
194#381—431no—
195#381—861no—
196C4×C22⋊C4—861no—
197#342—431no—
198#342—861no—
199#328—21no—
200#328—861no—
201#323—431no—
202#323C2×D4311yescharacteristic
203C43#1221611yescharacteristic, complemented, Sylow
204C22×Q8—861no—
205C23×C4—431no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C22⋊Q8—41no—
209C22⋊Q8—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4C22⋊D4311yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—431no—
217C2×C22⋊C4—861no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4C22×D4311yescharacteristic
220C2×C42—861no—
221C2×C42—861no—
222#107—41no—
223#107—1721no—
224#103—41no—
225#103—1721no—
226C22⋊C8—21no—
227C22⋊C8—861no—
228#95—431no—
229#95—861no—
230#95—861no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—1721no—
237#95—1721no—
238#95C22⋊D4311yescharacteristic
239C24D4×D4311yescharacteristic
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—3441no—
243C2×Q8—1722no—
244C2×Q8—1722no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—432no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—1721no—
256C22×C4—1721no—
257C22×C4—1721no—
258C22×C4D4×D4311yescharacteristic
259C22×C4C2×C22⋊D4311yescharacteristic
260C2×C8—41no—
261C2×C8—1721no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—1721no—
269C4⋊C4—1722no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—1722no—
275C22⋊C4—1721no—
276C22⋊C4—1721no—
277C22⋊C4—1721no—
278C42—3441no—
279C42—3441no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23#1306329311yescharacteristic
285C23Q16×D4311yescharacteristic
286C23#1306335711yescharacteristic
287Q8—81no—
288Q8—81no—
289Q8—3444no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—862no—
305C2×C4—862no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4—3441no—
309C2×C4—3441no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1722no—
321C8—81no—
322C8—3441no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—81no—
332C22#1458305311yescharacteristic
333C22#1458307511yescharacteristic
334C22#1458308511yescharacteristic
335C4—42no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—3441no—
342C4—3441no—
343C4—1722no—
344C4—1722no—
345C4—6881no—
346C2—21no—
347C2—21no—
348C2—41no—
349C2—41no—
350C2#1913355011yescharacteristic
351C2#1913658911yescharacteristic
352C2#1913659011yescharacteristic
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#12216
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
203. C43#12216semidirect

Maximal subgroups

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

subgroupindex
#191402572
#191357612
#191336202
#191326202
#191326192
#191325242
C43×#16142
#1221643