Finite Group Databasebeta

← #25005839

Subgroups — #25005839

Order 11008.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#19143292C211yesmaximal, characteristic
2#19136204C211yesmaximal, characteristic, complemented
3C22⋊C16×D43C211yesmaximal, characteristic, complemented
4#19132536C211yesmaximal, characteristic, complemented
5#19132536C211yesmaximal, characteristic, complemented
6#19132521C211yesmaximal, characteristic, complemented
7C43×#1315C211yesmaximal, characteristic, complemented
8C2×#13063332C411yescharacteristic
9C22×C8×D43C2211yescharacteristic
10#14583406C411yescharacteristic
11C2×#13063264—21no—
12C2×C16×D43—21no—
13#14582973—21no—
14#14582973—21no—
15(C22⋊D43)⋊C8—21no—
16(C22⋊D43)⋊C8—21no—
17#14582925C2211yescharacteristic
18#14582862C411yescharacteristic
19#14582857C411yescharacteristic
20C22⋊(C43⋊C16)C2211yescharacteristic
21C22⋊(C43⋊C16)C2211yescharacteristic
22(C2×D43)⋊C16—21no—
23(C2×D43)⋊C16—21no—
24C43×#408C2211yescharacteristic
25C43×C22⋊C16C2211yescharacteristic
26C43×C22⋊C16C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28#13063332—42no—
29C2×#10621877—21no—
30C2×#10621877C2×C411yescharacteristic
31C22×C43⋊C8—21no—
32C22×C43⋊C8C2×C411yescharacteristic
33C2×C8×D43—42no—
34C2×C8×D43D411yescharacteristic
35C2×C8×D43D411yescharacteristic
36C2×C8×D43D411yescharacteristic
37C2×C8×D43D411yescharacteristic
38#13063306—21no—
39#13063301C811yescharacteristic
40#13063301C811yescharacteristic
41#13063296C811yescharacteristic
42#13063296C811yescharacteristic
43#13063293—21no—
44C4×C22⋊D43—21no—
45C4×C22⋊D43—21no—
46#13063284C2×C411yescharacteristic
47#13063264—42no—
48C2×C43⋊C16—21no—
49C2×C43⋊C16—21no—
50C16×D43—42no—
51Dic43⋊C8—21no—
52Dic43⋊C8—21no—
53(C2×D43)⋊C8—21no—
54(C2×D43)⋊C8—21no—
55#13063235—21no—
56C8×Dic43—21no—
57C2×#41×C43C2×C411yescharacteristic
58C2×M16×C43C2×C411yescharacteristic
59C22×C8×C43C2311yescharacteristic
60C2×C16×C43—21no—
61C2×C16×C43—21no—
62C22⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64C23×D43M1611yescharacteristic
65#41×C43—41no—
66#41×C43—41no—
67C2×Q8×C43C2×C811yescharacteristic
68C2×D4×C43—21no—
69C2×D4×C43C2×C811yescharacteristic
70C22×C4×C43—21no—
71C22×C4×C43C22×C411yescharacteristic
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C22×Dic43M1611yescharacteristic
75C2×C4×D43—41no—
76C2×C4×D43—41no—
77C2×C4×D43C22⋊C411yescharacteristic
78C2×C4×D43C22⋊C411yescharacteristic
79C2×C4×D43C2×C811yescharacteristic
80C2×C4×D43C2×C811yescharacteristic
81M16×C43—41no—
82C2×C8×C43—21no—
83C2×C8×C43—41no—
84C2×C8×C43C2×D411yescharacteristic
85C2×C8×C43C2×D411yescharacteristic
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91C4⋊Dic43C2×C811yescharacteristic
92C4⋊Dic43C2×C811yescharacteristic
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95C4×Dic43—21no—
96#10621877—42no—
97#10621877—41no—
98C2×C43⋊C8—22no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—42no—
101C2×C43⋊C8C22⋊C411yescharacteristic
102C2×C43⋊C8C22⋊C411yescharacteristic
103C8×D43—22no—
104C8×D43—22no—
105C8×D43—41no—
106C8×D43—41no—
107C16×C43—41no—
108C16×C43—41no—
109C43⋊C16—41no—
110C43⋊C16—41no—
111C23×C43—21no—
112C23×C43C2×M1611yescharacteristic
113C22×D43—22no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43C22⋊C811yescharacteristic
117C22×D43C22⋊C811yescharacteristic
118Q8×C43—41no—
119D4×C43—41no—
120D4×C43—42no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C22×C811yescharacteristic
128C22⋊D43—42no—
129C22⋊D43—42no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—41no—
133C2×Dic43C22⋊C811yescharacteristic
134C2×Dic43C22⋊C811yescharacteristic
135C4×D43—21no—
136C4×D43—21no—
137C4×D43—21no—
138C4×D43—21no—
139C4×D43—41no—
140C4×D43—41no—
141C8×C43—21no—
142C8×C43—21no—
143C8×C43—41no—
144C43⋊C8—21no—
145C43⋊C8—41no—
146C43⋊C8#9912yes—
147#11470—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C2×C22⋊C811yescharacteristic
155C2×D43—21no—
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—44no—
161C2×D43#35012yes—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43C2×#9911yescharacteristic
165C4×C43#41311yescharacteristic
166Dic43—21no—
167Dic43—21no—
168Dic43—41no—
169Dic43—41no—
170#2929—431no—
171#2112—431no—
172C2×C22⋊C16—431no—
173#1323—431no—
174#1323—431no—
175#1315—431no—
176#1315D4311yescharacteristic, complemented
177C2×C43—41no—
178C2×C43—81no—
179C2×C43#145911yescharacteristic
180C2×C43C2×#35011yescharacteristic
181C2×C43#211711yescharacteristic
182D43—22no—
183D43—41no—
184C2×#131—431no—
185C23×C8—431no—
186#525—431no—
187C2×M32—861no—
188C22×C16—861no—
189#435—861no—
190#435—861no—
191C8×D4—861no—
192C8×D4—861no—
193#424—431no—
194#408C2×D4311yescharacteristic
195#407—431no—
196#405—431no—
197C22⋊C16—431no—
198C22⋊C16—431no—
199C22⋊C16—861no—
200C22⋊C16—861no—
201C22⋊C16C2×D4311yescharacteristic
202C22⋊C16C2×D4311yescharacteristic
203C43#1147011yescharacteristic, complemented, Sylow
204C2×#41C4×D4311yescharacteristic
205C23×C4—431no—
206#131—1722no—
207C2×M16—431no—
208C2×M16—861no—
209C2×M16C4×D4311yescharacteristic
210C22×C8—431no—
211C22×C8—431no—
212C22×C8—431no—
213C22×C8—431no—
214C22×C8—431no—
215C22×C8—861no—
216C22×C8—1722no—
217C22×C8C22×D4311yescharacteristic
218#123—861no—
219C22⋊Q8—431no—
220C22⋊Q8—431no—
221#121—431no—
222#121—431no—
223#120—861no—
224C4×D4—861no—
225C4×D4—861no—
226#117—431no—
227M32—1722no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16—861no—
231C2×C16—861no—
232C2×C16—1722no—
233C4⋊C8—861no—
234C4⋊C8—861no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—861no—
238C22⋊C8—861no—
239#97—861no—
240C4×C8—861no—
241C24—431no—
242#41—41no—
243#41—41no—
244C2×Q8C8×D4311yescharacteristic
245C2×D4—21no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4C8×D4311yescharacteristic
249C22×C4—21no—
250C22×C4—431no—
251C22×C4—431no—
252C22×C4—431no—
253C22×C4—431no—
254C22×C4—431no—
255C22×C4—1721no—
256C22×C4—1721no—
257C22×C4C2×C4×D4311yescharacteristic
258M16—41no—
259M16—1722no—
260M16—1721no—
261C2×C8—21no—
262C2×C8—41no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—862no—
266C2×C8—862no—
267C2×C8—862no—
268C2×C8—861no—
269C2×C8—1721no—
270C2×C8—1721no—
271C2×C8—1722no—
272C2×C8D4×D4311yescharacteristic
273C2×C8D4×D4311yescharacteristic
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C42—861no—
284C16—41no—
285C16—41no—
286C16—1721no—
287C16—1721no—
288C23—21no—
289C23—431no—
290C23—431no—
291C23—862no—
292C23—1721no—
293C23—1721no—
294C23M16×D4311yescharacteristic
295Q8—41no—
296D4—41no—
297D4—42no—
298D4—1722no—
299D4—1722no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—431no—
306C2×C4—431no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4C22⋊C4×D4311yescharacteristic
317C2×C4C2×C8×D4311yescharacteristic
318C8—21no—
319C8—21no—
320C8—41no—
321C8—432no—
322C8—861no—
323C8—1721no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—432no—
331C22—861no—
332C22—861no—
333C22—861no—
334C22—861no—
335C22—861no—
336C22—1724no—
337C22C22⋊C8×D4311yescharacteristic
338C4—21no—
339C4—41no—
340C4—861no—
341C4—861no—
342C4—1721no—
343C4—1721no—
344C4#99×D4311yescharacteristic
345C4#1458288011yescharacteristic
346C2—41no—
347C2—81no—
348C2—862no—
349C2—1721no—
350C2#1913291011yescharacteristic
351C2#350×D4311yescharacteristic
352C2#1913622111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#1315C2
socleC22×C43C2×C22⋊C8
prime radical#14583406C4
cosocleC22×C8×C43C23
hypercenter#1315D43
hypocenterC43#11470
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #19136204C2semidirect
3. C22⋊C16×D43C2semidirect
4. #19132536C2semidirect
5. #19132536C2semidirect
6. #19132521C2semidirect
7. C43×#1315C2semidirect
176. #1315D43semidirect
203. C43#11470semidirect

Maximal subgroups

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

subgroupindex
#191432922
#191362042
C22⋊C16×D432
#191325362
#191325212
C43×#13152
#1147043