Finite Group Databasebeta

← #25007410

Subgroups — #25007410

Order 11008.

384 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 71 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#19137887C211yesmaximal, characteristic
2#19134590C211yesmaximal, characteristic
3#19132937C211yesmaximal, characteristic
4#19132626C211yesmaximal, characteristic
5#19132624C211yesmaximal, characteristic
6#19132601C211yesmaximal, characteristic
7C43×#1346C211yesmaximal, characteristic
8C2×#13063290C411yescharacteristic
9C2×#13063290C2211yescharacteristic
10#14582953—21no—
11#14582922—21no—
12C2×#13063243—21no—
13#14582833—21no—
14#14582830C411yescharacteristic
15#14582820C411yescharacteristic
16#14582819—21no—
17#14582819C2211yescharacteristic
18C4⋊C4×Dic43—21no—
19#14582750—21no—
20#14582744C411yescharacteristic
21#14582668C2211yescharacteristic
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#398C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×Dic86D411yescharacteristic
29C2×#10621877—21no—
30#13063290—41no—
31#13063290—41no—
32#13063290—41no—
33#13063290—41no—
34C2×C4⋊Dic43—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4C2×C411yescharacteristic
39C2×Dic43⋊C4D411yescharacteristic
40C2×C4×Dic43—21no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43C2×C411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45Dic43⋊C8—41no—
46Dic43⋊C8—41no—
47Dic43⋊C8—41no—
48#13063243—42no—
49C22⋊(C43⋊C8)—21no—
50#13063235—41no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95C2×C411yescharacteristic
56C2×M16×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C4⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61#95×C43—21no—
62#95×C43C2×C411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86—42no—
80M16×C43—41no—
81M16×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊Dic43—42no—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91Dic43⋊C4—42no—
92Dic43⋊C4—42no—
93Dic43⋊C4—42no—
94C4×Dic43—24no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—41no—
102C4×Dic43—41no—
103#10621877—41no—
104#10621877—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43C2×C22⋊C411yescharacteristic
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—22no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—41no—
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×C43AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C43#13711yescharacteristic
122C2×Dic43—22no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43#9911yescharacteristic
138C2×Dic43#9911yescharacteristic
139Dic86—42no—
140Dic86—42no—
141Dic86—42no—
142Dic86—42no—
143C8×C43—81no—
144C8×C43—81no—
145C43⋊C8—81no—
146C43⋊C8—81no—
147#11831—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43C2×#9911yescharacteristic
151C22×C43#41711yescharacteristic
152C22×C43#42111yescharacteristic
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—42no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—81no—
159Dic43—21no—
160Dic43—42no—
161Dic43—42no—
162Dic43—41no—
163Dic43—41no—
164Dic43—41no—
165Dic43#35612yes—
166#2399—431no—
167#1801—431no—
168#1467—431no—
169#1354—431no—
170#1354—431no—
171#1346—431no—
172#1346D4311yescharacteristic
173C2×C43—21no—
174C2×C43—21no—
175C2×C43#151311yescharacteristic
176C2×C43#212011yescharacteristic
177C2×C43C2×#35611yescharacteristic
178C2×C4×Q8—431no—
179C2×C4×Q8—431no—
180#432—861no—
181#423—861no—
182C2×#101—861no—
183#398—431no—
184#398—861no—
185#398C2×D4311yescharacteristic
186#395—431no—
187#395—431no—
188#395—861no—
189C4×C4⋊C4—861no—
190C4×C4⋊C4—861no—
191#376—431no—
192#343—431no—
193#343C2×D4311yescharacteristic
194#324—431no—
195#324—861no—
196#324C2×D4311yescharacteristic
197C43#1183111yescharacteristic, complemented, Sylow
198C22×Q8—431no—
199C22×Q8—431no—
200C2×M16—21no—
201C2×M16—861no—
202C4×Q8—1721no—
203C4×Q8—1721no—
204C4×Q8—1721no—
205C4×Q8—1721no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4C4×D4311yescharacteristic
214C2×C4⋊C4C22×D4311yescharacteristic
215C2×C42—431no—
216C2×C42—431no—
217C2×C42—431no—
218C2×C42—861no—
219C2×C42—861no—
220C4⋊C8—1721no—
221C4⋊C8—1721no—
222C4⋊C8—1721no—
223#101—1722no—
224C22⋊C8—21no—
225C22⋊C8—861no—
226#97—1721no—
227#95—21no—
228#95—431no—
229#95—861no—
230#95—861no—
231#95—861no—
232#95—861no—
233#95C4×D4311yescharacteristic
234C2×Q8—861no—
235C2×Q8—861no—
236C2×Q8—1721no—
237C2×Q8—1721no—
238C2×Q8—1721no—
239C2×Q8—1722no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—431no—
243C22×C4—431no—
244C22×C4—431no—
245C22×C4—431no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4C2×C4×D4311yescharacteristic
249C22×C4D4×D4311yescharacteristic
250C22×C4D4×D4311yescharacteristic
251M16—41no—
252M16—41no—
253M16—1721no—
254M16—1721no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—1721no—
258C2×C8—1721no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1722no—
266C4⋊C4—1722no—
267C4⋊C4—1722no—
268C4⋊C4—1722no—
269C42—861no—
270C42—861no—
271C42—861no—
272C42—861no—
273C42—861no—
274C42—861no—
275C42—864no—
276C42—1721no—
277C42—1721no—
278C23C22⋊C4×D4311yescharacteristic
279Q8—1722no—
280Q8—1722no—
281Q8—1722no—
282Q8—1722no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—431no—
296C2×C4—431no—
297C2×C4—862no—
298C2×C4—862no—
299C2×C4—862no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4#1306334911yescharacteristic
313C2×C4#1306335411yescharacteristic
314C8—81no—
315C8—81no—
316C8—3441no—
317C8—3441no—
318C22—21no—
319C22—21no—
320C22#99×D4311yescharacteristic
321C22#1458289711yescharacteristic
322C22#1458291411yescharacteristic
323C4—21no—
324C4—21no—
325C4—42no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—432no—
330C4—861no—
331C4—1722no—
332C4—1721no—
333C4—1721no—
334C4—1722no—
335C4—1721no—
336C2—21no—
337C2—21no—
338C2#1913313511yescharacteristic
339C2#1913623511yescharacteristic
340C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1346C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1346D43
hypocenterC43#11831
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
197. C43#11831semidirect

Maximal subgroups

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

subgroupindex
#191378872
#191345902
#191329372
#191326262
#191326242
#191326012
C43×#13462
#1183143