Finite Group Databasebeta

← #25007190

Subgroups — #25007190

Order 11008.

414 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 73 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#19139579C211yesmaximal, characteristic
2#19134390C211yesmaximal, characteristic
3#19132937C211yesmaximal, characteristic
4#19132602C211yesmaximal, characteristic
5#19132601C211yesmaximal, characteristic
6#19132600C211yesmaximal, characteristic
7C43×#1346C211yesmaximal, characteristic
8C2×#13063324—21no—
9C2×#13063324C411yescharacteristic
10C2×#13063290C2211yescharacteristic
11#14582953—21no—
12C2×#13063243—21no—
13M16×Dic43—21no—
14#14582831C411yescharacteristic
15#14582830C411yescharacteristic
16#14582829C2211yescharacteristic
17#14582803—21no—
18#14582796—21no—
19#14582794—21no—
20#14582750C411yescharacteristic
21#14582668C2211yescharacteristic
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#398C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×Dic86—21no—
28C22×Dic86D411yescharacteristic
29C2×#10621877—21no—
30#13063324—41no—
31#13063324—41no—
32#13063324—42no—
33#13063324—42no—
34#13063290—41no—
35#13063290—41no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4C2×C411yescharacteristic
43C2×Dic43⋊C4D411yescharacteristic
44C2×C4×Dic43—21no—
45C2×C4×Dic43C2×C411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48Dic43⋊C8—41no—
49#13063243—24no—
50C22⋊(C43⋊C8)—21no—
51#13063235—41no—
52#13063235—41no—
53C8×Dic43—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95C2×C411yescharacteristic
58C2×M16×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C4⋊C4×C43C2311yescharacteristic
62C22⋊C8×C43—21no—
63#95×C43—21no—
64#95×C43C2×C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C2×Dic86—21no—
77C2×Dic86—21no—
78C2×Dic86—22no—
79C2×Dic86—41no—
80C2×Dic86—42no—
81C2×Dic86—42no—
82C2×Dic86—42no—
83M16×C43—22no—
84M16×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊Dic43—42no—
92C4⋊Dic43—41no—
93Dic43⋊C4—24no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—42no—
97Dic43⋊C4—41no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—42no—
108#10621877—22no—
109#10621877—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C23×C43C2×C22⋊C411yescharacteristic
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—22no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
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—41no—
125C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43#9911yescharacteristic
142C2×Dic43#9911yescharacteristic
143C2×Dic43#10412yes—
144Dic86—42no—
145Dic86—42no—
146Dic86—84no—
147C8×C43—42no—
148C8×C43—81no—
149C43⋊C8—42no—
150C43⋊C8—81no—
151#11782—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43C2×#9911yescharacteristic
155C22×C43#41811yescharacteristic
156C22×C43C2×#10411yescharacteristic
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—42no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—81no—
163Dic43—21no—
164Dic43—22no—
165Dic43—42no—
166Dic43—41no—
167Dic43—41no—
168Dic43—81no—
169Dic43#35612yes—
170#2546—431no—
171C4×#101—431no—
172#1467—431no—
173#1346—431no—
174#1346—431no—
175#1346—431no—
176#1346D4311yescharacteristic
177C2×C43—21no—
178C2×C43—21no—
179C2×C43#150711yescharacteristic
180C2×C43#212311yescharacteristic
181C2×C43C2×#35611yescharacteristic
182C2×C4⋊Q8—431no—
183C2×C4⋊Q8—861no—
184C2×C4×Q8—431no—
185#432—861no—
186C2×#101—861no—
187C4×M16—861no—
188#398—431no—
189#398—431no—
190#398—431no—
191#398C2×D4311yescharacteristic
192#391—861no—
193#389—861no—
194#389—861no—
195C4×C4⋊C4—431no—
196#343—431no—
197#343C2×D4311yescharacteristic
198#324—431no—
199#324—861no—
200#324C2×D4311yescharacteristic
201C43#1178211yescharacteristic, complemented, Sylow
202C22×Q8—431no—
203C22×Q8—861no—
204C2×M16—21no—
205C2×M16—861no—
206C4⋊Q8—1721no—
207C4⋊Q8—1721no—
208C4⋊Q8—1722no—
209C4⋊Q8—1722no—
210C4×Q8—1721no—
211C4×Q8—1721no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—431no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C4×D4311yescharacteristic
222C2×C4⋊C4C22×D4311yescharacteristic
223C2×C42—431no—
224C2×C42—431no—
225C2×C42—431no—
226C2×C42—861no—
227C4⋊C8—1721no—
228#101—864no—
229C22⋊C8—21no—
230C22⋊C8—861no—
231#97—1721no—
232#97—1721no—
233C4×C8—1721no—
234#95—21no—
235#95—431no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95C4×D4311yescharacteristic
240C2×Q8—862no—
241C2×Q8—861no—
242C2×Q8—861no—
243C2×Q8—1721no—
244C2×Q8—1722no—
245C2×Q8—1722no—
246C2×Q8—1722no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—431no—
250C22×C4—431no—
251C22×C4—431no—
252C22×C4—431no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4C2×C4×D4311yescharacteristic
256C22×C4D4×D4311yescharacteristic
257C22×C4D4×D4311yescharacteristic
258M16—22no—
259M16—41no—
260M16—862no—
261M16—1721no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—1721no—
265C2×C8—1721no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—864no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4—1721no—
276C4⋊C4—1722no—
277C4⋊C4—1722no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C42—861no—
281C42—861no—
282C42—861no—
283C42—861no—
284C42—861no—
285C42—861no—
286C42—1722no—
287C23C22⋊C4×D4311yescharacteristic
288Q8—3444no—
289Q8—1722no—
290Q8—1722no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—432no—
306C2×C4—862no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—862no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4#1306334911yescharacteristic
321C2×C4#1306335211yescharacteristic
322C8—42no—
323C8—81no—
324C8—3441no—
325C8—1722no—
326C22—21no—
327C22—21no—
328C22#99×D4311yescharacteristic
329C22#1458290211yescharacteristic
330C22#104×D4311yescharacteristic
331C4—21no—
332C4—21no—
333C4—42no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—432no—
338C4—861no—
339C4—862no—
340C4—3441no—
341C4—1722no—
342C4—1721no—
343C4—1721no—
344C2—21no—
345C2—21no—
346C2#1913310911yescharacteristic
347C2#1913624711yescharacteristic
348C2#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#11782
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
201. C43#11782semidirect

Maximal subgroups

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

subgroupindex
#191395792
#191343902
#191329372
#191326022
#191326012
#191326002
C43×#13462
#1178243