Finite Group Databasebeta

← #25007106

Subgroups — #25007106

Order 11008.

446 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 87 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#19138882C211yesmaximal, characteristic
2#19132925C211yesmaximal, characteristic
3#19132621C212yesmaximal, complemented
4#19132600C212yesmaximal, complemented
5C2×C43×#343C211yesmaximal, characteristic
6C2×#13063284C411yescharacteristic
7#14582863—21no—
8#14582838C411yescharacteristic
9#14582838C2211yescharacteristic
10#14582829C411yescharacteristic
11#14582829C2211yescharacteristic
12#14582780—21no—
13#14582780—21no—
14#14582772—21no—
15#14582762—21no—
16#14582762C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C22×M16×C43—21no—
20C22×C4⋊C4×C43C2211yescharacteristic
21C43×#343—21no—
22C43×#343C2212yes—
23C2×#10621877—41no—
24#13063284—41no—
25#13063284—41no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43—21no—
32C2×C4×Dic43—21no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—41no—
35C43⋊#95—21no—
36C43⋊#95—21no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C23×C4×C43C2×C411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C2×M16×C43—24no—
48C2×M16×C43—22no—
49C2×M16×C43—41no—
50C2×M16×C43—42no—
51C22×C8×C43—41no—
52C2×C4⋊C4×C43—41no—
53C2×C4⋊C4×C43—41no—
54C2×C4⋊C4×C43C2×C411yescharacteristic
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43C2311yescharacteristic
58C24×C43C22⋊C411yescharacteristic
59C22×C4×C43—22no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—42no—
69C22×C4×C43—42no—
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80M16×C43—24no—
81M16×C43—44no—
82M16×C43—42no—
83C2×C8×C43—44no—
84C2×C8×C43—42no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C22⋊Dic43—42no—
90C22⋊Dic43—41no—
91C22⋊Dic43—41no—
92C4⋊Dic43—41no—
93C4⋊Dic43—41no—
94Dic43⋊C4—42no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97C4×Dic43—42no—
98#10621877—82no—
99C2×C43⋊C8—42no—
100C23×C43—22no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—41no—
104C23×C43#9911yescharacteristic
105C23×C43#9911yescharacteristic
106C23×C43C2×C22⋊C411yescharacteristic
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—81no—
127C2×C4×C43#10412yes—
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—42no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C8×C43—44no—
142C43⋊C8—82no—
143#11764—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—42no—
152C22×C43—42no—
153C22×C43#35212yes—
154C22×C43C2×#9911yescharacteristic
155C22×C43#41711yescharacteristic
156C22×C43C2×#10411yescharacteristic
157C4×C43—21no—
158C4×C43—22no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164Dic43—81no—
165Dic43—81no—
166Dic43—81no—
167Dic43—81no—
168#2484—431no—
169C2×#343D4311yescharacteristic
170#1463—431no—
171#1353—432no—
172#1346—432no—
173C2×C43—21no—
174C2×C43—21no—
175C2×C43—22no—
176C2×C43—41no—
177C2×C43#150411yescharacteristic
178C2×C43C2×#35211yescharacteristic
179C2×C43#213311yescharacteristic
180C22×M16—21no—
181C2×#117—431no—
182C22×C4⋊C4C2×D4311yescharacteristic
183#407—861no—
184#400—431no—
185#400—431no—
186#398—431no—
187#398—431no—
188#387—861no—
189#387—861no—
190#385—861no—
191#381—431no—
192#381—861no—
193#343—21no—
194#343C2×D4312yes—
195#324—432no—
196#324—861no—
197C43#1176411yescharacteristic, complemented, Sylow
198C23×C4C4×D4311yescharacteristic
199C23×C4D17211yescharacteristic
200C23×C4C22⋊D4311yescharacteristic
201C2×M16—24no—
202C2×M16—22no—
203C2×M16—41no—
204C2×M16—42no—
205C2×M16—1721no—
206C22×C8—41no—
207#117—1721no—
208#117—1721no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—431no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4C4×D4311yescharacteristic
216C2×C4⋊C4D17211yescharacteristic
217C2×C4⋊C4C22⋊D4311yescharacteristic
218C2×C4⋊C4C22×D4311yescharacteristic
219C2×C22⋊C4—861no—
220C2×C22⋊C4—861no—
221C2×C42—861no—
222C22⋊C8—862no—
223C22⋊C8—1721no—
224#95—431no—
225#95—431no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231#95—861no—
232#95—861no—
233C24(C2×D43)⋊C411yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4(C2×D43)⋊C411yescharacteristic
250C22×C4(C2×D43)⋊C411yescharacteristic
251C22×C4(C2×D43)⋊C411yescharacteristic
252C22×C4C2×C4×D4311yescharacteristic
253C22×C4C2×D17211yescharacteristic
254C22×C4C2×C22⋊D4311yescharacteristic
255M16—24no—
256M16—44no—
257M16—42no—
258M16—3442no—
259C2×C8—44no—
260C2×C8—42no—
261C2×C8—1722no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1722no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C22⋊C4—1722no—
272C22⋊C4—1721no—
273C22⋊C4—1721no—
274C42—1722no—
275C23—21no—
276C23—21no—
277C23—22no—
278C23—41no—
279C23#1306323911yescharacteristic
280C23#1306323911yescharacteristic
281C23C2×(C2×D43)⋊C411yescharacteristic
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—1721no—
303C2×C4—1721no—
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#1306325312yes—
314C2×C4#1306335111yescharacteristic
315C2×C4#1306335611yescharacteristic
316C8—44no—
317C8—3442no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22#1458269012yes—
328C22C2×#1306323911yescharacteristic
329C22#1458289811yescharacteristic
330C22C2×#1306325311yescharacteristic
331C4—21no—
332C4—22no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—3441no—
339C4—3441no—
340C4—3441no—
341C4—3441no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—41no—
346C2#1913309711yescharacteristic
347C2C2×#1458269011yescharacteristic
348C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC2×C43×#343C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenterC2×#343D43
hypocenterC43#11764
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
3. #19132621C2semidirect
4. #19132600C2semidirect
197. C43#11764semidirect

Maximal subgroups

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

subgroupindex
#191388822
#191329252
#191326212
#191326002
C2×C43×#3432
#1176443