Finite Group Databasebeta

← #24994474

Subgroups — #24994474

Order 11008.

544 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 103 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#19143014C211yesmaximal, characteristic
2#19140172C211yesmaximal, characteristic
3#19133041C212yesmaximal, complemented
4#19132461C212yesmaximal, complemented
5C43×#1464C211yesmaximal, characteristic
6C22×#10621877—21no—
7C2×C4×Dic86C2211yescharacteristic
8#14582855—24no—
9C4×#10621877—21no—
10C4×#10621877C2212yes—
11#14582829C411yescharacteristic
12#14582824C411yescharacteristic
13#14582819C411yescharacteristic
14#14582811C411yescharacteristic
15#14582787—21no—
16#14582783—21no—
17#14582780—21no—
18#14582772—21no—
19#14582767C2211yescharacteristic
20#14582629—24no—
21C2×#117×C43C2211yescharacteristic
22C43×#432C2212yes—
23C43×#324—21no—
24C43×#323—21no—
25C22×Dic86C2×C411yescharacteristic
26C2×#10621877—22no—
27C2×#10621877—24no—
28C2×#10621877—24no—
29C2×#10621877—22no—
30C22×C43⋊C8—22no—
31C4×Dic86—22no—
32C4×Dic86—22no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C4×Dic43—21no—
40#13063236—22no—
41#13063236—22no—
42C4×C43⋊C8—22no—
43C4×C43⋊C8D414yes—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95C2×C411yescharacteristic
51C43⋊#95C2×C411yescharacteristic
52C23×C4×C43D411yescharacteristic
53#117×C43—22no—
54#117×C43—22no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43D411yescharacteristic
59C2×C42×C43D411yescharacteristic
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—22no—
62C22⋊C8×C43—22no—
63#97×C43—22no—
64C24×C43C22⋊C411yescharacteristic
65C22×C4×C43—22no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—22no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×Dic86—22no—
80C2×Dic86—42no—
81C2×C8×C43—42no—
82C4⋊C4×C43—22no—
83C4⋊C4×C43—22no—
84C22⋊C4×C43—22no—
85C22⋊C4×C43—22no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43C2×D412yes—
89C42×C43#4112yes—
90C22⋊Dic43—42no—
91C22⋊Dic43—42no—
92C4⋊Dic43—22no—
93Dic43⋊C4—42no—
94Dic43⋊C4—42no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97C4×Dic43—42no—
98#10621877—28no—
99#10621877—24no—
100#10621877—24no—
101C2×C43⋊C8—28no—
102C2×C43⋊C8—24no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43#10412yes—
108C23×C43C2×C22⋊C411yescharacteristic
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—24no—
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—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43#10412yes—
123C2×C4×C43C4×D412yes—
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43#12112yes—
126C2×C4×C43#12311yescharacteristic
127C2×Dic43—22no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139Dic86—24no—
140Dic86—42no—
141C8×C43—82no—
142C43⋊C8—28no—
143#9491—431nomaximal, Sylow
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—22no—
147C22×C43—42no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—81no—
151C22×C43#38611yescharacteristic
152C22×C43C2×#10411yescharacteristic
153C22×C43C2×#10411yescharacteristic
154C4×C43—22no—
155C4×C43—21no—
156C4×C43—22no—
157C4×C43—21no—
158C4×C43—22no—
159C4×C43—41no—
160C4×C43—41no—
161Dic43—42no—
162Dic43—81no—
163Dic43—81no—
164Dic43—81no—
165#2873—431no—
166#2599—431no—
167#1491—432no—
168#1464D4311yescharacteristic
169#1288—432no—
170C2×C43—21no—
171C2×C43—21no—
172C2×C43—42no—
173C2×C43#189111yescharacteristic
174C2×C43#189611yescharacteristic
175C2×C43#190911yescharacteristic
176C22×M16—861no—
177C2×C4×Q8—431no—
178C2×#117C2×D4311yescharacteristic
179#432C2×D4312yes—
180#405—864no—
181C4×M16—432no—
182C4×M16—861no—
183#398—431no—
184#397—431no—
185#395—431no—
186#393—431no—
187#388—861no—
188#387—861no—
189#387—861no—
190#385—861no—
191#383—431no—
192Q8⋊C8—864no—
193#324—21no—
194#323—21no—
195C43#949111yescharacteristic, complemented, Sylow
196C22×Q8—431no—
197C23×C4D17211yescharacteristic
198C2×M16—862no—
199C2×M16—864no—
200C2×M16—864no—
201C2×M16—862no—
202C22×C8—862no—
203C4×Q8—862no—
204C4×Q8—862no—
205#117—22no—
206#117—22no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4C4×D4311yescharacteristic
212C2×C4⋊C4C22⋊D4311yescharacteristic
213C2×C22⋊C4—861no—
214C2×C22⋊C4—861no—
215C2×C22⋊C4C4×D4311yescharacteristic
216C2×C22⋊C4C22⋊D4311yescharacteristic
217C2×C42—861no—
218C2×C42D17211yescharacteristic
219C2×C42C22×D4311yescharacteristic
220C4⋊C8—22no—
221C22⋊C8—22no—
222#97—22no—
223#97—862no—
224#97—862no—
225C4×C8—434no—
226C4×C8—862no—
227#95—431no—
228#95—431no—
229#95—861no—
230#95—861no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95—861no—
235C24(C2×D43)⋊C411yescharacteristic
236C2×Q8—862no—
237C2×Q8—1722no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4(C2×D43)⋊C411yescharacteristic
247C22×C4(C2×D43)⋊C411yescharacteristic
248C22×C4(C2×D43)⋊C411yescharacteristic
249C22×C4C2×C4×D4311yescharacteristic
250C22×C4C2×D17211yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252M16—868no—
253M16—864no—
254M16—864no—
255C2×C8—42no—
256C2×C8—868no—
257C2×C8—864no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—862no—
261C4⋊C4—1722no—
262C4⋊C4—1722no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—1722no—
268C22⋊C4—1722no—
269C42—21no—
270C42—21no—
271C42—1722no—
272C42D4×D4312yes—
273C42#1062190012yes—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23#1306325112yes—
279C23C2×(C2×D43)⋊C411yescharacteristic
280Q8—864no—
281Q8—1722no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—862no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4#1306325112yes—
308C2×C4(C22⋊D43)⋊C412yes—
309C2×C4#1306329511yescharacteristic
310C2×C4#1306329712yes—
311C2×C4#1306330911yescharacteristic
312C8—82no—
313C8—868no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#1458277611yescharacteristic
322C22C2×#1306325111yescharacteristic
323C22C2×#1306325111yescharacteristic
324C4—22no—
325C4—21no—
326C4—22no—
327C4—21no—
328C4—22no—
329C4—41no—
330C4—41no—
331C4—3441no—
332C4—3441no—
333C4—3441no—
334C4—1722no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1913501111yescharacteristic
339C2#1913503611yescharacteristic
340C2#1913511511yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1464C2
socleC22×C43#386
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1464D43
hypocenterC43#9491
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #19133041C2semidirect
4. #19132461C2semidirect
195. C43#9491semidirect

Maximal subgroups

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

subgroupindex
#191430142
#191401722
#191330412
#191324612
C43×#14642
#949143