Finite Group Databasebeta

← #24994481

Subgroups — #24994481

Order 11008.

600 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 107 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#19140161C211yesmaximal, characteristic
2#19133039C212yesmaximal, complemented
3#19132929C211yesmaximal, characteristic, complemented
4#19132460C212yesmaximal, complemented
5C43×#2873C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7#14582956C2212yes—
8#14582838C411yescharacteristic
9#14582835C411yescharacteristic
10#14582816C411yescharacteristic
11#14582808C411yescharacteristic
12#14582790—21no—
13#14582778—21no—
14#14582775—21no—
15#14582770—21no—
16#14582767C2211yescharacteristic
17#14582628—24no—
18#14582625—21no—
19#14582623—21no—
20C22×M16×C43—21no—
21C2×#117×C43C2211yescharacteristic
22C43×#405—24no—
23C4×M16×C43—21no—
24C4×M16×C43C2212yes—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C4×D43—21no—
28C4×D172—22no—
29C4×D172—22no—
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×C22⋊Dic43—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C4⋊(C43⋊C8)—22no—
38C22⋊(C43⋊C8)—22no—
39#13063236—22no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95C2×C411yescharacteristic
45C43⋊#95C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C2×M16×C43—24no—
48C2×M16×C43—24no—
49C2×M16×C43—22no—
50C2×M16×C43—22no—
51C22×C8×C43—22no—
52#117×C43—22no—
53#117×C43—22no—
54C2×C4⋊C4×C43C2×C411yescharacteristic
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60#97×C43—22no—
61#97×C43—22no—
62C4×C8×C43—22no—
63C4×C8×C43D414yescomplemented
64C24×C43C22⋊C411yescharacteristic
65C23×D43—21no—
66C22×C4×C43—22no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—22no—
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—42no—
77C2×C22⋊D43—42no—
78C2×C22⋊D43—81no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C2×D172—22no—
83C2×D172—42no—
84C2×C4×D43—42no—
85C2×C4×D43—81no—
86C2×C4×D43—81no—
87M16×C43—28no—
88M16×C43—24no—
89M16×C43—24no—
90C2×C8×C43—28no—
91C2×C8×C43—24no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—22no—
94C22⋊C4×C43—22no—
95C22⋊C4×C43—22no—
96C42×C43—21no—
97C42×C43—21no—
98C42×C43C2×D412yes—
99C42×C43#4112yes—
100C22⋊Dic43—81no—
101(C2×D43)⋊C4—42no—
102(C2×D43)⋊C4—42no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—81no—
106C4⋊Dic43—22no—
107Dic43⋊C4—81no—
108C2×C43⋊C8—42no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43#10412yes—
114C23×C43C2×C22⋊C411yescharacteristic
115C22×D43—22no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—24no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43#10412yes—
136C2×C4×C43C4×D412yes—
137C2×C4×C43#12011yescharacteristic
138C2×C4×C43#12112yes—
139C2×C4×C43#12311yescharacteristic
140C22⋊D43—84no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150D172—24no—
151D172—42no—
152C4×D43—84no—
153C8×C43—28no—
154C43⋊C8—82no—
155#9492—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—22no—
159C22×C43—42no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—81no—
163C22×C43#38611yescharacteristic
164C22×C43C2×#10411yescharacteristic
165C22×C43C2×#10411yescharacteristic
166C2×D43—42no—
167C2×D43—42no—
168C2×D43—42no—
169C2×D43—81no—
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C4×C43—22no—
174C4×C43—21no—
175C4×C43—22no—
176C4×C43—21no—
177C4×C43—22no—
178C4×C43—41no—
179C4×C43—41no—
180Dic43—81no—
181Dic43—81no—
182Dic43—81no—
183#2873D4311yescharacteristic, complemented
184#2598—431no—
185#1490—432no—
186#1464—431no—
187#1288—432no—
188C2×C43—21no—
189C2×C43—21no—
190C2×C43—42no—
191C2×C43#189111yescharacteristic
192C2×C43#189611yescharacteristic
193C2×C43#191011yescharacteristic
194D43—82no—
195C22×M16—21no—
196C2×C4×D4—431no—
197C2×#117C2×D4311yescharacteristic
198#432—432no—
199#405—24no—
200C4×M16—21no—
201C4×M16C2×D4312yes—
202#400—431no—
203#399—431no—
204#394—431no—
205#392—431no—
206#388—861no—
207#386—861no—
208#386—861no—
209#385—861no—
210#383—431no—
211D4⋊C8—864no—
212#324—861no—
213#323—861no—
214C43#949211yescharacteristic, complemented, Sylow
215C22×D4—431no—
216C22×D4—861no—
217C23×C4—861no—
218C23×C4C22⋊D4311yescharacteristic
219C2×M16—24no—
220C2×M16—24no—
221C2×M16—22no—
222C2×M16—22no—
223C22×C8—22no—
224C4×D4—862no—
225C4×D4—862no—
226#117—22no—
227#117—22no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4C4×D4311yescharacteristic
231C2×C4⋊C4D17211yescharacteristic
232C2×C22⋊C4—861no—
233C2×C22⋊C4—861no—
234C2×C22⋊C4—861no—
235C2×C22⋊C4—861no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4C4×D4311yescharacteristic
238C2×C22⋊C4D17211yescharacteristic
239C2×C42C22⋊D4311yescharacteristic
240C2×C42C22×D4311yescharacteristic
241C4⋊C8—862no—
242C22⋊C8—862no—
243#97—22no—
244#97—22no—
245#97—862no—
246C4×C8—22no—
247C4×C8C22⋊D4314yescomplemented
248#95—431no—
249#95—431no—
250#95—861no—
251#95—861no—
252#95—861no—
253#95—861no—
254C24—861no—
255C24(C2×D43)⋊C411yescharacteristic
256C2×D4—862no—
257C2×D4—3441no—
258C2×D4—1722no—
259C2×D4—1722no—
260C2×D4—1722no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—3441no—
269C22×C4—3441no—
270C22×C4—1722no—
271C22×C4(C2×D43)⋊C411yescharacteristic
272C22×C4(C2×D43)⋊C411yescharacteristic
273C22×C4(C2×D43)⋊C411yescharacteristic
274C22×C4C2×C4×D4311yescharacteristic
275C22×C4C2×D17211yescharacteristic
276C22×C4C2×C22⋊D4311yescharacteristic
277M16—28no—
278M16—24no—
279M16—24no—
280C2×C8—28no—
281C2×C8—24no—
282C2×C8—1722no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—862no—
286C4⋊C4—3441no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—3441no—
290C22⋊C4—3441no—
291C22⋊C4—1722no—
292C22⋊C4—1722no—
293C22⋊C4—1721no—
294C22⋊C4—1721no—
295C42—21no—
296C42—21no—
297C42#1062189812yes—
298C42C2×C22⋊D4312yes—
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—862no—
304C23—1721no—
305C23—1721no—
306C23—1721no—
307C23—1721no—
308C23—1721no—
309C23—1721no—
310C23#1306325312yes—
311C23C2×(C2×D43)⋊C411yescharacteristic
312D4—864no—
313D4—3444no—
314D4—1722no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—3444no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4#1306325312yes—
339C2×C4C4×C22⋊D4312yes—
340C2×C4#1306329411yescharacteristic
341C2×C4#1306329912yes—
342C2×C4#1306330811yescharacteristic
343C8—28no—
344C8—3442no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—42no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22—3441no—
353C22—3441no—
354C22—3441no—
355C22—3441no—
356C22—1722no—
357C22—1722no—
358C22—1722no—
359C22#1458277811yescharacteristic
360C22C2×#1306325311yescharacteristic
361C22C2×#1306325311yescharacteristic
362C4—22no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—3441no—
370C4—3441no—
371C4—3441no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—3442no—
376C2#1913501311yescharacteristic
377C2#1913503811yescharacteristic
378C2#1913512211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2873C2
socleC22×C43#386
prime radical#14582808C4
cosocleC2×C42×C43C23
hypercenter#2873D43
hypocenterC43#9492
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2873

Complements

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

NH ≅ G/Ntype
2. #19133039C2semidirect
3. #19132929C2semidirect
4. #19132460C2semidirect
5. C43×#2873C2semidirect
63. C4×C8×C43D4semidirect
183. #2873D43semidirect
214. C43#9492semidirect
247. C4×C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191401612
#191330392
#191329292
#191324602
C43×#28732
#949243