Finite Group Databasebeta

← #24994489

Subgroups — #24994489

Order 11008.

514 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 95 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#19143233C211yesmaximal, characteristic, complemented
2#19140161C211yesmaximal, characteristic
3#19133037C212yesmaximal, complemented
4#19132461C212yesmaximal, complemented
5C43×#1464C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7#14582960—24no—
8#14582923—21no—
9#14582863—21no—
10C4×#10621877C2212yes—
11#14582838C411yescharacteristic
12#14582835C411yescharacteristic
13#14582816C411yescharacteristic
14#14582808C411yescharacteristic
15#14582790—21no—
16#14582778—21no—
17#14582775—21no—
18#14582770—21no—
19#14582767C2211yescharacteristic
20#14582626—24no—
21C2×#117×C43C2211yescharacteristic
22C43×#432C2212yes—
23C43×#324—21no—
24C43×#323—21no—
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C4×D43—21no—
28C2×#10621877—22no—
29C4×D172—22no—
30C4×D172—22no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C4⋊(C43⋊C8)—24no—
39C22⋊(C43⋊C8)—24no—
40#13063236—22no—
41C4×C43⋊C8D414yescomplemented
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95C2×C411yescharacteristic
47C43⋊#95C2×C411yescharacteristic
48C23×C4×C43D411yescharacteristic
49#117×C43—22no—
50#117×C43—22no—
51C2×C4⋊C4×C43C2×C411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43C2×C411yescharacteristic
54C2×C22⋊C4×C43D411yescharacteristic
55C2×C42×C43D411yescharacteristic
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—22no—
58C22⋊C8×C43—22no—
59#97×C43—22no—
60C24×C43C22⋊C411yescharacteristic
61C23×D43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—42no—
73C2×C22⋊D43—42no—
74C2×C22⋊D43—81no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C2×D172—22no—
79C2×D172—42no—
80C2×C4×D43—42no—
81C2×C4×D43—81no—
82C2×C4×D43—81no—
83C2×C8×C43—42no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—22no—
86C22⋊C4×C43—22no—
87C22⋊C4×C43—22no—
88C42×C43—21no—
89C42×C43—21no—
90C42×C43C2×D412yes—
91C42×C43#4112yes—
92C22⋊Dic43—81no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—81no—
98C4⋊Dic43—22no—
99Dic43⋊C4—81no—
100#10621877—42no—
101#10621877—42no—
102C2×C43⋊C8—24no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43C2×C22⋊C411yescharacteristic
109C22×D43—22no—
110C22×D43—41no—
111C22×D43—41no—
112C22×D43—41no—
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43C4×D412yes—
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12112yes—
132C2×C4×C43#12311yescharacteristic
133C22⋊D43—84no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143D172—24no—
144D172—42no—
145C4×D43—84no—
146C8×C43—82no—
147C43⋊C8—44no—
148#9494—431nomaximal, Sylow
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—42no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—81no—
156C22×C43#38611yescharacteristic
157C22×C43#42111yescharacteristic
158C22×C43#42111yescharacteristic
159C2×D43—42no—
160C2×D43—42no—
161C2×D43—42no—
162C2×D43—81no—
163C2×D43—81no—
164C2×D43—81no—
165C2×D43—81no—
166C4×C43—22no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—22no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173Dic43—81no—
174Dic43—81no—
175Dic43—81no—
176#2921—431no—
177#2598—431no—
178#1490—432no—
179#1464D4311yescharacteristic, complemented
180#1288—432no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43—81no—
184C2×C43#189111yescharacteristic
185C2×C43#189711yescharacteristic
186C2×C43#191011yescharacteristic
187D43—82no—
188C2×C4×D4—431no—
189C2×#117C2×D4311yescharacteristic
190#433—864no—
191#432C2×D4312yes—
192#423—861no—
193#407—861no—
194C4×M16—432no—
195#400—431no—
196#399—431no—
197#394—431no—
198#392—431no—
199#388—861no—
200#386—861no—
201#386—861no—
202#385—861no—
203#383—431no—
204D4⋊C8—864no—
205#324—21no—
206#323—21no—
207C43#949411yescharacteristic, complemented, Sylow
208C22×D4—431no—
209C22×D4—861no—
210C23×C4—861no—
211C23×C4D17211yescharacteristic
212C2×M16—862no—
213C4×D4—862no—
214C4×D4—862no—
215#117—22no—
216#117—22no—
217C2×C4⋊C4—431no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4C4×D4311yescharacteristic
220C2×C4⋊C4C22⋊D4311yescharacteristic
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223C2×C22⋊C4—861no—
224C2×C22⋊C4—861no—
225C2×C22⋊C4—861no—
226C2×C22⋊C4C4×D4311yescharacteristic
227C2×C22⋊C4C22⋊D4311yescharacteristic
228C2×C42D17211yescharacteristic
229C2×C42C22×D4311yescharacteristic
230C4⋊C8—22no—
231C4⋊C8—864no—
232C22⋊C8—22no—
233C22⋊C8—864no—
234#97—22no—
235#97—862no—
236C4×C8—434no—
237#95—431no—
238#95—431no—
239#95—861no—
240#95—861no—
241#95—861no—
242#95—861no—
243C24—861no—
244C24(C2×D43)⋊C411yescharacteristic
245C2×D4—862no—
246C2×D4—3441no—
247C2×D4—1722no—
248C2×D4—1722no—
249C2×D4—1722no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—3441no—
258C22×C4—3441no—
259C22×C4—1722no—
260C22×C4(C2×D43)⋊C411yescharacteristic
261C22×C4(C2×D43)⋊C411yescharacteristic
262C22×C4(C2×D43)⋊C411yescharacteristic
263C22×C4C2×C4×D4311yescharacteristic
264C22×C4C2×D17211yescharacteristic
265C22×C4C2×C22⋊D4311yescharacteristic
266M16—1722no—
267M16—1722no—
268C2×C8—42no—
269C2×C8—864no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—862no—
273C4⋊C4—3441no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—3441no—
277C22⋊C4—3441no—
278C22⋊C4—1722no—
279C22⋊C4—1722no—
280C22⋊C4—1721no—
281C22⋊C4—1721no—
282C42—21no—
283C42—21no—
284C42D4×D4312yes—
285C42#1062190012yes—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—862no—
292C23—1721no—
293C23—1721no—
294C23—1721no—
295C23—1721no—
296C23—1721no—
297C23—1721no—
298C23C2×(C2×D43)⋊C411yescharacteristic
299D4—864no—
300D4—3444no—
301D4—1722no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—3444no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4(C22⋊D43)⋊C412yes—
326C2×C4#1306329511yescharacteristic
327C2×C4#1306329712yes—
328C2×C4#1306330911yescharacteristic
329C8—82no—
330C8—1724no—
331C22—21no—
332C22—21no—
333C22—42no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—3441no—
339C22—3441no—
340C22—3441no—
341C22—3441no—
342C22—1722no—
343C22—1722no—
344C22—1722no—
345C22#1458277611yescharacteristic
346C22#1458291511yescharacteristic
347C22#1458291511yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3441no—
356C4—3441no—
357C4—3441no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—3442no—
362C2#1913501111yescharacteristic
363C2#1913504111yescharacteristic
364C2#1913512011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1464C2
socleC22×C43#386
prime radical#14582808C4
cosocleC2×C42×C43C23
hypercenter#1464D43
hypocenterC43#9494
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
1. #19143233C2semidirect
3. #19133037C2semidirect
4. #19132461C2semidirect
5. C43×#1464C2semidirect
41. C4×C43⋊C8D4semidirect
179. #1464D43semidirect
207. C43#9494semidirect

Maximal subgroups

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

subgroupindex
#191432332
#191401612
#191330372
#191324612
C43×#14642
#949443