Finite Group Databasebeta

← #25006119

Subgroups — #25006119

Order 11008.

460 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 79 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#19138865C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic, complemented
3#19132542C212yesmaximal, complemented
4#19132522C212yesmaximal
5C43×#1464C211yesmaximal, characteristic, complemented
6C22×(C2×D43)⋊C4C411yescharacteristic
7#14582952—21no—
8#14582834—21no—
9#14582825—21no—
10#14582790—21no—
11#14582790—21no—
12#14582771C411yescharacteristic
13#14582771C2211yescharacteristic
14#14582762C411yescharacteristic
15#14582754C411yescharacteristic
16#14582754C2211yescharacteristic
17#14582625—21no—
18#14582623C2212yes—
19C2×#117×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#324—21no—
22C43×#323C2212yes—
23C24×D43C2×C411yescharacteristic
24C23×Dic43C2×C411yescharacteristic
25C2×Dic43⋊C4—21no—
26C2×Dic43⋊C4—21no—
27C2×C22⋊Dic43C2×C411yescharacteristic
28C2×C22⋊Dic43C2×C411yescharacteristic
29C2×(C2×D43)⋊C4—21no—
30C2×(C2×D43)⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—41no—
36C2×(C2×D43)⋊C4—41no—
37C4⋊(C43⋊C8)—41no—
38C22⋊(C43⋊C8)—22no—
39C4×C43⋊C8—41no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C23×C4×C43C2×C411yescharacteristic
45#117×C43—41no—
46#117×C43—41no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43C2×C411yescharacteristic
50C2×C22⋊C4×C43C2311yescharacteristic
51C2×C42×C43D411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C4⋊C8×C43—41no—
54C22⋊C8×C43—22no—
55#97×C43—41no—
56C24×C43C22×C411yescharacteristic
57C23×D43—21no—
58C23×D43—22no—
59C23×D43—42no—
60C23×D43—41no—
61C23×D43—41no—
62C23×D43—81no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—22no—
66C22×C4×C43—41no—
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—41no—
77C22×Dic43—81no—
78C2×C8×C43—42no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87C22⋊Dic43—22no—
88C22⋊Dic43—41no—
89(C2×D43)⋊C4—42no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—81no—
95(C2×D43)⋊C4—81no—
96Dic43⋊C4—81no—
97Dic43⋊C4—81no—
98C2×C43⋊C8—42no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43C2×C22⋊C411yescharacteristic
104C23×C43#13112yes—
105C22×D43—22no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—41no—
109C22×D43—42no—
110C22×D43—41no—
111C22×D43—41no—
112C22×D43—41no—
113C22×D43—42no—
114C22×D43—84no—
115C22×D43—84no—
116C22×D43—82no—
117C22×D43—82no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43#9911yescharacteristic
134C2×C4×C43#9911yescharacteristic
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—82no—
145C8×C43—82no—
146C43⋊C8—82no—
147#11542—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—22no—
151C22×C43—42no—
152C22×C43—42no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43#40811yescharacteristic
156C22×C43C2×#9911yescharacteristic
157C22×C43#41311yescharacteristic
158C2×D43—42no—
159C2×D43—42no—
160C2×D43—42no—
161C2×D43—81no—
162C2×D43—81no—
163C2×D43—84no—
164C2×D43—81no—
165C2×D43—81no—
166C2×D43—84no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174Dic43—81no—
175Dic43—81no—
176Dic43—81no—
177#2482—431no—
178#1464D4311yescharacteristic, complemented
179#1458—431no—
180#1326—432no—
181#1316—432no—
182C2×C43—21no—
183C2×C43—21no—
184C2×C43—42no—
185C2×C43#146811yescharacteristic
186C2×C43#212011yescharacteristic
187C2×C43#212211yescharacteristic
188D43—82no—
189C2×#117C2×D4311yescharacteristic
190C22×C22⋊C4—431no—
191#432—21no—
192#431—861no—
193#399—861no—
194#397—861no—
195#388—861no—
196#388—861no—
197#385—431no—
198#385—431no—
199#381—431no—
200#379—431no—
201#379—431no—
202#324—21no—
203#324—861no—
204#323—432no—
205#323C2×D4312yes—
206C43#1154211yescharacteristic, complemented, Sylow
207C25—431no—
208C23×C4—431no—
209C23×C4C4×D4311yescharacteristic
210#117—41no—
211#117—41no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4D17211yescharacteristic
215C2×C4⋊C4C22⋊D4311yescharacteristic
216C2×C22⋊C4—431no—
217C2×C22⋊C4—431no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4—861no—
220C2×C22⋊C4—861no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223C2×C22⋊C4—861no—
224C2×C22⋊C4—1721no—
225C2×C22⋊C4—1721no—
226C2×C22⋊C4C4×D4311yescharacteristic
227C2×C22⋊C4C22×D4311yescharacteristic
228C2×C42D17211yescharacteristic
229C2×C42C22⋊D4311yescharacteristic
230C4⋊C8—41no—
231C4⋊C8—1721no—
232C22⋊C8—22no—
233C22⋊C8—862no—
234#97—41no—
235C4×C8—1721no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95—861no—
240C24—861no—
241C24—862no—
242C24—3441no—
243C24—1721no—
244C24—1721no—
245C24—1722no—
246C24C2×C4×D4311yescharacteristic
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—3441no—
255C22×C4—1721no—
256C22×C4(C2×D43)⋊C411yescharacteristic
257C22×C4(C2×D43)⋊C411yescharacteristic
258C22×C4(C2×D43)⋊C411yescharacteristic
259C22×C4(C2×D43)⋊C411yescharacteristic
260C22×C4C2×D17211yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262C2×C8—42no—
263C2×C8—1722no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—3441no—
267C4⋊C4—3441no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—862no—
271C22⋊C4—3441no—
272C22⋊C4—3441no—
273C22⋊C4—1722no—
274C22⋊C4—1722no—
275C22⋊C4—1722no—
276C22⋊C4—1721no—
277C22⋊C4—1721no—
278C22⋊C4—1721no—
279C42—21no—
280C42—21no—
281C42—21no—
282C42—21no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—862no—
288C23—3442no—
289C23—3442no—
290C23—3444no—
291C23—3444no—
292C23—1721no—
293C23—1721no—
294C23—1721no—
295C23—1722no—
296C23—1722no—
297C23—1721no—
298C23—1721no—
299C23—1721no—
300C23C2×(C2×D43)⋊C411yescharacteristic
301C23#1306333312yes—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—3442no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4#1306323911yescharacteristic
328C2×C4#1306323911yescharacteristic
329C8—82no—
330C8—3442no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—3441no—
339C22—3441no—
340C22—3444no—
341C22—3444no—
342C22—3441no—
343C22—3441no—
344C22—1722no—
345C22—1722no—
346C22—1722no—
347C22#1458286711yescharacteristic
348C22C2×#1306323911yescharacteristic
349C22#1458288111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3441no—
358C4—3441no—
359C4—3441no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—3442no—
364C2#1913294411yescharacteristic
365C2#1913623711yescharacteristic
366C2#1913624411yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1464C2
socleC22×C43C2×#99
prime radicalC24×D43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1464D43
hypocenterC43#11542
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #19132909C2semidirect
3. #19132542C2semidirect
5. C43×#1464C2semidirect
178. #1464D43semidirect
206. C43#11542semidirect

Maximal subgroups

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

subgroupindex
#191388652
#191329092
#191325422
#191325222
C43×#14642
#1154243