Finite Group Databasebeta

← #25007478

Subgroups — #25007478

Order 11008.

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

normal subgroups only

This group has 432 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#19140282C211yesmaximal, characteristic
2#19132909C211yesmaximal, characteristic, complemented
3#19132615C212yesmaximal, complemented
4#19132591C212yesmaximal
5C43×#1820C211yesmaximal, characteristic, complemented
6C2×#13063313C411yescharacteristic, complemented
7#14582952—21no—
8#14582819C411yescharacteristic, complemented
9#14582816C411yescharacteristic, complemented
10#14582811C2211yescharacteristic
11#14582808C2211yescharacteristic
12#14582799—21no—
13#14582790—21no—
14#14582789—21no—
15#14582778—21no—
16#14582745C411yescharacteristic, complemented
17#14582625—21no—
18#14582623C2212yes—
19C2×#117×C43C2211yescharacteristic
20C43×#381—21no—
21C43×#342—21no—
22C43×#342C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C22×D172C2×C411yescharacteristic
25C22×C22⋊D43—21no—
26#13063313—41no—
27#13063313—41no—
28C2×Dic43⋊C4—21no—
29C2×C22⋊Dic43—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×C4×Dic43—21no—
36C4⋊(C43⋊C8)—41no—
37C22⋊(C43⋊C8)—22no—
38C4×C43⋊C8—41no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C23×C4×C43D411yescharacteristic
45#117×C43—41no—
46#117×C43—41no—
47C2×C4⋊C4×C43C2×C411yescharacteristic
48C2×C4⋊C4×C43D411yescharacteristic
49C2×C22⋊C4×C43—22no—
50C2×C22⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43C2311yescharacteristic
52C2×C42×C43C2×C411yescharacteristic
53C2×C42×C43D411yescharacteristic
54#95×C43—41no—
55#95×C43—41no—
56C24×C43C2×D411yescharacteristic
57C23×D43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43—42no—
63C22×C4×C43C22⋊C411yescharacteristic
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C2×C22⋊D43—42no—
70C2×C22⋊D43—42no—
71C2×C22⋊D43—81no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C2×D172—41no—
76C2×D172—81no—
77C2×Dic86—41no—
78C2×Dic86—81no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—42no—
84C22⋊C4×C43—42no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43—21no—
88C42×C43—21no—
89C22⋊Dic43—81no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—42no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—81no—
96Dic43⋊C4—81no—
97C4×Dic43—42no—
98C2×C43⋊C8—42no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43C2×C22⋊C411yescharacteristic
104C23×C43#13512yes—
105C22×D43—41no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—41no—
109C22×D43—41no—
110C22×D43—41no—
111C22×D43—41no—
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—21no—
120C2×C4×C43—21no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—82no—
128C2×C4×C43—82no—
129C2×C4×C43—82no—
130C2×C4×C43#9911yescharacteristic
131C2×C4×C43#9911yescharacteristic
132C22⋊D43—84no—
133C2×Dic43—22no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142D172—82no—
143Dic86—82no—
144C43⋊C8—82no—
145#11844—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—22no—
149C22×C43—42no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—81no—
153C22×C43C2×#9911yescharacteristic
154C22×C43#41611yescharacteristic
155C22×C43#42111yescharacteristic
156C2×D43—81no—
157C2×D43—81no—
158C2×D43—81no—
159C2×D43—81no—
160C2×D43—81no—
161C2×D43—81no—
162C2×D43—81no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—162no—
171Dic43—42no—
172Dic43—81no—
173Dic43—81no—
174#2610—431no—
175#1820D4311yescharacteristic, complemented
176#1458—431no—
177#1351—432no—
178#1343—432no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—42no—
182C2×C43#151611yescharacteristic
183C2×C43#212211yescharacteristic
184C2×C43#212611yescharacteristic
185D43—161no—
186C2×#124—431no—
187C2×#117C2×D4311yescharacteristic
188#431—861no—
189#395—431no—
190#394—431no—
191#393—431no—
192#392—431no—
193#390—861no—
194#388—861no—
195#388—861no—
196#386—861no—
197#381—21no—
198#376—431no—
199#342—21no—
200#342C2×D4312yes—
201#324—861no—
202#323—432no—
203C43#1184411yescharacteristic, complemented, Sylow
204C22×Q8—431no—
205C22×D4—431no—
206C22×D4—861no—
207C23×C4C22⋊D4311yescharacteristic
208#124—1721no—
209#124—1721no—
210#117—41no—
211#117—41no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4C4×D4311yescharacteristic
214C2×C4⋊C4D17211yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—861no—
217C2×C22⋊C4—861no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4—861no—
220C2×C22⋊C4—861no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4C22⋊D4311yescharacteristic
223C2×C22⋊C4C22×D4311yescharacteristic
224C2×C42—861no—
225C2×C42C4×D4311yescharacteristic
226C2×C42D17211yescharacteristic
227C4⋊C8—1721no—
228C22⋊C8—862no—
229C4×C8—1721no—
230#95—41no—
231#95—41no—
232#95—431no—
233#95—431no—
234#95—861no—
235#95—861no—
236#95—861no—
237C24—861no—
238C24C2×C22⋊D4311yescharacteristic
239C2×Q8—3441no—
240C2×Q8—1721no—
241C2×D4—3441no—
242C2×D4—3441no—
243C2×D4—1721no—
244C2×D4—1722no—
245C2×D4—1722no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4(C2×D43)⋊C411yescharacteristic
255C22×C4(C2×D43)⋊C411yescharacteristic
256C22×C4(C2×D43)⋊C411yescharacteristic
257C22×C4(C2×D43)⋊C411yescharacteristic
258C22×C4C2×C4×D4311yescharacteristic
259C22×C4C2×D17211yescharacteristic
260C2×C8—1722no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—3441no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—3441no—
269C22⋊C4—3441no—
270C22⋊C4—1722no—
271C22⋊C4—1722no—
272C22⋊C4—1722no—
273C22⋊C4—1721no—
274C22⋊C4—1721no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—1722no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—1721no—
285C23—1721no—
286C23—1721no—
287C23—1721no—
288C23—1721no—
289C23—1721no—
290C23—1721no—
291C23C2×(C2×D43)⋊C411yescharacteristic
292C23#1306334512yes—
293Q8—3442no—
294D4—3442no—
295D4—3444no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—862no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4#1306323911yescharacteristic
324C2×C4#1306323911yescharacteristic
325C8—3442no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—3441no—
334C22—3441no—
335C22—3441no—
336C22—3441no—
337C22—3441no—
338C22—3441no—
339C22—3441no—
340C22C2×#1306323911yescharacteristic
341C22#1458289311yescharacteristic
342C22#1458291711yescharacteristic
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—162no—
351C4—3441no—
352C4—3441no—
353C4—1722no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—6881no—
358C2#1913314911yescharacteristic
359C2#1913624411yescharacteristic
360C2#1913625811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1820C2
socleC22×C43C2×#99
prime radical#14582808C22
cosocleC2×C22⋊C4×C43C23
hypercenter#1820D43
hypocenterC43#11844
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
2. #19132909C2semidirect
3. #19132615C2semidirect
5. C43×#1820C2semidirect
6. C2×#13063313C4semidirect
8. #14582819C4semidirect
9. #14582816C4semidirect
16. #14582745C4semidirect
175. #1820D43semidirect
203. C43#11844semidirect

Maximal subgroups

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

subgroupindex
#191402822
#191329092
#191326152
#191325912
C43×#18202
#1184443