Finite Group Databasebeta

← #25007429

Subgroups — #25007429

Order 11008.

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

normal subgroups only

This group has 400 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#19140512C211yesmaximal, characteristic
2#19134587C211yesmaximal, characteristic
3#19132626C212yesmaximal, complemented
4#19132602C212yesmaximal, complemented
5C43×#1465C211yesmaximal, characteristic
6C2×#13063304C411yescharacteristic
7#14582923—21no—
8C2×#13063242—21no—
9#14582829C2211yescharacteristic
10#14582827—21no—
11#14582824C411yescharacteristic
12#14582819C2211yescharacteristic
13#14582813—21no—
14#14582811C411yescharacteristic
15#14582783—21no—
16#14582772—21no—
17#14582762C411yescharacteristic
18#14582668C2212yes—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C22×Dic86C2×C411yescharacteristic
24C2×#10621877—22no—
25#13063304—41no—
26#13063304—41no—
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×Dic43⋊C4—21no—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C4⋊(C43⋊C8)—41no—
36C4⋊(C43⋊C8)—41no—
37#13063242—42no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95C2×C411yescharacteristic
44C43⋊#95C2×C411yescharacteristic
45C22×D4×C43D411yescharacteristic
46C23×C4×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C2×M16×C43—41no—
49C4×D4×C43—41no—
50C4×D4×C43—41no—
51C2×C4⋊C4×C43C2311yescharacteristic
52C2×C22⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C22⋊C8×C43—22no—
56C22⋊C8×C43—41no—
57C24×C43C22⋊C411yescharacteristic
58C24×C43C22⋊C411yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—41no—
62C2×D4×C43—41no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—81no—
68C22×C4×C43—81no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22×C411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C2×Dic86—41no—
79C2×Dic86—81no—
80M16×C43—82no—
81C2×C8×C43—42no—
82C4⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C42×C43—21no—
86C42×C43—21no—
87C22⋊Dic43—42no—
88C22⋊Dic43—42no—
89C22⋊Dic43—81no—
90C22⋊Dic43—81no—
91C4⋊Dic43—41no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—81no—
97#10621877—42no—
98#10621877—42no—
99C2×C43⋊C8—42no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43C2×C22⋊C411yescharacteristic
111D4×C43—42no—
112D4×C43—42no—
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—42no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×C4×C43—81no—
126C2×C4×C43#9911yescharacteristic
127C2×C4×C43#9911yescharacteristic
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C43#13711yescharacteristic
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—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142Dic86—82no—
143C8×C43—82no—
144C43⋊C8—82no—
145#11834—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—42no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43—81no—
158C22×C43C2×#9911yescharacteristic
159C22×C43#41711yescharacteristic
160C22×C43#42111yescharacteristic
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—41no—
168Dic43—81no—
169Dic43—81no—
170Dic43—81no—
171Dic43—81no—
172#2638—431no—
173#1800—431no—
174#1465D4311yescharacteristic
175#1354—432no—
176#1346—432no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—81no—
180C2×C43—81no—
181C2×C43#151311yescharacteristic
182C2×C43#212111yescharacteristic
183C2×C43#213511yescharacteristic
184C2×C22⋊Q8—431no—
185C2×C4×D4C2×D4311yescharacteristic
186#423—861no—
187C2×#100—861no—
188#407—21no—
189#398—431no—
190#397—431no—
191#397—861no—
192#395—431no—
193#394—861no—
194#393—431no—
195#387—861no—
196#385—861no—
197#381—431no—
198#343—432no—
199#324C2×D4312yes—
200#323—21no—
201C43#1183411yescharacteristic, complemented, Sylow
202C22×Q8—431no—
203C22×D4D17211yescharacteristic
204C23×C4C4×D4311yescharacteristic
205C23×C4C22⋊D4311yescharacteristic
206C2×M16—41no—
207C2×M16—862no—
208C22⋊Q8—1721no—
209C22⋊Q8—1721no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—431no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4C22×D4311yescharacteristic
217C2×C22⋊C4—861no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4—861no—
220C2×C22⋊C4—861no—
221C2×C22⋊C4C4×D4311yescharacteristic
222C2×C22⋊C4C22⋊D4311yescharacteristic
223C2×C42D17211yescharacteristic
224C4⋊C8—1721no—
225C4⋊C8—1721no—
226#100—1722no—
227C22⋊C8—22no—
228C22⋊C8—41no—
229#95—431no—
230#95—431no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236C24(C2×D43)⋊C411yescharacteristic
237C24(C2×D43)⋊C411yescharacteristic
238C2×Q8—3441no—
239C2×Q8—1721no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—41no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4(C2×D43)⋊C411yescharacteristic
255C22×C4(C2×D43)⋊C411yescharacteristic
256C22×C4C2×C4×D4311yescharacteristic
257C22×C4C2×D17211yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259M16—82no—
260M16—1722no—
261M16—1722no—
262C2×C8—42no—
263C2×C8—1722no—
264C4⋊C4—41no—
265C4⋊C4—3441no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C4⋊C4—1721no—
270C4⋊C4—1721no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—3441no—
274C22⋊C4—3441no—
275C22⋊C4—1722no—
276C22⋊C4—1722no—
277C42—21no—
278C42—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×(C2×D43)⋊C411yescharacteristic
290Q8—3442no—
291D4—42no—
292D4—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4#1306323911yescharacteristic
319C2×C4#1306323911yescharacteristic
320C2×C4#1306335311yescharacteristic
321C2×C4#1306335811yescharacteristic
322C8—82no—
323C8—3442no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22C2×#1306323911yescharacteristic
337C22#1458290111yescharacteristic
338C22#1458291511yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3441no—
347C4—3441no—
348C4—3441no—
349C4—3441no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—81no—
354C2#1913313911yescharacteristic
355C2#1913623911yescharacteristic
356C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1465C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C4⋊C4×C43C23
hypercenter#1465D43
hypocenterC43#11834
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #19132626C2semidirect
4. #19132602C2semidirect
201. C43#11834semidirect

Maximal subgroups

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

subgroupindex
#191405122
#191345872
#191326262
#191326022
C43×#14652
#1183443