Finite Group Databasebeta

← #25007754

Subgroups — #25007754

Order 11008.

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

normal subgroups only

This group has 440 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#19139771C211yesmaximal, characteristic
2#19132913C211yesmaximal, characteristic
3#19132624C212yesmaximal, complemented
4#19132621C212yesmaximal, complemented
5C43×#1800C211yesmaximal, characteristic
6C2×#13063304C411yescharacteristic
7C2×C22⋊(C43⋊C8)—21no—
8#14582838C2211yescharacteristic
9#14582835C411yescharacteristic
10#14582819C2211yescharacteristic
11#14582811C411yescharacteristic
12#14582783—21no—
13#14582779—21no—
14#14582772—21no—
15#14582757—21no—
16C2×C43⋊#95C411yescharacteristic
17#14582625C2212yes—
18#14582623—21no—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#423—21no—
21C2×#100×C43—21no—
22C43×#343C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C23×Dic43—21no—
25C22×C43⋊C8—41no—
26#13063304—41no—
27#13063304—41no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C22⋊(C43⋊C8)—22no—
36C22⋊(C43⋊C8)—41no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C22×D4×C43D411yescharacteristic
45C23×C4×C43C2×C411yescharacteristic
46C23×C4×C43D411yescharacteristic
47C2×M16×C43—22no—
48C4×D4×C43—41no—
49C4×D4×C43—41no—
50C2×C4⋊C4×C43C2311yescharacteristic
51C2×C22⋊C4×C43C2×C411yescharacteristic
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C4⋊C8×C43—41no—
55C4⋊C8×C43—41no—
56#100×C43—42no—
57C24×C43C22⋊C411yescharacteristic
58C24×C43C22⋊C411yescharacteristic
59C2×D4×C43—41no—
60C2×D4×C43—41no—
61C2×D4×C43SD1612yes—
62C2×D4×C43Q1612yes—
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—
78C22×Dic43—42no—
79C22×Dic43—42no—
80C22×Dic43—81no—
81C2×Dic86—41no—
82C2×Dic86—81no—
83M16×C43—42no—
84M16×C43—42no—
85C2×C8×C43—42no—
86C4⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C42×C43—21no—
90C42×C43—21no—
91C22⋊Dic43—42no—
92C22⋊Dic43—42no—
93C22⋊Dic43—81no—
94C4⋊Dic43—41no—
95Dic43⋊C4—42no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—81no—
99C2×C43⋊C8—42no—
100C2×C43⋊C8—82no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43#10312yes—
110C23×C43#10312yes—
111C23×C43C2×C22⋊C411yescharacteristic
112D4×C43—42no—
113D4×C43—42no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—41no—
120C2×C4×C43—42no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—81no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43#9911yescharacteristic
128C2×C4×C43#9911yescharacteristic
129C2×C4×C43C2×SD1611yescharacteristic
130C2×C4×C43C2×Q1611yescharacteristic
131C2×Dic43—22no—
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—
142C2×Dic43—41no—
143C2×Dic43—84no—
144Dic86—82no—
145C8×C43—82no—
146C43⋊C8—82no—
147#11906—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—22no—
151C22×C43—22no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—81no—
160C22×C43C2×#9911yescharacteristic
161C22×C43C2×#10311yescharacteristic
162C22×C43#42111yescharacteristic
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170Dic43—42no—
171Dic43—81no—
172Dic43—81no—
173Dic43—81no—
174#2564—431no—
175#1800D4311yescharacteristic
176#1459—431no—
177#1354—432no—
178#1353—432no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—42no—
182C2×C43—42no—
183C2×C43#152011yescharacteristic
184C2×C43#212111yescharacteristic
185C2×C43#213211yescharacteristic
186C2×C22⋊Q8—431no—
187C2×C4×D4C2×D4311yescharacteristic
188#423—21no—
189C2×#100—21no—
190C2×C22⋊C8—861no—
191#400—431no—
192#399—431no—
193#395—431no—
194#393—431no—
195#387—861no—
196#386—861no—
197#385—861no—
198#380—861no—
199C2×#95—431no—
200#343C2×D4312yes—
201#324—432no—
202#323—861no—
203C43#1190611yescharacteristic, complemented, Sylow
204C22×Q8—431no—
205C22×D4C22⋊D4311yescharacteristic
206C23×C4—861no—
207C23×C4C4×D4311yescharacteristic
208C23×C4D17211yescharacteristic
209C2×M16—22no—
210C22×C8—1721no—
211C22⋊Q8—1721no—
212C22⋊Q8—1721no—
213C4×D4—41no—
214C4×D4—41no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4C22×D4311yescharacteristic
220C2×C22⋊C4—861no—
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223C2×C22⋊C4C4×D4311yescharacteristic
224C2×C22⋊C4D17211yescharacteristic
225C2×C42C22⋊D4311yescharacteristic
226C4⋊C8—41no—
227C4⋊C8—41no—
228#100—42no—
229C22⋊C8—862no—
230C22⋊C8—1721no—
231#95—431no—
232#95—431no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—861no—
237#95—861no—
238C24(C2×D43)⋊C411yescharacteristic
239C24(C2×D43)⋊C411yescharacteristic
240C2×Q8—3441no—
241C2×Q8—1721no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4#1062188312yes—
245C2×D4#1062188512yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—3441no—
257C22×C4—1722no—
258C22×C4—1722no—
259C22×C4(C2×D43)⋊C411yescharacteristic
260C22×C4(C2×D43)⋊C411yescharacteristic
261C22×C4C2×C4×D4311yescharacteristic
262C22×C4C2×D17211yescharacteristic
263C22×C4C2×C22⋊D4311yescharacteristic
264M16—42no—
265M16—42no—
266C2×C8—42no—
267C2×C8—3442no—
268C2×C8—1722no—
269C4⋊C4—41no—
270C4⋊C4—3441no—
271C4⋊C4—1721no—
272C4⋊C4—1722no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—3441no—
278C22⋊C4—1722no—
279C22⋊C4—1722no—
280C42—21no—
281C42—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23#1306324812yes—
291C23#1306324812yes—
292C23C2×(C2×D43)⋊C411yescharacteristic
293Q8—3442no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—862no—
310C2×C4—3444no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4#1306323911yescharacteristic
323C2×C4#1306323911yescharacteristic
324C2×C4C2×#1062188311yescharacteristic
325C2×C4C2×#1062188511yescharacteristic
326C8—82no—
327C8—3442no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—81no—
340C22C2×#1306323911yescharacteristic
341C22C2×#1306324811yescharacteristic
342C22#1458291711yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—3441no—
351C4—3441no—
352C4—3441no—
353C4—1722no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—42no—
358C2#1913316611yescharacteristic
359C2#1913624211yescharacteristic
360C2#1913627811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1800C2
socleC22×C43C2×#99
prime radicalC22×D4×C43D4
cosocleC2×C4⋊C4×C43C23
hypercenter#1800D43
hypocenterC43#11906
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #19132624C2semidirect
4. #19132621C2semidirect
203. C43#11906semidirect

Maximal subgroups

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

subgroupindex
#191397712
#191329132
#191326242
#191326212
C43×#18002
#1190643