Finite Group Databasebeta

← #25005700

Subgroups — #25005700

Order 11008.

602 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 93 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#19137082C211yesmaximal, characteristic
2#19132908C212yesmaximal, complemented
3#19132528C212yesmaximal, complemented
4#19132527C211yesmaximal, characteristic, complemented
5C43×#1318C211yesmaximal, characteristic, complemented
6C22×#10621900C411yescharacteristic
7C2×#13063283C2211yescharacteristic
8C2×C42×D43C411yescharacteristic
9#14582949—22no—
10#14582805C411yescharacteristic
11#14582804C2211yescharacteristic
12#14582802C411yescharacteristic
13#14582775—22no—
14C22⋊C4×Dic43—22no—
15#14582625C2212yes—
16#14582622—22no—
17C43×#390C2211yescharacteristic
18C43×#324C2212yes—
19C2×#10621900—22no—
20C2×#10621900—41no—
21C2×#10621900—41no—
22C2×#10621900—42no—
23C2×#10621900C814yescomplemented
24C22×Dic86C2×C411yescharacteristic
25C22×C22⋊D43—21no—
26C23×Dic43—21no—
27C22×C4×D43—21no—
28C22×C4×D43C2×C411yescharacteristic
29#13063283—41no—
30#13063283—41no—
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×C22⋊Dic43—22no—
33C2×(C2×D43)⋊C4D412yes—
34C2×C4×Dic43—21no—
35C2×C4×Dic43C2×C411yescharacteristic
36C2×C4×Dic43D412yes—
37C42×D43—42no—
38Dic43⋊C8—42no—
39C22⋊(C43⋊C8)—22no—
40C8×Dic43—42no—
41C43⋊#95—22no—
42C43⋊#95—22no—
43C22×D4×C43C2×C411yescharacteristic
44C2×C4⋊C4×C43C2311yescharacteristic
45C2×C22⋊C4×C43—22no—
46C2×C42×C43C2×C411yescharacteristic
47C22⋊C8×C43—22no—
48C24×C43—21no—
49C23×D43C22⋊C411yescharacteristic
50C2×D4×C43—21no—
51C2×D4×C43—41no—
52C2×D4×C43—41no—
53C2×D4×C43C2×C812yes—
54C22×C4×C43—21no—
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D412yes—
57C2×C22⋊D43—24no—
58C2×C22⋊D43—42no—
59C2×C22⋊D43—42no—
60C22×Dic43—24no—
61C22×Dic43—21no—
62C22×Dic43—21no—
63C22×Dic43—41no—
64C22×Dic43—41no—
65C22×Dic43—42no—
66C22×Dic43C22⋊C412yes—
67C22×Dic43C22⋊C411yescharacteristic
68#10621900—44no—
69#10621900—44no—
70#10621900—44no—
71#10621900—44no—
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—22no—
75C2×C4×D43—42no—
76C2×C4×D43—42no—
77C2×C4×D43—42no—
78C2×C4×D43C2×C812yes—
79C2×C4×D43M1612yes—
80C2×Dic86—21no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×Dic86C2×C812yes—
84C2×C8×C43—42no—
85C4⋊C4×C43—41no—
86C22⋊C4×C43—44no—
87C42×C43—41no—
88C22⋊Dic43—44no—
89(C2×D43)⋊C4—42no—
90C4⋊Dic43—41no—
91C4×Dic43—22no—
92C4×Dic43—22no—
93C4×Dic43—42no—
94C4×Dic43—41no—
95C2×C43⋊C8—42no—
96C23×C43—22no—
97C23×C43—42no—
98C23×C43—42no—
99C23×C43—41no—
100C23×C43—41no—
101C23×C43C2×C22⋊C411yescharacteristic
102C22×D43—21no—
103C22×D43—21no—
104C22×D43—41no—
105C22×D43—41no—
106C22×D43C22⋊C812yes—
107D4×C43—42no—
108D4×C43—42no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—42no—
116C2×C4×C43C22×C811yescharacteristic
117C2×C4×C43C2×M1611yescharacteristic
118C22⋊D43—48no—
119C2×Dic43—22no—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—44no—
127C2×Dic43—44no—
128C2×Dic43—42no—
129C2×Dic43C22⋊C812yes—
130C2×Dic43#9911yescharacteristic
131C2×Dic43#9911yescharacteristic
132C2×Dic43#10012yes—
133C4×D43—22no—
134C4×D43—22no—
135C4×D43—22no—
136C4×D43—22no—
137C4×D43—48no—
138Dic86—42no—
139Dic86—42no—
140C8×C43—82no—
141C43⋊C8—82no—
142#11431—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—44no—
146C22×C43—42no—
147C22×C43—82no—
148C22×C43—81no—
149C22×C43—81no—
150C22×C43C2×C22⋊C811yescharacteristic
151C22×C43C2×#9911yescharacteristic
152C22×C43C2×#10011yescharacteristic
153C2×D43—22no—
154C2×D43—42no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—42no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—42no—
161C4×C43—42no—
162Dic43—42no—
163Dic43—42no—
164Dic43—42no—
165Dic43#32312yes—
166Dic43#32312yes—
167#2297—431no—
168#1458—432no—
169#1319—432no—
170#1318—431no—
171#1318D4311yescharacteristic, complemented
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—82no—
175C2×C43C2×#32311yescharacteristic
176C2×C43#212611yescharacteristic
177C2×C43#213211yescharacteristic
178D43—42no—
179C22×#41—431no—
180C2×#117—431no—
181C22×C42—431no—
182#431—862no—
183#391—431no—
184#391—431no—
185#390—431no—
186#390C2×D4311yescharacteristic
187#386—862no—
188C4×C22⋊C4—862no—
189#324—432no—
190#324C2×D4312yes—
191#323—862no—
192C43#1143111yescharacteristic, complemented, Sylow
193C2×#41—434no—
194C2×#41—862no—
195C2×#41—1722no—
196C2×#41—1721no—
197C2×#41—1721no—
198C22×Q8—431no—
199C22×D4—861no—
200C22×D4C4×D4311yescharacteristic
201C23×C4—431no—
202C23×C4—861no—
203C23×C4—861no—
204#117—1721no—
205#117—1721no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4C22×D4311yescharacteristic
208C2×C22⋊C4—22no—
209C2×C22⋊C4—432no—
210C2×C22⋊C4—862no—
211C2×C42—432no—
212C2×C42—431no—
213C2×C42—861no—
214C2×C42—1722no—
215C2×C42C4×D4311yescharacteristic
216C4⋊C8—1722no—
217C22⋊C8—22no—
218C22⋊C8—862no—
219C4×C8—1722no—
220#95—862no—
221#95—862no—
222C24—21no—
223C24—431no—
224#41—1724no—
225#41—1724no—
226#41—1724no—
227#41—1724no—
228C2×Q8—432no—
229C2×Q8—861no—
230C2×Q8—1721no—
231C2×Q8—1721no—
232C2×D4—21no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4—864no—
236C2×D4—1722no—
237C2×D4—1722no—
238C2×D4C8×D4312yes—
239C22×C4—21no—
240C22×C4—431no—
241C22×C4—432no—
242C22×C4—432no—
243C22×C4—432no—
244C22×C4—862no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—864no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—1722no—
251C22×C4—1722no—
252C22×C4—1722no—
253C22×C4—1721no—
254C22×C4—1721no—
255C22×C4—1722no—
256C22×C4C2×C4×D4311yescharacteristic
257C22×C4D4×D4312yes—
258C2×C8—42no—
259C2×C8—1722no—
260C4⋊C4—41no—
261C4⋊C4—1721no—
262C22⋊C4—44no—
263C22⋊C4—1722no—
264C22⋊C4—1724no—
265C42—41no—
266C42—862no—
267C42—862no—
268C42—1721no—
269C42—1722no—
270C23—22no—
271C23—42no—
272C23—42no—
273C23—41no—
274C23—41no—
275C23—432no—
276C23—861no—
277C23—861no—
278C23—1721no—
279C23—1721no—
280C23C22⋊C4×D4311yescharacteristic
281Q8—1722no—
282Q8—1722no—
283D4—42no—
284D4—42no—
285D4—1728no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—432no—
294C2×C4—431no—
295C2×C4—431no—
296C2×C4—432no—
297C2×C4—862no—
298C2×C4—862no—
299C2×C4—862no—
300C2×C4—862no—
301C2×C4—862no—
302C2×C4—862no—
303C2×C4—862no—
304C2×C4—1728no—
305C2×C4—1724no—
306C2×C4—1724no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1722no—
312C2×C4C2×C8×D4311yescharacteristic
313C2×C4M16×D4311yescharacteristic
314C8—82no—
315C8—3442no—
316C22—21no—
317C22—21no—
318C22—44no—
319C22—42no—
320C22—82no—
321C22—81no—
322C22—81no—
323C22—862no—
324C22—1722no—
325C22—1722no—
326C22—1721no—
327C22—1721no—
328C22C22⋊C8×D4311yescharacteristic
329C22#99×D4311yescharacteristic
330C22#100×D4311yescharacteristic
331C4—21no—
332C4—21no—
333C4—42no—
334C4—42no—
335C4—432no—
336C4—432no—
337C4—1722no—
338C4—1722no—
339C4—1722no—
340C2—21no—
341C2—21no—
342C2—82no—
343C2—1722no—
344C2#323×D4311yescharacteristic
345C2#1913625711yescharacteristic
346C2#1913627711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1318C2
socleC22×C43C2×#99
prime radicalC22×#10621900C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1318D43
hypocenterC43#11431
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #19132908C2semidirect
3. #19132528C2semidirect
4. #19132527C2semidirect
5. C43×#1318C2semidirect
23. C2×#10621900C8semidirect
171. #1318D43semidirect
192. C43#11431semidirect

Maximal subgroups

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

subgroupindex
#191370822
#191329082
#191325282
#191325272
C43×#13182
#1143143