Finite Group Databasebeta

← #24988725

Subgroups — #24988725

Order 11008.

1330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 147 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#19134516C211yesmaximal, characteristic, complemented
2#19133099C214yesmaximal, complemented
3#19132836C211yesmaximal, characteristic, complemented
4C43×#3484C211yesmaximal, characteristic
5C22×C22⋊Dic43—22no—
6C2×#13063242—22no—
7#14582863C2212yescomplemented
8C2×C43⋊#95C2212yescomplemented
9#14582636—24no—
10#14582633—24no—
11C2×H(5,𝔽2)×C43C411yescharacteristic, complemented
12C23×D4×C43C2211yescharacteristic
13C43×#546—24no—
14D42×C43—24no—
15C43×#535C412yescomplemented
16C43×#534—22no—
17C43×#525C2212yes—
18C2×#120×C43—22no—
19C43×#518C411yescharacteristic, complemented
20C23×Dic43—22no—
21C2×#10621877—22no—
22C2×C22⋊Dic43—48no—
23C2×C22⋊Dic43—44no—
24#13063242—44no—
25C22⋊(C43⋊C8)—24no—
26C43⋊#95—24no—
27C25×C43D412yes—
28H(5,𝔽2)×C43—44no—
29C2×#41×C43—22no—
30C2×#41×C43C2×C412yes—
31C22×D4×C43—22no—
32C22×D4×C43—24no—
33C22×D4×C43—22no—
34C22×D4×C43—24no—
35C22×D4×C43—44no—
36C22×D4×C43C2×C411yescharacteristic
37C22×D4×C43C2×C411yescharacteristic
38C22×D4×C43D412yes—
39C23×C4×C43C2311yescharacteristic
40#127×C43—22no—
41#124×C43—22no—
42#123×C43—24no—
43#123×C43—22no—
44C22⋊Q8×C43D414yes—
45#121×C43—28no—
46#121×C43—24no—
47#121×C43D414yes—
48#120×C43—28no—
49#120×C43—24no—
50#120×C43—24no—
51#120×C43—22no—
52C4×D4×C43—24no—
53C4×D4×C43—24no—
54#117×C43C2×C412yes—
55C2×C22⋊C4×C43—24no—
56C2×C22⋊C4×C43—22no—
57C24×C43—22no—
58C24×C43—24no—
59C24×C43—24no—
60C24×C43—42no—
61C24×C43—44no—
62C24×C43—44no—
63C24×C43C22⋊C412yes—
64C24×C43C22⋊C412yes—
65C24×C43C2×D411yescharacteristic
66#41×C43—44no—
67#41×C43—48no—
68C2×Q8×C43C22⋊C412yescomplemented
69C2×D4×C43—24no—
70C2×D4×C43—28no—
71C2×D4×C43—22no—
72C2×D4×C43—22no—
73C2×D4×C43—24no—
74C2×D4×C43—24no—
75C2×D4×C43—24no—
76C2×D4×C43—22no—
77C2×D4×C43—24no—
78C2×D4×C43—42no—
79C2×D4×C43—42no—
80C2×D4×C43—44no—
81C2×D4×C43—416no—
82C2×D4×C43—48no—
83C2×D4×C43—44no—
84C2×D4×C43—84no—
85C2×D4×C43—84no—
86C2×D4×C43C22⋊C412yescomplemented
87C22×C4×C43—22no—
88C22×C4×C43—24no—
89C22×C4×C43—22no—
90C22×C4×C43—42no—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D414yes—
94C22×Dic43—24no—
95C22×Dic43—44no—
96C22×Dic43—44no—
97C22×Dic43—42no—
98C22×Dic43—42no—
99C4⋊C4×C43—24no—
100C4⋊C4×C43C22⋊C414yescomplemented
101C22⋊C4×C43—24no—
102C22⋊C4×C43—28no—
103C22⋊C4×C43—24no—
104C22⋊C4×C43—22no—
105C22⋊C4×C43—24no—
106C42×C43—22no—
107C22⋊Dic43—416no—
108#10621877—44no—
109C2×C43⋊C8—42no—
110C23×C43—22no—
111C23×C43—22no—
112C23×C43—22no—
113C23×C43—22no—
114C23×C43—22no—
115C23×C43—22no—
116C23×C43—22no—
117C23×C43—22no—
118C23×C43—22no—
119C23×C43—48no—
120C23×C43—44no—
121C23×C43—44no—
122C23×C43—44no—
123C23×C43—44no—
124C23×C43—48no—
125C23×C43—44no—
126C23×C43—44no—
127C23×C43—44no—
128C23×C43—84no—
129C23×C43—82no—
130C23×C43—82no—
131C23×C43—84no—
132C23×C43—84no—
133C23×C43#9914yes—
134C23×C43C2×C22⋊C411yescharacteristic
135C23×C43#12012yes—
136Q8×C43—42no—
137D4×C43—28no—
138D4×C43—48no—
139D4×C43—42no—
140D4×C43—44no—
141D4×C43—48no—
142D4×C43—44no—
143D4×C43—44no—
144D4×C43—44no—
145D4×C43—88no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—24no—
149C2×C4×C43—22no—
150C2×C4×C43—44no—
151C2×C4×C43—44no—
152C2×C4×C43—44no—
153C2×C4×C43—84no—
154C2×C4×C43C2×C22⋊C412yes—
155C2×C4×C43#12012yes—
156C2×Dic43—48no—
157C2×Dic43—44no—
158C2×Dic43—84no—
159C2×Dic43—82no—
160C2×Dic43—82no—
161C43⋊C8—82no—
162#8453—431nomaximal, Sylow
163C22×C43—22no—
164C22×C43—22no—
165C22×C43—24no—
166C22×C43—22no—
167C22×C43—22no—
168C22×C43—22no—
169C22×C43—24no—
170C22×C43—44no—
171C22×C43—44no—
172C22×C43—44no—
173C22×C43—44no—
174C22×C43—44no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43—82no—
178C22×C43—88no—
179C22×C43—88no—
180C22×C43—82no—
181C22×C43—164no—
182C22×C43#37911yescharacteristic
183C22×C43C2×#9912yes—
184C22×C43#45312yes—
185C22×C43#45512yes—
186C4×C43—22no—
187C4×C43—22no—
188C4×C43—44no—
189C4×C43—42no—
190Dic43—84no—
191#3484D4311yescharacteristic
192#1783—431no—
193#1504—434no—
194#1438—431no—
195C2×C43—22no—
196C2×C43—22no—
197C2×C43—22no—
198C2×C43—44no—
199C2×C43—82no—
200C2×C43—82no—
201C2×C43#178111yescharacteristic
202C2×C43#179212yes—
203C2×H(5,𝔽2)Dic4311yescharacteristic, complemented
204C23×D4C2×D4311yescharacteristic
205#546—24no—
206D42—24no—
207#535Dic4312yescomplemented
208#534—22no—
209#525C2×D4312yes—
210C2×#120—22no—
211#518Dic4311yescharacteristic, complemented
212C22×C22⋊C4—862no—
213C2×#100—862no—
214#407—432no—
215C2×#95—432no—
216#328—864no—
217#327—864no—
218C43#845311yescharacteristic, complemented, Sylow
219C25C22⋊D4312yes—
220H(5,𝔽2)—44no—
221C2×#41—22no—
222C2×#41C2×Dic4312yes—
223C22×D4—22no—
224C22×D4—24no—
225C22×D4—22no—
226C22×D4—24no—
227C22×D4—44no—
228C22×D4C2×Dic4311yescharacteristic
229C22×D4C2×Dic4311yescharacteristic
230C22×D4C22⋊D4312yes—
231C23×C4—862no—
232C23×C4C22×D4311yescharacteristic
233C2×M16—862no—
234#127—22no—
235#124—22no—
236#123—24no—
237#123—22no—
238C22⋊Q8C22⋊D4314yes—
239#121—28no—
240#121—24no—
241#121C22⋊D4314yes—
242#120—28no—
243#120—24no—
244#120—24no—
245#120—22no—
246C4×D4—24no—
247C4×D4—24no—
248#117C2×Dic4312yes—
249C2×C22⋊C4—24no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—1728no—
252C2×C22⋊C4—1724no—
253#100—1724no—
254C22⋊C8—864no—
255#95—864no—
256C24—22no—
257C24—24no—
258C24—24no—
259C24—42no—
260C24—44no—
261C24—44no—
262C24C22⋊Dic4312yes—
263C24C22⋊Dic4312yes—
264C24C2×C22⋊D4311yescharacteristic
265#41—44no—
266#41—48no—
267C2×Q8C22⋊Dic4312yescomplemented
268C2×D4—24no—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—22no—
272C2×D4—24no—
273C2×D4—28no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—24no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—416no—
280C2×D4—48no—
281C2×D4—44no—
282C2×D4—44no—
283C2×D4—84no—
284C2×D4—84no—
285C2×D4C22⋊Dic4312yescomplemented
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—42no—
290C22×C4—864no—
291C22×C4—1724no—
292C22×C4—1724no—
293C22×C4—1722no—
294C22×C4—1722no—
295C22×C4C22×Dic4311yescharacteristic
296C22×C4C2×C22⋊D4311yescharacteristic
297C22×C4C2×C22⋊D4314yes—
298M16—1724no—
299C2×C8—1722no—
300C4⋊C4—24no—
301C4⋊C4C22⋊Dic4314yescomplemented
302C22⋊C4—24no—
303C22⋊C4—28no—
304C22⋊C4—22no—
305C22⋊C4—24no—
306C22⋊C4—24no—
307C22⋊C4—17216no—
308C42—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—48no—
319C23—44no—
320C23—44no—
321C23—44no—
322C23—48no—
323C23—44no—
324C23—44no—
325C23—44no—
326C23—44no—
327C23—84no—
328C23—84no—
329C23—82no—
330C23—82no—
331C23—84no—
332C23#1306324014yes—
333C23C2×C22⋊Dic4311yescharacteristic
334C23#1306329412yes—
335Q8—42no—
336D4—28no—
337D4—48no—
338D4—42no—
339D4—44no—
340D4—48no—
341D4—44no—
342D4—44no—
343D4—44no—
344D4—88no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—22no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—84no—
353C2×C4—3444no—
354C2×C4—3442no—
355C2×C4—3442no—
356C2×C4—1728no—
357C2×C4—1724no—
358C2×C4C2×C22⋊Dic4312yes—
359C2×C4#1306329412yes—
360C8—3442no—
361C22—24no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—24no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—42no—
372C22—42no—
373C22—44no—
374C22—44no—
375C22—82no—
376C22—88no—
377C22—88no—
378C22—82no—
379C22—164no—
380C22#1458275511yescharacteristic
381C22C2×#1306324012yes—
382C22#1458306712yes—
383C22#1458307712yes—
384C4—22no—
385C4—22no—
386C4—42no—
387C4—44no—
388C4—3444no—
389C2—22no—
390C2—22no—
391C2—22no—
392C2—44no—
393C2—82no—
394C2—82no—
395C2#1913451011yescharacteristic
396C2#1913454912yes—
subgroupG/H
centerC22#14582755
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#3484C2
socleC22×C43#379
cosocleC23×C4×C43C23
hypercenter#3484D43
hypocenterC43#8453
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3484

Complements

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

NH ≅ G/Ntype
1. #19134516C2semidirect
2. #19133099C2semidirect
3. #19132836C2semidirect
7. #14582863C22semidirect
8. C2×C43⋊#95C22semidirect
11. C2×H(5,𝔽2)×C43C4semidirect
15. C43×#535C4semidirect
19. C43×#518C4semidirect
68. C2×Q8×C43C22⋊C4semidirect
86. C2×D4×C43C22⋊C4semidirect
100. C4⋊C4×C43C22⋊C4semidirect
203. C2×H(5,𝔽2)Dic43semidirect
207. #535Dic43semidirect
211. #518Dic43semidirect
218. C43#8453semidirect
267. C2×Q8C22⋊Dic43semidirect
285. C2×D4C22⋊Dic43semidirect
301. C4⋊C4C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
#191345162
#191330992
#191328362
C43×#34842
#845343