Finite Group Databasebeta

← #25006233

Subgroups — #25006233

Order 11008.

494 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 83 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#19139562C211yesmaximal, characteristic
2#19132913C211yesmaximal, characteristic, complemented
3#19132528C212yesmaximal, complemented
4#19132526C212yesmaximal, complemented
5C43×#1465C211yesmaximal, characteristic, complemented
6C2×#13063321C411yescharacteristic
7C2×#13063313C411yescharacteristic
8C2×#13063312C411yescharacteristic
9C2×C22⋊(C43⋊C8)—21no—
10#14582815—21no—
11#14582815—21no—
12#14582804C2211yescharacteristic
13#14582800C2211yescharacteristic
14#14582778—21no—
15#14582778—21no—
16C4×C4⋊Dic43C411yescharacteristic
17#14582625C2212yes—
18#14582623—21no—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C22×Dic86C2×C411yescharacteristic
24C22×D172C2×C411yescharacteristic
25C22×C22⋊D43—21no—
26C22×C22⋊D43—21no—
27C22×C43⋊C8—41no—
28#13063321—42no—
29#13063313—41no—
30#13063313—41no—
31#13063312—42no—
32C2×C4⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×C4×Dic43C2×C411yescharacteristic
40C2×C4×Dic43C2×C411yescharacteristic
41C22⋊(C43⋊C8)—22no—
42C22⋊(C43⋊C8)—41no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C22×D4×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C2×M16×C43—41no—
50C4×D4×C43—41no—
51C4×D4×C43—41no—
52C2×C4⋊C4×C43C2311yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43D411yescharacteristic
55C2×C42×C43C2×C411yescharacteristic
56C22⋊C8×C43—22no—
57C22⋊C8×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C24×C43C22⋊C411yescharacteristic
60C23×D43—21no—
61C2×D4×C43—22no—
62C2×D4×C43—22no—
63C2×D4×C43—41no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—81no—
69C22×C4×C43—81no—
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C2×C22⋊D43—42no—
76C2×C22⋊D43—42no—
77C2×C22⋊D43—42no—
78C2×C22⋊D43—42no—
79C2×C22⋊D43—81no—
80C2×C22⋊D43—81no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C2×D172—22no—
85C2×D172—41no—
86C2×D172—41no—
87C2×Dic86—22no—
88C2×Dic86—41no—
89C2×Dic86—41no—
90M16×C43—82no—
91C2×C8×C43—42no—
92C4⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C42×C43—21no—
96C42×C43—21no—
97C22⋊Dic43—42no—
98C22⋊Dic43—42no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—81no—
103(C2×D43)⋊C4—81no—
104C4⋊Dic43—42no—
105C4×Dic43—41no—
106C4×Dic43—41no—
107C2×C43⋊C8—42no—
108C2×C43⋊C8—82no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43#10012yes—
119C23×C43C2×C22⋊C411yescharacteristic
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127D4×C43—44no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—81no—
140C2×C4×C43—81no—
141C2×C4×C43#9911yescharacteristic
142C2×C4×C43#9911yescharacteristic
143C2×C4×C43#13112yes—
144C22⋊D43—84no—
145C22⋊D43—84no—
146C2×Dic43—22no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155D172—82no—
156Dic86—82no—
157C8×C43—82no—
158C43⋊C8—82no—
159#11566—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—22no—
163C22×C43—42no—
164C22×C43—42no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—81no—
171C22×C43—81no—
172C22×C43#40811yescharacteristic
173C22×C43C2×#9911yescharacteristic
174C22×C43C2×#10011yescharacteristic
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C2×D43—81no—
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—22no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—41no—
188Dic43—42no—
189Dic43—81no—
190Dic43—81no—
191#2544—431no—
192#1465D4311yescharacteristic, complemented
193#1459—431no—
194#1319—432no—
195#1318—432no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43—42no—
199C2×C43—81no—
200C2×C43#147111yescharacteristic
201C2×C43#212711yescharacteristic
202C2×C43#213211yescharacteristic
203D43—161no—
204C2×#127—431no—
205C2×#124—431no—
206C2×#124—431no—
207C2×C4×D4C2×D4311yescharacteristic
208#407—21no—
209C2×C22⋊C8—861no—
210#394—861no—
211#394—861no—
212#391—431no—
213#390—431no—
214#386—861no—
215#386—861no—
216C4×C4⋊C4—431no—
217#324—432no—
218#324C2×D4312yes—
219#323—21no—
220#323—861no—
221C43#1156611yescharacteristic, complemented, Sylow
222C22×Q8—431no—
223C22×D4—431no—
224C22×D4—861no—
225C22×D4—861no—
226C22×D4C4×D4311yescharacteristic
227C23×C4D17211yescharacteristic
228C23×C4C22⋊D4311yescharacteristic
229C2×M16—41no—
230C22×C8—1721no—
231#127—1722no—
232#124—1721no—
233#124—1721no—
234#124—1722no—
235C4×D4—41no—
236C4×D4—41no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4C22×D4311yescharacteristic
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4D17211yescharacteristic
246C2×C22⋊C4C22⋊D4311yescharacteristic
247C2×C42—431no—
248C2×C42—431no—
249C2×C42C4×D4311yescharacteristic
250C22⋊C8—22no—
251C22⋊C8—41no—
252C22⋊C8—862no—
253C22⋊C8—1721no—
254#95—861no—
255#95—861no—
256#95—861no—
257C24—861no—
258C24(C2×D43)⋊C411yescharacteristic
259C24(C2×D43)⋊C411yescharacteristic
260C2×Q8—862no—
261C2×Q8—1721no—
262C2×Q8—1721no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—862no—
267C2×D4—3441no—
268C2×D4—3441no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1722no—
272C2×D4—1722no—
273C2×D4—1722no—
274C2×D4—1722no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4(C2×D43)⋊C411yescharacteristic
285C22×C4(C2×D43)⋊C411yescharacteristic
286C22×C4C2×C4×D4311yescharacteristic
287C22×C4C2×D17211yescharacteristic
288C22×C4C2×C22⋊D4311yescharacteristic
289M16—82no—
290C2×C8—42no—
291C2×C8—3442no—
292C2×C8—1722no—
293C4⋊C4—41no—
294C4⋊C4—1722no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—3441no—
298C22⋊C4—3441no—
299C22⋊C4—1722no—
300C22⋊C4—1722no—
301C22⋊C4—1722no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C42—21no—
305C42—21no—
306C42—1721no—
307C42—1721no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—1721no—
318C23—1721no—
319C23—1721no—
320C23—1721no—
321C23—1721no—
322C23—1721no—
323C23—1721no—
324C23#1306324112yes—
325C23C2×(C2×D43)⋊C411yescharacteristic
326Q8—3442no—
327D4—44no—
328D4—3442no—
329D4—3444no—
330D4—3444no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—862no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4#1306323911yescharacteristic
354C2×C4#1306323911yescharacteristic
355C2×C4#1306333312yes—
356C8—82no—
357C8—3442no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—81no—
370C22—3441no—
371C22—3441no—
372C22—3441no—
373C22—3441no—
374C22—3441no—
375C22—3441no—
376C22—3441no—
377C22#1458286711yescharacteristic
378C22C2×#1306323911yescharacteristic
379C22C2×#1306324111yescharacteristic
380C4—21no—
381C4—21no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—3441no—
387C4—3441no—
388C4—1722no—
389C2—21no—
390C2—21no—
391C2—42no—
392C2—81no—
393C2—6881no—
394C2#1913295611yescharacteristic
395C2#1913626211yescharacteristic
396C2#1913627811yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1465C2
socleC22×C43C2×#99
prime radicalC2×#13063321C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1465D43
hypocenterC43#11566
LCSG ▷ C22×C4×C43 ▷ C22×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
2. #19132913C2semidirect
3. #19132528C2semidirect
4. #19132526C2semidirect
5. C43×#1465C2semidirect
192. #1465D43semidirect
221. C43#11566semidirect

Maximal subgroups

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

subgroupindex
#191395622
#191329132
#191325282
#191325262
C43×#14652
#1156643