Finite Group Databasebeta

← #25006232

Subgroups — #25006232

Order 11008.

494 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 91 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#19132933C211yesmaximal, characteristic, complemented
2#19132913C211yesmaximal, characteristic, complemented
3#19132529C212yesmaximal, complemented
4#19132527C212yesmaximal, complemented
5C43×#2544C211yesmaximal, characteristic
6#14582863—21no—
7C2×C22⋊(C43⋊C8)—21no—
8#14582625C2212yes—
9#14582625C2212yes—
10#14582623—21no—
11#14582623—21no—
12C2×#127×C43C411yescharacteristic
13C2×#124×C43C411yescharacteristic
14C2×#124×C43C411yescharacteristic
15C2×C4×D4×C43C2211yescharacteristic
16C43×#394—21no—
17C43×#394—21no—
18C43×#391C2211yescharacteristic
19C43×#390C2211yescharacteristic
20C43×#386—21no—
21C43×#386—21no—
22C4×C4⋊C4×C43C411yescharacteristic
23C2×#10621877—41no—
24C22×C43⋊C8—41no—
25C22⋊(C43⋊C8)—22no—
26C22⋊(C43⋊C8)—22no—
27C22⋊(C43⋊C8)—41no—
28C22⋊(C43⋊C8)—41no—
29C22×Q8×C43C2×C411yescharacteristic
30C22×D4×C43—21no—
31C22×D4×C43—21no—
32C22×D4×C43C2×C411yescharacteristic
33C22×D4×C43C2×C411yescharacteristic
34C23×C4×C43D411yescharacteristic
35C23×C4×C43D411yescharacteristic
36#127×C43—42no—
37#124×C43—41no—
38#124×C43—41no—
39#124×C43—42no—
40C4×D4×C43—41no—
41C4×D4×C43—41no—
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43C2311yescharacteristic
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C42×C43C2×C411yescharacteristic
53C2×C42×C43C2×C411yescharacteristic
54C2×C42×C43C2×C411yescharacteristic
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58C24×C43—21no—
59C24×C43C22⋊C411yescharacteristic
60C24×C43C22⋊C411yescharacteristic
61C2×Q8×C43—22no—
62C2×Q8×C43—41no—
63C2×Q8×C43—41no—
64C2×D4×C43—22no—
65C2×D4×C43—22no—
66C2×D4×C43—22no—
67C2×D4×C43—41no—
68C2×D4×C43—42no—
69C2×D4×C43—42no—
70C2×D4×C43—42no—
71C2×D4×C43—42no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—81no—
75C2×D4×C43—81no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—81no—
84C22×C4×C43—81no—
85C22×C4×C43C22⋊C411yescharacteristic
86C22×C4×C43C22⋊C411yescharacteristic
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C4⋊C4×C43—41no—
91C4⋊C4×C43—42no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—42no—
95C22⋊C4×C43—42no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—42no—
99C22⋊C4×C43—81no—
100C22⋊C4×C43—81no—
101C42×C43—21no—
102C42×C43—21no—
103C42×C43—41no—
104C42×C43—41no—
105#10621877—82no—
106C2×C43⋊C8—42no—
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—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43#10012yes—
126C23×C43C2×C22⋊C411yescharacteristic
127Q8×C43—82no—
128D4×C43—44no—
129D4×C43—82no—
130D4×C43—84no—
131D4×C43—84no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—22no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43#9911yescharacteristic
155C2×C4×C43#9911yescharacteristic
156C2×C4×C43#13112yes—
157C43⋊C8—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—81no—
173C22×C43—81no—
174C22×C43—81no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43#40811yescharacteristic
180C22×C43C2×#9911yescharacteristic
181C22×C43C2×#10011yescharacteristic
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—22no—
185C4×C43—42no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—81no—
190C4×C43—81no—
191#2544D4311yescharacteristic
192#1465—431no—
193#1459—431no—
194#1319—432no—
195#1318—432no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43—42no—
199C2×C43—81no—
200C2×C43—161no—
201C2×C43#147111yescharacteristic
202C2×C43#212711yescharacteristic
203C2×C43#213211yescharacteristic
204C2×#127Dic4311yescharacteristic
205C2×#124Dic4311yescharacteristic
206C2×#124Dic4311yescharacteristic
207C2×C4×D4C2×D4311yescharacteristic
208#407—861no—
209C2×C22⋊C8—861no—
210#394—21no—
211#394—21no—
212#391C2×D4311yescharacteristic
213#390C2×D4311yescharacteristic
214#386—21no—
215#386—21no—
216C4×C4⋊C4Dic4311yescharacteristic
217#324—432no—
218#324—432no—
219#323—861no—
220#323—861no—
221C43#1156611yescharacteristic, complemented, Sylow
222C22×Q8C2×Dic4311yescharacteristic
223C22×D4—21no—
224C22×D4—21no—
225C22×D4C2×Dic4311yescharacteristic
226C22×D4C2×Dic4311yescharacteristic
227C23×C4C22⋊D4311yescharacteristic
228C23×C4C22⋊D4311yescharacteristic
229C2×M16—1721no—
230C22×C8—1721no—
231#127—42no—
232#124—41no—
233#124—41no—
234#124—42no—
235C4×D4—41no—
236C4×D4—41no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C22×D4311yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4C22⋊D4311yescharacteristic
246C2×C22⋊C4C22⋊D4311yescharacteristic
247C2×C42C2×Dic4311yescharacteristic
248C2×C42C2×Dic4311yescharacteristic
249C2×C42C2×Dic4311yescharacteristic
250C22⋊C8—862no—
251C22⋊C8—862no—
252C22⋊C8—1721no—
253C22⋊C8—1721no—
254#95—21no—
255#95—21no—
256#95—21no—
257C24—21no—
258C24C22⋊Dic4311yescharacteristic
259C24C22⋊Dic4311yescharacteristic
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—81no—
274C2×D4—81no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—81no—
283C22×C4—81no—
284C22×C4C22⋊Dic4311yescharacteristic
285C22×C4C22⋊Dic4311yescharacteristic
286C22×C4C22×Dic4311yescharacteristic
287C22×C4C2×C22⋊D4311yescharacteristic
288C22×C4C2×C22⋊D4311yescharacteristic
289M16—3442no—
290C2×C8—3442no—
291C2×C8—1722no—
292C2×C8—1722no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C42—21no—
305C42—21no—
306C42—41no—
307C42—41no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23#1306324212yes—
325C23C2×C22⋊Dic4311yescharacteristic
326Q8—82no—
327D4—44no—
328D4—82no—
329D4—84no—
330D4—84no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4#1306324011yescharacteristic
354C2×C4#1306324011yescharacteristic
355C2×C4#1306333212yes—
356C8—3442no—
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—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22#1458286611yescharacteristic
378C22C2×#1306324011yescharacteristic
379C22C2×#1306324211yescharacteristic
380C4—21no—
381C4—21no—
382C4—22no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—81no—
388C4—81no—
389C2—21no—
390C2—21no—
391C2—42no—
392C2—81no—
393C2—161no—
394C2#1913295511yescharacteristic
395C2#1913626411yescharacteristic
396C2#1913628011yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2544C2
socleC22×C43C2×#99
prime radicalC2×#127×C43C4
cosocleC2×C4⋊C4×C43C23
hypercenter#2544D43
hypocenterC43#11566
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2544

Complements

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

NH ≅ G/Ntype
1. #19132933C2semidirect
2. #19132913C2semidirect
3. #19132529C2semidirect
4. #19132527C2semidirect
221. C43#11566semidirect

Maximal subgroups

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

subgroupindex
#191329332
#191329132
#191325292
#191325272
C43×#25442
#1156643