Finite Group Databasebeta

← #25007643

Subgroups — #25007643

Order 11008.

764 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 107 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#19134587C211yesmaximal, characteristic, complemented
2#19132913C211yesmaximal, characteristic, complemented
3#19132598C214yesmaximal, complemented
4C43×#2408C211yesmaximal, characteristic
5#14582923—21no—
6C2×#13063242—21no—
7C2×C22⋊(C43⋊C8)—21no—
8#14582668C2212yescomplemented
9#14582625C2212yescomplemented
10#14582623—21no—
11C23×D4×C43C411yescharacteristic
12C2×#121×C43—21no—
13C2×#120×C43—21no—
14C2×C4×D4×C43C2211yescharacteristic
15C43×#394C2212yes—
16C43×#392C412yes—
17C43×#390—21no—
18C43×#380C411yescharacteristic
19C43×#379—21no—
20C2×#10621877—22no—
21C22×C43⋊C8—41no—
22C4⋊(C43⋊C8)—41no—
23C4⋊(C43⋊C8)—41no—
24#13063242—42no—
25C22⋊(C43⋊C8)—22no—
26C22⋊(C43⋊C8)—41no—
27C25×C43—21no—
28C22×D4×C43—22no—
29C22×D4×C43—21no—
30C22×D4×C43—41no—
31C22×D4×C43—41no—
32C22×D4×C43—44no—
33C22×D4×C43C2×C412yes—
34C22×D4×C43D411yescharacteristic
35C23×C4×C43C2×C411yescharacteristic
36C23×C4×C43D411yescharacteristic
37#121×C43—44no—
38#120×C43—42no—
39#120×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—22no—
46C2×C22⋊C4×C43—22no—
47C2×C22⋊C4×C43—22no—
48C2×C22⋊C4×C43C2×C411yescharacteristic
49C2×C22⋊C4×C43D411yescharacteristic
50C2×C42×C43D411yescharacteristic
51#95×C43C2×C412yes—
52C24×C43—22no—
53C24×C43—42no—
54C24×C43—44no—
55C24×C43—42no—
56C24×C43—42no—
57C24×C43—82no—
58C24×C43C22⋊C411yescharacteristic
59C24×C43C22⋊C411yescharacteristic
60C2×D4×C43—24no—
61C2×D4×C43—41no—
62C2×D4×C43—41no—
63C2×D4×C43—44no—
64C2×D4×C43—44no—
65C2×D4×C43—42no—
66C2×D4×C43—44no—
67C2×D4×C43—48no—
68C2×D4×C43—44no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—44no—
72C2×D4×C43—42no—
73C2×D4×C43—82no—
74C2×D4×C43D812yes—
75C2×D4×C43SD1612yes—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—22no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C22⋊C411yescharacteristic
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C4⋊C4×C43—41no—
89C4⋊C4×C43—42no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—44no—
93C22⋊C4×C43—42no—
94C22⋊C4×C43—42no—
95C22⋊C4×C43—42no—
96C22⋊C4×C43—82no—
97C42×C43—21no—
98C42×C43—21no—
99#10621877—42no—
100#10621877—42no—
101C2×C43⋊C8—42no—
102C2×C43⋊C8—42no—
103C2×C43⋊C8—82no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—24no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—42no—
116C23×C43—48no—
117C23×C43—42no—
118C23×C43—42no—
119C23×C43—42no—
120C23×C43—84no—
121C23×C43—88no—
122C23×C43—88no—
123C23×C43—84no—
124C23×C43#10212yes—
125C23×C43#10212yes—
126C23×C43C2×C22⋊C411yescharacteristic
127D4×C43—42no—
128D4×C43—42no—
129D4×C43—44no—
130D4×C43—44no—
131D4×C43—44no—
132D4×C43—44no—
133D4×C43—88no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—22no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—81no—
150C2×C4×C43#9911yescharacteristic
151C2×C4×C43#9911yescharacteristic
152C2×C4×C43C2×D811yescharacteristic
153C2×C4×C43C2×SD1611yescharacteristic
154C43⋊C8—82no—
155C43⋊C8—82no—
156#11880—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—22no—
160C22×C43—22no—
161C22×C43—42no—
162C22×C43—42no—
163C22×C43—42no—
164C22×C43—44no—
165C22×C43—44no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—44no—
171C22×C43—81no—
172C22×C43—82no—
173C22×C43—82no—
174C22×C43—816no—
175C22×C43—82no—
176C22×C43—82no—
177C22×C43C2×#9911yescharacteristic
178C22×C43C2×#10211yescharacteristic
179C22×C43#42111yescharacteristic
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—82no—
187C4×C43AΣL(1,𝔽16)12yes—
188#2408D4311yescharacteristic
189#1800—431no—
190#1459—431no—
191#1345—434no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—42no—
195C2×C43—42no—
196C2×C43—84no—
197C2×C43#151911yescharacteristic
198C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
199C2×C43#213411yescharacteristic
200C23×D4Dic4311yescharacteristic
201C2×#121—21no—
202C2×#120—21no—
203C2×C4×D4C2×D4311yescharacteristic
204#423—861no—
205C2×#100—861no—
206C2×C22⋊C8—861no—
207#394C2×D4312yes—
208#392Dic4312yes—
209#390—21no—
210#380Dic4311yescharacteristic
211#379—21no—
212#343—432no—
213#324—432no—
214#323—861no—
215C43#1188011yescharacteristic, complemented, Sylow
216C25—21no—
217C22×D4—22no—
218C22×D4—21no—
219C22×D4—41no—
220C22×D4—41no—
221C22×D4—44no—
222C22×D4C2×Dic4312yes—
223C22×D4C22⋊D4311yescharacteristic
224C23×C4C2×Dic4311yescharacteristic
225C23×C4C22⋊D4311yescharacteristic
226C2×M16—862no—
227C22×C8—1721no—
228#121—44no—
229#120—42no—
230#120—42no—
231C4×D4—41no—
232C4×D4—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C22×D4311yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4C2×Dic4311yescharacteristic
240C2×C22⋊C4C22⋊D4311yescharacteristic
241C2×C42C22⋊D4311yescharacteristic
242C4⋊C8—1721no—
243C4⋊C8—1721no—
244#100—1722no—
245C22⋊C8—862no—
246C22⋊C8—1721no—
247#95C2×Dic4312yes—
248C24—22no—
249C24—42no—
250C24—44no—
251C24—42no—
252C24—42no—
253C24—82no—
254C24C22⋊Dic4311yescharacteristic
255C24C22⋊Dic4311yescharacteristic
256C2×D4—24no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—48no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4—44no—
265C2×D4—44no—
266C2×D4—44no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—82no—
270C2×D4#1062188212yes—
271C2×D4#1062188312yes—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4C22⋊Dic4311yescharacteristic
280C22×C4C22⋊Dic4311yescharacteristic
281C22×C4C22×Dic4311yescharacteristic
282C22×C4C2×C22⋊D4311yescharacteristic
283C22×C4C2×C22⋊D4311yescharacteristic
284M16—1722no—
285M16—1722no—
286C2×C8—3442no—
287C2×C8—1722no—
288C2×C8—1722no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—44no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—82no—
298C42—21no—
299C42—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—24no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—48no—
313C23—42no—
314C23—42no—
315C23—42no—
316C23—84no—
317C23—88no—
318C23—88no—
319C23—84no—
320C23#1306324612yes—
321C23#1306324612yes—
322C23C2×C22⋊Dic4311yescharacteristic
323D4—42no—
324D4—42no—
325D4—44no—
326D4—44no—
327D4—44no—
328D4—44no—
329D4—88no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4#1306324011yescharacteristic
347C2×C4#1306324011yescharacteristic
348C2×C4C2×#1062188211yescharacteristic
349C2×C4C2×#1062188311yescharacteristic
350C8—3442no—
351C8—3442no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—44no—
360C22—44no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—44no—
366C22—81no—
367C22—82no—
368C22—82no—
369C22—816no—
370C22—82no—
371C22—82no—
372C22C2×#1306324011yescharacteristic
373C22C2×#1306324611yescharacteristic
374C22#1458291611yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—82no—
382C4#1458268612yes—
383C2—21no—
384C2—21no—
385C2—42no—
386C2—42no—
387C2—84no—
388C2#1913316311yescharacteristic
389C2C2×#1458268611yescharacteristic
390C2#1913628711yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
Fitting, prime radicalC43×#2408C2
socleC22×C43C2×#99
cosocleC2×C4⋊C4×C43C23
hypercenter#2408D43
hypocenterC43#11880
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. #19134587C2semidirect
2. #19132913C2semidirect
3. #19132598C2semidirect
8. #14582668C22semidirect
9. #14582625C22semidirect
215. C43#11880semidirect

Maximal subgroups

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

subgroupindex
#191345872
#191329132
#191325982
C43×#24082
#1188043