Finite Group Databasebeta

← #25006016

Subgroups — #25006016

Order 11008.

446 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 77 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#19137074C211yesmaximal, characteristic
2#19132926C211yesmaximal, characteristic
3#19132926C211yesmaximal, characteristic
4#19132544C211yesmaximal, characteristic
5#19132543C211yesmaximal, characteristic
6#19132542C211yesmaximal, characteristic
7C43×#1326C211yesmaximal, characteristic
8C2×#13063281C411yescharacteristic
9C2×#13063281C2211yescharacteristic
10C22×C4×Dic43C411yescharacteristic
11#14582953—21no—
12#14582953—21no—
13#14582796—21no—
14#14582794—21no—
15#14582774C411yescharacteristic
16#14582772C411yescharacteristic
17#14582771C2211yescharacteristic
18C4⋊C4×Dic43—21no—
19#14582750—21no—
20#14582624—21no—
21#14582624—21no—
22#14582623C2211yescharacteristic
23#14582623C2211yescharacteristic
24C43×#385C2211yescharacteristic
25C43×#323C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C23×Dic43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29#13063281—22no—
30#13063281—22no—
31#13063281—41no—
32#13063281—41no—
33C2×C4⋊Dic43—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4D411yescharacteristic
38C2×Dic43⋊C4D411yescharacteristic
39C2×C22⋊Dic43C2×C411yescharacteristic
40C2×C22⋊Dic43C2×C411yescharacteristic
41C2×C4×Dic43—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43—41no—
45C2×C4×Dic43—41no—
46C2×C4×Dic43D411yescharacteristic
47C2×C4×Dic43D411yescharacteristic
48Dic43⋊C8—41no—
49Dic43⋊C8—41no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52#13063235—41no—
53#13063235—41no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C23×C4×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43—21no—
59C2×C22⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62C22⋊C8×C43—21no—
63#95×C43—21no—
64C24×C43C22×C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43—42no—
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—22no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—41no—
79C22×Dic43—42no—
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C4⋊C4×C43—42no—
87C22⋊C4×C43—21no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43M1612yes—
90C22⋊Dic43—21no—
91C22⋊Dic43—41no—
92C22⋊Dic43M1612yes—
93C4⋊Dic43—42no—
94Dic43⋊C4—24no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—42no—
98Dic43⋊C4—42no—
99C4×Dic43—24no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—42no—
105C4×Dic43—41no—
106C4×Dic43—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43C2×C22⋊C411yescharacteristic
114C23×C43C2×M1611yescharacteristic
115C23×C43C2×M1611yescharacteristic
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—42no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—22no—
131C2×Dic43—22no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—42no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—42no—
148C2×Dic43#9911yescharacteristic
149C2×Dic43#9911yescharacteristic
150C2×Dic43#10112yes—
151C8×C43—81no—
152C8×C43—81no—
153C43⋊C8—81no—
154C43⋊C8—81no—
155#11518—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—42no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43#40711yescharacteristic
166C22×C43C2×#9911yescharacteristic
167C22×C43C2×#10111yescharacteristic
168C4×C43—42no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—42no—
172Dic43—21no—
173Dic43—21no—
174Dic43—22no—
175Dic43—42no—
176Dic43—41no—
177Dic43—41no—
178Dic43—42no—
179#2296—431no—
180#1464—431no—
181#1464—431no—
182#1326—431no—
183#1326—431no—
184#1326—431no—
185#1326D4311yescharacteristic
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—41no—
189C2×C43—41no—
190C2×C43#146311yescharacteristic
191C2×C43#212011yescharacteristic
192C2×C43#212011yescharacteristic
193C2×#117—431no—
194C2×#117—431no—
195C22×C42—431no—
196#432—861no—
197#432—861no—
198#389—861no—
199#389—861no—
200#385—431no—
201#385—431no—
202#385—431no—
203#385C2×D4311yescharacteristic
204C4×C4⋊C4—861no—
205C4×C4⋊C4—861no—
206#324—861no—
207#324—861no—
208#323—431no—
209#323—431no—
210#323C2×D4311yescharacteristic
211#323C2×D4311yescharacteristic
212C43#1151811yescharacteristic, complemented, Sylow
213C23×C4—431no—
214C23×C4—431no—
215C23×C4C4×D4311yescharacteristic
216#117—862no—
217#117—862no—
218#117—1721no—
219#117—1721no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—861no—
227C2×C22⋊C4—431no—
228C2×C22⋊C4—431no—
229C2×C22⋊C4C4×D4311yescharacteristic
230C2×C22⋊C4C22×D4311yescharacteristic
231C2×C42—431no—
232C2×C42—431no—
233C2×C42—861no—
234C2×C42—861no—
235C2×C42—861no—
236C2×C42—1721no—
237C2×C42—1721no—
238C4⋊C8—1721no—
239C4⋊C8—1721no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—861no—
243C22⋊C8—861no—
244#97—1721no—
245#97—1721no—
246#95—21no—
247#95—861no—
248#95—861no—
249#95—861no—
250C24C2×C4×D4311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—42no—
254C22×C4—41no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—431no—
258C22×C4—431no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—862no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—1722no—
267C22×C4—1721no—
268C22×C4D4×D4311yescharacteristic
269C22×C4D4×D4311yescharacteristic
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—1721no—
273C2×C8—1721no—
274C4⋊C4—42no—
275C4⋊C4—864no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C4⋊C4—1722no—
279C4⋊C4—1722no—
280C4⋊C4—1722no—
281C22⋊C4—21no—
282C22⋊C4—41no—
283C22⋊C4—432no—
284C22⋊C4—861no—
285C22⋊C4—1721no—
286C22⋊C4#1062187212yes—
287C42—861no—
288C42—861no—
289C42—861no—
290C42—861no—
291C42—864no—
292C42—1721no—
293C42—1721no—
294C42—1722no—
295C23—21no—
296C23—21no—
297C23—41no—
298C23—41no—
299C23C22⋊C4×D4311yescharacteristic
300C23M16×D4311yescharacteristic
301C23C2×#1062187211yescharacteristic
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—431no—
315C2×C4—431no—
316C2×C4—432no—
317C2×C4—862no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—862no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—862no—
326C2×C4—862no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1722no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4—1722no—
337C8—81no—
338C8—81no—
339C8—3441no—
340C8—3441no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—42no—
348C22—41no—
349C22—41no—
350C22#1458286111yescharacteristic
351C22#99×D4311yescharacteristic
352C22#101×D4311yescharacteristic
353C4—42no—
354C4—41no—
355C4—42no—
356C4—41no—
357C4—861no—
358C4—861no—
359C4—862no—
360C4—1722no—
361C4—1721no—
362C4—1722no—
363C4—1721no—
364C2—21no—
365C2—21no—
366C2—41no—
367C2—41no—
368C2#1913292311yescharacteristic
369C2#1913623311yescharacteristic
370C2#1913623511yescharacteristic
subgroupG/H
centerC22#99×D43
commutator, prime radicalC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1326C2
socleC22×C43C2×#99
cosocleC2×C22⋊C4×C43C23
hypercenter#1326D43
hypocenterC43#11518
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1326

Complements

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

NH ≅ G/Ntype
212. C43#11518semidirect

Maximal subgroups

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

subgroupindex
#191370742
#191329262
#191325442
#191325432
#191325422
C43×#13262
#1151843