Finite Group Databasebeta

← #25007509

Subgroups — #25007509

Order 11008.

396 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 71 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#19138883C211yesmaximal, characteristic
2#19134674C211yesmaximal, characteristic
3#324×D43C211yesmaximal, characteristic
4#19132622C211yesmaximal, characteristic, complemented
5#19132602C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1353C211yesmaximal, characteristic, complemented
8C2×#13063283C411yescharacteristic
9C2×C4⋊C4×D43C2211yescharacteristic
10#14582862—21no—
11C22⋊C8×D43—21no—
12#14582837C411yescharacteristic
13#14582831C411yescharacteristic
14#14582829C2211yescharacteristic
15#14582786—21no—
16#14582782—21no—
17#14582773—21no—
18#14582761—21no—
19#14582761C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#400C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621877—21no—
31C2×C8×D43—41no—
32#13063283—41no—
33#13063283—41no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4C2×C411yescharacteristic
39C2×Dic43⋊C4D411yescharacteristic
40C4⋊C4×D43—41no—
41C4⋊C4×D43—41no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×C4×Dic43—21no—
45C22⋊(C43⋊C8)—21no—
46(C2×D43)⋊C8—41no—
47(C2×D43)⋊C8—41no—
48(C2×D43)⋊C8—41no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95C2×C411yescharacteristic
55C2×M16×C43—21no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C4⋊C4×C43C2311yescharacteristic
58C22⋊C8×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43C2×C411yescharacteristic
62C23×D43C22⋊C411yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C22×C411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C22×Dic43C22⋊C411yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—41no—
82C2×C4×D43—42no—
83C2×C4×D43—42no—
84M16×C43—41no—
85M16×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90(C2×D43)⋊C4—42no—
91(C2×D43)⋊C4—41no—
92(C2×D43)⋊C4—41no—
93C4⋊Dic43—41no—
94C4⋊Dic43—42no—
95C4⋊Dic43—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100C4×Dic43—42no—
101#10621877—41no—
102#10621877—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C8×D43—82no—
106C23×C43C2×C22⋊C411yescharacteristic
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—22no—
110C22×D43—41no—
111C22×D43#9911yescharacteristic
112C22×D43#9911yescharacteristic
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—42no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43#13511yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C4×D43—41no—
140C4×D43—41no—
141C4×D43—41no—
142C4×D43—41no—
143C4×D43—42no—
144C4×D43—42no—
145C4×D43—42no—
146C4×D43—81no—
147C8×C43—81no—
148C8×C43—81no—
149C43⋊C8—81no—
150C43⋊C8—81no—
151#11850—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43C2×#9911yescharacteristic
155C22×C43#41611yescharacteristic
156C22×C43#42111yescharacteristic
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—42no—
163C2×D43—42no—
164C2×D43#35212yes—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—81no—
170C4×C43—81no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174Dic43—81no—
175Dic43—81no—
176#2484—431no—
177#1821—431no—
178C2×#324—431no—
179#1353—431no—
180#1353D4311yescharacteristic, complemented
181#1346—431no—
182#1346—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43#151611yescharacteristic
186C2×C43C2×#35211yescharacteristic
187C2×C43#213311yescharacteristic
188D43—22no—
189D43—41no—
190C2×#117—431no—
191C22×C4⋊C4—431no—
192#407—861no—
193C2×C22⋊C8—861no—
194#400—431no—
195#400C2×D4311yescharacteristic
196#398—431no—
197#398—431no—
198#387—861no—
199#387—861no—
200#385—861no—
201#381—431no—
202#381—861no—
203#343—431no—
204#343—861no—
205#343C2×D4311yescharacteristic
206#324—431no—
207#324—861no—
208#324C2×D4311yescharacteristic
209C43#1185011yescharacteristic, complemented, Sylow
210C23×C4—431no—
211C23×C4—431no—
212C23×C4—431no—
213C2×M16—21no—
214C2×M16—861no—
215C22×C8—1721no—
216#117—1721no—
217#117—1721no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—1721no—
225C2×C4⋊C4—1721no—
226C2×C4⋊C4C4×D4311yescharacteristic
227C2×C4⋊C4C22×D4311yescharacteristic
228C2×C22⋊C4—861no—
229C2×C22⋊C4—861no—
230C2×C42—861no—
231C22⋊C8—21no—
232C22⋊C8—861no—
233C22⋊C8—1721no—
234C22⋊C8—1721no—
235C22⋊C8—1721no—
236#95—21no—
237#95—21no—
238#95—431no—
239#95—861no—
240#95—861no—
241#95—861no—
242#95—861no—
243#95—861no—
244#95C4×D4311yescharacteristic
245C24—431no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—431no—
249C22×C4—431no—
250C22×C4—431no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—1721no—
262C22×C4—1722no—
263C22×C4—1722no—
264C22×C4C2×C4×D4311yescharacteristic
265C22×C4D4×D4311yescharacteristic
266C22×C4D4×D4311yescharacteristic
267M16—41no—
268M16—41no—
269M16—1721no—
270M16—1721no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—3442no—
274C2×C8—1721no—
275C2×C8—1721no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C4⋊C4—1722no—
283C4⋊C4—1721no—
284C4⋊C4—1721no—
285C22⋊C4—1721no—
286C22⋊C4—1721no—
287C22⋊C4—1722no—
288C42—1722no—
289C23—431no—
290C23—431no—
291C23—862no—
292C23—861no—
293C23—861no—
294C23—1721no—
295C23C22⋊C4×D4311yescharacteristic
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—3441no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1722no—
318C2×C4—1722no—
319C2×C4—1722no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4#1306334611yescharacteristic
329C2×C4#1306334811yescharacteristic
330C8—81no—
331C8—81no—
332C8—3441no—
333C8—3441no—
334C22—21no—
335C22—21no—
336C22—432no—
337C22—861no—
338C22—861no—
339C22—861no—
340C22—861no—
341C22—861no—
342C22—1722no—
343C22—1722no—
344C22#99×D4311yescharacteristic
345C22#1458289411yescharacteristic
346C22#1458291411yescharacteristic
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—3441no—
354C4—3441no—
355C4—1721no—
356C4—1721no—
357C4—1721no—
358C2—21no—
359C2—21no—
360C2—862no—
361C2—1721no—
362C2#1913315011yescharacteristic
363C2#352×D4311yescharacteristic
364C2#1913628111yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1353C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1353D43
hypocenterC43#11850
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
4. #19132622C2semidirect
5. #19132602C2semidirect
6. #19132600C2semidirect
7. C43×#1353C2semidirect
180. #1353D43semidirect
209. C43#11850semidirect

Maximal subgroups

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

subgroupindex
#191388832
#191346742
#324×D432
#191326222
#191326022
#191326002
C43×#13532
#1185043