Finite Group Databasebeta

← #25007107

Subgroups — #25007107

Order 11008.

446 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 73 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#343×D43C211yesmaximal, characteristic
3#19132923C211yesmaximal, characteristic
4#19132622C211yesmaximal, characteristic, complemented
5#19132602C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1353C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063283C411yescharacteristic
10C2×C4⋊C4×D43C2211yescharacteristic
11#14582861—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×#10621872—41no—
32C2×#10621872—41no—
33M16×D43—24no—
34M16×D43—42no—
35C2×C8×D43—41no—
36#13063283—41no—
37#13063283—41no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4C2×C411yescharacteristic
43C2×Dic43⋊C4D411yescharacteristic
44C4⋊C4×D43—41no—
45C4⋊C4×D43—41no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×C4×Dic43—21no—
49C22⋊(C43⋊C8)—21no—
50(C2×D43)⋊C8—41no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C2×M16×C43—21no—
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C4⋊C4×C43C2311yescharacteristic
60C22⋊C8×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—22no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—42no—
85C2×C4×D43—42no—
86M16×C43—22no—
87M16×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92(C2×D43)⋊C4—42no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95C4⋊Dic43—41no—
96C4⋊Dic43—42no—
97C4⋊Dic43—41no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102C4×Dic43—42no—
103#10621877—22no—
104#10621877—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107#10621872—44no—
108#10621872—82no—
109C8×D43—44no—
110C23×C43C2×C22⋊C411yescharacteristic
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—22no—
114C22×D43—41no—
115C22×D43#9911yescharacteristic
116C22×D43#9911yescharacteristic
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43#10412yes—
143C4×D43—22no—
144C4×D43—22no—
145C4×D43—22no—
146C4×D43—22no—
147C4×D43—42no—
148C4×D43—42no—
149C4×D43—42no—
150C4×D43—81no—
151C8×C43—42no—
152C8×C43—81no—
153C43⋊C8—42no—
154C43⋊C8—81no—
155#11764—431nomaximal, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43C2×#9911yescharacteristic
159C22×C43#41711yescharacteristic
160C22×C43C2×#10411yescharacteristic
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—42no—
167C2×D43—42no—
168C2×D43#35212yes—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—81no—
174C4×C43—81no—
175Dic43—22no—
176Dic43—41no—
177Dic43—41no—
178Dic43—81no—
179Dic43—81no—
180#2484—431no—
181C2×#343—431no—
182#1463—431no—
183#1353—431no—
184#1353D4311yescharacteristic, complemented
185#1346—431no—
186#1346—431no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43#150411yescharacteristic
190C2×C43C2×#35211yescharacteristic
191C2×C43#213311yescharacteristic
192D43—22no—
193D43—41no—
194C22×M16—861no—
195C2×#117—431no—
196C22×C4⋊C4—431no—
197#407—861no—
198#400—431no—
199#400C2×D4311yescharacteristic
200#398—431no—
201#398—431no—
202#387—861no—
203#387—861no—
204#385—861no—
205#381—431no—
206#381—861no—
207#343—431no—
208#343—861no—
209#343C2×D4311yescharacteristic
210#324—431no—
211#324—861no—
212#324C2×D4311yescharacteristic
213C43#1176411yescharacteristic, complemented, Sylow
214C23×C4—431no—
215C23×C4—431no—
216C23×C4—431no—
217C2×M16—21no—
218C2×M16—864no—
219C2×M16—861no—
220C2×M16—1721no—
221C2×M16—1721no—
222C2×M16—1722no—
223C22×C8—1721no—
224#117—1721no—
225#117—1721no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—1721no—
233C2×C4⋊C4—1721no—
234C2×C4⋊C4C4×D4311yescharacteristic
235C2×C4⋊C4C22×D4311yescharacteristic
236C2×C22⋊C4—861no—
237C2×C22⋊C4—861no—
238C2×C42—861no—
239C22⋊C8—21no—
240C22⋊C8—861no—
241C22⋊C8—1721no—
242#95—21no—
243#95—21no—
244#95—431no—
245#95—861no—
246#95—861no—
247#95—861no—
248#95—861no—
249#95—861no—
250#95C4×D4311yescharacteristic
251C24—431no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—862no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—1722no—
269C22×C4—1722no—
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4D4×D4311yescharacteristic
272C22×C4D4×D4311yescharacteristic
273M16—22no—
274M16—41no—
275M16—862no—
276M16—3442no—
277M16—1724no—
278M16—1721no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—1724no—
282C2×C8—1721no—
283C2×C8—1721no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C4⋊C4—1722no—
291C4⋊C4—1721no—
292C4⋊C4—1721no—
293C22⋊C4—1721no—
294C22⋊C4—1721no—
295C22⋊C4—1722no—
296C42—1722no—
297C23—431no—
298C23—431no—
299C23—862no—
300C23—861no—
301C23—861no—
302C23—1721no—
303C23C22⋊C4×D4311yescharacteristic
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—432no—
316C2×C4—862no—
317C2×C4—862no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—3441no—
325C2×C4—1722no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1721no—
336C2×C4#1306335211yescharacteristic
337C2×C4#1306335711yescharacteristic
338C8—42no—
339C8—81no—
340C8—3441no—
341C8—1722no—
342C22—21no—
343C22—21no—
344C22—432no—
345C22—861no—
346C22—861no—
347C22—861no—
348C22—861no—
349C22—861no—
350C22—1722no—
351C22—1722no—
352C22#99×D4311yescharacteristic
353C22#1458289911yescharacteristic
354C22#104×D4311yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—862no—
362C4—3441no—
363C4—3441no—
364C4—1721no—
365C4—1721no—
366C2—21no—
367C2—21no—
368C2—862no—
369C2—1721no—
370C2#1913309811yescharacteristic
371C2#352×D4311yescharacteristic
372C2#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#11764
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
184. #1353D43semidirect
213. C43#11764semidirect

Maximal subgroups

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

subgroupindex
#191388832
#343×D432
#191329232
#191326222
#191326022
#191326002
C43×#13532
#1176443