Finite Group Databasebeta

← #25007329

Subgroups — #25007329

Order 11008.

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

normal subgroups only

This group has 434 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#400×D43C211yesmaximal, characteristic
2#19134674C211yesmaximal, characteristic
3#19132923C211yesmaximal, characteristic
4#19132623C211yesmaximal, characteristic, complemented
5#19132622C211yesmaximal, characteristic, complemented
6#19132621C211yesmaximal, characteristic, complemented
7C43×#1353C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D43C411yescharacteristic
9C2×C4⋊C4×D43C2211yescharacteristic
10#14582862—21no—
11#14582861—21no—
12#14582841—21no—
13#14582840—21no—
14#14582839C411yescharacteristic
15#14582838C2211yescharacteristic
16#14582837C411yescharacteristic
17#95×D43—21no—
18#95×D43—21no—
19#95×D43C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#400C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43—21no—
28C22×C4×D43—21no—
29C22×C4×D43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C22×C4×D43D411yescharacteristic
32C2×#10621877—21no—
33C2×#10621872—41no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4C2×C411yescharacteristic
38C2×Dic43⋊C4D411yescharacteristic
39C4⋊C4×D43—41no—
40C4⋊C4×D43—41no—
41C4⋊C4×D43—41no—
42C4⋊C4×D43—41no—
43C22⋊(C43⋊C8)—21no—
44(C2×D43)⋊C8—41no—
45(C2×D43)⋊C8—41no—
46(C2×D43)⋊C8—41no—
47C43⋊#95—21no—
48C43⋊#95—21no—
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—
84C2×C4×D43—42no—
85C2×C4×D43—42no—
86C2×C4×D43—42no—
87C2×C4×D43—44no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90M16×C43—41no—
91M16×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C4⋊Dic43—41no—
97C4⋊Dic43—41no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100Dic43⋊C4—42no—
101#10621877—41no—
102#10621877—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105#10621872—82no—
106C23×C43C2×C22⋊C411yescharacteristic
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—22no—
110C22×D43—22no—
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#13711yescharacteristic
125C2×C4×C43#13711yescharacteristic
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—42no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C4×D43—41no—
139C4×D43—41no—
140C4×D43—41no—
141C4×D43—41no—
142C4×D43—42no—
143C4×D43—42no—
144C4×D43—42no—
145C4×D43—81no—
146C4×D43—84no—
147C4×D43—82no—
148C4×D43—82no—
149C8×C43—81no—
150C8×C43—81no—
151C43⋊C8—81no—
152C43⋊C8—81no—
153#11814—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43C2×#9911yescharacteristic
157C22×C43#41911yescharacteristic
158C22×C43#42111yescharacteristic
159C2×D43—24no—
160C2×D43—24no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43#35212yes—
166C2×D43#35512yes—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—81no—
172C4×C43—81no—
173Dic43—41no—
174Dic43—41no—
175Dic43—41no—
176Dic43—81no—
177Dic43—81no—
178C2×#400—431no—
179#1821—431no—
180#1463—431no—
181#1353—431no—
182#1353—431no—
183#1353—431no—
184#1353D4311yescharacteristic, complemented
185C2×C43—21no—
186C2×C43—21no—
187C2×C43#151111yescharacteristic
188C2×C43C2×#35211yescharacteristic
189C2×C43C2×#35511yescharacteristic
190D43—22no—
191D43—22no—
192C22×C4⋊C4—431no—
193C22×C4⋊C4—431no—
194#407—861no—
195#407—861no—
196#400—431no—
197#400—431no—
198#400—431no—
199#400—861no—
200#400—861no—
201#400C2×D4311yescharacteristic
202C2×#95—431no—
203C2×#95—861no—
204C2×#95—861no—
205#343—431no—
206#343—861no—
207#343C2×D4311yescharacteristic
208#324—431no—
209#324—861no—
210#324C2×D4311yescharacteristic
211C43#1181411yescharacteristic, complemented, Sylow
212C23×C4—431no—
213C23×C4—431no—
214C23×C4—431no—
215C23×C4—861no—
216C23×C4—861no—
217C2×M16—21no—
218C2×M16—861no—
219C2×M16—1721no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—1721no—
226C2×C4⋊C4—1721no—
227C2×C4⋊C4—1721no—
228C2×C4⋊C4—1721no—
229C2×C4⋊C4C4×D4311yescharacteristic
230C2×C4⋊C4C22×D4311yescharacteristic
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#95—861no—
245#95—861no—
246#95C4×D4311yescharacteristic
247C24—431no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—431no—
251C22×C4—431no—
252C22×C4—431no—
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—861no—
262C22×C4—861no—
263C22×C4—1721no—
264C22×C4—1721no—
265C22×C4—1721no—
266C22×C4—1724no—
267C22×C4—1722no—
268C22×C4—1722no—
269C22×C4—1722no—
270C22×C4—1722no—
271C22×C4—1722no—
272C22×C4C2×C4×D4311yescharacteristic
273C22×C4D4×D4311yescharacteristic
274C22×C4D4×D4311yescharacteristic
275M16—41no—
276M16—41no—
277M16—3442no—
278M16—1721no—
279M16—1721no—
280C2×C8—41no—
281C2×C8—41no—
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—
291C23—431no—
292C23—431no—
293C23—862no—
294C23—862no—
295C23—861no—
296C23—861no—
297C23C22⋊C4×D4311yescharacteristic
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—3441no—
315C2×C4—3442no—
316C2×C4—3444no—
317C2×C4—3442no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1722no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1722no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4#1306335411yescharacteristic
333C2×C4#1306335711yescharacteristic
334C8—81no—
335C8—81no—
336C8—3441no—
337C8—3441no—
338C22—21no—
339C22—21no—
340C22—432no—
341C22—432no—
342C22—864no—
343C22—864no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—861no—
348C22#99×D4311yescharacteristic
349C22#1458290611yescharacteristic
350C22#1458291411yescharacteristic
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—3441no—
358C4—3441no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C2—21no—
363C2—21no—
364C2—862no—
365C2—862no—
366C2#1913312611yescharacteristic
367C2#352×D4311yescharacteristic
368C2#355×D4311yescharacteristic
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#11814
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. #19132623C2semidirect
5. #19132622C2semidirect
6. #19132621C2semidirect
7. C43×#1353C2semidirect
184. #1353D43semidirect
211. C43#11814semidirect

Maximal subgroups

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

subgroupindex
#400×D432
#191346742
#191329232
#191326232
#191326222
#191326212
C43×#13532
#1181443