Finite Group Databasebeta

← #25006087

Subgroups — #25006087

Order 11008.

440 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 83 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#19137307C211yesmaximal, characteristic
2#19132933C211yesmaximal, characteristic
3#19132540C212yesmaximal, complemented
4#19132528C212yesmaximal, complemented
5C43×#1465C211yesmaximal, characteristic
6C2×#13063312C411yescharacteristic
7C2×C4×Dic86C411yescharacteristic
8#14582863—21no—
9#14582804C2211yescharacteristic
10#14582802C411yescharacteristic
11#14582787—21no—
12#14582787—21no—
13#14582772—21no—
14#14582772—21no—
15#14582768C2211yescharacteristic
16#14582745C411yescharacteristic
17#14582625C2212yes—
18#14582623—21no—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#324C2212yes—
22C43×#323—21no—
23C22×Dic86C2×C411yescharacteristic
24C2×#10621877—41no—
25#13063312—22no—
26#13063312—22no—
27C4×Dic86—41no—
28C4×Dic86—41no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43C2×C411yescharacteristic
39C2×C4×Dic43C2×C411yescharacteristic
40C22⋊(C43⋊C8)—22no—
41C22⋊(C43⋊C8)—41no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C22×D4×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C2×M16×C43—41no—
50C4×D4×C43—41no—
51C4×D4×C43—41no—
52C2×C4⋊C4×C43C2311yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43D411yescharacteristic
55C2×C42×C43C2×C411yescharacteristic
56C22⋊C8×C43—22no—
57C22⋊C8×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C24×C43C22⋊C411yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—81no—
69C22×C4×C43—81no—
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×Dic86—21no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×Dic86M1612yescomplemented
83M16×C43—82no—
84C2×C8×C43—42no—
85C4⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C42×C43—21no—
89C42×C43—21no—
90C22⋊Dic43—24no—
91C22⋊Dic43—24no—
92C22⋊Dic43—81no—
93C22⋊Dic43—81no—
94C4⋊Dic43—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—81no—
98Dic43⋊C4—81no—
99C4×Dic43—21no—
100C4×Dic43—42no—
101C4×Dic43—41no—
102C4×Dic43M1612yescomplemented
103#10621877—82no—
104C2×C43⋊C8—42no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116D4×C43—42no—
117D4×C43—42no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43#9911yescharacteristic
132C2×C4×C43#9911yescharacteristic
133C2×C4×C43C2×M1611yescharacteristic
134C2×C4×C43C2×M1611yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147Dic86—42no—
148Dic86—42no—
149C8×C43—82no—
150C43⋊C8—82no—
151#11535—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—42no—
155C22×C43—42no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—81no—
163C22×C43—81no—
164C22×C43#40711yescharacteristic
165C22×C43C2×#9911yescharacteristic
166C22×C43#41311yescharacteristic
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174Dic43—42no—
175Dic43—42no—
176Dic43—81no—
177Dic43—81no—
178#2326—431no—
179#1465—431no—
180#1465D4311yescharacteristic
181#1325—432no—
182#1319—432no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—81no—
186C2×C43—81no—
187C2×C43#146511yescharacteristic
188C2×C43#212711yescharacteristic
189C2×C43#213511yescharacteristic
190C2×#124—431no—
191C2×C4×Q8—431no—
192C2×C4×D4C2×D4311yescharacteristic
193#407—21no—
194#407—861no—
195#391—431no—
196#390—431no—
197#388—861no—
198#388—861no—
199#385—861no—
200#385—861no—
201#384—431no—
202#376—431no—
203#324—432no—
204#324C2×D4312yes—
205#323—21no—
206#323—861no—
207C43#1153511yescharacteristic, complemented, Sylow
208C22×Q8—431no—
209C22×D4C4×D4311yescharacteristic
210C23×C4D17211yescharacteristic
211C23×C4C22⋊D4311yescharacteristic
212C2×M16—41no—
213C2×M16—1721no—
214#124—862no—
215#124—862no—
216C4×Q8—1721no—
217C4×Q8—1721no—
218C4×D4—41no—
219C4×D4—41no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4C22×D4311yescharacteristic
225C2×C22⋊C4—861no—
226C2×C22⋊C4—861no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—861no—
229C2×C22⋊C4D17211yescharacteristic
230C2×C22⋊C4C22⋊D4311yescharacteristic
231C2×C42—431no—
232C2×C42—431no—
233C2×C42—861no—
234C2×C42C4×D4311yescharacteristic
235C22⋊C8—22no—
236C22⋊C8—41no—
237C22⋊C8—862no—
238C22⋊C8—1721no—
239#95—861no—
240#95—861no—
241#95—861no—
242#95—861no—
243C24(C2×D43)⋊C411yescharacteristic
244C24(C2×D43)⋊C411yescharacteristic
245C2×Q8—432no—
246C2×Q8—861no—
247C2×Q8—1721no—
248C2×Q8—1721no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C2×D4—41no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4(C2×D43)⋊C411yescharacteristic
264C22×C4(C2×D43)⋊C411yescharacteristic
265C22×C4C2×C4×D4311yescharacteristic
266C22×C4C2×D17211yescharacteristic
267C22×C4C2×C22⋊D4311yescharacteristic
268M16—82no—
269M16—3442no—
270C2×C8—42no—
271C2×C8—1722no—
272C4⋊C4—41no—
273C4⋊C4—3441no—
274C4⋊C4—3441no—
275C4⋊C4—1721no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—864no—
281C22⋊C4—864no—
282C22⋊C4—3441no—
283C22⋊C4—3441no—
284C42—21no—
285C42—21no—
286C42—432no—
287C42—861no—
288C42—1721no—
289C42—1722no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C2×(C2×D43)⋊C411yescharacteristic
301Q8—1722no—
302Q8—1722no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—862no—
319C2×C4—862no—
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—1721no—
329C2×C4—1721no—
330C2×C4#1306323911yescharacteristic
331C2×C4#1306323911yescharacteristic
332C2×C4M16×D4311yescharacteristic
333C2×C4M16×D4311yescharacteristic
334C8—82no—
335C8—3442no—
336C22—21no—
337C22—21no—
338C22—42no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22#1458286211yescharacteristic
349C22C2×#1306323911yescharacteristic
350C22#1458288111yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—3441no—
359C4—3441no—
360C4—1722no—
361C4—1722no—
362C2—21no—
363C2—21no—
364C2—81no—
365C2—81no—
366C2#1913293111yescharacteristic
367C2#1913626211yescharacteristic
368C2#1913628911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1465C2
socleC22×C43C2×#99
prime radicalC22×D4×C43C2×C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1465D43
hypocenterC43#11535
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #19132540C2semidirect
4. #19132528C2semidirect
82. C2×Dic86M16semidirect
102. C4×Dic43M16semidirect
207. C43#11535semidirect

Maximal subgroups

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

subgroupindex
#191373072
#191329332
#191325402
#191325282
C43×#14652
#1153543