Finite Group Databasebeta

← #24989247

Subgroups — #24989247

Order 11008.

842 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×#13063320C211yesmaximal, characteristic
2#19134675C211yesmaximal, characteristic, complemented
3#19132924C212yesmaximal, complemented
4#19132921C212yesmaximal
5C43×#1821C211yesmaximal, characteristic, complemented
6C2×#13063320—24no—
7C2×#13063320—24no—
8C2×#13063320—22no—
9C2×#13063320—22no—
10C22×C4⋊Dic43C411yescharacteristic
11C22×Dic43⋊C4C2211yescharacteristic
12C22×(C2×D43)⋊C4C411yescharacteristic
13C22×(C2×D43)⋊C4C411yescharacteristic
14C22×(C2×D43)⋊C4C2211yescharacteristic
15C22×C4×Dic43C411yescharacteristic
16#14582863C2212yes—
17#14582668—22no—
18#14582624—24no—
19#14582622—24no—
20C22×C4⋊C4×C43C2211yescharacteristic
21C43×#407C2212yes—
22C43×#343—22no—
23C24×D43C2×C411yescharacteristic
24C23×Dic43C2×C411yescharacteristic
25C23×Dic43C2×C411yescharacteristic
26C23×Dic43C2×C411yescharacteristic
27C2×#10621877—22no—
28#13063320—216no—
29#13063320—216no—
30C2×C4⋊Dic43—22no—
31C2×C4⋊Dic43—22no—
32C2×C4⋊Dic43—22no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—22no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4D414yes—
37C2×(C2×D43)⋊C4—22no—
38C2×(C2×D43)⋊C4—22no—
39C2×(C2×D43)⋊C4—22no—
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4D414yes—
47C2×C4×Dic43—22no—
48C2×C4×Dic43—22no—
49C2×C4×Dic43—22no—
50C22⋊(C43⋊C8)—22no—
51C22⋊(C43⋊C8)—22no—
52C23×C4×C43C2×C411yescharacteristic
53C23×C4×C43C2×C411yescharacteristic
54C23×C4×C43C2311yescharacteristic
55C2×M16×C43—22no—
56C2×C4⋊C4×C43—22no—
57C2×C4⋊C4×C43—22no—
58C2×C4⋊C4×C43D412yes—
59C2×C4⋊C4×C43D412yes—
60C22⋊C8×C43—22no—
61C22⋊C8×C43—22no—
62C24×C43C22×C411yescharacteristic
63C23×D43—21no—
64C23×D43—21no—
65C23×D43—42no—
66C23×D43—42no—
67C23×D43—42no—
68C23×D43C22⋊C412yes—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—42no—
74C22×C4×C43—42no—
75C22×C4×C43—42no—
76C22×C4×C43C22⋊C412yes—
77C22×C4×C43C22⋊C412yes—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D412yes—
80C22×C4×C43C2×D412yes—
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—42no—
89C22×Dic43—42no—
90C22×Dic43—42no—
91C22×Dic43C22⋊C412yes—
92C22×Dic43C22⋊C412yes—
93C22×Dic43C22⋊C412yes—
94M16×C43—44no—
95C2×C8×C43—42no—
96C4⋊C4×C43—24no—
97C4⋊C4×C43—24no—
98(C2×D43)⋊C4—28no—
99(C2×D43)⋊C4—28no—
100(C2×D43)⋊C4—24no—
101(C2×D43)⋊C4—24no—
102C4⋊Dic43—28no—
103Dic43⋊C4—24no—
104Dic43⋊C4—24no—
105C4×Dic43—28no—
106#10621877—44no—
107C2×C43⋊C8—42no—
108C23×C43—22no—
109C23×C43—22no—
110C23×C43—22no—
111C23×C43C2×C22⋊C411yescharacteristic
112C23×C43C2×C22⋊C411yescharacteristic
113C23×C43C2×C22⋊C411yescharacteristic
114C22×D43—22no—
115C22×D43—24no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43—42no—
121C22×D43—42no—
122C22×D43—42no—
123C22×D43—42no—
124C22×D43—88no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43#12012yes—
138C2×C4×C43#12012yes—
139C2×Dic43—22no—
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—24no—
143C2×Dic43—42no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148C2×Dic43—42no—
149C2×Dic43—42no—
150C2×Dic43—42no—
151C8×C43—82no—
152C43⋊C8—82no—
153#8556—431nomaximal, Sylow
154C22×C43—28no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43#37911yescharacteristic
162C22×C43#41012yes—
163C22×C43#41312yes—
164C22×C43#41312yes—
165C2×D43—42no—
166C2×D43—42no—
167C2×D43—42no—
168C2×D43—84no—
169C2×D43—84no—
170C2×D43—84no—
171C4×C43—22no—
172C4×C43—22no—
173C4×C43—42no—
174C4×C43—42no—
175Dic43—42no—
176Dic43—42no—
177Dic43—42no—
178C22×#126—431no—
179#1821—431no—
180#1821D4311yescharacteristic, complemented
181#1463—432no—
182#1462—432no—
183C2×C43—22no—
184C2×C43—22no—
185C2×C43—22no—
186C2×C43#178211yescharacteristic
187C2×C43#178511yescharacteristic
188C2×C43#178511yescharacteristic
189D43—82no—
190C2×#126—864no—
191C2×#126—864no—
192C2×#126—862no—
193C2×#126—862no—
194C22×C4⋊C4—431no—
195C22×C4⋊C4—431no—
196C22×C4⋊C4C2×D4311yescharacteristic
197C22×C22⋊C4—431no—
198C22×C22⋊C4—431no—
199C22×C22⋊C4—431no—
200C22×C42—431no—
201#407—432no—
202#407C2×D4312yes—
203#343—22no—
204#343—862no—
205#324—864no—
206#323—864no—
207C43#855611yescharacteristic, complemented, Sylow
208C25—431no—
209C23×C4—431no—
210C23×C4—431no—
211C23×C4—431no—
212C23×C4C4×D4311yescharacteristic
213C23×C4C4×D4311yescharacteristic
214C23×C4C22×D4311yescharacteristic
215C2×M16—22no—
216C2×M16—862no—
217#126—8616no—
218#126—8616no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—434no—
222C2×C4⋊C4—862no—
223C2×C4⋊C4—862no—
224C2×C4⋊C4—862no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—862no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4D17212yes—
229C2×C4⋊C4C22⋊D4312yes—
230C2×C22⋊C4—434no—
231C2×C22⋊C4—862no—
232C2×C22⋊C4—862no—
233C2×C22⋊C4—862no—
234C2×C22⋊C4—862no—
235C2×C22⋊C4—862no—
236C2×C22⋊C4—862no—
237C2×C22⋊C4—861no—
238C2×C22⋊C4—862no—
239C2×C22⋊C4—861no—
240C2×C42—862no—
241C2×C42—862no—
242C2×C42—862no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245C22⋊C8—862no—
246C22⋊C8—862no—
247C24—432no—
248C24—861no—
249C24—861no—
250C24—1722no—
251C24—1722no—
252C24—1722no—
253C24C2×C4×D4311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—432no—
262C22×C4—432no—
263C22×C4—432no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—1722no—
271C22×C4—1722no—
272C22×C4—1722no—
273C22×C4(C2×D43)⋊C412yes—
274C22×C4(C2×D43)⋊C412yes—
275C22×C4C2×D17211yescharacteristic
276C22×C4D4×D4312yes—
277C22×C4D4×D4312yes—
278C22×C4C2×C22⋊D4311yescharacteristic
279M16—44no—
280M16—1724no—
281C2×C8—42no—
282C2×C8—1722no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—868no—
286C4⋊C4—864no—
287C4⋊C4—864no—
288C22⋊C4—868no—
289C22⋊C4—868no—
290C22⋊C4—864no—
291C22⋊C4—864no—
292C42—868no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—864no—
297C23—862no—
298C23—3448no—
299C23—1722no—
300C23—1722no—
301C23—1722no—
302C23—1722no—
303C23—1722no—
304C23—1722no—
305C23—1722no—
306C23—1722no—
307C23C22⋊C4×D4311yescharacteristic
308C23C22⋊C4×D4311yescharacteristic
309C23C2×(C2×D43)⋊C411yescharacteristic
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—864no—
323C2×C4—862no—
324C2×C4—862no—
325C2×C4—862no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4—1722no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4#1306329312yes—
335C2×C4#1306329512yes—
336C8—82no—
337C8—3442no—
338C22—28no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—3444no—
346C22—3444no—
347C22—3444no—
348C22—1722no—
349C22—1722no—
350C22—1722no—
351C22#1458275411yescharacteristic
352C22#1458287212yes—
353C22#1458288012yes—
354C22#1458288212yes—
355C4—22no—
356C4—22no—
357C4—42no—
358C4—42no—
359C4—1722no—
360C4—1722no—
361C4—1722no—
362C2—22no—
363C2—22no—
364C2—22no—
365C2—3442no—
366C2#1913451211yescharacteristic
367C2#1913452011yescharacteristic
368C2#1913452211yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1821C2
socleC22×C43#379
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1821D43
hypocenterC43#8556
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. #19134675C2semidirect
3. #19132924C2semidirect
5. C43×#1821C2semidirect
180. #1821D43semidirect
207. C43#8556semidirect

Maximal subgroups

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

subgroupindex
C22×#130633202
#191346752
#191329242
#191329212
C43×#18212
#855643