Finite Group Databasebeta

← #25012105

Subgroups — #25012105

Order 11008.

1018 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 123 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×#13063323C211yesmaximal, characteristic
2C2×#14582697C214yesmaximal, complemented
3#19134519C211yesmaximal, characteristic
4C43×#1784C211yesmaximal, characteristic
5C23×Dic86C411yescharacteristic
6C2×#13063323—28no—
7C2×#13063323—21no—
8C2×#13063323—21no—
9C2×#13063323C412yes—
10C2×#13063323C2212yes—
11C22×Dic43⋊C4—21no—
12C22×Dic43⋊C4—21no—
13C22×C4×Dic43C411yescharacteristic
14C2×#13063244—21no—
15C2×#13063244C2212yes—
16#14582863—21no—
17#14582697—28no—
18C23×Q8×C43C2211yescharacteristic
19C2×#101×C43—21no—
20C2×#101×C43C2212yes—
21C43×#407—21no—
22C22×Dic86—21no—
23C22×Dic86—24no—
24C22×Dic86—42no—
25C22×Dic86—42no—
26C22×Dic86C2×C412yes—
27C23×Dic43—21no—
28C23×Dic43—21no—
29C2×#10621877—22no—
30#13063323—28no—
31#13063323—28no—
32#13063323—24no—
33#13063323—24no—
34#13063323—24no—
35#13063323D418yes—
36C2×Dic43⋊C4—28no—
37C2×Dic43⋊C4—28no—
38C2×Dic43⋊C4—22no—
39C2×Dic43⋊C4—22no—
40C2×Dic43⋊C4—22no—
41C2×Dic43⋊C4—22no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—24no—
44C2×C4×Dic43C2×C412yes—
45#13063244—24no—
46#13063244—42no—
47C22⋊(C43⋊C8)—42no—
48C22×Q8×C43—24no—
49C22×Q8×C43—42no—
50C22×Q8×C43—42no—
51C22×Q8×C43C2×C411yescharacteristic
52C22×Q8×C43D411yescharacteristic
53C22×Q8×C43D411yescharacteristic
54C22×Q8×C43C2311yescharacteristic
55C23×C4×C43C2×C411yescharacteristic
56C23×C4×C43D411yescharacteristic
57C23×C4×C43D411yescharacteristic
58C2×M16×C43—22no—
59#101×C43—24no—
60#101×C43—42no—
61C22⋊C8×C43—42no—
62C24×C43C22⋊C411yescharacteristic
63C2×Q8×C43—22no—
64C2×Q8×C43—22no—
65C2×Q8×C43—22no—
66C2×Q8×C43—22no—
67C2×Q8×C43—22no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43—41no—
74C2×Q8×C43—416no—
75C2×Q8×C43C2×D414yes—
76C22×C4×C43—22no—
77C22×C4×C43—22no—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43C22⋊C411yescharacteristic
86C22×C4×C43C22⋊C411yescharacteristic
87C22×C4×C43C22⋊C411yescharacteristic
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×Dic43—24no—
92C22×Dic43—28no—
93C22×Dic43—24no—
94C22×Dic43—22no—
95C22×Dic43—22no—
96C22×Dic43—42no—
97C22×Dic43—42no—
98C2×Dic86—24no—
99C2×Dic86—22no—
100C2×Dic86—42no—
101C2×Dic86—416no—
102C2×Dic86—42no—
103C2×Dic86—42no—
104C2×Dic86—42no—
105C2×Dic86C22⋊C414yes—
106M16×C43—42no—
107M16×C43—42no—
108C2×C8×C43—42no—
109Dic43⋊C4—28no—
110Dic43⋊C4—28no—
111Dic43⋊C4—28no—
112Dic43⋊C4—28no—
113C4×Dic43—24no—
114C4×Dic43—22no—
115C4×Dic43C22⋊C414yes—
116#10621877—42no—
117#10621877—42no—
118C2×C43⋊C8—42no—
119C23×C43—24no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43#9912yes—
123C23×C43C2×C22⋊C411yescharacteristic
124Q8×C43—44no—
125Q8×C43—44no—
126Q8×C43—44no—
127Q8×C43—44no—
128C2×C4×C43—28no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—44no—
144C2×C4×C43—44no—
145C2×C4×C43#9912yes—
146C2×C4×C43C2×C22⋊C412yes—
147C2×C4×C43#12012yes—
148C2×C4×C43#12012yes—
149C2×Dic43—216no—
150C2×Dic43—28no—
151C2×Dic43—24no—
152C2×Dic43—24no—
153C2×Dic43—48no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156Dic86—48no—
157Dic86—44no—
158Dic86—44no—
159C8×C43—82no—
160C43⋊C8—82no—
161#12700—431nomaximal, Sylow
162C22×C43—24no—
163C22×C43—24no—
164C22×C43—22no—
165C22×C43—22no—
166C22×C43—22no—
167C22×C43#35614yescomplemented
168C22×C43#37911yescharacteristic
169C22×C43C2×#9911yescharacteristic
170C22×C43C2×#9911yescharacteristic
171C4×C43—22no—
172C4×C43—22no—
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—41no—
176C4×C43—41no—
177Dic43—28no—
178Dic43—44no—
179C22×C4⋊Q8—431no—
180C2×#356—434no—
181#1784—431no—
182#1784D4311yescharacteristic
183C2×C43—21no—
184C2×C43—24no—
185C2×C43—21no—
186C2×C43#178111yescharacteristic
187C2×C43C2×#35612yes—
188C23×Q8—431no—
189C23×Q8C2×D4311yescharacteristic
190C2×C4⋊Q8—432no—
191C2×C4⋊Q8—432no—
192C2×C4⋊Q8—868no—
193C2×C4⋊Q8—861no—
194C2×C4⋊Q8—861no—
195C22×C4⋊C4—861no—
196C22×C4⋊C4—861no—
197C22×C42—431no—
198C2×#101—21no—
199C2×#101—432no—
200C2×#101—861no—
201C2×#101C2×D4312yes—
202#407—21no—
203#407—861no—
204#356—868no—
205C43#1270011yescharacteristic, complemented, Sylow
206C22×Q8—24no—
207C22×Q8—42no—
208C22×Q8—42no—
209C22×Q8—432no—
210C22×Q8—864no—
211C22×Q8—861no—
212C22×Q8—1722no—
213C22×Q8—1722no—
214C22×Q8C4×D4311yescharacteristic
215C22×Q8D17211yescharacteristic
216C22×Q8C22⋊D4311yescharacteristic
217C22×Q8C22×D4311yescharacteristic
218C23×C4—861no—
219C23×C4—861no—
220C23×C4C4×D4311yescharacteristic
221C23×C4D17211yescharacteristic
222C23×C4C22⋊D4311yescharacteristic
223C2×M16—22no—
224C2×M16—862no—
225C4⋊Q8—438no—
226C4⋊Q8—864no—
227C4⋊Q8—864no—
228C4⋊Q8—868no—
229C4⋊Q8—868no—
230C4⋊Q8—864no—
231C2×C4⋊C4—868no—
232C2×C4⋊C4—868no—
233C2×C4⋊C4—862no—
234C2×C4⋊C4—862no—
235C2×C4⋊C4—862no—
236C2×C4⋊C4—862no—
237C2×C42—432no—
238C2×C42—864no—
239C2×C42—861no—
240#101—24no—
241#101—42no—
242#101—864no—
243#101—1722no—
244C22⋊C8—42no—
245C22⋊C8—1722no—
246C24(C2×D43)⋊C411yescharacteristic
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—416no—
259C2×Q8—434no—
260C2×Q8—864no—
261C2×Q8—862no—
262C2×Q8—17216no—
263C2×Q8—1722no—
264C2×Q8—1722no—
265C2×Q8—1722no—
266C2×Q8—1722no—
267C2×Q8D4×D4314yes—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—864no—
278C22×C4—868no—
279C22×C4—862no—
280C22×C4—864no—
281C22×C4—862no—
282C22×C4—1722no—
283C22×C4—1722no—
284C22×C4(C2×D43)⋊C411yescharacteristic
285C22×C4(C2×D43)⋊C411yescharacteristic
286C22×C4(C2×D43)⋊C411yescharacteristic
287C22×C4C2×C4×D4311yescharacteristic
288C22×C4C2×D17211yescharacteristic
289C22×C4C2×C22⋊D4311yescharacteristic
290M16—42no—
291M16—42no—
292M16—1722no—
293M16—1722no—
294C2×C8—42no—
295C2×C8—1722no—
296C4⋊C4—868no—
297C4⋊C4—868no—
298C4⋊C4—868no—
299C4⋊C4—868no—
300C42—434no—
301C42—864no—
302C42—862no—
303C23—21no—
304C23—24no—
305C23—21no—
306C23#1306323912yes—
307C23C2×(C2×D43)⋊C411yescharacteristic
308Q8—44no—
309Q8—44no—
310Q8—44no—
311Q8—44no—
312Q8—1724no—
313Q8—1728no—
314Q8—1724no—
315C2×C4—28no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—8616no—
333C2×C4—868no—
334C2×C4—864no—
335C2×C4—864no—
336C2×C4—1728no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4#1306323912yes—
340C2×C4C22⋊C4×D4312yes—
341C2×C4#1306329312yes—
342C2×C4#1306329512yes—
343C8—82no—
344C8—3442no—
345C22—24no—
346C22—24no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22#1458269714yescomplemented
351C22#1458275411yescharacteristic
352C22C2×#1306323911yescharacteristic
353C22C2×#1306323911yescharacteristic
354C4—22no—
355C4—22no—
356C4—22no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—868no—
361C4—1724no—
362C2—21no—
363C2—21no—
364C2—24no—
365C2#1913450911yescharacteristic
366C2C2×#1458269712yes—
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1784C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC22×Q8×C43C23
hypercenter#1784D43
hypocenterC43#12700
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #1784

Complements

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

NH ≅ G/Ntype
2. C2×#14582697C2semidirect
167. C22×C43#356semidirect
205. C43#12700semidirect
350. C22#14582697semidirect

Maximal subgroups

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

subgroupindex
C22×#130633232
C2×#145826972
#191345192
C43×#17842
#1270043