Finite Group Databasebeta

← #25105587

Subgroups — #25105587

Order 11008.

1254 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583470C211yesmaximal, characteristic
2#19143040C211yesmaximal, characteristic
3#19135063C214yesmaximal, complemented
4#19135061C214yesmaximal, complemented
5#19134676C212yesmaximal, complemented
6#19134518C212yesmaximal, complemented
7C43×#2879C211yesmaximal, characteristic
8C23×Dic86C2211yescharacteristic
9C22×#10621877C2212yes—
10#14583470—24no—
11#14583470—24no—
12C2×#13063323C412yes—
13C2×#13063312C412yes—
14C2×#13063306C412yes—
15C2×#13063306C412yes—
16C2×#13063304C2212yes—
17C2×#13063304C2212yes—
18C2×#13063284C2211yescharacteristic
19C2×#13063243C2218yes—
20#14582866—24no—
21#14582863C2212yes—
22#14582863C2212yes—
23#14582667C2218yes—
24C22×#41×C43C2211yescharacteristic
25C22×M16×C43C2212yes—
26C43×#408—24no—
27C43×#407C2212yes—
28C43×#407C2212yes—
29C22×Dic86—22no—
30C22×Dic86—22no—
31C22×Dic86—44no—
32C22×Dic86C2×C412yes—
33C22×Dic86C2312yes—
34C23×Dic43C2×C412yes—
35C2×#10621877—22no—
36C2×#10621877—44no—
37C2×#10621877C2314yes—
38C22×C43⋊C8—22no—
39#13063323—28no—
40#13063312—28no—
41#13063306—28no—
42#13063306—28no—
43#13063304—24no—
44#13063304—24no—
45#13063304—24no—
46#13063304—24no—
47#13063284—22no—
48#13063284—22no—
49C2×C4⋊Dic43C2312yes—
50C2×Dic43⋊C4C2×C414yes—
51C2×Dic43⋊C4C2×C414yes—
52C2×C22⋊Dic43C2×C412yes—
53C2×C22⋊Dic43C2×C414yes—
54C2×C22⋊Dic43C2×C414yes—
55C2×C4×Dic43C2×C412yes—
56#13063243—48no—
57C22⋊(C43⋊C8)—24no—
58C22⋊(C43⋊C8)—24no—
59C2×#41×C43—44no—
60C2×#41×C43D414yes—
61C2×#41×C43D414yes—
62C22×Q8×C43C2×C411yescharacteristic
63C22×D4×C43C2×C411yescharacteristic
64C22×D4×C43C2×C411yescharacteristic
65C22×D4×C43C2×C411yescharacteristic
66C23×C4×C43C2311yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C2×M16×C43—22no—
70C2×M16×C43—44no—
71C2×M16×C43C2314yes—
72C22×C8×C43—22no—
73C22⋊C8×C43—24no—
74C22⋊C8×C43—24no—
75C24×C43C22×C411yescharacteristic
76C24×C43C22×C411yescharacteristic
77C24×C43C22×C411yescharacteristic
78#41×C43—44no—
79#41×C43—44no—
80#41×C43—44no—
81#41×C43—44no—
82C2×Q8×C43—42no—
83C2×Q8×C43C22⋊C414yes—
84C2×D4×C43—42no—
85C2×D4×C43—42no—
86C2×D4×C43—42no—
87C2×D4×C43C22⋊C414yes—
88C2×D4×C43C22⋊C414yes—
89C2×D4×C43C22⋊C414yes—
90C22×C4×C43—24no—
91C22×C4×C43—24no—
92C22×C4×C43—24no—
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C22×C411yescharacteristic
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D412yes—
98C22×C4×C43C2×D412yes—
99C22×C4×C43C2×D412yes—
100C22×C4×C43C2×D412yes—
101C22×C4×C43C2×D412yes—
102C22×C4×C43C2411yescharacteristic
103C22×Dic43—24no—
104C22×Dic43—44no—
105C22×Dic43C22×C414yes—
106C22×Dic43C22×C414yes—
107C2×Dic86—24no—
108C2×Dic86—22no—
109C2×Dic86—22no—
110C2×Dic86—28no—
111C2×Dic86—44no—
112C2×Dic86—48no—
113C2×Dic86—48no—
114M16×C43—28no—
115M16×C43—44no—
116C2×C8×C43—24no—
117C2×C8×C43—44no—
118C22⋊Dic43—24no—
119C22⋊Dic43—28no—
120C22⋊Dic43—28no—
121C4⋊Dic43—22no—
122C4⋊Dic43—22no—
123Dic43⋊C4—28no—
124Dic43⋊C4—28no—
125C4×Dic43—24no—
126#10621877—28no—
127#10621877—44no—
128C2×C43⋊C8—24no—
129C2×C43⋊C8—44no—
130C23×C43—22no—
131C23×C43—22no—
132C23×C43—22no—
133C23×C43—42no—
134C23×C43—42no—
135C23×C43—42no—
136C23×C43C2×C22⋊C412yes—
137C23×C43C2×C22⋊C412yes—
138C23×C43C2×C22⋊C412yes—
139C23×C43C23×C411yescharacteristic
140Q8×C43—44no—
141D4×C43—44no—
142D4×C43—44no—
143D4×C43—44no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—24no—
152C2×C4×C43—24no—
153C2×C4×C43—24no—
154C2×C4×C43—24no—
155C2×C4×C43C2×C22⋊C412yes—
156C2×C4×C43C2×C22⋊C412yes—
157C2×C4×C43C2×C22⋊C412yes—
158C2×C4×C43C22×D411yescharacteristic
159C2×C4×C43C22×D411yescharacteristic
160C2×C4×C43H(5,𝔽2)14yes—
161C2×Dic43—24no—
162C2×Dic43—24no—
163C2×Dic43—28no—
164C2×Dic43—48no—
165C2×Dic43—44no—
166Dic86—48no—
167Dic86—44no—
168Dic86—44no—
169C8×C43—44no—
170C43⋊C8—44no—
171#21756—431nomaximal, Sylow
172C22×C43—22no—
173C22×C43—22no—
174C22×C43—22no—
175C22×C43—22no—
176C22×C43—24no—
177C22×C43—24no—
178C22×C43—24no—
179C22×C43—44no—
180C22×C43—82no—
181C22×C43—82no—
182C22×C43C22×C22⋊C411yescharacteristic
183C22×C43#51812yes—
184C4×C43—22no—
185C4×C43—22no—
186C4×C43—22no—
187C4×C43#53412yes—
188C4×C43#53412yes—
189Dic43—44no—
190Dic43—44no—
191C2×#536—431no—
192#2879—431no—
193#2879D4311yescharacteristic
194#1901—434no—
195#1901—434no—
196#1822—432no—
197#1784—432no—
198C2×C43—22no—
199C2×C43—42no—
200C2×C43—42no—
201C2×C43—42no—
202C2×C43#230811yescharacteristic
203C2×C43#288912yes—
204C22×#41C2×D4311yescharacteristic
205C23×Q8—431no—
206C22×M16—432no—
207C22×M16C2×D4312yes—
208#536—864no—
209#536—864no—
210C2×C4⋊Q8—432no—
211C2×#124—432no—
212C2×#123—432no—
213C2×#123—432no—
214C2×C22⋊Q8—432no—
215C2×C22⋊Q8—432no—
216C2×#117—431no—
217C2×#101—438no—
218#408—24no—
219#408—864no—
220#407—432no—
221#407—432no—
222#407C2×D4312yes—
223#407C2×D4312yes—
224#343—438no—
225C43#2175611yescharacteristic, complemented, Sylow
226C2×#41—44no—
227C2×#41D17214yes—
228C2×#41C22⋊D4314yes—
229C22×Q8—432no—
230C22×Q8—432no—
231C22×Q8—862no—
232C22×Q8—862no—
233C22×Q8—1724no—
234C22×Q8C4×D4311yescharacteristic
235C22×D4C4×D4311yescharacteristic
236C22×D4C4×D4311yescharacteristic
237C22×D4C4×D4311yescharacteristic
238C23×C4—432no—
239C23×C4C22×D4311yescharacteristic
240C23×C4C22×D4311yescharacteristic
241C23×C4C22×D4311yescharacteristic
242C2×M16—22no—
243C2×M16—44no—
244C2×M16—434no—
245C2×M16—862no—
246C2×M16—1724no—
247C2×M16C22×D4314yes—
248C22×C8—22no—
249C22×C8—862no—
250C4⋊Q8—868no—
251#124—868no—
252#123—868no—
253#123—868no—
254C22⋊Q8—864no—
255C22⋊Q8—864no—
256C22⋊Q8—864no—
257C22⋊Q8—864no—
258#117—862no—
259#117—862no—
260C2×C4⋊C4—434no—
261C2×C4⋊C4—434no—
262C2×C4⋊C4—432no—
263C2×C22⋊C4—432no—
264C2×C22⋊C4—434no—
265C2×C22⋊C4—434no—
266C2×C42—432no—
267#101—1728no—
268C22⋊C8—24no—
269C22⋊C8—24no—
270C22⋊C8—864no—
271C22⋊C8—864no—
272C24C2×C4×D4311yescharacteristic
273C24C2×C4×D4311yescharacteristic
274C24C2×C4×D4311yescharacteristic
275#41—44no—
276#41—44no—
277#41—44no—
278#41—44no—
279C2×Q8—42no—
280C2×Q8—864no—
281C2×Q8—862no—
282C2×Q8—862no—
283C2×Q8—868no—
284C2×Q8—1724no—
285C2×Q8—1728no—
286C2×Q8—1728no—
287C2×Q8(C2×D43)⋊C414yes—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4(C2×D43)⋊C414yes—
292C2×D4(C2×D43)⋊C414yes—
293C2×D4(C2×D43)⋊C414yes—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—434no—
298C22×C4—434no—
299C22×C4—864no—
300C22×C4—1724no—
301C22×C4C2×C4×D4311yescharacteristic
302C22×C4C2×C4×D4311yescharacteristic
303C22×C4C2×C4×D4311yescharacteristic
304C22×C4C2×D17212yes—
305C22×C4C2×D17212yes—
306C22×C4C2×D17212yes—
307C22×C4C2×C22⋊D4312yes—
308C22×C4C2×C22⋊D4312yes—
309C22×C4C2×C22⋊D4312yes—
310C22×C4C23×D4311yescharacteristic
311M16—28no—
312M16—44no—
313M16—868no—
314M16—1724no—
315C2×C8—24no—
316C2×C8—44no—
317C2×C8—864no—
318C2×C8—1724no—
319C4⋊C4—868no—
320C4⋊C4—868no—
321C4⋊C4—862no—
322C4⋊C4—862no—
323C22⋊C4—864no—
324C22⋊C4—868no—
325C22⋊C4—868no—
326C42—864no—
327C23—22no—
328C23—22no—
329C23—22no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23C2×(C2×D43)⋊C412yes—
334C23C2×(C2×D43)⋊C412yes—
335C23C2×(C2×D43)⋊C412yes—
336C23C22×C4×D4311yescharacteristic
337Q8—44no—
338Q8—1728no—
339Q8—1724no—
340Q8—1724no—
341D4—44no—
342D4—44no—
343D4—44no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—864no—
356C2×C4—864no—
357C2×C4—868no—
358C2×C4—1728no—
359C2×C4—1724no—
360C2×C4C2×(C2×D43)⋊C412yes—
361C2×C4C2×(C2×D43)⋊C412yes—
362C2×C4C2×(C2×D43)⋊C412yes—
363C2×C4C22×C22⋊D4311yescharacteristic
364C2×C4C22×D17211yescharacteristic
365C2×C4#1306337014yes—
366C8—44no—
367C8—1724no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—24no—
373C22—24no—
374C22—24no—
375C22—44no—
376C22—82no—
377C22—82no—
378C22C22×(C2×D43)⋊C411yescharacteristic
379C22#1458337212yes—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—1724no—
384C4—1724no—
385C4#1458345812yes—
386C4#1458346112yes—
387C2—22no—
388C2—42no—
389C2—42no—
390C2—42no—
391C2#1913717011yescharacteristic
392C2#1914307712yes—
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2879C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#2879D43
hypocenterC43#21756
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ #2879

Complements

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

NH ≅ G/Ntype
3. #19135063C2semidirect
4. #19135061C2semidirect
5. #19134676C2semidirect
6. #19134518C2semidirect
225. C43#21756semidirect

Maximal subgroups

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

subgroupindex
C2×#145834702
#191430402
#191350632
#191350612
#191346762
#191345182
C43×#28792
#2175643