Finite Group Databasebeta

← #24995541

Subgroups — #24995541

Order 11008.

466 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×C4×#10621873C211yesmaximal, characteristic
2#19132991C211yesmaximal, characteristic, complemented
3#19132987C211yesmaximal, characteristic
4#19132918C211yesmaximal, characteristic, complemented
5#19132915C211yesmaximal, characteristic
6#19132887C211yesmaximal, characteristic, complemented
7C43×#1564C211yesmaximal, characteristic, complemented
8C22×#10621873C411yescharacteristic
9C2×C4×Dic86C2211yescharacteristic
10C2×C4×D172C2211yescharacteristic
11C4×#10621873—21no—
12C4×#10621873—21no—
13C4×#10621873—21no—
14C4×#10621873—21no—
15#14582952C2211yescharacteristic
16#14582952C2211yescharacteristic
17C2×#13063257C411yescharacteristic
18C2×#13063250C411yescharacteristic
19C2×#13063247C411yescharacteristic
20#14582631—22no—
21#14582628—22no—
22#14582624—22no—
23#14582622—22no—
24#14582621—21no—
25#14582621—21no—
26C43×#431C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C2×C4×C8×C43C2211yescharacteristic
29C43×#335—21no—
30C43×#334—21no—
31C22×Dic86C2×C411yescharacteristic
32C22×D172C2×C411yescharacteristic
33C22×C4×D43—21no—
34C2×#10621873—22no—
35C2×#10621873—22no—
36C2×#10621873—21no—
37C2×#10621873—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42C4×D172—21no—
43C4×D172—21no—
44C4×D172—21no—
45C4×D172—21no—
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×Dic43⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×C4×Dic43—21no—
51#13063257—21no—
52#13063257—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)D412yes—
55#13063250—21no—
56#13063250—21no—
57#13063247—21no—
58#13063247—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)D412yes—
61C4×C43⋊C8—21no—
62C4×C43⋊C8—21no—
63C22×C8×C43C2×C411yescharacteristic
64C22×C8×C43C2×C411yescharacteristic
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70C4×C8×C43—21no—
71C4×C8×C43—21no—
72C4×C8×C43D411yescharacteristic
73C4×C8×C43D411yescharacteristic
74C4×C8×C43D411yescharacteristic
75C4×C8×C43D411yescharacteristic
76C23×D43—21no—
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172M1612yes—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C4×D43—82no—
92C2×Dic86—21no—
93C2×Dic86—21no—
94C2×Dic86—21no—
95C2×Dic86—21no—
96C2×Dic86—21no—
97C2×Dic86M1612yes—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C2×C8×C43—21no—
101C2×C8×C43—21no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C2×C8×C43C22⋊C411yescharacteristic
105C2×C8×C43C22⋊C411yescharacteristic
106C2×C8×C43C22⋊C411yescharacteristic
107C2×C8×C43C22⋊C411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43#4111yescharacteristic
112(C2×D43)⋊C4—41no—
113(C2×D43)⋊C4—41no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120C4×Dic43—41no—
121C4×Dic43—41no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—22no—
124#10621873—24no—
125#10621873—24no—
126C23×C43C4×D411yescharacteristic
127C22×D43—22no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—81no—
131C22×D43—81no—
132C2×C4×C43—22no—
133C2×C4×C43—41no—
134C2×C4×C43C2×C22⋊C411yescharacteristic
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12111yescharacteristic
138C2×C4×C43#12411yescharacteristic
139C2×C4×C43#12711yescharacteristic
140C2×C4×C43C2×M1611yescharacteristic
141C2×C4×C43C2×M1611yescharacteristic
142C2×C4×C43#13111yescharacteristic
143C2×C4×C43#13111yescharacteristic
144C2×Dic43—22no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151D172—22no—
152D172—22no—
153D172—41no—
154D172—41no—
155C4×D43—82no—
156C4×D43—82no—
157Dic86—22no—
158Dic86—22no—
159Dic86—41no—
160Dic86—41no—
161C8×C43—21no—
162C8×C43—21no—
163C8×C43—21no—
164C8×C43—21no—
165C8×C43—81no—
166C8×C43—81no—
167C43⋊C8—42no—
168C43⋊C8—42no—
169#9672—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#39011yescharacteristic
173C22×C43#43511yescharacteristic
174C22×C43#43511yescharacteristic
175C2×D43—42no—
176C2×D43—82no—
177C2×D43—81no—
178C2×D43—81no—
179C2×D43—82no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43#40711yescharacteristic
184C4×C43#40811yescharacteristic
185C4×C43#43511yescharacteristic
186C4×C43#43511yescharacteristic
187C4×C43#47112yes—
188Dic43—42no—
189Dic43—81no—
190Dic43—81no—
191C2×C4×SD16—431no—
192#1564D4311yescharacteristic, complemented
193#1479—431no—
194#1478—431no—
195#1461—431no—
196#1460—431no—
197#1452—431no—
198C2×C43—21no—
199C2×C43—21no—
200C2×C43#195511yescharacteristic
201C2×C43#197611yescharacteristic
202C2×C43#197711yescharacteristic
203D43—82no—
204C22×SD16—431no—
205C2×C4×Q8—431no—
206C2×C4×D4—431no—
207C4×SD16—861no—
208C4×SD16—861no—
209C4×SD16—861no—
210C4×SD16—861no—
211#431—431no—
212#431—431no—
213#431C2×D4311yescharacteristic
214#431C2×D4311yescharacteristic
215C2×#106—431no—
216C2×#103—431no—
217C2×#102—431no—
218C2×C4×C8C2×D4311yescharacteristic
219#335—21no—
220#334—21no—
221Q8⋊C8—862no—
222D4⋊C8—862no—
223#324—862no—
224#323—862no—
225#322—861no—
226#322—861no—
227C43#967211yescharacteristic, complemented, Sylow
228C22×Q8—431no—
229C22×D4—431no—
230C23×C4—861no—
231C2×SD16—862no—
232C2×SD16—862no—
233C2×SD16—861no—
234C2×SD16—861no—
235C22×C8C4×D4311yescharacteristic
236C22×C8C4×D4311yescharacteristic
237C4×Q8—861no—
238C4×Q8—861no—
239C4×Q8—861no—
240C4×Q8—861no—
241C4×D4—861no—
242C4×D4—861no—
243C4×D4—861no—
244C4×D4—861no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C42—861no—
250C2×C42C22×D4311yescharacteristic
251#106—861no—
252#106—861no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—432no—
256C4⋊C8—861no—
257#103—861no—
258#103—861no—
259#102—861no—
260#102—861no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—432no—
264C22⋊C8—861no—
265C4×C8—21no—
266C4×C8—21no—
267C4×C8—861no—
268C4×C8—861no—
269C4×C8D17211yescharacteristic
270C4×C8D17211yescharacteristic
271C4×C8C22⋊D4311yescharacteristic
272C4×C8C22⋊D4311yescharacteristic
273C24—861no—
274C2×Q8—432no—
275C2×Q8—861no—
276C2×Q8—861no—
277C2×Q8—861no—
278C2×Q8—861no—
279C2×Q8—861no—
280C2×D4—432no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—3442no—
290C22×C4—1721no—
291C22×C4—1721no—
292C22×C4C2×C4×D4311yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4#1062190211yescharacteristic
295SD16—864no—
296SD16—864no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—862no—
304C2×C8—862no—
305C2×C8(C2×D43)⋊C411yescharacteristic
306C2×C8(C2×D43)⋊C411yescharacteristic
307C2×C8(C2×D43)⋊C411yescharacteristic
308C2×C8(C2×D43)⋊C411yescharacteristic
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C42—1721no—
318C42—1721no—
319C42C2×D17211yescharacteristic
320C42D4×D4311yescharacteristic
321C42#1062190211yescharacteristic
322C42C2×C22⋊D4311yescharacteristic
323C23—862no—
324C23—3441no—
325C23—3441no—
326C23—1721no—
327C23—1721no—
328C23#1306328711yescharacteristic
329Q8—862no—
330Q8—862no—
331Q8—1721no—
332Q8—1721no—
333D4—862no—
334D4—862no—
335D4—1721no—
336D4—1721no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—862no—
340C2×C4—3442no—
341C2×C4—3442no—
342C2×C4—3441no—
343C2×C4—3441no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4C2×(C2×D43)⋊C411yescharacteristic
349C2×C4#1306328711yescharacteristic
350C2×C4#1306330011yescharacteristic
351C2×C4#1306330011yescharacteristic
352C2×C4#1306331411yescharacteristic
353C2×C4#1306332111yescharacteristic
354C2×C4M16×D4311yescharacteristic
355C2×C4M16×D4311yescharacteristic
356C2×C4#1306333111yescharacteristic
357C2×C4#1306333111yescharacteristic
358C8—21no—
359C8—21no—
360C8—21no—
361C8—21no—
362C8—81no—
363C8—81no—
364C8—1722no—
365C8—1722no—
366C22—21no—
367C22—21no—
368C22—3442no—
369C22—3442no—
370C22—3441no—
371C22—3441no—
372C22—1722no—
373C22#1458280011yescharacteristic
374C22#1458296911yescharacteristic
375C22#1458296911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—3441no—
380C4—3441no—
381C4—1722no—
382C4#1458286211yescharacteristic
383C4#1458286511yescharacteristic
384C4#1458296911yescharacteristic
385C4#1458296911yescharacteristic
386C4#1458316312yes—
387C2—21no—
388C2—21no—
389C2—3442no—
390C2#1913539211yescharacteristic
391C2#1913549111yescharacteristic
392C2#1913549611yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1564C2
socleC22×C43#390
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1564D43
hypocenterC43#9672
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
2. #19132991C2semidirect
4. #19132918C2semidirect
6. #19132887C2semidirect
7. C43×#1564C2semidirect
192. #1564D43semidirect
227. C43#9672semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106218732
#191329912
#191329872
#191329182
#191329152
#191328872
C43×#15642
#967243