Finite Group Databasebeta

← #24995542

Subgroups — #24995542

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×#10621884C211yesmaximal, characteristic
2#19133341C211yesmaximal, characteristic, complemented
3#19132985C211yesmaximal, characteristic
4#19132919C211yesmaximal, characteristic, complemented
5#19132915C211yesmaximal, characteristic
6#19132888C211yesmaximal, characteristic, complemented
7C43×#1479C211yesmaximal, characteristic, complemented
8C22×#10621884C411yescharacteristic
9C2×C4×D172C2211yescharacteristic
10C4×#10621884—21no—
11C4×#10621884—21no—
12C4×#10621884—21no—
13C4×#10621884—21no—
14#14582952C2211yescharacteristic
15#14582952C2211yescharacteristic
16C2×#13063256C411yescharacteristic
17C2×#13063249C411yescharacteristic
18C2×#13063245C411yescharacteristic
19C2×C4×C43⋊C8C2211yescharacteristic
20#14582651—21no—
21#14582649—21no—
22#14582626—22no—
23#14582625—22no—
24#14582622—22no—
25#14582621—21no—
26#14582620—21no—
27C2×C4×Q8×C43C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#431C2211yescharacteristic
30C43×Q8⋊C8—22no—
31C22×D172C2×C411yescharacteristic
32C22×C4×D43—21no—
33C2×#10621884—22no—
34C2×#10621884—22no—
35C2×#10621884—21no—
36C2×#10621884—21no—
37C22×C43⋊C8C2×C411yescharacteristic
38C22×C43⋊C8C2×C411yescharacteristic
39C4×D172—21no—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172—21no—
43C2×C4⋊Dic43C2×C411yescharacteristic
44C2×(C2×D43)⋊C4—21no—
45#13063256—21no—
46#13063256—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49#13063249—21no—
50#13063249—21no—
51#13063245—21no—
52#13063245—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)D412yes—
55C4×C43⋊C8—21no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8D411yescharacteristic
58C4×C43⋊C8D411yescharacteristic
59C4×C43⋊C8D411yescharacteristic
60C4×C43⋊C8D411yescharacteristic
61C22×Q8×C43C2×C411yescharacteristic
62C4×Q8×C43—21no—
63C4×Q8×C43—21no—
64C4×Q8×C43—21no—
65C4×Q8×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43C2×C411yescharacteristic
68C2×C42×C43—21no—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43D412yes—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C4×C8×C43—21no—
75C4×C8×C43—21no—
76C23×D43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43M1612yes—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C22×Dic43—21no—
89C2×D172—21no—
90C2×D172—21no—
91C2×D172—21no—
92C2×D172—21no—
93C2×D172—21no—
94C2×D172M1612yes—
95C2×C4×D43—41no—
96C2×C4×D43—41no—
97C2×C4×D43—82no—
98C2×C8×C43—22no—
99C2×C8×C43—41no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C42×C43—41no—
105C42×C43—41no—
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43#4111yescharacteristic
110#10621884—24no—
111#10621884—24no—
112(C2×D43)⋊C4—41no—
113(C2×D43)⋊C4—41no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—21no—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8C22⋊C411yescharacteristic
123C2×C43⋊C8C22⋊C411yescharacteristic
124C2×C43⋊C8C22⋊C411yescharacteristic
125C2×C43⋊C8C22⋊C411yescharacteristic
126C23×C43C4×D411yescharacteristic
127C22×D43—22no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—81no—
131C22×D43—81no—
132Q8×C43—22no—
133Q8×C43—22no—
134Q8×C43—41no—
135Q8×C43—41no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—81no—
143C2×C4×C43C2×C22⋊C411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12411yescharacteristic
148C2×C4×C43#12711yescharacteristic
149C2×C4×C43C2×M1611yescharacteristic
150C2×C4×C43C2×M1611yescharacteristic
151C2×C4×C43#13111yescharacteristic
152C2×C4×C43#13111yescharacteristic
153C2×Dic43—41no—
154C2×Dic43—81no—
155D172—22no—
156D172—22no—
157D172—41no—
158D172—41no—
159C4×D43—82no—
160C4×D43—82no—
161C8×C43—42no—
162C8×C43—81no—
163C43⋊C8—21no—
164C43⋊C8—21no—
165C43⋊C8—21no—
166C43⋊C8—21no—
167C43⋊C8—42no—
168C43⋊C8—81no—
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—42no—
184C4×C43—81no—
185C4×C43#40711yescharacteristic
186C4×C43#40811yescharacteristic
187C4×C43#43511yescharacteristic
188C4×C43#43511yescharacteristic
189C4×C43#47112yes—
190Dic43—81no—
191C2×C4×SD16—431no—
192#1564—431no—
193#1479D4311yescharacteristic, complemented
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×Q8C2×D4311yescharacteristic
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×C8—431no—
219#335—861no—
220#334—861no—
221Q8⋊C8—22no—
222D4⋊C8—862no—
223#324—862no—
224#323—862no—
225#322—861no—
226#322—861no—
227C43#967211yescharacteristic, complemented, Sylow
228C22×Q8C4×D4311yescharacteristic
229C22×D4—431no—
230C23×C4—861no—
231C2×SD16—861no—
232C2×SD16—861no—
233C2×SD16—862no—
234C2×SD16—862no—
235C22×C8—431no—
236C22×C8—431no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—861no—
242C4×D4—861no—
243C4×D4—861no—
244C4×D4—861no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4C4×D4311yescharacteristic
248C2×C22⋊C4—861no—
249C2×C42—21no—
250C2×C42C22×D4311yescharacteristic
251#106—861no—
252#106—861no—
253C4⋊C8—21no—
254C4⋊C8—861no—
255C4⋊C8—861no—
256C4⋊C8C22⋊D4312yes—
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—431no—
268C4×C8—431no—
269C4×C8—431no—
270C4×C8—431no—
271C4×C8—861no—
272C4×C8—861no—
273C24—861no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8#1062187212yes—
280C2×D4—432no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—861no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—861no—
289C22×C4—3442no—
290C22×C4—1721no—
291C22×C4—1721no—
292C22×C4C2×C4×D4311yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4#1062190011yescharacteristic
295SD16—864no—
296SD16—864no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—431no—
300C2×C8—431no—
301C2×C8—431no—
302C2×C8—431no—
303C2×C8—861no—
304C2×C8—861no—
305C2×C8—861no—
306C2×C8—861no—
307C2×C8—862no—
308C2×C8—1721no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C42—41no—
318C42—41no—
319C42#1062189811yescharacteristic
320C42D4×D4311yescharacteristic
321C42D4×D4311yescharacteristic
322C42C2×C22⋊D4311yescharacteristic
323C23—862no—
324C23—3441no—
325C23—3441no—
326C23—1721no—
327C23—1721no—
328C23(C22⋊D43)⋊C411yescharacteristic
329Q8—22no—
330Q8—22no—
331Q8—41no—
332Q8—41no—
333D4—862no—
334D4—862no—
335D4—1721no—
336D4—1721no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—3442no—
345C2×C4—3442no—
346C2×C4—3441no—
347C2×C4—1721no—
348C2×C4C22⋊C4×D4311yescharacteristic
349C2×C4C4×C22⋊D4311yescharacteristic
350C2×C4#1306329711yescharacteristic
351C2×C4#1306329811yescharacteristic
352C2×C4#1306331111yescharacteristic
353C2×C4#1306332111yescharacteristic
354C2×C4M16×D4311yescharacteristic
355C2×C4C2×#1062187211yescharacteristic
356C2×C4#1306333111yescharacteristic
357C2×C4#1306333311yescharacteristic
358C8—42no—
359C8—81no—
360C8—861no—
361C8—861no—
362C8—861no—
363C8—861no—
364C8—3441no—
365C8—1722no—
366C22—21no—
367C22—21no—
368C22—3442no—
369C22—3442no—
370C22—3441no—
371C22—3441no—
372C22—1722no—
373C22#1458279911yescharacteristic
374C22#1458296711yescharacteristic
375C22#1458297311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—81no—
381C4—3441no—
382C4#1458286111yescharacteristic
383C4#1458286411yescharacteristic
384C4#1458296811yescharacteristic
385C4#1458297011yescharacteristic
386C4#1458316412yes—
387C2—21no—
388C2—21no—
389C2—3442no—
390C2#1913539111yescharacteristic
391C2#1913549211yescharacteristic
392C2#1913549711yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1479C2
socleC22×C43#390
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1479D43
hypocenterC43#9672
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #19133341C2semidirect
4. #19132919C2semidirect
6. #19132888C2semidirect
7. C43×#1479C2semidirect
193. #1479D43semidirect
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×#106218842
#191333412
#191329852
#191329192
#191329152
#191328882
C43×#14792
#967243