Finite Group Databasebeta

← #25013656

Subgroups — #25013656

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic43C211yesmaximal, characteristic, complemented
2C2×#14582700C211yesmaximal, characteristic, complemented
3C2×#14582700C211yesmaximal, characteristic, complemented
4#19135462C211yesmaximal, characteristic, complemented
5#19132687C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C22×D16×C43C211yesmaximal, characteristic
8C2×D4×Dic43—21no—
9C22×C43⋊C16C2211yescharacteristic
10D8×Dic43—22no—
11D8×Dic43—22no—
12C2×#13063259C2211yescharacteristic
13C2×#13063259C2211yescharacteristic
14C2×#13063246—21no—
15C2×#13063246—21no—
16C2×C8×Dic43C2211yescharacteristic
17#14582802—21no—
18#14582700—22no—
19#14582700—22no—
20C22×D8×C43C2211yescharacteristic
21C22×D8×C43C2211yescharacteristic
22C2×D16×C43—22no—
23C2×D16×C43—22no—
24C2×D16×C43C414yescomplemented
25C22×C16×C43C2211yescharacteristic
26C23×Dic43—41no—
27C22×C43⋊C8D411yescharacteristic
28D4×Dic43—24no—
29D4×Dic43—42no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C22⋊Dic43—41no—
33C2×C22⋊Dic43—41no—
34C2×C22⋊Dic43—41no—
35C2×C4×Dic43D411yescharacteristic
36C2×C43⋊C16—21no—
37C2×C43⋊C16—21no—
38C2×C43⋊C16—21no—
39#13063259—21no—
40#13063259—21no—
41#13063259—21no—
42#13063259D412yes—
43#13063246—24no—
44#13063246—42no—
45C8×Dic43—21no—
46C8×Dic43—21no—
47C22×D4×C43—21no—
48C22×D4×C43—21no—
49C2×D8×C43—21no—
50C2×D8×C43—21no—
51C2×D8×C43—21no—
52C2×D8×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43—21no—
56C2×D8×C43—21no—
57C2×D8×C43C2×C412yes—
58C2×D8×C43C2×C412yescomplemented
59C2×D8×C43D412yes—
60C2×D8×C43D412yes—
61C22×C8×C43C2311yescharacteristic
62D16×C43—28no—
63C2×C16×C43—21no—
64C2×C16×C43—21no—
65C2×C16×C43C2×C412yescomplemented
66C24×C43—41no—
67C24×C43—41no—
68C2×D4×C43—22no—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C2×D4×C43—41no—
80C22×C4×C43C2×D411yescharacteristic
81C22×Dic43—44no—
82C22×Dic43—41no—
83C22×Dic43—41no—
84C22×Dic43—82no—
85C22×Dic43—82no—
86C22×Dic43D811yescharacteristic
87C22×Dic43D811yescharacteristic
88D8×C43—22no—
89D8×C43—22no—
90D8×C43—22no—
91D8×C43—22no—
92D8×C43—22no—
93D8×C43—41no—
94D8×C43—41no—
95D8×C43C22⋊C414yescomplemented
96C2×C8×C43C22×C411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C2×C8×C43#4111yescharacteristic
102C22⋊Dic43—44no—
103C22⋊Dic43—82no—
104C22⋊Dic43—82no—
105C4⋊Dic43—22no—
106C4⋊Dic43—41no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C4×Dic43—21no—
110C4×Dic43—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8—21no—
114C16×C43—22no—
115C43⋊C16—41no—
116C23×C43—42no—
117C23×C43—42no—
118C23×C43—42no—
119C23×C43—42no—
120C23×C43—81no—
121C23×C43—81no—
122C23×C43—81no—
123C23×C43—81no—
124C23×C43—81no—
125C23×C43—81no—
126C23×C43—81no—
127C23×C43—81no—
128C23×C43—81no—
129C23×C43—81no—
130C23×C43C2×D811yescharacteristic
131D4×C43—24no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—42no—
136D4×C43—42no—
137D4×C43—81no—
138D4×C43—81no—
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43#12011yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—42no—
151C2×Dic43—88no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154C2×Dic43—81no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157C2×Dic43D1612yescomplemented
158C8×C43C2×C22⋊C411yescharacteristic
159C8×C43C4×D411yescharacteristic
160C8×C43#12111yescharacteristic
161C8×C43#12311yescharacteristic
162C43⋊C8—41no—
163#13012—431nomaximal, Sylow
164C22×C43—44no—
165C22×C43—82no—
166C22×C43—82no—
167C22×C43—82no—
168C22×C43—82no—
169C22×C43—82no—
170C22×C43—82no—
171C22×C43—82no—
172C22×C43—82no—
173C22×C43—82no—
174C22×C43—161no—
175C22×C43—161no—
176C22×C43—161no—
177C22×C43—161no—
178C22×C43C4×D811yescharacteristic
179C22×C43#44711yescharacteristic
180C22×C43#45911yescharacteristic
181C22×C43C2×D1611yescharacteristic
182C22×C43#50811yescharacteristic
183C22×C43#50911yescharacteristic
184C22×C43#50911yescharacteristic
185C4×C43#38611yescharacteristic
186C4×C43#44211yescharacteristic
187C4×C43#44911yescharacteristic
188C4×C43#46311yescharacteristic
189Dic43—22no—
190Dic43—41no—
191Dic43—82no—
192Dic43—161no—
193C22×D16D4311yescharacteristic
194C2×C4×D8—431no—
195C2×#357—431no—
196C2×#357—431no—
197#1970—431no—
198#1380—431no—
199#1374—431no—
200C2×C43—84no—
201C2×C43—162no—
202C2×C43#187911yescharacteristic
203C2×C43C4×D1611yescharacteristic
204C2×C43#217711yescharacteristic
205C2×C43#218411yescharacteristic
206C2×C43#218611yescharacteristic
207C2×C43#220611yescharacteristic
208C2×C43#221011yescharacteristic
209C22×D8C2×D4311yescharacteristic
210C22×D8C2×D4311yescharacteristic
211C2×C4×D4—861no—
212C2×D16—22no—
213C2×D16—22no—
214C2×D16Dic4314yescomplemented
215C22×C16—431no—
216C22×C16C2×D4311yescharacteristic
217C4×D8—862no—
218C4×D8—862no—
219C2×#107—431no—
220C2×#107—431no—
221C2×#102—861no—
222C2×#102—861no—
223C2×C4×C8—431no—
224#390—861no—
225#357—862no—
226#357—862no—
227C43#1301211yescharacteristic, complemented, Sylow
228C22×D4—21no—
229C22×D4—21no—
230C23×C4—1721no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8C2×Dic4312yes—
240C2×D8C2×Dic4312yescomplemented
241C2×D8C22⋊D4312yes—
242C2×D8C22⋊D4312yes—
243C22×C8—431no—
244C22×C8C22×D4311yescharacteristic
245C4×D4—864no—
246C4×D4—1722no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C22⋊C4—1721no—
250C2×C22⋊C4—1721no—
251C2×C22⋊C4—1721no—
252C2×C42—431no—
253D16—28no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—861no—
257C2×C16—861no—
258C2×C16—861no—
259C2×C16C2×Dic4312yescomplemented
260#107—432no—
261#107—861no—
262#107—861no—
263#107—861no—
264#102—864no—
265#102—1722no—
266C4×C8—861no—
267C4×C8—861no—
268C24—41no—
269C24—41no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—3442no—
285C22×C4—3442no—
286C22×C4—1724no—
287C22×C4—1721no—
288C22×C4—1721no—
289C22×C4D4×D4311yescharacteristic
290D8—22no—
291D8—22no—
292D8—22no—
293D8—22no—
294D8—22no—
295D8—41no—
296D8—41no—
297D8C22⋊Dic4314yescomplemented
298C2×C8—861no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8D4×D4311yescharacteristic
302C2×C8#1062190011yescharacteristic
303C2×C8#1062190011yescharacteristic
304C2×C8C22×Dic4311yescharacteristic
305C2×C8C2×C22⋊D4311yescharacteristic
306C2×C8C2×C22⋊D4311yescharacteristic
307C4⋊C4—862no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C22⋊C4—3442no—
312C22⋊C4—3442no—
313C22⋊C4—1724no—
314C42—861no—
315C42—861no—
316C16—22no—
317C16—1721no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23D8×D4311yescharacteristic
333D4—24no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—81no—
340D4—81no—
341C2×C4—432no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—3448no—
348C2×C4—3441no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—3441no—
353C2×C4—1722no—
354C2×C4D4×Dic4311yescharacteristic
355C2×C4#1306329311yescharacteristic
356C2×C4#1306329711yescharacteristic
357C2×C4#1306334411yescharacteristic
358C2×C4#1306334911yescharacteristic
359C2×C4#1306334911yescharacteristic
360C8—1721no—
361C8C2×C22⋊Dic4311yescharacteristic
362C8D4×Dic4311yescharacteristic
363C8#1306329711yescharacteristic
364C8#1306330611yescharacteristic
365C22—44no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—82no—
373C22—82no—
374C22—82no—
375C22—161no—
376C22—161no—
377C22—161no—
378C22—161no—
379C22D8×Dic4311yescharacteristic
380C22#1458303111yescharacteristic
381C22#1458309211yescharacteristic
382C22D16×D4311yescharacteristic
383C22#1458332811yescharacteristic
384C22#1458333311yescharacteristic
385C22#1458333311yescharacteristic
386C4—862no—
387C4—3442no—
388C4—1721no—
389C4—6881no—
390C4#1458277911yescharacteristic
391C4#1458301111yescharacteristic
392C4#1458304111yescharacteristic
393C4#1458311211yescharacteristic
394C2—84no—
395C2—162no—
396C2#1913494511yescharacteristic
397C2D16×Dic4311yescharacteristic
398C2#1913647111yescharacteristic
399C2#1913650511yescharacteristic
400C2#1913651511yescharacteristic
401C2#1913662811yescharacteristic
402C2#1913664811yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC22×D16×C43C2
socleC23×C43C2×D8
cosocleC22×C8×C43C23
hypercenterC22×D16D43
hypocenterC43#13012
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×Dic43C2semidirect
2. C2×#14582700C2semidirect
3. C2×#14582700C2semidirect
4. #19135462C2semidirect
5. #19132687C2semidirect
6. #19132672C2semidirect
24. C2×D16×C43C4semidirect
58. C2×D8×C43C2×C4semidirect
65. C2×C16×C43C2×C4semidirect
95. D8×C43C22⋊C4semidirect
157. C2×Dic43D16semidirect
214. C2×D16Dic43semidirect
227. C43#13012semidirect
240. C2×D8C2×Dic43semidirect
259. C2×C16C2×Dic43semidirect
297. D8C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic432
C2×#145827002
#191354622
#191326872
#191326722
C22×D16×C432
#1301243