Finite Group Databasebeta

← #25015940

Subgroups — #25015940

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583274C211yesmaximal, characteristic
2C2×#14582701C211yesmaximal, characteristic, complemented
3C2×#14582700C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5#19135329C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C2×C43×#357C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C22×#10621882—21no—
10C2×#13063321—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583274—22no—
13#14583274—22no—
14C2×#13063259C2211yescharacteristic
15C2×C8×Dic43C2211yescharacteristic
16#14582798—21no—
17#14582701—22no—
18#14582700—22no—
19#14582699—22no—
20#14582661—21no—
21C22×D8×C43C2211yescharacteristic
22C22×C16×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C43×#357—22no—
25C22×D172—21no—
26C22×C22⋊D43—41no—
27C22×C22⋊D43—41no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344D412yes—
34C2×#10621882—24no—
35C2×#10621882—42no—
36C2×#10621882—42no—
37C22×C43⋊C8D411yescharacteristic
38#13063321—24no—
39#13063321—42no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—41no—
42C2×C4×Dic43D411yescharacteristic
43C2×C43⋊C16—21no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46#13063259—21no—
47#13063259—21no—
48C8×Dic43—21no—
49C8×Dic43—21no—
50C43⋊#95—41no—
51C22×D4×C43—21no—
52C2×D8×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43—21no—
56C2×D8×C43—21no—
57C2×D8×C43D412yes—
58C22×C8×C43C2311yescharacteristic
59C2×C4⋊C4×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63#107×C43—21no—
64#107×C43D412yescomplemented
65C24×C43—41no—
66C23×D43—41no—
67C2×D4×C43—22no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43C2×D411yescharacteristic
75C2×C22⋊D43—44no—
76C2×C22⋊D43—44no—
77C2×C22⋊D43—82no—
78C2×C22⋊D43—82no—
79C2×C22⋊D43—82no—
80C2×C22⋊D43—82no—
81C22×Dic43—41no—
82C22×Dic43D811yescharacteristic
83C22×Dic43D811yescharacteristic
84C2×D172—22no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90D8×C43—22no—
91D8×C43—22no—
92D8×C43—41no—
93D8×C43—41no—
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43C2×D411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43#4111yescharacteristic
98C2×C8×C43#4111yescharacteristic
99C2×C8×C43#4111yescharacteristic
100C4⋊C4×C43—22no—
101C4⋊C4×C43—41no—
102#10621882—48no—
103C4⋊Dic43—41no—
104C4⋊Dic43—41no—
105C4⋊Dic43—82no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C2×C43⋊C8—21no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8SD1612yes—
111D344—22no—
112D344—22no—
113D344—41no—
114D344—41no—
115C16×C43—41no—
116C43⋊C16—41no—
117C23×C43—42no—
118C23×C43—81no—
119C23×C43—81no—
120C23×C43—81no—
121C23×C43—81no—
122C23×C43—81no—
123C23×C43—81no—
124C23×C43C2×D811yescharacteristic
125C22×D43—42no—
126C22×D43—81no—
127C22×D43—81no—
128C22×D43—81no—
129C22×D43—81no—
130C22×D43—81no—
131C22×D43—81no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—81no—
135D4×C43—81no—
136C2×C4×C43—42no—
137C2×C4×C43—81no—
138C2×C4×C43—81no—
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12411yescharacteristic
142C2×C4×C43C2×SD1611yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C22⋊D43—88no—
146C22⋊D43—88no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154C2×Dic43D1612yes—
155C2×Dic43SD3212yes—
156D172—42no—
157D172—42no—
158D172—81no—
159D172—81no—
160C8×C43#12111yescharacteristic
161C8×C43#12111yescharacteristic
162C8×C43#12311yescharacteristic
163C8×C43#12311yescharacteristic
164C43⋊C8—22no—
165#13407—431nomaximal, Sylow
166C22×C43—82no—
167C22×C43—82no—
168C22×C43—82no—
169C22×C43—161no—
170C22×C43—161no—
171C22×C43—161no—
172C22×C43—161no—
173C22×C43#44711yescharacteristic
174C22×C43#45911yescharacteristic
175C22×C43#48611yescharacteristic
176C22×C43C2×D1611yescharacteristic
177C22×C43C2×SD3211yescharacteristic
178C22×C43#50911yescharacteristic
179C22×C43#50911yescharacteristic
180C2×D43—82no—
181C2×D43—82no—
182C2×D43—82no—
183C2×D43—161no—
184C2×D43—161no—
185C2×D43—161no—
186C2×D43—161no—
187C4×C43—82no—
188C4×C43#39411yescharacteristic
189C4×C43#45011yescharacteristic
190C4×C43#46011yescharacteristic
191C4×C43#49011yescharacteristic
192Dic43—22no—
193Dic43—22no—
194Dic43—161no—
195C2×#493—431no—
196C2×#357—431no—
197C2×#357—431no—
198C2×#357—431no—
199C2×#357D4311yescharacteristic, complemented
200#1942—431no—
201#1374—431no—
202C2×C43—162no—
203C2×C43#204111yescharacteristic
204C2×C43#218411yescharacteristic
205C2×C43#218711yescharacteristic
206C2×C43#220611yescharacteristic
207C2×C43#220711yescharacteristic
208C2×C43#224011yescharacteristic
209C2×C43#224411yescharacteristic
210D43—162no—
211C22×D8—431no—
212C22×D8—861no—
213C22×D8C2×D4311yescharacteristic
214C2×#127—861no—
215C22×C16—431no—
216C22×C16C2×D4311yescharacteristic
217#493—862no—
218#493—862no—
219C2×#107—431no—
220C2×#107C2×D4311yescharacteristic
221C2×C4×C8—431no—
222#389—861no—
223#357—22no—
224#357—862no—
225#357—862no—
226#357—862no—
227#340—861no—
228C43#1340711yescharacteristic, complemented, Sylow
229C22×D4—21no—
230C22×D4—861no—
231C22×D4—1721no—
232C22×D4—1721no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—432no—
239C2×D8—864no—
240C2×D8—861no—
241C2×D8—861no—
242C2×D8—861no—
243C2×D8—861no—
244C2×D8—861no—
245C2×D8—1722no—
246C2×D8—1722no—
247C2×D8D17212yes—
248C22×C8—431no—
249C22×C8C22×D4311yescharacteristic
250#127—864no—
251#127—1722no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—1721no—
255C2×C42—431no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16—861no—
260C2×C16—861no—
261C2×C16—861no—
262#107—21no—
263#107—861no—
264#107—861no—
265#107C22⋊D4312yescomplemented
266C4×C8—861no—
267C4×C8—861no—
268#95—1721no—
269C24—41no—
270C24—1721no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—862no—
278C2×D4—3442no—
279C2×D4—3442no—
280C2×D4—3442no—
281C2×D4—3442no—
282C2×D4—1724no—
283C2×D4—1724no—
284C2×D4—1721no—
285C2×D4—1721no—
286C2×D4—1721no—
287C2×D4—1721no—
288C2×D4—1721no—
289C22×C4—41no—
290C22×C4—431no—
291C22×C4—431no—
292C22×C4—1721no—
293C22×C4D4×D4311yescharacteristic
294D8—22no—
295D8—22no—
296D8—41no—
297D8—41no—
298D8—862no—
299D8—862no—
300D8—1728no—
301D8—1721no—
302D8—1721no—
303C2×C8—432no—
304C2×C8—861no—
305C2×C8—861no—
306C2×C8C2×D17211yescharacteristic
307C2×C8#1062189811yescharacteristic
308C2×C8D4×D4311yescharacteristic
309C2×C8#1062190011yescharacteristic
310C2×C8#1062190011yescharacteristic
311C2×C8C2×C22⋊D4311yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—3442no—
315C4⋊C4—1721no—
316C4⋊C4—1721no—
317C42—861no—
318C42—861no—
319C16—41no—
320C16—1721no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—3441no—
329C23—3441no—
330C23—3441no—
331C23—3441no—
332C23—3441no—
333C23—3441no—
334C23—1722no—
335C23D8×D4311yescharacteristic
336D4—42no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—3448no—
341D4—3448no—
342D4—3441no—
343D4—3441no—
344D4—1722no—
345D4—1722no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—432no—
350C2×C4—432no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—3441no—
358C2×C4#1306329511yescharacteristic
359C2×C4#1306329711yescharacteristic
360C2×C4#1306331111yescharacteristic
361C2×C4SD16×D4311yescharacteristic
362C2×C4#1306334911yescharacteristic
363C2×C4#1306335211yescharacteristic
364C8—862no—
365C8#1306329611yescharacteristic
366C8#1306329911yescharacteristic
367C8#1306330711yescharacteristic
368C8#1306330911yescharacteristic
369C22—82no—
370C22—82no—
371C22—82no—
372C22—161no—
373C22—161no—
374C22—161no—
375C22—161no—
376C22—3442no—
377C22—3442no—
378C22—3442no—
379C22—6881no—
380C22—6881no—
381C22—6881no—
382C22—6881no—
383C22#1458303411yescharacteristic
384C22#1458309211yescharacteristic
385C22#1458324411yescharacteristic
386C22D16×D4311yescharacteristic
387C22SD32×D4311yescharacteristic
388C22#1458333311yescharacteristic
389C22#1458333611yescharacteristic
390C4—82no—
391C4—862no—
392C4—862no—
393C4—6881no—
394C4#1458281511yescharacteristic
395C4#1458305111yescharacteristic
396C4#1458309711yescharacteristic
397C4#1458326211yescharacteristic
398C2—162no—
399C2—6882no—
400C2#1913582811yescharacteristic
401C2#1913650811yescharacteristic
402C2#1913652511yescharacteristic
403C2#1913662811yescharacteristic
404C2#1913663311yescharacteristic
405C2#1913681711yescharacteristic
406C2#1913683511yescharacteristic
subgroupG/H
centerC23D8×D43
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC2×C43×#357C2
socleC23×C43C2×D8
prime radicalC2×#14583274C2
hypercenterC2×#357D43
hypocenterC43#13407
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#14582701C2semidirect
3. C2×#14582700C2semidirect
4. C2×#14582699C2semidirect
5. #19135329C2semidirect
6. #19132672C2semidirect
7. C2×C43×#357C2semidirect
64. #107×C43D4semidirect
199. C2×#357D43semidirect
228. C43#13407semidirect
265. #107C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832742
C2×#145827012
C2×#145827002
C2×#145826992
#191353292
#191326722
C2×C43×#3572
#1340743