Finite Group Databasebeta

← #24999424

Subgroups — #24999424

Order 11008.

570 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583304C211yesmaximal, characteristic
2C2×#14583295C211yesmaximal, characteristic
3C2×#14583251C211yesmaximal, characteristic
4#19135555C211yesmaximal, characteristic
5#19135396C211yesmaximal, characteristic
6C43⋊#1273C211yesmaximal, characteristic
7C43×#1956C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×#13063325C2211yescharacteristic
10#14583304—22no—
11#14583304—22no—
12#14583295—22no—
13#14583295—22no—
14#14583251—22no—
15#14583251—22no—
16C2×#13063259—22no—
17C2×#13063256—22no—
18C2×#13063248—22no—
19C2×#13063248—22no—
20C2×C4×C43⋊C8C2211yescharacteristic
21C2×C4×C43⋊C8C2211yescharacteristic
22#14582661—22no—
23C2×C4⋊Q8×C43C2211yescharacteristic
24C2×#103×C43—22no—
25C2×C4×C8×C43C2211yescharacteristic
26C43×#384C2211yescharacteristic
27C22×Dic86—21no—
28C22×Dic86—21no—
29C22×C43⋊C8D412yes—
30C22×C43⋊C8D412yes—
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325—21no—
37#13063325D412yes—
38#13063325D412yes—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43#13063259—28no—
44#13063256—28no—
45#13063248—28no—
46#13063248—44no—
47C4×C43⋊C8—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C4×C43⋊C8—21no—
51C22×Q8×C43—21no—
52C22×C8×C43D412yes—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43D412yes—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C42×C43C2311yescharacteristic
63#103×C43—44no—
64C4×C8×C43—21no—
65C4×C8×C43—21no—
66C2×Q8×C43—22no—
67C2×Q8×C43—41no—
68C2×Q8×C43—42no—
69C2×Q8×C43—42no—
70C22×C4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—41no—
76C22×Dic43—41no—
77C2×Dic86—22no—
78C2×Dic86—22no—
79C2×Dic86—42no—
80C2×Dic86—42no—
81C2×Dic86—42no—
82C2×Dic86—42no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×C8×C43—22no—
86C2×C8×C43—22no—
87C2×C8×C43SD1614yes—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—42no—
93C4⋊C4×C43—42no—
94C4⋊C4×C43—42no—
95C42×C43C2×D411yescharacteristic
96C42×C43C2×D411yescharacteristic
97C42×C43C2×D411yescharacteristic
98C42×C43#4111yescharacteristic
99C4⋊Dic43—22no—
100C4⋊Dic43—22no—
101C4⋊Dic43—22no—
102C4⋊Dic43—22no—
103C4⋊Dic43—41no—
104C4⋊Dic43—41no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8Q1614yes—
113C23×C43#12711yescharacteristic
114Q8×C43—44no—
115Q8×C43—82no—
116C2×C4×C43—42no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43#12011yescharacteristic
123C2×C4×C43#12011yescharacteristic
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43#12111yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43C2×SD1612yes—
129C2×C4×C43C2×Q1612yes—
130C2×C4×C43#13512yes—
131C2×C4×C43AGL(1,ℤ/8)12yes—
132C2×C4×C43#13712yes—
133C2×C4×C43#13712yes—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—81no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140Dic86—44no—
141Dic86—44no—
142Dic86—82no—
143Dic86—82no—
144C8×C43—24no—
145C43⋊C8—24no—
146C43⋊C8—42no—
147#10314—431nomaximal, Sylow
148C22×C43#39211yescharacteristic
149C22×C43#49211yescharacteristic
150C22×C43#49411yescharacteristic
151C22×C43#49511yescharacteristic
152C22×C43#49611yescharacteristic
153C22×C43#49711yescharacteristic
154C22×C43#49711yescharacteristic
155C4×C43—82no—
156C4×C43—161no—
157C4×C43#44812yes—
158C4×C43#44912yes—
159C4×C43#45112yes—
160C4×C43#46112yes—
161C4×C43#46212yes—
162C4×C43#46312yes—
163Dic43—82no—
164Dic43—82no—
165C2×#500—431no—
166C2×#498—431no—
167C2×#487—431no—
168#1990—431no—
169#1956—431no—
170#1956D4311yescharacteristic
171#1273—431no—
172C2×C43#170711yescharacteristic
173C2×C43#171411yescharacteristic
174C2×C43#171811yescharacteristic
175C2×C43#172311yescharacteristic
176C2×C43#201211yescharacteristic
177C2×C43#201311yescharacteristic
178C2×C43#201611yescharacteristic
179C2×C4⋊Q8—431no—
180C2×C4⋊Q8—431no—
181C2×C4⋊Q8C2×D4311yescharacteristic
182#500—862no—
183#500—862no—
184#498—862no—
185#498—862no—
186#487—862no—
187#487—862no—
188C2×#107—862no—
189C2×#106—862no—
190C2×#103—22no—
191C2×#103—862no—
192C2×#103—862no—
193C2×C4×C8—431no—
194C2×C4×C8—431no—
195C2×C4×C8C2×D4311yescharacteristic
196#384C2×D4311yescharacteristic
197#340—862no—
198C43#1031411yescharacteristic, complemented, Sylow
199C22×Q8—21no—
200C22×Q8—861no—
201C22×Q8—861no—
202C22×C8—432no—
203C22×C8—432no—
204C22×C8C22⋊D4312yes—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—432no—
209C4⋊Q8—432no—
210C4⋊Q8—861no—
211C4⋊Q8—861no—
212C4⋊Q8—861no—
213C4⋊Q8—861no—
214C4⋊Q8—861no—
215C4⋊Q8—861no—
216C4⋊Q8D17212yes—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C42C22×D4311yescharacteristic
227#107—868no—
228#106—868no—
229#103—44no—
230#103—868no—
231#103—1724no—
232C4×C8—21no—
233C4×C8—21no—
234C4×C8—861no—
235C4×C8—861no—
236C4×C8—861no—
237C4×C8—861no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—862no—
243C2×Q8—862no—
244C2×Q8—1722no—
245C2×Q8—1722no—
246C2×Q8—1722no—
247C2×Q8—1722no—
248C2×Q8—1721no—
249C2×Q8—1721no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—1721no—
253C22×C4—1721no—
254C22×C4D4×D4311yescharacteristic
255C22×C4D4×D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—434no—
260C2×C8—862no—
261C2×C8—862no—
262C2×C8—862no—
263C2×C8—862no—
264C2×C8—862no—
265C2×C8#1062188314yes—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—862no—
274C4⋊C4—862no—
275C4⋊C4—862no—
276C4⋊C4—862no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C42C2×D17211yescharacteristic
282C42#1062189811yescharacteristic
283C42D4×D4311yescharacteristic
284C42D4×D4311yescharacteristic
285C23#1306332111yescharacteristic
286Q8—44no—
287Q8—82no—
288Q8—3442no—
289Q8—3442no—
290Q8—1724no—
291Q8—1724no—
292C2×C4—42no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—3441no—
299C2×C4—3441no—
300C2×C4—3441no—
301C2×C4—3441no—
302C2×C4—1722no—
303C2×C4—1722no—
304C2×C4#1306329311yescharacteristic
305C2×C4#1306329511yescharacteristic
306C2×C4#1306329511yescharacteristic
307C2×C4#1306329811yescharacteristic
308C2×C4#1306329811yescharacteristic
309C2×C4#1306329911yescharacteristic
310C2×C4C2×#1062188312yes—
311C2×C4Q16×D4312yes—
312C2×C4#1306334812yes—
313C2×C4#1306335212yes—
314C2×C4#1306335412yes—
315C2×C4#1306335512yes—
316C8—24no—
317C8—864no—
318C8—1722no—
319C22#1458280811yescharacteristic
320C22#1458327111yescharacteristic
321C22#1458327711yescharacteristic
322C22#1458328411yescharacteristic
323C22#1458328511yescharacteristic
324C22#1458329011yescharacteristic
325C22#1458329411yescharacteristic
326C4—82no—
327C4—161no—
328C4—3442no—
329C4—3442no—
330C4#1458303712yes—
331C4#1458304712yes—
332C4#1458305612yes—
333C4#1458310412yes—
334C4#1458310812yes—
335C4#1458311712yes—
336C2#1913418911yescharacteristic
337C2#1913421411yescharacteristic
338C2#1913424411yescharacteristic
339C2#1913427511yescharacteristic
340C2#1913567311yescharacteristic
341C2#1913567711yescharacteristic
342C2#1913569611yescharacteristic
subgroupG/H
centerC23#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1956C2
socle, prime radicalC23×C43#127
hypercenter#1956D43
hypocenterC43#10314
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
198. C43#10314semidirect

Maximal subgroups

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

subgroupindex
C2×#145833042
C2×#145832952
C2×#145832512
#191355552
#191353962
C43⋊#12732
C43×#19562
#1031443