Finite Group Databasebeta

← #24993382

Subgroups — #24993382

Order 11008.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143636C211yesmaximal, characteristic
2#19134605C211yesmaximal, characteristic
3#19133159C211yesmaximal, characteristic, complemented
4#19132998C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132455C211yesmaximal, characteristic, complemented
7C43×#3077C211yesmaximal, characteristic
8#14582977—22no—
9#14582977—22no—
10#14582952C2211yescharacteristic
11#14582952C2211yescharacteristic
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×#13063246—21no—
14#14582863—22no—
15#14582765C2211yescharacteristic
16#14582661—21no—
17#14582636—22no—
18Q8⋊(C43⋊C8)—22no—
19C43×#533C2211yescharacteristic
20C2×C4×D4×C43C2211yescharacteristic
21C43×#478—22no—
22C43×#476C412yescomplemented
23C43×#474C412yescomplemented
24C43×#428—21no—
25C43×#423C2211yescharacteristic
26C43×#418—21no—
27C2×#10621877—24no—
28C22×C43⋊C8—21no—
29C2×C4⋊Dic43—21no—
30C4⋊(C43⋊C8)—21no—
31C4⋊(C43⋊C8)—21no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34#13063246—42no—
35C22⋊(C43⋊C8)—24no—
36C22⋊(C43⋊C8)—21no—
37C22⋊(C43⋊C8)D412yes—
38C4×C43⋊C8—21no—
39C4×C43⋊C8D412yes—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C22×D4×C43D411yescharacteristic
43C23×C4×C43—21no—
44C2×M16×C43—21no—
45C4⋊Q8×C43C2×C411yescharacteristic
46C4⋊Q8×C43C2×C411yescharacteristic
47#125×C43—21no—
48C22⋊Q8×C43—21no—
49C22⋊Q8×C43—21no—
50C4×Q8×C43—21no—
51C4×Q8×C43—21no—
52C4×D4×C43—21no—
53C4×D4×C43—21no—
54C4×D4×C43C2×C412yes—
55C4×D4×C43D412yes—
56#117×C43—21no—
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C42×C43C2311yescharacteristic
60#107×C43—22no—
61#106×C43—22no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43C2×C412yes—
64#102×C43—22no—
65#102×C43—22no—
66C24×C43—21no—
67C2×Q8×C43—21no—
68C2×Q8×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43C22⋊C412yes—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—21no—
78C22×C4×C43—82no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×Dic43—41no—
83M16×C43—41no—
84M16×C43—41no—
85C2×C8×C43—22no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43C22⋊C412yes—
94C22⋊C4×C43—22no—
95C22⋊C4×C43—22no—
96C22⋊C4×C43—41no—
97C42×C43—41no—
98C42×C43C22×C411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43C2×D411yescharacteristic
101C42×C43#4111yescharacteristic
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104#10621877—84no—
105C2×C43⋊C8—22no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43—22no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43—81no—
114C23×C43—81no—
115C23×C43#12111yescharacteristic
116Q8×C43—42no—
117Q8×C43—81no—
118D4×C43—22no—
119D4×C43—22no—
120D4×C43—41no—
121D4×C43—41no—
122C2×C4×C43—22no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—44no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—82no—
129C2×C4×C43—81no—
130C2×C4×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12311yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43#13711yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C2×Dic43—81no—
141C2×Dic43—81no—
142C2×Dic43—81no—
143C8×C43—42no—
144C43⋊C8—42no—
145C43⋊C8—42no—
146C43⋊C8—81no—
147#9307—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—42no—
151C22×C43—42no—
152C22×C43—42no—
153C22×C43—82no—
154C22×C43—82no—
155C22×C43#38611yescharacteristic
156C22×C43#46811yescharacteristic
157C22×C43#47011yescharacteristic
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—42no—
163C4×C43—81no—
164C4×C43—81no—
165C4×C43#41711yescharacteristic
166C4×C43#41911yescharacteristic
167C4×C43#46811yescharacteristic
168C4×C43#47011yescharacteristic
169Dic43—161no—
170#3077D4311yescharacteristic
171#2975—431no—
172#1804—431no—
173#1518—431no—
174#1481—431no—
175#1301—431no—
176#1286—431no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—82no—
180C2×C43#188111yescharacteristic
181C2×C43#189411yescharacteristic
182C2×C43#190411yescharacteristic
183#533C2×D4311yescharacteristic
184C2×C4×D4C2×D4311yescharacteristic
185#478—22no—
186#476Dic4312yescomplemented
187#474Dic4312yescomplemented
188#436—862no—
189#436—862no—
190#431—431no—
191#431—431no—
192#428—21no—
193#423C2×D4311yescharacteristic
194C2×C4⋊C8—431no—
195#418—21no—
196C2×#102—861no—
197#407—862no—
198#382—431no—
199#340—861no—
200#328—862no—
201Q8⋊C8—862no—
202C43#930711yescharacteristic, complemented, Sylow
203C22×D4C22⋊D4311yescharacteristic
204C23×C4—21no—
205C2×M16—21no—
206C2×M16—864no—
207C22×C8—861no—
208C4⋊Q8C2×Dic4311yescharacteristic
209C4⋊Q8C2×Dic4311yescharacteristic
210#125—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×D4—21no—
216C4×D4—21no—
217C4×D4C2×Dic4312yes—
218C4×D4C22⋊D4312yes—
219#117—21no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C22⋊D4311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C42C22×D4311yescharacteristic
224#107—22no—
225#106—22no—
226C4⋊C8—21no—
227C4⋊C8—861no—
228C4⋊C8—861no—
229C4⋊C8—861no—
230C4⋊C8—861no—
231C4⋊C8C2×Dic4312yes—
232#102—22no—
233#102—22no—
234#102—1722no—
235C22⋊C8—432no—
236C22⋊C8—864no—
237C22⋊C8—861no—
238C4×C8—432no—
239C4×C8—861no—
240#95—861no—
241#95—861no—
242C24—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4C22⋊Dic4312yes—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—82no—
255C22×C4—1721no—
256C22×C4D4×D4311yescharacteristic
257C22×C4#1062190011yescharacteristic
258C22×C4C2×C22⋊D4311yescharacteristic
259M16—41no—
260M16—41no—
261M16—3444no—
262C2×C8—22no—
263C2×C8—862no—
264C2×C8—862no—
265C2×C8—1721no—
266C2×C8—1721no—
267C2×C8—1721no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—1721no—
276C4⋊C4—1721no—
277C4⋊C4C22⋊Dic4312yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—41no—
281C42—41no—
282C42D4×D4311yescharacteristic
283C42#1062190011yescharacteristic
284C42C22×Dic4311yescharacteristic
285C42C2×C22⋊D4311yescharacteristic
286C23—22no—
287C23—41no—
288C23—41no—
289C23—81no—
290C23—81no—
291C23#1306329711yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—22no—
295D4—22no—
296D4—41no—
297D4—41no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—44no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—82no—
305C2×C4—81no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4—3441no—
309C2×C4C2×C22⋊Dic4311yescharacteristic
310C2×C4D4×Dic4311yescharacteristic
311C2×C4D4×Dic4311yescharacteristic
312C2×C4#1306329311yescharacteristic
313C2×C4#1306329711yescharacteristic
314C2×C4#1306330611yescharacteristic
315C2×C4#1306335011yescharacteristic
316C2×C4#1306335511yescharacteristic
317C2×C4#1306335611yescharacteristic
318C2×C4#1306335611yescharacteristic
319C8—42no—
320C8—3441no—
321C8—1722no—
322C8—1722no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22#1458277911yescharacteristic
331C22#1458314711yescharacteristic
332C22#1458315511yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—81no—
340C4—6881no—
341C4#1458290011yescharacteristic
342C4#1458290811yescharacteristic
343C4#1458314711yescharacteristic
344C4#1458315511yescharacteristic
345C2—21no—
346C2—21no—
347C2—82no—
348C2#1913495911yescharacteristic
349C2#1913502911yescharacteristic
350C2#1913508411yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3077C2
socleC22×C43#386
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#3077D43
hypocenterC43#9307
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
3. #19133159C2semidirect
4. #19132998C2semidirect
5. #19132490C2semidirect
6. #19132455C2semidirect
22. C43×#476C4semidirect
23. C43×#474C4semidirect
186. #476Dic43semidirect
187. #474Dic43semidirect
202. C43#9307semidirect

Maximal subgroups

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

subgroupindex
#191436362
#191346052
#191331592
#191329982
#191324902
#191324552
C43×#30772
#930743