Finite Group Databasebeta

← #24989574

Subgroups — #24989574

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134633C211yesmaximal, characteristic, complemented
2#19134624C211yesmaximal, characteristic, complemented
3#19133138C212yesmaximal
4#19132500C212yesmaximal, complemented
5C43×#2929C211yesmaximal, characteristic
6C2×#13063261—21no—
7C2×#13063259—21no—
8#14582863C2212yes—
9#14582759C2212yes—
10#14582664—21no—
11#14582662—21no—
12#14582636—22no—
13#14582633—22no—
14C2×#131×C43C411yescharacteristic, complemented
15C23×C8×C43C2211yescharacteristic
16C43×#525C2211yescharacteristic
17C43×#435—21no—
18C43×#435—21no—
19C8×D4×C43—21no—
20C8×D4×C43—21no—
21C43×#424C411yescharacteristic, complemented
22C43×#408C411yescharacteristic, complemented
23C43×#407C2211yescharacteristic
24C43×#405C411yescharacteristic, complemented
25C2×#10621877—22no—
26C2×C4⋊Dic43—22no—
27C2×C22⋊Dic43—22no—
28#13063261—42no—
29#13063259—42no—
30C22⋊(C43⋊C8)—22no—
31C22⋊(C43⋊C8)—22no—
32C43⋊#95—22no—
33C2×#41×C43C2×C411yescharacteristic
34C23×C4×C43C2311yescharacteristic
35#131×C43—42no—
36C2×M16×C43—21no—
37C2×M16×C43C2×C411yescharacteristic
38C2×M16×C43C2×C411yescharacteristic
39C22×C8×C43—21no—
40C22×C8×C43—42no—
41C22×C8×C43C2×C411yescharacteristic
42C22×C8×C43C2×C411yescharacteristic
43C22×C8×C43D411yescharacteristic
44C22×C8×C43D411yescharacteristic
45C22×C8×C43D411yescharacteristic
46C22×C8×C43D411yescharacteristic
47#123×C43—21no—
48C22⋊Q8×C43D411yescharacteristic
49C22⋊Q8×C43Q811yescharacteristic
50#121×C43D411yescharacteristic
51#121×C43Q811yescharacteristic
52#120×C43—21no—
53C4×D4×C43—21no—
54C4×D4×C43—21no—
55#117×C43C2×C411yescharacteristic
56C4⋊C8×C43—21no—
57C4⋊C8×C43—21no—
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62#97×C43—21no—
63C4×C8×C43—21no—
64C24×C43#4111yescharacteristic
65#41×C43—41no—
66#41×C43—41no—
67C2×Q8×C43C4⋊C411yescharacteristic
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43C4⋊C411yescharacteristic
72C22×C4×C43—21no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×Q811yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×Dic43—42no—
82M16×C43—42no—
83M16×C43—41no—
84M16×C43—41no—
85C2×C8×C43—22no—
86C2×C8×C43—22no—
87C2×C8×C43—22no—
88C2×C8×C43—21no—
89C2×C8×C43—21no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—42no—
94C2×C8×C43C22⋊C411yescharacteristic
95C2×C8×C43C22⋊C411yescharacteristic
96C2×C8×C43C22⋊C411yescharacteristic
97C2×C8×C43C22⋊C411yescharacteristic
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43C4⋊C411yescharacteristic
101C4⋊C4×C43C4⋊C411yescharacteristic
102C22⋊C4×C43—21no—
103C22⋊C4×C43—21no—
104C22⋊C4×C43—21no—
105C22⋊C4×C43—21no—
106C22⋊C4×C43—21no—
107C42×C43—21no—
108C22⋊Dic43—82no—
109C4⋊Dic43—42no—
110C4⋊Dic43—42no—
111#10621877—42no—
112#10621877—42no—
113C2×C43⋊C8—42no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43#11711yescharacteristic
120C23×C43#12111yescharacteristic
121C23×C43C22⋊Q811yescharacteristic
122Q8×C43—41no—
123D4×C43—41no—
124D4×C43—42no—
125D4×C43—42no—
126D4×C43—41no—
127D4×C43—41no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43C2×C22⋊C411yescharacteristic
143C2×C4×C43C2×C4⋊C411yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43C22⋊Q811yescharacteristic
146C2×Dic43—82no—
147C2×Dic43—82no—
148C2×Dic43—82no—
149C8×C43—21no—
150C8×C43—21no—
151C8×C43—21no—
152C8×C43—41no—
153C8×C43—41no—
154C8×C43#9912yes—
155C43⋊C8—82no—
156#8627—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—42no—
166C22×C43—42no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43#38011yescharacteristic
171C22×C43#47211yescharacteristic
172C22×C43#47311yescharacteristic
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43C2×#9911yescharacteristic
180C4×C43#41011yescharacteristic
181Dic43—162no—
182#2929D4311yescharacteristic
183#1810—431no—
184#1808—431no—
185#1513—432no—
186#1305—432no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—41no—
190C2×C43—41no—
191C2×C43—81no—
192C2×C43#179911yescharacteristic
193C2×C43#181411yescharacteristic
194C2×C43#181611yescharacteristic
195C2×#131Dic4311yescharacteristic, complemented
196C23×C8C2×D4311yescharacteristic
197#525C2×D4311yescharacteristic
198#435—21no—
199#435—21no—
200C8×D4—21no—
201C8×D4—21no—
202C2×#108—861no—
203C2×#107—861no—
204#424Dic4311yescharacteristic, complemented
205#408Dic4311yescharacteristic, complemented
206#407—432no—
207#407C2×D4311yescharacteristic
208#405Dic4311yescharacteristic, complemented
209#380—432no—
210#341—861no—
211#340—861no—
212#328—862no—
213#327—862no—
214C43#862711yescharacteristic, complemented, Sylow
215C2×#41C2×Dic4311yescharacteristic
216C23×C4C22×D4311yescharacteristic
217#131—42no—
218C2×M16—21no—
219C2×M16—862no—
220C2×M16C2×Dic4311yescharacteristic
221C2×M16C2×Dic4311yescharacteristic
222C22×C8—21no—
223C22×C8—42no—
224C22×C8C2×Dic4311yescharacteristic
225C22×C8C2×Dic4311yescharacteristic
226C22×C8C22⋊D4311yescharacteristic
227C22×C8C22⋊D4311yescharacteristic
228C22×C8C22⋊D4311yescharacteristic
229C22×C8C22⋊D4311yescharacteristic
230#123—21no—
231C22⋊Q8Dic8611yescharacteristic
232C22⋊Q8D17211yescharacteristic
233#121Dic8611yescharacteristic
234#121D17211yescharacteristic
235#120—21no—
236C4×D4—21no—
237C4×D4—21no—
238#117C2×Dic4311yescharacteristic
239C2×C4⋊C4—862no—
240C2×C22⋊C4—862no—
241#108—1722no—
242#107—1722no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—862no—
250C22⋊C8—862no—
251#97—21no—
252C4×C8—21no—
253#95—862no—
254C24#1062189811yescharacteristic
255#41—41no—
256#41—41no—
257C2×Q8C4⋊Dic4311yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4C4⋊Dic4311yescharacteristic
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—1722no—
266C22×C4C2×Dic8611yescharacteristic
267C22×C4C2×D17211yescharacteristic
268C22×C4#1062189811yescharacteristic
269C22×C4C22×Dic4311yescharacteristic
270C22×C4C2×C22⋊D4311yescharacteristic
271C22×C4C2×C22⋊D4311yescharacteristic
272M16—42no—
273M16—41no—
274M16—41no—
275M16—1722no—
276M16—1722no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—42no—
286C2×C8—1722no—
287C2×C8C22⋊Dic4311yescharacteristic
288C2×C8C22⋊Dic4311yescharacteristic
289C2×C8C22⋊Dic4311yescharacteristic
290C2×C8C22⋊Dic4311yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—1722no—
294C4⋊C4—1722no—
295C4⋊C4C4⋊Dic4311yescharacteristic
296C4⋊C4C4⋊Dic4311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—3442no—
303C42—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—41no—
308C23—41no—
309C23#1306328411yescharacteristic
310C23#1306329911yescharacteristic
311C23#1306330411yescharacteristic
312Q8—41no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—41no—
317D4—41no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—3442no—
333C2×C4—3442no—
334C2×C4—3442no—
335C2×C4C2×C22⋊Dic4311yescharacteristic
336C2×C4C2×C4⋊Dic4311yescharacteristic
337C2×C4#1306329911yescharacteristic
338C2×C4#1306330411yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—41no—
343C8—41no—
344C8—3442no—
345C8#1306324012yes—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22#1458275911yescharacteristic
360C22#1458316911yescharacteristic
361C22#1458317411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—6882no—
369C4C2×#1306324011yescharacteristic
370C4#1458287311yescharacteristic
371C2—21no—
372C2—21no—
373C2—41no—
374C2—41no—
375C2—81no—
376C2#1913458311yescharacteristic
377C2#1913464911yescharacteristic
378C2#1913465911yescharacteristic
subgroupG/H
centerC22#14582759
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2929C2
socleC22×C43#380
prime radicalC43×#525C22
cosocleC23×C4×C43C23
hypercenter#2929D43
hypocenterC43#8627
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #19134633C2semidirect
2. #19134624C2semidirect
4. #19132500C2semidirect
14. C2×#131×C43C4semidirect
21. C43×#424C4semidirect
22. C43×#408C4semidirect
24. C43×#405C4semidirect
195. C2×#131Dic43semidirect
204. #424Dic43semidirect
205. #408Dic43semidirect
208. #405Dic43semidirect
214. C43#8627semidirect

Maximal subgroups

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

subgroupindex
#191346332
#191346242
#191331382
#191325002
C43×#29292
#862743