Finite Group Databasebeta

← #26111733

Subgroups — #26111733

Order 12032.

536 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252429C211yesmaximal, characteristic, complemented
2#20241779C211yesmaximal, characteristic, complemented
3#20241779C211yesmaximal, characteristic, complemented
4#20241709C211yesmaximal, characteristic, complemented
5#20241233C211yesmaximal, characteristic, complemented
6#20241219C211yesmaximal, characteristic, complemented
7C2×C47×#442C211yesmaximal, characteristic
8#15689201—22no—
9#15689201—22no—
10#15689176C2211yescharacteristic
11#15689176C2211yescharacteristic
12#15689176C2211yescharacteristic
13#15689176C2211yescharacteristic
14#15689087—22no—
15D4⋊(C47⋊C8)—22no—
16D4⋊(C47⋊C8)—22no—
17#15688847—22no—
18C22×D8×C47C411yescharacteristic
19C2×C4×D4×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C47×#442—22no—
22C47×#442—22no—
23C2×#106×C47C411yescharacteristic
24C2×#102×C47C411yescharacteristic
25C2×#102×C47C411yescharacteristic
26C2×#97×C47C2211yescharacteristic
27C2×#10625329—24no—
28C4⋊(C47⋊C8)—21no—
29C4⋊(C47⋊C8)—21no—
30C4⋊(C47⋊C8)—21no—
31C4⋊(C47⋊C8)—21no—
32C22⋊(C47⋊C8)—24no—
33C22⋊(C47⋊C8)—21no—
34C22⋊(C47⋊C8)—21no—
35C22⋊(C47⋊C8)—21no—
36C22⋊(C47⋊C8)D412yes—
37C4×C47⋊C8—21no—
38C4×C47⋊C8—21no—
39C4×C47⋊C8—21no—
40C4×C47⋊C8D412yes—
41C22×D4×C47C2×C411yescharacteristic
42C22×D4×C47C2×C411yescharacteristic
43C23×C4×C47—21no—
44C23×C4×C47—21no—
45C2×D8×C47—22no—
46C2×D8×C47—22no—
47C2×D8×C47—22no—
48C22×C8×C47C2×C411yescharacteristic
49C22×C8×C47C2×C411yescharacteristic
50C4×D4×C47—21no—
51C4×D4×C47—21no—
52C4×D4×C47—21no—
53C4×D4×C47—21no—
54C4×D4×C47—21no—
55C4×D4×C47—21no—
56C4×D4×C47D412yes—
57C4×D4×C47D412yes—
58C2×C4⋊C4×C47C2×C411yescharacteristic
59C2×C4⋊C4×C47C2×C411yescharacteristic
60C2×C22⋊C4×C47—21no—
61C2×C22⋊C4×C47—21no—
62C2×C42×C47C2311yescharacteristic
63#106×C47—22no—
64#102×C47—22no—
65#102×C47—22no—
66#97×C47—21no—
67#97×C47—21no—
68C24×C47—21no—
69C24×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47—21no—
74C2×D4×C47—21no—
75C2×D4×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47—21no—
79C2×D4×C47—21no—
80C2×D4×C47C22⋊C412yes—
81C2×D4×C47M1612yescomplemented
82C22×C4×C47—21no—
83C22×C4×C47—22no—
84C22×C4×C47—22no—
85C22×C4×C47—21no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47—82no—
89C22×C4×C47—82no—
90C22×C4×C47C22×C411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47#4111yescharacteristic
93D8×C47—28no—
94C2×C8×C47—21no—
95C2×C8×C47—21no—
96C2×C8×C47—21no—
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C2×C8×C47M1612yescomplemented
100C4⋊C4×C47—21no—
101C4⋊C4×C47—21no—
102C4⋊C4×C47—21no—
103C4⋊C4×C47C22⋊C412yes—
104C22⋊C4×C47—22no—
105C22⋊C4×C47—22no—
106C22⋊C4×C47—41no—
107C22⋊C4×C47—41no—
108C42×C47C2×D411yescharacteristic
109C42×C47C2×D411yescharacteristic
110C42×C47C2×D411yescharacteristic
111C42×C47#4111yescharacteristic
112#10625329—84no—
113C2×C47⋊C8—22no—
114C2×C47⋊C8—22no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C23×C47—22no—
118C23×C47—22no—
119C23×C47—41no—
120C23×C47—41no—
121C23×C47—41no—
122C23×C47—41no—
123C23×C47—81no—
124C23×C47—81no—
125C23×C47—81no—
126C23×C47—81no—
127C23×C47C4×D411yescharacteristic
128D4×C47—22no—
129D4×C47—22no—
130D4×C47—22no—
131D4×C47—22no—
132D4×C47—41no—
133D4×C47—41no—
134D4×C47—41no—
135D4×C47—41no—
136C2×C4×C47—22no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—44no—
140C2×C4×C47—41no—
141C2×C4×C47—82no—
142C2×C4×C47—82no—
143C2×C4×C47—82no—
144C2×C4×C47—81no—
145C2×C4×C47—81no—
146C2×C4×C47C2×C22⋊C411yescharacteristic
147C2×C4×C47C4×D411yescharacteristic
148C2×C4×C47#12011yescharacteristic
149C2×C4×C47#12111yescharacteristic
150C2×C4×C47#12111yescharacteristic
151C2×C4×C47#12311yescharacteristic
152C2×C4×C47C2×M1611yescharacteristic
153C2×C4×C47C2×M1611yescharacteristic
154C2×C4×C47#13111yescharacteristic
155C2×C4×C47#13111yescharacteristic
156C8×C47—22no—
157C8×C47—41no—
158C47⋊C8—42no—
159C47⋊C8—42no—
160C47⋊C8—81no—
161C47⋊C8—81no—
162#9093—471nomaximal, Sylow
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—42no—
166C22×C47—42no—
167C22×C47—42no—
168C22×C47—42no—
169C22×C47—82no—
170C22×C47—82no—
171C22×C47—82no—
172C22×C47—82no—
173C22×C47—81no—
174C22×C47—81no—
175C22×C47#38611yescharacteristic
176C22×C47#43511yescharacteristic
177C22×C47#43611yescharacteristic
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—42no—
183C4×C47—81no—
184C4×C47#40711yescharacteristic
185C4×C47#40811yescharacteristic
186C4×C47#43511yescharacteristic
187C4×C47#43611yescharacteristic
188#2975—471no—
189C2×#442D4711yescharacteristic
190#1478—471no—
191#1478—471no—
192#1460—471no—
193#1281—471no—
194#1275—471no—
195C2×C47—21no—
196C2×C47—21no—
197C2×C47—82no—
198C2×C47—82no—
199C2×C47#187011yescharacteristic
200C2×C47#190311yescharacteristic
201C2×C47#190411yescharacteristic
202C22×D8Dic4711yescharacteristic
203C2×C4×D4C2×D4711yescharacteristic
204C2×C4×D4C2×D4711yescharacteristic
205#442—22no—
206#442—22no—
207#436—942no—
208#436—942no—
209#431—471no—
210#431—471no—
211#431—471no—
212#431—471no—
213C2×#106Dic4711yescharacteristic
214C2×#102Dic4711yescharacteristic
215C2×#102Dic4711yescharacteristic
216#407—942no—
217C2×#97C2×D4711yescharacteristic
218D4⋊C8—942no—
219D4⋊C8—942no—
220#323—942no—
221C47#909311yescharacteristic, complemented, Sylow
222C22×D4C2×Dic4711yescharacteristic
223C22×D4C2×Dic4711yescharacteristic
224C23×C4—21no—
225C23×C4—21no—
226C2×D8—22no—
227C2×D8—22no—
228C2×D8—22no—
229C2×M16—944no—
230C22×C8C2×Dic4711yescharacteristic
231C22×C8C2×Dic4711yescharacteristic
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4C22⋊D4712yes—
239C4×D4C22⋊D4712yes—
240C2×C4⋊C4C2×Dic4711yescharacteristic
241C2×C4⋊C4C2×Dic4711yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42C22×D4711yescharacteristic
245#106—22no—
246C4⋊C8—941no—
247C4⋊C8—941no—
248C4⋊C8—941no—
249C4⋊C8—941no—
250#102—22no—
251#102—22no—
252C22⋊C8—472no—
253C22⋊C8—944no—
254C22⋊C8—941no—
255C22⋊C8—941no—
256C22⋊C8—941no—
257#97—21no—
258#97—21no—
259C4×C8—472no—
260C4×C8—941no—
261C4×C8—941no—
262C4×C8—941no—
263C24—21no—
264C24—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4#1062532912yescomplemented
276C2×D4C22⋊Dic4712yes—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4D4×D4711yescharacteristic
286C22×C4#1062535211yescharacteristic
287C22×C4C22×Dic4711yescharacteristic
288D8—28no—
289M16—3764no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—942no—
296C2×C8—942no—
297C2×C8—1881no—
298C2×C8—1881no—
299C2×C8#1062532912yescomplemented
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4C22⋊Dic4712yes—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42D4×D4711yescharacteristic
309C42#1062535211yescharacteristic
310C42C2×C22⋊D4711yescharacteristic
311C42C2×C22⋊D4711yescharacteristic
312C23—22no—
313C23—22no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23D4×Dic4711yescharacteristic
323D4—22no—
324D4—22no—
325D4—22no—
326D4—22no—
327D4—41no—
328D4—41no—
329D4—41no—
330D4—41no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4C2×C22⋊Dic4711yescharacteristic
342C2×C4D4×Dic4711yescharacteristic
343C2×C4#1309399211yescharacteristic
344C2×C4#1309399611yescharacteristic
345C2×C4#1309399611yescharacteristic
346C2×C4#1309400511yescharacteristic
347C2×C4C2×#1062532911yescharacteristic
348C2×C4C2×#1062532911yescharacteristic
349C2×C4#1309403111yescharacteristic
350C2×C4#1309403111yescharacteristic
351C8—22no—
352C8—41no—
353C8—3761no—
354C8—3761no—
355C8—1882no—
356C8—1882no—
357C22—21no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—81no—
368C22—81no—
369C22#1568900311yescharacteristic
370C22#1568919511yescharacteristic
371C22#1568920111yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4#1568908711yescharacteristic
379C4#1568909011yescharacteristic
380C4#1568919511yescharacteristic
381C4#1568920111yescharacteristic
382C2—21no—
383C2—21no—
384C2—82no—
385C2—82no—
386C2#2024368611yescharacteristic
387C2#2024387011yescharacteristic
388C2#2024387711yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#442C2
socleC22×C47#386
prime radicalC22×D8×C47C4
cosocleC2×C42×C47C23
hypercenterC2×#442D47
hypocenterC47#9093
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. #20252429C2semidirect
2. #20241779C2semidirect
3. #20241779C2semidirect
4. #20241709C2semidirect
5. #20241233C2semidirect
6. #20241219C2semidirect
81. C2×D4×C47M16semidirect
99. C2×C8×C47M16semidirect
221. C47#9093semidirect
275. C2×D4#10625329semidirect
299. C2×C8#10625329semidirect

Maximal subgroups

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

subgroupindex
#202524292
#202417792
#202417092
#202412332
#202412192
C2×C47×#4422
#909347