Finite Group Databasebeta

← #26104700

Subgroups — #26104700

Order 12032.

550 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251719C211yesmaximal, characteristic
2#20243150C211yesmaximal, characteristic, complemented
3#20241212C212yesmaximal, complemented
4#20241208C212yesmaximal, complemented
5C4×C22⋊C8×C47C211yesmaximal, characteristic, complemented
6C2×#13094007—21no—
7C2×#13093998C411yescharacteristic
8C2×C22⋊(C47⋊C8)—21no—
9C2×#13093935—21no—
10#15689025C411yescharacteristic
11#15689025C2211yescharacteristic
12#15689021C411yescharacteristic
13#15689021C2211yescharacteristic
14#15689014—21no—
15#15689014—21no—
16#15689002—21no—
17#15688983C411yescharacteristic
18#15688878C2212yes—
19C22×C42×C47C2211yescharacteristic
20C2×C22⋊C8×C47—21no—
21C2×C4×C8×C47—21no—
22C47×#336C2212yes—
23C22×D188C2×C411yescharacteristic
24C22×C22⋊D47—21no—
25C22×C47⋊C8—22no—
26#13094007—44no—
27#13093998—42no—
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×C4⋊Dic47C2×C411yescharacteristic
30C2×C4⋊Dic47C2×C411yescharacteristic
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C2×C22⋊Dic47—21no—
34C2×(C2×D47)⋊C4—21no—
35C2×(C2×D47)⋊C4—21no—
36C2×(C2×D47)⋊C4—21no—
37C2×(C2×D47)⋊C4—21no—
38C2×(C2×D47)⋊C4—21no—
39C22⋊(C47⋊C8)—24no—
40#13093935—42no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C23×C4×C47C2×C411yescharacteristic
45C23×C4×C47D411yescharacteristic
46C23×C4×C47D411yescharacteristic
47C22×C8×C47—22no—
48C2×C42×C47—42no—
49C2×C42×C47C2×C411yescharacteristic
50C2×C42×C47D411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47C2311yescharacteristic
53C22⋊C8×C47—24no—
54C4×C8×C47—42no—
55C24×C47C22⋊C411yescharacteristic
56C23×D47—21no—
57C22×C4×C47—22no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—22no—
63C22×C4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22×C411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C2×C22⋊D47—42no—
73C2×C22⋊D47—42no—
74C2×C22⋊D47—42no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C2×D188—22no—
79C2×D188—41no—
80C2×D188—41no—
81C2×C8×C47—24no—
82C2×C8×C47—42no—
83C2×C8×C47—42no—
84C42×C47—22no—
85C42×C47—22no—
86C42×C47—41no—
87C42×C47—41no—
88C22⋊Dic47—42no—
89(C2×D47)⋊C4—42no—
90(C2×D47)⋊C4—42no—
91(C2×D47)⋊C4—42no—
92(C2×D47)⋊C4—42no—
93(C2×D47)⋊C4—42no—
94C4⋊Dic47—22no—
95C4⋊Dic47—41no—
96C4⋊Dic47—41no—
97Dic47⋊C4—42no—
98Dic47⋊C4—42no—
99C2×C47⋊C8—24no—
100C2×C47⋊C8—42no—
101C2×C47⋊C8—42no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47#10412yes—
109C23×C47C2×C22⋊C411yescharacteristic
110C22×D47—41no—
111C22×D47—41no—
112C22×D47—41no—
113C22×D47—41no—
114C22×D47—41no—
115C22×D47—41no—
116C22×D47—41no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—44no—
131C2×C4×C47—44no—
132C2×C4×C47—44no—
133C2×C4×C47#9912yes—
134C2×C4×C47#10412yes—
135C2×C4×C47#13112yes—
136C2×C4×C47#13512yes—
137C2×C4×C47AGL(1,ℤ/8)12yes—
138C22⋊D47—84no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144C2×Dic47—41no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147C2×Dic47—41no—
148D188—82no—
149C8×C47—44no—
150C47⋊C8—44no—
151#7674—471nomaximal, Sylow
152C22×C47—22no—
153C22×C47—22no—
154C22×C47—22no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47#40811yescharacteristic
160C22×C47C2×#9911yescharacteristic
161C22×C47#41311yescharacteristic
162C22×C47#41611yescharacteristic
163C22×C47#41811yescharacteristic
164C22×C47C2×#10411yescharacteristic
165C22×C47C2×#10411yescharacteristic
166C2×D47—81no—
167C2×D47—81no—
168C2×D47—81no—
169C2×D47—81no—
170C2×D47—81no—
171C2×D47—81no—
172C2×D47—81no—
173C4×C47—22no—
174C4×C47—22no—
175C4×C47—22no—
176C4×C47—22no—
177C4×C47—22no—
178C4×C47—41no—
179Dic47—81no—
180Dic47—81no—
181Dic47—81no—
182#2854—471no—
183#1749—471no—
184C4×C22⋊C8D4711yescharacteristic, complemented
185#1271—472no—
186#1270—472no—
187C2×C47—42no—
188C2×C47#146811yescharacteristic
189C2×C47#148411yescharacteristic
190C2×C47#149411yescharacteristic
191C2×C47#150111yescharacteristic
192C2×C47#150711yescharacteristic
193C2×C47#152411yescharacteristic
194C2×C47#155311yescharacteristic
195D47—161no—
196C2×#123—941no—
197C2×#121—471no—
198C22×C42C2×D4711yescharacteristic
199C2×C22⋊C8—21no—
200C2×C22⋊C8—941no—
201C2×#97—941no—
202C2×C4×C8—21no—
203#390—471no—
204#390—471no—
205#389—471no—
206#389—471no—
207#388—941no—
208#388—941no—
209#386—941no—
210#380—471no—
211#336—472no—
212#336C2×D4712yes—
213C47#767411yescharacteristic, complemented, Sylow
214C22×D4—471no—
215C22×D4—941no—
216C23×C4C4×D4711yescharacteristic
217C23×C4D18811yescharacteristic
218C23×C4C22⋊D4711yescharacteristic
219C22×C8—22no—
220C22×C8—942no—
221#123—1884no—
222#121—1882no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—941no—
227C2×C4⋊C4—941no—
228C2×C22⋊C4—941no—
229C2×C22⋊C4—941no—
230C2×C22⋊C4—941no—
231C2×C22⋊C4—941no—
232C2×C22⋊C4—941no—
233C2×C22⋊C4—941no—
234C2×C42—42no—
235C2×C42C4×D4711yescharacteristic
236C2×C42D18811yescharacteristic
237C2×C42C22⋊D4711yescharacteristic
238C2×C42C22×D4711yescharacteristic
239C22⋊C8—24no—
240C22⋊C8—944no—
241#97—1882no—
242C4×C8—42no—
243#95—941no—
244#95—941no—
245#95—941no—
246C24—941no—
247C24(C2×D47)⋊C411yescharacteristic
248C2×D4—942no—
249C2×D4—1881no—
250C2×D4—1881no—
251C2×D4—1882no—
252C2×D4—1882no—
253C2×D4—1882no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4(C2×D47)⋊C411yescharacteristic
267C22×C4(C2×D47)⋊C411yescharacteristic
268C22×C4(C2×D47)⋊C411yescharacteristic
269C22×C4C2×C4×D4711yescharacteristic
270C22×C4C2×D18811yescharacteristic
271C22×C4C2×C22⋊D4711yescharacteristic
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—944no—
276C2×C8—1882no—
277C2×C8—1882no—
278C4⋊C4—942no—
279C4⋊C4—1881no—
280C4⋊C4—1881no—
281C4⋊C4—1882no—
282C4⋊C4—1882no—
283C22⋊C4—1882no—
284C22⋊C4—1882no—
285C22⋊C4—1882no—
286C22⋊C4—1882no—
287C22⋊C4—1882no—
288C22⋊C4—1882no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—41no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—1881no—
300C23—1881no—
301C23—1881no—
302C23—1881no—
303C23—1881no—
304C23—1881no—
305C23—1881no—
306C23#1309395212yes—
307C23C2×(C2×D47)⋊C411yescharacteristic
308D4—3762no—
309D4—3764no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4—1881no—
329C2×C4—1881no—
330C2×C4—1881no—
331C2×C4—1881no—
332C2×C4—1881no—
333C2×C4—1881no—
334C2×C4—1881no—
335C2×C4#1309393812yes—
336C2×C4#1309395012yes—
337C2×C4#1309403012yes—
338C2×C4#1309404612yes—
339C2×C4#1309404912yes—
340C8—44no—
341C8—1884no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—3761no—
350C22—3761no—
351C22—3761no—
352C22—3761no—
353C22—3761no—
354C22—3761no—
355C22—3761no—
356C22#1568908911yescharacteristic
357C22C2×#1309393811yescharacteristic
358C22#1568910511yescharacteristic
359C22#1568912011yescharacteristic
360C22#1568912711yescharacteristic
361C22C2×#1309395011yescharacteristic
362C22C2×#1309395211yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—3761no—
370C4—3761no—
371C4—3761no—
372C2—42no—
373C2—7521no—
374C2#2024173411yescharacteristic
375C2#2024180411yescharacteristic
376C2#2024184911yescharacteristic
377C2#2024188011yescharacteristic
378C2#2024190311yescharacteristic
379C2#2024197711yescharacteristic
380C2#2024209111yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC4×C22⋊C8×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093998C4
cosocleC2×C42×C47C23
hypercenterC4×C22⋊C8D47
hypocenterC47#7674
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #20243150C2semidirect
3. #20241212C2semidirect
4. #20241208C2semidirect
5. C4×C22⋊C8×C47C2semidirect
184. C4×C22⋊C8D47semidirect
213. C47#7674semidirect

Maximal subgroups

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

subgroupindex
#202517192
#202431502
#202412122
#202412082
C4×C22⋊C8×C472
#767447