Finite Group Databasebeta

← #26125852

Subgroups — #26125852

Order 12032.

440 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 83 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#20247876C211yesmaximal, characteristic
2#20241718C211yesmaximal, characteristic, complemented
3#20241331C212yesmaximal, complemented
4#20241319C212yesmaximal, complemented
5C2×C47×#324C211yesmaximal, characteristic, complemented
6C2×#13093998C411yescharacteristic
7#15689087—21no—
8#15689049—21no—
9#15689049—21no—
10#15689024C411yescharacteristic
11#15689024C2211yescharacteristic
12#15689002—21no—
13#15689002—21no—
14#15688988C411yescharacteristic
15#15688988C2211yescharacteristic
16C4×C22⋊Dic47C411yescharacteristic
17#15688849—21no—
18#15688849C2212yes—
19C22×C4⋊C4×C47C2211yescharacteristic
20C2×C22⋊C8×C47—21no—
21C47×#324—21no—
22C47×#324C2212yes—
23C22×D188C2×C411yescharacteristic
24C22×C22⋊D47—21no—
25C2×#10625329—41no—
26#13093998—41no—
27#13093998—41no—
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×C22⋊Dic47—21no—
30C2×(C2×D47)⋊C4—21no—
31C2×(C2×D47)⋊C4—21no—
32C2×(C2×D47)⋊C4—21no—
33C2×(C2×D47)⋊C4—21no—
34C2×(C2×D47)⋊C4—21no—
35C2×C4×Dic47C2×C411yescharacteristic
36C2×C4×Dic47C2×C411yescharacteristic
37C22⋊(C47⋊C8)—22no—
38C22⋊(C47⋊C8)—41no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C23×C4×C47C2×C411yescharacteristic
45C23×C4×C47D411yescharacteristic
46C23×C4×C47D411yescharacteristic
47C22×C8×C47—41no—
48C2×C4⋊C4×C47—41no—
49C2×C4⋊C4×C47—41no—
50C2×C4⋊C4×C47C2×C411yescharacteristic
51C2×C4⋊C4×C47D411yescharacteristic
52C2×C4⋊C4×C47D411yescharacteristic
53C2×C4⋊C4×C47C2311yescharacteristic
54C22⋊C8×C47—22no—
55C22⋊C8×C47—41no—
56C24×C47C22⋊C411yescharacteristic
57C23×D47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—22no—
65C22×C4×C47—41no—
66C22×C4×C47—81no—
67C22×C4×C47—81no—
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C2×C22⋊D47—42no—
75C2×C22⋊D47—42no—
76C2×C22⋊D47—41no—
77C2×C22⋊D47—41no—
78C22×Dic47—21no—
79C22×Dic47—21no—
80C22×Dic47—21no—
81C2×D188—22no—
82C2×D188—41no—
83C2×D188—41no—
84C2×C8×C47—42no—
85C2×C8×C47—82no—
86C4⋊C4×C47—41no—
87C4⋊C4×C47—41no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C22⋊Dic47—42no—
91(C2×D47)⋊C4—42no—
92(C2×D47)⋊C4—81no—
93(C2×D47)⋊C4—81no—
94(C2×D47)⋊C4—81no—
95(C2×D47)⋊C4—81no—
96C4⋊Dic47—41no—
97C4×Dic47—22no—
98C4×Dic47—41no—
99#10625329—82no—
100C2×C47⋊C8—42no—
101C23×C47—22no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—41no—
105C23×C47#9911yescharacteristic
106C23×C47#9911yescharacteristic
107C23×C47C2×C22⋊C411yescharacteristic
108C22×D47—41no—
109C22×D47—41no—
110C22×D47—41no—
111C22×D47—41no—
112C22×D47—41no—
113C22×D47—41no—
114C22×D47—41no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
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—42no—
125C2×C4×C47—42no—
126C2×C4×C47—42no—
127C2×C4×C47—42no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—81no—
133C2×C4×C47—81no—
134C2×C4×C47#13112yes—
135C22⋊D47—82no—
136C22⋊D47—82no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144C2×Dic47—41no—
145C2×Dic47—41no—
146D188—82no—
147C8×C47—82no—
148C47⋊C8—82no—
149#11553—471nomaximal, Sylow
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—42no—
158C22×C47—42no—
159C22×C47#35512yes—
160C22×C47#40811yescharacteristic
161C22×C47C2×#9911yescharacteristic
162C22×C47#41311yescharacteristic
163C2×D47—81no—
164C2×D47—81no—
165C2×D47—81no—
166C2×D47—81no—
167C2×D47—81no—
168C2×D47—81no—
169C2×D47—81no—
170C4×C47—22no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47—41no—
176Dic47—81no—
177Dic47—81no—
178Dic47—81no—
179#2504—471no—
180#1463—471no—
181C2×#324D4711yescharacteristic, complemented
182#1324—472no—
183#1318—472no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—22no—
187C2×C47—41no—
188C2×C47#146811yescharacteristic
189C2×C47#212711yescharacteristic
190C2×C47C2×#35511yescharacteristic
191D47—161no—
192C2×#121—471no—
193C22×C4⋊C4C2×D4711yescharacteristic
194#407—941no—
195C2×C22⋊C8—21no—
196#397—941no—
197#397—941no—
198#390—471no—
199#390—471no—
200#386—941no—
201#386—941no—
202#382—471no—
203#382—471no—
204C4×C22⋊C4—471no—
205#324—21no—
206#324—472no—
207#324—941no—
208#324C2×D4712yes—
209C47#1155311yescharacteristic, complemented, Sylow
210C22×D4—471no—
211C22×D4—941no—
212C23×C4C4×D4711yescharacteristic
213C23×C4D18811yescharacteristic
214C23×C4C22⋊D4711yescharacteristic
215C2×M16—1881no—
216C22×C8—41no—
217#121—1881no—
218#121—1881no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4C4×D4711yescharacteristic
223C2×C4⋊C4D18811yescharacteristic
224C2×C4⋊C4C22⋊D4711yescharacteristic
225C2×C4⋊C4C22×D4711yescharacteristic
226C2×C22⋊C4—941no—
227C2×C22⋊C4—941no—
228C2×C22⋊C4—941no—
229C2×C22⋊C4—941no—
230C2×C22⋊C4—941no—
231C2×C22⋊C4—941no—
232C2×C42—471no—
233C2×C42—471no—
234C22⋊C8—22no—
235C22⋊C8—41no—
236C22⋊C8—942no—
237C22⋊C8—1881no—
238#95—941no—
239#95—941no—
240#95—941no—
241#95—941no—
242#95—941no—
243C24—941no—
244C24(C2×D47)⋊C411yescharacteristic
245C2×D4—942no—
246C2×D4—1881no—
247C2×D4—1881no—
248C2×D4—1882no—
249C2×D4—1882no—
250C2×D4—1881no—
251C2×D4—1881no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4(C2×D47)⋊C411yescharacteristic
266C22×C4(C2×D47)⋊C411yescharacteristic
267C22×C4(C2×D47)⋊C411yescharacteristic
268C22×C4C2×C4×D4711yescharacteristic
269C22×C4C2×D18811yescharacteristic
270C22×C4C2×C22⋊D4711yescharacteristic
271M16—3762no—
272C2×C8—42no—
273C2×C8—82no—
274C2×C8—1882no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—1881no—
280C22⋊C4—3761no—
281C22⋊C4—3761no—
282C22⋊C4—3761no—
283C22⋊C4—3761no—
284C22⋊C4—1882no—
285C22⋊C4—1882no—
286C42—942no—
287C42—1881no—
288C23—21no—
289C23—21no—
290C23—22no—
291C23—41no—
292C23—1881no—
293C23—1881no—
294C23—1881no—
295C23—1881no—
296C23—1881no—
297C23—1881no—
298C23—1881no—
299C23#1309393811yescharacteristic
300C23#1309393811yescharacteristic
301C23C2×(C2×D47)⋊C411yescharacteristic
302D4—3762no—
303D4—3762no—
304D4—3762no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—1881no—
325C2×C4—1881no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4—1881no—
329C2×C4—1881no—
330C2×C4—1881no—
331C2×C4—1881no—
332C2×C4—1881no—
333C2×C4#1309403012yes—
334C8—82no—
335C8—3762no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—3761no—
346C22—3761no—
347C22—3761no—
348C22—3761no—
349C22—3761no—
350C22—3761no—
351C22—3761no—
352C22#1568891912yes—
353C22#1568908911yescharacteristic
354C22C2×#1309393811yescharacteristic
355C22#1568910511yescharacteristic
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—3761no—
363C4—3761no—
364C4—3761no—
365C2—21no—
366C2—21no—
367C2—22no—
368C2—41no—
369C2—7521no—
370C2#2024173411yescharacteristic
371C2#2024505511yescharacteristic
372C2C2×#1568891911yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC2×C47×#324C2
socleC22×C47C2×#99
prime radicalC2×#13093998C4
cosocleC2×C4⋊C4×C47C23
hypercenterC2×#324D47
hypocenterC47#11553
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #20241718C2semidirect
3. #20241331C2semidirect
4. #20241319C2semidirect
5. C2×C47×#324C2semidirect
181. C2×#324D47semidirect
209. C47#11553semidirect

Maximal subgroups

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

subgroupindex
#202478762
#202417182
#202413312
#202413192
C2×C47×#3242
#1155347