Finite Group Databasebeta

← #26110174

Subgroups — #26110174

Order 12032.

440 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252506C211yesmaximal, characteristic
2C4×#13093952C211yesmaximal, characteristic
3#20242138C211yesmaximal, characteristic, complemented
4#20241773C211yesmaximal, characteristic
5#20241238C211yesmaximal, characteristic, complemented
6#20241221C211yesmaximal, characteristic, complemented
7C47×#1842C211yesmaximal, characteristic, complemented
8C4×#10625350C2211yescharacteristic
9#15689250—21no—
10#15689200—21no—
11#15689194—22no—
12#15689179—21no—
13#15689176C2211yescharacteristic
14#15689176C2211yescharacteristic
15#15689145—21no—
16C2×#13093952C411yescharacteristic
17C2×#13093952C411yescharacteristic
18C4×#10625329C2211yescharacteristic
19#15688883C411yescharacteristic
20#15688883C411yescharacteristic
21#15688875—21no—
22#15688873—21no—
23#15688853—21no—
24#15688850—21no—
25C2×C4⋊C8×C47—22no—
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C43×C47C2211yescharacteristic
29C2×#10625350C2×C411yescharacteristic
30C2×#10625329C2×C411yescharacteristic
31C2×#10625329C2×C411yescharacteristic
32C2×#10625324—22no—
33C4×Dic94D411yescharacteristic
34C4×Dic94Q811yescharacteristic
35C4×D188D411yescharacteristic
36C4×D188Q811yescharacteristic
37C4×C22⋊D47—21no—
38C4×C22⋊D47—21no—
39#13093983C2×C411yescharacteristic
40#13093981—21no—
41C42×D47—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)D411yescharacteristic
44C4⋊(C47⋊C8)D411yescharacteristic
45Dic47⋊C8—22no—
46#13093952—22no—
47#13093952—22no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50(C2×D47)⋊C8—22no—
51#13093935—21no—
52#13093934—22no—
53C4×C47⋊C8—21no—
54C4×C47⋊C8—21no—
55C4×C47⋊C8—21no—
56C22×C8×C47—21no—
57C22×C8×C47D412yes—
58C2×C42×C47—21no—
59C2×C42×C47—21no—
60C2×C42×C47C2×C411yescharacteristic
61C2×C42×C47C2×C411yescharacteristic
62C2×C42×C47C2311yescharacteristic
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65C4⋊C8×C47—21no—
66C4⋊C8×C47—21no—
67C4⋊C8×C47—44no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47C22×C411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47#4111yescharacteristic
73C2×C22⋊D47—21no—
74#10625350—21no—
75#10625350—21no—
76#10625350—21no—
77#10625350—21no—
78C2×D188C4⋊C411yescharacteristic
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×Dic94C4⋊C411yescharacteristic
83C2×C8×C47—22no—
84C2×C8×C47—42no—
85C2×C8×C47—42no—
86C2×C8×C47—41no—
87C42×C47—22no—
88C42×C47—22no—
89C42×C47—21no—
90C42×C47—21no—
91C42×C47—21no—
92C42×C47—42no—
93C42×C47M1612yescomplemented
94C42×C47C2×D411yescharacteristic
95C42×C47C2×D411yescharacteristic
96C42×C47C2×Q811yescharacteristic
97C42×C47#4111yescharacteristic
98C22⋊Dic47—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101C4⋊Dic47C4⋊C411yescharacteristic
102C4⋊Dic47C4⋊C411yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47—21no—
108#10625329—21no—
109#10625329—21no—
110#10625329—21no—
111#10625329M1612yescomplemented
112C2×C47⋊C8—21no—
113C2×C47⋊C8—21no—
114C2×C47⋊C8—21no—
115C2×C47⋊C8—21no—
116C2×C47⋊C8—41no—
117#10625324—82no—
118C23×C47C4×D411yescharacteristic
119C22×D47—21no—
120C2×C4×C47—22no—
121C2×C4×C47—22no—
122C2×C4×C47—22no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—22no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47C2×C4⋊C411yescharacteristic
130C2×C4×C47C4×D411yescharacteristic
131C2×C4×C47#12011yescharacteristic
132C2×C4×C47C22⋊Q811yescharacteristic
133C2×C4×C47C22⋊Q811yescharacteristic
134C2×C4×C47#12311yescharacteristic
135C2×C4×C47C2×M1611yescharacteristic
136C2×C4×C47C2×M1611yescharacteristic
137C2×C4×C47#13111yescharacteristic
138C2×C4×C47#13111yescharacteristic
139C22⋊D47—41no—
140C22⋊D47—41no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144D188—21no—
145D188—21no—
146C4×D47—41no—
147C4×D47—41no—
148C4×D47—41no—
149C4×D47—41no—
150C4×D47—81no—
151Dic94—21no—
152Dic94—21no—
153C8×C47—42no—
154C8×C47—81no—
155C47⋊C8—22no—
156C47⋊C8—41no—
157C47⋊C8—41no—
158C47⋊C8—41no—
159C47⋊C8—81no—
160#8841—471nomaximal, Sylow
161C22×C47—21no—
162C22×C47—21no—
163C22×C47#38511yescharacteristic
164C22×C47#43511yescharacteristic
165C22×C47#43611yescharacteristic
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C4×C47—24no—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47—21no—
173C4×C47—42no—
174C4×C47#42311yescharacteristic
175C4×C47#42411yescharacteristic
176C4×C47#43511yescharacteristic
177C4×C47#43611yescharacteristic
178C4×C47#45311yescharacteristic
179C4×C47#45611yescharacteristic
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183#2989—471no—
184#1842D4711yescharacteristic, complemented
185C4×#104—471no—
186#1565—471no—
187#1477—471no—
188#1283—471no—
189#1276—471no—
190C2×C47—21no—
191C2×C47—21no—
192C2×C47#185111yescharacteristic
193C2×C47#185911yescharacteristic
194C2×C47#186111yescharacteristic
195D47—81no—
196C4×#41—471no—
197#446—941no—
198#436—941no—
199#435—942no—
200#432—941no—
201#431—471no—
202#431—471no—
203#423—941no—
204C2×C4⋊C8—22no—
205C2×C4⋊C8C2×D4711yescharacteristic
206C2×C4⋊C8C2×D4711yescharacteristic
207C2×#104—471no—
208C2×#104—471no—
209C4×M16—471no—
210C43C2×D4711yescharacteristic
211#339—471no—
212#339—471no—
213#335—941no—
214#334—941no—
215Q8⋊C8—941no—
216D4⋊C8—941no—
217C47#884111yescharacteristic, complemented, Sylow
218C2×#41—471no—
219C2×M16—471no—
220C2×M16—471no—
221C2×M16—942no—
222C22×C8—21no—
223C22×C8C22⋊D4712yes—
224C4×Q8—471no—
225C4×Q8—471no—
226C4×D4—471no—
227C4×D4—471no—
228C4×D4—941no—
229C4×D4—941no—
230#117—471no—
231#117—941no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—941no—
235C2×C42C4×D4711yescharacteristic
236C2×C42C4×D4711yescharacteristic
237C2×C42C22×D4711yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—44no—
243C4⋊C8—471no—
244C4⋊C8—471no—
245C4⋊C8—942no—
246C4⋊C8—941no—
247#104—942no—
248#104—942no—
249C22⋊C8—942no—
250C22⋊C8—941no—
251C22⋊C8—941no—
252#97—942no—
253#97—941no—
254C4×C8—941no—
255C4×C8—941no—
256C4×C8—941no—
257#41—941no—
258#41—941no—
259#41—941no—
260#41—941no—
261C2×Q8—471no—
262C2×D4—471no—
263C2×D4—941no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4C2×C4×D4711yescharacteristic
270C22×C4#1062535011yescharacteristic
271C22×C4C2×C22⋊D4711yescharacteristic
272M16—472no—
273M16—941no—
274M16—941no—
275M16—941no—
276M16—3762no—
277C2×C8—22no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—41no—
281C2×C8—941no—
282C2×C8—941no—
283C2×C8—941no—
284C2×C8—941no—
285C2×C8—1881no—
286C4⋊C4—471no—
287C4⋊C4—471no—
288C4⋊C4—941no—
289C4⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C42—22no—
294C42—22no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—42no—
299C42—941no—
300C42—941no—
301C42—941no—
302C42#1062532412yescomplemented
303C42D4×D4711yescharacteristic
304C42D4×D4711yescharacteristic
305C42Q8×D4711yescharacteristic
306C42#1062535411yescharacteristic
307C23—941no—
308C23C4×C22⋊D4711yescharacteristic
309Q8—941no—
310Q8—941no—
311D4—941no—
312D4—941no—
313D4—1881no—
314D4—1881no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—3761no—
328C2×C4—1881no—
329C2×C4—1881no—
330C2×C4—1881no—
331C2×C4—1881no—
332C2×C4C4⋊C4×D4711yescharacteristic
333C2×C4#1309398611yescharacteristic
334C2×C4#1309399211yescharacteristic
335C2×C4#1309400011yescharacteristic
336C2×C4#1309400211yescharacteristic
337C2×C4#1309400911yescharacteristic
338C2×C4M16×D4711yescharacteristic
339C2×C4C2×#1062532411yescharacteristic
340C2×C4#1309403011yescharacteristic
341C2×C4#1309403211yescharacteristic
342C8—42no—
343C8—81no—
344C8—942no—
345C8—3761no—
346C8—1881no—
347C8—1881no—
348C8—1881no—
349C22—21no—
350C22—21no—
351C22—1881no—
352C22—1881no—
353C22—1881no—
354C22#1568899411yescharacteristic
355C22#1568919411yescharacteristic
356C22#1568919911yescharacteristic
357C4—24no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—42no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4#1568914511yescharacteristic
366C4#1568914811yescharacteristic
367C4#1568919311yescharacteristic
368C4#1568920011yescharacteristic
369C4#1568929011yescharacteristic
370C4#1568930511yescharacteristic
371C2—21no—
372C2—21no—
373C2—3761no—
374C2#2024356911yescharacteristic
375C2#2024361311yescharacteristic
376C2#2024362711yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1842C2
socleC22×C47#385
prime radicalC2×#10625350C2×C4
cosocleC2×C42×C47C23
hypercenter#1842D47
hypocenterC47#8841
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1842

Complements

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

NH ≅ G/Ntype
3. #20242138C2semidirect
5. #20241238C2semidirect
6. #20241221C2semidirect
7. C47×#1842C2semidirect
93. C42×C47M16semidirect
111. #10625329M16semidirect
184. #1842D47semidirect
217. C47#8841semidirect
302. C42#10625324semidirect

Maximal subgroups

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

subgroupindex
#202525062
C4×#130939522
#202421382
#202417732
#202412382
#202412212
C47×#18422
#884147