Finite Group Databasebeta

← #26112146

Subgroups — #26112146

Order 12032.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253197C211yesmaximal, characteristic
2#20251953C211yesmaximal, characteristic
3#20242073C211yesmaximal, characteristic, complemented
4#20241773C211yesmaximal, characteristic
5#20241285C211yesmaximal, characteristic, complemented
6#20241263C211yesmaximal, characteristic, complemented
7C2×C47×#333C211yesmaximal, characteristic, complemented
8C2×#13094030—21no—
9C4×#10625350C2211yescharacteristic
10#15689415—21no—
11#15689410—21no—
12#15689405C412yes—
13#15689400C412yes—
14#15689176C2211yescharacteristic
15#15689163—21no—
16#15689149—21no—
17#15689148—22no—
18#15689147C2211yescharacteristic
19#15689147C2211yescharacteristic
20#15689145—21no—
21C4⋊C8×D47—21no—
22#15689122—21no—
23#15688869—22no—
24#15688853—21no—
25#15688850—21no—
26C2×C4⋊Q8×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C47×#333—21no—
30C47×#333—21no—
31C2×#10625350D411yescharacteristic
32#13094030—42no—
33#13094030—42no—
34C2×#10625329—21no—
35C2×#10625329—21no—
36C2×#10625324—22no—
37C2×C8×D47—22no—
38C4×Dic94C2×C411yescharacteristic
39C4×Dic94D411yescharacteristic
40C4×D188C2×C411yescharacteristic
41C4×D188D411yescharacteristic
42C4×C22⋊D47—21no—
43C4×C22⋊D47—21no—
44#13093983D411yescharacteristic
45#13093981—21no—
46C42×D47—21no—
47#13093957—22no—
48#13093955—22no—
49C4⋊(C47⋊C8)—21no—
50C4⋊(C47⋊C8)—21no—
51C4⋊(C47⋊C8)—21no—
52C4⋊(C47⋊C8)C2×C412yes—
53C4⋊(C47⋊C8)D412yes—
54Dic47⋊C8—22no—
55Dic47⋊C8—22no—
56#13093947—22no—
57#13093944—22no—
58C22⋊(C47⋊C8)—21no—
59C4×C47⋊C8—21no—
60C22×Q8×C47—21no—
61C22×C8×C47—21no—
62C22×C8×C47—21no—
63C4⋊Q8×C47—21no—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47C2×C412yes—
67C2×C4⋊C4×C47—21no—
68C2×C4⋊C4×C47—21no—
69C2×C42×C47C2311yescharacteristic
70C4⋊C8×C47—21no—
71C4⋊C8×C47—21no—
72C4⋊C8×C47—21no—
73C4⋊C8×C47D411yescharacteristic
74C4⋊C8×C47D411yescharacteristic
75C2×Q8×C47—22no—
76C2×Q8×C47—41no—
77C2×Q8×C47—82no—
78C22×C4×C47—41no—
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47#4111yescharacteristic
81C22×C4×C47#4111yescharacteristic
82C2×C22⋊D47—21no—
83#10625350—21no—
84#10625350—21no—
85#10625350SD1612yes—
86#10625350Q1612yes—
87C2×D188C22⋊C411yescharacteristic
88C2×C4×D47—21no—
89C2×C4×D47—21no—
90C2×C4×D47—21no—
91C2×Dic94C22⋊C411yescharacteristic
92C2×C8×C47—21no—
93C2×C8×C47—21no—
94C2×C8×C47—41no—
95C2×C8×C47—41no—
96C2×C8×C47—41no—
97C2×C8×C47—81no—
98C4⋊C4×C47—22no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C42×C47C22×C411yescharacteristic
103C42×C47C2×D411yescharacteristic
104C42×C47C2×D411yescharacteristic
105C42×C47C2×D411yescharacteristic
106C22⋊Dic47—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109C4⋊Dic47C22⋊C411yescharacteristic
110C4⋊Dic47C22⋊C411yescharacteristic
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113C4×Dic47—21no—
114C4×Dic47—21no—
115C4×Dic47—21no—
116#10625329—41no—
117#10625329—41no—
118#10625329—41no—
119#10625329—41no—
120C2×C47⋊C8—22no—
121C2×C47⋊C8—22no—
122C2×C47⋊C8—41no—
123#10625324—44no—
124C8×D47—44no—
125C23×C47#12311yescharacteristic
126C22×D47—21no—
127Q8×C47—82no—
128Q8×C47—82no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—41no—
132C2×C4×C47—42no—
133C2×C4×C47—82no—
134C2×C4×C47C2×C22⋊C411yescharacteristic
135C2×C4×C47C4×D411yescharacteristic
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47#12011yescharacteristic
138C2×C4×C47#12111yescharacteristic
139C2×C4×C47#12111yescharacteristic
140C2×C4×C47C2×SD1611yescharacteristic
141C2×C4×C47C2×Q1611yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47#13711yescharacteristic
144C22⋊D47—22no—
145C22⋊D47—22no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149D188—21no—
150D188#10312yes—
151C4×D47—22no—
152C4×D47—22no—
153C4×D47—41no—
154C4×D47—41no—
155C4×D47—81no—
156Dic94—21no—
157Dic94#10312yes—
158C8×C47—41no—
159C8×C47—41no—
160C8×C47—81no—
161C47⋊C8—42no—
162C47⋊C8—42no—
163C47⋊C8—81no—
164#9169—471nomaximal, Sylow
165C22×C47—21no—
166C22×C47—21no—
167C22×C47#38611yescharacteristic
168C22×C47#48311yescharacteristic
169C22×C47#48411yescharacteristic
170C2×D47—22no—
171C2×D47—41no—
172C2×D47—41no—
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—82no—
177C4×C47C2×#10311yescharacteristic
178C4×C47#41711yescharacteristic
179C4×C47#45011yescharacteristic
180C4×C47#45111yescharacteristic
181C4×C47#47111yescharacteristic
182C4×C47#47311yescharacteristic
183Dic47—22no—
184Dic47—41no—
185Dic47—41no—
186#3079—471no—
187#2906—471no—
188#1549—471no—
189C2×#333D4711yescharacteristic, complemented
190#1477—471no—
191#1301—471no—
192#1292—471no—
193C2×C47—21no—
194C2×C47—21no—
195C2×C47#187211yescharacteristic
196C2×C47#190311yescharacteristic
197C2×C47#190811yescharacteristic
198D47—42no—
199C2×#131—941no—
200C2×C4⋊Q8C2×D4711yescharacteristic
201C4×#41—471no—
202#477—941no—
203#476—941no—
204#475—472no—
205#474—472no—
206#431—471no—
207#428—941no—
208#424—942no—
209#424—941no—
210#423—471no—
211#423—471no—
212#423—941no—
213C2×C4⋊C8—941no—
214C2×C4⋊C8C2×D4711yescharacteristic
215C2×C4⋊C8C2×D4711yescharacteristic
216#417—941no—
217#333—21no—
218#333—21no—
219#332—942no—
220Q8⋊C8—941no—
221D4⋊C8—941no—
222C47#916911yescharacteristic, complemented, Sylow
223C2×#41—471no—
224C22×Q8—21no—
225#131—1882no—
226#131—1882no—
227C2×M16—942no—
228C2×M16—941no—
229C2×M16—941no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—942no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8C4×D4712yes—
237C4×Q8—471no—
238C4×Q8—471no—
239C4×D4—471no—
240C4×D4—471no—
241C4×D4—941no—
242C4×D4—941no—
243#117—471no—
244#117—941no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—941no—
248C2×C42C22×D4711yescharacteristic
249#107—942no—
250#106—942no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—472no—
255C4⋊C8—472no—
256C4⋊C8—942no—
257C4⋊C8—942no—
258C4⋊C8—941no—
259C4⋊C8—941no—
260C4⋊C8—941no—
261C4⋊C8C22⋊D4711yescharacteristic
262C4⋊C8C22⋊D4711yescharacteristic
263#103—942no—
264#102—942no—
265C22⋊C8—941no—
266C4×C8—941no—
267#41—472no—
268#41—472no—
269#41—941no—
270#41—941no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—82no—
274C2×Q8—471no—
275C2×D4—471no—
276C2×D4—941no—
277C22×C4—41no—
278C22×C4—941no—
279C22×C4—941no—
280C22×C4—941no—
281C22×C4#1062535011yescharacteristic
282C22×C4D4×D4711yescharacteristic
283C22×C4#1062535211yescharacteristic
284M16—1884no—
285M16—1881no—
286M16—1881no—
287M16—1881no—
288M16—1881no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—81no—
295C2×C8—942no—
296C2×C8—942no—
297C2×C8—1884no—
298C2×C8—1881no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—471no—
304C4⋊C4—471no—
305C4⋊C4—941no—
306C4⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C42—941no—
311C42—941no—
312C42—941no—
313C42C2×C4×D4711yescharacteristic
314C42D4×D4711yescharacteristic
315C42D4×D4711yescharacteristic
316C42C2×C22⋊D4711yescharacteristic
317C23—941no—
318C23#1309400611yescharacteristic
319Q8—82no—
320Q8—82no—
321Q8—472no—
322Q8—941no—
323D4—472no—
324D4—942no—
325D4—942no—
326D4—941no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—941no—
333C2×C4—942no—
334C2×C4—942no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—3761no—
338C2×C4—1881no—
339C2×C4—1881no—
340C2×C4C22⋊C4×D4711yescharacteristic
341C2×C4(C22⋊D47)⋊C411yescharacteristic
342C2×C4C4×C22⋊D4711yescharacteristic
343C2×C4#1309399211yescharacteristic
344C2×C4#1309399511yescharacteristic
345C2×C4#1309399711yescharacteristic
346C2×C4SD16×D4711yescharacteristic
347C2×C4Q16×D4711yescharacteristic
348C2×C4#1309405111yescharacteristic
349C2×C4#1309405611yescharacteristic
350C8—41no—
351C8—41no—
352C8—81no—
353C8—3761no—
354C8—1882no—
355C8—1882no—
356C22—21no—
357C22—21no—
358C22—942no—
359C22—1881no—
360C22—1881no—
361C22#1568899911yescharacteristic
362C22#1568945211yescharacteristic
363C22#1568945711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—942no—
369C4—1881no—
370C4—1881no—
371C4#103×D4711yescharacteristic
372C4#1568912311yescharacteristic
373C4#1568927211yescharacteristic
374C4#1568927711yescharacteristic
375C4#1568938311yescharacteristic
376C4#1568939511yescharacteristic
377C2—21no—
378C2—21no—
379C2—1882no—
380C2#2024369211yescharacteristic
381C2#2024387111yescharacteristic
382C2#2024390611yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#333C2
socleC22×C47#386
prime radicalC2×#10625350D4
cosocleC2×C42×C47C23
hypercenterC2×#333D47
hypocenterC47#9169
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. #20242073C2semidirect
5. #20241285C2semidirect
6. #20241263C2semidirect
7. C2×C47×#333C2semidirect
189. C2×#333D47semidirect
222. C47#9169semidirect

Maximal subgroups

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

subgroupindex
#202531972
#202519532
#202420732
#202417732
#202412852
#202412632
C2×C47×#3332
#916947