Finite Group Databasebeta

← #26115082

Subgroups — #26115082

Order 12032.

558 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094013C211yesmaximal, characteristic
2#20243504C211yesmaximal, characteristic, complemented
3#20243133C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
5C2×#15688852C211yesmaximal, characteristic
6C2×#15688850C211yesmaximal, characteristic
7C2×C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#13094013C411yescharacteristic
9C2×C4×D188C2211yescharacteristic
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×C4×C47⋊C8C2211yescharacteristic
12#15689030C411yescharacteristic
13#15689024C411yescharacteristic
14#15689013—22no—
15#15688988C411yescharacteristic
16C4×(C2×D47)⋊C4—22no—
17C42×Dic47C2211yescharacteristic
18#15688877—22no—
19#15688877—22no—
20Q8⋊(C47⋊C8)—22no—
21#15688852—22no—
22#15688850—22no—
23C2×C4×Q8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4×C8×C47C2211yescharacteristic
26C47×Q8⋊C8—22no—
27C22×D188C2×C411yescharacteristic
28C22×C4×D47—21no—
29C22×C47⋊C8—21no—
30C22×C47⋊C8—21no—
31#13094013—22no—
32#13094013—22no—
33C4×D188—21no—
34C4×D188—21no—
35C4×D188—21no—
36C4×D188—21no—
37C2×C4⋊Dic47C2×C411yescharacteristic
38C2×(C2×D47)⋊C4—22no—
39C2×(C2×D47)⋊C4—21no—
40C2×(C2×D47)⋊C4—22no—
41C2×C4×Dic47C2×C411yescharacteristic
42C2×C4×Dic47C2×C411yescharacteristic
43C2×C4×Dic47D412yes—
44C2×C4×Dic47D412yes—
45C4⋊(C47⋊C8)—21no—
46C4⋊(C47⋊C8)—21no—
47C4×C47⋊C8—21no—
48C4×C47⋊C8D412yes—
49C47⋊#95—22no—
50C47⋊#95—22no—
51C22×Q8×C47C2×C411yescharacteristic
52C22×C8×C47—21no—
53C22×C8×C47—21no—
54C4×Q8×C47—21no—
55C4×Q8×C47—21no—
56C4×Q8×C47—21no—
57C4×Q8×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47C2×C411yescharacteristic
60C2×C42×C47—21no—
61C2×C42×C47C2311yescharacteristic
62C4⋊C8×C47—21no—
63C4⋊C8×C47—21no—
64C4×C8×C47—21no—
65C4×C8×C47D412yes—
66C23×D47—21no—
67C2×Q8×C47—21no—
68C2×Q8×C47—21no—
69C2×Q8×C47—21no—
70C2×Q8×C47—21no—
71C2×Q8×C47—21no—
72C2×Q8×C47M1612yes—
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47C22×C411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C22×C4×C47C2×D411yescharacteristic
78C22×Dic47—21no—
79C22×Dic47C22⋊C412yes—
80C22×Dic47C22⋊C412yes—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188—21no—
84C2×D188—21no—
85C2×D188—21no—
86C2×D188M1612yes—
87C2×C4×D47—41no—
88C2×C4×D47—41no—
89C2×C4×D47—42no—
90C2×C4×D47—42no—
91C2×C8×C47—22no—
92C2×C8×C47—42no—
93C2×C8×C47—41no—
94C2×C8×C47—42no—
95C4⋊C4×C47—21no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—41no—
98C4⋊C4×C47—41no—
99C42×C47—41no—
100C42×C47—41no—
101C42×C47C2×D411yescharacteristic
102C42×C47C2×D411yescharacteristic
103C42×C47#4111yescharacteristic
104C42×C47#4111yescharacteristic
105(C2×D47)⋊C4—28no—
106(C2×D47)⋊C4—44no—
107(C2×D47)⋊C4—41no—
108(C2×D47)⋊C4—41no—
109C4⋊Dic47—21no—
110C4⋊Dic47—21no—
111C4×Dic47—21no—
112C4×Dic47—21no—
113C4×Dic47—21no—
114C4×Dic47—21no—
115C4×Dic47—22no—
116C4×Dic47—22no—
117C4×Dic47—42no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8—42no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8—42no—
122C23×C47C2×C22⋊C411yescharacteristic
123C22×D47—22no—
124C22×D47—41no—
125C22×D47—41no—
126C22×D47—42no—
127C22×D47—42no—
128Q8×C47—22no—
129Q8×C47—22no—
130Q8×C47—41no—
131Q8×C47—41no—
132C2×C4×C47—22no—
133C2×C4×C47—22no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—42no—
138C2×C4×C47C4×D411yescharacteristic
139C2×C4×C47C4×D411yescharacteristic
140C2×C4×C47#12111yescharacteristic
141C2×C4×C47#12111yescharacteristic
142C2×C4×C47#12411yescharacteristic
143C2×C4×C47#12711yescharacteristic
144C2×C4×C47C2×M1611yescharacteristic
145C2×C4×C47C2×M1611yescharacteristic
146C2×C4×C47#13111yescharacteristic
147C2×C4×C47#13111yescharacteristic
148C2×C4×C47#13512yes—
149C2×C4×C47#13512yes—
150C2×Dic47—22no—
151C2×Dic47—22no—
152C2×Dic47—22no—
153C2×Dic47—22no—
154C2×Dic47—22no—
155C2×Dic47—22no—
156C2×Dic47—41no—
157C2×Dic47—42no—
158D188—22no—
159D188—22no—
160D188—41no—
161D188—41no—
162C4×D47—82no—
163C4×D47—81no—
164C4×D47—81no—
165C8×C47—42no—
166C8×C47—81no—
167C47⋊C8—42no—
168C47⋊C8—81no—
169#9645—471nomaximal, Sylow
170C22×C47#39011yescharacteristic
171C22×C47#40711yescharacteristic
172C22×C47#40811yescharacteristic
173C22×C47#41612yes—
174C22×C47#42112yes—
175C2×D47—42no—
176C2×D47—44no—
177C2×D47—81no—
178C2×D47—81no—
179C2×D47—82no—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—42no—
183C4×C47—81no—
184C4×C47#43511yescharacteristic
185C4×C47#43511yescharacteristic
186C4×C47#43511yescharacteristic
187C4×C47#43511yescharacteristic
188C4×C47#48812yes—
189C4×C47#49511yescharacteristic
190C4×C47#49511yescharacteristic
191Dic47—42no—
192Dic47—42no—
193Dic47—81no—
194C4×#124—471no—
195#1831—471no—
196#1744—471no—
197C2×Q8⋊C8—471no—
198C2×Q8⋊C8D4711yescharacteristic, complemented
199C2×D4⋊C8—471no—
200C2×D4⋊C8—471no—
201C2×C47#148212yes—
202C2×C47#148812yes—
203C2×C47#195511yescharacteristic
204C2×C47#195811yescharacteristic
205C2×C47#196311yescharacteristic
206D47—82no—
207C2×#124—471no—
208C2×C4×Q8C2×D4711yescharacteristic
209C2×C4×D4—471no—
210C2×C4⋊C8—471no—
211C2×C4⋊C8C2×D4711yescharacteristic
212C2×C4×C8—471no—
213C2×C4×C8C2×D4711yescharacteristic
214#391—471no—
215#390—471no—
216#388—942no—
217#382—471no—
218C4×C22⋊C4—942no—
219C43—471no—
220#336—942no—
221#336—942no—
222Q8⋊C8—22no—
223Q8⋊C8—942no—
224D4⋊C8—942no—
225D4⋊C8—942no—
226C47#964511yescharacteristic, complemented, Sylow
227C22×Q8C4×D4711yescharacteristic
228C22×D4—471no—
229C23×C4—941no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—941no—
233C22×C8—941no—
234#124—942no—
235#124—942no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—941no—
241C4×D4—941no—
242C4×D4—941no—
243C4×D4—941no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4C4×D4711yescharacteristic
247C2×C22⋊C4—942no—
248C2×C22⋊C4—942no—
249C2×C22⋊C4—941no—
250C2×C42—21no—
251C2×C42—471no—
252C2×C42—471no—
253C2×C42—472no—
254C2×C42—472no—
255C2×C42C22×D4711yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—941no—
259C4⋊C8—941no—
260C4×C8—21no—
261C4×C8—472no—
262C4×C8—941no—
263C4×C8C22⋊D4712yes—
264#95—942no—
265#95—942no—
266C24—941no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8#1062532412yes—
273C2×D4—472no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—472no—
282C22×C4—472no—
283C22×C4—941no—
284C22×C4—1881no—
285C22×C4—1881no—
286C22×C4—1882no—
287C22×C4—1882no—
288C22×C4C2×C4×D4711yescharacteristic
289C22×C4D4×D4711yescharacteristic
290C22×C4D4×D4711yescharacteristic
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—41no—
294C2×C8—42no—
295C2×C8—942no—
296C2×C8—1881no—
297C2×C8—1882no—
298C2×C8—1882no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—941no—
304C4⋊C4—941no—
305C22⋊C4—948no—
306C22⋊C4—1884no—
307C22⋊C4—1881no—
308C22⋊C4—1881no—
309C42—41no—
310C42—41no—
311C42—941no—
312C42—941no—
313C42—941no—
314C42—941no—
315C42—942no—
316C42—942no—
317C42—1882no—
318C42#1062535011yescharacteristic
319C42D4×D4711yescharacteristic
320C42#1062535211yescharacteristic
321C42C2×C22⋊D4711yescharacteristic
322C23—942no—
323C23—1881no—
324C23—1881no—
325C23—1882no—
326C23—1882no—
327C23C22⋊C4×D4711yescharacteristic
328Q8—22no—
329Q8—22no—
330Q8—41no—
331Q8—41no—
332D4—942no—
333D4—942no—
334D4—1881no—
335D4—1881no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—942no—
343C2×C4—942no—
344C2×C4—942no—
345C2×C4—942no—
346C2×C4—942no—
347C2×C4—942no—
348C2×C4—3762no—
349C2×C4—3761no—
350C2×C4—3761no—
351C2×C4—1881no—
352C2×C4—1882no—
353C2×C4(C22⋊D47)⋊C411yescharacteristic
354C2×C4C4×C22⋊D4711yescharacteristic
355C2×C4#1309399611yescharacteristic
356C2×C4#1309399711yescharacteristic
357C2×C4#1309401011yescharacteristic
358C2×C4#1309402011yescharacteristic
359C2×C4M16×D4711yescharacteristic
360C2×C4C2×#1062532411yescharacteristic
361C2×C4#1309403011yescharacteristic
362C2×C4#1309403211yescharacteristic
363C2×C4#1309404512yes—
364C2×C4#1309404712yes—
365C8—42no—
366C8—81no—
367C8—3761no—
368C8—1882no—
369C22—3762no—
370C22—3761no—
371C22—3761no—
372C22—1884no—
373C22—1882no—
374C22#1568902311yescharacteristic
375C22#1568908511yescharacteristic
376C22#1568908811yescharacteristic
377C22#1568911812yes—
378C22#1568913812yes—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—81no—
383C4—3761no—
384C4—1882no—
385C4—1882no—
386C4#1568919111yescharacteristic
387C4#1568919211yescharacteristic
388C4#1568919411yescharacteristic
389C4#1568919711yescharacteristic
390C4#1568947912yes—
391C4#1568950411yescharacteristic
392C4#1568950811yescharacteristic
393C2—3762no—
394C2#2024179512yes—
395C2#2024182112yes—
396C2#2024418411yescharacteristic
397C2#2024419611yescharacteristic
398C2#2024421811yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×Q8⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D188C2×C4
cosocleC2×C42×C47C23
hypercenterC2×Q8⋊C8D47
hypocenterC47#9645
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #20243504C2semidirect
3. #20243133C2semidirect
4. C2×Q8⋊(C47⋊C8)C2semidirect
7. C2×C47×Q8⋊C8C2semidirect
198. C2×Q8⋊C8D47semidirect
226. C47#9645semidirect

Maximal subgroups

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

subgroupindex
C4×#130940132
#202435042
#202431332
C2×Q8⋊(C47⋊C8)2
C2×#156888522
C2×#156888502
C2×C47×Q8⋊C82
#964547