Finite Group Databasebeta

← #26107620

Subgroups — #26107620

Order 12032.

1050 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093989C211yesmaximal, characteristic
2#20243454C212yesmaximal
3C2×#15688849C211yesmaximal, characteristic
4C2×#15688848C212yesmaximal
5C2×C47×#324C211yesmaximal, characteristic
6C23×Dic94C411yescharacteristic
7C2×#13093989—24no—
8C2×#13093989—24no—
9C2×#13093989—22no—
10C2×#13093989—22no—
11C22×Dic47⋊C4C411yescharacteristic
12C22×Dic47⋊C4C2211yescharacteristic
13C22×C4×Dic47C411yescharacteristic
14C22×C4×Dic47C411yescharacteristic
15C22×C4×Dic47C2211yescharacteristic
16C2×C22⋊(C47⋊C8)C2212yes—
17#15688877—24no—
18#15688849—22no—
19#15688848—24no—
20C22×C4⋊C4×C47C2211yescharacteristic
21C2×C22⋊C8×C47C2212yes—
22C47×#324—22no—
23C22×Dic94—22no—
24C22×Dic94—22no—
25C22×Dic94—22no—
26C22×Dic94—22no—
27C22×Dic94—22no—
28C22×Dic94—22no—
29C22×Dic94C814yescomplemented
30C23×Dic47C2×C411yescharacteristic
31C23×Dic47C2×C411yescharacteristic
32C23×Dic47C2×C411yescharacteristic
33C23×Dic47C2×C411yescharacteristic
34C22×C47⋊C8—22no—
35#13093989—216no—
36#13093989—216no—
37C2×Dic47⋊C4—22no—
38C2×Dic47⋊C4—22no—
39C2×Dic47⋊C4—21no—
40C2×Dic47⋊C4—21no—
41C2×Dic47⋊C4—22no—
42C2×Dic47⋊C4—22no—
43C2×Dic47⋊C4D414yes—
44C2×C4×Dic47—22no—
45C2×C4×Dic47—22no—
46C2×C4×Dic47—21no—
47C2×C4×Dic47—22no—
48C2×C4×Dic47—21no—
49C2×C4×Dic47—22no—
50C2×C4×Dic47—22no—
51C2×C4×Dic47—22no—
52C2×C4×Dic47—22no—
53C2×C4×Dic47D414yes—
54C22⋊(C47⋊C8)—22no—
55C22⋊(C47⋊C8)—22no—
56C23×C4×C47C2×C411yescharacteristic
57C23×C4×C47C2×C411yescharacteristic
58C23×C4×C47C2311yescharacteristic
59C22×C8×C47—22no—
60C2×C4⋊C4×C47—22no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47D412yes—
63C2×C4⋊C4×C47D412yes—
64C22⋊C8×C47—22no—
65C22⋊C8×C47—22no—
66C24×C47C22×C411yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—42no—
74C22×C4×C47—42no—
75C22×C4×C47C22⋊C412yes—
76C22×C4×C47C22⋊C412yes—
77C22×C4×C47C2×C812yes—
78C22×C4×C47M1612yes—
79C22×C4×C47C2×D412yes—
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47C2×D412yes—
82C22×C4×C47C2×D411yescharacteristic
83C22×Dic47—21no—
84C22×Dic47—21no—
85C22×Dic47—21no—
86C22×Dic47—21no—
87C22×Dic47—21no—
88C22×Dic47—21no—
89C22×Dic47—21no—
90C22×Dic47—21no—
91C22×Dic47—21no—
92C22×Dic47—21no—
93C22×Dic47—24no—
94C22×Dic47—21no—
95C22×Dic47—21no—
96C22×Dic47—42no—
97C22×Dic47C22⋊C412yes—
98C22×Dic47C22⋊C412yes—
99C22×Dic47C22⋊C412yes—
100C22×Dic47C22⋊C412yes—
101C22×Dic47C2×C812yes—
102C22×Dic47C2×C812yes—
103C22×Dic47M1612yes—
104C22×Dic47M1612yes—
105C2×Dic94—28no—
106C2×Dic94—28no—
107C2×Dic94—28no—
108C2×Dic94—28no—
109C2×Dic94—28no—
110C2×Dic94—28no—
111C2×Dic94—28no—
112C2×C8×C47—44no—
113C2×C8×C47—42no—
114C4⋊C4×C47—24no—
115C4⋊C4×C47—24no—
116Dic47⋊C4—28no—
117Dic47⋊C4—24no—
118Dic47⋊C4—24no—
119C4×Dic47—28no—
120C4×Dic47—28no—
121C4×Dic47—24no—
122C4×Dic47—24no—
123C2×C47⋊C8—44no—
124C2×C47⋊C8—42no—
125C23×C47—22no—
126C23×C47—22no—
127C23×C47C2×C22⋊C411yescharacteristic
128C23×C47C2×C22⋊C411yescharacteristic
129C23×C47C2×C22⋊C411yescharacteristic
130C23×C47C22×C811yescharacteristic
131C23×C47C2×M1611yescharacteristic
132C23×C47C2×M1611yescharacteristic
133C23×C47C2×M1611yescharacteristic
134C2×C4×C47—22no—
135C2×C4×C47—22no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—22no—
139C2×C4×C47—22no—
140C2×C4×C47—24no—
141C2×C4×C47—22no—
142C2×C4×C47—41no—
143C2×C4×C47—42no—
144C2×C4×C47—41no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47—42no—
148C2×C4×C47C22⋊C814yes—
149C2×C4×C47#12012yes—
150C2×C4×C47#12012yes—
151C2×Dic47—24no—
152C2×Dic47—24no—
153C2×Dic47—22no—
154C2×Dic47—22no—
155C2×Dic47—22no—
156C2×Dic47—22no—
157C2×Dic47—22no—
158C2×Dic47—22no—
159C2×Dic47—22no—
160C2×Dic47—22no—
161C2×Dic47—22no—
162C2×Dic47—22no—
163C2×Dic47—22no—
164C2×Dic47—22no—
165C2×Dic47—22no—
166C2×Dic47—22no—
167C2×Dic47—22no—
168C2×Dic47—42no—
169C2×Dic47—42no—
170C2×Dic47—42no—
171C2×Dic47C22⋊C814yes—
172C2×Dic47C22⋊C814yes—
173C2×Dic47#10114yes—
174Dic94—232no—
175C8×C47—82no—
176C47⋊C8—82no—
177#8303—471nomaximal, Sylow
178C22×C47—22no—
179C22×C47—22no—
180C22×C47—22no—
181C22×C47—22no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—21no—
186C22×C47#37911yescharacteristic
187C22×C47C2×C22⋊C811yescharacteristic
188C22×C47C2×C22⋊C811yescharacteristic
189C22×C47C2×C22⋊C811yescharacteristic
190C22×C47#40711yescharacteristic
191C22×C47#40711yescharacteristic
192C22×C47#40711yescharacteristic
193C22×C47#41012yes—
194C22×C47C2×#10112yes—
195C4×C47—24no—
196C4×C47—22no—
197C4×C47—22no—
198C4×C47—42no—
199Dic47—24no—
200Dic47—24no—
201Dic47—24no—
202Dic47—42no—
203C22×C4×Q8—471no—
204#1817—472no—
205C2×#324—472no—
206C2×#324—471no—
207C2×#324D4711yescharacteristic
208C2×C47—21no—
209C2×C47—21no—
210C2×C47—21no—
211C2×C47—21no—
212C2×C47#146112yes—
213C2×C47#146712yes—
214C2×C47#177911yescharacteristic
215C2×C47#178211yescharacteristic
216C2×C47#178411yescharacteristic
217C23×Q8—471no—
218C2×C4×Q8—944no—
219C2×C4×Q8—944no—
220C2×C4×Q8—942no—
221C2×C4×Q8—942no—
222C22×C4⋊C4—471no—
223C22×C4⋊C4—471no—
224C22×C4⋊C4C2×D4711yescharacteristic
225C22×C42—471no—
226C22×C42—471no—
227C22×C42—471no—
228C2×C22⋊C8—472no—
229C2×C22⋊C8C2×D4712yes—
230#336—944no—
231#324—22no—
232#324—944no—
233#324—942no—
234C47#830311yescharacteristic, complemented, Sylow
235C22×Q8—474no—
236C22×Q8—942no—
237C22×Q8—942no—
238C22×Q8—942no—
239C22×Q8—942no—
240C22×Q8—942no—
241C22×Q8—942no—
242C23×C4—471no—
243C23×C4—471no—
244C23×C4—471no—
245C23×C4—471no—
246C23×C4C4×D4711yescharacteristic
247C23×C4C4×D4711yescharacteristic
248C23×C4C22×D4711yescharacteristic
249C22×C8—22no—
250C22×C8—942no—
251C4×Q8—9416no—
252C4×Q8—9416no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—474no—
256C2×C4⋊C4—942no—
257C2×C4⋊C4—942no—
258C2×C4⋊C4—942no—
259C2×C4⋊C4—941no—
260C2×C4⋊C4—942no—
261C2×C4⋊C4—941no—
262C2×C4⋊C4D18812yes—
263C2×C4⋊C4C22⋊D4712yes—
264C2×C42—474no—
265C2×C42—942no—
266C2×C42—942no—
267C2×C42—942no—
268C2×C42—942no—
269C2×C42—942no—
270C2×C42—942no—
271C2×C42—941no—
272C2×C42—942no—
273C2×C42—941no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276C22⋊C8—942no—
277C22⋊C8—942no—
278C24C2×C4×D4711yescharacteristic
279C2×Q8—948no—
280C2×Q8—948no—
281C2×Q8—948no—
282C2×Q8—948no—
283C2×Q8—948no—
284C2×Q8—948no—
285C2×Q8—948no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—472no—
295C22×C4—472no—
296C22×C4—472no—
297C22×C4—472no—
298C22×C4—472no—
299C22×C4—472no—
300C22×C4—472no—
301C22×C4—472no—
302C22×C4—944no—
303C22×C4—941no—
304C22×C4—941no—
305C22×C4—941no—
306C22×C4—941no—
307C22×C4—941no—
308C22×C4—941no—
309C22×C4—941no—
310C22×C4—941no—
311C22×C4—941no—
312C22×C4—941no—
313C22×C4—941no—
314C22×C4—941no—
315C22×C4—1882no—
316C22×C4C8×D4712yes—
317C22×C4#1062532412yes—
318C22×C4(C2×D47)⋊C412yes—
319C22×C4(C2×D47)⋊C412yes—
320C22×C4C2×D18811yescharacteristic
321C22×C4D4×D4712yes—
322C22×C4D4×D4712yes—
323C22×C4C2×C22⋊D4711yescharacteristic
324C2×C8—44no—
325C2×C8—42no—
326C2×C8—1884no—
327C2×C8—1882no—
328C4⋊C4—24no—
329C4⋊C4—24no—
330C4⋊C4—948no—
331C4⋊C4—944no—
332C4⋊C4—944no—
333C42—948no—
334C42—948no—
335C42—944no—
336C42—944no—
337C23—22no—
338C23—22no—
339C23C22⋊C4×D4711yescharacteristic
340C23C22⋊C4×D4711yescharacteristic
341C23C2×(C2×D47)⋊C411yescharacteristic
342C23C2×C8×D4711yescharacteristic
343C23M16×D4711yescharacteristic
344C23M16×D4711yescharacteristic
345C23C2×#1062532411yescharacteristic
346Q8—9432no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—474no—
362C2×C4—474no—
363C2×C4—474no—
364C2×C4—944no—
365C2×C4—944no—
366C2×C4—942no—
367C2×C4—942no—
368C2×C4—942no—
369C2×C4—942no—
370C2×C4—942no—
371C2×C4—942no—
372C2×C4—942no—
373C2×C4—942no—
374C2×C4—942no—
375C2×C4—942no—
376C2×C4—942no—
377C2×C4—942no—
378C2×C4—942no—
379C2×C4—942no—
380C2×C4—942no—
381C2×C4—1882no—
382C2×C4—1882no—
383C2×C4—1882no—
384C2×C4(C2×D47)⋊C814yes—
385C2×C4#1309399212yes—
386C2×C4#1309399412yes—
387C8—82no—
388C8—3762no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22#1568897811yescharacteristic
398C22C22⋊C8×D4711yescharacteristic
399C22C22⋊C8×D4711yescharacteristic
400C22C2×(C2×D47)⋊C811yescharacteristic
401C22#1568908511yescharacteristic
402C22#1568908511yescharacteristic
403C22#1568908611yescharacteristic
404C22#1568909512yes—
405C22#101×D4712yes—
406C4—24no—
407C4—22no—
408C4—22no—
409C4—42no—
410C4—944no—
411C4—944no—
412C4—944no—
413C4—1882no—
414C2—21no—
415C2—21no—
416C2—21no—
417C2—21no—
418C2#2024171012yes—
419C2#2024173012yes—
420C2#2024329711yescharacteristic
421C2#2024330411yescharacteristic
422C2#2024331011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC23×C47C22×C8
FrattiniC23×C4C22×D47
FittingC2×C47×#324C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenterC2×#324D47
hypocenterC47#8303
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
29. C22×Dic94C8semidirect
234. C47#8303semidirect

Maximal subgroups

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

subgroupindex
C22×#130939892
#202434542
C2×#156888492
C2×#156888482
C2×C47×#3242
#830347