Finite Group Databasebeta

← #26112594

Subgroups — #26112594

Order 12032.

452 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252046C211yesmaximal, characteristic
2#20243487C211yesmaximal, characteristic
3#20241908C211yesmaximal, characteristic
4#20241752C211yesmaximal, characteristic
5#20241265C211yesmaximal, characteristic
6#20241235C211yesmaximal, characteristic
7C2×C47×#485C211yesmaximal, characteristic
8#15689184—22no—
9#15689180—21no—
10#15689176—21no—
11#15689150—21no—
12#15689087C2211yescharacteristic
13#15689087C2211yescharacteristic
14C2×C22⋊(C47⋊C8)C2211yescharacteristic
15#15689079—21no—
16C4×C22⋊Dic47C2211yescharacteristic
17#15688882—21no—
18#15688882—21no—
19#15688860—22no—
20#15688849—21no—
21#15688849—21no—
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×#117×C47C2211yescharacteristic
24C47×#485—21no—
25C47×#485—21no—
26C47×#485—21no—
27C47×#485—21no—
28C2×#107×C47C411yescharacteristic, complemented
29C2×#106×C47C411yescharacteristic, complemented
30C2×#103×C47C411yescharacteristic, complemented
31C2×#103×C47C411yescharacteristic, complemented
32C2×C22⋊C8×C47C2211yescharacteristic
33C2×#10625329—21no—
34C2×#10625329—21no—
35C22×C47⋊C8—21no—
36C2×C22⋊Dic47—21no—
37C2×C4×Dic47—21no—
38C4⋊(C47⋊C8)—22no—
39C4⋊(C47⋊C8)—22no—
40C22⋊(C47⋊C8)—21no—
41C22⋊(C47⋊C8)—21no—
42C22⋊(C47⋊C8)—21no—
43C22⋊(C47⋊C8)—21no—
44C22⋊(C47⋊C8)D411yescharacteristic
45C22⋊(C47⋊C8)D411yescharacteristic
46C22⋊(C47⋊C8)D412yes—
47#13093935—22no—
48C4×C47⋊C8—22no—
49C47⋊#95—21no—
50C22×Q8×C47C2×C411yescharacteristic
51C23×C4×C47C2311yescharacteristic
52C22×C8×C47C2×C411yescharacteristic
53C22×C8×C47C2×C411yescharacteristic
54C22⋊Q8×C47—21no—
55C22⋊Q8×C47—21no—
56C22⋊Q8×C47—21no—
57C22⋊Q8×C47—21no—
58#117×C47—21no—
59#117×C47—21no—
60#117×C47D411yescharacteristic
61#117×C47D411yescharacteristic
62#117×C47D411yescharacteristic
63#117×C47D411yescharacteristic
64C2×C4⋊C4×C47—21no—
65C2×C4⋊C4×C47C2×C411yescharacteristic
66C2×C4⋊C4×C47C2×C411yescharacteristic
67C2×C4⋊C4×C47C2×C411yescharacteristic
68C2×C22⋊C4×C47—21no—
69C2×C22⋊C4×C47—21no—
70C2×C42×C47—21no—
71#107×C47—21no—
72#107×C47—21no—
73#106×C47—21no—
74#106×C47—21no—
75#103×C47—21no—
76#103×C47—21no—
77#103×C47—21no—
78#103×C47—21no—
79C22⋊C8×C47—21no—
80C22⋊C8×C47—21no—
81C24×C47#4111yescharacteristic
82C2×Q8×C47—21no—
83C2×Q8×C47—21no—
84C2×Q8×C47—41no—
85C2×Q8×C47—41no—
86C22×C4×C47—21no—
87C22×C4×C47—21no—
88C22×C4×C47—21no—
89C22×C4×C47—21no—
90C22×C4×C47—41no—
91C22×C4×C47—41no—
92C22×C4×C47C22×C411yescharacteristic
93C22×C4×C47C2×D411yescharacteristic
94C22×C4×C47C2×D411yescharacteristic
95C22×C4×C47C2×D411yescharacteristic
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47#4111yescharacteristic
98C22×Dic47—41no—
99C2×C8×C47—21no—
100C2×C8×C47—21no—
101C2×C8×C47—41no—
102C2×C8×C47—41no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—21no—
106C4⋊C4×C47—21no—
107C4⋊C4×C47—41no—
108C4⋊C4×C47—41no—
109C4⋊C4×C47C22⋊C411yescharacteristic
110C4⋊C4×C47C22⋊C411yescharacteristic
111C4⋊C4×C47C22⋊C411yescharacteristic
112C4⋊C4×C47C22⋊C411yescharacteristic
113C22⋊C4×C47—21no—
114C22⋊C4×C47—21no—
115C22⋊C4×C47—21no—
116C22⋊C4×C47—21no—
117C22⋊C4×C47—41no—
118C22⋊C4×C47—41no—
119C42×C47—21no—
120C42×C47—21no—
121C42×C47—21no—
122C42×C47—21no—
123C22⋊Dic47—22no—
124C22⋊Dic47—41no—
125C4×Dic47—41no—
126C4×Dic47—41no—
127#10625329—41no—
128#10625329—41no—
129#10625329—41no—
130#10625329—41no—
131C2×C47⋊C8—21no—
132C2×C47⋊C8—22no—
133C2×C47⋊C8—21no—
134C2×C47⋊C8—41no—
135C2×C47⋊C8—41no—
136C2×C47⋊C8—41no—
137C23×C47—21no—
138C23×C47—21no—
139C23×C47—41no—
140C23×C47—41no—
141C23×C47C4×D411yescharacteristic
142C23×C47#12111yescharacteristic
143C23×C47#12311yescharacteristic
144Q8×C47—41no—
145Q8×C47—41no—
146Q8×C47—81no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—41no—
158C2×C4×C47—41no—
159C2×C4×C47—41no—
160C2×C4×C47—41no—
161C2×C4×C47—41no—
162C2×C4×C47—41no—
163C2×C4×C47—41no—
164C2×C4×C47—41no—
165C2×C4×C47—41no—
166C2×C4×C47—81no—
167C2×C4×C47—81no—
168C2×C4×C47C2×C22⋊C411yescharacteristic
169C2×C4×C47C4×D411yescharacteristic
170C2×C4×C47#12011yescharacteristic
171C2×C4×C47#12111yescharacteristic
172C2×Dic47—42no—
173C2×Dic47—81no—
174C2×Dic47—81no—
175C8×C47—41no—
176C8×C47—41no—
177C47⋊C8—41no—
178C47⋊C8—41no—
179C47⋊C8—42no—
180C47⋊C8—81no—
181#9240—471nomaximal, Sylow
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—21no—
189C22×C47—21no—
190C22×C47—81no—
191C22×C47—81no—
192C22×C47#38611yescharacteristic
193C22×C47#44311yescharacteristic
194C22×C47#44411yescharacteristic
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—21no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47—41no—
201C4×C47—41no—
202C4×C47—81no—
203C4×C47—81no—
204C4×C47#41011yescharacteristic
205C4×C47#41011yescharacteristic
206Dic47—82no—
207C2×#485D4711yescharacteristic
208#2924—471no—
209#1826—471no—
210#1508—471no—
211#1472—471no—
212#1293—471no—
213#1282—471no—
214C2×C47—21no—
215C2×C47—21no—
216C2×C47—41no—
217C2×C47—41no—
218C2×C47#187611yescharacteristic
219C2×C47#189911yescharacteristic
220C2×C47#190211yescharacteristic
221C2×C22⋊Q8C2×D4711yescharacteristic
222C2×#117C2×D4711yescharacteristic
223#485—21no—
224#485—21no—
225#485—21no—
226#485—21no—
227#433—942no—
228#432—941no—
229#431—941no—
230C2×#107Dic4711yescharacteristic, complemented
231C2×#106Dic4711yescharacteristic, complemented
232#424—941no—
233C2×#103Dic4711yescharacteristic, complemented
234C2×#103Dic4711yescharacteristic, complemented
235#407—471no—
236#407—471no—
237C2×C22⋊C8—471no—
238C2×C22⋊C8C2×D4711yescharacteristic
239#405—941no—
240C4×C22⋊C4—471no—
241#339—941no—
242#339—941no—
243#328—942no—
244#324—941no—
245#324—941no—
246C47#924011yescharacteristic, complemented, Sylow
247C22×Q8C2×Dic4711yescharacteristic
248C23×C4C22×D4711yescharacteristic
249C2×M16—941no—
250C2×M16—941no—
251C22×C8—941no—
252C22×C8C2×Dic4711yescharacteristic
253C22×C8C2×Dic4711yescharacteristic
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258#117—21no—
259#117—21no—
260#117C22⋊D4711yescharacteristic
261#117C22⋊D4711yescharacteristic
262#117C22⋊D4711yescharacteristic
263#117C22⋊D4711yescharacteristic
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×Dic4711yescharacteristic
266C2×C4⋊C4C2×Dic4711yescharacteristic
267C2×C4⋊C4C2×Dic4711yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—941no—
271C2×C42—21no—
272C2×C42—941no—
273#107—21no—
274#107—21no—
275#106—21no—
276#106—21no—
277C4⋊C8—942no—
278C4⋊C8—942no—
279#103—21no—
280#103—21no—
281#103—21no—
282#103—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—471no—
286C22⋊C8—471no—
287C22⋊C8—472no—
288C22⋊C8—941no—
289C22⋊C8—941no—
290C22⋊C8—941no—
291C22⋊C8—941no—
292#97—942no—
293C4×C8—942no—
294#95—941no—
295C24#1062535211yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—1881no—
307C22×C4D4×D4711yescharacteristic
308C22×C4D4×D4711yescharacteristic
309C22×C4#1062535211yescharacteristic
310C22×C4C22×Dic4711yescharacteristic
311C22×C4C2×C22⋊D4711yescharacteristic
312C22×C4C2×C22⋊D4711yescharacteristic
313M16—1881no—
314M16—1881no—
315M16—1881no—
316M16—1881no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—941no—
322C2×C8—942no—
323C2×C8—941no—
324C2×C8—1881no—
325C2×C8—1881no—
326C2×C8—1881no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊Dic4711yescharacteristic
334C4⋊C4C22⋊Dic4711yescharacteristic
335C4⋊C4C22⋊Dic4711yescharacteristic
336C4⋊C4C22⋊Dic4711yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—942no—
344C22⋊C4—1881no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—1881no—
350C42—1881no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23D4×Dic4711yescharacteristic
356C23#1309399611yescharacteristic
357C23#1309400511yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—3761no—
383C2×C4—3761no—
384C2×C4—1882no—
385C2×C4C2×C22⋊Dic4711yescharacteristic
386C2×C4D4×Dic4711yescharacteristic
387C2×C4#1309399211yescharacteristic
388C2×C4#1309399611yescharacteristic
389C8—41no—
390C8—41no—
391C8—3761no—
392C8—1881no—
393C8—1881no—
394C8—1882no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22#1568900311yescharacteristic
406C22#1568924011yescharacteristic
407C22#1568924511yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—81no—
417C4—3762no—
418C4#1568909711yescharacteristic
419C4#1568909711yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2#2024371711yescharacteristic
425C2#2024384711yescharacteristic
426C2#2024386311yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#485C2
socleC22×C47#386
prime radicalC24×C47#41
cosocleC23×C4×C47C23
hypercenterC2×#485D47
hypocenterC47#9240
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
28. C2×#107×C47C4semidirect
29. C2×#106×C47C4semidirect
30. C2×#103×C47C4semidirect
31. C2×#103×C47C4semidirect
230. C2×#107Dic47semidirect
231. C2×#106Dic47semidirect
233. C2×#103Dic47semidirect
234. C2×#103Dic47semidirect
246. C47#9240semidirect

Maximal subgroups

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

subgroupindex
#202520462
#202434872
#202419082
#202417522
#202412652
#202412352
C2×C47×#4852
#924047