Finite Group Databasebeta

← #26109173

Subgroups — #26109173

Order 12032.

550 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C22⋊D47C211yesmaximal, characteristic
2#20243417C211yesmaximal, characteristic, complemented
3#20243373C212yesmaximal
4#20241255C212yesmaximal, complemented
5C47×#1808C211yesmaximal, characteristic, complemented
6C22×C8×D47C411yescharacteristic, complemented
7C2×C4×C22⋊D47C2211yescharacteristic
8C8×C22⋊D47—21no—
9C8×C22⋊D47—21no—
10C8×C22⋊D47—21no—
11C8×C22⋊D47—21no—
12C2×#13093958—21no—
13C2×Dic47⋊C8C411yescharacteristic, complemented
14C2×#13093938—22no—
15C2×C22⋊(C47⋊C8)C2211yescharacteristic
16C2×(C2×D47)⋊C8C411yescharacteristic, complemented
17C2×C8×Dic47C411yescharacteristic, complemented
18#15688983C2212yes—
19#15688889—22no—
20#15688886—21no—
21C23×C8×C47C2211yescharacteristic
22C2×#107×C47—21no—
23C47×#380C2212yes—
24C47×#340—21no—
25C22×C22⋊D47D411yescharacteristic
26C22×C4×D47C2×C411yescharacteristic
27C22×C47⋊C8C2×C411yescharacteristic
28C22×C47⋊C8C2×C411yescharacteristic
29C2×C8×D47—21no—
30C2×C8×D47—21no—
31C2×C8×D47—42no—
32C4×C22⋊D47—21no—
33C4×C22⋊D47—21no—
34C4×C22⋊D47—21no—
35C4×C22⋊D47—21no—
36C2×C4⋊Dic47—22no—
37C2×Dic47⋊C4Q811yescharacteristic
38C2×C22⋊Dic47—22no—
39C2×C22⋊Dic47D411yescharacteristic
40C2×(C2×D47)⋊C4Q811yescharacteristic
41C2×C4×Dic47C2×C411yescharacteristic
42#13093958—42no—
43Dic47⋊C8—21no—
44Dic47⋊C8—21no—
45#13093938—44no—
46C22⋊(C47⋊C8)—21no—
47C22⋊(C47⋊C8)—21no—
48(C2×D47)⋊C8—21no—
49(C2×D47)⋊C8—21no—
50C8×Dic47—21no—
51C8×Dic47—21no—
52C47⋊#95—22no—
53C23×C4×C47C2311yescharacteristic
54C22×C8×C47—42no—
55C22×C8×C47C2×C411yescharacteristic
56C22×C8×C47C2×C411yescharacteristic
57C22×C8×C47D411yescharacteristic
58C22×C8×C47D411yescharacteristic
59C22×C8×C47D411yescharacteristic
60C22×C8×C47D411yescharacteristic
61C2×C4⋊C4×C47—22no—
62C2×C22⋊C4×C47—22no—
63#107×C47—42no—
64#95×C47—22no—
65C24×C47C2×D411yescharacteristic
66C23×D47C4⋊C411yescharacteristic
67C22×C4×C47—41no—
68C22×C4×C47—41no—
69C22×C4×C47—42no—
70C22×C4×C47C22×C411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×Q811yescharacteristic
74C22×C4×C47#4111yescharacteristic
75C22×C4×C47#4111yescharacteristic
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80C2×C22⋊D47D812yes—
81C2×C22⋊D47Q1612yes—
82C22×Dic47—42no—
83C22×Dic47C4⋊C411yescharacteristic
84C22×Dic47C4⋊C411yescharacteristic
85C22×Dic47C4⋊C411yescharacteristic
86C2×C4×D47—21no—
87C2×C4×D47—21no—
88C2×C4×D47—41no—
89C2×C4×D47—41no—
90C2×C8×C47—22no—
91C2×C8×C47—22no—
92C2×C8×C47—22no—
93C2×C8×C47—41no—
94C2×C8×C47—41no—
95C2×C8×C47—41no—
96C2×C8×C47C22⋊C411yescharacteristic
97C2×C8×C47C22⋊C411yescharacteristic
98C2×C8×C47C22⋊C411yescharacteristic
99C2×C8×C47C22⋊C411yescharacteristic
100C4⋊C4×C47—42no—
101C4⋊C4×C47—42no—
102C22⋊C4×C47—42no—
103C22⋊C4×C47—42no—
104C22⋊Dic47—21no—
105C22⋊Dic47—21no—
106C22⋊Dic47—42no—
107C22⋊Dic47—42no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110C4⋊Dic47—42no—
111C4⋊Dic47—42no—
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114C4×Dic47—21no—
115C4×Dic47—21no—
116C2×C47⋊C8—21no—
117C2×C47⋊C8—21no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8—41no—
120C8×D47—42no—
121C8×D47—42no—
122C23×C47—41no—
123C23×C47—41no—
124C23×C47C2×C4⋊C411yescharacteristic
125C23×C47#12111yescharacteristic
126C23×C47#12111yescharacteristic
127C23×C47C2×D811yescharacteristic
128C23×C47C2×Q1611yescharacteristic
129C23×C47#13511yescharacteristic
130C23×C47#13511yescharacteristic
131C22×D47—21no—
132C22×D47—21no—
133C22×D47—41no—
134C22×D47—41no—
135C22×D47#10712yescomplemented
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—82no—
146C2×C4×C47—82no—
147C2×C4×C47—82no—
148C2×C4×C47C2×C22⋊C411yescharacteristic
149C2×C4×C47#11711yescharacteristic
150C2×C4×C47C22⋊Q811yescharacteristic
151C2×C4×C47C22⋊Q811yescharacteristic
152C22⋊D47—22no—
153C22⋊D47—22no—
154C22⋊D47—22no—
155C22⋊D47—22no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—41no—
161C2×Dic47—41no—
162C2×Dic47—82no—
163C2×Dic47—82no—
164C2×Dic47—82no—
165C2×Dic47#10712yescomplemented
166C4×D47—42no—
167C4×D47—41no—
168C4×D47—41no—
169C8×C47—21no—
170C8×C47—21no—
171C8×C47—21no—
172C8×C47#9912yescomplemented
173C47⋊C8—41no—
174C47⋊C8—41no—
175#8609—471nomaximal, Sylow
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47#38011yescharacteristic
187C22×C47C2×#10711yescharacteristic
188C22×C47#42711yescharacteristic
189C22×C47#46611yescharacteristic
190C22×C47#46611yescharacteristic
191C22×C47#46711yescharacteristic
192C22×C47#46711yescharacteristic
193C2×D47—22no—
194C2×D47—42no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—42no—
198C4×C47—21no—
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—162no—
202C4×C47C2×#9911yescharacteristic
203C4×C47#41011yescharacteristic
204Dic47—22no—
205Dic47—41no—
206Dic47—41no—
207Dic47—162no—
208C2×C8×D4—471no—
209#1808—471no—
210#1808D4711yescharacteristic, complemented
211#1799—472no—
212#1289—472no—
213C2×C47—21no—
214C2×C47—21no—
215C2×C47—21no—
216C2×C47—21no—
217C2×C47—21no—
218C2×C47—21no—
219C2×C47#179911yescharacteristic
220C2×C47#180811yescharacteristic
221C2×C47#181211yescharacteristic
222D47—42no—
223C23×C8—471no—
224C23×C8C2×D4711yescharacteristic
225C2×C4×D4—471no—
226C8×D4—941no—
227C8×D4—941no—
228C8×D4—941no—
229C8×D4—941no—
230C2×#107—21no—
231C2×#107—941no—
232C2×C4⋊C8—471no—
233C2×#99—942no—
234C2×C22⋊C8—471no—
235C2×C22⋊C8—471no—
236C2×C4×C8—471no—
237#380—472no—
238#380C2×D4712yes—
239#342—942no—
240#340—21no—
241#340—941no—
242C47#860911yescharacteristic, complemented, Sylow
243C22×D4—471no—
244C23×C4—471no—
245C23×C4C22×D4711yescharacteristic
246C22×C8—42no—
247C22×C8—471no—
248C22×C8—471no—
249C22×C8—941no—
250C22×C8—941no—
251C22×C8—1882no—
252C22×C8C4×D4711yescharacteristic
253C22×C8C4×D4711yescharacteristic
254C22×C8D18811yescharacteristic
255C22×C8D18811yescharacteristic
256C22×C8C22⋊D4711yescharacteristic
257C22×C8C22⋊D4711yescharacteristic
258C4×D4—941no—
259C4×D4—941no—
260C4×D4—941no—
261C4×D4—941no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—471no—
264C2×C4⋊C4—942no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—471no—
267C2×C22⋊C4—471no—
268C2×C22⋊C4—942no—
269C2×C42—471no—
270#107—42no—
271#107—1882no—
272C4⋊C8—941no—
273C4⋊C8—941no—
274#99—1884no—
275C22⋊C8—941no—
276C22⋊C8—941no—
277C22⋊C8—941no—
278C22⋊C8—941no—
279C4×C8—941no—
280C4×C8—941no—
281#95—22no—
282#95—942no—
283C24—471no—
284C24D4×D4711yescharacteristic
285C2×D4—472no—
286C2×D4—472no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4—941no—
290C2×D4—941no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—471no—
295C22×C4—471no—
296C22×C4—471no—
297C22×C4—941no—
298C22×C4—941no—
299C22×C4—1881no—
300C22×C4—1881no—
301C22×C4—1882no—
302C22×C4C2×C4×D4711yescharacteristic
303C22×C4C2×D18811yescharacteristic
304C22×C4#1062535211yescharacteristic
305C22×C4Q8×D4711yescharacteristic
306C22×C4#1062535411yescharacteristic
307C22×C4C2×C22⋊D4711yescharacteristic
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—941no—
315C2×C8—941no—
316C2×C8—1882no—
317C2×C8—1882no—
318C2×C8—1881no—
319C2×C8—1881no—
320C2×C8(C2×D47)⋊C411yescharacteristic
321C2×C8(C2×D47)⋊C411yescharacteristic
322C2×C8(C2×D47)⋊C411yescharacteristic
323C2×C8(C2×D47)⋊C411yescharacteristic
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—941no—
327C4⋊C4—941no—
328C4⋊C4—1882no—
329C4⋊C4—1882no—
330C22⋊C4—42no—
331C22⋊C4—42no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C22⋊C4—1882no—
337C22⋊C4—1882no—
338C42—941no—
339C42—941no—
340C23—41no—
341C23—41no—
342C23—472no—
343C23—941no—
344C23—941no—
345C23—1881no—
346C23—1881no—
347C23C4⋊C4×D4711yescharacteristic
348C23#1309399511yescharacteristic
349C23#1309399911yescharacteristic
350C23D8×D4711yescharacteristic
351C23Q16×D4711yescharacteristic
352C23#1309404311yescharacteristic
353C23#1309404711yescharacteristic
354D4—942no—
355D4—942no—
356D4—942no—
357D4—942no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—472no—
371C2×C4—941no—
372C2×C4—941no—
373C2×C4—941no—
374C2×C4—941no—
375C2×C4—3762no—
376C2×C4—3762no—
377C2×C4—3762no—
378C2×C4—1882no—
379C2×C4—1881no—
380C2×C4—1881no—
381C2×C4—1881no—
382C2×C4—1881no—
383C2×C4C2×(C2×D47)⋊C411yescharacteristic
384C2×C4#1309398211yescharacteristic
385C2×C4#1309400011yescharacteristic
386C2×C4#1309400411yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—1881no—
391C8—1881no—
392C8#1309393812yescomplemented
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—942no—
404C22—1882no—
405C22—1882no—
406C22—1881no—
407C22—1881no—
408C22#1568898011yescharacteristic
409C22#107×D4711yescharacteristic
410C22#1568916011yescharacteristic
411C22#1568935611yescharacteristic
412C22#1568936011yescharacteristic
413C22#1568936111yescharacteristic
414C22#1568936511yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—162no—
419C4—942no—
420C4—1881no—
421C4—1881no—
422C4—7522no—
423C4C2×#1309393811yescharacteristic
424C4#1568909611yescharacteristic
425C2—21no—
426C2—21no—
427C2—21no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—1882no—
432C2#2024337311yescharacteristic
433C2#2024341411yescharacteristic
434C2#2024343111yescharacteristic
subgroupG/H
centerC22#15688980
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1808C2
socleC22×C47#380
prime radicalC22×C22⋊D47D4
cosocleC23×C4×C47C23
hypercenter#1808D47
hypocenterC47#8609
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. #20243417C2semidirect
4. #20241255C2semidirect
5. C47×#1808C2semidirect
6. C22×C8×D47C4semidirect
13. C2×Dic47⋊C8C4semidirect
16. C2×(C2×D47)⋊C8C4semidirect
17. C2×C8×Dic47C4semidirect
135. C22×D47#107semidirect
165. C2×Dic47#107semidirect
172. C8×C47#99semidirect
210. #1808D47semidirect
242. C47#8609semidirect
392. C8#13093938semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C22⋊D472
#202434172
#202433732
#202412552
C47×#18082
#860947