Finite Group Databasebeta

← #26126459

Subgroups — #26126459

Order 12032.

670 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688890C211yesmaximal, characteristic, complemented
2C2×#15688847C211yesmaximal, characteristic, complemented
3#20241388C212yesmaximal, complemented
4#20241385C212yesmaximal, complemented
5C47×#2617C211yesmaximal, characteristic
6C22×C22⋊Dic47—21no—
7C2×C22⋊(C47⋊C8)—21no—
8#15688890—21no—
9#15688890C2212yes—
10#15688847—21no—
11#15688847C2212yes—
12C2×#121×C47C411yescharacteristic, complemented
13C2×#120×C47—21no—
14C22×C22⋊C4×C47C2211yescharacteristic
15C47×#397C411yescharacteristic, complemented
16C47×#397C2211yescharacteristic
17C47×#394—21no—
18C47×#394—21no—
19C47×#392C411yescharacteristic, complemented
20C47×#392C2211yescharacteristic
21C47×#386—21no—
22C47×#380C411yescharacteristic, complemented
23C23×Dic47—41no—
24C22×C47⋊C8—41no—
25C2×C22⋊Dic47—24no—
26C2×C22⋊Dic47—22no—
27C2×C22⋊Dic47—41no—
28C2×C22⋊Dic47—42no—
29C22⋊(C47⋊C8)—22no—
30C22⋊(C47⋊C8)—41no—
31C25×C47D411yescharacteristic
32C22×D4×C47—21no—
33C22×D4×C47—21no—
34C22×D4×C47—21no—
35C22×D4×C47C2×C411yescharacteristic, complemented
36C23×C4×C47C2×C411yescharacteristic
37C23×C4×C47D411yescharacteristic
38#121×C47—41no—
39#121×C47—41no—
40#120×C47—42no—
41#120×C47—42no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47—21no—
46C2×C22⋊C4×C47—21no—
47C2×C22⋊C4×C47—21no—
48C2×C22⋊C4×C47—21no—
49C2×C22⋊C4×C47—21no—
50C2×C22⋊C4×C47—41no—
51C2×C22⋊C4×C47—41no—
52C2×C22⋊C4×C47C2×C411yescharacteristic
53C2×C22⋊C4×C47D411yescharacteristic
54C2×C22⋊C4×C47D411yescharacteristic
55C2×C22⋊C4×C47C2311yescharacteristic
56#95×C47—21no—
57#95×C47—21no—
58#95×C47C2×C411yescharacteristic, complemented
59#95×C47C2×C411yescharacteristic, complemented
60C24×C47—21no—
61C24×C47—21no—
62C24×C47—22no—
63C24×C47—21no—
64C24×C47—81no—
65C24×C47—81no—
66C24×C47C22⋊C411yescharacteristic
67C24×C47C22⋊C411yescharacteristic
68C24×C47D812yes—
69C24×C47SD1612yes—
70C24×C47C2×D411yescharacteristic
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C2×D4×C47—41no—
74C2×D4×C47—42no—
75C2×D4×C47—42no—
76C2×D4×C47—42no—
77C2×D4×C47—41no—
78C2×D4×C47—41no—
79C2×D4×C47—81no—
80C2×D4×C47—81no—
81C2×D4×C47—81no—
82C2×D4×C47—81no—
83C2×D4×C47—81no—
84C22×C4×C47—21no—
85C22×C4×C47—21no—
86C22×C4×C47—21no—
87C22×C4×C47—21no—
88C22×C4×C47—21no—
89C22×C4×C47—21no—
90C22×C4×C47—21no—
91C22×C4×C47—81no—
92C22×C4×C47—81no—
93C22×C4×C47C22⋊C411yescharacteristic
94C22×C4×C47C22⋊C411yescharacteristic
95C22×C4×C47C22×C411yescharacteristic
96C22×C4×C47C2×D411yescharacteristic
97C22×Dic47—44no—
98C22×Dic47—42no—
99C22×Dic47—82no—
100C22×Dic47—82no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—81no—
103C22⋊C4×C47—41no—
104C22⋊C4×C47—41no—
105C22⋊C4×C47—41no—
106C22⋊C4×C47—41no—
107C22⋊C4×C47—42no—
108C22⋊C4×C47—42no—
109C22⋊C4×C47—42no—
110C22⋊C4×C47—41no—
111C22⋊C4×C47—41no—
112C22⋊C4×C47—81no—
113C22⋊C4×C47—81no—
114C22⋊Dic47—24no—
115C22⋊Dic47—44no—
116C22⋊Dic47—42no—
117C2×C47⋊C8—42no—
118C2×C47⋊C8—82no—
119C23×C47—22no—
120C23×C47—22no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—22no—
124C23×C47—22no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—41no—
128C23×C47—41no—
129C23×C47—42no—
130C23×C47—42no—
131C23×C47—41no—
132C23×C47—41no—
133C23×C47—41no—
134C23×C47—41no—
135C23×C47—41no—
136C23×C47—41no—
137C23×C47—41no—
138C23×C47—41no—
139C23×C47—41no—
140C23×C47—41no—
141C23×C47—41no—
142C23×C47—81no—
143C23×C47—81no—
144C23×C47—82no—
145C23×C47—82no—
146C23×C47—84no—
147C23×C47#9911yescharacteristic
148C23×C47#9911yescharacteristic
149C23×C47#10212yes—
150C23×C47#10212yes—
151C23×C47#10412yes—
152C23×C47C2×C22⋊C411yescharacteristic
153C23×C47C2×D811yescharacteristic
154C23×C47C2×SD1611yescharacteristic
155D4×C47—82no—
156D4×C47—84no—
157D4×C47—82no—
158D4×C47—82no—
159D4×C47—82no—
160D4×C47—82no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—42no—
166C2×C4×C47—41no—
167C2×C4×C47—41no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47—41no—
173C2×C4×C47—41no—
174C2×C4×C47—41no—
175C2×C4×C47—41no—
176C2×C4×C47—41no—
177C2×C4×C47—41no—
178C2×C4×C47—41no—
179C2×C4×C47—81no—
180C2×C4×C47—81no—
181C2×C4×C47—81no—
182C2×Dic47—44no—
183C2×Dic47—88no—
184C2×Dic47—82no—
185C2×Dic47—82no—
186C47⋊C8—82no—
187#11692—471nomaximal, Sylow
188C22×C47—21no—
189C22×C47—21no—
190C22×C47—21no—
191C22×C47—21no—
192C22×C47—21no—
193C22×C47—21no—
194C22×C47—21no—
195C22×C47—22no—
196C22×C47—21no—
197C22×C47—42no—
198C22×C47—42no—
199C22×C47—42no—
200C22×C47—41no—
201C22×C47—41no—
202C22×C47—44no—
203C22×C47—44no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—41no—
208C22×C47—81no—
209C22×C47—81no—
210C22×C47—82no—
211C22×C47—82no—
212C22×C47—81no—
213C22×C47—81no—
214C22×C47—81no—
215C22×C47—81no—
216C22×C47—81no—
217C22×C47—81no—
218C22×C47—81no—
219C22×C47#32712yes—
220C22×C47#32712yes—
221C22×C47C2×#9911yescharacteristic
222C22×C47C2×#10211yescharacteristic
223C22×C47C2×#10411yescharacteristic
224C4×C47—41no—
225C4×C47—41no—
226C4×C47—41no—
227C4×C47—41no—
228C4×C47—81no—
229C4×C47—81no—
230C4×C47—81no—
231Dic47—84no—
232#2617D4711yescharacteristic
233C2×#342—471no—
234C2×#323—471no—
235#1344—472no—
236#1343—472no—
237C2×C47—21no—
238C2×C47—22no—
239C2×C47—21no—
240C2×C47—22no—
241C2×C47—41no—
242C2×C47—42no—
243C2×C47—41no—
244C2×C47—161no—
245C2×C47C2×#32711yescharacteristic
246C2×C47#212111yescharacteristic
247C2×C47#212711yescharacteristic
248C2×#121Dic4711yescharacteristic, complemented
249C2×#120—21no—
250C22×C22⋊C4—941no—
251C22×C22⋊C4C2×D4711yescharacteristic
252C2×C22⋊C8—941no—
253#397Dic4711yescharacteristic, complemented
254#397C2×D4711yescharacteristic
255#394—21no—
256#394—21no—
257#392Dic4711yescharacteristic, complemented
258#392C2×D4711yescharacteristic
259#386—21no—
260#380Dic4711yescharacteristic, complemented
261#342—472no—
262#342—941no—
263#323—472no—
264#323—941no—
265C47#1169211yescharacteristic, complemented, Sylow
266C25C22⋊D4711yescharacteristic
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4C2×Dic4711yescharacteristic, complemented
271C23×C4—1881no—
272C23×C4C2×Dic4711yescharacteristic
273C23×C4C22⋊D4711yescharacteristic
274C22×C8—1881no—
275#121—41no—
276#121—41no—
277#120—42no—
278#120—42no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4C2×Dic4711yescharacteristic, complemented
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—41no—
288C2×C22⋊C4—41no—
289C2×C22⋊C4—944no—
290C2×C22⋊C4—942no—
291C2×C22⋊C4—1881no—
292C2×C22⋊C4—1882no—
293C2×C22⋊C4C2×Dic4711yescharacteristic
294C2×C22⋊C4C22⋊D4711yescharacteristic
295C2×C22⋊C4C22⋊D4711yescharacteristic
296C2×C22⋊C4C22×D4711yescharacteristic
297C22⋊C8—942no—
298C22⋊C8—1881no—
299#95—21no—
300#95—21no—
301#95C2×Dic4711yescharacteristic, complemented
302#95C2×Dic4711yescharacteristic, complemented
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—81no—
308C24—81no—
309C24#1062533412yes—
310C24#1062533512yes—
311C24C22⋊Dic4711yescharacteristic
312C24C22⋊Dic4711yescharacteristic
313C24C2×C22⋊D4711yescharacteristic
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—42no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—81no—
323C2×D4—81no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4—81no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—81no—
335C22×C4—81no—
336C22×C4—3762no—
337C22×C4—3762no—
338C22×C4—1882no—
339C22×C4—1884no—
340C22×C4C22⋊Dic4711yescharacteristic
341C22×C4C22⋊Dic4711yescharacteristic
342C22×C4C22×Dic4711yescharacteristic
343C22×C4C2×C22⋊D4711yescharacteristic
344C2×C8—3762no—
345C2×C8—1882no—
346C4⋊C4—41no—
347C4⋊C4—81no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—81no—
358C22⋊C4—81no—
359C22⋊C4—944no—
360C22⋊C4—1884no—
361C22⋊C4—1882no—
362C23—21no—
363C23—21no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—21no—
369C23—21no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—42no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—81no—
386C23—81no—
387C23—82no—
388C23—82no—
389C23—84no—
390C23#1309393911yescharacteristic
391C23#1309393911yescharacteristic
392C23#1309394512yes—
393C23#1309394512yes—
394C23#1309395112yes—
395C23C2×C22⋊Dic4711yescharacteristic
396C23C2×#1062533411yescharacteristic
397C23C2×#1062533511yescharacteristic
398D4—82no—
399D4—84no—
400D4—82no—
401D4—82no—
402D4—82no—
403D4—82no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—3768no—
426C2×C4—3762no—
427C2×C4—3762no—
428C2×C4—1884no—
429C8—3762no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—21no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—41no—
443C22—41no—
444C22—44no—
445C22—44no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—81no—
451C22—81no—
452C22—82no—
453C22—82no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#1568885712yes—
462C22#1568885712yes—
463C22C2×#1309393911yescharacteristic
464C22C2×#1309394511yescharacteristic
465C22C2×#1309395111yescharacteristic
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—81no—
471C4—81no—
472C4—81no—
473C4—3764no—
474C2—21no—
475C2—22no—
476C2—21no—
477C2—22no—
478C2—41no—
479C2—42no—
480C2—41no—
481C2—161no—
482C2C2×#1568885711yescharacteristic
483C2#2024503411yescharacteristic
484C2#2024505711yescharacteristic
subgroupG/H
centerC22C2×#13093939
commutatorC22×C4×C47C22×C4
FrattiniC2×C22⋊C4C22×D47
Fitting, prime radicalC47×#2617C2
socleC22×C47C2×#99
cosocleC2×C22⋊C4×C47C23
hypercenter#2617D47
hypocenterC47#11692
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. C2×#15688890C2semidirect
2. C2×#15688847C2semidirect
3. #20241388C2semidirect
4. #20241385C2semidirect
12. C2×#121×C47C4semidirect
15. C47×#397C4semidirect
19. C47×#392C4semidirect
22. C47×#380C4semidirect
35. C22×D4×C47C2×C4semidirect
43. C2×C4⋊C4×C47C2×C4semidirect
58. #95×C47C2×C4semidirect
59. #95×C47C2×C4semidirect
248. C2×#121Dic47semidirect
253. #397Dic47semidirect
257. #392Dic47semidirect
260. #380Dic47semidirect
265. C47#11692semidirect
270. C22×D4C2×Dic47semidirect
280. C2×C4⋊C4C2×Dic47semidirect
301. #95C2×Dic47semidirect
302. #95C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156888902
C2×#156888472
#202413882
#202413852
C47×#26172
#1169247