Finite Group Databasebeta

← #26112841

Subgroups — #26112841

Order 12032.

522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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
1#20254160C211yesmaximal, characteristic
2#20246468C211yesmaximal, characteristic
3#20244374C211yesmaximal, characteristic
4#20241961C211yesmaximal, characteristic
5#20241267C211yesmaximal, characteristic
6#20241235C211yesmaximal, characteristic
7C2×C47×#328C211yesmaximal, characteristic
8C2×#13094003C2211yescharacteristic
9#15689458C412yescomplemented
10#15689456—21no—
11#15689362—22no—
12#15689279C412yescomplemented
13#15689278—21no—
14C2×C22⋊(C47⋊C8)C2211yescharacteristic
15#15689027—21no—
16#15689008—21no—
17#15689005—21no—
18#15688996—21no—
19#15688983C2211yescharacteristic
20#15688974—21no—
21C4×C22⋊Dic47—21no—
22C4×C22⋊Dic47C2211yescharacteristic
23#15688890—21no—
24#15688890—21no—
25#15688861—22no—
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×C22⋊C8×C47C2211yescharacteristic
28C2×#95×C47C2211yescharacteristic
29C47×#328—21no—
30C47×#328—21no—
31C22×Dic94D411yescharacteristic
32C2×#10625337—22no—
33C22×C47⋊C8—21no—
34#13094003—21no—
35#13094003—21no—
36#13094003C2×C412yes—
37#13094003D412yes—
38C2×C4⋊Dic47—21no—
39C2×C4⋊Dic47D411yescharacteristic
40C2×Dic47⋊C4—21no—
41C2×Dic47⋊C4—21no—
42C2×Dic47⋊C4—21no—
43C2×C22⋊Dic47—21no—
44C2×C22⋊Dic47—21no—
45C2×C22⋊Dic47D411yescharacteristic
46C2×C22⋊Dic47D411yescharacteristic
47C2×C4×Dic47—21no—
48C2×C4×Dic47—21no—
49C2×C4×Dic47—21no—
50#13093957—22no—
51#13093948—22no—
52#13093947—22no—
53C22⋊(C47⋊C8)—21no—
54C22⋊(C47⋊C8)C2×C412yes—
55C47⋊#95—21no—
56C47⋊#95—21no—
57C47⋊#95—21no—
58C47⋊#95—21no—
59C47⋊#95—21no—
60C47⋊#95—21no—
61C22×Q8×C47C2×C411yescharacteristic
62C23×C4×C47—21no—
63C23×C4×C47C2311yescharacteristic
64C22×C8×C47—21no—
65C22⋊Q8×C47—21no—
66C22⋊Q8×C47—21no—
67C22⋊Q8×C47—21no—
68C22⋊Q8×C47—21no—
69C2×C4⋊C4×C47—21no—
70C2×C4⋊C4×C47C2×C411yescharacteristic
71C2×C22⋊C4×C47—21no—
72C22⋊C8×C47—21no—
73C22⋊C8×C47—21no—
74#95×C47—21no—
75#95×C47D411yescharacteristic
76#95×C47D411yescharacteristic
77C24×C47C2×D411yescharacteristic
78C2×Q8×C47—21no—
79C2×Q8×C47—21no—
80C2×Q8×C47—81no—
81C22×C4×C47—21no—
82C22×C4×C47—21no—
83C22×C4×C47—21no—
84C22×C4×C47—21no—
85C22×C4×C47—42no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47—81no—
89C22×C4×C47—81no—
90C22×C4×C47C22×C411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47C2×D411yescharacteristic
93C22×C4×C47C2×D411yescharacteristic
94C22×C4×C47#4111yescharacteristic
95C22×C4×C47#4111yescharacteristic
96C22×Dic47—21no—
97C22×Dic47—21no—
98C22×Dic47—21no—
99C22×Dic47—21no—
100C22×Dic47—41no—
101C2×Dic94—21no—
102C2×Dic94—81no—
103C2×Dic94C22⋊C412yes—
104C2×C8×C47—41no—
105C2×C8×C47—81no—
106C4⋊C4×C47—21no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—41no—
109C4⋊C4×C47—41no—
110C22⋊C4×C47—41no—
111C22⋊C4×C47—41no—
112C22⋊Dic47—22no—
113C22⋊Dic47—22no—
114C22⋊Dic47—21no—
115C22⋊Dic47—21no—
116C22⋊Dic47—21no—
117C22⋊Dic47—41no—
118C22⋊Dic47—41no—
119C22⋊Dic47Q1612yescomplemented
120#10625337—82no—
121C4⋊Dic47—21no—
122C4⋊Dic47—81no—
123C4⋊Dic47C22⋊C412yes—
124Dic47⋊C4—22no—
125Dic47⋊C4—22no—
126Dic47⋊C4—42no—
127Dic47⋊C4—81no—
128C4×Dic47—42no—
129C4×Dic47—81no—
130C4×Dic47—81no—
131C2×C47⋊C8—22no—
132C2×C47⋊C8—81no—
133C23×C47—41no—
134C23×C47—41no—
135C23×C47C4×D411yescharacteristic
136C23×C47#12011yescharacteristic
137C23×C47#12111yescharacteristic
138C23×C47C2×Q1611yescharacteristic
139C23×C47#13511yescharacteristic
140C23×C47#13711yescharacteristic
141C23×C47#13711yescharacteristic
142Q8×C47—42no—
143Q8×C47—81no—
144C2×C4×C47—22no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—82no—
159C2×C4×C47—82no—
160C2×C4×C47—81no—
161C2×C4×C47—81no—
162C2×C4×C47C2×C22⋊C411yescharacteristic
163C2×C4×C47C4×D411yescharacteristic
164C2×C4×C47#12111yescharacteristic
165C2×C4×C47#12311yescharacteristic
166C2×Dic47—22no—
167C2×Dic47—22no—
168C2×Dic47—22no—
169C2×Dic47—41no—
170C2×Dic47—41no—
171C2×Dic47—41no—
172C2×Dic47—41no—
173C2×Dic47—41no—
174C2×Dic47—41no—
175C2×Dic47—41no—
176C2×Dic47—41no—
177C2×Dic47—41no—
178C2×Dic47—81no—
179C2×Dic47—81no—
180C2×Dic47—81no—
181Dic94—42no—
182Dic94—81no—
183C8×C47—81no—
184C47⋊C8—42no—
185#9276—471nomaximal, Sylow
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—21no—
189C22×C47—21no—
190C22×C47—21no—
191C22×C47—21no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47—41no—
196C22×C47#38611yescharacteristic
197C22×C47C4×Q1611yescharacteristic
198C22×C47#44111yescharacteristic
199C22×C47#45111yescharacteristic
200C22×C47#45211yescharacteristic
201C22×C47#46211yescharacteristic
202C22×C47#46411yescharacteristic
203C4×C47—21no—
204C4×C47—21no—
205C4×C47—21no—
206C4×C47—21no—
207C4×C47—42no—
208C4×C47—81no—
209C4×C47—81no—
210C4×C47—81no—
211Dic47—42no—
212Dic47—42no—
213Dic47—42no—
214Dic47—81no—
215Dic47—161no—
216#3189—471no—
217#2368—471no—
218#1996—471no—
219#1520—471no—
220C2×#328D4711yescharacteristic
221#1294—471no—
222#1282—471no—
223C2×C47—21no—
224C2×C47—21no—
225C2×C47—21no—
226C2×C47—21no—
227C2×C47—21no—
228C2×C47—21no—
229C2×C47#187811yescharacteristic
230C2×C47#190611yescharacteristic
231C2×C47#191311yescharacteristic
232C2×C22⋊Q8—471no—
233C2×C22⋊Q8C2×D4711yescharacteristic
234#484—472no—
235#484—941no—
236#467—942no—
237#451—472no—
238#451—941no—
239C2×C22⋊C8—471no—
240C2×C22⋊C8C2×D4711yescharacteristic
241#391—941no—
242#387—941no—
243#387—941no—
244#385—941no—
245#380—471no—
246C4×C4⋊C4—941no—
247C4×C22⋊C4—471no—
248C4×C22⋊C4—941no—
249C2×#95C2×D4711yescharacteristic
250#342—941no—
251#342—941no—
252#328—21no—
253#328—21no—
254#328—942no—
255C47#927611yescharacteristic, complemented, Sylow
256C22×Q8—471no—
257C22×Q8C4×D4711yescharacteristic
258C23×C4—21no—
259C23×C4C22×D4711yescharacteristic
260C2×Q16—942no—
261C22×C8—21no—
262C22×C8—941no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—472no—
268C22⋊Q8—472no—
269C22⋊Q8—941no—
270C22⋊Q8—941no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—471no—
273C2×C4⋊C4—941no—
274C2×C4⋊C4—941no—
275C2×C4⋊C4—941no—
276C2×C4⋊C4—941no—
277C2×C4⋊C4C4×D4711yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—471no—
280C2×C22⋊C4—471no—
281C2×C22⋊C4—941no—
282C2×C22⋊C4—941no—
283C2×C42—941no—
284C2×C42—941no—
285C2×C42—941no—
286#107—942no—
287#103—942no—
288#103—942no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8—472no—
292C22⋊C8—941no—
293#95—21no—
294#95—941no—
295#95—941no—
296#95—941no—
297#95—941no—
298#95—941no—
299#95—941no—
300#95C22⋊D4711yescharacteristic
301#95C22⋊D4711yescharacteristic
302C24D4×D4711yescharacteristic
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—81no—
306C2×Q8—472no—
307C2×Q8—941no—
308C2×Q8—3761no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—81no—
317C22×C4—81no—
318C22×C4—941no—
319C22×C4—941no—
320C22×C4—941no—
321C22×C4—941no—
322C22×C4—1881no—
323C22×C4C2×C4×D4711yescharacteristic
324C22×C4#1062535011yescharacteristic
325C22×C4D4×D4711yescharacteristic
326C22×C4D4×D4711yescharacteristic
327C22×C4#1062535211yescharacteristic
328C22×C4C2×C22⋊D4711yescharacteristic
329Q16—3762no—
330C2×C8—41no—
331C2×C8—81no—
332C2×C8—942no—
333C2×C8—3761no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—472no—
339C4⋊C4—942no—
340C4⋊C4—942no—
341C4⋊C4—941no—
342C4⋊C4—3761no—
343C4⋊C4—3761no—
344C4⋊C4—1882no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—472no—
348C22⋊C4—942no—
349C22⋊C4—942no—
350C22⋊C4—941no—
351C22⋊C4—941no—
352C22⋊C4—941no—
353C22⋊C4—1881no—
354C22⋊C4—1881no—
355C42—3761no—
356C42—3761no—
357C42—1882no—
358C23—41no—
359C23—41no—
360C23(C22⋊D47)⋊C411yescharacteristic
361C23#1309399211yescharacteristic
362C23#1309399711yescharacteristic
363C23Q16×D4711yescharacteristic
364C23#1309404511yescharacteristic
365C23#1309405311yescharacteristic
366C23#1309405611yescharacteristic
367Q8—42no—
368Q8—81no—
369Q8—3761no—
370Q8—1882no—
371C2×C4—22no—
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—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—942no—
390C2×C4—942no—
391C2×C4—942no—
392C2×C4—3761no—
393C2×C4—3761no—
394C2×C4—3761no—
395C2×C4—1881no—
396C2×C4—1881no—
397C2×C4—1881no—
398C2×C4—1881no—
399C2×C4—1881no—
400C2×C4—1881no—
401C2×C4—1881no—
402C2×C4—1881no—
403C2×C4—1881no—
404C2×C4C22⋊C4×D4711yescharacteristic
405C2×C4C4×C22⋊D4711yescharacteristic
406C2×C4#1309399511yescharacteristic
407C2×C4#1309400611yescharacteristic
408C8—81no—
409C8—1882no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22#1568899911yescharacteristic
421C22#1568921511yescharacteristic
422C22#1568922711yescharacteristic
423C22#1568927711yescharacteristic
424C22#1568928211yescharacteristic
425C22#1568933211yescharacteristic
426C22#1568934811yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—81no—
433C4—81no—
434C4—81no—
435C4—3761no—
436C4—1882no—
437C4—1882no—
438C4—1882no—
439C4—7521no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—21no—
446C2#2024372611yescharacteristic
447C2#2024389211yescharacteristic
448C2#2024392711yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#328C2
socleC22×C47#386
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#328D47
hypocenterC47#9276
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
9. #15689458C4semidirect
12. #15689279C4semidirect
119. C22⋊Dic47Q16semidirect
255. C47#9276semidirect

Maximal subgroups

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

subgroupindex
#202541602
#202464682
#202443742
#202419612
#202412672
#202412352
C2×C47×#3282
#927647