Finite Group Databasebeta

← #26132262

Subgroups — #26132262

Order 12032.

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

normal subgroups only

This group has 544 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
1C4×#13094011C211yesmaximal, characteristic
2C2×#15688917C212yesmaximal
3#20243376C211yesmaximal, characteristic
4#20241512C212yesmaximal
5C47×#1799C211yesmaximal, characteristic
6C2×#13094011C2211yescharacteristic
7C2×C4×Dic94C411yescharacteristic, complemented
8C2×#13093939C2212yes—
9#15689028C411yescharacteristic, complemented
10#15689026C2211yescharacteristic
11#15689017—21no—
12#15689017—21no—
13#15688988C411yescharacteristic, complemented
14#15688983—21no—
15C4×C22⋊Dic47—21no—
16C4×C22⋊Dic47—21no—
17C42×Dic47C411yescharacteristic, complemented
18#15688917—24no—
19#15688890—21no—
20C2×C4×D4×C47C2211yescharacteristic
21C2×#99×C47C2212yes—
22C47×#380—21no—
23C47×#342—21no—
24C22×Dic94C2×C411yescharacteristic
25#13094011—21no—
26#13094011—21no—
27#13094011D412yes—
28#13094011Q812yes—
29C4×Dic94—41no—
30C4×Dic94—41no—
31C2×C4⋊Dic47—41no—
32C2×C4⋊Dic47C2×C411yescharacteristic
33C2×Dic47⋊C4—21no—
34C2×C22⋊Dic47—21no—
35C2×C22⋊Dic47—21no—
36C2×C22⋊Dic47—21no—
37C2×C22⋊Dic47—21no—
38C2×C22⋊Dic47—22no—
39C2×C4×Dic47—21no—
40C2×C4×Dic47—21no—
41C2×C4×Dic47—21no—
42C2×C4×Dic47C2×C411yescharacteristic
43C2×C4×Dic47C2×C411yescharacteristic
44#13093939—22no—
45#13093939—22no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C47⋊#95—41no—
51C22×D4×C47C2311yescharacteristic
52C23×C4×C47D411yescharacteristic
53C23×C4×C47D411yescharacteristic
54C4×D4×C47—41no—
55C4×D4×C47—41no—
56C2×C4⋊C4×C47—41no—
57C2×C4⋊C4×C47C2×C411yescharacteristic
58C2×C22⋊C4×C47—22no—
59C2×C22⋊C4×C47D411yescharacteristic
60C2×C22⋊C4×C47D411yescharacteristic
61C2×C42×C47C2×C411yescharacteristic
62#99×C47—22no—
63#99×C47—22no—
64#95×C47—41no—
65C24×C47C2×D411yescharacteristic
66C24×C47C2×D411yescharacteristic
67C2×D4×C47—41no—
68C2×D4×C47—41no—
69C2×D4×C47C2×D411yescharacteristic
70C2×D4×C47C2×Q811yescharacteristic
71C2×D4×C47#4111yescharacteristic
72C2×D4×C47#4111yescharacteristic
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—42no—
78C22×C4×C47—42no—
79C22×C4×C47—42no—
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47C22⋊C411yescharacteristic
82C22×C4×C47C22⋊C411yescharacteristic
83C22×C4×C47C22⋊C411yescharacteristic
84C22×C4×C47C22×C411yescharacteristic
85C22×Dic47—21no—
86C22×Dic47—21no—
87C22×Dic47—21no—
88C22×Dic47—21no—
89C22×Dic47—42no—
90C2×Dic94—21no—
91C2×Dic94—41no—
92C2×Dic94—41no—
93C2×Dic94C4⋊C412yescomplemented
94C4⋊C4×C47—41no—
95C4⋊C4×C47—82no—
96C22⋊C4×C47—41no—
97C22⋊C4×C47—41no—
98C22⋊C4×C47—42no—
99C22⋊C4×C47—42no—
100C42×C47—21no—
101C42×C47—21no—
102C22⋊Dic47—22no—
103C22⋊Dic47—22no—
104C22⋊Dic47—22no—
105C22⋊Dic47—22no—
106C22⋊Dic47—42no—
107C22⋊Dic47—42no—
108C22⋊Dic47—42no—
109C22⋊Dic47—42no—
110C4⋊Dic47—41no—
111C4⋊Dic47—82no—
112Dic47⋊C4—42no—
113C4×Dic47—21no—
114C4×Dic47—42no—
115C4×Dic47—42no—
116C4×Dic47—41no—
117C4×Dic47—41no—
118C4×Dic47—41no—
119C4×Dic47C4⋊C412yescomplemented
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—41no—
125C23×C47—41no—
126C23×C47—41no—
127C23×C47—41no—
128C23×C47C2×C22⋊C411yescharacteristic
129C23×C47#12111yescharacteristic
130C23×C47#12111yescharacteristic
131C23×C47C22⋊Q811yescharacteristic
132C23×C47C22⋊Q811yescharacteristic
133D4×C47—41no—
134D4×C47—41no—
135D4×C47—41no—
136D4×C47—41no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—22no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—42no—
144C2×C4×C47—42no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—81no—
149C2×C4×C47—81no—
150C2×C4×C47—82no—
151C2×C4×C47—82no—
152C2×C4×C47—82no—
153C2×C4×C47#9911yescharacteristic
154C2×C4×C47#9911yescharacteristic
155C2×C4×C47C2×C4⋊C411yescharacteristic
156C2×C4×C47#11711yescharacteristic
157C2×Dic47—22no—
158C2×Dic47—22no—
159C2×Dic47—22no—
160C2×Dic47—41no—
161C2×Dic47—41no—
162C2×Dic47—41no—
163C2×Dic47—41no—
164C2×Dic47—41no—
165C2×Dic47—41no—
166C2×Dic47—41no—
167C2×Dic47—41no—
168C2×Dic47—41no—
169C2×Dic47—82no—
170C2×Dic47—82no—
171C2×Dic47—82no—
172Dic94—42no—
173Dic94—42no—
174#12798—471nomaximal, Sylow
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—81no—
190C22×C47—81no—
191C22×C47#38011yescharacteristic
192C22×C47C2×#9911yescharacteristic
193C22×C47#41011yescharacteristic
194C4×C47—21no—
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—41no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47—162no—
201C4×C47#35412yescomplemented
202Dic47—42no—
203Dic47—42no—
204Dic47—42no—
205Dic47—81no—
206Dic47—162no—
207C4×#124—471no—
208C2×#354—472no—
209#1799—471no—
210#1799D4711yescharacteristic
211#1393—472no—
212C2×C47—21no—
213C2×C47—21no—
214C2×C47—41no—
215C2×C47—41no—
216C2×C47—41no—
217C2×C47—41no—
218C2×C47#179911yescharacteristic
219C2×C47C2×#35411yescharacteristic
220C2×C47#212611yescharacteristic
221C2×#124—471no—
222C2×C4×Q8—471no—
223C2×C4×D4C2×D4711yescharacteristic
224C2×#99—472no—
225C2×#99C2×D4712yes—
226#391—471no—
227#390—471no—
228#388—941no—
229#388—941no—
230#382—471no—
231#380—21no—
232#380—941no—
233C4×C22⋊C4—941no—
234C4×C22⋊C4—941no—
235C43—471no—
236#354—944no—
237#342—21no—
238#342—941no—
239C47#1279811yescharacteristic, complemented, Sylow
240C22×Q8—471no—
241C22×D4C22×D4711yescharacteristic
242C23×C4D18811yescharacteristic
243C23×C4C22⋊D4711yescharacteristic
244#124—472no—
245#124—472no—
246#124—941no—
247#124—941no—
248C4×Q8—1881no—
249C4×Q8—1881no—
250C4×D4—41no—
251C4×D4—41no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—471no—
254C2×C4⋊C4—941no—
255C2×C4⋊C4—1881no—
256C2×C4⋊C4C4×D4711yescharacteristic
257C2×C22⋊C4—22no—
258C2×C22⋊C4—941no—
259C2×C22⋊C4—941no—
260C2×C22⋊C4—941no—
261C2×C22⋊C4—941no—
262C2×C22⋊C4—942no—
263C2×C22⋊C4D18811yescharacteristic
264C2×C22⋊C4C22⋊D4711yescharacteristic
265C2×C42—471no—
266C2×C42—471no—
267C2×C42—941no—
268C2×C42—941no—
269C2×C42—941no—
270C2×C42C4×D4711yescharacteristic
271#99—22no—
272#99—22no—
273#99—942no—
274#99—942no—
275#95—41no—
276#95—941no—
277#95—941no—
278#95—941no—
279#95—941no—
280#95—1881no—
281C24C2×D18811yescharacteristic
282C24C2×C22⋊D4711yescharacteristic
283C2×Q8—472no—
284C2×Q8—941no—
285C2×Q8—1881no—
286C2×Q8—1881no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4D4×D4711yescharacteristic
290C2×D4#1062535211yescharacteristic
291C2×D4Q8×D4711yescharacteristic
292C2×D4#1062535411yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—941no—
301C22×C4—941no—
302C22×C4—941no—
303C22×C4—941no—
304C22×C4—1882no—
305C22×C4(C2×D47)⋊C411yescharacteristic
306C22×C4(C2×D47)⋊C411yescharacteristic
307C22×C4(C2×D47)⋊C411yescharacteristic
308C22×C4(C2×D47)⋊C411yescharacteristic
309C22×C4C2×C4×D4711yescharacteristic
310C4⋊C4—41no—
311C4⋊C4—82no—
312C4⋊C4—3762no—
313C4⋊C4—1881no—
314C4⋊C4—1882no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—942no—
320C22⋊C4—942no—
321C22⋊C4—942no—
322C22⋊C4—942no—
323C22⋊C4—1882no—
324C22⋊C4—1882no—
325C22⋊C4—1882no—
326C22⋊C4—1882no—
327C42—21no—
328C42—21no—
329C42—472no—
330C42—941no—
331C42—1881no—
332C42—1882no—
333C42—1882no—
334C42—1881no—
335C42—1881no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23C2×(C2×D47)⋊C411yescharacteristic
345C23#1309399511yescharacteristic
346C23#1309399911yescharacteristic
347C23#1309400011yescharacteristic
348C23#1309400411yescharacteristic
349Q8—1882no—
350Q8—1882no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—942no—
372C2×C4—942no—
373C2×C4—942no—
374C2×C4—3762no—
375C2×C4—3762no—
376C2×C4—3762no—
377C2×C4—1881no—
378C2×C4—1881no—
379C2×C4—1881no—
380C2×C4—1881no—
381C2×C4—1881no—
382C2×C4—1881no—
383C2×C4—1881no—
384C2×C4—1881no—
385C2×C4—1881no—
386C2×C4#1309393811yescharacteristic
387C2×C4#1309393811yescharacteristic
388C2×C4C4⋊C4×D4711yescharacteristic
389C2×C4#1309398211yescharacteristic
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22—81no—
406C22#1568898011yescharacteristic
407C22C2×#1309393811yescharacteristic
408C22#1568909611yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—162no—
416C4—3761no—
417C4—1882no—
418C4—1882no—
419C4—1882no—
420C4—7522no—
421C4#1568891712yescomplemented
422C2—21no—
423C2—21no—
424C2—41no—
425C2—41no—
426C2—41no—
427C2—41no—
428C2#2024337311yescharacteristic
429C2C2×#1568891711yescharacteristic
430C2#2024505111yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC22×D4C22×D47
FittingC47×#1799C2
socleC22×C47C2×#99
prime radical, cosocleC22×D4×C47C23
hypercenter#1799D47
hypocenterC47#12798
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
7. C2×C4×Dic94C4semidirect
9. #15689028C4semidirect
13. #15688988C4semidirect
17. C42×Dic47C4semidirect
93. C2×Dic94C4⋊C4semidirect
119. C4×Dic47C4⋊C4semidirect
201. C4×C47#354semidirect
239. C47#12798semidirect
421. C4#15688917semidirect

Maximal subgroups

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

subgroupindex
C4×#130940112
C2×#156889172
#202433762
#202415122
C47×#17992
#1279847