Finite Group Databasebeta

← #26215943

Subgroups — #26215943

Order 12032.

1308 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic
2C2×#15689172C211yesmaximal, characteristic, complemented
3C2×#15689141C212yesmaximal
4#20243439C218yesmaximal, complemented
5C2×#15688893C212yesmaximal, complemented
6C47×#2911C211yesmaximal, characteristic, complemented
7C22×#10625350C2211yescharacteristic
8#15689889—24no—
9#15689889C418yescomplemented
10C2×#13094032—22no—
11C2×#13094030C2214yes—
12C22×#10625329C2212yes—
13C22×#10625329C2211yescharacteristic
14C2×M16×D47—22no—
15#15689172—22no—
16#15689172—22no—
17C2×#13093960C2214yescomplemented
18#15689141—24no—
19#15689141C2218yes—
20C2×#13093952—24no—
21#15688893C2218yescomplemented
22C22×M16×C47C2211yescharacteristic
23C2×#117×C47C2212yes—
24C47×#428—24no—
25C47×#427C2214yescomplemented
26C2×#10625350—21no—
27C2×#10625350—22no—
28C2×#10625350—22no—
29C2×#10625350—21no—
30C2×#10625350C2×C414yes—
31C2×#10625350D414yes—
32C2×#10625350Q812yes—
33C2×#10625350C2312yes—
34C22×Dic94Q811yescharacteristic
35C22×D188Q811yescharacteristic
36C22×C22⋊D47—21no—
37C22×C4×D47—21no—
38#13094032—216no—
39#13094030—28no—
40#13094030C2×C4116yescomplemented
41C2×#10625329—21no—
42C2×#10625329—22no—
43C2×#10625329—22no—
44C2×#10625329—22no—
45C2×#10625329—22no—
46C2×#10625329—22no—
47C2×#10625329—22no—
48C2×#10625329C2×C414yes—
49C2×#10625329C2314yes—
50C2×#10625329C2312yes—
51C2×#10625324—24no—
52M16×D47—216no—
53C22×C47⋊C8—21no—
54C22×C47⋊C8—22no—
55C2×C8×D47—24no—
56#13093960—28no—
57#13093952—216no—
58C23×C4×C47C2311yescharacteristic
59C2×M16×C47C2×C414yes—
60C2×M16×C47D412yes—
61C2×M16×C47D412yes—
62C2×M16×C47D414yes—
63C22×C8×C47C2312yes—
64#117×C47—22no—
65#117×C47—22no—
66#117×C47—22no—
67#117×C47C2314yes—
68C2×C4⋊C4×C47—22no—
69C2×C22⋊C4×C47—22no—
70C2×C42×C47—22no—
71#107×C47—24no—
72#106×C47—24no—
73C24×C47#4111yescharacteristic
74C23×D47—21no—
75C22×C4×C47—42no—
76C22×C4×C47C22×C412yes—
77C22×C4×C47C2×D411yescharacteristic
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×D412yes—
80C22×C4×C47C2×D412yes—
81C22×C4×C47C2×Q811yescharacteristic
82C22×C4×C47C2×Q811yescharacteristic
83C22×C4×C47#4111yescharacteristic
84C22×C4×C47#4112yes—
85C22×C4×C47C2411yescharacteristic
86C2×C22⋊D47—24no—
87C2×C22⋊D47—24no—
88C2×C22⋊D47—22no—
89C2×C22⋊D47—22no—
90C22×Dic47—21no—
91#10625350—24no—
92#10625350—24no—
93#10625350—24no—
94#10625350—24no—
95#10625350—24no—
96#10625350—22no—
97#10625350—22no—
98#10625350C4⋊C418yes—
99#10625350C22×C414yes—
100#10625350C2×D414yes—
101C2×D188—22no—
102C2×D188—21no—
103C2×D188C4⋊C414yes—
104C2×D188C2×Q812yes—
105C2×C4×D47—24no—
106C2×C4×D47—24no—
107C2×C4×D47—22no—
108C2×C4×D47—22no—
109C2×Dic94—22no—
110C2×Dic94—21no—
111C2×Dic94C4⋊C414yes—
112C2×Dic94C2×Q812yes—
113M16×C47C22⋊C418yes—
114M16×C47C22⋊C418yes—
115C2×C8×C47C22×C414yes—
116C2×C8×C47C2×D414yes—
117C2×C8×C47C2×D414yes—
118C4⋊C4×C47—24no—
119C4⋊C4×C47—42no—
120C22⋊C4×C47—24no—
121C22⋊C4×C47—42no—
122C42×C47—24no—
123C42×C47—42no—
124#10625329—24no—
125#10625329—22no—
126#10625329—24no—
127#10625329—24no—
128#10625329—42no—
129#10625329—42no—
130#10625329C22×C414yes—
131C2×C47⋊C8—24no—
132C2×C47⋊C8—22no—
133C2×C47⋊C8—24no—
134C2×C47⋊C8—42no—
135C2×C47⋊C8—42no—
136#10625324—216no—
137C8×D47—216no—
138C23×C47—81no—
139C23×C47#11712yes—
140C23×C47#12112yes—
141C23×C47C22⋊Q811yescharacteristic
142C23×C47C22⋊Q811yescharacteristic
143C23×C47C2×#4111yescharacteristic
144C22×D47—22no—
145C22×D47—24no—
146C22×D47—82no—
147C2×C4×C47—44no—
148C2×C4×C47—84no—
149C2×C4×C47C2×C22⋊C412yes—
150C2×C4×C47C2×C22⋊C412yes—
151C2×C4×C47C2×C4⋊C412yes—
152C2×C4×C47C2×C4⋊C412yes—
153C2×C4×C47#11712yes—
154C2×C4×C47#12112yes—
155C2×C4×C47#12112yes—
156C2×C4×C47#12112yes—
157C2×C4×C47C22⋊Q812yes—
158C2×C4×C47C22⋊Q812yes—
159C2×C4×C47C22⋊Q811yescharacteristic
160C2×C4×C47C22⋊Q811yescharacteristic
161C2×C4×C47C23×C411yescharacteristic
162C2×C4×C47C22×D411yescharacteristic
163C2×C4×C47C22×D411yescharacteristic
164C2×C4×C47C22×D411yescharacteristic
165C2×C4×C47C22×Q811yescharacteristic
166C2×C4×C47C2×#4111yescharacteristic
167C22⋊D47—24no—
168C22⋊D47—24no—
169C22⋊D47—28no—
170C2×Dic47—22no—
171C2×Dic47—24no—
172D188—22no—
173D188—24no—
174D188C2×C4⋊C414yes—
175C4×D47—24no—
176C4×D47—24no—
177C4×D47—28no—
178Dic94—22no—
179Dic94—24no—
180Dic94C2×C4⋊C414yes—
181C8×C47C2×C22⋊C418yes—
182C47⋊C8—24no—
183C47⋊C8—44no—
184#20675—471nomaximal, Sylow
185C22×C47—42no—
186C22×C47—41no—
187C22×C47—42no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47#38012yes—
191C22×C47#38012yes—
192C22×C47C2×#11711yescharacteristic
193C22×C47C2×#12111yescharacteristic
194C22×C47C2×C22⋊Q811yescharacteristic
195C2×D47—24no—
196C2×D47—44no—
197C2×D47—84no—
198C4×C47—84no—
199C4×C47#38012yes—
200C4×C47#38012yes—
201C4×C47C22×C22⋊C411yescharacteristic
202C4×C47C22×C4⋊C411yescharacteristic
203C4×C47C2×#12111yescharacteristic
204C4×C47C2×C22⋊Q811yescharacteristic
205Dic47—24no—
206C2×#568—471no—
207C2×#430—471no—
208#2911D4711yescharacteristic, complemented
209C2×#421—472no—
210#1814—478no—
211C2×#344—472no—
212C2×C47—21no—
213C2×C47—21no—
214C2×C47—22no—
215C2×C47—21no—
216C2×C47—22no—
217C2×C47C2×#38011yescharacteristic
218D47—44no—
219C22×#41—471no—
220#568—478no—
221#568—944no—
222C2×#131—474no—
223C2×#131—942no—
224C22×M16—471no—
225C22×M16—472no—
226C22×M16—942no—
227C22×M16C2×D4711yescharacteristic
228C2×#117C2×D4712yes—
229#430—942no—
230#430—942no—
231C2×#108—474no—
232#428—24no—
233#427C2×D4714yescomplemented
234#421—478no—
235#421—944no—
236C2×#104—944no—
237#344—478no—
238C47#2067511yescharacteristic, complemented, Sylow
239C2×#41—474no—
240C2×#41—474no—
241C2×#41—472no—
242C2×#41—472no—
243C2×#41—941no—
244C2×#41—941no—
245C2×#41—942no—
246C2×#41—942no—
247C22×Q8—471no—
248C22×D4—471no—
249C22×D4—941no—
250C23×C4—941no—
251C23×C4C22×D4711yescharacteristic
252#131—4716no—
253#131—9416no—
254#131—948no—
255C2×M16—474no—
256C2×M16—472no—
257C2×M16—474no—
258C2×M16—941no—
259C2×M16—942no—
260C2×M16—9416no—
261C2×M16—942no—
262C2×M16—944no—
263C2×M16—942no—
264C2×M16—942no—
265C2×M16—942no—
266C2×M16—942no—
267C2×M16C4×D4714yes—
268C2×M16D18812yes—
269C2×M16D18812yes—
270C2×M16C22⋊D4714yes—
271C22×C8—941no—
272C22×C8—944no—
273C22×C8—942no—
274C22×C8C22×D4712yes—
275#117—22no—
276#117—22no—
277#117—22no—
278#117C22×D4714yes—
279C2×C4⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C42—22no—
282#108—948no—
283#107—24no—
284#106—24no—
285#104—9416no—
286C24—941no—
287C24#1062535211yescharacteristic
288#41—478no—
289#41—474no—
290#41—474no—
291#41—944no—
292#41—944no—
293#41—944no—
294#41—944no—
295#41—944no—
296#41—942no—
297#41—942no—
298C2×Q8—474no—
299C2×Q8—472no—
300C2×Q8—942no—
301C2×Q8—941no—
302C2×D4—474no—
303C2×D4—472no—
304C2×D4—944no—
305C2×D4—944no—
306C2×D4—942no—
307C2×D4—942no—
308C2×D4—942no—
309C2×D4—941no—
310C22×C4—42no—
311C22×C4—941no—
312C22×C4—944no—
313C22×C4—944no—
314C22×C4—942no—
315C22×C4—942no—
316C22×C4C2×C4×D4712yes—
317C22×C4C2×D18811yescharacteristic
318C22×C4C2×D18811yescharacteristic
319C22×C4D4×D4712yes—
320C22×C4#1062535211yescharacteristic
321C22×C4Q8×D4711yescharacteristic
322C22×C4Q8×D4711yescharacteristic
323C22×C4#1062535412yes—
324C22×C4C2×C22⋊D4712yes—
325C22×C4C23×D4711yescharacteristic
326M16—474no—
327M16—944no—
328M16—942no—
329M16—9416no—
330M16—944no—
331M16—944no—
332M16—1882no—
333M16—1882no—
334M16(C2×D47)⋊C418yes—
335M16(C2×D47)⋊C418yes—
336C2×C8—944no—
337C2×C8—942no—
338C2×C8—9416no—
339C2×C8—944no—
340C2×C8—1882no—
341C2×C8—1882no—
342C2×C8C2×C4×D4714yes—
343C2×C8C2×D18814yes—
344C2×C8C2×C22⋊D4714yes—
345C4⋊C4—24no—
346C4⋊C4—42no—
347C22⋊C4—24no—
348C22⋊C4—42no—
349C42—24no—
350C42—42no—
351C23—81no—
352C23—944no—
353C23—942no—
354C23—3762no—
355C23#1309398212yes—
356C23#1309399512yes—
357C23#1309400411yescharacteristic
358C23#1309400411yescharacteristic
359C23C2×#1062535211yescharacteristic
360Q8—474no—
361Q8—944no—
362Q8—942no—
363D4—474no—
364D4—948no—
365D4—944no—
366D4—944no—
367D4—944no—
368D4—942no—
369C2×C4—44no—
370C2×C4—84no—
371C2×C4—944no—
372C2×C4—942no—
373C2×C4—948no—
374C2×C4—944no—
375C2×C4—944no—
376C2×C4C2×(C2×D47)⋊C412yes—
377C2×C4C2×(C2×D47)⋊C412yes—
378C2×C4C4⋊C4×D4712yes—
379C2×C4C4⋊C4×D4712yes—
380C2×C4#1309398212yes—
381C2×C4#1309399512yes—
382C2×C4#1309399912yes—
383C2×C4#1309399912yes—
384C2×C4#1309400012yes—
385C2×C4#1309400012yes—
386C2×C4#1309400411yescharacteristic
387C2×C4#1309400411yescharacteristic
388C2×C4C22×C4×D4711yescharacteristic
389C2×C4C2×D4×D4711yescharacteristic
390C2×C4C22×C22⋊D4711yescharacteristic
391C2×C4C22×D18811yescharacteristic
392C2×C4C2×Q8×D4711yescharacteristic
393C2×C4C2×#1062535411yescharacteristic
394C8—944no—
395C8—1884no—
396C8C2×(C2×D47)⋊C418yes—
397C22—42no—
398C22—41no—
399C22—42no—
400C22—41no—
401C22—41no—
402C22—944no—
403C22—3764no—
404C22—1884no—
405C22#1568898012yes—
406C22#1568898012yes—
407C22C2×#1309398211yescharacteristic
408C22C2×#1309399511yescharacteristic
409C22C2×#1309400411yescharacteristic
410C4—84no—
411C4—944no—
412C4#1568898012yes—
413C4#1568898012yes—
414C4C22×(C2×D47)⋊C411yescharacteristic
415C4C2×C4⋊C4×D4711yescharacteristic
416C4C2×#1309399911yescharacteristic
417C4C2×#1309400011yescharacteristic
418C2—21no—
419C2—22no—
420C2—21no—
421C2—22no—
422C2—21no—
423C2—1884no—
424C2C2×#1568898011yescharacteristic
subgroupG/H
centerC4C2×#13093999
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2911C2
socleC2×C47C2×#380
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#2911D47
hypocenterC47#20675
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2911

Complements

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

NH ≅ G/Ntype
2. C2×#15689172C2semidirect
4. #20243439C2semidirect
5. C2×#15688893C2semidirect
6. C47×#2911C2semidirect
9. #15689889C4semidirect
17. C2×#13093960C22semidirect
21. #15688893C22semidirect
25. C47×#427C22semidirect
40. #13094030C2×C4semidirect
208. #2911D47semidirect
233. #427C2×D47semidirect
238. C47#20675semidirect

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156891722
C2×#156891412
#202434392
C2×#156888932
C47×#29112
#2067547