Finite Group Databasebeta

← #11787784

Subgroups — #11787784

Order 1152.

819 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596303C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic, complemented
3C3×#5240C211yesmaximal, characteristic, complemented
4#10591113C212yesmaximal, complemented
5#10589160C212yesmaximal, complemented
6#72021—31nomaximal
7#70045—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C2×#3828C2211yescharacteristic
10#64156C411yescharacteristic, complemented
11#64153C411yescharacteristic, complemented
12#64149C411yescharacteristic, complemented
13#64148—22no—
14#64145C411yescharacteristic, complemented
15C4×#638—22no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C3×#948—24no—
18C3×#926C2212yes—
19C2×C3×#208—22no—
20C2×C3×#208C2212yes—
21C3×#834—22no—
22#63570—24no—
23C3×#568—31no—
24#5832—31no—
25#5832—31no—
26#5832—61no—
27#5819D311yescharacteristic, complemented
28C3×#410—31no—
29#5240D311yescharacteristic, complemented
30#5139—32no—
31#5005—32no—
32#4555—32no—
33#4532—32no—
34C32×#41—22no—
35C32×#41—22no—
36C2×C32×Q8C2×C411yescharacteristic
37C2×C32×D4C2×C411yescharacteristic
38C2×C32×D4D412yes—
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×#638—22no—
42C2×#638—21no—
43C22×C3⋊Dic3—21no—
44#3828—22no—
45#3828—22no—
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×#634C2×C411yescharacteristic
49#3757—22no—
50#3752—22no—
51#3750—22no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3C2×C411yescharacteristic
55C3×#217—22no—
56C3×C4⋊Dic3—22no—
57C3×C4×Dic3—22no—
58C3×#208—24no—
59C3×#208—22no—
60C3×#208D414yescomplemented
61C2×C3×C3⋊C8—24no—
62C2×C3×C3⋊C8—22no—
63#1884—91noSylow
64C2×C3×#41—21no—
65C2×C3×#41C2×D311yescharacteristic
66C2×C3×#41C2×D311yescharacteristic
67C2×#235—31no—
68C2×#235—31no—
69C2×#235—61no—
70C3×#131—64no—
71C2×C3×M16—32no—
72C2×C3×M16—62no—
73C3×#117—32no—
74#948—24no—
75#947—31no—
76#947—31no—
77#947—61no—
78#944—31no—
79#944—31no—
80#944—61no—
81#940—31no—
82#940—31no—
83#940—61no—
84#939—64no—
85#939—62no—
86#939—62no—
87#936—31no—
88#936—31no—
89#936—61no—
90C4×#67—64no—
91C4×#67—62no—
92C4×#67—62no—
93#926C2×D312yes—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—61no—
97C2×#208—22no—
98C2×#208C2×D312yes—
99C3×#99—62no—
100#834—22no—
101#825—64no—
102#805—64no—
103C23×C32C22⋊C412yes—
104C23×C32C2×D411yescharacteristic
105C22×C3⋊D3—21no—
106C32×Q8—22no—
107C32×D4—24no—
108C32×D4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4C22⋊C412yes—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D412yes—
115C2×C32×C4#4112yes—
116#638—44no—
117#638—42no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—42no—
122C4⋊(C3⋊D3)—22no—
123C4×C3⋊D3—41no—
124C4×C3⋊D3—41no—
125#634—22no—
126C2×C3×Dic3—42no—
127C3×C3⋊C8—24no—
128#568—31no—
129#532—91no—
130#421—92no—
131#410—31no—
132#339—92no—
133C3×#41—22no—
134C3×#41—22no—
135C3×#41—22no—
136C3×#41—22no—
137C3×#41—42no—
138C3×#41—42no—
139C2×C3×Q8—21no—
140C2×C3×Q8C4×D311yescharacteristic
141C2×C3×Q8C4×D311yescharacteristic
142C2×C3×D4—21no—
143C2×C3×D4—22no—
144C2×C3×D4C4×D311yescharacteristic
145C2×C3×D4C4×D311yescharacteristic
146C2×C3×D4D1212yes—
147C2×C3×D4#6712yes—
148C22×C3×C4—22no—
149C22×C3×C4—21no—
150C22×C3×C4D1212yes—
151C22×C3×C4#6712yes—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—64no—
155C2×#67—62no—
156C2×#67—62no—
157C2×#67—62no—
158C2×#67—61no—
159C2×#67—61no—
160C22×Dic3—62no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163#235—62no—
164#235—62no—
165#235—62no—
166#235—62no—
167#235—122no—
168#235—122no—
169C2×D12—31no—
170C2×D12—31no—
171C2×D12—61no—
172C2×C4×D3—62no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×Dic6—31no—
176C2×Dic6—31no—
177C2×Dic6—61no—
178C3×M16—34no—
179C3×M16—64no—
180C3×M16—62no—
181C2×C3×C8—64no—
182C2×C3×C8—62no—
183C3×C4⋊C4—62no—
184C3×C22⋊C4—62no—
185C3×C42—62no—
186#217—22no—
187#217—64no—
188#217—62no—
189#217—62no—
190(C2×D3)⋊C4—64no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—62no—
193C4⋊Dic3—22no—
194Dic3⋊C4—64no—
195Dic3⋊C4—62no—
196Dic3⋊C4—62no—
197C4×Dic3—22no—
198C4×Dic3—31no—
199C4×Dic3—31no—
200C4×Dic3—31no—
201C4×Dic3—31no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—62no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207#208—24no—
208#208—22no—
209#208#6714yescomplemented
210C2×C3⋊C8—24no—
211C2×C3⋊C8—22no—
212C22×C32—22no—
213C22×C32—41no—
214C22×C32—42no—
215C22×C32C2×C22⋊C411yescharacteristic
216C22×C32#12112yes—
217C2×C3⋊D3—42no—
218C2×C3⋊D3—41no—
219C32×C4—22no—
220C32×C4C4×D412yes—
221C32×C4#12011yescharacteristic
222C32×C4#12311yescharacteristic
223C3⋊Dic3—22no—
224C3⋊Dic3—41no—
225C3⋊Dic3—41no—
226C3×Dic3—82no—
227C2×#41—91no—
228C2×#41D3211yescharacteristic
229#131—64no—
230C2×M16—32no—
231C2×M16—62no—
232C4⋊Q8—91no—
233#127—91no—
234#124—91no—
235#124—91no—
236#121—182no—
237C4×D4—182no—
238#117—32no—
239C2×C42—91no—
240#104—184no—
241#99—62no—
242C23×C3—22no—
243C23×C3—21no—
244C23×C3(C2×D3)⋊C412yes—
245C23×C3(C2×D3)⋊C412yes—
246C23×C3C2×D1211yescharacteristic
247C23×C3C2×#6711yescharacteristic
248C22×D3—62no—
249C22×D3—61no—
250C22×D3—61no—
251C3×Q8—22no—
252C3×Q8—22no—
253C3×Q8—42no—
254C3×D4—24no—
255C3×D4—24no—
256C3×D4—22no—
257C3×D4—22no—
258C3×D4—42no—
259C3×D4—44no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—22no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—122no—
272C2×C3×C4(C2×D3)⋊C412yes—
273C2×C3×C4(C2×D3)⋊C412yes—
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4C2×C4×D311yescharacteristic
276C2×C3×C4C2×D1211yescharacteristic
277C2×C3×C4#23512yes—
278C2×C3×C4D3×D412yes—
279C2×C3×C4#23712yes—
280C2×C3×C4C2×#6711yescharacteristic
281C2×C3×C4C2×#6712yes—
282#67—124no—
283#67—124no—
284#67—128no—
285#67—124no—
286#67—122no—
287#67—122no—
288C2×Dic3—42no—
289C2×Dic3—62no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—122no—
299C2×Dic3—122no—
300C2×Dic3—124no—
301D12—62no—
302D12—62no—
303D12—122no—
304C4×D3—122no—
305C4×D3—122no—
306C4×D3—121no—
307C4×D3—121no—
308C4×D3—121no—
309C4×D3—121no—
310Dic6—62no—
311Dic6—62no—
312Dic6—122no—
313C3×C8—64no—
314C3⋊C8—24no—
315C2×C32—21no—
316C2×C32—22no—
317C2×C32—42no—
318C2×C32#38611yescharacteristic
319C3⋊D3—81no—
320#41—22no—
321#41—22no—
322#41—182no—
323#41—182no—
324C2×Q8—91no—
325C2×Q8#62411yescharacteristic
326C2×D4—91no—
327C2×D4—182no—
328C2×D4—181no—
329C2×D4#62411yescharacteristic
330C2×D4#62612yes—
331C22×C4—181no—
332C22×C4—181no—
333C22×C4#62612yes—
334C22×C4C2×D3211yescharacteristic
335M16—34no—
336M16—64no—
337M16—62no—
338C2×C8—64no—
339C2×C8—62no—
340C4⋊C4—62no—
341C4⋊C4—182no—
342C22⋊C4—62no—
343C22⋊C4—182no—
344C22⋊C4—182no—
345C42—62no—
346C42—91no—
347C42—91no—
348C42—181no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—21no—
352C22×C3—22no—
353C22×C3—42no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—42no—
359C22×C3—44no—
360C22×C3C2×(C2×D3)⋊C411yescharacteristic
361C22×C3C2×(C2×D3)⋊C411yescharacteristic
362C22×C3#93012yes—
363C22×C3#93912yes—
364C2×D3—122no—
365C2×D3—124no—
366C2×D3—122no—
367C2×D3—122no—
368C2×D3—121no—
369C2×D3—121no—
370C3×C4—22no—
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—42no—
376C3×C4—242no—
377C3×C4#67⋊C412yes—
378C3×C4#88211yescharacteristic
379C3×C4#88611yescharacteristic
380C3×C4C4×#6712yes—
381C3×C4#92911yescharacteristic
382C3×C4#95311yescharacteristic
383Dic3—64no—
384Dic3—62no—
385Dic3—62no—
386Dic3—82no—
387Dic3—122no—
388Dic3—122no—
389Dic3—121no—
390Dic3—121no—
391Dic3—121no—
392Dic3—121no—
393C32#188411yescharacteristic, complemented, Sylow
394C23—181no—
395C23#372212yes—
396C23C2×#62611yescharacteristic
397Q8—22no—
398Q8—182no—
399D4—24no—
400D4—22no—
401D4—182no—
402D4—364no—
403D4—362no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—122no—
407C2×C4—181no—
408C2×C4—181no—
409C2×C4—181no—
410C2×C4—362no—
411C2×C4—361no—
412C2×C4—361no—
413C2×C4#372212yes—
414C2×C4#380412yes—
415C2×C4C2×#62411yescharacteristic
416C2×C4C2×#62611yescharacteristic
417C2×C4D3×#6712yes—
418C8—64no—
419C2×C3—22no—
420C2×C3—21no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—42no—
426C2×C3—42no—
427C2×C3—42no—
428C2×C3—82no—
429C2×C3#495811yescharacteristic
430C2×C3#521311yescharacteristic
431D3—242no—
432D3—241no—
433D3—241no—
434C22—22no—
435C22—41no—
436C22—42no—
437C22—362no—
438C22—361no—
439C22C2×#372211yescharacteristic
440C22#6397812yes—
441C4—22no—
442C4—182no—
443C4—242no—
444C4—361no—
445C4—361no—
446C4#6395212yes—
447C4#6396611yescharacteristic
448C4#6397711yescharacteristic
449C3—21no—
450C3#7004511yescharacteristic, complemented
451C3#7202111yescharacteristic, complemented
452C2—21no—
453C2—22no—
454C2—42no—
455C2—721no—
456C2#1059171111yescharacteristic
subgroupG/H
centerC4#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5819C2semidirect
3. C3×#5240C2semidirect
4. #10591113C2semidirect
5. #10589160C2semidirect
10. #64156C4semidirect
11. #64153C4semidirect
12. #64149C4semidirect
14. #64145C4semidirect
27. #5819D3semidirect
29. #5240D3semidirect
60. C3×#208D4semidirect
209. #208#67semidirect
393. C32#1884semidirect
450. C3#70045semidirect
451. C3#72021semidirect

Maximal subgroups

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

subgroupindex
#105963032
C3×#58192
C3×#52402
#105911132
#105891602
#720213
#700453