Finite Group Databasebeta

← #11860760

Subgroups — #11860760

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic
4#10592697C211yesmaximal, characteristic, complemented
5C3×#5004C211yesmaximal, characteristic, complemented
6#10591086C211yesmaximal, characteristic
7#10591057C211yesmaximal, characteristic, complemented
8#10590478C214yesmaximal, complemented
9#10590475C214yesmaximal, complemented
10#82543—31nomaximal
11#78947—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C32×#117C2211yescharacteristic
15#64135C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#893C2214yes—
20C3×D3×C22⋊C4—22no—
21C3×C4×D12—22no—
22#63955—22no—
23#63843—22no—
24Dic3×Dic6C2214yescomplemented
25C2×#3715C418yescomplemented
26C2×#3715C2212yes—
27C2×#3715C2212yes—
28#63635C2212yescomplemented
29#63634C2212yescomplemented
30C3×#810C2214yescomplemented
31#63563C2214yes—
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C3×#518—31no—
35#5812—31no—
36C22×#215—31no—
37C22×#214—31no—
38#5521D311yescharacteristic
39#5516—31no—
40C3×#419—31no—
41#5215—31no—
42#5131—31no—
43#5122—31no—
44#5018—34no—
45C4×#214—34no—
46#5004D311yescharacteristic, complemented
47#4998—31no—
48#4998—31no—
49#4998—61no—
50#4997—31no—
51#4817—34no—
52#4788—34no—
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—24no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6C2×C414yescomplemented
64C2×C3×Dic6C2312yes—
65C32×C4⋊C4C2312yes—
66C32×C22⋊C4—21no—
67C32×C42—21no—
68#3757—21no—
69C4⋊(C3⋊Dic3)C2312yes—
70C4×C3⋊Dic3—21no—
71C2×C3⋊(C3⋊C8)C2×C414yescomplemented
72C2×C3⋊(C3⋊C8)C2311yescharacteristic
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74C3×#217D412yes—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C3×#208—22no—
79C2×C3×C3⋊C8C2312yes—
80Dic3⋊Dic3—24no—
81Dic32—24no—
82#3715C2×C418yescomplemented
83#3715C2×C418yescomplemented
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C2×C3×M16—31no—
90C3×C4×D4—34no—
91C3×C4×D4—62no—
92C3×#117—21no—
93C3×#117—31no—
94C3×#117C2×D311yescharacteristic
95C3×#117C2×D311yescharacteristic
96C2×C3×C22⋊C4—62no—
97Q8×Dic3—34no—
98Q8×Dic3—62no—
99C2×#215—38no—
100C2×#215—32no—
101C2×#215—32no—
102C2×#214—38no—
103C2×#214—32no—
104C2×#214—32no—
105#926—31no—
106#926—31no—
107#926—61no—
108#926—62no—
109#926C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114#893C2×D314yes—
115#887—62no—
116D3×C22⋊C4—22no—
117#877—62no—
118C4×D12—22no—
119C4×Dic6—34no—
120C3×#103—34no—
121#832—34no—
122#821—34no—
123#815—32no—
124C8×Dic3—32no—
125#810C2×D314yescomplemented
126#808—32no—
127#808—32no—
128#808—62no—
129#807—32no—
130#807—32no—
131#807—62no—
132#803—32no—
133C4×C3⋊C8—32no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—24no—
137C22×C3×D3—82no—
138C2×C32×C4—22no—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3C2×D414yes—
147C3×D12—24no—
148C3×D12—22no—
149C3×D12C22×C414yes—
150C3×C4×D3—84no—
151C3×Dic6—24no—
152C3×Dic6—22no—
153C3×Dic6C22×C414yes—
154C3⋊(C3⋊C8)C22×C412yes—
155C3⋊(C3⋊C8)C22×C412yes—
156C3×C3⋊C8—22no—
157C22×SD16—91no—
158#519—91no—
159#518—31no—
160#440—94no—
161C4×SD16—94no—
162#427—91no—
163#419—31no—
164#418—91no—
165#405—91no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—34no—
169C2×C3×Q8—32no—
170C2×C3×Q8—62no—
171C2×C3×Q8—61no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C22×C3×C4—21no—
177C22×C3×C4—64no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×Dic3—21no—
182C2×D12—22no—
183C2×D12—21no—
184C2×D12C4×D314yes—
185C2×D12C22×D312yes—
186C2×C4×D3—24no—
187C2×Dic6—21no—
188C2×Dic6—22no—
189C2×Dic6C4×D314yescomplemented
190C2×Dic6C22×D312yes—
191C3×M16—62no—
192C2×C3×C8—32no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—32no—
195C3×C4⋊C4C22×D312yes—
196C3×C4⋊C4C22×D312yes—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—32no—
200C3×C22⋊C4—41no—
201C3×C22⋊C4—64no—
202C3×C42—21no—
203C3×C42—21no—
204C3×C42—32no—
205C3×C42—41no—
206#217—61no—
207#217—61no—
208#217—121no—
209#217#6712yes—
210#215—38no—
211#215—38no—
212#214—38no—
213#214—38no—
214(C2×D3)⋊C4—24no—
215C4⋊Dic3—32no—
216C4⋊Dic3—32no—
217C4⋊Dic3—62no—
218C4⋊Dic3—64no—
219C4⋊Dic3#6712yes—
220Dic3⋊C4—64no—
221C4×Dic3—64no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—64no—
225C4×Dic3—121no—
226C4×Dic3C22×D312yes—
227#208—22no—
228C2×C3⋊C8—34no—
229C2×C3⋊C8—34no—
230C2×C3⋊C8—31no—
231C2×C3⋊C8—31no—
232C2×C3⋊C8—31no—
233C2×C3⋊C8—31no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—64no—
237C2×C3⋊C8C22×D312yes—
238C22×C32—22no—
239C22×C32C4×D412yes—
240C22×C32C22×D411yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—44no—
243C2×C3×D3—84no—
244C32×C4—42no—
245C32×C4C4×D412yes—
246C32×C4C23×C411yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3⋊Dic3—42no—
249C3×Dic3—24no—
250C3×Dic3—24no—
251C22×Q8—31no—
252C22×D4—31no—
253C2×SD16—98no—
254C2×SD16—92no—
255C2×SD16—92no—
256C2×M16—31no—
257C22×C8—91no—
258C4×Q8—94no—
259C4×Q8—182no—
260C4×D4—34no—
261C4×D4—62no—
262#117—31no—
263#117—91no—
264#117—182no—
265#117D3211yescharacteristic
266C2×C22⋊C4—62no—
267#107—92no—
268#106—92no—
269#103—34no—
270#102—94no—
271#97—92no—
272C4×C8—92no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—64no—
276C23×C3—242no—
277C23×C3D3×D411yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C22×D3—22no—
280C22×D3—24no—
281C22×D3—82no—
282C3×Q8—34no—
283C3×Q8—64no—
284C3×Q8—62no—
285C3×D4—34no—
286C3×D4—64no—
287C3×D4—62no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—34no—
295C2×C3×C4—42no—
296C2×C3×C4—64no—
297C2×C3×C4—62no—
298C2×C3×C4—244no—
299C2×C3×C4C2×C4×D312yes—
300C2×C3×C4C2×C4×D312yes—
301C2×C3×C4#23512yes—
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4#23712yes—
304C2×C3×C4C2×#6711yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×C3×C4C23×D311yescharacteristic
307C2×Dic3—24no—
308C2×Dic3—22no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—122no—
312C2×Dic3C2×#6714yes—
313D12—24no—
314D12—22no—
315D12C2×C4×D314yes—
316C4×D3—84no—
317Dic6—24no—
318Dic6—22no—
319Dic6C2×C4×D314yes—
320C3×C8—62no—
321C3⋊C8—22no—
322C3⋊C8—32no—
323C3⋊C8—32no—
324C3⋊C8—32no—
325C3⋊C8—32no—
326C3⋊C8—62no—
327C3⋊C8—62no—
328C2×C32—22no—
329C2×C32C2×C4×D411yescharacteristic
330C2×C32#57712yes—
331C3×D3—44no—
332C24—61no—
333C2×Q8—32no—
334C2×Q8—34no—
335C2×Q8—62no—
336C2×Q8—61no—
337C2×D4—32no—
338C2×D4—34no—
339C2×D4—62no—
340C2×D4—61no—
341C22×C4—64no—
342C22×C4—61no—
343C22×C4C2×D3211yescharacteristic
344SD16—98no—
345SD16—98no—
346M16—62no—
347C2×C8—32no—
348C2×C8—91no—
349C2×C8—91no—
350C2×C8—94no—
351C4⋊C4—32no—
352C4⋊C4—92no—
353C4⋊C4—184no—
354C4⋊C4C2×D3212yes—
355C22⋊C4—21no—
356C22⋊C4—32no—
357C22⋊C4—64no—
358C22⋊C4—181no—
359C42—21no—
360C42—32no—
361C42—184no—
362C42—181no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—42no—
368C22×C3—64no—
369C22×C3—124no—
370C22×C3—244no—
371C22×C3#67⋊C412yes—
372C22×C3C4×#6712yes—
373C22×C3C2×D3×D411yescharacteristic
374C22×C3C22×#6711yescharacteristic
375C2×D3—24no—
376C2×D3—44no—
377C2×D3—84no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—22no—
381C3×C4—42no—
382C3×C4—42no—
383C3×C4—64no—
384C3×C4—64no—
385C3×C4—82no—
386C3×C4#67⋊C412yes—
387C3×C4C4×#6712yes—
388C3×C4C22×C4×D311yescharacteristic
389C3×C4C22×C4×D311yescharacteristic
390C3×C4C2×#23511yescharacteristic
391C3×C4C2×#23711yescharacteristic
392Dic3—24no—
393Dic3—24no—
394Dic3—122no—
395Dic3—122no—
396Dic3—242no—
397C32#294911yescharacteristic, complemented, Sylow
398C23—62no—
399C23—64no—
400C23—242no—
401C23D3×#6711yescharacteristic
402Q8—34no—
403Q8—62no—
404Q8—64no—
405D4—34no—
406D4—62no—
407D4—64no—
408C2×C4—22no—
409C2×C4—34no—
410C2×C4—62no—
411C2×C4—64no—
412C2×C4—182no—
413C2×C4—244no—
414C2×C4#379512yes—
415C2×C4C4×D3212yes—
416C2×C4D3×#6711yescharacteristic
417C2×C4C22×D3211yescharacteristic
418C8—62no—
419C8—92no—
420C8—92no—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—21no—
424C2×C3—22no—
425C2×C3—42no—
426C2×C3—124no—
427C2×C3C2×#67⋊C411yescharacteristic
428C2×C3#577812yes—
429C2×C3C2×C4×#6711yescharacteristic
430C2×C3#583612yes—
431D3—44no—
432C22—22no—
433C22—64no—
434C22—124no—
435C22—244no—
436C22#6387912yes—
437C22C2×D3×#6711yescharacteristic
438C4—42no—
439C4—64no—
440C4—64no—
441C4—362no—
442C4#6387912yes—
443C4C2×#379511yescharacteristic
444C4C2×C4×D3211yescharacteristic
445C3—21no—
446C3#7894711yescharacteristic, complemented
447C3#8254311yescharacteristic, complemented
448C2—22no—
449C2—124no—
450C2C2×#6387911yescharacteristic
451C2#1059546412yes—
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594818C2semidirect
4. #10592697C2semidirect
5. C3×#5004C2semidirect
7. #10591057C2semidirect
8. #10590478C2semidirect
9. #10590475C2semidirect
24. Dic3×Dic6C22semidirect
25. C2×#3715C4semidirect
28. #63635C22semidirect
29. #63634C22semidirect
30. C3×#810C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
46. #5004D3semidirect
63. C2×C3×Dic6C2×C4semidirect
71. C2×C3⋊(C3⋊C8)C2×C4semidirect
82. #3715C2×C4semidirect
83. #3715C2×C4semidirect
125. #810C2×D3semidirect
189. C2×Dic6C4×D3semidirect
397. C32#2949semidirect
446. C3#78947semidirect
447. C3#82543semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105948182
C22×#37152
#105926972
C3×#50042
#105910862
#105910572
#105904782
#105904752
#825433
#789473