Finite Group Databasebeta

← #11860766

Subgroups — #11860766

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic
4#10592696C211yesmaximal, characteristic, complemented
5#10591138C211yesmaximal, characteristic, complemented
6#10591099C211yesmaximal, characteristic, complemented
7#10591085C211yesmaximal, characteristic
8#10590358C214yesmaximal, complemented
9C4×#3715C214yesmaximal, complemented
10#82548—31nomaximal
11#82543—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#893—22no—
20C3×#887—22no—
21C3×D3×C22⋊C4—22no—
22C3×#877—22no—
23C3×C4×D12C2214yes—
24C3×C4×Dic6C2214yescomplemented
25C2×#3715C418yescomplemented
26C2×#3715C2212yes—
27C2×#3715C2212yes—
28#63630C2212yescomplemented
29C4×C3⋊(C3⋊C8)C2212yescomplemented
30#63576C2212yescomplemented
31#63574C2212yescomplemented
32#63565C2214yescomplemented
33#63562C2214yes—
34C3×#519—31no—
35C3×#518—31no—
36C22×#215—31no—
37C22×#214—31no—
38#5521D311yescharacteristic
39#5516D311yescharacteristic, complemented
40#5225—31no—
41#5215—31no—
42#5026—34no—
43C4×#215—34no—
44#5018—34no—
45C4×#214—34no—
46#5004—31no—
47#5001—31no—
48#4998—31no—
49#4998—31no—
50#4997—31no—
51#4997—31no—
52#4997—61no—
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⋊C4D412yes—
66C32×C22⋊C4D412yes—
67C32×C42C2312yes—
68#3748—22no—
69C2×C3⋊(C3⋊C8)C2×C414yescomplemented
70C2×C3⋊(C3⋊C8)C2312yes—
71C2×C3⋊(C3⋊C8)C2311yescharacteristic
72C2×C3⋊(C3⋊C8)C2311yescharacteristic
73C3×#217—21no—
74C3×#217—21no—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3C2312yes—
77C3×C4⋊Dic3C2312yes—
78C3×Dic3⋊C4—24no—
79C3×C4×Dic3—24no—
80C3×C4×Dic3—21no—
81C3×C4×Dic3—21no—
82#3715C2×C418yescomplemented
83#3715C2×C418yescomplemented
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C3×C4×Q8—34no—
90C3×C4×Q8—62no—
91C3×C4×D4—34no—
92C3×C4×D4—62no—
93C3×#117—21no—
94C3×#117—31no—
95C3×#117—31no—
96C3×#117—62no—
97C3×#117C2×D311yescharacteristic
98C3×#117C2×D311yescharacteristic
99C2×C3×C22⋊C4—62no—
100C2×#215—38no—
101C2×#215—32no—
102C2×#215—32no—
103C2×#214—38no—
104C2×#214—32no—
105C2×#214—32no—
106#926C2×D311yescharacteristic
107#926C2×D311yescharacteristic
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—61no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114#893—22no—
115#887—22no—
116D3×C22⋊C4—22no—
117#877—22no—
118C4×D12C2×D314yes—
119C4×Dic6C2×D314yescomplemented
120#835—34no—
121#832—34no—
122#810—34no—
123#809—34no—
124#808—32no—
125#808—32no—
126#807—32no—
127#807—32no—
128#803—32no—
129#803—32no—
130#803—62no—
131C4×C3⋊C8—32no—
132C4×C3⋊C8—32no—
133C4×C3⋊C8—62no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—24no—
137C22×C3×D3—82no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D414yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3×Dic3—24no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
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)—22no—
155C3⋊(C3⋊C8)C22×C412yes—
156C3⋊(C3⋊C8)C22×C412yes—
157C22×SD16—91no—
158#519—31no—
159#518—31no—
160#440—94no—
161C4×SD16—94no—
162#427—91no—
163#419—91no—
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—62no—
175C2×C3×D4—61no—
176C22×C3×C4—21no—
177C22×C3×C4—61no—
178C22×C3×C4—64no—
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—22no—
188C2×Dic6—21no—
189C2×Dic6C4×D314yescomplemented
190C2×Dic6C22×D312yes—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—32no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4—64no—
195C3×C4⋊C4#6712yes—
196C3×C4⋊C4#6712yes—
197C3×C22⋊C4—22no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—64no—
201C3×C22⋊C4#6712yes—
202C3×C22⋊C4#6712yes—
203C3×C42—22no—
204C3×C42—61no—
205C3×C42—61no—
206C3×C42—64no—
207C3×C42C22×D312yes—
208C3×C42C22×D312yes—
209#217—21no—
210#217—21no—
211#215—38no—
212#215—38no—
213#214—38no—
214#214—38no—
215(C2×D3)⋊C4—24no—
216C4⋊Dic3C22×D312yes—
217C4⋊Dic3C22×D312yes—
218Dic3⋊C4—24no—
219C4×Dic3—24no—
220C4×Dic3—21no—
221C4×Dic3—21no—
222#208—64no—
223#208—62no—
224#208—62no—
225C2×C3⋊C8—34no—
226C2×C3⋊C8—34no—
227C2×C3⋊C8—31no—
228C2×C3⋊C8—31no—
229C2×C3⋊C8—31no—
230C2×C3⋊C8—31no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—64no—
237C22×C32—22no—
238C22×C32C4×D412yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—24no—
241C2×C3×D3—44no—
242C2×C3×D3—84no—
243C32×C4—24no—
244C32×C4C4×D412yes—
245C32×C4C23×C411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C22×Q8—31no—
251C22×D4—31no—
252C2×SD16—98no—
253C2×SD16—92no—
254C2×SD16—92no—
255C2×M16—91no—
256C22×C8—91no—
257C4×Q8—34no—
258C4×Q8—62no—
259C4×D4—34no—
260C4×D4—62no—
261#117—31no—
262#117—31no—
263#117—62no—
264#117D3211yescharacteristic
265C2×C22⋊C4—62no—
266#107—92no—
267#106—92no—
268#103—94no—
269#102—94no—
270#97—92no—
271C4×C8—92no—
272C23×C3—21no—
273C23×C3—62no—
274C23×C3—64no—
275C23×C3—242no—
276C23×C3C2×#6711yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C22×D3—22no—
279C22×D3—24no—
280C22×D3—82no—
281C3×Q8—34no—
282C3×Q8—64no—
283C3×Q8—62no—
284C3×D4—34no—
285C3×D4—64no—
286C3×D4—62no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—24no—
292C2×C3×C4—64no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—244no—
297C2×C3×C4C2×C4×D312yes—
298C2×C3×C4C2×C4×D312yes—
299C2×C3×C4#23512yes—
300C2×C3×C4#23512yes—
301C2×C3×C4C2×#6714yes—
302C2×C3×C4C2×#6714yes—
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×C3×C4C23×D311yescharacteristic
307C2×Dic3—24no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311D12—24no—
312D12—22no—
313D12C2×C4×D314yes—
314C4×D3—84no—
315Dic6—24no—
316Dic6—22no—
317Dic6C2×C4×D314yes—
318C3⋊C8—32no—
319C3⋊C8—32no—
320C3⋊C8—32no—
321C3⋊C8—32no—
322C3⋊C8—62no—
323C3⋊C8—62no—
324C3⋊C8—64no—
325C3⋊C8—62no—
326C3⋊C8—62no—
327C2×C32—22no—
328C2×C32C2×C4×D411yescharacteristic
329C2×C32#57712yes—
330C3×D3—44no—
331C24—61no—
332C2×Q8—32no—
333C2×Q8—34no—
334C2×Q8—62no—
335C2×Q8—61no—
336C2×D4—32no—
337C2×D4—34no—
338C2×D4—62no—
339C2×D4—61no—
340C22×C4—61no—
341C22×C4—64no—
342C22×C4C2×D3211yescharacteristic
343SD16—98no—
344SD16—98no—
345M16—182no—
346C2×C8—91no—
347C2×C8—91no—
348C2×C8—94no—
349C2×C8—92no—
350C4⋊C4—32no—
351C4⋊C4—32no—
352C4⋊C4—64no—
353C4⋊C4#62512yes—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—64no—
357C22⋊C4#62512yes—
358C42—61no—
359C42—61no—
360C42—64no—
361C42C2×D3212yes—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—22no—
366C22×C3—42no—
367C22×C3—64no—
368C22×C3—124no—
369C22×C3—244no—
370C22×C3C4×#6712yes—
371C22×C3C4×#6712yes—
372C22×C3C22×#6711yescharacteristic
373C22×C3C22×#6711yescharacteristic
374C2×D3—24no—
375C2×D3—44no—
376C2×D3—84no—
377C3×C4—24no—
378C3×C4—24no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—22no—
382C3×C4—44no—
383C3×C4—64no—
384C3×C4—122no—
385C3×C4—122no—
386C3×C4C4×#6712yes—
387C3×C4C4×#6712yes—
388C3×C4C22×C4×D311yescharacteristic
389C3×C4C22×C4×D311yescharacteristic
390C3×C4C2×#23511yescharacteristic
391C3×C4C2×#23511yescharacteristic
392Dic3—24no—
393Dic3—42no—
394Dic3—42no—
395C32#294911yescharacteristic, complemented, Sylow
396C23—62no—
397C23—64no—
398C23—242no—
399C23C2×#62511yescharacteristic
400Q8—34no—
401Q8—62no—
402Q8—64no—
403D4—34no—
404D4—62no—
405D4—64no—
406C2×C4—62no—
407C2×C4—64no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—244no—
411C2×C4#379812yes—
412C2×C4C4×D3212yes—
413C2×C4C2×#62514yes—
414C2×C4C2×#62511yescharacteristic
415C2×C4C22×D3211yescharacteristic
416C8—92no—
417C8—92no—
418C8—182no—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—42no—
424C2×C3—124no—
425C2×C3C2×C4×#6711yescharacteristic
426C2×C3C2×C4×#6711yescharacteristic
427C2×C3#583612yes—
428C2×C3#583712yes—
429D3—44no—
430C22—22no—
431C22—64no—
432C22—124no—
433C22—244no—
434C22C4×#62512yes—
435C22C22×#62511yescharacteristic
436C4—24no—
437C4—64no—
438C4—122no—
439C4—122no—
440C4C4×#62512yes—
441C4C2×#379811yescharacteristic
442C4C2×C4×D3211yescharacteristic
443C3—21no—
444C3#8254311yescharacteristic, complemented
445C3#8254811yescharacteristic, complemented
446C2—22no—
447C2—124no—
448C2C2×C4×#62511yescharacteristic
449C2#1059544612yes—
subgroupG/H
centerC22C22×#625
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 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
4. #10592696C2semidirect
5. #10591138C2semidirect
6. #10591099C2semidirect
8. #10590358C2semidirect
9. C4×#3715C2semidirect
24. C3×C4×Dic6C22semidirect
25. C2×#3715C4semidirect
28. #63630C22semidirect
29. C4×C3⋊(C3⋊C8)C22semidirect
30. #63576C22semidirect
31. #63574C22semidirect
32. #63565C22semidirect
39. #5516D3semidirect
63. C2×C3×Dic6C2×C4semidirect
69. C2×C3⋊(C3⋊C8)C2×C4semidirect
82. #3715C2×C4semidirect
83. #3715C2×C4semidirect
119. C4×Dic6C2×D3semidirect
189. C2×Dic6C4×D3semidirect
395. C32#2949semidirect
444. C3#82543semidirect
445. C3#82548semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
C3×#55162
C22×#37152
#105926962
#105911382
#105910992
#105910852
#105903582
C4×#37152
#825483
#825433