Finite Group Databasebeta

← #11859362

Subgroups — #11859362

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5524C211yesmaximal, characteristic
2C2×#63814C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4#10592698C211yesmaximal, characteristic, complemented
5C3×#4997C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic, complemented
7#10591069C211yesmaximal, characteristic, complemented
8#10590326C214yesmaximal, complemented
9C3⋊C8×D12C214yesmaximal, complemented
10#82916—31nomaximal
11#78553—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#897C412yes—
20C3×#895C412yes—
21C3×#886C412yes—
22C3×#882C412yes—
23C3×C4×D12C2214yes—
24C2×#3711C2212yescomplemented
25#63814—24no—
26C2×D3×C3⋊C8—24no—
27C2×D3×C3⋊C8C2212yes—
28C2×D3×C3⋊C8C2212yes—
29C2×D3×C3⋊C8C2212yescomplemented
30C4⋊(C3⋊(C3⋊C8))C2214yescomplemented
31C3×#803C2212yescomplemented
32C3×C4×C3⋊C8C2212yescomplemented
33(C2×D3)⋊(C3⋊C8)C2214yes—
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C3×#525—31no—
36C2×#948—31no—
37C23×C3⋊C8—31no—
38C2×#901—31no—
39C22×D3×C8—31no—
40#5524D311yescharacteristic
41C3×#405—31no—
42#5234—31no—
43#5207—31no—
44#5129—31no—
45#5126—31no—
46#5011—34no—
47D4×C3⋊C8—34no—
48#4999—31no—
49#4999—31no—
50#4999—61no—
51#4997D311yescharacteristic, complemented
52#4706—34no—
53C8×D12—34no—
54C23×C3×D3C2×C411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67C2×C412yes—
57C22×C3×Dic3C2×C411yescharacteristic
58C3×#235—22no—
59C3×#235—22no—
60C2×C3×D12C2×C414yes—
61C2×C3×D12C2×C411yescharacteristic
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3C2×C412yes—
65C2×C3×C4×D3C2312yes—
66C2×C3×C4×D3C2312yes—
67C2×C3×Dic6C2×C411yescharacteristic
68C32×C4⋊C4C2×C412yes—
69C32×C22⋊C4C2×C412yes—
70C32×C42C2312yes—
71#3748—22no—
72C2×C3⋊(C3⋊C8)—22no—
73C2×C3⋊(C3⋊C8)C2312yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×(C2×D3)⋊C4C2×C414yes—
76C3×(C2×D3)⋊C4C2×C414yes—
77C3×C4⋊Dic3C2×C414yes—
78C3×#208—22no—
79C2×C3×C3⋊C8D414yescomplemented
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83#3711—24no—
84D3×C3⋊C8—24no—
85D3×C3⋊C8—24no—
86D3×C3⋊C8—24no—
87#2929—91noSylow
88C2×C3×#41—31no—
89C23×C3×C4—31no—
90C2×#235C2×D311yescharacteristic
91C22×C4×D3C2×D311yescharacteristic
92C2×C3×M16—31no—
93C22×C3×C8—31no—
94C3×#123—32no—
95C3×C22⋊Q8—32no—
96C3×#121—32no—
97C3×#120—32no—
98C3×C4×D4—34no—
99C3×#117—21no—
100C3×#117C2×D311yescharacteristic
101C3×#117C2×D311yescharacteristic
102#948—64no—
103C2×#208—31no—
104C2×#208—31no—
105C2×#208—32no—
106C2×#208—61no—
107C2×#208C2×D311yescharacteristic
108C22×C3⋊C8—31no—
109C22×C3⋊C8—31no—
110C22×C3⋊C8—32no—
111C22×C3⋊C8—32no—
112C22×C3⋊C8—32no—
113C22×C3⋊C8—61no—
114C22×C3⋊C8—64no—
115C22×C3⋊C8C2×D311yescharacteristic
116#901—64no—
117C2×ΓL(1,𝔽25)—32no—
118C2×D3×C8—32no—
119C2×D3×C8—32no—
120C2×D3×C8—32no—
121C2×D3×C8—64no—
122#897Dic312yes—
123#895Dic312yes—
124#886Dic312yes—
125#882Dic312yes—
126C4×D12C2×D314yes—
127C3×#97—32no—
128C3×C4×C8—32no—
129#830—34no—
130#830—34no—
131(C2×D3)⋊C8—34no—
132(C2×D3)⋊C8—34no—
133C4⋊(C3⋊C8)—34no—
134C4⋊(C3⋊C8)—34no—
135C4⋊(C3⋊C8)—64no—
136#803C2×D312yescomplemented
137C4×C3⋊C8C2×D312yescomplemented
138C23×C32C22×C411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—24no—
141C22×C3×D3C22×C412yes—
142C22×C3×D3C22×C412yes—
143C2×C32×C4C22×C414yes—
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C3×#67—24no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3C22×C412yes—
151C2×C3×Dic3C22×C412yes—
152C3×D12—28no—
153C3×D12—22no—
154C3×C4×D3—24no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×Dic6—22no—
160C3⋊(C3⋊C8)—22no—
161C3⋊(C3⋊C8)—22no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8C2×D412yes—
164C3×C3⋊C8C2×D412yes—
165C2×#131—91no—
166C23×C8—91no—
167#525—31no—
168#435—94no—
169C8×D4—94no—
170#424—91no—
171#408—91no—
172#407—91no—
173#405—31no—
174C24×C3—31no—
175C23×D3C2×Dic311yescharacteristic
176C3×#41—62no—
177C3×#41—62no—
178C2×C3×Q8—31no—
179C2×C3×D4—32no—
180C2×C3×D4—34no—
181C2×C3×D4—31no—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—62no—
188C22×C3×C4—62no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67C2×Dic312yes—
192C22×Dic3C2×Dic311yescharacteristic
193#235—22no—
194#235—22no—
195C2×D12C2×Dic314yes—
196C2×D12C2×Dic311yescharacteristic
197C2×C4×D3—22no—
198C2×C4×D3—22no—
199C2×C4×D3C2×Dic312yes—
200C2×C4×D3C22×D312yes—
201C2×C4×D3C22×D312yes—
202C2×Dic6C2×Dic311yescharacteristic
203C3×M16—62no—
204C2×C3×C8—34no—
205C2×C3×C8—31no—
206C2×C3×C8—31no—
207C2×C3×C8—32no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—34no—
210C3×C4⋊C4C4×D312yes—
211C3×C4⋊C4C2×Dic312yes—
212C3×C22⋊C4—22no—
213C3×C22⋊C4—34no—
214C3×C22⋊C4—34no—
215C3×C22⋊C4C4×D312yes—
216C3×C22⋊C4C2×Dic312yes—
217C3×C42—22no—
218C3×C42C22×D312yes—
219C3×C42C22×D312yes—
220(C2×D3)⋊C4C2×Dic314yes—
221(C2×D3)⋊C4C2×Dic314yes—
222C4⋊Dic3C2×Dic314yes—
223#208—22no—
224#208—62no—
225#208—62no—
226#208—64no—
227#208—122no—
228C2×C3⋊C8—32no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—62no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—64no—
237C2×C3⋊C8—64no—
238C2×C3⋊C8—64no—
239C2×C3⋊C8—122no—
240C2×C3⋊C8D1214yescomplemented
241C2×C3⋊C8C22×D312yes—
242C2×C3⋊C8C22×D311yescharacteristic
243C2×C3⋊C8C22×D311yescharacteristic
244ΓL(1,𝔽25)—64no—
245D3×C8—64no—
246D3×C8—64no—
247D3×C8—64no—
248C22×C32—22no—
249C22×C32C4×D412yes—
250C22×C32C23×C411yescharacteristic
251C2×C3×D3—28no—
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254C2×C3×D3—22no—
255C2×C3×D3—24no—
256C2×C3×D3#13114yescomplemented
257C32×C4—24no—
258C32×C4C4×D412yes—
259C32×C4C22×D411yescharacteristic
260C32×C4C2×#4111yescharacteristic
261C3×Dic3—22no—
262C3×Dic3—22no—
263C2×#41—31no—
264C23×C4—31no—
265#131—184no—
266C2×M16—31no—
267C2×M16—92no—
268C2×M16—91no—
269C22×C8—31no—
270C22×C8—92no—
271C22×C8—92no—
272C22×C8—92no—
273C22×C8—91no—
274C22×C8—184no—
275#123—32no—
276C22⋊Q8—32no—
277#121—32no—
278#120—32no—
279C4×D4—34no—
280#117D3211yescharacteristic
281C4⋊C8—94no—
282C22⋊C8—94no—
283C22⋊C8—94no—
284#97—32no—
285C4×C8—32no—
286C23×C3—21no—
287C23×C3—32no—
288C23×C3—32no—
289C23×C3—64no—
290C23×C3—62no—
291C23×C3C2×C4×D311yescharacteristic
292C23×C3C22×Dic311yescharacteristic
293C22×D3—22no—
294C22×D3—24no—
295C22×D3C22×Dic312yes—
296C22×D3C22×Dic312yes—
297C3×Q8—62no—
298C3×D4—68no—
299C3×D4—64no—
300C3×D4—62no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—24no—
306C2×C3×C4—32no—
307C2×C3×C4—32no—
308C2×C3×C4—62no—
309C2×C3×C4—64no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4C2×C4×D314yes—
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×D1212yes—
317C2×C3×C4#23512yes—
318C2×C3×C4D3×D412yes—
319C2×C3×C4#23712yes—
320C2×C3×C4C22×Dic314yes—
321C2×C3×C4C22×Dic311yescharacteristic
322C2×C3×C4C23×D311yescharacteristic
323C2×C3×C4C23×D311yescharacteristic
324#67—24no—
325C2×Dic3—22no—
326C2×Dic3C22×Dic312yes—
327C2×Dic3C22×Dic312yes—
328D12—28no—
329D12—22no—
330C4×D3—24no—
331C4×D3—22no—
332C4×D3—22no—
333C4×D3—22no—
334C4×D3—22no—
335Dic6—22no—
336C3×C8—32no—
337C3×C8—32no—
338C3×C8—62no—
339C3⋊C8—22no—
340C3⋊C8—62no—
341C3⋊C8—62no—
342C3⋊C8—62no—
343C3⋊C8—62no—
344C3⋊C8—122no—
345C3⋊C8—122no—
346C3⋊C8C2×D1212yes—
347C3⋊C8C2×D1212yes—
348C2×C32—22no—
349C2×C32C2×C4×D411yescharacteristic
350C2×C32C2×#13112yes—
351C3×D3—24no—
352C3×D3—42no—
353C24—31no—
354#41—62no—
355#41—62no—
356C2×Q8—31no—
357C2×D4—32no—
358C2×D4—34no—
359C2×D4—31no—
360C22×C4—31no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—62no—
365C22×C4—62no—
366C22×C4C2×D3211yescharacteristic
367M16—62no—
368M16—184no—
369M16—182no—
370C2×C8—31no—
371C2×C8—31no—
372C2×C8—34no—
373C2×C8—32no—
374C2×C8—92no—
375C2×C8—92no—
376C2×C8—184no—
377C2×C8—184no—
378C2×C8—184no—
379C2×C8—182no—
380C4⋊C4—34no—
381C4⋊C4D3×Dic312yes—
382C22⋊C4—34no—
383C22⋊C4—34no—
384C22⋊C4D3×Dic312yes—
385C42C2×D3212yes—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—22no—
390C22×C3—34no—
391C22×C3—42no—
392C22×C3—68no—
393C22×C3—62no—
394C22×C3—62no—
395C22×C3—62no—
396C22×C3—64no—
397C22×C3C4×D1212yes—
398C22×C3D4×Dic312yes—
399C22×C3C22×C4×D311yescharacteristic
400C22×C3C23×Dic311yescharacteristic
401C2×D3—28no—
402C2×D3—22no—
403C2×D3—22no—
404C2×D3—22no—
405C2×D3—24no—
406C2×D3#94814yescomplemented
407C3×C4—24no—
408C3×C4—24no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—22no—
412C3×C4—44no—
413C3×C4—62no—
414C3×C4—62no—
415C3×C4C4×D1212yes—
416C3×C4D4×Dic312yes—
417C3×C4C22×D1211yescharacteristic
418C3×C4C2×#23511yescharacteristic
419C3×C4C2×D3×D411yescharacteristic
420C3×C4C2×#23711yescharacteristic
421Dic3—22no—
422Dic3—22no—
423C32#292911yescharacteristic, complemented, Sylow
424C23—32no—
425C23—32no—
426C23—64no—
427C23—62no—
428C23C2×D3×Dic311yescharacteristic
429Q8—62no—
430D4—68no—
431D4—64no—
432D4—62no—
433C2×C4—32no—
434C2×C4—32no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—64no—
441C2×C4#379512yes—
442C2×C4D3×D1212yes—
443C2×C4C2×D3×Dic314yes—
444C2×C4C2×D3×Dic311yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—32no—
447C8—32no—
448C8—62no—
449C8—182no—
450C8—182no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—22no—
455C2×C3—42no—
456C2×C3—64no—
457C2×C3—122no—
458C2×C3C2×C4×D1211yescharacteristic
459C2×C3D3×#13112yes—
460C2×C3C2×D4×Dic311yescharacteristic
461C2×C3C2×#94812yes—
462D3—24no—
463D3—42no—
464C22—22no—
465C22—34no—
466C22—68no—
467C22—62no—
468C22—62no—
469C22—62no—
470C22—64no—
471C22Dic3×D1212yes—
472C22C22×D3×Dic311yescharacteristic
473C4—24no—
474C4—62no—
475C4—62no—
476C4Dic3×D1212yes—
477C4C2×#379511yescharacteristic
478C4C2×D3×D1211yescharacteristic
479C3—21no—
480C3#7855311yescharacteristic, complemented
481C3#8291611yescharacteristic, complemented
482C2—22no—
483C2—64no—
484C2—122no—
485C2C2×Dic3×D1211yescharacteristic
486C2D3×#94812yes—
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#117C22
prime radicalC3×#5524C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63814C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. #10592698C2semidirect
5. C3×#4997C2semidirect
6. #10591071C2semidirect
7. #10591069C2semidirect
8. #10590326C2semidirect
9. C3⋊C8×D12C2semidirect
24. C2×#3711C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. C4⋊(C3⋊(C3⋊C8))C22semidirect
31. C3×#803C22semidirect
32. C3×C4×C3⋊C8C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
51. #4997D3semidirect
79. C2×C3×C3⋊C8D4semidirect
136. #803C2×D3semidirect
137. C4×C3⋊C8C2×D3semidirect
240. C2×C3⋊C8D12semidirect
256. C2×C3×D3#131semidirect
406. C2×D3#948semidirect
423. C32#2929semidirect
480. C3#78553semidirect
481. C3#82916semidirect

Maximal subgroups

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

subgroupindex
C3×#55242
C2×#638142
C22×D3×C3⋊C82
#105926982
C3×#49972
#105910712
#105910692
#105903262
C3⋊C8×D122
#829163
#785533