Finite Group Databasebeta

← #11859361

Subgroups — #11859361

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5524C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4#10592696C211yesmaximal, characteristic, complemented
5C3×#4999C211yesmaximal, characteristic, complemented
6#10591070C211yesmaximal, characteristic, complemented
7#10591069C211yesmaximal, characteristic, complemented
8#10590330C214yesmaximal, complemented
9#10590329C214yesmaximal, complemented
10#82916—31nomaximal
11#79073—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#63815—24no—
26C2×D3×C3⋊C8—24no—
27C2×D3×C3⋊C8C2212yes—
28C2×D3×C3⋊C8C2212yes—
29C2×D3×C3⋊C8C2212yescomplemented
30#63630C2212yescomplemented
31C4×C3⋊(C3⋊C8)C2212yescomplemented
32C3×C4⋊(C3⋊C8)C2214yescomplemented
33(C2×D3)⋊(C3⋊C8)C2214yes—
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C3×#525—31no—
36C2×#948—31no—
37C23×C3⋊C8—31no—
38C2×#907—31no—
39C22×D3×C8—31no—
40#5524D311yescharacteristic
41C3×#424—31no—
42#5234—31no—
43#5207—31no—
44#5126—31no—
45#5110—31no—
46#5011—34no—
47D4×C3⋊C8—34no—
48#4999D311yescharacteristic, complemented
49#4997—31no—
50#4997—31no—
51#4997—61no—
52#4836—34no—
53#4834—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)D414yescomplemented
73C2×C3⋊(C3⋊C8)C2312yes—
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C3×(C2×D3)⋊C4C2×C414yes—
77C3×(C2×D3)⋊C4C2×C414yes—
78C3×C4⋊Dic3C2×C414yes—
79C3×#208—22no—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82C2×C3×C3⋊C8C2312yes—
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#907—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×C4⋊C8—34no—
128#830—34no—
129#830—34no—
130(C2×D3)⋊C8—34no—
131(C2×D3)⋊C8—34no—
132C4⋊(C3⋊C8)C2×D314yescomplemented
133#803—32no—
134#803—32no—
135#803—62no—
136C4×C3⋊C8—32no—
137C4×C3⋊C8—32no—
138C4×C3⋊C8—62no—
139C23×C32C22×C411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3C22×C412yes—
143C22×C3×D3C22×C412yes—
144C2×C32×C4C22×C414yes—
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C3×#67—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3C22×C412yes—
152C2×C3×Dic3C22×C412yes—
153C3×D12—28no—
154C3×D12—22no—
155C3×C4×D3—24no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×Dic6—22no—
161C3⋊(C3⋊C8)—22no—
162C3⋊(C3⋊C8)C2×D412yes—
163C3⋊(C3⋊C8)C2×D412yes—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166C2×#131—91no—
167C23×C8—91no—
168#525—31no—
169#435—94no—
170C8×D4—94no—
171#424—31no—
172#408—91no—
173#407—91no—
174#405—91no—
175C24×C3—31no—
176C23×D3C2×Dic311yescharacteristic
177C3×#41—62no—
178C3×#41—62no—
179C2×C3×Q8—31no—
180C2×C3×D4—32no—
181C2×C3×D4—34no—
182C2×C3×D4—31no—
183C22×C3×C4—21no—
184C22×C3×C4—31no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4—62no—
189C22×C3×C4—62no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67C2×Dic312yes—
193C22×Dic3C2×Dic311yescharacteristic
194#235—22no—
195#235—22no—
196C2×D12C2×Dic314yes—
197C2×D12C2×Dic311yescharacteristic
198C2×C4×D3—22no—
199C2×C4×D3—22no—
200C2×C4×D3C2×Dic312yes—
201C2×C4×D3C22×D312yes—
202C2×C4×D3C22×D312yes—
203C2×Dic6C2×Dic311yescharacteristic
204C3×M16—62no—
205C2×C3×C8—32no—
206C2×C3×C8—32no—
207C2×C3×C8—62no—
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—64no—
225#208—64no—
226#208—62no—
227#208—62no—
228C2×C3⋊C8—22no—
229C2×C3⋊C8—34no—
230C2×C3⋊C8—34no—
231C2×C3⋊C8—31no—
232C2×C3⋊C8—31no—
233C2×C3⋊C8—31no—
234C2×C3⋊C8—31no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—64no—
241C2×C3⋊C8—64no—
242C2×C3⋊C8—64no—
243C2×C3⋊C8—64no—
244C2×C3⋊C8C22×D312yes—
245C2×C3⋊C8C22×D312yes—
246ΓL(1,𝔽25)—64no—
247D3×C8—64no—
248D3×C8—64no—
249D3×C8—64no—
250C22×C32—22no—
251C22×C32C4×D412yes—
252C22×C32C23×C411yescharacteristic
253C2×C3×D3—28no—
254C2×C3×D3—22no—
255C2×C3×D3—22no—
256C2×C3×D3—22no—
257C2×C3×D3—24no—
258C2×C3×D3#13114yescomplemented
259C32×C4—24no—
260C32×C4C4×D412yes—
261C32×C4C22×D411yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3×Dic3—22no—
264C3×Dic3—22no—
265C2×#41—31no—
266C23×C4—31no—
267#131—184no—
268C2×M16—31no—
269C2×M16—92no—
270C2×M16—91no—
271C22×C8—31no—
272C22×C8—92no—
273C22×C8—92no—
274C22×C8—92no—
275C22×C8—91no—
276C22×C8—184no—
277#123—32no—
278C22⋊Q8—32no—
279#121—32no—
280#120—32no—
281C4×D4—34no—
282#117D3211yescharacteristic
283C4⋊C8—34no—
284C22⋊C8—94no—
285C22⋊C8—94no—
286#97—92no—
287C4×C8—92no—
288C23×C3—21no—
289C23×C3—32no—
290C23×C3—32no—
291C23×C3—64no—
292C23×C3—62no—
293C23×C3C2×C4×D311yescharacteristic
294C23×C3C22×Dic311yescharacteristic
295C22×D3—22no—
296C22×D3—24no—
297C22×D3C22×Dic312yes—
298C22×D3C22×Dic312yes—
299C3×Q8—62no—
300C3×D4—68no—
301C3×D4—64no—
302C3×D4—62no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—24no—
308C2×C3×C4—32no—
309C2×C3×C4—32no—
310C2×C3×C4—62no—
311C2×C3×C4—64no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4C2×C4×D314yes—
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4D3×D412yes—
319C2×C3×C4D3×D412yes—
320C2×C3×C4#23712yes—
321C2×C3×C4#23912yes—
322C2×C3×C4C22×Dic314yes—
323C2×C3×C4C22×Dic311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326#67—24no—
327C2×Dic3—22no—
328C2×Dic3C22×Dic312yes—
329C2×Dic3C22×Dic312yes—
330D12—28no—
331D12—22no—
332C4×D3—24no—
333C4×D3—22no—
334C4×D3—22no—
335C4×D3—22no—
336C4×D3—22no—
337Dic6—22no—
338C3×C8—62no—
339C3×C8—62no—
340C3⋊C8—22no—
341C3⋊C8—22no—
342C3⋊C8—32no—
343C3⋊C8—32no—
344C3⋊C8—32no—
345C3⋊C8—32no—
346C3⋊C8—62no—
347C3⋊C8—62no—
348C3⋊C8—64no—
349C3⋊C8—62no—
350C3⋊C8—62no—
351C2×C32—22no—
352C2×C32C2×C4×D411yescharacteristic
353C2×C32C2×#13112yes—
354C3×D3—24no—
355C3×D3—42no—
356C24—31no—
357#41—62no—
358#41—62no—
359C2×Q8—31no—
360C2×D4—32no—
361C2×D4—34no—
362C2×D4—31no—
363C22×C4—31no—
364C22×C4—32no—
365C22×C4—32no—
366C22×C4—32no—
367C22×C4—62no—
368C22×C4—62no—
369C22×C4C2×D3211yescharacteristic
370M16—62no—
371M16—184no—
372M16—182no—
373C2×C8—32no—
374C2×C8—32no—
375C2×C8—62no—
376C2×C8—91no—
377C2×C8—91no—
378C2×C8—94no—
379C2×C8—92no—
380C2×C8—184no—
381C2×C8—184no—
382C2×C8—184no—
383C4⋊C4—34no—
384C4⋊C4D3×Dic312yes—
385C22⋊C4—34no—
386C22⋊C4—34no—
387C22⋊C4D3×Dic312yes—
388C42C2×D3212yes—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—21no—
392C22×C3—22no—
393C22×C3—34no—
394C22×C3—42no—
395C22×C3—68no—
396C22×C3—62no—
397C22×C3—62no—
398C22×C3—64no—
399C22×C3—62no—
400C22×C3#89312yes—
401C22×C3D4×Dic312yes—
402C22×C3C22×C4×D311yescharacteristic
403C22×C3C23×Dic311yescharacteristic
404C2×D3—28no—
405C2×D3—22no—
406C2×D3—22no—
407C2×D3—22no—
408C2×D3—24no—
409C2×D3#94814yescomplemented
410C3×C4—24no—
411C3×C4—24no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—22no—
415C3×C4—44no—
416C3×C4—62no—
417C3×C4—62no—
418C3×C4#89312yes—
419C3×C4D4×Dic312yes—
420C3×C4C2×D3×D411yescharacteristic
421C3×C4C2×D3×D411yescharacteristic
422C3×C4C2×#23711yescharacteristic
423C3×C4C2×#23911yescharacteristic
424Dic3—22no—
425Dic3—22no—
426C32#292911yescharacteristic, complemented, Sylow
427C23—32no—
428C23—32no—
429C23—64no—
430C23—62no—
431C23C2×D3×Dic311yescharacteristic
432Q8—62no—
433D4—68no—
434D4—64no—
435D4—62no—
436C2×C4—32no—
437C2×C4—32no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—64no—
444C2×C4#379612yes—
445C2×C4#380212yes—
446C2×C4C2×D3×Dic314yes—
447C2×C4C2×D3×Dic311yescharacteristic
448C2×C4C22×D3211yescharacteristic
449C8—62no—
450C8—62no—
451C8—92no—
452C8—92no—
453C8—182no—
454C2×C3—22no—
455C2×C3—22no—
456C2×C3—21no—
457C2×C3—22no—
458C2×C3—42no—
459C2×C3—64no—
460C2×C3—122no—
461C2×C3C2×#89311yescharacteristic
462C2×C3D3×#13112yes—
463C2×C3C2×D4×Dic311yescharacteristic
464C2×C3C2×#94812yes—
465D3—24no—
466D3—42no—
467C22—22no—
468C22—34no—
469C22—68no—
470C22—62no—
471C22—62no—
472C22—62no—
473C22—64no—
474C22#6389812yes—
475C22C22×D3×Dic311yescharacteristic
476C4—24no—
477C4—62no—
478C4—62no—
479C4#6389812yes—
480C4C2×#379611yescharacteristic
481C4C2×#380211yescharacteristic
482C3—21no—
483C3#7907311yescharacteristic, complemented
484C3#8291611yescharacteristic, complemented
485C2—22no—
486C2—64no—
487C2—122no—
488C2C2×#6389811yescharacteristic
489C2D3×#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×#63815C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. #10592696C2semidirect
5. C3×#4999C2semidirect
6. #10591070C2semidirect
7. #10591069C2semidirect
8. #10590330C2semidirect
9. #10590329C2semidirect
24. C2×#3711C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63630C22semidirect
31. C4×C3⋊(C3⋊C8)C22semidirect
32. C3×C4⋊(C3⋊C8)C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
48. #4999D3semidirect
72. C2×C3⋊(C3⋊C8)D4semidirect
132. C4⋊(C3⋊C8)C2×D3semidirect
258. C2×C3×D3#131semidirect
409. C2×D3#948semidirect
426. C32#2929semidirect
483. C3#79073semidirect
484. 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×#638152
C22×D3×C3⋊C82
#105926962
C3×#49992
#105910702
#105910692
#105903302
#105903292
#829163
#790733