Finite Group Databasebeta

← #11859356

Subgroups — #11859356

Order 1152.

1119 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5828C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4#10592933C211yesmaximal, characteristic, complemented
5#10591147C214yesmaximal, complemented
6C3⋊C8×#67C214yesmaximal, complemented
7#10591117C211yesmaximal, characteristic, complemented
8#10591069C211yesmaximal, characteristic, complemented
9#10591055C211yesmaximal, characteristic, complemented
10#83794—31nomaximal
11#82916—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#948—24no—
17C3×#946C412yes—
18C3×#938C412yes—
19C3×#937C412yes—
20C3×#935C412yes—
21C3×C4×#67C2214yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2212yescomplemented
25C22×C3×C3⋊C8C2211yescharacteristic
26C22×C3×C3⋊C8C2212yescomplemented
27C2×D3×C3⋊C8—24no—
28C2×D3×C3⋊C8C2212yes—
29C2×D3×C3⋊C8C2212yes—
30#63657C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32(C2×D3)⋊(C3⋊C8)C2214yes—
33#63554C2212yescomplemented
34Dic3×C3⋊C8C2212yescomplemented
35C2×C3×#131—31no—
36C3×#525—31no—
37#5828D311yescharacteristic
38C2×#948D311yescharacteristic, complemented
39C23×C3⋊C8—31no—
40C22×D3×C8—31no—
41#5234—31no—
42#5234—31no—
43#5234—61no—
44#5207—31no—
45#5127—34no—
46#5126—31no—
47#5119—31no—
48C8×#67—34no—
49#5101—31no—
50#5011—34no—
51D4×C3⋊C8—34no—
52#4999—31no—
53#4997—31no—
54C23×C3×D3C2×C411yescharacteristic
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8C2×C411yescharacteristic
58C2×C32×D4C2×C412yes—
59C2×C32×D4C2×C411yescharacteristic
60C22×C32×C4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×C3×#67C2×C414yes—
63C22×C3×Dic3C2×C411yescharacteristic
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3C2×C412yes—
67C2×C3×C4×D3C2312yes—
68#3748—22no—
69C2×C3⋊(C3⋊C8)—22no—
70C2×C3⋊(C3⋊C8)C2312yes—
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×#217C2×C412yes—
73C3×#217C2×C414yes—
74C3×(C2×D3)⋊C4C2×C414yes—
75C3×C4⋊Dic3C2×C412yes—
76C3×Dic3⋊C4C2×C414yes—
77C3×C4×Dic3C2312yes—
78C3×#208—22no—
79C3×#208—24no—
80C2×C3×C3⋊C8—24no—
81C2×C3×C3⋊C8D414yescomplemented
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85D3×C3⋊C8—24no—
86D3×C3⋊C8—24no—
87#2929—91noSylow
88C2×C3×#41—21no—
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×#41C2×D311yescharacteristic
91C23×C3×C4—31no—
92C22×C4×D3C2×D311yescharacteristic
93C3×#131—64no—
94C2×C3×M16—31no—
95C2×C3×M16—32no—
96C22×C3×C8—31no—
97C22×C3×C8—32no—
98C3×#123—32no—
99C3×C22⋊Q8—32no—
100C3×#121—32no—
101C3×#120—32no—
102C3×C4×D4—34no—
103C3×#117—31no—
104#948—24no—
105#946Dic312yes—
106#938Dic312yes—
107#937Dic312yes—
108#935Dic312yes—
109C4×#67C2×D314yes—
110#926C2×D311yescharacteristic
111C2×#208—31no—
112C2×#208—31no—
113C2×#208—61no—
114C2×#208C2×D311yescharacteristic
115C2×#208C2×D312yescomplemented
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—32no—
119C22×C3⋊C8—32no—
120C22×C3⋊C8—61no—
121C22×C3⋊C8—64no—
122C22×C3⋊C8C2×D311yescharacteristic
123C22×C3⋊C8C2×D312yescomplemented
124C2×D3×C8—32no—
125C2×D3×C8—32no—
126C2×D3×C8—64no—
127#830—34no—
128#830—34no—
129#830—34no—
130#830—64no—
131(C2×D3)⋊C8—34no—
132#815—32no—
133Dic3⋊C8—34no—
134C8×Dic3—32no—
135C4⋊(C3⋊C8)—34no—
136#803—32no—
137C4×C3⋊C8—32no—
138C23×C32C22×C412yes—
139C23×C32C22×C411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3C22×C412yes—
143C32×Q8—22no—
144C32×D4—24no—
145C32×D4—22no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4C22×C412yes—
149C2×C32×C4C22×C411yescharacteristic
150C2×C32×C4C2×D412yes—
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153C3×#67—28no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3C22×C414yes—
156C2×C3×Dic3C22×C412yes—
157C3×C4×D3—24no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3⋊(C3⋊C8)—22no—
161C3⋊(C3⋊C8)—22no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8C2×D412yes—
164C3×C3⋊C8C2×D412yes—
165C2×#131—31no—
166C23×C8—91no—
167#525—31no—
168#435—94no—
169C8×D4—94no—
170#424—91no—
171#408—91no—
172#407—91no—
173#405—91no—
174C24×C3—31no—
175C23×D3C2×Dic311yescharacteristic
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—22no—
179C3×#41—22no—
180C3×#41—42no—
181C3×#41—42no—
182C2×C3×Q8—21no—
183C2×C3×Q8C4×D311yescharacteristic
184C2×C3×Q8C2×Dic311yescharacteristic
185C2×C3×D4—22no—
186C2×C3×D4—21no—
187C2×C3×D4—34no—
188C2×C3×D4C4×D312yes—
189C2×C3×D4C4×D311yescharacteristic
190C2×C3×D4C2×Dic312yes—
191C2×C3×D4C2×Dic311yescharacteristic
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—31no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—62no—
198C22×C3×C4—62no—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67C2×Dic314yes—
204C22×Dic3C2×Dic311yescharacteristic
205C2×C4×D3—22no—
206C2×C4×D3—22no—
207C2×C4×D3C2×Dic312yes—
208C2×C4×D3C22×D312yes—
209C3×M16—64no—
210C3×M16—62no—
211C2×C3×C8—34no—
212C2×C3×C8—31no—
213C2×C3×C8—31no—
214C2×C3×C8—32no—
215C2×C3×C8—64no—
216C3×C4⋊C4—34no—
217C3×C4⋊C4—32no—
218C3×C22⋊C4—32no—
219C3×C22⋊C4—34no—
220C3×C22⋊C4—34no—
221C3×C42—32no—
222#217C2×Dic312yes—
223#217C2×Dic314yes—
224(C2×D3)⋊C4C2×Dic314yes—
225C4⋊Dic3C2×Dic312yes—
226Dic3⋊C4C2×Dic314yes—
227C4×Dic3C22×D312yes—
228#208—22no—
229#208—24no—
230#208—62no—
231#208—62no—
232#208—122no—
233C2×C3⋊C8—24no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—32no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8—62no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—64no—
243C2×C3⋊C8—64no—
244C2×C3⋊C8—122no—
245C2×C3⋊C8#6714yescomplemented
246C2×C3⋊C8C22×D312yes—
247C2×C3⋊C8C22×D311yescharacteristic
248C2×C3⋊C8C22×D311yescharacteristic
249D3×C8—64no—
250D3×C8—64no—
251C22×C32—22no—
252C22×C32—22no—
253C22×C32—24no—
254C22×C32C4×D412yes—
255C22×C32C23×C411yescharacteristic
256C2×C3×D3—28no—
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3#13114yescomplemented
260C32×C4—22no—
261C32×C4C4×D412yes—
262C32×C4C22×D411yescharacteristic
263C32×C4C2×#4111yescharacteristic
264C3×Dic3—22no—
265C3×Dic3—24no—
266C2×#41D3211yescharacteristic
267C23×C4—31no—
268#131—64no—
269C2×M16—31no—
270C2×M16—32no—
271C2×M16—91no—
272C22×C8—31no—
273C22×C8—32no—
274C22×C8—92no—
275C22×C8—92no—
276C22×C8—91no—
277C22×C8—184no—
278#123—32no—
279C22⋊Q8—32no—
280#121—32no—
281#120—32no—
282C4×D4—34no—
283#117—31no—
284C4⋊C8—94no—
285C22⋊C8—94no—
286C22⋊C8—94no—
287#97—92no—
288C4×C8—92no—
289C23×C3—21no—
290C23×C3—22no—
291C23×C3—32no—
292C23×C3—64no—
293C23×C3—62no—
294C23×C3C2×C4×D312yes—
295C23×C3C2×C4×D311yescharacteristic
296C23×C3C22×Dic312yes—
297C23×C3C22×Dic311yescharacteristic
298C22×D3—22no—
299C22×D3—24no—
300C22×D3C22×Dic312yes—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—42no—
304C3×D4—24no—
305C3×D4—24no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—42no—
309C3×D4—44no—
310C3×D4—68no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—34no—
321C2×C3×C4—32no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—62no—
325C2×C3×C4—64no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4C2×C4×D312yes—
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4#23512yes—
331C2×C3×C4D3×D412yes—
332C2×C3×C4#23712yes—
333C2×C3×C4C22×Dic312yes—
334C2×C3×C4C22×Dic311yescharacteristic
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338#67—28no—
339C2×Dic3—22no—
340C2×Dic3C22×Dic314yes—
341C2×Dic3C22×Dic312yes—
342C4×D3—24no—
343C4×D3—22no—
344C4×D3—22no—
345C3×C8—32no—
346C3×C8—32no—
347C3×C8—62no—
348C3⋊C8—22no—
349C3⋊C8—62no—
350C3⋊C8—62no—
351C3⋊C8—62no—
352C3⋊C8—62no—
353C3⋊C8—122no—
354C3⋊C8—122no—
355C3⋊C8C2×#6712yes—
356C3⋊C8C2×#6712yes—
357C2×C32—22no—
358C2×C32—42no—
359C2×C32C2×C4×D411yescharacteristic
360C2×C32C2×#13112yes—
361C3×D3—24no—
362C24—31no—
363#41—22no—
364#41—22no—
365C2×Q8D3×Dic311yescharacteristic
366C2×D4—34no—
367C2×D4D3×Dic312yes—
368C2×D4D3×Dic311yescharacteristic
369C22×C4—31no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—62no—
373C22×C4—62no—
374C22×C4C2×D3212yes—
375C22×C4C2×D3211yescharacteristic
376M16—64no—
377M16—62no—
378M16—182no—
379C2×C8—31no—
380C2×C8—31no—
381C2×C8—34no—
382C2×C8—32no—
383C2×C8—64no—
384C2×C8—92no—
385C2×C8—92no—
386C2×C8—184no—
387C2×C8—184no—
388C2×C8—182no—
389C4⋊C4—32no—
390C4⋊C4—34no—
391C22⋊C4—32no—
392C22⋊C4—34no—
393C22⋊C4—34no—
394C42—32no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—24no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—24no—
401C22×C3—21no—
402C22×C3—22no—
403C22×C3—34no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—44no—
407C22×C3—68no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3C4×#6712yes—
411C22×C3D4×Dic312yes—
412C22×C3C22×C4×D311yescharacteristic
413C22×C3C23×Dic311yescharacteristic
414C2×D3—28no—
415C2×D3—22no—
416C2×D3—22no—
417C2×D3#94814yescomplemented
418C3×C4—22no—
419C3×C4—22no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—22no—
423C3×C4—42no—
424C3×C4—64no—
425C3×C4—62no—
426C3×C4C4×#6712yes—
427C3×C4D4×Dic312yes—
428C3×C4C2×#23511yescharacteristic
429C3×C4C2×D3×D411yescharacteristic
430C3×C4C2×#23711yescharacteristic
431C3×C4C22×#6711yescharacteristic
432Dic3—22no—
433Dic3—24no—
434C32#292911yescharacteristic, complemented, Sylow
435C23—32no—
436C23—64no—
437C23—62no—
438C23C2×D3×Dic312yes—
439C23C2×D3×Dic311yescharacteristic
440Q8—22no—
441D4—24no—
442D4—22no—
443D4—68no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—34no—
447C2×C4—32no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—64no—
452C2×C4C2×D3×Dic312yes—
453C2×C4C2×D3×Dic311yescharacteristic
454C2×C4#380412yes—
455C2×C4D3×#6712yes—
456C2×C4C22×D3211yescharacteristic
457C8—32no—
458C8—32no—
459C8—62no—
460C8—182no—
461C8—182no—
462C2×C3—22no—
463C2×C3—22no—
464C2×C3—22no—
465C2×C3—21no—
466C2×C3—42no—
467C2×C3—42no—
468C2×C3—42no—
469C2×C3—64no—
470C2×C3—82no—
471C2×C3D3×#13112yes—
472C2×C3C2×C4×#6711yescharacteristic
473C2×C3C2×D4×Dic311yescharacteristic
474C2×C3C2×#94812yes—
475D3—24no—
476C22—22no—
477C22—24no—
478C22—22no—
479C22—34no—
480C22—68no—
481C22—62no—
482C22—62no—
483C22Dic3×#6712yes—
484C22C22×D3×Dic311yescharacteristic
485C4—22no—
486C4—64no—
487C4—62no—
488C4Dic3×#6712yes—
489C4C2×#380411yescharacteristic
490C4C2×D3×#6711yescharacteristic
491C3—21no—
492C3#8291611yescharacteristic, complemented
493C3#8379411yescharacteristic, complemented
494C2—22no—
495C2—42no—
496C2—64no—
497C2D3×#94812yes—
498C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×#41C22
prime radicalC3×#5828C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#948C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. #10592933C2semidirect
5. #10591147C2semidirect
6. C3⋊C8×#67C2semidirect
7. #10591117C2semidirect
8. #10591069C2semidirect
9. #10591055C2semidirect
24. C2×C3×#208C22semidirect
26. C22×C3×C3⋊C8C22semidirect
30. #63657C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
33. #63554C22semidirect
34. Dic3×C3⋊C8C22semidirect
38. C2×#948D3semidirect
81. C2×C3×C3⋊C8D4semidirect
115. C2×#208C2×D3semidirect
123. C22×C3⋊C8C2×D3semidirect
245. C2×C3⋊C8#67semidirect
259. C2×C3×D3#131semidirect
417. C2×D3#948semidirect
434. C32#2929semidirect
492. C3#82916semidirect
493. C3#83794semidirect

Maximal subgroups

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

subgroupindex
C3×#58282
C2×C3×#9482
C22×D3×C3⋊C82
#105929332
#105911472
C3⋊C8×#672
#105911172
#105910692
#105910552
#837943
#829163