Finite Group Databasebeta

← #11786738

Subgroups — #11786738

Order 1152.

631 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic
2#10592694C211yesmaximal, characteristic, complemented
3#10591224C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic
5#10591088C211yesmaximal, characteristic
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#71665—31nomaximal
9#68772—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#892—21no—
18C3×D3×C4⋊C4—21no—
19C3×#67⋊C4—22no—
20C3×C4×D12—21no—
21C3×C4×Dic6—21no—
22#63635—21no—
23#63634—21no—
24#63579—22no—
25#63569C414yescomplemented
26#63566—21no—
27#63563—21no—
28C3×#520—31no—
29#5523D311yescharacteristic
30C2×#837—31no—
31#5232—31no—
32#5133—31no—
33#4995—31no—
34#4995—31no—
35#4995—61no—
36#4977—31no—
37#4936—31no—
38C2×#805—31no—
39C3×#339—31no—
40#4554—31no—
41#4532D311yescharacteristic, complemented
42#4530—31no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D412yes—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235C2×C412yes—
51C3×#235Q812yes—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—22no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C42—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62#3748—21no—
63#3748C2×C412yescomplemented
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—22no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×Dic3⋊C4—22no—
69C3×C4×Dic3—22no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3C2×C412yescomplemented
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8—21no—
75#1860—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C2×C3×M16—31no—
79C3×C4×Q8—61no—
80C3×C4×D4—61no—
81C3×C4×D4—62no—
82C3×#117—21no—
83C3×#117—61no—
84C3×#117C2×D311yescharacteristic
85C3×#117C2×D311yescharacteristic
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—61no—
88C2×C3×C42—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×C4×Dic3C2×D311yescharacteristic
94C2×#208—31no—
95C2×#208—31no—
96C2×#208—61no—
97C2×#208C2×D311yescharacteristic
98#892—21no—
99D3×C4⋊C4—21no—
100#67⋊C4—22no—
101C4×D12—21no—
102C4×Dic6—21no—
103#837—34no—
104#835—61no—
105#832—61no—
106C3⋊#95—62no—
107C3⋊#95—62no—
108#821—61no—
109#816—61no—
110#808—62no—
111#808—61no—
112#808—61no—
113#807—62no—
114#807—61no—
115#807—61no—
116#805—34no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q811yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—42no—
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—42no—
137C3×D12—21no—
138C3×D12C4⋊C412yes—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×C4×D3—82no—
142C3×Dic6—21no—
143C3×Dic6C4⋊C412yes—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—41no—
146#520—31no—
147#428—91no—
148C2×#104—91no—
149#417—91no—
150#382—91no—
151#343—91no—
152#339—31no—
153C3×#41—32no—
154C3×#41—32no—
155C3×#41—61no—
156C3×#41—61no—
157C2×C3×Q8—31no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—32no—
162C22×C3×C4—62no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—21no—
168C22×Dic3—21no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—121no—
172C22×Dic3#6712yes—
173#235—21no—
174#235—21no—
175#235Dic612yes—
176#235C4×D312yes—
177C2×D12#6711yescharacteristic
178C2×C4×D3—21no—
179C2×C4×D3—22no—
180C2×Dic6#6711yescharacteristic
181C3×M16—61no—
182C3×M16—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—62no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4D1211yescharacteristic
190C3×C4⋊C4D1211yescharacteristic
191C3×C4⋊C4#6711yescharacteristic
192C3×C4⋊C4#6711yescharacteristic
193C3×C22⋊C4—21no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—41no—
196C3×C22⋊C4—62no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42—32no—
200C3×C42—41no—
201C3×C42—62no—
202C3×C42—61no—
203(C2×D3)⋊C4—22no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—62no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—121no—
212Dic3⋊C4—22no—
213C4×Dic3—22no—
214C4×Dic3—21no—
215C4×Dic3C4×D312yescomplemented
216#208—21no—
217#208—21no—
218#208—32no—
219#208—32no—
220#208—62no—
221#208—62no—
222#208—61no—
223#208—61no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32C4×D411yescharacteristic
231C22×C32#12011yescharacteristic
232C22×C32C22⋊Q811yescharacteristic
233C2×C3×D3—22no—
234C2×C3×D3—41no—
235C2×C3×D3—41no—
236C32×C4—41no—
237C32×C4—41no—
238C32×C4C2×C4⋊C411yescharacteristic
239C32×C4C4×D411yescharacteristic
240C32×C4C22⋊Q811yescharacteristic
241C32×C4#12311yescharacteristic
242C3⋊Dic3—81no—
243C3×Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C2×#41—31no—
247C2×M16—31no—
248C2×M16—91no—
249C4×Q8—61no—
250C4×D4—61no—
251C4×D4—62no—
252#117—61no—
253#117D3211yescharacteristic
254C2×C4⋊C4—31no—
255C2×C4⋊C4—61no—
256C2×C4⋊C4—91no—
257C2×C42—31no—
258#107—181no—
259#106—181no—
260#104—94no—
261#103—181no—
262#102—181no—
263#95—182no—
264C23×C3—21no—
265C23×C3—61no—
266C23×C3D3×D411yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C22×D3—21no—
269C3×Q8—32no—
270C3×Q8—61no—
271C3×D4—32no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—61no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—61no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4—122no—
295C2×C3×C4—242no—
296C2×C3×C4C2×Dic611yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4C2×D1211yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4#23511yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4D3×Q811yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308#67—22no—
309#67—22no—
310C2×Dic3—21no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—42no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—242no—
322D12—21no—
323D12Dic3⋊C412yes—
324C4×D3—22no—
325C4×D3—22no—
326C4×D3—82no—
327Dic6—21no—
328Dic6Dic3⋊C412yes—
329C3×C8—121no—
330C3⋊C8—41no—
331C3⋊C8—64no—
332C3⋊C8—62no—
333C3⋊C8—62no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38511yescharacteristic
337C2×C32#45411yescharacteristic
338C2×C32#45511yescharacteristic
339C3×D3—42no—
340#41—32no—
341#41—32no—
342#41—61no—
343#41—61no—
344C2×Q8—31no—
345C2×D4—31no—
346C2×D4—61no—
347C22×C4—32no—
348C22×C4—62no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4—181no—
352C22×C4C2×D3211yescharacteristic
353M16—61no—
354M16—61no—
355M16—92no—
356M16—181no—
357C2×C8—61no—
358C2×C8—181no—
359C4⋊C4—62no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—181no—
363C4⋊C4—181no—
364C4⋊C4#62611yescharacteristic
365C4⋊C4#62611yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—62no—
368C42—21no—
369C42—32no—
370C42—62no—
371C42—61no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—62no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3#67⋊C411yescharacteristic
385C22×C3#88211yescharacteristic
386C22×C3#89611yescharacteristic
387C22×C3#92411yescharacteristic
388C22×C3C4×#6711yescharacteristic
389C22×C3#95311yescharacteristic
390C2×D3—22no—
391C2×D3—41no—
392C2×D3—41no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4—62no—
402C3×C4—81no—
403C3×C4—81no—
404C3×C4—122no—
405C3×C4—122no—
406C3×C4C4×D1211yescharacteristic
407C3×C4#88311yescharacteristic
408C3×C4D3×C4⋊C411yescharacteristic
409C3×C4#89711yescharacteristic
410C3×C4C2×Dic3⋊C411yescharacteristic
411C3×C4#92411yescharacteristic
412C3×C4C4×#6711yescharacteristic
413C3×C4#92911yescharacteristic
414Dic3—22no—
415Dic3—42no—
416Dic3—42no—
417Dic3—242no—
418Dic3—241no—
419Dic3—241no—
420C32#186011yescharacteristic, complemented, Sylow
421C23—61no—
422C23D3×#6711yescharacteristic
423Q8—32no—
424Q8—61no—
425D4—32no—
426D4—62no—
427D4—62no—
428D4—61no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—61no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—121no—
437C2×C4—121no—
438C2×C4—122no—
439C2×C4—242no—
440C2×C4—362no—
441C2×C4—361no—
442C2×C4D3×Dic611yescharacteristic
443C2×C4#379511yescharacteristic
444C2×C4#379811yescharacteristic
445C2×C4C4×D3211yescharacteristic
446C2×C4C2×#62611yescharacteristic
447C2×C4D3×#6711yescharacteristic
448C8—121no—
449C8—182no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—41no—
458C2×C3—41no—
459C2×C3—122no—
460C2×C3#466811yescharacteristic
461C2×C3#482511yescharacteristic
462C2×C3#482711yescharacteristic
463C2×C3#521011yescharacteristic
464C2×C3#524211yescharacteristic
465C2×C3#524511yescharacteristic
466D3—42no—
467C22—21no—
468C22—21no—
469C22—62no—
470C22—121no—
471C22—121no—
472C22#6385111yescharacteristic
473C22#6387911yescharacteristic
474C22#6397711yescharacteristic
475C4—41no—
476C4—41no—
477C4—62no—
478C4—122no—
479C4—122no—
480C4—721no—
481C4#6385711yescharacteristic
482C4D3×Dic3⋊C411yescharacteristic
483C4C4×#62611yescharacteristic
484C4#6390511yescharacteristic
485C3—21no—
486C3#6877211yescharacteristic, complemented
487C3#7166511yescharacteristic, complemented
488C2—21no—
489C2—21no—
490C2—122no—
491C2#1059127811yescharacteristic
492C2#1059168511yescharacteristic
493C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1860
LCSG ▷ C2×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. #10592694C2semidirect
3. #10591224C2semidirect
6. C3×#4532C2semidirect
7. #10589167C2semidirect
25. #63569C4semidirect
41. #4532D3semidirect
63. #3748C2×C4semidirect
71. C3×C4×Dic3C2×C4semidirect
215. C4×Dic3C4×D3semidirect
420. C32#1860semidirect
486. C3#68772semidirect
487. C3#71665semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
#105926942
#105912242
C2×#635692
#105910882
C3×#45322
#105891672
#716653
#687723