Finite Group Databasebeta

← #11786739

Subgroups — #11786739

Order 1152.

719 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic
2C3×#4995C211yesmaximal, characteristic, complemented
3#10591224C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic
5#10591106C211yesmaximal, characteristic
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70681—31nomaximal
9#68772—31nomaximal
10C2×#3828C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13#64101—21no—
14C4⋊C4×C3⋊D3—21no—
15#64090—22no—
16C4×C4⋊(C3⋊D3)—21no—
17C4×#634—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#808—21no—
23C3×#807—21no—
24#63579—22no—
25#63570C414yescomplemented
26#63567—21no—
27#63564—21no—
28#5523—31no—
29#5523—31no—
30#5523—61no—
31C3×#428—31no—
32C2×#825—31no—
33#5133—31no—
34#4995D311yescharacteristic, complemented
35#4977—31no—
36#4966—31no—
37#4936—31no—
38C2×#805—31no—
39C3×#339—31no—
40#4554—31no—
41#4554—31no—
42#4532D311yescharacteristic, complemented
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45C22×C3⋊Dic3D412yes—
46#3828—21no—
47#3828—21no—
48#3828C2×C412yes—
49#3828Q812yes—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—22no—
53C2×#634D411yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C42—21no—
60#3752—22no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63#3750—22no—
64C4×C3⋊Dic3—22no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C412yescomplemented
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yescomplemented
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#1860—91noSylow
76C2×#235—31no—
77C2×#235—31no—
78C2×#235—61no—
79C2×C3×M16—31no—
80C2×C3×M16—31no—
81C3×#117—21no—
82C3×#117C2×D311yescharacteristic
83C3×#117C2×D311yescharacteristic
84C2×C3×C4⋊C4—31no—
85C2×C3×C42—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—61no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4×Dic3C2×D311yescharacteristic
91C2×#208C2×D311yescharacteristic
92C2×#208C2×D311yescharacteristic
93#892—62no—
94#892—61no—
95#892—61no—
96D3×C4⋊C4—62no—
97D3×C4⋊C4—61no—
98D3×C4⋊C4—61no—
99#67⋊C4—62no—
100#67⋊C4—62no—
101#67⋊C4—64no—
102C4×D12—61no—
103C4×D12—61no—
104C4×D12—62no—
105C4×Dic6—61no—
106C4×Dic6—61no—
107C4×Dic6—62no—
108C3×#107—61no—
109C3×#106—61no—
110C3⋊#95—62no—
111C3⋊#95—62no—
112#825—34no—
113#821—61no—
114#816—61no—
115#810—61no—
116#809—61no—
117#808—21no—
118#807—21no—
119#805—34no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130#638—22no—
131#638—22no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—42no—
135C4⋊(C3⋊D3)—21no—
136C4⋊(C3⋊D3)C4⋊C412yes—
137C4×C3⋊D3—22no—
138C4×C3⋊D3—22no—
139C4×C3⋊D3—82no—
140#634—21no—
141#634C4⋊C412yes—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149#520—91no—
150#428—31no—
151C2×#104—91no—
152#417—91no—
153#382—91no—
154#343—91no—
155#339—31no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—62no—
162C2×#67—61no—
163C2×#67—61no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—62no—
169#235—32no—
170#235—32no—
171#235—32no—
172#235—32no—
173#235—62no—
174#235—62no—
175#235—62no—
176#235—62no—
177#235—61no—
178#235—61no—
179#235—61no—
180#235—61no—
181C2×D12—31no—
182C2×D12—31no—
183C2×D12—61no—
184C2×C4×D3—62no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×C4×D3—64no—
188C2×C4×D3—62no—
189C2×C4×D3—62no—
190C2×Dic6—31no—
191C2×Dic6—31no—
192C2×Dic6—61no—
193C3×M16—32no—
194C3×M16—61no—
195C3×M16—61no—
196C3×M16—61no—
197C2×C3×C8—61no—
198C2×C3×C8—61no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4D1211yescharacteristic
204C3×C4⋊C4D1211yescharacteristic
205C3×C4⋊C4#6711yescharacteristic
206C3×C4⋊C4#6711yescharacteristic
207C3×C22⋊C4—22no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C42—22no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—32no—
214C3×C42—61no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—62no—
217(C2×D3)⋊C4—62no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226Dic3⋊C4—64no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229C4×Dic3—21no—
230C4×Dic3—64no—
231C4×Dic3—62no—
232C4×Dic3—62no—
233C4×Dic3C4×D312yescomplemented
234#208—21no—
235#208—21no—
236#208—21no—
237#208C4×D312yescomplemented
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C22×C32—21no—
241C22×C32—21no—
242C22×C32C4×D411yescharacteristic
243C22×C32#12011yescharacteristic
244C22×C32C22⋊Q811yescharacteristic
245C2×C3⋊D3—22no—
246C2×C3⋊D3—41no—
247C2×C3⋊D3—41no—
248C32×C4—41no—
249C32×C4—41no—
250C32×C4C2×C4⋊C411yescharacteristic
251C32×C4C4×D411yescharacteristic
252C32×C4C22⋊Q811yescharacteristic
253C32×C4#12311yescharacteristic
254C3⋊Dic3—22no—
255C3⋊Dic3—42no—
256C3×Dic3—42no—
257C3×Dic3—81no—
258C2×#41—91no—
259C2×M16—31no—
260C2×M16—31no—
261C4×Q8—181no—
262C4×D4—181no—
263C4×D4—182no—
264#117—181no—
265#117D3211yescharacteristic
266C2×C4⋊C4—31no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—181no—
269C2×C42—31no—
270#107—61no—
271#106—61no—
272#104—94no—
273#103—181no—
274#102—181no—
275#95—182no—
276C23×C3—21no—
277C23×C3D3×D411yescharacteristic
278C23×C3D3×D411yescharacteristic
279C22×D3—62no—
280C22×D3—61no—
281C22×D3—61no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—62no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—122no—
298C2×C3×C4—121no—
299C2×C3×C4C2×C4×D311yescharacteristic
300C2×C3×C4C2×C4×D311yescharacteristic
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4#23511yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4#23711yescharacteristic
307C2×C3×C4D3×Q811yescharacteristic
308C2×C3×C4D3×Q811yescharacteristic
309C2×C3×C4#23911yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311#67—64no—
312#67—64no—
313#67—62no—
314#67—62no—
315#67—62no—
316#67—62no—
317C2×Dic3—22no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—42no—
321C2×Dic3—41no—
322C2×Dic3—62no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—64no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—122no—
329C2×Dic3—122no—
330C2×Dic3—242no—
331D12—32no—
332D12—32no—
333D12—62no—
334D12—62no—
335D12—61no—
336D12—61no—
337C4×D3—64no—
338C4×D3—64no—
339C4×D3—62no—
340C4×D3—62no—
341C4×D3—62no—
342C4×D3—62no—
343C4×D3—244no—
344C4×D3—242no—
345C4×D3—242no—
346Dic6—32no—
347Dic6—32no—
348Dic6—62no—
349Dic6—62no—
350Dic6—61no—
351Dic6—61no—
352C3×C8—62no—
353C3×C8—121no—
354C3⋊C8—22no—
355C3⋊C8—41no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32#38511yescharacteristic
359C2×C32#45411yescharacteristic
360C2×C32#45511yescharacteristic
361C3⋊D3—42no—
362#41—92no—
363#41—92no—
364#41—181no—
365#41—181no—
366C2×Q8—91no—
367C2×D4—91no—
368C2×D4—181no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—92no—
372C22×C4—182no—
373C22×C4—181no—
374C22×C4C2×D3211yescharacteristic
375M16—32no—
376M16—61no—
377M16—61no—
378M16—61no—
379C2×C8—61no—
380C2×C8—61no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4—182no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4#62611yescharacteristic
387C4⋊C4#62611yescharacteristic
388C22⋊C4—21no—
389C22⋊C4—182no—
390C42—21no—
391C42—32no—
392C42—61no—
393C42—182no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3#67⋊C411yescharacteristic
404C22×C3#88211yescharacteristic
405C22×C3#89311yescharacteristic
406C22×C3#89611yescharacteristic
407C22×C3#89611yescharacteristic
408C22×C3#93711yescharacteristic
409C2×D3—64no—
410C2×D3—62no—
411C2×D3—62no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—121no—
415C2×D3—121no—
416C2×D3—121no—
417C2×D3—121no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—42no—
423C3×C4—42no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—122no—
429C3×C4—241no—
430C3×C4C4×D1211yescharacteristic
431C3×C4#88311yescharacteristic
432C3×C4D3×C4⋊C411yescharacteristic
433C3×C4D3×C4⋊C411yescharacteristic
434C3×C4#89411yescharacteristic
435C3×C4#89711yescharacteristic
436C3×C4C4×#6711yescharacteristic
437C3×C4#94611yescharacteristic
438Dic3—42no—
439Dic3—64no—
440Dic3—62no—
441Dic3—62no—
442Dic3—81no—
443Dic3—124no—
444Dic3—122no—
445Dic3—122no—
446C32#186011yescharacteristic, complemented, Sylow
447C23—181no—
448C23#381111yescharacteristic
449Q8—92no—
450Q8—181no—
451D4—92no—
452D4—182no—
453D4—182no—
454D4—181no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—62no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—122no—
461C2×C4—121no—
462C2×C4—181no—
463C2×C4—182no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4—362no—
467C2×C4—722no—
468C2×C4#379611yescharacteristic
469C2×C4#379711yescharacteristic
470C2×C4#379811yescharacteristic
471C2×C4C4×D3211yescharacteristic
472C2×C4C2×#62611yescharacteristic
473C2×C4#381111yescharacteristic
474C8—62no—
475C8—121no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3#466811yescharacteristic
486C2×C3#482511yescharacteristic
487C2×C3#482711yescharacteristic
488C2×C3#498911yescharacteristic
489C2×C3#520111yescharacteristic
490C2×C3#520211yescharacteristic
491D3—124no—
492D3—122no—
493D3—122no—
494C22—21no—
495C22—21no—
496C22—182no—
497C22—361no—
498C22—361no—
499C22#6386511yescharacteristic
500C22#6388111yescharacteristic
501C22#6398111yescharacteristic
502C4—41no—
503C4—41no—
504C4—122no—
505C4—182no—
506C4—241no—
507C4—362no—
508C4#6385311yescharacteristic
509C4#6387111yescharacteristic
510C4#6388311yescharacteristic
511C4C4×#62611yescharacteristic
512C3—21no—
513C3#6877211yescharacteristic, complemented
514C3#7068111yescharacteristic, complemented
515C2—21no—
516C2—21no—
517C2—362no—
518C2#1059129011yescharacteristic
519C2#1059168611yescharacteristic
520C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×#3828C22
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. C3×#4995C2semidirect
3. #10591224C2semidirect
6. C3×#4532C2semidirect
7. #10589168C2semidirect
25. #63570C4semidirect
34. #4995D3semidirect
42. #4532D3semidirect
68. C3×C4×Dic3C2×C4semidirect
72. C3×#208C2×C4semidirect
233. C4×Dic3C4×D3semidirect
237. #208C4×D3semidirect
446. C32#1860semidirect
513. C3#68772semidirect
514. C3#70681semidirect

Maximal subgroups

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

subgroupindex
#105959942
C3×#49952
#105912242
C2×#635702
#105911062
C3×#45322
#105891682
#706813
#687723