Finite Group Databasebeta

← #11786584

Subgroups — #11786584

Order 1152.

817 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic
2C3×#4995C211yesmaximal, characteristic, complemented
3#10591320C211yesmaximal, characteristic
4#10591130C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70674—31nomaximal
9#68758—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13#64102—21no—
14#64102—21no—
15C22⋊C4×C3⋊D3—22no—
16C4×C4⋊(C3⋊D3)—21no—
17C4×C4⋊(C3⋊D3)—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×#3722—22no—
23C3×#808—21no—
24C3×#807—21no—
25#63575—21no—
26#63573—21no—
27#63559C414yescomplemented
28#5521—31no—
29#5521—31no—
30#5521—61no—
31C3×#428—31no—
32C2×#823—31no—
33C2×#823—31no—
34#5121—31no—
35#4995D311yescharacteristic, complemented
36#4988—31no—
37#4964—31no—
38#4939—31no—
39C3×#339—31no—
40#4555—31no—
41#4532D311yescharacteristic, complemented
42#4523—31no—
43C23×C3⋊D3D412yes—
44C22×C32×C4C2311yescharacteristic
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C2×C4⋊(C3⋊D3)Q812yes—
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—22no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C32×C42—21no—
59#3757—21no—
60#3752—22no—
61#3752—22no—
62C4⋊(C3⋊Dic3)D411yescharacteristic
63C4⋊(C3⋊Dic3)D411yescharacteristic
64C4×C3⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208C2×C412yescomplemented
72C3×#208C2×C412yescomplemented
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#3722—44no—
76#1856—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C2×C3×M16—31no—
81C2×C3×M16—31no—
82C3×#117—21no—
83C3×#117C2×D311yescharacteristic
84C3×#117C2×D311yescharacteristic
85C2×C3×C4⋊C4—31no—
86C2×C3×C42—31no—
87C2×(C2×D3)⋊C4—62no—
88C2×(C2×D3)⋊C4—62no—
89#926—31no—
90#926—31no—
91#926—61no—
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×C4×Dic3C2×D311yescharacteristic
94C2×#208C2×D311yescharacteristic
95C2×#208C2×D311yescharacteristic
96#893—62no—
97#893—62no—
98#893—61no—
99#893—61no—
100#893—61no—
101#893—61no—
102D3×C22⋊C4—62no—
103D3×C22⋊C4—62no—
104D3×C22⋊C4—64no—
105C4×D12—61no—
106C4×D12—61no—
107C4×D12—61no—
108C4×D12—61no—
109C4×D12—62no—
110C4×D12—62no—
111C3×#107—61no—
112C3×#106—61no—
113#823—34no—
114#823—34no—
115#818—61no—
116#817—61no—
117#808—21no—
118#808—61no—
119#807—21no—
120#807—61no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—22no—
123C22×C3⋊D3—22no—
124C22×C3⋊D3—42no—
125C22×C3⋊D3—42no—
126C22×C3⋊D3C4⋊C414yes—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×Q811yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C4⋊(C3⋊D3)—22no—
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—22no—
141C4×C3⋊D3—82no—
142C4×C3⋊D3—82no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3—41no—
148C3×C3⋊C8—22no—
149C3×C3⋊C8—22no—
150#518—91no—
151#428—31no—
152#428—91no—
153C2×#100—91no—
154#390—91no—
155#339—31no—
156#339—91no—
157C23×D3—32no—
158C23×D3—32no—
159C23×D3—62no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C22×Dic3—21no—
166C22×Dic3—21no—
167C2×D12—32no—
168C2×D12—32no—
169C2×D12—32no—
170C2×D12—32no—
171C2×D12—62no—
172C2×D12—62no—
173C2×D12—62no—
174C2×D12—62no—
175C2×D12—62no—
176C2×D12—62no—
177C2×D12—61no—
178C2×D12—61no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×C4×D3—64no—
186C2×C4×D3—64no—
187C2×C4×D3—62no—
188C2×C4×D3—62no—
189C2×C4×D3—62no—
190C2×C4×D3—62no—
191C3×M16—32no—
192C3×M16—32no—
193C3×M16—61no—
194C3×M16—61no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4D1211yescharacteristic
202C3×C4⋊C4D1211yescharacteristic
203C3×C4⋊C4#6711yescharacteristic
204C3×C4⋊C4#6711yescharacteristic
205C3×C22⋊C4—22no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C42—22no—
209C3×C42—21no—
210C3×C42—21no—
211C3×C42—61no—
212C3×C42—61no—
213#217—62no—
214#217—61no—
215#217—61no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—62no—
219(C2×D3)⋊C4—62no—
220(C2×D3)⋊C4—62no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—124no—
223(C2×D3)⋊C4—124no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226C4⋊Dic3—31no—
227C4⋊Dic3—31no—
228C4⋊Dic3—31no—
229C4⋊Dic3—31no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4×Dic3—21no—
233C4×Dic3—21no—
234C4×Dic3—62no—
235C4×Dic3—61no—
236C4×Dic3—61no—
237#208—21no—
238#208—21no—
239#208C4×D312yescomplemented
240#208C4×D312yescomplemented
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32C2×C4⋊C411yescharacteristic
246C22×C32#12011yescharacteristic
247C22×C32#12311yescharacteristic
248C2×C3⋊D3—24no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—42no—
251C2×C3⋊D3—44no—
252C2×C3⋊D3—82no—
253C32×C4—41no—
254C32×C4—41no—
255C32×C4C4×D411yescharacteristic
256C32×C4C4×D411yescharacteristic
257C32×C4C22⋊Q811yescharacteristic
258C32×C4C22⋊Q811yescharacteristic
259C3⋊Dic3—41no—
260C3⋊Dic3—41no—
261C3×Dic3—42no—
262C3×Dic3—81no—
263C22×D4—91no—
264C2×M16—31no—
265C2×M16—31no—
266C4×D4—181no—
267C4×D4—181no—
268C4×D4—181no—
269C4×D4—181no—
270#117—91no—
271#117D3211yescharacteristic
272C2×C4⋊C4—31no—
273C2×C22⋊C4—182no—
274C2×C22⋊C4—182no—
275C2×C42—31no—
276#107—61no—
277#107—181no—
278#106—61no—
279#106—181no—
280#100—94no—
281C23×C3—21no—
282C23×C3D3×D411yescharacteristic
283C23×C3D3×D411yescharacteristic
284C22×D3—34no—
285C22×D3—34no—
286C22×D3—64no—
287C22×D3—64no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—64no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3—242no—
298C22×D3—242no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—62no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—122no—
315C2×C3×C4—121no—
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4#23511yescharacteristic
320C2×C3×C4#23511yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4D3×Q811yescharacteristic
325C2×C3×C4D3×Q811yescharacteristic
326C2×C3×C4#23911yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328C2×Dic3—22no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—42no—
332C2×Dic3—41no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339D12—64no—
340D12—64no—
341D12—64no—
342D12—64no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—62no—
347D12—62no—
348D12—62no—
349D12—62no—
350D12—62no—
351C4×D3—244no—
352C4×D3—244no—
353C4×D3—242no—
354C4×D3—242no—
355C4×D3—242no—
356C4×D3—242no—
357C3×C8—62no—
358C3×C8—62no—
359C3⋊C8—22no—
360C3⋊C8—22no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32#38511yescharacteristic
364C2×C32#45311yescharacteristic
365C2×C32#45511yescharacteristic
366C3⋊D3—44no—
367C24—92no—
368C2×D4—92no—
369C2×D4—92no—
370C2×D4—181no—
371C2×D4—181no—
372C2×D4—181no—
373C2×D4—181no—
374C22×C4—61no—
375C22×C4—61no—
376C22×C4—182no—
377C22×C4—182no—
378C22×C4C2×D3211yescharacteristic
379M16—32no—
380M16—32no—
381M16—61no—
382M16—61no—
383C2×C8—61no—
384C2×C8—61no—
385C4⋊C4—61no—
386C4⋊C4—61no—
387C4⋊C4—91no—
388C4⋊C4—91no—
389C4⋊C4#62611yescharacteristic
390C4⋊C4#62611yescharacteristic
391C22⋊C4—21no—
392C22⋊C4—182no—
393C22⋊C4—182no—
394C22⋊C4—181no—
395C22⋊C4—364no—
396C42—21no—
397C42—61no—
398C42—61no—
399C42—181no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3#88211yescharacteristic
410C22×C3#88311yescharacteristic
411C22×C3D3×C4⋊C411yescharacteristic
412C22×C3D3×C4⋊C411yescharacteristic
413C22×C3#89411yescharacteristic
414C22×C3#93711yescharacteristic
415C2×D3—68no—
416C2×D3—64no—
417C2×D3—64no—
418C2×D3—124no—
419C2×D3—124no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—124no—
425C2×D3—124no—
426C2×D3—244no—
427C2×D3—242no—
428C2×D3—242no—
429C2×D3—244no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—122no—
441C3×C4—241no—
442C3×C4C4×D1211yescharacteristic
443C3×C4#67⋊C411yescharacteristic
444C3×C4#89311yescharacteristic
445C3×C4#89611yescharacteristic
446C3×C4#89611yescharacteristic
447C3×C4#89711yescharacteristic
448C3×C4C4×#6711yescharacteristic
449C3×C4#94611yescharacteristic
450Dic3—42no—
451Dic3—81no—
452Dic3—122no—
453Dic3—122no—
454Dic3—121no—
455Dic3—121no—
456Dic3—121no—
457Dic3—121no—
458C32#185611yescharacteristic, complemented, Sylow
459C23—94no—
460C23—182no—
461C23—182no—
462C23—362no—
463C23—362no—
464C23#381111yescharacteristic
465D4—182no—
466D4—182no—
467D4—182no—
468D4—182no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—62no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—122no—
475C2×C4—121no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—722no—
479C2×C4—722no—
480C2×C4#379611yescharacteristic
481C2×C4#379711yescharacteristic
482C2×C4#379811yescharacteristic
483C2×C4C4×D3211yescharacteristic
484C2×C4C2×#62611yescharacteristic
485C2×C4#381111yescharacteristic
486C8—62no—
487C8—62no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—41no—
496C2×C3—41no—
497C2×C3#466811yescharacteristic
498C2×C3#482211yescharacteristic
499C2×C3#482511yescharacteristic
500C2×C3#498911yescharacteristic
501C2×C3#519811yescharacteristic
502C2×C3#520211yescharacteristic
503D3—128no—
504D3—124no—
505D3—124no—
506C22—21no—
507C22—21no—
508C22—184no—
509C22—364no—
510C22—362no—
511C22—362no—
512C22—722no—
513C22#6385311yescharacteristic
514C22#6388311yescharacteristic
515C22#6398111yescharacteristic
516C4—41no—
517C4—41no—
518C4—122no—
519C4—241no—
520C4—361no—
521C4—361no—
522C4#6386511yescharacteristic
523C4#6387111yescharacteristic
524C4#6388111yescharacteristic
525C4C4×#62611yescharacteristic
526C3—21no—
527C3#6875811yescharacteristic, complemented
528C3#7067411yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—364no—
532C2#1059129011yescharacteristic
533C2#1059166711yescharacteristic
534C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1856
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
4. #10591130C2semidirect
6. C3×#4532C2semidirect
7. #10589162C2semidirect
27. #63559C4semidirect
35. #4995D3semidirect
41. #4532D3semidirect
71. C3×#208C2×C4semidirect
72. C3×#208C2×C4semidirect
239. #208C4×D3semidirect
240. #208C4×D3semidirect
458. C32#1856semidirect
527. C3#68758semidirect
528. C3#70674semidirect

Maximal subgroups

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

subgroupindex
#105959922
C3×#49952
#105913202
#105911302
C2×#635592
C3×#45322
#105891622
#706743
#687583