Finite Group Databasebeta

← #11786702

Subgroups — #11786702

Order 1152.

751 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595975C211yesmaximal, characteristic
2C3×#4975C211yesmaximal, characteristic, complemented
3#10591130C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic
5#10591106C211yesmaximal, characteristic
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#69592—31nomaximal
9#69002—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C4×#638—22no—
13#64135C2211yescharacteristic
14#64102—21no—
15#64101—21no—
16C4⋊C4×C3⋊D3—21no—
17#64096—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4—22no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23#63575—21no—
24#63573—21no—
25#63570C414yescomplemented
26#63567—21no—
27#63564—21no—
28#5504—31no—
29#5504—31no—
30#5504—61no—
31C3×#384—31no—
32C2×#825—31no—
33#5133—31no—
34#5121—31no—
35#4975D311yescharacteristic, complemented
36#4966—31no—
37#4964—31no—
38C2×#805—31no—
39C3×#343—31no—
40#4555—31no—
41#4530D311yescharacteristic, complemented
42#4523—31no—
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
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⋊C4—21no—
57C32×C4⋊C4—21no—
58#3757—21no—
59#3752—22no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61C4⋊(C3⋊Dic3)D411yescharacteristic
62#3750—22no—
63C4×C3⋊Dic3—22no—
64C4×C3⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×Dic3⋊C4—44no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3C2×C412yescomplemented
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208C2×C412yescomplemented
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#1859—91noSylow
77C2×#235—31no—
78C2×#235—31no—
79C2×#235—61no—
80C2×C3×M16—31no—
81C2×C3×M16—31no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—62no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C42—31no—
88C4×#67—64no—
89C4×#67—62no—
90C4×#67—62no—
91#926—31no—
92#926—31no—
93#926—61no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×Dic3⋊C4—22no—
96C2×C4×Dic3C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99#893—61no—
100#893—61no—
101#893—62no—
102#892—61no—
103#892—61no—
104#892—62no—
105D3×C4⋊C4—61no—
106D3×C4⋊C4—61no—
107D3×C4⋊C4—62no—
108#887—61no—
109#887—61no—
110#887—62no—
111#825—34no—
112#821—61no—
113#818—61no—
114#817—61no—
115#816—61no—
116#810—61no—
117#809—61no—
118#808—61no—
119#807—61no—
120#805—34no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—21no—
123C2×C32×C4—22no—
124C2×C32×C4—42no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131#638—22no—
132#638—22no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)C4⋊C412yescomplemented
138C4×C3⋊D3—22no—
139C4×C3⋊D3—22no—
140C4×C3⋊D3—82no—
141#634—21no—
142#634C4⋊C412yescomplemented
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3—41no—
148C3×C3⋊C8—22no—
149C3×C3⋊C8—41no—
150#520—91no—
151#428—91no—
152C2×#104—91no—
153#417—91no—
154#384—31no—
155#343—31no—
156#339—91no—
157C22×C3×C4—22no—
158C22×C3×C4—21no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4D1212yes—
162C22×C3×C4#6712yes—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—62no—
166C2×#67—61no—
167C2×#67—61no—
168C22×Dic3—21no—
169C22×Dic3—21no—
170#235—32no—
171#235—32no—
172#235—32no—
173#235—32no—
174#235—62no—
175#235—62no—
176#235—62no—
177#235—62no—
178#235—61no—
179#235—61no—
180#235—61no—
181#235—61no—
182C2×D12—31no—
183C2×D12—31no—
184C2×D12—61no—
185C2×C4×D3—62no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—64no—
189C2×C4×D3—62no—
190C2×C4×D3—62no—
191C2×Dic6—31no—
192C2×Dic6—31no—
193C2×Dic6—61no—
194C3×M16—32no—
195C3×M16—61no—
196C3×M16—61no—
197C3×M16—61no—
198C2×C3×C8—61no—
199C2×C3×C8—61no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—124no—
209C3×C42—32no—
210C3×C42—61no—
211#217—62no—
212#217—61no—
213#217—61no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—62no—
216(C2×D3)⋊C4—62no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—31no—
222C4⋊Dic3—31no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225Dic3⋊C4—44no—
226Dic3⋊C4—64no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229C4×Dic3—21no—
230C4×Dic3—64no—
231C4×Dic3—62no—
232C4×Dic3—62no—
233C4×Dic3—62no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C4×Dic3C4×D312yescomplemented
237#208—21no—
238#208—21no—
239#208—21no—
240#208C4×D312yescomplemented
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32C4×D411yescharacteristic
246C22×C32#12011yescharacteristic
247C22×C32C22⋊Q811yescharacteristic
248C2×C3⋊D3—22no—
249C2×C3⋊D3—41no—
250C2×C3⋊D3—41no—
251C32×C4—42no—
252C32×C4C2×C4⋊C411yescharacteristic
253C32×C4C4×D411yescharacteristic
254C32×C4C22⋊Q811yescharacteristic
255C32×C4#12311yescharacteristic
256C3⋊Dic3—22no—
257C3⋊Dic3—41no—
258C3⋊Dic3—41no—
259C3×Dic3—24no—
260C3×Dic3—81no—
261C2×#41—91no—
262C2×M16—31no—
263C2×M16—31no—
264C4×Q8—181no—
265C4×D4—181no—
266C4×D4—182no—
267#117—91no—
268#117—181no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—62no—
271C2×C4⋊C4—181no—
272C2×C4⋊C4D3211yescharacteristic
273C2×C42—31no—
274#107—181no—
275#106—181no—
276#104—94no—
277#103—181no—
278#102—181no—
279C23×C3—21no—
280C23×C3C2×D1211yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C22×D3—62no—
283C22×D3—61no—
284C22×D3—61no—
285C2×C3×C4—24no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
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—42no—
295C2×C3×C4—42no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—82no—
300C2×C3×C4—122no—
301C2×C3×C4—121no—
302C2×C3×C4C2×C4×D311yescharacteristic
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4D3×Q811yescharacteristic
312C2×C3×C4D3×Q811yescharacteristic
313C2×C3×C4#23911yescharacteristic
314#67—64no—
315#67—64no—
316#67—62no—
317#67—62no—
318#67—62no—
319#67—62no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—42no—
324C2×Dic3—41no—
325C2×Dic3—62no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334D12—32no—
335D12—32no—
336D12—62no—
337D12—62no—
338D12—61no—
339D12—61no—
340C4×D3—64no—
341C4×D3—64no—
342C4×D3—62no—
343C4×D3—62no—
344C4×D3—62no—
345C4×D3—62no—
346C4×D3—244no—
347C4×D3—242no—
348C4×D3—242no—
349Dic6—32no—
350Dic6—32no—
351Dic6—62no—
352Dic6—62no—
353Dic6—61no—
354Dic6—61no—
355C3×C8—62no—
356C3×C8—121no—
357C3⋊C8—22no—
358C3⋊C8—41no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32#38511yescharacteristic
362C2×C32#45311yescharacteristic
363C2×C32#45611yescharacteristic
364C3⋊D3—42no—
365#41—92no—
366#41—92no—
367#41—181no—
368#41—181no—
369C2×Q8—91no—
370C2×D4—91no—
371C2×D4—181no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4—182no—
375C22×C4—181no—
376C22×C4#62612yes—
377C22×C4C2×D3211yescharacteristic
378M16—32no—
379M16—61no—
380M16—61no—
381M16—61no—
382C2×C8—61no—
383C2×C8—61no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—91no—
389C4⋊C4—91no—
390C4⋊C4—124no—
391C4⋊C4—182no—
392C22⋊C4—182no—
393C22⋊C4—181no—
394C42—32no—
395C42—61no—
396C42—182no—
397C42—181no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3C4×D1211yescharacteristic
408C22×C3#88211yescharacteristic
409C22×C3#89711yescharacteristic
410C22×C3C4×#6711yescharacteristic
411C22×C3#93711yescharacteristic
412C22×C3#94611yescharacteristic
413C2×D3—64no—
414C2×D3—62no—
415C2×D3—62no—
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—121no—
419C2×D3—121no—
420C2×D3—121no—
421C2×D3—121no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—44no—
427C3×C4—42no—
428C3×C4—42no—
429C3×C4—64no—
430C3×C4—241no—
431C3×C4#67⋊C411yescharacteristic
432C3×C4#88311yescharacteristic
433C3×C4D3×C4⋊C411yescharacteristic
434C3×C4D3×C4⋊C411yescharacteristic
435C3×C4#89311yescharacteristic
436C3×C4#89411yescharacteristic
437C3×C4#89611yescharacteristic
438C3×C4#89611yescharacteristic
439Dic3—24no—
440Dic3—64no—
441Dic3—62no—
442Dic3—62no—
443Dic3—81no—
444Dic3—122no—
445Dic3—122no—
446Dic3—121no—
447Dic3—121no—
448Dic3—121no—
449Dic3—121no—
450C32#185911yescharacteristic, complemented, Sylow
451C23—181no—
452C23C2×#62611yescharacteristic
453Q8—92no—
454Q8—181no—
455D4—92no—
456D4—182no—
457D4—182no—
458D4—181no—
459C2×C4—22no—
460C2×C4—42no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—122no—
465C2×C4—121no—
466C2×C4—181no—
467C2×C4—182no—
468C2×C4—182no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—722no—
472C2×C4#379611yescharacteristic
473C2×C4#379711yescharacteristic
474C2×C4#379811yescharacteristic
475C2×C4C4×D3211yescharacteristic
476C2×C4#381111yescharacteristic
477C2×C4#381111yescharacteristic
478C8—62no—
479C8—121no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3#466811yescharacteristic
490C2×C3#474711yescharacteristic
491C2×C3#475211yescharacteristic
492C2×C3#498911yescharacteristic
493C2×C3#507711yescharacteristic
494C2×C3#509511yescharacteristic
495D3—124no—
496D3—122no—
497D3—122no—
498C22—21no—
499C22—21no—
500C22—182no—
501C22—361no—
502C22—361no—
503C22#6387111yescharacteristic
504C22C4×#62611yescharacteristic
505C22#6398111yescharacteristic
506C4—42no—
507C4—64no—
508C4—182no—
509C4—241no—
510C4—361no—
511C4—361no—
512C4#6385311yescharacteristic
513C4#6386511yescharacteristic
514C4#6388111yescharacteristic
515C4#6388311yescharacteristic
516C3—21no—
517C3#6900211yescharacteristic, complemented
518C3#6959211yescharacteristic, complemented
519C2—21no—
520C2—21no—
521C2—362no—
522C2#1059129011yescharacteristic
523C2#1059151111yescharacteristic
524C2#1059165011yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1859
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4975C2semidirect
3. #10591130C2semidirect
6. C3×#4530C2semidirect
7. #10589162C2semidirect
25. #63570C4semidirect
35. #4975D3semidirect
41. #4530D3semidirect
69. C3×C4×Dic3C2×C4semidirect
73. C3×#208C2×C4semidirect
137. C4⋊(C3⋊D3)C4⋊C4semidirect
142. #634C4⋊C4semidirect
236. C4×Dic3C4×D3semidirect
240. #208C4×D3semidirect
450. C32#1859semidirect
517. C3#69002semidirect
518. C3#69592semidirect

Maximal subgroups

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

subgroupindex
#105959752
C3×#49752
#105911302
C2×#635702
#105911062
C3×#45302
#105891622
#695923
#690023