Finite Group Databasebeta

← #11786754

Subgroups — #11786754

Order 1152.

657 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594990C211yesmaximal, characteristic
2C2×#63632C211yesmaximal, characteristic
3C3×#4936C211yesmaximal, characteristic, complemented
4#10591139C211yesmaximal, characteristic, complemented
5#10591106C211yesmaximal, characteristic
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#69562—31nomaximal
9#68772—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63952—22no—
18#63900—21no—
19#63894—21no—
20#63849—21no—
21#63844—21no—
22#63632C414yescomplemented
23C3×C3⋊#95—22no—
24#63576—21no—
25#63574—21no—
26#63567—21no—
27#63564—21no—
28#5523—31no—
29#5504—31no—
30C3×#382—31no—
31#5133—31no—
32#4995—31no—
33#4966—31no—
34#4964—31no—
35#4936D311yescharacteristic, complemented
36C2×#805—31no—
37C2×#805—31no—
38C2×#805—61no—
39C3×#339—31no—
40#4554—31no—
41#4530—31no—
42#4523D311yescharacteristic, complemented
43C22×C32×C4—21no—
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×#634D411yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3D412yes—
55C2×#624—22no—
56C32×C42—21no—
57C32×C42C2×C412yescomplemented
58#3748—21no—
59#3748C2×C412yescomplemented
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×C4⋊Dic3D411yescharacteristic
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72#3724—22no—
73#3722—22no—
74Dic32—22no—
75#1860—91noSylow
76C2×#235—31no—
77C2×#235—31no—
78C2×#235—61no—
79C2×C3×M16—31no—
80C3×#117—31no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C42—21no—
84C2×C3×C42C2×D311yescharacteristic
85C2×C3×C42C2×D311yescharacteristic
86C4×#67—62no—
87#926C2×D311yescharacteristic
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×#208—31no—
91C2×#208—31no—
92C2×#208—61no—
93C2×#208C2×D311yescharacteristic
94#893—61no—
95#892—61no—
96#892—61no—
97D3×C4⋊C4—61no—
98D3×C4⋊C4—61no—
99#887—61no—
100#67⋊C4—62no—
101C4×D12—61no—
102C4×Dic6—61no—
103C3×#95—62no—
104C3⋊#95—22no—
105#821—61no—
106#816—61no—
107#810—61no—
108#809—61no—
109#808—61no—
110#808—61no—
111#807—61no—
112#807—61no—
113#805—34no—
114#805—34no—
115#805—64no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C2×C32×C4—22no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q811yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127#638—22no—
128#638—22no—
129C2×C3⋊Dic3—21no—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)C4⋊C412yes—
132C4×C3⋊D3—22no—
133C4×C3⋊D3—22no—
134#634—21no—
135#634C4⋊C412yes—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—41no—
142#624—82no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—41no—
145#520—91no—
146#428—91no—
147C2×#104—91no—
148#417—91no—
149#382—31no—
150#343—91no—
151#339—31no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—32no—
156C22×C3×C4—41no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—61no—
161C2×#67—61no—
162C2×#67—121no—
163C22×Dic3—21no—
164C22×Dic3#6712yes—
165#235—32no—
166#235—32no—
167#235—32no—
168#235—32no—
169#235—62no—
170#235—62no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—121no—
176#235—121no—
177C2×D12—31no—
178C2×D12—31no—
179C2×D12—61no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3—62no—
183C2×C4×D3—62no—
184C2×C4×D3—121no—
185C2×Dic6—31no—
186C2×Dic6—31no—
187C2×Dic6—61no—
188C3×M16—61no—
189C3×M16—61no—
190C2×C3×C8—61no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—31no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42—22no—
201C3×C42—41no—
202C3×C42—61no—
203C3×C42C4×D312yescomplemented
204C3×C42C4×D312yescomplemented
205#217—21no—
206(C2×D3)⋊C4—62no—
207(C2×D3)⋊C4—62no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3D1211yescharacteristic
213C4⋊Dic3D1211yescharacteristic
214Dic3⋊C4—62no—
215Dic3⋊C4—62no—
216C4×Dic3—21no—
217C4×Dic3—62no—
218C4×Dic3—62no—
219#208—21no—
220#208—21no—
221#208—32no—
222#208—32no—
223#208—62no—
224#208—61no—
225#208—61no—
226#208—121no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32C4×D411yescharacteristic
234C22×C32#12011yescharacteristic
235C22×C32C22⋊Q811yescharacteristic
236C2×C3⋊D3—22no—
237C2×C3⋊D3—41no—
238C2×C3⋊D3—41no—
239C32×C4—42no—
240C32×C4C2×C4⋊C411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C32×C4#12311yescharacteristic
244C3⋊Dic3—22no—
245C3×Dic3—41no—
246C3×Dic3—41no—
247C3×Dic3—42no—
248C3×Dic3—81no—
249C2×#41—91no—
250C2×M16—31no—
251C2×M16—91no—
252C4×Q8—181no—
253C4×D4—181no—
254C4×D4—182no—
255#117—31no—
256#117—181no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—181no—
260C2×C42D3211yescharacteristic
261#107—181no—
262#106—181no—
263#104—94no—
264#103—181no—
265#102—181no—
266#95—62no—
267C23×C3—21no—
268C23×C3D3×D411yescharacteristic
269C23×C3C2×#6711yescharacteristic
270C22×D3—61no—
271C22×D3—61no—
272C22×D3—121no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
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—42no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—62no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—122no—
292C2×C3×C4—122no—
293C2×C3×C4—121no—
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×D1211yescharacteristic
297C2×C3×C4#23511yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4#23711yescharacteristic
303C2×C3×C4D3×Q811yescharacteristic
304C2×C3×C4D3×Q811yescharacteristic
305C2×C3×C4#23911yescharacteristic
306#67—62no—
307#67—62no—
308#67—62no—
309#67—62no—
310#67—122no—
311#67—122no—
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—22no—
315C2×Dic3—42no—
316C2×Dic3—42no—
317C2×Dic3—41no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—121no—
321D12—32no—
322D12—32no—
323D12—62no—
324D12—61no—
325D12—61no—
326D12—121no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331C4×D3—122no—
332C4×D3—122no—
333C4×D3—242no—
334C4×D3—242no—
335Dic6—32no—
336Dic6—32no—
337Dic6—62no—
338Dic6—61no—
339Dic6—61no—
340Dic6—121no—
341C3×C8—121no—
342C3⋊C8—41no—
343C3⋊C8—62no—
344C3⋊C8—62no—
345C3⋊C8—122no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32#38511yescharacteristic
349C2×C32#45411yescharacteristic
350C2×C32#45511yescharacteristic
351C3⋊D3—42no—
352#41—92no—
353#41—92no—
354#41—181no—
355#41—181no—
356C2×Q8—91no—
357C2×D4—91no—
358C2×D4—181no—
359C22×C4—21no—
360C22×C4—32no—
361C22×C4—61no—
362C22×C4—182no—
363C22×C4—181no—
364C22×C4C2×D3211yescharacteristic
365M16—61no—
366M16—61no—
367M16—92no—
368M16—181no—
369C2×C8—61no—
370C2×C8—181no—
371C4⋊C4—31no—
372C4⋊C4—31no—
373C4⋊C4—61no—
374C4⋊C4—61no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—182no—
378C22⋊C4—61no—
379C22⋊C4—182no—
380C42—21no—
381C42—61no—
382C42—182no—
383C42#62412yescomplemented
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3#67⋊C411yescharacteristic
394C22×C3#88211yescharacteristic
395C22×C3#89611yescharacteristic
396C22×C3C4×#6711yescharacteristic
397C22×C3#93711yescharacteristic
398C22×C3#94611yescharacteristic
399C2×D3—62no—
400C2×D3—62no—
401C2×D3—122no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—121no—
406C2×D3—241no—
407C2×D3—241no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—44no—
415C3×C4—121no—
416C3×C4—121no—
417C3×C4—122no—
418C3×C4—241no—
419C3×C4C4×D1211yescharacteristic
420C3×C4#88311yescharacteristic
421C3×C4D3×C4⋊C411yescharacteristic
422C3×C4D3×C4⋊C411yescharacteristic
423C3×C4#89311yescharacteristic
424C3×C4#89411yescharacteristic
425C3×C4#89611yescharacteristic
426C3×C4#89711yescharacteristic
427Dic3—42no—
428Dic3—41no—
429Dic3—41no—
430Dic3—62no—
431Dic3—62no—
432Dic3—81no—
433Dic3—122no—
434C32#186011yescharacteristic, complemented, Sylow
435C23—181no—
436C23D3×#6711yescharacteristic
437Q8—92no—
438Q8—181no—
439D4—92no—
440D4—182no—
441D4—182no—
442D4—181no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—62no—
449C2×C4—122no—
450C2×C4—122no—
451C2×C4—121no—
452C2×C4—181no—
453C2×C4—182no—
454C2×C4—182no—
455C2×C4—722no—
456C2×C4#379711yescharacteristic
457C2×C4#379911yescharacteristic
458C2×C4D3×D1211yescharacteristic
459C2×C4#380211yescharacteristic
460C2×C4#380411yescharacteristic
461C2×C4C2×#62411yescharacteristic
462C8—121no—
463C8—182no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—41no—
472C2×C3—41no—
473C2×C3#466811yescharacteristic
474C2×C3#482511yescharacteristic
475C2×C3#482711yescharacteristic
476C2×C3#498911yescharacteristic
477C2×C3#506111yescharacteristic
478C2×C3#506211yescharacteristic
479D3—122no—
480D3—122no—
481D3—242no—
482C22—21no—
483C22—21no—
484C22—182no—
485C22—361no—
486C22—361no—
487C22#6388811yescharacteristic
488C22#6392211yescharacteristic
489C22#6395211yescharacteristic
490C4—42no—
491C4—122no—
492C4—121no—
493C4—121no—
494C4—182no—
495C4—241no—
496C4#6385411yescharacteristic
497C4#6389411yescharacteristic
498C4#6389511yescharacteristic
499C4#6390011yescharacteristic
500C3—21no—
501C3#6877211yescharacteristic, complemented
502C3#6956211yescharacteristic, complemented
503C2—21no—
504C2—21no—
505C2—362no—
506C2#1059039611yescharacteristic
507C2#1059040011yescharacteristic
508C2#1059137811yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1860
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×#4936C2semidirect
4. #10591139C2semidirect
6. C3×#4523C2semidirect
7. #10589167C2semidirect
22. #63632C4semidirect
35. #4936D3semidirect
42. #4523D3semidirect
57. C32×C42C2×C4semidirect
59. #3748C2×C4semidirect
203. C3×C42C4×D3semidirect
204. C3×C42C4×D3semidirect
383. C42#624semidirect
434. C32#1860semidirect
501. C3#68772semidirect
502. C3#69562semidirect

Maximal subgroups

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

subgroupindex
#105949902
C2×#636322
C3×#49362
#105911392
#105911062
C3×#45232
#105891672
#695623
#687723