Finite Group Databasebeta

← #11786736

Subgroups — #11786736

Order 1152.

653 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
2#10592665C211yesmaximal, characteristic
3C3×#4977C211yesmaximal, characteristic, complemented
4C3×#4964C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6#10589167C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70681—31nomaximal
9#69562—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
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#63637—21no—
23#63636—21no—
24C3×C3⋊#95—22no—
25C3×#808—21no—
26C3×#807—21no—
27#63570C414yescomplemented
28#5523—31no—
29#5504—31no—
30C3×#428—31no—
31C3×#382—31no—
32C2×#825—31no—
33#4977D311yescharacteristic, complemented
34#4966—31no—
35#4966—31no—
36#4966—61no—
37#4964D311yescharacteristic, complemented
38C2×#805—31no—
39#4554—31no—
40#4532—31no—
41#4530—31no—
42#4523—31no—
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×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58#3748—21no—
59#3748—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C412yescomplemented
69C3×#208—21no—
70C3×#208C2×C412yescomplemented
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—21no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C42—31no—
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×#107—61no—
104C3×#106—61no—
105C3×#95—62no—
106C3⋊#95—22no—
107#825—34no—
108#810—61no—
109#810—61no—
110#810—62no—
111#809—61no—
112#809—61no—
113#809—62no—
114#808—21no—
115#807—21no—
116#805—34no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C2×C32×C4—41no—
120C2×C32×C4—42no—
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—22no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—42no—
143#624—82no—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—22no—
146#520—91no—
147#428—31no—
148C2×#104—91no—
149#417—91no—
150#382—31no—
151#343—91no—
152#339—91no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—32no—
157C22×C3×C4—41no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—61no—
162C2×#67—61no—
163C2×#67—121no—
164C22×Dic3—21no—
165C22×Dic3#6712yes—
166#235—32no—
167#235—32no—
168#235—32no—
169#235—32no—
170#235—62no—
171#235—62no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—121no—
177#235—121no—
178C2×D12—31no—
179C2×D12—31no—
180C2×D12—61no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×C4×D3—121no—
186C2×Dic6—31no—
187C2×Dic6—31no—
188C2×Dic6—61no—
189C3×M16—32no—
190C3×M16—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—31no—
199C3×C4⋊C4—41no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C42—32no—
204C3×C42—61no—
205C3×C42—61no—
206#217—21no—
207(C2×D3)⋊C4—62no—
208(C2×D3)⋊C4—62no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3#6711yescharacteristic
212C4⋊Dic3#6711yescharacteristic
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215C4×Dic3—21no—
216C4×Dic3—21no—
217C4×Dic3—62no—
218C4×Dic3—62no—
219C4×Dic3C4×D312yescomplemented
220#208—21no—
221#208—61no—
222#208—61no—
223#208—61no—
224#208—61no—
225#208—121no—
226#208—121no—
227#208C4×D312yescomplemented
228C2×C3⋊C8—21no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32C4×D411yescharacteristic
235C22×C32#12011yescharacteristic
236C22×C32C22⋊Q811yescharacteristic
237C2×C3⋊D3—22no—
238C2×C3⋊D3—41no—
239C2×C3⋊D3—41no—
240C32×C4—81no—
241C32×C4C2×C4⋊C411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C32×C4#12311yescharacteristic
245C3⋊Dic3—22no—
246C3×Dic3—42no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C3×Dic3—42no—
250C2×#41—91no—
251C2×M16—31no—
252C2×M16—91no—
253C4×Q8—181no—
254C4×D4—181no—
255C4×D4—182no—
256#117—31no—
257#117—181no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—181no—
260C2×C4⋊C4D3211yescharacteristic
261C2×C42—31no—
262#107—61no—
263#106—61no—
264#104—94no—
265#103—181no—
266#102—181no—
267#95—62no—
268C23×C3—21no—
269C23×C3D3×D411yescharacteristic
270C23×C3C2×#6711yescharacteristic
271C22×D3—61no—
272C22×D3—61no—
273C22×D3—121no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—62no—
286C2×C3×C4—61no—
287C2×C3×C4—62no—
288C2×C3×C4—61no—
289C2×C3×C4—82no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—122no—
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×Q811yescharacteristic
301C2×C3×C4D3×Q811yescharacteristic
302C2×C3×C4#23911yescharacteristic
303C2×C3×C4#23911yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305#67—62no—
306#67—62no—
307#67—62no—
308#67—62no—
309#67—122no—
310#67—122no—
311C2×Dic3—22no—
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—22no—
315C2×Dic3—41no—
316C2×Dic3—41no—
317C2×Dic3—42no—
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—62no—
342C3⋊C8—22no—
343C3⋊C8—122no—
344C3⋊C8—121no—
345C3⋊C8—121no—
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—32no—
366M16—61no—
367M16—181no—
368M16—181no—
369C2×C8—61no—
370C2×C8—181no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—31no—
374C4⋊C4—31no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—182no—
378C22⋊C4—61no—
379C22⋊C4—182no—
380C42—32no—
381C42—61no—
382C42—61no—
383C42—182no—
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#89311yescharacteristic
394C22×C3#89611yescharacteristic
395C22×C3C4×#6711yescharacteristic
396C22×C3#93711yescharacteristic
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—82no—
413C3×C4—81no—
414C3×C4—81no—
415C3×C4—122no—
416C3×C4—122no—
417C3×C4—121no—
418C3×C4—121no—
419C3×C4D3×C4⋊C411yescharacteristic
420C3×C4D3×C4⋊C411yescharacteristic
421C3×C4#89311yescharacteristic
422C3×C4#89411yescharacteristic
423C3×C4#89411yescharacteristic
424C3×C4#89611yescharacteristic
425C3×C4C4×#6711yescharacteristic
426C3×C4#94611yescharacteristic
427Dic3—42no—
428Dic3—41no—
429Dic3—41no—
430Dic3—42no—
431Dic3—62no—
432Dic3—62no—
433Dic3—122no—
434C32#186011yescharacteristic, complemented, Sylow
435C23—181no—
436C23D3×#6711yescharacteristic
437Q8—92no—
438Q8—181no—
439D4—92no—
440D4—182no—
441D4—182no—
442D4—181no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—62no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—62no—
449C2×C4—121no—
450C2×C4—121no—
451C2×C4—122no—
452C2×C4—181no—
453C2×C4—182no—
454C2×C4—182no—
455C2×C4—722no—
456C2×C4#379711yescharacteristic
457C2×C4#379911yescharacteristic
458C2×C4#379911yescharacteristic
459C2×C4C4×D3211yescharacteristic
460C2×C4D3×#6711yescharacteristic
461C2×C4#381111yescharacteristic
462C8—62no—
463C8—361no—
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#498911yescharacteristic
474C2×C3#498911yescharacteristic
475C2×C3#506111yescharacteristic
476C2×C3#506211yescharacteristic
477C2×C3#520111yescharacteristic
478C2×C3#520211yescharacteristic
479D3—122no—
480D3—122no—
481D3—242no—
482C22—21no—
483C22—21no—
484C22—182no—
485C22—361no—
486C22—361no—
487C22#6388811yescharacteristic
488C22#6390411yescharacteristic
489C22#6398311yescharacteristic
490C4—81no—
491C4—122no—
492C4—121no—
493C4—122no—
494C4—121no—
495C4—182no—
496C4#6388311yescharacteristic
497C4#6388811yescharacteristic
498C4#6389711yescharacteristic
499C4#6390411yescharacteristic
500C3—21no—
501C3#6956211yescharacteristic, complemented
502C3#7068111yescharacteristic, complemented
503C2—21no—
504C2—21no—
505C2—362no—
506C2#1059137411yescharacteristic
507C2#1059152511yescharacteristic
508C2#1059165911yescharacteristic
subgroupG/H
centerC22#63983
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1860
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
3. C3×#4977C2semidirect
4. C3×#4964C2semidirect
6. #10589167C2semidirect
7. #10589161C2semidirect
27. #63570C4semidirect
33. #4977D3semidirect
37. #4964D3semidirect
68. C3×C4×Dic3C2×C4semidirect
70. C3×#208C2×C4semidirect
219. C4×Dic3C4×D3semidirect
227. #208C4×D3semidirect
434. C32#1860semidirect
501. C3#69562semidirect
502. C3#70681semidirect

Maximal subgroups

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

subgroupindex
#105949902
#105926652
C3×#49772
C3×#49642
C2×#635702
#105891672
#105891612
#706813
#695623