Finite Group Databasebeta

← #11786687

Subgroups — #11786687

Order 1152.

685 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594990C211yesmaximal, characteristic
2#10592665C211yesmaximal, characteristic
3C3×#4975C211yesmaximal, characteristic, complemented
4C3×#4964C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic
6#10589167C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70680—31nomaximal
9#69592—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4—22no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63952—22no—
19#63900—21no—
20#63894—21no—
21#63849—21no—
22#63844—21no—
23#63637—21no—
24#63636—21no—
25C3×#808—21no—
26C3×#807—21no—
27#63570C414yescomplemented
28#5523—31no—
29#5504—31no—
30C3×#428—31no—
31C3×#384—31no—
32C2×#825—31no—
33#4975D311yescharacteristic, 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×Dic3⋊C4—44no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3C2×C412yescomplemented
70C3×#208—21no—
71C3×#208C2×C412yescomplemented
72C2×C3×C3⋊C8—21no—
73#3724—22no—
74#3722—22no—
75Dic32—22no—
76#1859—91noSylow
77C2×#235—31no—
78C2×#235—31no—
79C2×#235—61no—
80C2×C3×M16—31no—
81C3×#117—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—62no—
89#926C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×Dic3⋊C4—22no—
92C2×C4×Dic3C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—61no—
96C2×#208C2×D311yescharacteristic
97#893—61no—
98#892—61no—
99#892—61no—
100D3×C4⋊C4—61no—
101D3×C4⋊C4—61no—
102#887—61no—
103#67⋊C4—62no—
104C4×D12—61no—
105C4×Dic6—61no—
106C3×#107—61no—
107C3×#106—61no—
108#825—34no—
109#810—61no—
110#810—61no—
111#810—62no—
112#809—61no—
113#809—61no—
114#809—62no—
115#808—21no—
116#807—21no—
117#805—34no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—21no—
120C2×C32×C4—41no—
121C2×C32×C4—42no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×Q811yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128#638—22no—
129#638—22no—
130C2×C3⋊Dic3—21no—
131C4⋊(C3⋊D3)—21no—
132C4⋊(C3⋊D3)C4⋊C412yescomplemented
133C4×C3⋊D3—22no—
134C4×C3⋊D3—22no—
135#634—21no—
136#634C4⋊C412yescomplemented
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—42no—
144#624—82no—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—22no—
147#520—91no—
148#428—31no—
149C2×#104—91no—
150#417—91no—
151#384—31no—
152#343—91no—
153#339—91no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—32no—
158C22×C3×C4—41no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—61no—
163C2×#67—61no—
164C2×#67—121no—
165C22×Dic3—21no—
166C22×Dic3#6712yes—
167#235—32no—
168#235—32no—
169#235—32no—
170#235—32no—
171#235—62no—
172#235—62no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177#235—121no—
178#235—121no—
179C2×D12—31no—
180C2×D12—31no—
181C2×D12—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—121no—
187C2×Dic6—31no—
188C2×Dic6—31no—
189C2×Dic6—61no—
190C3×M16—32no—
191C3×M16—61no—
192C2×C3×C8—61no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—31no—
199C3×C4⋊C4—31no—
200C3×C4⋊C4—41no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—124no—
204C3×C22⋊C4—61no—
205C3×C42—32no—
206C3×C42—61no—
207C3×C42—61no—
208#217—21no—
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3#6711yescharacteristic
214C4⋊Dic3#6711yescharacteristic
215Dic3⋊C4—44no—
216Dic3⋊C4—62no—
217Dic3⋊C4—62no—
218C4×Dic3—21no—
219C4×Dic3—21no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C4×Dic3C4×D312yescomplemented
223#208—21no—
224#208—61no—
225#208—61no—
226#208—61no—
227#208—61no—
228#208—121no—
229#208—121no—
230#208C4×D312yescomplemented
231C2×C3⋊C8—21no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32C4×D411yescharacteristic
238C22×C32#12011yescharacteristic
239C22×C32C22⋊Q811yescharacteristic
240C2×C3⋊D3—22no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—41no—
243C32×C4—81no—
244C32×C4C2×C4⋊C411yescharacteristic
245C32×C4C4×D411yescharacteristic
246C32×C4C22⋊Q811yescharacteristic
247C32×C4#12311yescharacteristic
248C3⋊Dic3—22no—
249C3×Dic3—24no—
250C3×Dic3—41no—
251C3×Dic3—42no—
252C3×Dic3—41no—
253C2×#41—91no—
254C2×M16—31no—
255C2×M16—91no—
256C4×Q8—181no—
257C4×D4—181no—
258C4×D4—182no—
259#117—31no—
260#117—181no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—62no—
263C2×C4⋊C4—181no—
264C2×C4⋊C4D3211yescharacteristic
265C2×C42—31no—
266#107—61no—
267#106—61no—
268#104—94no—
269#103—181no—
270#102—181no—
271C23×C3—21no—
272C23×C3D3×D411yescharacteristic
273C23×C3C2×#6711yescharacteristic
274C22×D3—61no—
275C22×D3—61no—
276C22×D3—121no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—61no—
292C2×C3×C4—62no—
293C2×C3×C4—61no—
294C2×C3×C4—82no—
295C2×C3×C4—122no—
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×Q811yescharacteristic
304C2×C3×C4D3×Q811yescharacteristic
305C2×C3×C4#23911yescharacteristic
306C2×C3×C4#23911yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308#67—62no—
309#67—62no—
310#67—62no—
311#67—62no—
312#67—122no—
313#67—122no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—21no—
318C2×Dic3—21no—
319C2×Dic3—22no—
320C2×Dic3—42no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—121no—
324D12—32no—
325D12—32no—
326D12—62no—
327D12—61no—
328D12—61no—
329D12—121no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—62no—
333C4×D3—62no—
334C4×D3—122no—
335C4×D3—122no—
336C4×D3—242no—
337C4×D3—242no—
338Dic6—32no—
339Dic6—32no—
340Dic6—62no—
341Dic6—61no—
342Dic6—61no—
343Dic6—121no—
344C3×C8—62no—
345C3⋊C8—22no—
346C3⋊C8—122no—
347C3⋊C8—121no—
348C3⋊C8—121no—
349C2×C32—21no—
350C2×C32—21no—
351C2×C32#38511yescharacteristic
352C2×C32#45311yescharacteristic
353C2×C32#45611yescharacteristic
354C3⋊D3—42no—
355#41—92no—
356#41—92no—
357#41—181no—
358#41—181no—
359C2×Q8—91no—
360C2×D4—91no—
361C2×D4—181no—
362C22×C4—21no—
363C22×C4—32no—
364C22×C4—61no—
365C22×C4—182no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368M16—32no—
369M16—61no—
370M16—181no—
371M16—181no—
372C2×C8—61no—
373C2×C8—181no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—31no—
377C4⋊C4—31no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—124no—
381C4⋊C4—182no—
382C22⋊C4—61no—
383C22⋊C4—182no—
384C42—32no—
385C42—61no—
386C42—61no—
387C42—182no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3#89311yescharacteristic
398C22×C3#89611yescharacteristic
399C22×C3C4×#6711yescharacteristic
400C22×C3#93711yescharacteristic
401C22×C3#93711yescharacteristic
402C22×C3#94611yescharacteristic
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—122no—
406C2×D3—121no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—121no—
410C2×D3—241no—
411C2×D3—241no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—64no—
417C3×C4—82no—
418C3×C4—81no—
419C3×C4—81no—
420C3×C4—122no—
421C3×C4—121no—
422C3×C4—121no—
423C3×C4D3×C4⋊C411yescharacteristic
424C3×C4D3×C4⋊C411yescharacteristic
425C3×C4#89311yescharacteristic
426C3×C4#89411yescharacteristic
427C3×C4#89411yescharacteristic
428C3×C4#89611yescharacteristic
429C3×C4C4×#6711yescharacteristic
430C3×C4#94611yescharacteristic
431Dic3—24no—
432Dic3—41no—
433Dic3—41no—
434Dic3—42no—
435Dic3—62no—
436Dic3—62no—
437Dic3—122no—
438C32#185911yescharacteristic, complemented, Sylow
439C23—181no—
440C23D3×#6711yescharacteristic
441Q8—92no—
442Q8—181no—
443D4—92no—
444D4—182no—
445D4—182no—
446D4—181no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—62no—
455C2×C4—122no—
456C2×C4—181no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—722no—
460C2×C4#379711yescharacteristic
461C2×C4#379911yescharacteristic
462C2×C4#379911yescharacteristic
463C2×C4C4×D3211yescharacteristic
464C2×C4D3×#6711yescharacteristic
465C2×C4#381111yescharacteristic
466C8—62no—
467C8—361no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—41no—
476C2×C3—41no—
477C2×C3#498911yescharacteristic
478C2×C3#498911yescharacteristic
479C2×C3#507711yescharacteristic
480C2×C3#509511yescharacteristic
481C2×C3#519811yescharacteristic
482C2×C3#520511yescharacteristic
483D3—122no—
484D3—122no—
485D3—242no—
486C22—21no—
487C22—21no—
488C22—182no—
489C22—361no—
490C22—361no—
491C22#6388811yescharacteristic
492C22#6390411yescharacteristic
493C22#6398311yescharacteristic
494C4—64no—
495C4—81no—
496C4—122no—
497C4—121no—
498C4—121no—
499C4—182no—
500C4#6388311yescharacteristic
501C4#6388811yescharacteristic
502C4#6389711yescharacteristic
503C4#6390411yescharacteristic
504C3—21no—
505C3#6959211yescharacteristic, complemented
506C3#7068011yescharacteristic, complemented
507C2—21no—
508C2—21no—
509C2—362no—
510C2#1059137411yescharacteristic
511C2#1059152311yescharacteristic
512C2#1059166111yescharacteristic
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#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
3. C3×#4975C2semidirect
4. C3×#4964C2semidirect
6. #10589167C2semidirect
7. #10589161C2semidirect
27. #63570C4semidirect
33. #4975D3semidirect
37. #4964D3semidirect
69. C3×C4×Dic3C2×C4semidirect
71. C3×#208C2×C4semidirect
132. C4⋊(C3⋊D3)C4⋊C4semidirect
136. #634C4⋊C4semidirect
222. C4×Dic3C4×D3semidirect
230. #208C4×D3semidirect
438. C32#1859semidirect
505. C3#69592semidirect
506. C3#70680semidirect

Maximal subgroups

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

subgroupindex
#105949902
#105926652
C3×#49752
C3×#49642
C2×#635702
#105891672
#105891612
#706803
#695923