Finite Group Databasebeta

← #11786701

Subgroups — #11786701

Order 1152.

697 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic
2#10592674C211yesmaximal, characteristic, complemented
3#10591131C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591088C211yesmaximal, characteristic
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71664—31nomaximal
9#69002—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3750—22no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C3×C4×#67—22no—
16C3×#926C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#893—21no—
20C3×#892—21no—
21C3×D3×C4⋊C4—21no—
22C3×#887—21no—
23#63575—21no—
24#63573—21no—
25#63568C414yescomplemented
26#63566—21no—
27#63563—21no—
28C3×#520—31no—
29#5504D311yescharacteristic
30C2×#837—31no—
31#5232—31no—
32C2×#825—31no—
33#5133—31no—
34#5121—31no—
35#4995—31no—
36#4975—31no—
37#4975—31no—
38#4975—61no—
39C3×#343—31no—
40#4555—31no—
41#4532—31no—
42#4530D311yescharacteristic, complemented
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235C2×C412yes—
51C3×#235Q812yes—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—22no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60#3750—44no—
61C4×C3⋊Dic3—21no—
62C4×C3⋊Dic3C2×C412yescomplemented
63C3×#217—21no—
64C3×(C2×D3)⋊C4—22no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—22no—
68C3×C4×Dic3—22no—
69C3×C4×Dic3—21no—
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×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C2×C3×M16—31no—
80C2×C3×M16—31no—
81C3×C4×Q8—61no—
82C3×C4×D4—61no—
83C3×C4×D4—62no—
84C3×#117—31no—
85C3×#117—61no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—61no—
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C4×#67—22no—
91#926C2×D311yescharacteristic
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—61no—
95C2×Dic3⋊C4—64no—
96C2×Dic3⋊C4—62no—
97C2×Dic3⋊C4—62no—
98C2×C4×Dic3—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—61no—
101C2×#208C2×D311yescharacteristic
102C2×#208C2×D311yescharacteristic
103#893—21no—
104#892—21no—
105D3×C4⋊C4—21no—
106#887—21no—
107#837—34no—
108#835—61no—
109#832—61no—
110#825—34no—
111#821—61no—
112#818—61no—
113#817—61no—
114#816—61no—
115#808—61no—
116#807—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C2×C32×C4—22no—
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
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—42no—
131C2×C3⋊Dic3—41no—
132C3×#67—22no—
133C3×#67—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C3×D12—21no—
138C3×D12C4⋊C412yescomplemented
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×C4×D3—82no—
142C3×Dic6—21no—
143C3×Dic6C4⋊C412yescomplemented
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146#520—31no—
147#428—91no—
148C2×#104—91no—
149#417—91no—
150#384—91no—
151#343—31no—
152#339—91no—
153C3×#41—32no—
154C3×#41—32no—
155C3×#41—61no—
156C3×#41—61no—
157C2×C3×Q8—31no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—62no—
163C22×C3×C4—61no—
164C22×C3×C4D1212yes—
165C22×C3×C4#6712yes—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—21no—
169C22×Dic3—62no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—62no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175#235—21no—
176#235—21no—
177#235Dic612yes—
178#235C4×D312yes—
179C2×D12#6711yescharacteristic
180C2×C4×D3—21no—
181C2×C4×D3—22no—
182C2×Dic6#6711yescharacteristic
183C3×M16—32no—
184C3×M16—61no—
185C3×M16—61no—
186C3×M16—61no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—41no—
196C3×C4⋊C4—41no—
197C3×C4⋊C4—62no—
198C3×C22⋊C4—62no—
199C3×C22⋊C4—61no—
200C3×C42—62no—
201C3×C42—61no—
202#217—21no—
203(C2×D3)⋊C4—22no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—121no—
209C4⋊Dic3—121no—
210C4⋊Dic3#6711yescharacteristic
211C4⋊Dic3#6711yescharacteristic
212Dic3⋊C4—22no—
213Dic3⋊C4—124no—
214Dic3⋊C4—124no—
215Dic3⋊C4—128no—
216C4×Dic3—22no—
217C4×Dic3—21no—
218C4×Dic3—32no—
219C4×Dic3—32no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208C4×D312yescomplemented
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32C4×D411yescharacteristic
233C22×C32#12011yescharacteristic
234C22×C32C22⋊Q811yescharacteristic
235C2×C3×D3—22no—
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C32×C4—42no—
239C32×C4C2×C4⋊C411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4C22⋊Q811yescharacteristic
242C32×C4#12311yescharacteristic
243C3⋊Dic3—24no—
244C3⋊Dic3—81no—
245C3×Dic3—22no—
246C3×Dic3—41no—
247C3×Dic3—41no—
248C2×#41—31no—
249C2×M16—31no—
250C2×M16—31no—
251C4×Q8—61no—
252C4×D4—61no—
253C4×D4—62no—
254#117—31no—
255#117—61no—
256C2×C4⋊C4—61no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—182no—
259C2×C4⋊C4D3211yescharacteristic
260C2×C42—91no—
261#107—181no—
262#106—181no—
263#104—94no—
264#103—181no—
265#102—181no—
266C23×C3—21no—
267C23×C3—61no—
268C23×C3C2×D1211yescharacteristic
269C23×C3C2×#6711yescharacteristic
270C22×D3—21no—
271C3×Q8—32no—
272C3×Q8—61no—
273C3×D4—32no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—61no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—44no—
289C2×C3×C4—61no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—242no—
295C2×C3×C4C2×Dic611yescharacteristic
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4#23711yescharacteristic
304C2×C3×C4D3×Q811yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307#67—22no—
308#67—22no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—64no—
313C2×Dic3—64no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—64no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—124no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324C2×Dic3—122no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327D12—21no—
328D12Dic3⋊C412yescomplemented
329C4×D3—22no—
330C4×D3—22no—
331C4×D3—82no—
332Dic6—21no—
333Dic6Dic3⋊C412yescomplemented
334C3×C8—62no—
335C3×C8—121no—
336C3⋊C8—22no—
337C3⋊C8—41no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32#38511yescharacteristic
341C2×C32#45311yescharacteristic
342C2×C32#45611yescharacteristic
343C3×D3—42no—
344#41—32no—
345#41—32no—
346#41—61no—
347#41—61no—
348C2×Q8—31no—
349C2×D4—31no—
350C2×D4—61no—
351C22×C4—62no—
352C22×C4—61no—
353C22×C4—181no—
354C22×C4—181no—
355C22×C4#62612yes—
356C22×C4C2×D3211yescharacteristic
357M16—32no—
358M16—61no—
359M16—61no—
360M16—61no—
361C2×C8—61no—
362C2×C8—61no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—31no—
366C4⋊C4—31no—
367C4⋊C4—62no—
368C4⋊C4—181no—
369C4⋊C4—181no—
370C4⋊C4—364no—
371C22⋊C4—62no—
372C22⋊C4—61no—
373C42—62no—
374C42—61no—
375C42—92no—
376C42—181no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—62no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3C4×D1211yescharacteristic
390C22×C3#88211yescharacteristic
391C22×C3#89711yescharacteristic
392C22×C3#92411yescharacteristic
393C22×C3C4×#6711yescharacteristic
394C22×C3#95311yescharacteristic
395C2×D3—22no—
396C2×D3—41no—
397C2×D3—41no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—42no—
403C3×C4—42no—
404C3×C4—62no—
405C3×C4—82no—
406C3×C4—121no—
407C3×C4—121no—
408C3×C4#67⋊C411yescharacteristic
409C3×C4#88311yescharacteristic
410C3×C4D3×C4⋊C411yescharacteristic
411C3×C4#89611yescharacteristic
412C3×C4C2×Dic3⋊C411yescharacteristic
413C3×C4#92411yescharacteristic
414C3×C4C4×#6711yescharacteristic
415C3×C4#92911yescharacteristic
416Dic3—22no—
417Dic3—41no—
418Dic3—41no—
419Dic3—68no—
420Dic3—64no—
421Dic3—64no—
422Dic3—242no—
423Dic3—241no—
424Dic3—241no—
425C32#185911yescharacteristic, complemented, Sylow
426C23—61no—
427C23C2×#62611yescharacteristic
428Q8—32no—
429Q8—61no—
430D4—32no—
431D4—62no—
432D4—62no—
433D4—61no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—61no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4—242no—
445C2×C4—362no—
446C2×C4—361no—
447C2×C4D3×Dic611yescharacteristic
448C2×C4#379511yescharacteristic
449C2×C4#379811yescharacteristic
450C2×C4C4×D3211yescharacteristic
451C2×C4D3×#6711yescharacteristic
452C2×C4D3×#6711yescharacteristic
453C8—62no—
454C8—121no—
455C2×C3—22no—
456C2×C3—22no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—122no—
465C2×C3#466811yescharacteristic
466C2×C3#474711yescharacteristic
467C2×C3#475211yescharacteristic
468C2×C3#521011yescharacteristic
469C2×C3#524111yescharacteristic
470C2×C3#524611yescharacteristic
471D3—42no—
472C22—21no—
473C22—21no—
474C22—62no—
475C22—121no—
476C22—121no—
477C22#6385711yescharacteristic
478C22C4×#62611yescharacteristic
479C22#6397711yescharacteristic
480C4—42no—
481C4—62no—
482C4—121no—
483C4—121no—
484C4—184no—
485C4—721no—
486C4#6385111yescharacteristic
487C4D3×Dic3⋊C411yescharacteristic
488C4#6387911yescharacteristic
489C4#6390511yescharacteristic
490C3—21no—
491C3#6900211yescharacteristic, complemented
492C3#7166411yescharacteristic, complemented
493C2—21no—
494C2—21no—
495C2—122no—
496C2#1059127811yescharacteristic
497C2#1059151011yescharacteristic
498C2#1059164911yescharacteristic
subgroupG/H
centerC22#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC2×C3×#235C22
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. #10592674C2semidirect
3. #10591131C2semidirect
6. C3×#4530C2semidirect
7. #10589160C2semidirect
25. #63568C4semidirect
42. #4530D3semidirect
62. C4×C3⋊Dic3C2×C4semidirect
73. C3×#208C2×C4semidirect
138. C3×D12C4⋊C4semidirect
143. C3×Dic6C4⋊C4semidirect
227. #208C4×D3semidirect
328. D12Dic3⋊C4semidirect
333. Dic6Dic3⋊C4semidirect
425. C32#1859semidirect
491. C3#69002semidirect
492. C3#71664semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
#105926742
#105911312
C2×#635682
#105910882
C3×#45302
#105891602
#716643
#690023