Finite Group Databasebeta

← #11794286

Subgroups — #11794286

Order 1152.

519 conjugacy classes of subgroups.

The subgroup lattice has 431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595051C211yesmaximal, characteristic
2#10592663C211yesmaximal, characteristic
3C3×#4977C211yesmaximal, characteristic
4C3×#4964C211yesmaximal, characteristic
5#10589167C211yesmaximal, characteristic
6#10589162C211yesmaximal, characteristic
7#10589161C211yesmaximal, characteristic
8#70667—31nomaximal
9#69543—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11#64135C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63964—22no—
18#63919—21no—
19#63918—21no—
20#63872—21no—
21#63869—21no—
22#63635—21no—
23#63634—21no—
24C3×C3⋊#95—22no—
25C3×#808—21no—
26C3×#807—21no—
27#5519—31no—
28#5500—31no—
29C3×#428—31no—
30C3×#382—31no—
31#4977D311yescharacteristic
32#4964—31no—
33#4964—31no—
34#4964—61no—
35#4964D311yescharacteristic
36#4555—31no—
37#4554—31no—
38#4532—31no—
39#4530—31no—
40#4523—31no—
41#4523—31no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3×Dic3—21no—
45C22×C3×Dic3D412yes—
46C2×#627—22no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49#3757—21no—
50C4⋊(C3⋊Dic3)D411yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C4×C3⋊Dic3—21no—
53#3748—21no—
54#3748Q812yescomplemented
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4×Dic3—21no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3Q812yescomplemented
64C3×#208—21no—
65C3×#208Q812yescomplemented
66C2×C3×C3⋊C8—21no—
67#3724—22no—
68Dic3⋊Dic3—22no—
69Dic3⋊Dic3—22no—
70#2061—91noSylow
71C2×C3×M16—31no—
72C3×#117—31no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C42—31no—
78#926—31no—
79#926—31no—
80#926—61no—
81#926C2×D311yescharacteristic
82C2×C4⋊Dic3C2×D311yescharacteristic
83#924—62no—
84C2×C4×Dic3C2×D311yescharacteristic
85C2×#208—31no—
86C2×#208—31no—
87C2×#208—61no—
88C2×#208C2×D311yescharacteristic
89#890—61no—
90#890—61no—
91#890—61no—
92#888—61no—
93#888—61no—
94#888—61no—
95#878—62no—
96#870—61no—
97#869—61no—
98C3×#107—61no—
99C3×#106—61no—
100C3×#95—62no—
101C3⋊#95—22no—
102#808—21no—
103#808—61no—
104#808—61no—
105#808—62no—
106#807—21no—
107#807—61no—
108#807—61no—
109#807—62no—
110C23×C32C2×D411yescharacteristic
111C2×C32×C4—41no—
112C2×C32×C4—42no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×Q811yescharacteristic
116C2×C32×C4C2×Q811yescharacteristic
117C2×C32×C4C2×Q811yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—42no—
128#627—82no—
129C3⋊(C3⋊C8)—22no—
130C3×C3⋊C8—22no—
131#544—91no—
132#428—31no—
133#428—91no—
134#382—31no—
135#343—91no—
136#339—91no—
137#339—91no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—32no—
142C22×C3×C4—41no—
143C22×C3×C4—61no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×Dic3—21no—
147C22×Dic3#6712yes—
148C2×Dic6—62no—
149C2×Dic6—62no—
150C3×M16—32no—
151C3×M16—61no—
152C2×C3×C8—61no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—41no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C22⋊C4—61no—
164C3×C42—32no—
165C3×C42—61no—
166C3×C42—61no—
167#217—21no—
168#217—61no—
169#217—61no—
170#217—121no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—31no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—62no—
180C4⋊Dic3—62no—
181C4⋊Dic3#6711yescharacteristic
182C4⋊Dic3#6711yescharacteristic
183Dic3⋊C4—62no—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186Dic3⋊C4—62no—
187C4×Dic3—21no—
188C4×Dic3—21no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C4×Dic3—121no—
192C4×Dic3Dic612yescomplemented
193#208—21no—
194#208—32no—
195#208—32no—
196#208—62no—
197#208—62no—
198#208—61no—
199#208—61no—
200#208Dic612yescomplemented
201C2×C3⋊C8—21no—
202C2×C3⋊C8—62no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C22×C32—21no—
206C22×C32—21no—
207C22×C32#12011yescharacteristic
208C22×C32C22⋊Q811yescharacteristic
209C22×C32C4⋊Q811yescharacteristic
210C32×C4—81no—
211C32×C4C22⋊Q811yescharacteristic
212C32×C4C22⋊Q811yescharacteristic
213C32×C4C4⋊Q811yescharacteristic
214C32×C4C4⋊Q811yescharacteristic
215C3⋊Dic3—41no—
216C3⋊Dic3—41no—
217C3×Dic3—42no—
218C3×Dic3—41no—
219C3×Dic3—41no—
220C3×Dic3—42no—
221C2×M16—31no—
222C2×M16—91no—
223C4⋊Q8—181no—
224C4⋊Q8—181no—
225#125—181no—
226#125—181no—
227C22⋊Q8—182no—
228#117—31no—
229#117—91no—
230C2×C4⋊C4—31no—
231C2×C4⋊C4D3211yescharacteristic
232C2×C42—31no—
233#107—61no—
234#107—181no—
235#106—61no—
236#106—181no—
237#95—62no—
238C23×C3—21no—
239C23×C3D3×D411yescharacteristic
240C23×C3C2×#6711yescharacteristic
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—42no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—62no—
253C2×C3×C4—61no—
254C2×C3×C4—62no—
255C2×C3×C4—61no—
256C2×C3×C4—82no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4—122no—
260C2×C3×C4C2×Dic611yescharacteristic
261C2×C3×C4C2×Dic611yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×Q811yescharacteristic
268C2×C3×C4D3×Q811yescharacteristic
269C2×C3×C4D3×Q811yescharacteristic
270C2×C3×C4D3×Q811yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—22no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—22no—
276C2×Dic3—41no—
277C2×Dic3—41no—
278C2×Dic3—42no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285Dic6—242no—
286Dic6—242no—
287C3×C8—62no—
288C3⋊C8—22no—
289C3⋊C8—64no—
290C3⋊C8—62no—
291C3⋊C8—62no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32#39511yescharacteristic
295C2×C32#45411yescharacteristic
296C2×C32#45511yescharacteristic
297C2×Q8—182no—
298C22×C4—21no—
299C22×C4—32no—
300C22×C4—61no—
301C22×C4C2×D3211yescharacteristic
302M16—32no—
303M16—61no—
304M16—92no—
305M16—181no—
306C2×C8—61no—
307C2×C8—181no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—31no—
311C4⋊C4—31no—
312C4⋊C4—61no—
313C4⋊C4—61no—
314C4⋊C4—91no—
315C4⋊C4—91no—
316C4⋊C4—182no—
317C4⋊C4—182no—
318C4⋊C4—182no—
319C22⋊C4—61no—
320C22⋊C4—181no—
321C42—32no—
322C42—61no—
323C42—61no—
324C42—181no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3#88811yescharacteristic
335C22×C3#89611yescharacteristic
336C22×C3#92411yescharacteristic
337C22×C3#93711yescharacteristic
338C22×C3#93711yescharacteristic
339C22×C3#94411yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—82no—
345C3×C4—81no—
346C3×C4—81no—
347C3×C4—122no—
348C3×C4—122no—
349C3×C4—121no—
350C3×C4—121no—
351C3×C4#88811yescharacteristic
352C3×C4#88811yescharacteristic
353C3×C4#88811yescharacteristic
354C3×C4#89611yescharacteristic
355C3×C4#89611yescharacteristic
356C3×C4#89611yescharacteristic
357C3×C4#92411yescharacteristic
358C3×C4#94411yescharacteristic
359Dic3—42no—
360Dic3—41no—
361Dic3—41no—
362Dic3—42no—
363Dic3—121no—
364Dic3—121no—
365Dic3—121no—
366Dic3—121no—
367Dic3—241no—
368Dic3—241no—
369C32#206111yescharacteristic, complemented, Sylow
370C23D3×#6711yescharacteristic
371Q8—722no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—62no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—62no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4—122no—
381C2×C4—181no—
382C2×C4—181no—
383C2×C4D3×Dic611yescharacteristic
384C2×C4D3×Dic611yescharacteristic
385C2×C4#379711yescharacteristic
386C2×C4#379811yescharacteristic
387C2×C4D3×#6711yescharacteristic
388C2×C4#381111yescharacteristic
389C8—62no—
390C8—182no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3#497911yescharacteristic
401C2×C3#497911yescharacteristic
402C2×C3#506111yescharacteristic
403C2×C3#506211yescharacteristic
404C2×C3#520111yescharacteristic
405C2×C3#520211yescharacteristic
406C22—21no—
407C22—21no—
408C22#6383911yescharacteristic
409C22#6385111yescharacteristic
410C22#6398311yescharacteristic
411C4—81no—
412C4—122no—
413C4—121no—
414C4—122no—
415C4—121no—
416C4—361no—
417C4—361no—
418C4#6383911yescharacteristic
419C4#6384011yescharacteristic
420C4#6385111yescharacteristic
421C4#6386511yescharacteristic
422C3—21no—
423C3#6954311yescharacteristic, complemented
424C3#7066711yescharacteristic, complemented
425C2—21no—
426C2—21no—
427C2#1059119511yescharacteristic
428C2#1059152511yescharacteristic
429C2#1059165911yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#2061
LCSG ▷ C22×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
54. #3748Q8semidirect
63. C3×C4×Dic3Q8semidirect
65. C3×#208Q8semidirect
192. C4×Dic3Dic6semidirect
200. #208Dic6semidirect
369. C32#2061semidirect
423. C3#69543semidirect
424. C3#70667semidirect

Maximal subgroups

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

subgroupindex
#105950512
#105926632
C3×#49772
C3×#49642
#105891672
#105891622
#105891612
#706673
#695433