Finite Group Databasebeta

← #11785329

Subgroups — #11785329

Order 1152.

779 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic
2C4×#3724C211yesmaximal, characteristic, complemented
3#10591120C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal
5C3×#4532C212yesmaximal, complemented
6#68770—32nomaximal
7C2×#3828C2211yescharacteristic
8C32×#117C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10#64102C411yescharacteristic, complemented
11#64102C411yescharacteristic, complemented
12#64096C411yescharacteristic, complemented
13#64096C411yescharacteristic, complemented
14#64090—21no—
15#64090—21no—
16#64081—21no—
17C42×C3⋊D3—21no—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×#208C2212yes—
20C2×#3724—21no—
21#63579—21no—
22#63572—21no—
23#63572—21no—
24#63570—24no—
25#5522—32no—
26#5522—61no—
27C2×#825—32no—
28#5118—32no—
29C4×Dic3⋊C4—32no—
30C2×#805—32no—
31C3×#339—32no—
32#4532D312yescomplemented
33C22×C32×C4C2311yescharacteristic
34C2×#638—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37#3828—21no—
38#3828—21no—
39#3828D412yes—
40#3828Q812yes—
41C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—21no—
45C2×#634C2×C411yescharacteristic
46C22×C3×Dic3—22no—
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42—21no—
51#3752—21no—
52#3752—21no—
53#3750—21no—
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3C2×C411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C3×C4×Dic3—22no—
62C3×C4×Dic3—22no—
63C3×#208—22no—
64C3×#208—22no—
65C2×C3×C3⋊C8—22no—
66#3724—24no—
67#1806—91noSylow
68C2×#235—32no—
69C2×#235—61no—
70C2×C3×M16—32no—
71C3×#117—21no—
72C3×#117C2×D312yes—
73C2×C3×C42—32no—
74C2×Dic3⋊C4—62no—
75C2×C4×Dic3—32no—
76C2×C4×Dic3—61no—
77C2×C4×Dic3C2×D312yes—
78C2×#208C2×D312yes—
79#893—32no—
80#893—32no—
81#893—61no—
82#893—61no—
83#887—32no—
84#887—32no—
85#887—61no—
86#887—61no—
87#67⋊C4—62no—
88#67⋊C4—62no—
89#67⋊C4—62no—
90#67⋊C4—62no—
91#872—62no—
92#872—62no—
93C42×D3—62no—
94C42×D3—62no—
95C3⋊#95—62no—
96#825—64no—
97Dic3⋊C8—62no—
98Dic3⋊C8—62no—
99#805—64no—
100C23×C32C2×D411yescharacteristic
101C22×C3⋊D3—21no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×Q811yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110#638—22no—
111#638—22no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3C22⋊C411yescharacteristic
116C2×C3⋊Dic3C22⋊C411yescharacteristic
117C2×C3⋊Dic3C22⋊C411yescharacteristic
118C2×C3⋊Dic3C22⋊C411yescharacteristic
119C4⋊(C3⋊D3)—21no—
120C4⋊(C3⋊D3)C4⋊C412yescomplemented
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3—42no—
124C4×C3⋊D3—42no—
125#634—21no—
126#634C4⋊C412yescomplemented
127C2×C3×Dic3—24no—
128C2×C3×Dic3—42no—
129C2×C3×Dic3—42no—
130C3×C3⋊C8—42no—
131C4×#41—91no—
132#423—91no—
133C2×#104—92no—
134C4×C4⋊C4—91no—
135#339—32no—
136C22×C3×C4—21no—
137C22×C3×C4—62no—
138C22×C3×C4C22×D312yes—
139C2×#67—62no—
140C2×#67—62no—
141C22×Dic3—22no—
142C22×Dic3—32no—
143C22×Dic3—32no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146#235—34no—
147#235—34no—
148#235—62no—
149#235—62no—
150#235—62no—
151#235—62no—
152#235—62no—
153#235—62no—
154C2×D12—32no—
155C2×D12—61no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×C4×D3—62no—
161C2×C4×D3—62no—
162C2×Dic6—32no—
163C2×Dic6—61no—
164C3×M16—62no—
165C3×M16—62no—
166C2×C3×C8—62no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4C4×D312yes—
170C3×C4⋊C4C4×D312yes—
171C3×C22⋊C4—22no—
172C3×C22⋊C4—22no—
173C3×C42—22no—
174C3×C42—22no—
175C3×C42—62no—
176C3×C42—62no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181Dic3⋊C4—68no—
182Dic3⋊C4—62no—
183Dic3⋊C4—62no—
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186C4×Dic3—22no—
187C4×Dic3—22no—
188C4×Dic3—32no—
189C4×Dic3—32no—
190C4×Dic3—32no—
191C4×Dic3—32no—
192C4×Dic3—61no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3—62no—
197C4×Dic3—62no—
198C4×Dic3—62no—
199C4×Dic3—62no—
200#208—22no—
201#208—22no—
202C2×C3⋊C8—22no—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32C2×C22⋊C411yescharacteristic
206C22×C32#12111yescharacteristic
207C22×C32C22⋊Q811yescharacteristic
208C2×C3⋊D3—22no—
209C2×C3⋊D3—41no—
210C2×C3⋊D3—41no—
211C32×C4—41no—
212C32×C4—41no—
213C32×C4C2×C4⋊C411yescharacteristic
214C32×C4#11711yescharacteristic
215C32×C4#12111yescharacteristic
216C32×C4C22⋊Q811yescharacteristic
217C3⋊Dic3—22no—
218C3⋊Dic3—21no—
219C3⋊Dic3—21no—
220C3⋊Dic3—21no—
221C3⋊Dic3#10412yescomplemented
222C3×Dic3—44no—
223C2×#41—91no—
224C2×M16—32no—
225C4×Q8—91no—
226C4×Q8—91no—
227C4×D4—91no—
228C4×D4—91no—
229C4×D4—181no—
230C4×D4—181no—
231#117—181no—
232#117D3211yescharacteristic
233C2×C4⋊C4—181no—
234C2×C42—32no—
235C2×C42—91no—
236C2×C42—181no—
237C4⋊C8—181no—
238C4⋊C8—181no—
239#104—184no—
240#95—181no—
241C23×C3—21no—
242C23×C3D3×D412yes—
243C22×D3—62no—
244C22×D3—62no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—64no—
256C2×C3×C4—122no—
257C2×C3×C4—122no—
258C2×C3×C4C2×C4×D312yes—
259C2×C3×C4#23512yes—
260C2×C3×C4#23512yes—
261C2×C3×C4D3×D412yes—
262C2×C3×C4D3×D412yes—
263C2×C3×C4D3×Q812yes—
264#67—64no—
265#67—64no—
266#67—64no—
267#67—64no—
268C2×Dic3—24no—
269C2×Dic3—32no—
270C2×Dic3—32no—
271C2×Dic3—32no—
272C2×Dic3—32no—
273C2×Dic3—42no—
274C2×Dic3—42no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—64no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—122no—
283C2×Dic3—122no—
284C2×Dic3—122no—
285D12—34no—
286D12—62no—
287D12—62no—
288D12—62no—
289C4×D3—64no—
290C4×D3—64no—
291C4×D3—64no—
292C4×D3—64no—
293C4×D3—124no—
294C4×D3—124no—
295C4×D3—124no—
296C4×D3—124no—
297Dic6—34no—
298Dic6—62no—
299Dic6—62no—
300Dic6—62no—
301C3×C8—122no—
302C3⋊C8—42no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32#38011yescharacteristic
306C2×C32C2×#10411yescharacteristic
307C2×C32#42111yescharacteristic
308C3⋊D3—42no—
309#41—92no—
310#41—92no—
311#41—181no—
312#41—181no—
313C2×Q8—91no—
314C2×D4—91no—
315C2×D4—181no—
316C22×C4—62no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—181no—
320C22×C4—181no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323M16—62no—
324M16—62no—
325C2×C8—62no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—184no—
329C4⋊C4#62411yescharacteristic
330C4⋊C4#62411yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—181no—
333C22⋊C4—181no—
334C42—21no—
335C42—62no—
336C42—62no—
337C42—91no—
338C42—91no—
339C42—91no—
340C42—91no—
341C42—181no—
342C42—181no—
343C22×C3—22no—
344C22×C3—22no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3D3×C22⋊C412yes—
351C22×C3#88412yes—
352C22×C3#89612yes—
353C2×D3—64no—
354C2×D3—64no—
355C2×D3—122no—
356C2×D3—122no—
357C2×D3—122no—
358C2×D3—122no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—42no—
366C3×C4—42no—
367C3×C4—124no—
368C3×C4#87212yes—
369C3×C4#88412yes—
370C3×C4D3×C4⋊C412yes—
371C3×C4#89612yes—
372Dic3—34no—
373Dic3—44no—
374Dic3—62no—
375Dic3—64no—
376Dic3—62no—
377Dic3—64no—
378Dic3—62no—
379Dic3—62no—
380Dic3—62no—
381Dic3—121no—
382Dic3—121no—
383C32#180611yescharacteristic, complemented, Sylow
384C23—181no—
385C23#381111yescharacteristic
386Q8—92no—
387Q8—181no—
388D4—92no—
389D4—182no—
390D4—182no—
391D4—181no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—64no—
395C2×C4—91no—
396C2×C4—91no—
397C2×C4—91no—
398C2×C4—91no—
399C2×C4—122no—
400C2×C4—122no—
401C2×C4—182no—
402C2×C4—181no—
403C2×C4—182no—
404C2×C4—182no—
405C2×C4—362no—
406C2×C4—362no—
407C2×C4—361no—
408C2×C4#379711yescharacteristic
409C2×C4#379811yescharacteristic
410C2×C4#379811yescharacteristic
411C2×C4#380211yescharacteristic
412C2×C4C2×#62411yescharacteristic
413C2×C4#381111yescharacteristic
414C8—122no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3#466712yes—
423C2×C3D3×#10412yes—
424C2×C3#482112yes—
425D3—124no—
426D3—124no—
427C22—21no—
428C22—21no—
429C22—182no—
430C22—361no—
431C22—361no—
432C22#6386511yescharacteristic
433C22#6391211yescharacteristic
434C22#6397411yescharacteristic
435C4—41no—
436C4—41no—
437C4—92no—
438C4—124no—
439C4—182no—
440C4—181no—
441C4—181no—
442C4—181no—
443C4#6386511yescharacteristic
444C4#6387411yescharacteristic
445C4#6390011yescharacteristic
446C4#6391211yescharacteristic
447C3—21no—
448C3#6877012yescomplemented
449C2—21no—
450C2—21no—
451C2—362no—
452C2#1059135511yescharacteristic
453C2#1059167111yescharacteristic
454C2#1059167211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C4×#3724C2semidirect
3. #10591120C2semidirect
5. C3×#4532C2semidirect
10. #64102C4semidirect
11. #64102C4semidirect
12. #64096C4semidirect
13. #64096C4semidirect
32. #4532D3semidirect
120. C4⋊(C3⋊D3)C4⋊C4semidirect
126. #634C4⋊C4semidirect
221. C3⋊Dic3#104semidirect
383. C32#1806semidirect
448. C3#68770semidirect

Maximal subgroups

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

subgroupindex
#105959932
C4×#37242
#105911202
C2×#635702
C3×#45322
#687703