Finite Group Databasebeta

← #11868689

Subgroups — #11868689

Order 1152.

1093 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2#10595050C211yesmaximal, characteristic, complemented
3C3×#4964C212yesmaximal, complemented
4#10591120C211yesmaximal, characteristic, complemented
5#10591096C212yesmaximal
6#10590435C214yesmaximal, complemented
7#10590433C212yesmaximal, complemented
8#10590430C212yesmaximal, complemented
9#79239—32nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—21no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64102—21no—
16#64102—21no—
17#64102C2212yes—
18#64102C2212yes—
19C3×#926C2212yes—
20C2×C3×#208C2212yes—
21#63982—21no—
22#63982—21no—
23#63919C2211yescharacteristic, complemented
24#63919C2211yescharacteristic, complemented
25C4×#627—21no—
26C4×#627—21no—
27#63872C2212yescomplemented
28C3×#808C2214yescomplemented
29C3×#807C2214yescomplemented
30#63572C2212yescomplemented
31#63572C2212yescomplemented
32#63564C2214yes—
33#63564C2214yes—
34#5517—32no—
35C2×#893—32no—
36C2×#893—61no—
37C3×#428—32no—
38#5131—32no—
39#5118—32no—
40#5001—32no—
41#4964D312yescomplemented
42#4891—34no—
43#4890—34no—
44#4871—34no—
45#4870—34no—
46C23×C3⋊D3—21no—
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3D411yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)Q814yescomplemented
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—44no—
58C2×#627—21no—
59C2×#627—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62#3752—22no—
63#3752—22no—
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3D411yescharacteristic
66C4×C3⋊Dic3C2311yescharacteristic
67C4×C3⋊Dic3C2311yescharacteristic
68C3×#217—22no—
69C3×C4⋊Dic3C2312yes—
70C3×C4⋊Dic3C2312yes—
71C3×C4×Dic3—22no—
72C3×#208—24no—
73C2×C3×C3⋊C8C2314yes—
74#3724—21no—
75#3724—21no—
76Dic3⋊Dic3—22no—
77Dic3⋊Dic3—22no—
78#3077—91noSylow
79C22×D12—32no—
80C22×D12—61no—
81C22×C4×D3—62no—
82C22×C4×D3—62no—
83C2×C3×M16—32no—
84C3×#117—32no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4C2×D312yes—
87C2×(C2×D3)⋊C4—62no—
88C2×(C2×D3)⋊C4—62no—
89#926C2×D312yes—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—61no—
92C2×#208C2×D312yes—
93#893—34no—
94#893—34no—
95#893—62no—
96#893—62no—
97#893—62no—
98#893—62no—
99#893—62no—
100#893—62no—
101#890—32no—
102#890—32no—
103#888—32no—
104#888—32no—
105#878—62no—
106#878—62no—
107C4×Dic6—62no—
108C4×Dic6—62no—
109C3×#107—34no—
110C3×#106—34no—
111#821—34no—
112#821—34no—
113Dic3⋊C8—34no—
114Dic3⋊C8—34no—
115#809—34no—
116#809—34no—
117#808C2×D314yescomplemented
118#807C2×D314yescomplemented
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—24no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3—42no—
123C22×C3⋊D3—42no—
124C2×C32×C4—22no—
125C2×C32×C4—42no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q812yes—
128C2×C32×C4#4112yes—
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3C2×D411yescharacteristic
133C2×C3⋊Dic3C2×D411yescharacteristic
134C2×C3⋊Dic3C2×D411yescharacteristic
135C2×C3⋊Dic3C2×D411yescharacteristic
136C4⋊(C3⋊D3)—24no—
137C4⋊(C3⋊D3)—22no—
138C4⋊(C3⋊D3)C2×Q814yes—
139C4×C3⋊D3—44no—
140C4×C3⋊D3—44no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143#627—42no—
144#627—42no—
145C3×C3⋊C8—24no—
146#533—91no—
147C2×C4×D4—91no—
148#478—94no—
149#476—92no—
150#474—92no—
151#428—32no—
152#423—91no—
153#418—92no—
154C23×D3—62no—
155C23×D3—62no—
156C22×C3×C4—22no—
157C22×C3×C4—22no—
158C22×C3×C4—21no—
159C22×C3×C4C22×D312yes—
160C22×Dic3—32no—
161C22×Dic3—32no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C2×D12—38no—
165C2×D12—34no—
166C2×D12—62no—
167C2×D12—64no—
168C2×D12—62no—
169C2×D12—64no—
170C2×D12—64no—
171C2×D12—62no—
172C2×C4×D3—64no—
173C2×C4×D3—64no—
174C2×C4×D3—64no—
175C2×C4×D3—64no—
176C2×C4×D3—128no—
177C2×C4×D3—128no—
178C2×Dic6—62no—
179C2×Dic6—62no—
180C3×M16—64no—
181C2×C3×C8—34no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—32no—
186C3×C4⋊C4—32no—
187C3×C4⋊C4C22×D314yes—
188C3×C22⋊C4—62no—
189C3×C42—62no—
190#217—22no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—64no—
195C4⋊Dic3—62no—
196C4⋊Dic3—62no—
197C4⋊Dic3C22×D312yes—
198C4⋊Dic3C22×D312yes—
199Dic3⋊C4—62no—
200Dic3⋊C4—62no—
201Dic3⋊C4—62no—
202Dic3⋊C4—62no—
203C4×Dic3—22no—
204C4×Dic3—32no—
205C4×Dic3—32no—
206C4×Dic3—32no—
207C4×Dic3—32no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212#208—24no—
213C2×C3⋊C8C22×D314yes—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32C22⋊Q812yes—
217C22×C32C22×D411yescharacteristic
218C2×C3⋊D3—24no—
219C2×C3⋊D3—48no—
220C2×C3⋊D3—42no—
221C2×C3⋊D3—42no—
222C32×C4—42no—
223C32×C4C22⋊Q812yes—
224C32×C4C22×Q811yescharacteristic
225C32×C4C2×#4111yescharacteristic
226C3⋊Dic3—21no—
227C3⋊Dic3—21no—
228C3⋊Dic3—21no—
229C3⋊Dic3AGL(1,ℤ/8)12yes—
230C3×Dic3—42no—
231C3×Dic3—42no—
232C22×D4—91no—
233C23×C4—181no—
234C2×M16—32no—
235C4⋊Q8—91no—
236C4⋊Q8—91no—
237#125—92no—
238C22⋊Q8—181no—
239C22⋊Q8—181no—
240C4×Q8—181no—
241C4×Q8—181no—
242C4×D4—92no—
243C4×D4—92no—
244C4×D4—181no—
245C4×D4—181no—
246#117—32no—
247C2×C4⋊C4D3211yescharacteristic
248C2×C22⋊C4—181no—
249C2×C42—91no—
250#107—34no—
251#106—34no—
252C4⋊C8—92no—
253C4⋊C8—92no—
254#102—94no—
255#102—94no—
256C23×C3—21no—
257C23×C3D3×D412yes—
258C22×D3—64no—
259C22×D3—68no—
260C22×D3—68no—
261C22×D3—64no—
262C22×D3—124no—
263C22×D3—124no—
264C22×D3—124no—
265C22×D3—124no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—44no—
273C2×C3×C4—44no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4#23514yes—
277C2×C3×C4D3×D412yes—
278C2×C3×C4D3×Q814yes—
279C2×C3×C4C23×D312yes—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—32no—
283C2×Dic3—32no—
284C2×Dic3—32no—
285C2×Dic3—32no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—64no—
291C2×Dic3—64no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294D12—38no—
295D12—64no—
296D12—64no—
297D12—68no—
298D12—68no—
299D12—64no—
300C4×D3—128no—
301C4×D3—128no—
302C4×D3—128no—
303C4×D3—128no—
304Dic6—124no—
305Dic6—124no—
306C3×C8—64no—
307C3⋊C8—24no—
308C2×C32—22no—
309C2×C32C2×C22⋊Q811yescharacteristic
310C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
311C2×C32#57511yescharacteristic
312C3⋊D3—44no—
313C24—181no—
314C2×Q8—181no—
315C2×Q8—181no—
316C2×D4—92no—
317C2×D4—94no—
318C2×D4—182no—
319C2×D4—181no—
320C22×C4—21no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—182no—
324C22×C4—182no—
325C22×C4—364no—
326C22×C4C2×D3211yescharacteristic
327M16—64no—
328C2×C8—34no—
329C4⋊C4—21no—
330C4⋊C4—32no—
331C4⋊C4—32no—
332C4⋊C4—182no—
333C4⋊C4—182no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4C2×D3212yes—
337C22⋊C4—62no—
338C22⋊C4—182no—
339C22⋊C4—182no—
340C42—62no—
341C42—91no—
342C42—91no—
343C42—91no—
344C42—91no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—21no—
350C22×C3—22no—
351C22×C3#89614yes—
352C22×C3C2×D3×D412yes—
353C2×D3—68no—
354C2×D3—68no—
355C2×D3—124no—
356C2×D3—1216no—
357C2×D3—1216no—
358C2×D3—124no—
359C2×D3—124no—
360C2×D3—124no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—22no—
364C3×C4—44no—
365C3×C4—44no—
366C3×C4—122no—
367C3×C4—122no—
368C3×C4#89614yes—
369C3×C4C2×#23512yes—
370C3×C4C2×D3×Q812yes—
371Dic3—34no—
372Dic3—42no—
373Dic3—42no—
374Dic3—62no—
375Dic3—62no—
376Dic3—62no—
377Dic3—62no—
378Dic3—62no—
379Dic3—121no—
380Dic3—121no—
381C32#307711yescharacteristic, complemented, Sylow
382C23—182no—
383C23—184no—
384C23—362no—
385C23—362no—
386C23#381111yescharacteristic
387Q8—362no—
388Q8—362no—
389D4—94no—
390D4—182no—
391D4—184no—
392C2×C4—22no—
393C2×C4—42no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—91no—
397C2×C4—91no—
398C2×C4—91no—
399C2×C4—91no—
400C2×C4—182no—
401C2×C4—364no—
402C2×C4—364no—
403C2×C4—361no—
404C2×C4#379712yes—
405C2×C4#379812yes—
406C2×C4#381111yescharacteristic
407C2×C4C22×D3211yescharacteristic
408C8—64no—
409C2×C3—24no—
410C2×C3—24no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3C2×#89612yes—
415C2×C3D3×AGL(1,ℤ/8)12yes—
416C2×C3#577712yes—
417D3—128no—
418D3—128no—
419C22—21no—
420C22—21no—
421C22—184no—
422C22—368no—
423C22—362no—
424C22—362no—
425C22#6386512yes—
426C22C2×#381111yescharacteristic
427C4—42no—
428C4—92no—
429C4—122no—
430C4—122no—
431C4—181no—
432C4—181no—
433C4—181no—
434C4#6386512yes—
435C4C2×#379711yescharacteristic
436C4C2×#379811yescharacteristic
437C3—21no—
438C3#7923912yescomplemented
439C2—22no—
440C2—364no—
441C2C2×#6386511yescharacteristic
442C2#1059510011yescharacteristic
443C2#1059532311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3077
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. #10595050C2semidirect
3. C3×#4964C2semidirect
4. #10591120C2semidirect
6. #10590435C2semidirect
7. #10590433C2semidirect
8. #10590430C2semidirect
23. #63919C22semidirect
24. #63919C22semidirect
27. #63872C22semidirect
28. C3×#808C22semidirect
29. C3×#807C22semidirect
30. #63572C22semidirect
31. #63572C22semidirect
41. #4964D3semidirect
53. C2×C4⋊(C3⋊D3)Q8semidirect
117. #808C2×D3semidirect
118. #807C2×D3semidirect
381. C32#3077semidirect
438. C3#79239semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
#105950502
C3×#49642
#105911202
#105910962
#105904352
#105904332
#105904302
#792393