Finite Group Databasebeta

← #11868403

Subgroups — #11868403

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 449 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2#10593909C211yesmaximal, characteristic
3C3×#5020C212yesmaximal, complemented
4#10591630C212yesmaximal, complemented
5#10591552C212yesmaximal
6#10590575C212yesmaximal
7#10590431C212yesmaximal, complemented
8#10590331C211yesmaximal, characteristic
9#10590307C212yesmaximal, complemented
10D3×#475—32nomaximal
11C2×Q8×C3⋊D3C2211yescharacteristic
12C2×#3797—21no—
13C32×C4×Q8C2211yescharacteristic
14Q8×C3⋊Dic3C2211yescharacteristic
15C4⋊C4×C3⋊D3—21no—
16C4⋊C4×C3⋊D3C2211yescharacteristic
17#64096—21no—
18#64096C2211yescharacteristic
19C42×C3⋊D3—21no—
20C42×C3⋊D3C2211yescharacteristic
21C4×#634—21no—
22C4×#634C2211yescharacteristic
23C3×#869C2212yes—
24#63919—21no—
25#63919C2212yes—
26#63900—21no—
27#63900C2212yes—
28#63873—21no—
29C2×#3710C2212yes—
30C3×#835C2214yes—
31C3×#808C2214yes—
32C3×C4⋊(C3⋊C8)C2212yes—
33#63573C2214yes—
34#63572C2212yes—
35#63567C2214yes—
36D3×C4⋊Q8—32no—
37C4×D3×Q8—32no—
38C4×D3×Q8—61no—
39C3×#475—32no—
40#5094—32no—
41#5020D312yescomplemented
42D3×#106—34no—
43#4854—34no—
44#4851—32no—
45D3×C4⋊C8—32no—
46D3×#103—34no—
47#4791—34no—
48C2×C32×Q8C2311yescharacteristic
49Q8×C3⋊D3—22no—
50Q8×C3⋊D3Q814yescomplemented
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3C2311yescharacteristic
56C2×#634—21no—
57C2×#634C2311yescharacteristic
58C2×C3×Dic6—22no—
59C2×#627—22no—
60C2×#624—22no—
61#3797—44no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4C2311yescharacteristic
64C32×C42—21no—
65C32×C42C2311yescharacteristic
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2311yescharacteristic
68#3750—21no—
69#3750—21no—
70#3750—21no—
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3—21no—
73C4×C3⋊Dic3—21no—
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3D411yescharacteristic
76C4×C3⋊Dic3C2311yescharacteristic
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2314yes—
79C2×C3×C3⋊C8C2314yes—
80#3724—22no—
81#3724—22no—
82#3710—24no—
83C2×#475—91noSylow
84C2×D3×Q8—32no—
85C2×D3×Q8—61no—
86C2×D3×Q8—62no—
87C3×C4⋊Q8—32no—
88C3×C4×Q8—21no—
89C3×C4×Q8C2×D312yes—
90Q8×Dic3—32no—
91Q8×Dic3—61no—
92#944—62no—
93C2×D3×C8—34no—
94D3×C4⋊C4—32no—
95D3×C4⋊C4—34no—
96D3×C4⋊C4—61no—
97D3×C4⋊C4—62no—
98D3×C4⋊C4—62no—
99D3×C4⋊C4—62no—
100#888—34no—
101#888—62no—
102#887—32no—
103#887—61no—
104#887—62no—
105#887—62no—
106C42×D3—32no—
107C42×D3—61no—
108C42×D3—62no—
109C42×D3—62no—
110#869C2×D312yes—
111C4×Dic6—32no—
112C4×Dic6—61no—
113C4×Dic6—62no—
114C4×Dic6—62no—
115C3×#106—34no—
116C3×C4⋊C8—32no—
117C3×#103—34no—
118#835C2×D314yes—
119#817—34no—
120#816—34no—
121Dic3⋊C8—34no—
122#810—34no—
123#808—34no—
124#808C2×D314yes—
125C4⋊(C3⋊C8)C2×D312yes—
126C22×C3⋊D3C2×D411yescharacteristic
127C32×Q8—21no—
128C32×Q8C2×Q812yescomplemented
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2411yescharacteristic
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3C2×D411yescharacteristic
137C2×C3⋊Dic3C2×D411yescharacteristic
138C2×C3⋊Dic3C2×D411yescharacteristic
139C4×C3⋊D3—24no—
140C4×C3⋊D3—22no—
141C4×C3⋊D3—42no—
142C4×C3⋊D3SD1614yes—
143C4×C3⋊D3C2×Q812yes—
144C4×C3⋊D3#4112yes—
145#634—21no—
146#634—24no—
147#634C2×Q812yescomplemented
148C2×C3×Dic3—24no—
149C3×Dic6—44no—
150#627—44no—
151#624—44no—
152C3×C3⋊C8—24no—
153C2×C4⋊Q8—91no—
154C2×C4×Q8—91no—
155#475—32no—
156#475—92no—
157#475—92no—
158#475—92no—
159C2×#106—92no—
160C2×C4⋊C8—91no—
161C2×#103—92no—
162C2×C3×Q8—21no—
163C2×C3×Q8—62no—
164C2×C3×Q8C22×D312yes—
165D3×Q8—38no—
166D3×Q8—64no—
167D3×Q8—64no—
168D3×Q8—64no—
169D3×Q8—128no—
170C2×C4×D3—32no—
171C2×C4×D3—32no—
172C2×C4×D3—32no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—62no—
177C2×C4×D3—62no—
178C2×C4×D3—64no—
179C2×C4×D3—62no—
180C2×C4×D3—62no—
181C2×Dic6—22no—
182C2×Dic6—32no—
183C2×Dic6—61no—
184C2×Dic6—62no—
185C2×Dic6—62no—
186C2×Dic6—64no—
187C2×C3×C8—34no—
188C3×C4⋊C4—22no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—34no—
192C3×C4⋊C4—62no—
193C3×C4⋊C4C22×D312yes—
194C3×C42—22no—
195C3×C42—22no—
196C3×C42—21no—
197C3×C42C22×D312yes—
198C4⋊Dic3—22no—
199C4⋊Dic3—32no—
200C4⋊Dic3—61no—
201C4⋊Dic3—62no—
202C4⋊Dic3—62no—
203C4⋊Dic3C22×D314yes—
204Dic3⋊C4—64no—
205Dic3⋊C4—64no—
206Dic3⋊C4—62no—
207Dic3⋊C4—62no—
208Dic3⋊C4—62no—
209Dic3⋊C4—62no—
210Dic3⋊C4—62no—
211Dic3⋊C4—62no—
212C4×Dic3—32no—
213C4×Dic3—32no—
214C4×Dic3—32no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—62no—
219C4×Dic3—62no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C4×Dic3—62no—
223C4×Dic3—62no—
224C2×C3⋊C8C22×D314yes—
225D3×C8—68no—
226C22×C32C22×D411yescharacteristic
227C2×C3⋊D3C22⋊Q812yes—
228C2×C3⋊D3C2×SD1612yes—
229C2×C3⋊D3#13712yes—
230C32×C4—22no—
231C32×C4—21no—
232C32×C4—41no—
233C32×C4C2×SD1612yes—
234C32×C4C22×Q811yescharacteristic
235C32×C4C2×#4111yescharacteristic
236C3⋊Dic3—22no—
237C3⋊Dic3—21no—
238C3⋊Dic3—41no—
239C3⋊Dic3C22⋊Q812yes—
240C3⋊Dic3C2×SD1612yes—
241C3×Dic3—44no—
242C22×Q8—91no—
243C22×Q8—181no—
244C22×C8—92no—
245C4⋊Q8—32no—
246C4⋊Q8—92no—
247C4⋊Q8—181no—
248C4⋊Q8—181no—
249C4×Q8—91no—
250C4×Q8—91no—
251C4×Q8—91no—
252C4×Q8—181no—
253C4×Q8—181no—
254C4×Q8D3211yescharacteristic
255C2×C4⋊C4—92no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—181no—
258C2×C4⋊C4—181no—
259C2×C42—91no—
260C2×C42—181no—
261#106—34no—
262#106—94no—
263C4⋊C8—32no—
264C4⋊C8—92no—
265#103—34no—
266#103—94no—
267C22×D3—32no—
268C22×D3—61no—
269C3×Q8—22no—
270C3×Q8—22no—
271C3×Q8—22no—
272C3×Q8—124no—
273C3×Q8D3×Q814yescomplemented
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—64no—
282C2×C3×C4D3×D412yes—
283C2×C3×C4D3×D412yes—
284C2×C3×C4C23×D312yes—
285C2×Dic3—24no—
286C2×Dic3—32no—
287C2×Dic3—32no—
288C2×Dic3—32no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C4×D3—38no—
297C4×D3—34no—
298C4×D3—34no—
299C4×D3—64no—
300C4×D3—62no—
301C4×D3—62no—
302C4×D3—64no—
303C4×D3—68no—
304C4×D3—68no—
305C4×D3—122no—
306C4×D3—128no—
307C4×D3—124no—
308C4×D3—124no—
309Dic6—34no—
310Dic6—44no—
311Dic6—62no—
312Dic6—68no—
313Dic6—68no—
314Dic6—62no—
315Dic6—62no—
316Dic6—128no—
317C3×C8—64no—
318C3⋊C8—24no—
319C2×C32C2×C22⋊Q811yescharacteristic
320C2×C32C22×SD1611yescharacteristic
321C2×C32C2×#13711yescharacteristic
322C3⋊D3#47514yescomplemented
323C2×Q8—62no—
324C2×Q8—94no—
325C2×Q8—91no—
326C2×Q8—181no—
327C2×Q8—182no—
328C2×Q8—182no—
329C2×Q8—364no—
330C2×Q8C2×D3211yescharacteristic
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—91no—
334C22×C4—181no—
335C22×C4—181no—
336C22×C4—182no—
337C2×C8—34no—
338C2×C8—184no—
339C4⋊C4—21no—
340C4⋊C4—34no—
341C4⋊C4—62no—
342C4⋊C4—91no—
343C4⋊C4—181no—
344C4⋊C4—181no—
345C4⋊C4—181no—
346C4⋊C4—182no—
347C4⋊C4—182no—
348C4⋊C4—181no—
349C4⋊C4C2×D3211yescharacteristic
350C42—21no—
351C42—91no—
352C42—91no—
353C42—91no—
354C42—181no—
355C42—181no—
356C42—181no—
357C42C2×D3211yescharacteristic
358C22×C3—21no—
359C22×C3C2×D3×D412yes—
360C2×D3—34no—
361C2×D3—34no—
362C2×D3—34no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—62no—
366C3×C4—24no—
367C3×C4—22no—
368C3×C4—24no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—22no—
372C3×C4—41no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—124no—
376C3×C4D3×SD1614yes—
377C3×C4C2×D3×Q812yes—
378C3×C4D3×#4112yes—
379Dic3—34no—
380Dic3—34no—
381Dic3—44no—
382Dic3—62no—
383Dic3—62no—
384Dic3—64no—
385Dic3—62no—
386Dic3—64no—
387Dic3—121no—
388Dic3—122no—
389Dic3—122no—
390C32C2×#47511yescharacteristic, complemented, Sylow
391C23—91no—
392Q8—21no—
393Q8—92no—
394Q8—124no—
395Q8—184no—
396Q8—181no—
397Q8—364no—
398Q8#379712yescomplemented
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—64no—
402C2×C4—91no—
403C2×C4—91no—
404C2×C4—92no—
405C2×C4—92no—
406C2×C4—94no—
407C2×C4—91no—
408C2×C4—182no—
409C2×C4—184no—
410C2×C4—181no—
411C2×C4—181no—
412C2×C4—362no—
413C2×C4—364no—
414C2×C4#381111yescharacteristic
415C2×C4#381111yescharacteristic
416C2×C4C22×D3211yescharacteristic
417C8—64no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3D3×C22⋊Q812yes—
422C2×C3C2×D3×SD1612yes—
423C2×C3D3×#13712yes—
424D3—38no—
425D3—64no—
426C22—92no—
427C22—92no—
428C22—92no—
429C22C2×#381111yescharacteristic
430C4—22no—
431C4—21no—
432C4—41no—
433C4—92no—
434C4—92no—
435C4—124no—
436C4—182no—
437C4—181no—
438C4—361no—
439C4#6394012yes—
440C4C2×#379711yescharacteristic
441C4#6430611yescharacteristic
442C3—21no—
443C3D3×#47512yescomplemented
444C2—94no—
445C2#1059492511yescharacteristic
446C2C2×#6394011yescharacteristic
447C2#1059546811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×Q8D32
hypocenterC32C2×#475
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5020C2semidirect
4. #10591630C2semidirect
7. #10590431C2semidirect
9. #10590307C2semidirect
41. #5020D3semidirect
50. Q8×C3⋊D3Q8semidirect
128. C32×Q8C2×Q8semidirect
147. #634C2×Q8semidirect
273. C3×Q8D3×Q8semidirect
322. C3⋊D3#475semidirect
390. C32C2×#475semidirect
398. Q8#3797semidirect
443. C3D3×#475semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105939092
C3×#50202
#105916302
#105915522
#105905752
#105904312
#105903312
#105903072
D3×#4753