Finite Group Databasebeta

← #11878691

Subgroups — #11878691

Order 1152.

1284 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic, complemented
2#10596067C211yesmaximal, characteristic
3C32×#448C211yesmaximal, characteristic, complemented
4#10592926C211yesmaximal, characteristic, complemented
5#10592874C212yesmaximal, complemented
6#10592861C212yesmaximal, complemented
7#10592739C211yesmaximal, characteristic, complemented
8#10592517C212yesmaximal, complemented
9#10592491C212yesmaximal, complemented
10#10592437C211yesmaximal, characteristic, complemented
11#10592417C211yesmaximal, characteristic, complemented
12#80034—34nomaximal
13C22×C32×Q8C2211yescharacteristic
14C2×#3830—21no—
15C22×#634C2211yescharacteristic
16C2×C32×SD16C2212yes—
17C32×#121C2211yescharacteristic
18#64153—21no—
19#64153—21no—
20#64153C2212yes—
21#64153C2212yes—
22C2×#3755C2212yes—
23#64149C2211yescharacteristic
24#64148—21no—
25D4×C3⋊Dic3C2211yescharacteristic
26C2×#3754C2212yes—
27#64139C2211yescharacteristic
28C2×#3750—21no—
29C2×#3750—21no—
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C2×#3744C2212yes—
32#64102C2211yescharacteristic
33#64097C2211yescharacteristic
34#64094—21no—
35#64090—21no—
36C32×#103C2212yes—
37C32×C22⋊C8C2211yescharacteristic
38#63662C2212yes—
39#63657C2211yescharacteristic
40#63643C2212yes—
41#63641C2212yes—
42C8×C3⋊Dic3C2212yes—
43#63637C2212yes—
44C2×#944—34no—
45#5596—34no—
46C3×#448D314yescomplemented
47#5227—34no—
48#5175—38no—
49#5162—38no—
50#5040—34no—
51#4818—38no—
52#4792—38no—
53#4738—34no—
54#4718—34no—
55C2×C32×Q8—21no—
56C2×C32×Q8—42no—
57C2×C32×Q8C2312yes—
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C2×#638—21no—
63C2×#638—21no—
64C2×#638—21no—
65C22×C3⋊Dic3—21no—
66C22×C3⋊Dic3—21no—
67C22×C3⋊Dic3D411yescharacteristic
68C22×C3⋊Dic3D411yescharacteristic
69#3830—44no—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×#634—21no—
73C2×#634—21no—
74C2×#634—42no—
75C2×#634C2312yes—
76C32×SD16—42no—
77C2×C32×C8C2312yes—
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80#3757—21no—
81#3755—42no—
82#3754—42no—
83#3752—21no—
84#3752—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87#3750—22no—
88#3750—22no—
89#3750—22no—
90#3750—22no—
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C2×C3⋊(C3⋊C8)C2312yes—
96#3744—42no—
97#3206—91noSylow
98C22×C3×Q8C2×D314yes—
99C2×#237—64no—
100C22×Dic6—34no—
101C2×C3×SD16C2×D318yes—
102C3×#121C2×D314yes—
103#944—38no—
104#944—38no—
105#944—64no—
106#944—64no—
107C2×#215—38no—
108#940—34no—
109#939—64no—
110D4×Dic3—34no—
111C2×#214—38no—
112#930—34no—
113C2×Dic3⋊C4—64no—
114C2×Dic3⋊C4—64no—
115C2×C4×Dic3—34no—
116C2×#204—38no—
117#893—34no—
118#888—34no—
119#885—64no—
120#67⋊C4—64no—
121C3×#103C2×D318yes—
122C3×C22⋊C8C2×D314yes—
123#835—38no—
124#830—34no—
125#816—38no—
126Dic3⋊C8—38no—
127C8×Dic3—38no—
128#810—38no—
129C23×C32—21no—
130C23×C32C2×D411yescharacteristic
131C22×C3⋊D3—21no—
132C32×Q8—22no—
133C32×Q8—22no—
134C32×Q8—42no—
135C32×D4—22no—
136C32×D4—42no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4—21no—
140C2×C32×C4—42no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2411yescharacteristic
143#638—42no—
144#638—42no—
145#638—42no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—42no—
150C2×C3⋊Dic3—42no—
151C2×C3⋊Dic3SD1614yescomplemented
152C2×C3⋊Dic3C2×D411yescharacteristic
153C2×C3⋊Dic3C2×D411yescharacteristic
154C2×C3⋊Dic3C2×D411yescharacteristic
155C2×C3⋊Dic3C2×D411yescharacteristic
156C4⋊(C3⋊D3)—22no—
157C4×C3⋊D3—42no—
158#634—22no—
159#634—22no—
160#634—42no—
161#634—42no—
162C32×C8—22no—
163C3⋊(C3⋊C8)—22no—
164#532—91no—
165C2×C4⋊Q8—91no—
166#492—92no—
167#487—92no—
168#461—92no—
169#461—92no—
170#448—91no—
171#448—91no—
172#448—91no—
173#448C3⋊D311yescharacteristic, complemented
174#431—91no—
175C2×C3×Q8—24no—
176C2×C3×Q8—48no—
177C2×C3×Q8C22×D318yes—
178C2×C3×D4—24no—
179C2×C3×D4C22×D314yes—
180C22×C3×C4—24no—
181C22×C3×C4C22×D314yes—
182C2×#67—64no—
183C2×#67—64no—
184C2×#67—64no—
185C22×Dic3—34no—
186C22×Dic3—34no—
187C22×Dic3—64no—
188C22×Dic3—64no—
189#237—1216no—
190C2×D12—34no—
191C2×C4×D3—64no—
192C2×Dic6—38no—
193C2×Dic6—64no—
194C2×Dic6—64no—
195C2×Dic6—128no—
196C3×SD16—48no—
197C2×C3×C8C22×D318yes—
198C3×C4⋊C4C22×D314yes—
199C3×C22⋊C4—24no—
200#217—64no—
201#215—128no—
202#214—128no—
203(C2×D3)⋊C4—64no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—34no—
206Dic3⋊C4—64no—
207Dic3⋊C4—68no—
208Dic3⋊C4—68no—
209Dic3⋊C4—68no—
210Dic3⋊C4—68no—
211C4×Dic3—34no—
212C4×Dic3—34no—
213C4×Dic3—34no—
214C4×Dic3—34no—
215C2×C3⋊C8—38no—
216#204—128no—
217C22×C32—21no—
218C22×C32—21no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32C2×SD1612yes—
223C22×C32C22×D411yescharacteristic
224C2×C3⋊D3—41no—
225C2×C3⋊D3—41no—
226C2×C3⋊D3—41no—
227C32×C4—21no—
228C32×C4—42no—
229C32×C4—41no—
230C32×C4H(5,𝔽2)12yes—
231C3⋊Dic3—21no—
232C3⋊Dic3—42no—
233C3⋊Dic3—41no—
234C3⋊Dic3C2×SD1612yes—
235C3⋊Dic3C2×SD1612yes—
236C3⋊Dic3#13712yes—
237C2×#41—181no—
238C22×Q8—91no—
239C22×Q8C2×C3⋊D311yescharacteristic
240C2×SD16—92no—
241C2×SD16—92no—
242C2×SD16—92no—
243C2×SD16C2×C3⋊D312yes—
244C4⋊Q8—91no—
245C4⋊Q8—92no—
246C4⋊Q8—92no—
247C4⋊Q8—181no—
248C4⋊Q8—181no—
249#127—91no—
250#124—181no—
251#121—91no—
252#121—181no—
253#121C2×C3⋊D311yescharacteristic
254C4×D4—91no—
255C4×D4—91no—
256C4×D4—181no—
257C2×C4⋊C4—181no—
258C2×C4⋊C4—181no—
259C2×C42—91no—
260C4⋊C8—92no—
261#103—92no—
262#103—92no—
263#103—92no—
264#103C2×C3⋊D312yes—
265C22⋊C8—91no—
266C22⋊C8C2×C3⋊D311yescharacteristic
267C4×C8—92no—
268C23×C3—24no—
269C23×C3D3×D414yes—
270C22×D3—64no—
271C3×Q8—28no—
272C3×Q8—28no—
273C3×Q8—48no—
274C3×D4—28no—
275C3×D4—48no—
276C2×C3×C4—28no—
277C2×C3×C4—28no—
278C2×C3×C4—24no—
279C2×C3×C4—48no—
280C2×C3×C4D3×D414yes—
281C2×C3×C4C23×D314yes—
282#67—128no—
283#67—128no—
284#67—128no—
285C2×Dic3—316no—
286C2×Dic3—34no—
287C2×Dic3—34no—
288C2×Dic3—34no—
289C2×Dic3—34no—
290C2×Dic3—68no—
291C2×Dic3—68no—
292C2×Dic3—64no—
293C2×Dic3—128no—
294C2×Dic3—128no—
295D12—68no—
296C4×D3—128no—
297Dic6—68no—
298Dic6—68no—
299Dic6—128no—
300Dic6—128no—
301C3×C8—28no—
302C3⋊C8—68no—
303C2×C32—22no—
304C2×C32—81no—
305C2×C32#53511yescharacteristic
306C2×C32C22×SD1611yescharacteristic
307C2×C32C2×#13711yescharacteristic
308C3⋊D3—81no—
309#41—364no—
310C2×Q8—21no—
311C2×Q8—42no—
312C2×Q8—92no—
313C2×Q8—181no—
314C2×Q8—181no—
315C2×Q8—362no—
316C2×Q8C22×C3⋊D312yes—
317C2×D4—21no—
318C2×D4—91no—
319C2×D4—181no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4C22×C3⋊D311yescharacteristic
323C22×C4—21no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—181no—
327C22×C4—181no—
328C22×C4—181no—
329C22×C4C22×C3⋊D311yescharacteristic
330SD16—42no—
331SD16—362no—
332SD16—362no—
333SD16—362no—
334C2×C8—92no—
335C2×C8C22×C3⋊D312yes—
336C4⋊C4—91no—
337C4⋊C4—182no—
338C4⋊C4—182no—
339C4⋊C4—182no—
340C4⋊C4—182no—
341C4⋊C4—181no—
342C4⋊C4C22×C3⋊D311yescharacteristic
343C22⋊C4—21no—
344C22⋊C4—181no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C42—91no—
348C42—91no—
349C42—91no—
350C42—91no—
351C22×C3—24no—
352C22×C3—24no—
353C22×C3—44no—
354C22×C3—44no—
355C22×C3—44no—
356C22×C3D3×SD1618yes—
357C22×C3C2×D3×D414yes—
358C2×D3—124no—
359C2×D3—124no—
360C2×D3—124no—
361C3×C4—24no—
362C3×C4—44no—
363C3×C4—48no—
364C3×C4#100418yes—
365Dic3—38no—
366Dic3—38no—
367Dic3—38no—
368Dic3—64no—
369Dic3—124no—
370Dic3—128no—
371C32#320611yescharacteristic, complemented, Sylow
372C23—21no—
373C23—181no—
374C23D4×C3⋊D311yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—42no—
378Q8—182no—
379Q8—182no—
380Q8—362no—
381Q8—362no—
382D4—22no—
383D4—42no—
384D4—182no—
385D4—362no—
386D4—362no—
387D4—362no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—42no—
392C2×C4—91no—
393C2×C4—91no—
394C2×C4—91no—
395C2×C4—94no—
396C2×C4—91no—
397C2×C4—182no—
398C2×C4—181no—
399C2×C4—182no—
400C2×C4—362no—
401C2×C4—362no—
402C2×C4—362no—
403C2×C4D4×C3⋊D311yescharacteristic
404C2×C4C23×C3⋊D311yescharacteristic
405C8—22no—
406C8—182no—
407C2×C3—28no—
408C2×C3—84no—
409C2×C3#559214yes—
410C2×C3C2×D3×SD1614yes—
411C2×C3D3×#13714yes—
412D3—244no—
413C22—21no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—361no—
419C22—361no—
420C22—361no—
421C22SD16×C3⋊D312yes—
422C22C2×D4×C3⋊D311yescharacteristic
423C4—21no—
424C4—41no—
425C4—42no—
426C4—92no—
427C4—92no—
428C4—92no—
429C4—181no—
430C4—361no—
431C4—362no—
432C4#6436112yes—
433C3#8003414yescomplemented
434C2—22no—
435C2—81no—
436C2—721no—
437C2#1059606311yescharacteristic
438C2C2×SD16×C3⋊D311yescharacteristic
439C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#448C2
socleC22×C32C22×D4
prime radical#10596067C2
hypercenter#448C3⋊D3
hypocenterC32#3206
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#64153C2semidirect
3. C32×#448C2semidirect
4. #10592926C2semidirect
5. #10592874C2semidirect
6. #10592861C2semidirect
7. #10592739C2semidirect
8. #10592517C2semidirect
9. #10592491C2semidirect
10. #10592437C2semidirect
11. #10592417C2semidirect
46. C3×#448D3semidirect
151. C2×C3⋊Dic3SD16semidirect
173. #448C3⋊D3semidirect
371. C32#3206semidirect
433. C3#80034semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
#105960672
C32×#4482
#105929262
#105928742
#105928612
#105927392
#105925172
#105924912
#105924372
#105924172
#800343