Finite Group Databasebeta

← #11895675

Subgroups — #11895675

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic
3#10592793C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic
5#10590533C212yesmaximal, complemented
6#10590532C212yesmaximal, complemented
7#10590469C212yesmaximal, complemented
8#10590453C212yesmaximal, complemented
9C4×#3719C211yesmaximal, characteristic, complemented
10#10590364C211yesmaximal, characteristic
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83697—31nomaximal
13#81589—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15C4×#634C2211yescharacteristic
16C3×Q8×Dic3—21no—
17C3×#944—21no—
18C3×#890C2212yes—
19C3×#889—22no—
20C3×#887C2212yes—
21C3×#874C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63898—21no—
25Dic3×D12C2212yes—
26#63884—22no—
27#63863—21no—
28#63860C2212yes—
29C2×#3719C2211yescharacteristic
30C2×#3715C2212yes—
31#63637C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#809C2212yes—
35C3×#809C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2211yescharacteristic
40#63566C2211yescharacteristic
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5721D311yescharacteristic, complemented
45#5713—31no—
46#5585—31no—
47C3×#486—31no—
48#5094—31no—
49#5094—31no—
50#5094—61no—
51#5088D311yescharacteristic
52#5075—31no—
53#5068—32no—
54#5066—32no—
55C4×#216—31no—
56#5028—32no—
57#5027—31no—
58C4×#215—32no—
59Q8×C3⋊C8—31no—
60#4768—32no—
61#4767—32no—
62#4766—32no—
63#4758—32no—
64C4×Dic12—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×D3×Dic3—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78#3750—21no—
79C4×C3⋊Dic3—21no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×C4⋊Dic3—22no—
82C3×C4⋊Dic3D411yescharacteristic
83C3×C4⋊Dic3C2311yescharacteristic
84C3×Dic3⋊C4—21no—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4—22no—
87C3×Dic3⋊C4D412yes—
88C3×C4×Dic3—21no—
89C3×C4×Dic3—22no—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96#3719—22no—
97#3715—24no—
98#3365—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—61no—
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×#127—31no—
104C3×#125—32no—
105C3×#125—62no—
106C3×C4×Q8—31no—
107C3×C4×Q8—32no—
108C3×C4×Q8—31no—
109C3×C4×Q8—61no—
110#947—61no—
111Q8×Dic3—21no—
112#944—21no—
113C2×#216—31no—
114C2×#215—32no—
115#936—32no—
116#936—61no—
117#935—62no—
118D4×Dic3—32no—
119D4×Dic3—61no—
120C2×#214—32no—
121C2×Dic12—31no—
122#894—62no—
123#893—61no—
124#890C2×D312yes—
125#889—22no—
126#887C2×D312yes—
127#875—32no—
128#874C2×D311yescharacteristic
129C4×D12—32no—
130C4×Dic6—31no—
131C4×Dic6—31no—
132C4×Dic6—61no—
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#102—32no—
136C3×#102—32no—
137C3×C4×C8—31no—
138#835—31no—
139#832—32no—
140#818—31no—
141#816—31no—
142#816—31no—
143Dic3⋊C8—32no—
144C8×Dic3—32no—
145#810—32no—
146#810—32no—
147#810—31no—
148#810—62no—
149#809—32no—
150#809C2×D312yes—
151#809C2×D312yes—
152#808—32no—
153#808—32no—
154#808—62no—
155#807—31no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3×D3—22no—
163C32×Q8—42no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170#634—21no—
171#634—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—22no—
177C3×D12—22no—
178C3×D12—42no—
179C3×D12—81no—
180C3×Dic6—22no—
181C3×Dic6—21no—
182C3×Dic6#4112yes—
183D3×Dic3—82no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#559—91no—
188#557—31no—
189#488—92no—
190#486—31no—
191#478—92no—
192#475—91no—
193#464—92no—
194#460—91no—
195C8×Q8—91no—
196C4×Q16—91no—
197C4×SD16—92no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—41no—
203C2×C3×D4—32no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C22×Dic3—62no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12C22×D312yes—
210C2×C4×D3—62no—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—61no—
214C2×Dic6#6711yescharacteristic
215C2×Dic6C22×D311yescharacteristic
216C2×C3×C8—31no—
217C2×C3×C8—31no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—31no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C22×D312yes—
231C3×C42—21no—
232C3×C42—32no—
233C3×C42—62no—
234C3×C42—61no—
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237#217—62no—
238#217—62no—
239#217—62no—
240#216—62no—
241#215—64no—
242#214—64no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246C4⋊Dic3—22no—
247C4⋊Dic3—31no—
248C4⋊Dic3—31no—
249C4⋊Dic3—61no—
250C4⋊Dic3#6711yescharacteristic
251C4⋊Dic3C22×D311yescharacteristic
252Dic3⋊C4—21no—
253Dic3⋊C4—22no—
254Dic3⋊C4—22no—
255Dic3⋊C4—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—121no—
258Dic3⋊C4#6712yes—
259C4×Dic3—21no—
260C4×Dic3—22no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—121no—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8C22×D311yescharacteristic
269C2×C3⋊C8C22×D311yescharacteristic
270Dic12—62no—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C32×C4—21no—
276C32×C4—42no—
277C32×C4#13512yes—
278C32×C4C2×#4111yescharacteristic
279C32×C42−1+411yescharacteristic
280C3⋊Dic3—41no—
281C3⋊Dic3—41no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—41no—
286C2×Q16—91no—
287C2×SD16—92no—
288C4⋊Q8—61no—
289C4⋊Q8D3211yescharacteristic
290#127—31no—
291#125—32no—
292#125—62no—
293#124—92no—
294#124—181no—
295#123—182no—
296C4×Q8—31no—
297C4×Q8—32no—
298C4×Q8—31no—
299C4×Q8—61no—
300C4×Q8—91no—
301C4×D4—92no—
302C4×D4—181no—
303#107—91no—
304#106—92no—
305C4⋊C8—92no—
306C4⋊C8—91no—
307#103—91no—
308#103—91no—
309#103—92no—
310#102—32no—
311#102—32no—
312#102—92no—
313C4×C8—31no—
314C4×C8—92no—
315C23×C3—62no—
316C22×D3—22no—
317C3×Q8—32no—
318C3×Q8—42no—
319C3×Q8—42no—
320C3×Q8—62no—
321C3×Q8—61no—
322C3×Q8—82no—
323C3×D4—62no—
324C3×D4—62no—
325C3×D4—122no—
326C3×D4—241no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—42no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—242no—
352C2×Dic3C2×#6712yes—
353C2×Dic3C2×#6712yes—
354D12—22no—
355D12—22no—
356D12—42no—
357D12—81no—
358C4×D3—242no—
359Dic6—22no—
360Dic6—21no—
361Dic6—62no—
362Dic6—61no—
363Dic6—61no—
364Dic6—61no—
365Dic6—61no—
366Dic6—121no—
367Dic6#23912yes—
368C3×C8—61no—
369C3×C8—61no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—122no—
375C2×C32#54811yescharacteristic
376C2×C32C2×#13511yescharacteristic
377C2×C32#57711yescharacteristic
378C3×D3—82no—
379C2×Q8—21no—
380C2×Q8—31no—
381C2×Q8—31no—
382C2×Q8—91no—
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C22×C4—182no—
387Q16—182no—
388SD16—184no—
389C2×C8—31no—
390C2×C8—31no—
391C2×C8—92no—
392C4⋊C4—21no—
393C4⋊C4—31no—
394C4⋊C4—32no—
395C4⋊C4—31no—
396C4⋊C4—62no—
397C4⋊C4—62no—
398C4⋊C4—62no—
399C4⋊C4—61no—
400C4⋊C4—91no—
401C4⋊C4—181no—
402C4⋊C4C2×D3212yes—
403C22⋊C4—182no—
404C22⋊C4—182no—
405C22⋊C4—182no—
406C42—32no—
407C42—62no—
408C42—61no—
409C42—181no—
410C42C2×D3211yescharacteristic
411C22×C3—21no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×#6711yescharacteristic
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—41no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4—62no—
429C3×C4—62no—
430C3×C4—62no—
431C3×C4—82no—
432C3×C4—121no—
433C3×C4#91212yes—
434C3×C4#95012yes—
435C3×C4C2×#23911yescharacteristic
436C3×C4#100711yescharacteristic
437C3×C4D3×#4111yescharacteristic
438C3×C4#101011yescharacteristic
439Dic3—22no—
440Dic3—22no—
441Dic3—22no—
442Dic3—41no—
443Dic3—122no—
444Dic3—121no—
445Dic3—121no—
446Dic3—121no—
447Dic3—121no—
448Dic3—241no—
449C32#336511yescharacteristic, complemented, Sylow
450C23—62no—
451Q8—32no—
452Q8—42no—
453Q8—61no—
454Q8—62no—
455Q8—181no—
456Q8—181no—
457D4—62no—
458D4—62no—
459D4—122no—
460D4—241no—
461C2×C4—22no—
462C2×C4—32no—
463C2×C4—32no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—722no—
469C2×C4D3×#6711yescharacteristic
470C2×C4D3×#6711yescharacteristic
471C2×C4C22×D3211yescharacteristic
472C8—61no—
473C8—61no—
474C8—182no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—242no—
479C2×C3#567711yescharacteristic
480C2×C3C2×#91211yescharacteristic
481C2×C3#576211yescharacteristic
482C2×C3#581711yescharacteristic
483C2×C3C2×#95011yescharacteristic
484C2×C3#583711yescharacteristic
485D3—82no—
486C22—122no—
487C22—122no—
488C22—122no—
489C22C2×D3×#6711yescharacteristic
490C4—21no—
491C4—42no—
492C4—62no—
493C4—62no—
494C4—62no—
495C4—121no—
496C4—361no—
497C4—361no—
498C4#6393312yes—
499C4#6431511yescharacteristic
500C4D3×#23911yescharacteristic
501C3—21no—
502C3#8158911yescharacteristic, complemented
503C3#8369711yescharacteristic, complemented
504C2—242no—
505C2C2×#6393311yescharacteristic
506C2#1059531811yescharacteristic
507C2#1059540111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC4⋊Q8D32
hypocenterC32#3365
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
1. C3×#5721C2semidirect
3. #10592793C2semidirect
5. #10590533C2semidirect
6. #10590532C2semidirect
7. #10590469C2semidirect
8. #10590453C2semidirect
9. C4×#3719C2semidirect
11. C3⋊C8×Dic6C2semidirect
44. #5721D3semidirect
449. C32#3365semidirect
502. C3#81589semidirect
503. C3#83697semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
#105939512
#105927932
C3×#50882
#105905332
#105905322
#105904692
#105904532
C4×#37192
#105903642
C3⋊C8×Dic62
#836973
#815893