Finite Group Databasebeta

← #11895180

Subgroups — #11895180

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3#10592793C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5#10590560C212yesmaximal, complemented
6#10590559C212yesmaximal
7#10590486C212yesmaximal, complemented
8#10590475C212yesmaximal
9#10590363C211yesmaximal, characteristic
10C4×#3716C211yesmaximal, characteristic
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83568—31nomaximal
13#81620—31nomaximal
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#946—21no—
18C3×#896—22no—
19C3×#893C2212yes—
20C3×#888C2212yes—
21C3×C4×D12C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63872—21no—
25#63866C2212yes—
26#63846—22no—
27#63843—21no—
28Dic3×Dic6C2212yes—
29C2×#3716C2211yescharacteristic
30C2×#3715C2212yes—
31#63637C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#810C2212yes—
35C3×#810C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2211yescharacteristic
40#63565C2212yes—
41#63563C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×D4×Q8—31no—
44#5727D311yescharacteristic
45#5721—31no—
46#5570—31no—
47C3×#487—31no—
48#5094—31no—
49#5094—31no—
50#5094—32no—
51#5094—61no—
52#5093—32no—
53#5093D311yescharacteristic, complemented
54#5083—31no—
55Q8×C3⋊C8—31no—
56#5019—31no—
57#5019—32no—
58C4×#214—32no—
59C4×#214—31no—
60#4818—32no—
61#4792—32no—
62#4791—32no—
63#4788—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67C2×#634C2311yescharacteristic
68C3×D3×Q8—44no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2312yes—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2312yes—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80C4×C3⋊Dic3—21no—
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×(C2×D3)⋊C4—21no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3716—22no—
98#3715—24no—
99#3359—91noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C22⋊Q8—62no—
108C3×C22⋊Q8—61no—
109C3×C4×Q8—31no—
110C3×C4×D4—32no—
111C3×C4×D4—31no—
112#946—21no—
113Q8×Dic3—32no—
114Q8×Dic3—61no—
115#944—32no—
116C2×#215—32no—
117C2×#214—32no—
118C2×#214—31no—
119C2×#204—31no—
120#896—22no—
121#893C2×D312yes—
122#890—62no—
123#890—61no—
124#890—61no—
125#889—62no—
126#888C2×D312yes—
127#887—61no—
128C4×D12C2×D311yescharacteristic
129#869—32no—
130#869C2×D311yescharacteristic
131C4×Dic6—32no—
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×#103—32no—
137C3×#103—32no—
138C3×C4×C8—31no—
139#835—32no—
140#832—31no—
141#821—31no—
142#817—31no—
143#816—31no—
144Dic3⋊C8—32no—
145C8×Dic3—32no—
146#810—32no—
147#810—32no—
148#810—32no—
149#810—31no—
150#810—62no—
151#810C2×D312yes—
152#810C2×D312yes—
153#808—32no—
154#808—32no—
155#808—31no—
156#808—62no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3×D3—21no—
164C32×Q8—42no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171#634—21no—
172#634—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×C4×D3—44no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—44no—
184C3×Dic6SD1614yescomplemented
185C3⋊(C3⋊C8)—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—21no—
188#557—91no—
189D4×Q8—31no—
190#487—31no—
191#487—92no—
192#475—92no—
193#475—91no—
194#461—92no—
195#461—91no—
196C8×Q8—91no—
197C4×SD16—91no—
198C4×SD16—92no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—31no—
202C2×C3×Q8—32no—
203C2×C3×Q8—41no—
204C2×C3×Q8—62no—
205C2×C3×Q8—124no—
206C2×C3×D4—31no—
207C22×C3×C4—62no—
208C22×C3×C4—61no—
209D3×Q8—44no—
210C2×D12C22×D311yescharacteristic
211C2×C4×D3—21no—
212C2×C4×D3—22no—
213C2×Dic6—22no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C2×Dic6#6711yescharacteristic
218C2×Dic6C22×D312yes—
219C2×C3×C8—31no—
220C2×C3×C8—31no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D312yes—
232C3×C4⋊C4C22×D312yes—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—61no—
235C3×C42—21no—
236C3×C42—32no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#215—64no—
240#214—62no—
241#214—64no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—22no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—61no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3#6711yescharacteristic
253C4⋊Dic3C22×D311yescharacteristic
254Dic3⋊C4—22no—
255Dic3⋊C4—62no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—121no—
261Dic3⋊C4#6712yes—
262C4×Dic3—62no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C4×Dic3—62no—
266C4×Dic3—121no—
267C4×Dic3C22×D312yes—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—62no—
271C2×C3⋊C8C22×D311yescharacteristic
272C2×C3⋊C8C22×D311yescharacteristic
273#204—62no—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—42no—
280C32×C4C2×SD1612yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—41no—
284C3⋊Dic3—41no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C3×Dic3C2×SD1614yes—
289C22×Q8—61no—
290C2×SD16—91no—
291C2×SD16—92no—
292C4⋊Q8—32no—
293C4⋊Q8—31no—
294C4⋊Q8—92no—
295C4⋊Q8D3211yescharacteristic
296#125—182no—
297#125—181no—
298C22⋊Q8—62no—
299C22⋊Q8—61no—
300C4×Q8—31no—
301C4×Q8—92no—
302C4×Q8—91no—
303C4×Q8—181no—
304C4×D4—32no—
305C4×D4—31no—
306#106—91no—
307#106—92no—
308C4⋊C8—92no—
309C4⋊C8—91no—
310#103—32no—
311#103—32no—
312#103—91no—
313#103—92no—
314#103—92no—
315#102—91no—
316C4×C8—31no—
317C4×C8—92no—
318C23×C3—61no—
319C22×D3—21no—
320C3×Q8—34no—
321C3×Q8—42no—
322C3×Q8—42no—
323C3×Q8—62no—
324C3×Q8—62no—
325C3×Q8—82no—
326C3×Q8—124no—
327C3×D4—32no—
328C3×D4—61no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—42no—
337C2×C3×C4—61no—
338C2×C3×C4—62no—
339C2×C3×C4—124no—
340C2×C3×C4—122no—
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3C2×#6712yes—
356C2×Dic3C2×#6712yes—
357D12—21no—
358D12#23912yes—
359C4×D3—42no—
360C4×D3—44no—
361Dic6—22no—
362Dic6—22no—
363Dic6—44no—
364Dic6—62no—
365Dic6—61no—
366Dic6—61no—
367Dic6—61no—
368Dic6—61no—
369Dic6—121no—
370Dic6#21414yescomplemented
371C3×C8—61no—
372C3×C8—61no—
373C3⋊C8—21no—
374C3⋊C8—21no—
375C3⋊C8—62no—
376C3⋊C8—62no—
377C3⋊C8—122no—
378C2×C32#54811yescharacteristic
379C2×C32C22×SD1611yescharacteristic
380C2×C32#57811yescharacteristic
381C3×D3—42no—
382C2×Q8—21no—
383C2×Q8—31no—
384C2×Q8—32no—
385C2×Q8—62no—
386C2×Q8—91no—
387C2×Q8—124no—
388C2×D4—31no—
389C22×C4—62no—
390C22×C4—61no—
391SD16—182no—
392SD16—184no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8—92no—
396C4⋊C4—21no—
397C4⋊C4—32no—
398C4⋊C4—31no—
399C4⋊C4—31no—
400C4⋊C4—62no—
401C4⋊C4—61no—
402C4⋊C4—61no—
403C4⋊C4—91no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—181no—
408C4⋊C4C2×D3212yes—
409C22⋊C4—62no—
410C22⋊C4—61no—
411C42—32no—
412C42—182no—
413C42—181no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—62no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×#6711yescharacteristic
421C2×D3—22no—
422C2×D3—41no—
423C2×D3—41no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—34no—
430C3×C4—41no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—62no—
434C3×C4—82no—
435C3×C4—121no—
436C3×C4—122no—
437C3×C4D3×SD1612yes—
438C3×C4C2×#21412yes—
439C3×C4C2×#23911yescharacteristic
440C3×C4#100711yescharacteristic
441C3×C4D3×#4111yescharacteristic
442C3×C4#101011yescharacteristic
443Dic3—22no—
444Dic3—42no—
445Dic3—41no—
446Dic3—122no—
447Dic3—121no—
448Dic3—121no—
449Dic3—121no—
450Dic3—121no—
451Dic3—241no—
452Dic3C2×#21414yes—
453C32#335911yescharacteristic, complemented, Sylow
454C23—61no—
455Q8—34no—
456Q8—42no—
457Q8—62no—
458Q8—62no—
459Q8—124no—
460Q8—181no—
461Q8—181no—
462D4—32no—
463D4—61no—
464C2×C4—22no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—62no—
468C2×C4—61no—
469C2×C4—124no—
470C2×C4—122no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4D3×#6711yescharacteristic
474C2×C4D3×#6711yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—61no—
477C8—61no—
478C8—182no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—122no—
483C2×C3#567711yescharacteristic
484C2×C3C2×D3×SD1611yescharacteristic
485C2×C3#576611yescharacteristic
486C2×C3C22×#21411yescharacteristic
487C2×C3#581711yescharacteristic
488C2×C3#583811yescharacteristic
489D3—42no—
490C22—62no—
491C22—121no—
492C22—121no—
493C22C2×D3×#6711yescharacteristic
494C4—21no—
495C4—34no—
496C4—42no—
497C4—62no—
498C4—121no—
499C4—122no—
500C4—361no—
501C4—361no—
502C4D3×#21412yes—
503C4#6431511yescharacteristic
504C4D3×#23911yescharacteristic
505C3—21no—
506C3#8162011yescharacteristic, complemented
507C3#8356811yescharacteristic, complemented
508C2—122no—
509C2C2×D3×#21411yescharacteristic
510C2#1059532711yescharacteristic
511C2#1059540111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊Q8D32
hypocenterC32#3359
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
2. #10593861C2semidirect
3. #10592793C2semidirect
4. C3×#5093C2semidirect
5. #10590560C2semidirect
7. #10590486C2semidirect
11. C3⋊C8×Dic6C2semidirect
53. #5093D3semidirect
184. C3×Dic6SD16semidirect
370. Dic6#214semidirect
453. C32#3359semidirect
506. C3#81620semidirect
507. C3#83568semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
#105938612
#105927932
C3×#50932
#105905602
#105905592
#105904862
#105904752
#105903632
C4×#37162
C3⋊C8×Dic62
#835683
#816203