Finite Group Databasebeta

← #11895182

Subgroups — #11895182

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592792C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5#10590560C212yesmaximal, complemented
6#10590559C212yesmaximal
7#10590487C212yesmaximal, complemented
8#10590479C212yesmaximal
9#10590365C211yesmaximal, characteristic
10C4×#3715C211yesmaximal, characteristic
11#10590250C211yesmaximal, characteristic, complemented
12#83568—31nomaximal
13#81037—31nomaximal
14C2×C3×D3×Q8—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#946—21no—
18C3×#896—22no—
19C3×#893C2212yes—
20C3×#888C2212yes—
21C3×C4×D12C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63869—21no—
25#63866C2212yes—
26#63845—22no—
27#63844C2212yes—
28Dic3×Dic6—21no—
29C2×#3716C2212yes—
30C2×#3715C2211yescharacteristic
31#63637C2212yes—
32#63637C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#810C2212yes—
35C3×#808C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63574C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63565C2211yescharacteristic
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×D4×Q8—31no—
44#5727D311yescharacteristic
45#5570—31no—
46#5567—31no—
47C3×#475—31no—
48#5094—32no—
49#5094D311yescharacteristic, complemented
50#5093—31no—
51#5093—31no—
52#5093—32no—
53#5093—61no—
54C4×#215—31no—
55Q8×C3⋊C8—31no—
56#5019—32no—
57#5019—31no—
58C4×#214—31no—
59C4×#214—32no—
60#4854—32no—
61#4852—32no—
62#4841—31no—
63#4830—31no—
64#4818—32no—
65#4792—32no—
66C2×C32×Q8—21no—
67C2×#634C2312yes—
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×Dic6C2311yescharacteristic
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2312yes—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×(C2×D3)⋊C4—21no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—21no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3724—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3716—24no—
98#3715—22no—
99#3359—91noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C22⋊Q8—62no—
107C3×C22⋊Q8—61no—
108C3×C4×Q8—31no—
109C3×C4×Q8—31no—
110C3×C4×D4—32no—
111C3×C4×D4—31no—
112#946—21no—
113Q8×Dic3—61no—
114#944—32no—
115C2×#215—31no—
116C2×#214—31no—
117C2×#214—32no—
118C2×#204—32no—
119#896—22no—
120#893C2×D312yes—
121#890—61no—
122#890—62no—
123#889—62no—
124#888C2×D312yes—
125#887—32no—
126C4×D12C2×D311yescharacteristic
127#870—61no—
128#869—32no—
129#869—31no—
130#869—31no—
131#869—61no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#106—32no—
137C3×C4⋊C8—31no—
138C3×#103—32no—
139#835—31no—
140#832—31no—
141#816—32no—
142Dic3⋊C8—32no—
143C8×Dic3—32no—
144#810—31no—
145#810—32no—
146#810—32no—
147#810—32no—
148#810—32no—
149#810—32no—
150#810—62no—
151#810—62no—
152#810C2×D312yes—
153#809—31no—
154#808—31no—
155#808—31no—
156#808C2×D312yes—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8—61no—
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—22no—
170#634—22no—
171#634—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
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—21no—
182C3×Dic6—21no—
183C3×Dic6—44no—
184C3×Dic6SD1614yescomplemented
185C3⋊(C3⋊C8)—21no—
186C3⋊(C3⋊C8)—21no—
187C3×C3⋊C8—22no—
188#557—91no—
189D4×Q8—31no—
190#487—92no—
191#487—91no—
192#475—31no—
193#475—92no—
194#461—92no—
195#461—91no—
196C8×Q8—91no—
197C4×SD16—92no—
198C4×SD16—91no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—31no—
202C2×C3×Q8—31no—
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—32no—
215C2×Dic6—32no—
216C2×Dic6—62no—
217C2×Dic6#6711yescharacteristic
218C2×Dic6C22×D311yescharacteristic
219C2×C3×C8—32no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4C22×D312yes—
231C3×C4⋊C4C22×D312yes—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—61no—
234C3×C42—21no—
235C3×C42—32no—
236C3×C42—61no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#215—62no—
240#214—64no—
241#214—62no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—22no—
244C4⋊Dic3—62no—
245C4⋊Dic3—62no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—121no—
251C4⋊Dic3—121no—
252C4⋊Dic3#6711yescharacteristic
253C4⋊Dic3C22×D311yescharacteristic
254C4⋊Dic3C22×D311yescharacteristic
255Dic3⋊C4—21no—
256Dic3⋊C4—22no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4#6712yes—
262C4×Dic3—21no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C4×Dic3C22×D312yes—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8C22×D312yes—
273#204—64no—
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—42no—
284C3×Dic3—22no—
285C3×Dic3—41no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C3×Dic3C2×SD1614yes—
289C22×Q8—61no—
290C2×SD16—92no—
291C2×SD16—91no—
292C4⋊Q8—32no—
293C4⋊Q8—92no—
294C4⋊Q8—91no—
295C4⋊Q8D3211yescharacteristic
296#125—181no—
297#125—182no—
298C22⋊Q8—62no—
299C22⋊Q8—61no—
300C4×Q8—31no—
301C4×Q8—31no—
302C4×Q8—92no—
303C4×Q8—181no—
304C4×D4—32no—
305C4×D4—31no—
306#106—32no—
307#106—91no—
308C4⋊C8—31no—
309C4⋊C8—92no—
310#103—32no—
311#103—92no—
312#103—91no—
313#103—92no—
314#103—92no—
315#102—91no—
316C4×C8—92no—
317C4×C8—91no—
318C23×C3—61no—
319C22×D3—21no—
320C3×Q8—34no—
321C3×Q8—42no—
322C3×Q8—42no—
323C3×Q8—61no—
324C3×Q8—61no—
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—61no—
339C2×C3×C4—61no—
340C2×C3×C4—124no—
341C2×C3×C4—122no—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—122no—
354C2×Dic3C2×#6712yes—
355C2×Dic3C2×#6712yes—
356D12—21no—
357D12#23912yes—
358C4×D3—42no—
359C4×D3—44no—
360Dic6—21no—
361Dic6—21no—
362Dic6—44no—
363Dic6—62no—
364Dic6—62no—
365Dic6—62no—
366Dic6—62no—
367Dic6—122no—
368Dic6—122no—
369Dic6#21414yescomplemented
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—61no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—61no—
376C3⋊C8—121no—
377C3⋊C8—121no—
378C2×C32#54811yescharacteristic
379C2×C32C22×SD1611yescharacteristic
380C2×C32#57811yescharacteristic
381C3×D3—42no—
382C2×Q8—21no—
383C2×Q8—31no—
384C2×Q8—31no—
385C2×Q8—62no—
386C2×Q8—92no—
387C2×Q8—124no—
388C2×D4—31no—
389C22×C4—62no—
390C22×C4—61no—
391SD16—184no—
392SD16—182no—
393C2×C8—32no—
394C2×C8—91no—
395C2×C8—91no—
396C4⋊C4—21no—
397C4⋊C4—32no—
398C4⋊C4—31no—
399C4⋊C4—31no—
400C4⋊C4—31no—
401C4⋊C4—62no—
402C4⋊C4—61no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4C2×D3212yes—
409C22⋊C4—62no—
410C22⋊C4—61no—
411C42—32no—
412C42—61no—
413C42—182no—
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—22no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—34no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—62no—
434C3×C4—82no—
435C3×C4—121no—
436C3×C4—121no—
437C3×C4—121no—
438C3×C4D3×SD1612yes—
439C3×C4C2×#21412yes—
440C3×C4C2×#23911yescharacteristic
441C3×C4#100711yescharacteristic
442C3×C4#100711yescharacteristic
443C3×C4D3×#4111yescharacteristic
444Dic3—22no—
445Dic3—41no—
446Dic3—41no—
447Dic3—41no—
448Dic3—122no—
449Dic3—122no—
450Dic3—242no—
451Dic3C2×#21414yes—
452C32#335911yescharacteristic, complemented, Sylow
453C23—61no—
454Q8—34no—
455Q8—42no—
456Q8—61no—
457Q8—61no—
458Q8—124no—
459Q8—182no—
460Q8—182no—
461D4—32no—
462D4—61no—
463C2×C4—22no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—124no—
470C2×C4—122no—
471C2×C4—182no—
472C2×C4D3×#6711yescharacteristic
473C2×C4D3×#6711yescharacteristic
474C2×C4C22×D3211yescharacteristic
475C8—62no—
476C8—181no—
477C8—181no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—122no—
482C2×C3#563311yescharacteristic
483C2×C3C2×D3×SD1611yescharacteristic
484C2×C3#577911yescharacteristic
485C2×C3C22×#21411yescharacteristic
486C2×C3#581711yescharacteristic
487C2×C3#583811yescharacteristic
488D3—42no—
489C22—62no—
490C22—121no—
491C22—121no—
492C22C2×D3×#6711yescharacteristic
493C4—21no—
494C4—34no—
495C4—42no—
496C4—62no—
497C4—121no—
498C4—121no—
499C4—121no—
500C4—362no—
501C4D3×#21412yes—
502C4#6431611yescharacteristic
503C4D3×#23911yescharacteristic
504C3—21no—
505C3#8103711yescharacteristic, complemented
506C3#8356811yescharacteristic, complemented
507C2—122no—
508C2C2×D3×#21411yescharacteristic
509C2#1059532811yescharacteristic
510C2#1059540211yescharacteristic
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. #10593860C2semidirect
3. #10592792C2semidirect
4. C3×#5094C2semidirect
5. #10590560C2semidirect
7. #10590487C2semidirect
11. #10590250C2semidirect
49. #5094D3semidirect
184. C3×Dic6SD16semidirect
369. Dic6#214semidirect
452. C32#3359semidirect
505. C3#81037semidirect
506. C3#83568semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
#105938602
#105927922
C3×#50942
#105905602
#105905592
#105904872
#105904792
#105903652
C4×#37152
#105902502
#835683
#810373