Finite Group Databasebeta

← #11870824

Subgroups — #11870824

Order 1152.

820 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic
2#10594808C211yesmaximal, characteristic
3#10592669C211yesmaximal, characteristic
4C3×#4970C211yesmaximal, characteristic
5#10591186C211yesmaximal, characteristic
6#10591185C211yesmaximal, characteristic
7#10591053C211yesmaximal, characteristic
8#10590561C212yesmaximal, complemented
9#10590557C212yesmaximal, complemented
10#10590481C212yesmaximal, complemented
11#10590476C212yesmaximal, complemented
12#82447—31nomaximal
13#81452—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16#64133C2211yescharacteristic
17C3×#924C2211yescharacteristic
18C2×C3×Dic3⋊C4—21no—
19C2×C3×C4×Dic3—21no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C3×#887—21no—
22C3×#887—21no—
23C3×#887C2212yes—
24C3×#887C2212yes—
25#63964—21no—
26#63955—21no—
27#63918C2211yescharacteristic
28#63867—21no—
29#63866C2211yescharacteristic
30#63844C2211yescharacteristic
31Dic3×Dic6C2211yescharacteristic
32#63837—21no—
33C2×#3719C2212yes—
34C2×#3718C2212yes—
35#63657C2211yescharacteristic
36#63637C2212yes—
37#63634C2212yes—
38C3×#830C2211yescharacteristic
39C3×#810C2212yes—
40C3×#807C2212yes—
41Dic3⋊(C3⋊C8)C2212yes—
42#63566C2212yes—
43#63565C2212yes—
44Dic3×C3⋊C8C2212yes—
45C2×C3×C4×Q8—31no—
46#5622—31no—
47C2×#887D311yescharacteristic
48#5470—31no—
49C3×#484—31no—
50#5228—31no—
51#5228—31no—
52#5050—31no—
53#5031—32no—
54C4×#216—32no—
55C4×#216—32no—
56#5021—32no—
57#4970—31no—
58#4970—31no—
59#4970—61no—
60#4970D311yescharacteristic
61#4925—31no—
62#4875—32no—
63#4873—32no—
64#4795—32no—
65#4790—32no—
66#4739—31no—
67#4718—31no—
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C2×#634C2311yescharacteristic
71C22×C3×Dic3—21no—
72C22×C3×Dic3D411yescharacteristic
73C22×C3×Dic3D411yescharacteristic
74C2×C3×Dic6—21no—
75C2×C3×Dic6—24no—
76C2×C3×Dic6C2311yescharacteristic
77C2×C3×Dic6C2312yes—
78C2×#627—21no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81#3757—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#217—21no—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3D411yescharacteristic
93C3×C4×Dic3D411yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C3×C4×Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97#3724—21no—
98Dic3⋊Dic3—21no—
99Dic3⋊Dic3—21no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102Dic32—21no—
103Dic32—21no—
104#3719—24no—
105#3718—24no—
106#3104—91noSylow
107C22×C3×Q8—31no—
108C22×Dic6C2×D311yescharacteristic
109C3×C22⋊Q8—31no—
110C3×C4×Q8—32no—
111C3×C4×Q8—32no—
112C3×C4×Q8—61no—
113C3×C4×Q8—61no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—61no—
116C2×C3×C4⋊C4C2×D311yescharacteristic
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C42—31no—
119C2×C3×C42—61no—
120Q8×Dic3—31no—
121#944—31no—
122C2×#216—32no—
123C2×#216—32no—
124C2×#216—32no—
125#926—61no—
126#924—31no—
127#924—31no—
128#924—61no—
129#924—61no—
130#924C2×D311yescharacteristic
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3C2×D311yescharacteristic
134C2×Dic12—32no—
135#889—61no—
136#888—31no—
137#887—21no—
138#887—21no—
139#887—31no—
140#887—61no—
141#887C2×D312yes—
142#887C2×D312yes—
143#878—61no—
144#877—61no—
145#870—61no—
146#869—31no—
147#869—31no—
148C4×Dic6—31no—
149C4×Dic6—31no—
150C4×Dic6—61no—
151C3×#107—32no—
152C3×#103—32no—
153C3×C22⋊C8—31no—
154#835—32no—
155#835—32no—
156#830—31no—
157#830—31no—
158#830—61no—
159#830C2×D311yescharacteristic
160#816—32no—
161Dic3⋊C8—32no—
162C8×Dic3—32no—
163#810—32no—
164#810—32no—
165#810—32no—
166#810—62no—
167#810C2×D312yes—
168#807—32no—
169#807—32no—
170#807—62no—
171#807C2×D312yes—
172C4⋊(C3⋊C8)—32no—
173C4×C3⋊C8—32no—
174C23×C32C2×D411yescharacteristic
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4—42no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182#634—22no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—41no—
188C2×C3×Dic3Q1614yescomplemented
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C3×Dic6—24no—
194C3×Dic6—22no—
195C3×Dic6—22no—
196C3×Dic6#4114yes—
197#627—42no—
198C3⋊(C3⋊C8)—22no—
199C3×C3⋊C8—22no—
200#533—91no—
201C2×C4×Q8—31no—
202#484—31no—
203#484—91no—
204#477—92no—
205#462—92no—
206#451—91no—
207#451—91no—
208C4×Q16—92no—
209C4×Q16—92no—
210#431—91no—
211C2×C3×Q8—32no—
212C2×C3×Q8—31no—
213C2×C3×Q8—64no—
214C2×C3×Q8—61no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—41no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×Dic3—21no—
225C22×Dic3#6711yescharacteristic
226C22×Dic3#6711yescharacteristic
227C2×Dic6—21no—
228C2×Dic6—24no—
229C2×Dic6—31no—
230C2×Dic6—31no—
231C2×Dic6—61no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C2×Dic6C22×D311yescharacteristic
235C2×Dic6C22×D312yes—
236C2×C3×C8—32no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4C22×D312yes—
246C3×C4⋊C4C22×D312yes—
247C3×C22⋊C4—61no—
248C3×C42—31no—
249C3×C42—31no—
250C3×C42—31no—
251C3×C42—31no—
252C3×C42—62no—
253C3×C42—62no—
254#217—21no—
255#217—61no—
256#217—61no—
257#217—121no—
258#216—64no—
259#216—64no—
260#216—64no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3C22×D311yescharacteristic
269Dic3⋊C4—21no—
270Dic3⋊C4—22no—
271Dic3⋊C4—22no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274Dic3⋊C4—61no—
275Dic3⋊C4—61no—
276Dic3⋊C4—61no—
277Dic3⋊C4—61no—
278Dic3⋊C4—61no—
279Dic3⋊C4—61no—
280Dic3⋊C4—121no—
281C4×Dic3—22no—
282C4×Dic3—22no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3#6711yescharacteristic
288C4×Dic3#6711yescharacteristic
289C4×Dic3C22×D311yescharacteristic
290C4×Dic3C22×D311yescharacteristic
291C2×C3⋊C8—32no—
292C2×C3⋊C8—32no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8C22×D312yes—
295Dic12—64no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32C2×Q1612yes—
299C22×C32C22×D411yescharacteristic
300C32×C4—21no—
301C32×C4—42no—
302C32×C4C2×#4112yes—
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C3×Dic3—24no—
306C3×Dic3—21no—
307C3×Dic3—21no—
308C3×Dic3—41no—
309C3×Dic3—41no—
310C3×Dic3C2×Q1612yes—
311C3×Dic3C2×Q1612yes—
312C22×Q8—31no—
313C2×Q16—92no—
314C2×Q16—92no—
315C4⋊Q8—91no—
316C4⋊Q8—91no—
317#125—181no—
318C22⋊Q8—31no—
319C22⋊Q8—91no—
320C22⋊Q8—181no—
321C4×Q8—32no—
322C4×Q8—32no—
323C4×Q8—61no—
324C4×Q8—61no—
325C4×Q8—91no—
326C4×Q8—91no—
327C4×Q8—181no—
328#117—181no—
329C2×C4⋊C4—61no—
330C2×C4⋊C4D3211yescharacteristic
331C2×C42—31no—
332C2×C42—61no—
333#107—32no—
334#107—92no—
335C4⋊C8—92no—
336#103—32no—
337#103—92no—
338#103—92no—
339#103—92no—
340C22⋊C8—31no—
341C22⋊C8—91no—
342C4×C8—92no—
343C23×C3—21no—
344C23×C3D3×D411yescharacteristic
345C23×C3C2×#6711yescharacteristic
346C3×Q8—34no—
347C3×Q8—64no—
348C3×Q8—62no—
349C3×Q8—62no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—34no—
357C2×C3×C4—31no—
358C2×C3×C4—31no—
359C2×C3×C4—31no—
360C2×C3×C4—31no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—64no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—82no—
370C2×C3×C4—121no—
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×Dic3—24no—
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—41no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3#21614yescomplemented
387C2×Dic3C2×#6711yescharacteristic
388C2×Dic3C2×#6711yescharacteristic
389C2×Dic3C2×#6711yescharacteristic
390C2×Dic3C2×#6711yescharacteristic
391Dic6—24no—
392Dic6—22no—
393Dic6—22no—
394Dic6—62no—
395Dic6—62no—
396Dic6—122no—
397Dic6—122no—
398Dic6—122no—
399Dic6#23514yes—
400C3×C8—62no—
401C3⋊C8—22no—
402C3⋊C8—62no—
403C3⋊C8—62no—
404C3⋊C8—122no—
405C2×C32—22no—
406C2×C32#52511yescharacteristic
407C2×C32C22×Q1611yescharacteristic
408C2×C32#57511yescharacteristic
409C2×Q8—32no—
410C2×Q8—31no—
411C2×Q8—64no—
412C2×Q8—61no—
413C2×Q8—91no—
414C2×Q8—181no—
415C22×C4—21no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—61no—
419C22×C4C2×D3211yescharacteristic
420Q16—184no—
421Q16—184no—
422C2×C8—32no—
423C2×C8—92no—
424C4⋊C4—21no—
425C4⋊C4—31no—
426C4⋊C4—62no—
427C4⋊C4—62no—
428C4⋊C4—61no—
429C4⋊C4—91no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4—181no—
434C4⋊C4—181no—
435C4⋊C4—181no—
436C4⋊C4C2×D3212yes—
437C22⋊C4—61no—
438C22⋊C4—181no—
439C42—31no—
440C42—31no—
441C42—31no—
442C42—31no—
443C42—62no—
444C42—62no—
445C42—181no—
446C42—181no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3D3×Q1612yes—
456C22×C3C2×#21612yes—
457C22×C3C2×D3×D411yescharacteristic
458C22×C3C22×#6711yescharacteristic
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—32no—
463C3×C4—32no—
464C3×C4—41no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—64no—
468C3×C4—61no—
469C3×C4—61no—
470C3×C4—82no—
471C3×C4—121no—
472C3×C4—121no—
473C3×C4C2×#23512yes—
474C3×C4D3×#4112yes—
475Dic3—24no—
476Dic3—21no—
477Dic3—21no—
478Dic3—41no—
479Dic3—41no—
480Dic3—121no—
481Dic3—121no—
482Dic3—121no—
483Dic3—121no—
484Dic3—241no—
485Dic3—241no—
486Dic3C2×#21612yes—
487Dic3C2×#21612yes—
488C32#310411yescharacteristic, complemented, Sylow
489C23D3×#6711yescharacteristic
490Q8—34no—
491Q8—64no—
492Q8—62no—
493Q8—62no—
494Q8—182no—
495Q8—362no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—31no—
499C2×C4—31no—
500C2×C4—34no—
501C2×C4—31no—
502C2×C4—31no—
503C2×C4—42no—
504C2×C4—64no—
505C2×C4—62no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—121no—
509C2×C4—181no—
510C2×C4—181no—
511C2×C4D3×#6711yescharacteristic
512C2×C4C22×D3211yescharacteristic
513C8—62no—
514C8—182no—
515C2×C3—22no—
516C2×C3—22no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—42no—
521C2×C3#565611yescharacteristic
522C2×C3C2×D3×Q1611yescharacteristic
523C2×C3#577311yescharacteristic
524C2×C3#579111yescharacteristic
525C2×C3C22×#21611yescharacteristic
526C2×C3#582211yescharacteristic
527C22—21no—
528C22—21no—
529C22D3×#21612yes—
530C22C2×D3×#6711yescharacteristic
531C4—21no—
532C4—32no—
533C4—32no—
534C4—42no—
535C4—61no—
536C4—61no—
537C4—64no—
538C4—121no—
539C4—121no—
540C4—361no—
541C4—361no—
542C4D3×#23512yes—
543C3—21no—
544C3#8145211yescharacteristic, complemented
545C3#8244711yescharacteristic, complemented
546C2—22no—
547C2#1059489611yescharacteristic
548C2#1059509511yescharacteristic
549C2C2×D3×#21611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. #10590561C2semidirect
9. #10590557C2semidirect
10. #10590481C2semidirect
11. #10590476C2semidirect
188. C2×C3×Dic3Q16semidirect
386. C2×Dic3#216semidirect
488. C32#3104semidirect
544. C3#81452semidirect
545. C3#82447semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
#105948082
#105926692
C3×#49702
#105911862
#105911852
#105910532
#105905612
#105905572
#105904812
#105904762
#824473
#814523