Finite Group Databasebeta

← #11887662

Subgroups — #11887662

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic
2#10593904C211yesmaximal, characteristic
3#10592790C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5#10590604C212yesmaximal, complemented
6D3×#810C212yesmaximal, complemented
7#10590518C212yesmaximal, complemented
8#10590517C212yesmaximal, complemented
9#10590384C211yesmaximal, characteristic, complemented
10C4×#3719C211yesmaximal, characteristic, complemented
11C3⋊C8×D12C211yesmaximal, characteristic
12#83640—31nomaximal
13#81613—31nomaximal
14C2×D3×Dic6C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#946—22no—
18C3×#897C2212yes—
19C3×#893—21no—
20C3×D3×C4⋊C4C2212yes—
21C3×#890—21no—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919—21no—
26#63899—22no—
27#63898—21no—
28#63856C2212yes—
29C2×#3719C2211yescharacteristic
30C2×#3718C2212yes—
31C2×D3×C3⋊C8C2212yes—
32#63637C2212yes—
33#63634C2212yes—
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
35C3×#810C2212yes—
36C3×#810C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63567C2211yescharacteristic
40#63566C2211yescharacteristic
41#63565C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×#554—31no—
44#5730D311yescharacteristic
45#5727—31no—
46D4×Dic6—31no—
47C3×#487—31no—
48#5093D311yescharacteristic, complemented
49#5091—31no—
50#5091—31no—
51#5091—61no—
52#5090—31no—
53#5051—32no—
54#5050—32no—
55#5031—31no—
56C4×#216—31no—
57D4×C3⋊C8—31no—
58#4970—32no—
59C2×#810—32no—
60#4813—32no—
61#4811—32no—
62#4809—32no—
63D3×#103—32no—
64C4×Dic12—31no—
65C8×D12—31no—
66C2×C32×Q8—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12D411yescharacteristic
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6C2311yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×#627—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—24no—
76D3×Dic6—42no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C4×C3⋊Dic3—21no—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4D412yes—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—21no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96#3724—22no—
97(C2×D3)⋊Dic3—22no—
98#3719—22no—
99#3718—42no—
100D3×C3⋊C8—42no—
101#3299—91noSylow
102C2×D3×Q8—32no—
103C22×Dic6—32no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C2×D311yescharacteristic
108C3×#125—61no—
109C3×C22⋊Q8—32no—
110C3×C22⋊Q8—62no—
111C3×C4×Q8—31no—
112C3×C4×D4—31no—
113C3×C4×D4—61no—
114C2×C3×C4⋊C4—32no—
115#946—22no—
116#946—32no—
117C2×#216—32no—
118C2×#216—32no—
119C2×#216—31no—
120D4×Dic3—61no—
121#924—32no—
122C22×C3⋊C8—32no—
123C2×Dic12—31no—
124C2×D3×C8—32no—
125#897C2×D312yes—
126#896—62no—
127#893—21no—
128#893—61no—
129D3×C4⋊C4C2×D312yes—
130#890—21no—
131#888—61no—
132#888—61no—
133#878—62no—
134C4×D12C2×D311yescharacteristic
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6C2×D311yescharacteristic
140C3×#103—32no—
141C3×#103—32no—
142C3×C4×C8—31no—
143#835—32no—
144#835—31no—
145#830—32no—
146(C2×D3)⋊C8—32no—
147#818—31no—
148#816—31no—
149#816—31no—
150#810—32no—
151#810—32no—
152#810—32no—
153#810—31no—
154#810—62no—
155#810C2×D312yes—
156#810C2×D312yes—
157#807—32no—
158#807—32no—
159#807—31no—
160#807—62no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—61no—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3×D3C2×D412yes—
166C32×Q8—81no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173#634—21no—
174#634#4112yes—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C3×D12Q1614yescomplemented
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×C4×D3—82no—
183C3×Dic6—21no—
184C3×Dic6—22no—
185C3×Dic6—21no—
186C3×Dic6—22no—
187#627—44no—
188D3×Dic3—44no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#554—31no—
193D4×Q8—91no—
194#487—31no—
195#484—92no—
196#477—91no—
197#467—92no—
198#462—91no—
199#451—92no—
200C4×Q16—91no—
201C8×D4—91no—
202C2×#103—92no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—32no—
206C2×C3×Q8—31no—
207C2×C3×Q8—41no—
208C2×C3×D4—31no—
209C22×C3×C4—32no—
210C22×C3×C4—62no—
211C22×Dic3—62no—
212D3×Q8—64no—
213D3×Q8—122no—
214C2×D12#6711yescharacteristic
215C2×C4×D3—22no—
216C2×C4×D3—62no—
217C2×C4×D3C22×D312yes—
218C2×Dic6—31no—
219C2×Dic6—31no—
220C2×Dic6—61no—
221C2×Dic6—64no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—122no—
225C2×Dic6C22×D312yes—
226C2×Dic6C22×D311yescharacteristic
227C2×C3×C8—31no—
228C2×C3×C8—31no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D312yes—
241C3×C4⋊C4C22×D312yes—
242C3×C22⋊C4—32no—
243C3×C22⋊C4—62no—
244C3×C42—21no—
245C3×C42—61no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#217—62no—
249#216—62no—
250#216—122no—
251#216—122no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4#6712yes—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—22no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—61no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—21no—
264Dic3⋊C4—22no—
265Dic3⋊C4—62no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268Dic3⋊C4—62no—
269Dic3⋊C4—121no—
270C4×Dic3—21no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C4×Dic3—121no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—122no—
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D311yescharacteristic
280Dic12—62no—
281D3×C8—122no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3C2×Q1614yes—
286C32×C4—21no—
287C32×C4—42no—
288C32×C4C2×Q1612yes—
289C32×C4C2×#4111yescharacteristic
290C32×C4H(5,𝔽2)11yescharacteristic
291C3⋊Dic3—22no—
292C3⋊Dic3—41no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×Q8—92no—
298C2×Q16—91no—
299C2×Q16—92no—
300C22×C8—92no—
301C4⋊Q8—31no—
302C4⋊Q8—181no—
303C4⋊Q8D3211yescharacteristic
304#125—61no—
305C22⋊Q8—32no—
306C22⋊Q8—62no—
307C22⋊Q8—92no—
308C22⋊Q8—182no—
309C4×Q8—31no—
310C4×Q8—91no—
311C4×D4—31no—
312C4×D4—61no—
313C4×D4—181no—
314C2×C4⋊C4—32no—
315#107—91no—
316#107—92no—
317C4⋊C8—91no—
318#103—32no—
319#103—32no—
320#103—91no—
321#103—92no—
322#103—91no—
323#103—92no—
324C22⋊C8—92no—
325C4×C8—31no—
326C23×C3—32no—
327C22×D3C2×#6712yes—
328C3×Q8—61no—
329C3×Q8—62no—
330C3×Q8—61no—
331C3×Q8—62no—
332C3×Q8—81no—
333C3×Q8—81no—
334C3×Q8—82no—
335C3×D4—34no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—32no—
342C2×C3×C4—42no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—242no—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×Dic3—22no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—124no—
365C2×Dic3C2×#6712yes—
366D12#21614yescomplemented
367C4×D3—22no—
368C4×D3—22no—
369C4×D3—82no—
370C4×D3—124no—
371Dic6—21no—
372Dic6—22no—
373Dic6—21no—
374Dic6—22no—
375Dic6—32no—
376Dic6—32no—
377Dic6—62no—
378Dic6—61no—
379Dic6—61no—
380Dic6—121no—
381Dic6—124no—
382Dic6—124no—
383C3×C8—61no—
384C3×C8—61no—
385C3⋊C8—21no—
386C3⋊C8—21no—
387C3⋊C8—62no—
388C3⋊C8—62no—
389C3⋊C8—122no—
390C2×C32#54611yescharacteristic
391C2×C32C22×Q1611yescharacteristic
392C2×C32#57711yescharacteristic
393C3×D3—24no—
394C2×Q8—21no—
395C2×Q8—32no—
396C2×Q8—31no—
397C2×Q8—91no—
398C2×Q8—182no—
399C2×Q8—184no—
400C2×Q8—362no—
401C2×D4—31no—
402C22×C4—32no—
403C22×C4—62no—
404C22×C4—182no—
405Q16—182no—
406Q16—362no—
407C2×C8—31no—
408C2×C8—31no—
409C2×C8—92no—
410C2×C8—362no—
411C4⋊C4—21no—
412C4⋊C4—31no—
413C4⋊C4—31no—
414C4⋊C4—62no—
415C4⋊C4—62no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—91no—
420C4⋊C4—182no—
421C4⋊C4—181no—
422C4⋊C4C2×D3212yes—
423C22⋊C4—32no—
424C22⋊C4—62no—
425C22⋊C4—182no—
426C42—61no—
427C42—181no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—34no—
431C22×C3—62no—
432C22×C3—62no—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×#6711yescharacteristic
435C2×D3—22no—
436C2×D3—22no—
437C2×D3C2×#21614yes—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—41no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—62no—
447C3×C4—82no—
448C3×C4—121no—
449C3×C4—121no—
450C3×C4—122no—
451C3×C4D3×Q1612yes—
452C3×C4C2×#21612yes—
453C3×C4D3×#4111yescharacteristic
454C3×C4D3×#4111yescharacteristic
455C3×C4#100911yescharacteristic
456C3×C4#100911yescharacteristic
457Dic3—22no—
458Dic3—42no—
459Dic3—41no—
460Dic3—41no—
461Dic3—62no—
462Dic3—62no—
463Dic3—122no—
464Dic3—121no—
465Dic3—121no—
466Dic3—241no—
467C32#329911yescharacteristic, complemented, Sylow
468C23—32no—
469Q8—61no—
470Q8—62no—
471Q8—61no—
472Q8—62no—
473Q8—81no—
474Q8—92no—
475Q8—181no—
476Q8—364no—
477D4—34no—
478C2×C4—22no—
479C2×C4—32no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—242no—
488C2×C4—364no—
489C2×C4D3×#6711yescharacteristic
490C2×C4D3×#6711yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—61no—
493C8—61no—
494C8—182no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—64no—
499C2×C3#567611yescharacteristic
500C2×C3#576211yescharacteristic
501C2×C3C2×D3×Q1611yescharacteristic
502C2×C3C22×#21611yescharacteristic
503C2×C3#582911yescharacteristic
504C2×C3#583611yescharacteristic
505D3—24no—
506C22—34no—
507C22—62no—
508C22—62no—
509C22C2×D3×#6711yescharacteristic
510C4—21no—
511C4—42no—
512C4—62no—
513C4—121no—
514C4—122no—
515C4—121no—
516C4—182no—
517C4—361no—
518C4D3×#21612yes—
519C4#6431911yescharacteristic
520C4#6432011yescharacteristic
521C3—21no—
522C3#8161311yescharacteristic, complemented
523C3#8364011yescharacteristic, complemented
524C2—64no—
525C2#1059510511yescharacteristic
526C2C2×D3×#21611yescharacteristic
527C2#1059542811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#3299
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
3. #10592790C2semidirect
4. C3×#5093C2semidirect
5. #10590604C2semidirect
6. D3×#810C2semidirect
7. #10590518C2semidirect
8. #10590517C2semidirect
9. #10590384C2semidirect
10. C4×#3719C2semidirect
48. #5093D3semidirect
179. C3×D12Q16semidirect
366. D12#216semidirect
467. C32#3299semidirect
522. C3#81613semidirect
523. C3#83640semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
#105939042
#105927902
C3×#50932
#105906042
D3×#8102
#105905182
#105905172
#105903842
C4×#37192
C3⋊C8×D122
#836403
#816133