Finite Group Databasebeta

← #11887673

Subgroups — #11887673

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593960C211yesmaximal, characteristic
2Dic6×D12C211yesmaximal, characteristic
3#10592380C211yesmaximal, characteristic, complemented
4C3×C4×Dic12C211yesmaximal, characteristic, complemented
5C3×C8×D12C211yesmaximal, characteristic
6#10590949C212yesmaximal, complemented
7#10590848C212yesmaximal, complemented
8#10590684C212yesmaximal, complemented
9D3×#816C212yesmaximal, complemented
10#10590385C211yesmaximal, characteristic, complemented
11#10590283C211yesmaximal, characteristic, complemented
12#79735—31nomaximal
13#79448—31nomaximal
14C2×D3×Dic6C2212yes—
15#64078C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63918—21no—
23#63896—22no—
24#63893—22no—
25Dic3×D12—21no—
26Dic3×D12—21no—
27D3×C4⋊Dic3C2212yes—
28#63869—21no—
29#63857C2212yes—
30#63856C2212yes—
31C2×#3719C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63643C2212yes—
34#63643C2212yes—
35C3×(C2×D3)⋊C8C2212yes—
36C3×#818C2211yescharacteristic
37C3×#816C2211yescharacteristic
38C3×#816C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63567C2212yes—
42#63566C2212yes—
43#5579—31no—
44Q8×D12—31no—
45#5543—31no—
46D4×Dic6—31no—
47C3×C4×Q16—31no—
48C3×C8×D4—31no—
49#5186—32no—
50#5116—32no—
51C2×#816—32no—
52#5031—31no—
53#5021—31no—
54#4884—32no—
55#4850—31no—
56#4849—31no—
57#4813—32no—
58D3×#103—32no—
59#4739—32no—
60#4722—32no—
61C4×Dic12D311yescharacteristic, complemented
62C8×D12D311yescharacteristic
63#4681—31no—
64#4681—31no—
65#4681—61no—
66C2×#634—21no—
67C2×#634C2312yes—
68C2×C3×D12D411yescharacteristic
69C2×C3×C4×D3C2312yes—
70C2×C3×Dic6C2311yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×D3×Dic3—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—24no—
76D3×Dic6—42no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C3×(C2×D3)⋊C4D412yes—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3—21no—
91C3×C4×Dic3—21no—
92C2×C3×C3⋊C8C2312yes—
93C3×Dic12—22no—
94C3×D3×C8—42no—
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3719—42no—
101#3299—91noSylow
102C2×D3×Q8—32no—
103C22×Dic6—32no—
104C2×C3×Q16—31no—
105C22×C3×C8—32no—
106C3×C4×Q8—31no—
107C3×C4×Q8—31no—
108C3×C4×D4—31no—
109#946—32no—
110C2×#216—32no—
111D4×Dic3—61no—
112D4×Dic3—61no—
113C2×C4⋊Dic3—32no—
114#924—32no—
115#924—32no—
116C2×Dic12—32no—
117C2×Dic12C2×D311yescharacteristic
118C2×D3×C8C2×D312yes—
119#897—32no—
120#897—62no—
121#896—62no—
122D3×C4⋊C4—32no—
123#890—61no—
124#888—61no—
125#878—62no—
126#878—62no—
127C4×D12—61no—
128C4×D12—61no—
129C4×D12C2×D311yescharacteristic
130#870—61no—
131#869—31no—
132#869—31no—
133#869—31no—
134#869—31no—
135#869—61no—
136#869—61no—
137#869—61no—
138C4×Dic6C2×D311yescharacteristic
139C4×Dic6C2×D311yescharacteristic
140C3×#107—31no—
141C3×C4⋊C8—31no—
142C3×#103—31no—
143C3×#103—31no—
144C3×C22⋊C8—32no—
145C3×C4×C8—21no—
146C3×C4×C8C2×D311yescharacteristic
147C3×C4×C8C2×D311yescharacteristic
148#835—32no—
149(C2×D3)⋊C8C2×D312yes—
150#818—32no—
151#818C2×D311yescharacteristic
152#816—32no—
153#816—32no—
154#816—32no—
155#816—32no—
156#816—32no—
157#816—32no—
158#816—62no—
159#816—62no—
160#816C2×D311yescharacteristic
161#816C2×D311yescharacteristic
162#810—32no—
163#807—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C22×C3×D3C2×D412yes—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171#634—22no—
172#634—22no—
173#634—81no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C3×D12Q1614yescomplemented
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×Dic6—21no—
183C3×Dic6—21no—
184C3×Dic6—21no—
185C3×Dic6#4112yes—
186#627—44no—
187D3×Dic3—44no—
188D3×Dic3—82no—
189C32×C8—21no—
190C32×C8—21no—
191C3×C3⋊C8—22no—
192#554—91no—
193D4×Q8—91no—
194#487—91no—
195#484—92no—
196#477—91no—
197#467—92no—
198#462—91no—
199#451—92no—
200C4×Q16—31no—
201C8×D4—31no—
202C2×#103—92no—
203C2×C3×Q8—31no—
204C2×C3×Q8—31no—
205C2×C3×D4—31no—
206C22×C3×C4—32no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209D3×Q8—64no—
210D3×Q8—122no—
211C2×D12D1211yescharacteristic
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3C22×D312yes—
215C2×Dic6—32no—
216C2×Dic6—32no—
217C2×Dic6—62no—
218C2×Dic6—64no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—121no—
224C2×Dic6—122no—
225C2×Dic6C22×D311yescharacteristic
226C2×Dic6C22×D311yescharacteristic
227C3×Q16—62no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—32no—
231C2×C3×C8—122no—
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C22×D311yescharacteristic
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C22⋊C4—32no—
242C3×C42—21no—
243C3×C42—61no—
244C3×C42—61no—
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247#217—62no—
248#217—62no—
249#216—122no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4D1212yes—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3—62no—
264C4⋊Dic3—121no—
265C4⋊Dic3—121no—
266C4⋊Dic3—121no—
267C4⋊Dic3D1211yescharacteristic
268C4⋊Dic3C22×D311yescharacteristic
269C4⋊Dic3C22×D311yescharacteristic
270Dic3⋊C4—21no—
271Dic3⋊C4—21no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276C4×Dic3—21no—
277C4×Dic3—21no—
278C2×C3⋊C8C22×D312yes—
279Dic12—22no—
280Dic12—122no—
281D3×C8—42no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3C2×Q1614yes—
286C32×C4—21no—
287C32×C4C2×Q1612yes—
288C32×C4C2×#4111yescharacteristic
289C32×C4H(5,𝔽2)11yescharacteristic
290C3⋊Dic3—42no—
291C3⋊Dic3—42no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—41no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×Q8—92no—
298C2×Q16—31no—
299C2×Q16—92no—
300C22×C8—32no—
301C4⋊Q8—91no—
302C4⋊Q8—91no—
303C4⋊Q8—181no—
304#125—181no—
305C22⋊Q8—92no—
306C22⋊Q8—92no—
307C22⋊Q8—182no—
308C22⋊Q8—182no—
309C4×Q8—31no—
310C4×Q8—31no—
311C4×D4—31no—
312C4×D4—181no—
313C4×D4—181no—
314C2×C4⋊C4—92no—
315#107—31no—
316#107—92no—
317C4⋊C8—31no—
318#103—31no—
319#103—31no—
320#103—92no—
321#103—92no—
322#103—92no—
323#103—92no—
324C22⋊C8—32no—
325C4×C8D3211yescharacteristic
326C23×C3—32no—
327C22×D3C2×D1212yes—
328C3×Q8—32no—
329C3×Q8—61no—
330C3×Q8—61no—
331C3×Q8—61no—
332C3×D4—34no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—61no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—124no—
360C2×Dic3—242no—
361C2×Dic3C2×D1212yes—
362D12Dic1214yescomplemented
363C4×D3—22no—
364C4×D3—22no—
365C4×D3—124no—
366C4×D3—242no—
367Dic6—21no—
368Dic6—21no—
369Dic6—21no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—62no—
374Dic6—122no—
375Dic6—122no—
376Dic6—124no—
377Dic6—124no—
378Dic6—241no—
379Dic6—241no—
380Dic6—242no—
381Dic6#23512yes—
382C3×C8—21no—
383C3×C8—21no—
384C3×C8—21no—
385C3×C8—21no—
386C3×C8—41no—
387C3×C8—41no—
388C3×C8—62no—
389C3⋊C8—22no—
390C2×C32#54611yescharacteristic
391C2×C32C22×Q1611yescharacteristic
392C2×C32#57711yescharacteristic
393C3×D3—24no—
394C2×Q8—31no—
395C2×Q8—31no—
396C2×Q8—92no—
397C2×Q8—182no—
398C2×Q8—184no—
399C2×Q8—181no—
400C2×Q8—362no—
401C2×D4—31no—
402C22×C4—32no—
403C22×C4—182no—
404C22×C4—182no—
405Q16—62no—
406Q16—362no—
407C2×C8—32no—
408C2×C8—122no—
409C2×C8C2×D3211yescharacteristic
410C2×C8C2×D3211yescharacteristic
411C4⋊C4—31no—
412C4⋊C4—31no—
413C4⋊C4—31no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4—92no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C22⋊C4—32no—
424C22⋊C4—182no—
425C22⋊C4—182no—
426C42—61no—
427C42—61no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—34no—
431C22×C3—62no—
432C22×C3—62no—
433C22×C3C22×D1211yescharacteristic
434C22×C3C2×D3×D411yescharacteristic
435C2×D3—22no—
436C2×D3—22no—
437C2×D3C2×Dic1214yes—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—62no—
445C3×C4—62no—
446C3×C4—121no—
447C3×C4—121no—
448C3×C4—121no—
449C3×C4C2×Dic1212yes—
450C3×C4D3×Q1612yes—
451C3×C4C2×#23511yescharacteristic
452C3×C4#100411yescharacteristic
453C3×C4D3×#4111yescharacteristic
454C3×C4#100911yescharacteristic
455Dic3—22no—
456Dic3—22no—
457Dic3—41no—
458Dic3—41no—
459Dic3—41no—
460Dic3—122no—
461Dic3—122no—
462Dic3—122no—
463Dic3—122no—
464Dic3—242no—
465Dic3—242no—
466C32#329911yescharacteristic, complemented, Sylow
467C23—32no—
468Q8—32no—
469Q8—61no—
470Q8—61no—
471Q8—61no—
472Q8—182no—
473Q8—182no—
474Q8—364no—
475Q8—721no—
476D4—34no—
477C2×C4—32no—
478C2×C4—61no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—364no—
487C2×C4—722no—
488C2×C4D3×D1211yescharacteristic
489C2×C4D3×D1211yescharacteristic
490C2×C4C22×D3211yescharacteristic
491C8—21no—
492C8—21no—
493C8—62no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—64no—
498C2×C3#555011yescharacteristic
499C2×C3#555411yescharacteristic
500C2×C3C22×Dic1211yescharacteristic
501C2×C3#575111yescharacteristic
502C2×C3C2×D3×Q1611yescharacteristic
503C2×C3#577011yescharacteristic
504D3—24no—
505C22—34no—
506C22—62no—
507C22—62no—
508C22C2×D3×D1211yescharacteristic
509C4—21no—
510C4—62no—
511C4—62no—
512C4—121no—
513C4—121no—
514C4—121no—
515C4—362no—
516C4—362no—
517C4D3×Dic1212yes—
518C4D3×#23511yescharacteristic
519C4#6430711yescharacteristic
520C3—21no—
521C3#7944811yescharacteristic, complemented
522C3#7973511yescharacteristic, complemented
523C2—64no—
524C2#1059400311yescharacteristic
525C2#1059467911yescharacteristic
526C2C2×D3×Dic1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4×C8D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. #10592380C2semidirect
4. C3×C4×Dic12C2semidirect
6. #10590949C2semidirect
7. #10590848C2semidirect
8. #10590684C2semidirect
9. D3×#816C2semidirect
10. #10590385C2semidirect
11. #10590283C2semidirect
61. C4×Dic12D3semidirect
179. C3×D12Q16semidirect
362. D12Dic12semidirect
466. C32#3299semidirect
521. C3#79448semidirect
522. C3#79735semidirect

Maximal subgroups

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

subgroupindex
#105939602
Dic6×D122
#105923802
C3×C4×Dic122
C3×C8×D122
#105909492
#105908482
#105906842
D3×#8162
#105903852
#105902832
#797353
#794483