Finite Group Databasebeta

← #11895357

Subgroups — #11895357

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic, complemented
2#10593963C211yesmaximal, characteristic, complemented
3#10592714C211yesmaximal, characteristic
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591471C212yesmaximal, complemented
6#10591400C212yesmaximal, complemented
7#10590537C212yesmaximal, complemented
8#10590470C212yesmaximal, complemented
9#10590310C211yesmaximal, characteristic, complemented
10#10590281C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83643—31nomaximal
13#79621—31nomaximal
14C32×C4×D4C2211yescharacteristic
15C2×#3753C2212yes—
16#64083C2211yescharacteristic
17C3×D4×Dic3C2212yes—
18C2×C3×#214C2211yescharacteristic
19C2×C3×C4⋊Dic3—21no—
20C3×#924—21no—
21C3×#890C2212yes—
22C3×#878—22no—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63897—22no—
27#63894—21no—
28#63894C2212yes—
29#63864—21no—
30#63864C2212yes—
31#63636C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2211yescharacteristic
34C3×#810C2211yescharacteristic
35C3×#808C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63576C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2212yes—
40#63564C2212yes—
41#63564C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#554—31no—
44#5585—31no—
45#5585—31no—
46#5543D311yescharacteristic, complemented
47C3×C4×SD16—31no—
48#5165—32no—
49#5091—31no—
50#5088—31no—
51#5068—32no—
52#5066—32no—
53Q8×C3⋊C8—31no—
54#5021—31no—
55C4×#214D311yescharacteristic, complemented
56#5016—32no—
57#5015—31no—
58#5015—31no—
59#5015—61no—
60C4×#213—32no—
61#4871—32no—
62#4800—32no—
63#4756—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C22×C3×Dic3—22no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C2×#624—22no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3753—24no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×#217—22no—
82C3×#214—22no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3722—22no—
96#3722—22no—
97#3722—22no—
98#3361—91noSylow
99C2×C3×SD16—31no—
100C3×C4⋊Q8—31no—
101C3×#125—32no—
102C3×C22⋊Q8—62no—
103C3×C22⋊Q8—61no—
104C3×C4×Q8—31no—
105C3×C4×Q8—31no—
106C3×C4×D4—21no—
107C3×C4×D4—32no—
108C3×C4×D4C2×D311yescharacteristic
109C3×C4×D4C2×D311yescharacteristic
110C2×C3×C4⋊C4—61no—
111#947—32no—
112#947—61no—
113D4×Dic3C2×D312yes—
114C2×#214C2×D311yescharacteristic
115C2×#213—32no—
116C2×#213—32no—
117C2×#213—62no—
118C2×C4⋊Dic3—21no—
119#924—21no—
120#894—62no—
121#894—62no—
122#893—32no—
123#893—61no—
124#890C2×D312yes—
125#878—22no—
126#875—32no—
127#875—61no—
128#874—31no—
129#874—31no—
130#874—61no—
131C4×D12—32no—
132C4×D12—61no—
133#869C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#106—31no—
137C3×#103—31no—
138C3×#102—31no—
139C3×C4×C8—31no—
140#835—32no—
141#832C2×D311yescharacteristic
142#821—32no—
143#821—32no—
144Dic3⋊C8—32no—
145C8×Dic3—32no—
146#810—32no—
147#810C2×D311yescharacteristic
148#809—32no—
149#809—32no—
150#809—32no—
151#809—32no—
152#809—62no—
153#808C2×D311yescharacteristic
154#807—32no—
155#807—32no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C23×C32—21no—
163C22×C3⋊D3—22no—
164C32×D4—21no—
165C32×D4#4112yes—
166C2×C32×C4—21no—
167C2×C32×C4—42no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—42no—
174C4⋊(C3⋊D3)—81no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—82no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×Dic6—22no—
182C3×Dic6—21no—
183C3×Dic6—21no—
184C3×Dic6—81no—
185#624—82no—
186C3⋊(C3⋊C8)—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#559—91no—
190#554—31no—
191#488—92no—
192#486—91no—
193#478—92no—
194#477—91no—
195#463—92no—
196#459—91no—
197C8×Q8—91no—
198C4×SD16—31no—
199C4×D8—92no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×D4—21no—
204C2×C3×D4C22×D311yescharacteristic
205C2×C3×D4C22×D311yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—41no—
209C22×C3×C4—62no—
210C22×Dic3—22no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—62no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—61no—
218C2×D12—121no—
219C2×D12—121no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×Dic6—21no—
223C2×Dic6#6711yescharacteristic
224C2×Dic6C22×D311yescharacteristic
225C3×SD16—62no—
226C2×C3×C8—31no—
227C2×C3×C8—31no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—41no—
242C3×C22⋊C4—62no—
243C3×C42—21no—
244C3×C42—32no—
245C3×C42—61no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#217—22no—
249#214—22no—
250#213—64no—
251#213—64no—
252#213—124no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259C4⋊Dic3—21no—
260C4⋊Dic3—22no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—21no—
265Dic3⋊C4—22no—
266Dic3⋊C4#6712yes—
267C4×Dic3—21no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—62no—
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D311yescharacteristic
274C22×C32—22no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32C22×D411yescharacteristic
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C32×C4—21no—
282C32×C4—41no—
283C32×C4#13512yes—
284C32×C4C2×#4111yescharacteristic
285C32×C42−1+411yescharacteristic
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3—42no—
291C2×SD16—31no—
292C2×D8—92no—
293C4⋊Q8—31no—
294#127—91no—
295#125—32no—
296#124—92no—
297#124—181no—
298#123—182no—
299C22⋊Q8—62no—
300C22⋊Q8—61no—
301C4×Q8—31no—
302C4×Q8—31no—
303C4×D4—32no—
304C4×D4—92no—
305C4×D4—181no—
306C4×D4D3211yescharacteristic
307C2×C4⋊C4—61no—
308#107—92no—
309#106—31no—
310C4⋊C8—92no—
311C4⋊C8—91no—
312#103—31no—
313#103—92no—
314#102—31no—
315#102—92no—
316#102—92no—
317#102—92no—
318C4×C8—31no—
319C4×C8—92no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—41no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—122no—
326C3×Q8—62no—
327C3×Q8—61no—
328C3×Q8—61no—
329C3×Q8—241no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—22no—
333C3×D4—41no—
334C3×D4#23512yes—
335C3×D4#23912yes—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—41no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—62no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—82no—
350C2×C3×C4—242no—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—22no—
360C2×Dic3—82no—
361C2×Dic3C2×#6712yes—
362C2×Dic3C2×#6712yes—
363D12—62no—
364D12—62no—
365D12—62no—
366D12—62no—
367D12—122no—
368D12—122no—
369D12—122no—
370D12—122no—
371D12—242no—
372D12—241no—
373D12—241no—
374D12—242no—
375C4×D3—242no—
376C4×D3—242no—
377Dic6—22no—
378Dic6—21no—
379Dic6—21no—
380Dic6—81no—
381C3×C8—61no—
382C3×C8—61no—
383C3⋊C8—21no—
384C3⋊C8—21no—
385C3⋊C8—62no—
386C3⋊C8—62no—
387C3⋊C8—122no—
388C2×C32—42no—
389C2×C32#54811yescharacteristic
390C2×C32C2×#13511yescharacteristic
391C2×C32#57611yescharacteristic
392C3⋊D3—82no—
393C2×Q8—31no—
394C2×Q8—31no—
395C2×Q8—61no—
396C2×D4—92no—
397C2×D4—181no—
398C2×D4—181no—
399C2×D4C2×D3211yescharacteristic
400C22×C4—21no—
401C22×C4—62no—
402C22×C4—182no—
403SD16—62no—
404D8—184no—
405C2×C8—31no—
406C2×C8—31no—
407C2×C8—92no—
408C4⋊C4—31no—
409C4⋊C4—32no—
410C4⋊C4—31no—
411C4⋊C4—32no—
412C4⋊C4—62no—
413C4⋊C4—62no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4C2×D3211yescharacteristic
417C22⋊C4—21no—
418C22⋊C4—62no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22⋊C4—182no—
422C42—32no—
423C42—61no—
424C42C2×D3211yescharacteristic
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—42no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—242no—
444C2×D3—242no—
445C2×D3—242no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—62no—
455C3×C4—62no—
456C3×C4—81no—
457C3×C4—122no—
458C3×C4—121no—
459C3×C4—121no—
460C3×C4#91612yes—
461C3×C4#95012yes—
462C3×C4C2×#23511yescharacteristic
463C3×C4C2×#23911yescharacteristic
464C3×C4#100711yescharacteristic
465C3×C4#101011yescharacteristic
466Dic3—22no—
467Dic3—22no—
468Dic3—41no—
469Dic3—41no—
470Dic3—42no—
471C32#336111yescharacteristic, complemented, Sylow
472C23—21no—
473C23—182no—
474Q8—62no—
475Q8—61no—
476Q8—61no—
477Q8—241no—
478D4—21no—
479D4—182no—
480D4—182no—
481D4—362no—
482D4—721no—
483D4#379912yes—
484C2×C4—21no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—42no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—62no—
491C2×C4—242no—
492C2×C4—722no—
493C2×C4D3×#6711yescharacteristic
494C2×C4D3×#6711yescharacteristic
495C2×C4C22×D3211yescharacteristic
496C8—61no—
497C8—61no—
498C8—182no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—42no—
503C2×C3—42no—
504C2×C3—82no—
505C2×C3#555211yescharacteristic
506C2×C3C2×#91611yescharacteristic
507C2×C3#576911yescharacteristic
508C2×C3#581711yescharacteristic
509C2×C3C2×#95011yescharacteristic
510C2×C3#583511yescharacteristic
511D3—242no—
512D3—242no—
513D3—482no—
514C22—22no—
515C22—41no—
516C22—41no—
517C22—362no—
518C22—362no—
519C22—362no—
520C22C2×D3×#6711yescharacteristic
521C4—21no—
522C4—41no—
523C4—62no—
524C4—62no—
525C4—121no—
526C4—122no—
527C4—121no—
528C4#6393512yes—
529C4#6429711yescharacteristic
530C4C2×#379911yescharacteristic
531C3—21no—
532C3#7962111yescharacteristic, complemented
533C3#8364311yescharacteristic, complemented
534C2—42no—
535C2—722no—
536C2#1059490211yescharacteristic
537C2C2×#6393511yescharacteristic
538C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10592714C2
hypercenterC4×D4D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5543C2semidirect
2. #10593963C2semidirect
4. C3×C4×#214C2semidirect
5. #10591471C2semidirect
6. #10591400C2semidirect
7. #10590537C2semidirect
8. #10590470C2semidirect
9. #10590310C2semidirect
10. #10590281C2semidirect
11. C3⋊C8×Dic6C2semidirect
46. #5543D3semidirect
55. C4×#214D3semidirect
471. C32#3361semidirect
532. C3#79621semidirect
533. C3#83643semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
#105939632
#105927142
C3×C4×#2142
#105914712
#105914002
#105905372
#105904702
#105903102
#105902812
C3⋊C8×Dic62
#836433
#796213