Finite Group Databasebeta

← #11895359

Subgroups — #11895359

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×#5713C211yesmaximal, characteristic, complemented
2#10593958C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591478C212yesmaximal, complemented
6#10591432C212yesmaximal, complemented
7#10591409C212yesmaximal, complemented
8#10591400C212yesmaximal, complemented
9C4×#3717C211yesmaximal, characteristic, complemented
10#10590310C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83713—31nomaximal
13#81585—31nomaximal
14C32×#127C2211yescharacteristic
15C2×#3753C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#936—21no—
18C3×#936C2212yes—
19C3×#935—22no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2212yes—
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63900—21no—
26#63894C2212yes—
27#63888—22no—
28#63871—21no—
29#63869C2212yes—
30C2×#3717C2211yescharacteristic
31#63659C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2212yes—
34C3×#832C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63576C2212yes—
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2211yescharacteristic
40#63565C2212yes—
41#63564C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#559—31no—
44#5730—31no—
45#5713D311yescharacteristic, complemented
46#5579—31no—
47C3×#486—31no—
48#5091—31no—
49#5072—31no—
50#5072—31no—
51#5072—61no—
52#5070D311yescharacteristic, complemented
53#5057—32no—
54#5056—32no—
55C4×#215—31no—
56Q8×C3⋊C8—31no—
57#5021—31no—
58C4×#213—32no—
59#5009—32no—
60#4787—32no—
61#4768—32no—
62#4763—32no—
63#4756—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C22×C3×Dic3—22no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C2×#624—22no—
76C32×C42C2311yescharacteristic
77#3753—24no—
78#3752—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×#217—22no—
82C3×#217—22no—
83C3×#217—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—21no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97#3717—22no—
98#3361—91noSylow
99C3×C4⋊Q8—31no—
100C3×#127—21no—
101C3×#127C2×D311yescharacteristic
102C3×#127C2×D311yescharacteristic
103C3×#124—32no—
104C3×#124—61no—
105C3×#123—62no—
106C3×C4×Q8—31no—
107C3×C4×Q8—31no—
108C3×C4×D4—32no—
109C3×C4×D4—61no—
110#946—61no—
111#946—62no—
112C2×#215—31no—
113#936—21no—
114#936C2×D312yes—
115#935—22no—
116D4×Dic3—21no—
117D4×Dic3C2×D312yes—
118C2×#213—32no—
119C2×#213—32no—
120C2×#213—62no—
121C2×#204—31no—
122#897—61no—
123#896—62no—
124#893—32no—
125D3×C4⋊C4—61no—
126D3×C4⋊C4—61no—
127#890—32no—
128C4×D12—31no—
129C4×D12—31no—
130C4×D12—32no—
131C4×D12—61no—
132#870—32no—
133#869C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#102—32no—
137C3×#102—32no—
138C3×C4×C8—31no—
139#835—32no—
140#835—31no—
141#832—32no—
142#832—32no—
143#832—62no—
144#832C2×D312yes—
145#832C2×D312yes—
146#821—31no—
147#817—31no—
148#816—31no—
149Dic3⋊C8—32no—
150C8×Dic3—32no—
151#810—32no—
152#809—31no—
153#808—31no—
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—22no—
163C22×C3⋊D3—21no—
164C32×D4—22no—
165C32×D4—22no—
166C32×D4—42no—
167C32×D4—81no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)#4112yes—
174C4×C3⋊D3—42no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
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—31no—
190#554—91no—
191#488—92no—
192#486—31no—
193#478—92no—
194#477—91no—
195#463—92no—
196#459—91no—
197C8×Q8—91no—
198C4×SD16—91no—
199C4×D8—92no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—22no—
208C2×C3×D4—41no—
209C2×C3×D4—41no—
210C2×C3×D4C22×D312yes—
211C2×C3×D4C22×D312yes—
212C22×C3×C4—62no—
213C22×Dic3—22no—
214C2×D12—31no—
215C2×D12—31no—
216C2×D12—61no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—121no—
222C2×Dic6—21no—
223C2×Dic6#6711yescharacteristic
224C2×Dic6C22×D311yescharacteristic
225C2×C3×C8—31no—
226C2×C3×C8—31no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C42—21no—
237C3×C42—32no—
238C3×C42—61no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#217—22no—
242#217—22no—
243#217—22no—
244#215—62no—
245#213—64no—
246#213—64no—
247#213—124no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—121no—
253C4⋊Dic3—21no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—61no—
257C4⋊Dic3—62no—
258C4⋊Dic3#6711yescharacteristic
259C4⋊Dic3C22×D311yescharacteristic
260C4⋊Dic3C22×D312yes—
261Dic3⋊C4—21no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4#6712yes—
266C4×Dic3—21no—
267C4×Dic3C22×D312yes—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—62no—
271C2×C3⋊C8C22×D311yescharacteristic
272C2×C3⋊C8C22×D311yescharacteristic
273#204—62no—
274C22×C32—42no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32C22×D411yescharacteristic
278C2×C3⋊D3—22no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C32×C4—21no—
282C32×C4#13512yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3⋊Dic3—41no—
286C3×Dic3—22no—
287C3×Dic3—22no—
288C3×Dic3—41no—
289C3×Dic3—42no—
290C3×Dic3—41no—
291C2×SD16—91no—
292C2×D8—92no—
293C4⋊Q8—31no—
294#127D3211yescharacteristic
295#125—92no—
296#124—32no—
297#124—61no—
298#123—62no—
299C22⋊Q8—182no—
300C22⋊Q8—181no—
301C4×Q8—31no—
302C4×Q8—31no—
303C4×D4—32no—
304C4×D4—61no—
305C4×D4—92no—
306C4×D4—91no—
307C2×C4⋊C4—181no—
308#107—92no—
309#106—91no—
310C4⋊C8—92no—
311C4⋊C8—91no—
312#103—92no—
313#103—91no—
314#102—32no—
315#102—32no—
316#102—91no—
317#102—92no—
318C4×C8—31no—
319C4×C8—92no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—42no—
323C22×D3—61no—
324C22×D3—61no—
325C22×D3—121no—
326C3×Q8—62no—
327C3×Q8—61no—
328C3×Q8—61no—
329C3×Q8—241no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—82no—
339C3×D4—81no—
340C3×D4—81no—
341C3×D4—82no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—32no—
346C2×C3×C4—32no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—62no—
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—22no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—82no—
363C2×Dic3—121no—
364C2×Dic3C2×#6712yes—
365C2×Dic3C2×#6712yes—
366D12—32no—
367D12—32no—
368D12—62no—
369D12—61no—
370D12—61no—
371D12—121no—
372C4×D3—122no—
373C4×D3—122no—
374C4×D3—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—82no—
389C2×C32#54811yescharacteristic
390C2×C32C2×#13511yescharacteristic
391C2×C32#57611yescharacteristic
392C3⋊D3—42no—
393C2×Q8—31no—
394C2×Q8—31no—
395C2×Q8—61no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—91no—
399C2×D4C2×D3212yes—
400C22×C4—62no—
401C22×C4—182no—
402C22×C4—181no—
403SD16—182no—
404D8—184no—
405C2×C8—31no—
406C2×C8—31no—
407C2×C8—92no—
408C4⋊C4—31no—
409C4⋊C4—32no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C4⋊C4—91no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C22⋊C4—62no—
418C22⋊C4—62no—
419C22⋊C4—62no—
420C22⋊C4—182no—
421C22⋊C4—181no—
422C42—32no—
423C42—61no—
424C42C2×D3211yescharacteristic
425C22×C3—21no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—82no—
433C22×C3—82no—
434C22×C3—82no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—122no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—241no—
445C2×D3—241no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—62no—
453C3×C4—62no—
454C3×C4—121no—
455C3×C4—121no—
456C3×C4—122no—
457C3×C4#91612yes—
458C3×C4#95012yes—
459C3×C4D3×#4111yescharacteristic
460C3×C4D3×#4111yescharacteristic
461C3×C4#101011yescharacteristic
462C3×C4#101011yescharacteristic
463Dic3—22no—
464Dic3—22no—
465Dic3—42no—
466Dic3—41no—
467Dic3—41no—
468Dic3—121no—
469Dic3—121no—
470Dic3—241no—
471C32#336111yescharacteristic, complemented, Sylow
472C23—22no—
473C23—181no—
474Q8—62no—
475Q8—61no—
476Q8—61no—
477Q8—241no—
478D4—22no—
479D4—22no—
480D4—42no—
481D4—81no—
482D4—92no—
483D4—181no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—181no—
490C2×C4—242no—
491C2×C4—362no—
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—82no—
503C2×C3—82no—
504C2×C3—162no—
505C2×C3#567711yescharacteristic
506C2×C3#575711yescharacteristic
507C2×C3C2×#91611yescharacteristic
508C2×C3C2×#95011yescharacteristic
509C2×C3#583111yescharacteristic
510C2×C3#583511yescharacteristic
511D3—122no—
512D3—122no—
513D3—242no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—182no—
518C22—361no—
519C22—361no—
520C22C2×D3×#6711yescharacteristic
521C4—21no—
522C4—62no—
523C4—62no—
524C4—121no—
525C4—122no—
526C4—121no—
527C4—361no—
528C4#6393512yes—
529C4#6430911yescharacteristic
530C4#6431211yescharacteristic
531C3—21no—
532C3#8158511yescharacteristic, complemented
533C3#8371311yescharacteristic, complemented
534C2—82no—
535C2—362no—
536C2#1059509611yescharacteristic
537C2C2×#6393511yescharacteristic
538C2#1059523711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radical#10592771C2
hypercenter#127D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5713C2semidirect
2. #10593958C2semidirect
4. C3×#5070C2semidirect
5. #10591478C2semidirect
6. #10591432C2semidirect
7. #10591409C2semidirect
8. #10591400C2semidirect
9. C4×#3717C2semidirect
10. #10590310C2semidirect
11. C3⋊C8×Dic6C2semidirect
45. #5713D3semidirect
52. #5070D3semidirect
471. C32#3361semidirect
532. C3#81585semidirect
533. C3#83713semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
#105939582
#105927712
C3×#50702
#105914782
#105914322
#105914092
#105914002
C4×#37172
#105903102
C3⋊C8×Dic62
#837133
#815853