Finite Group Databasebeta

← #11895360

Subgroups — #11895360

Order 1152.

783 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5713C211yesmaximal, characteristic, complemented
2#10593960C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic
5#10591478C212yesmaximal, complemented
6#10591431C212yesmaximal, complemented
7Dic3×#213C212yesmaximal, complemented
8#10591411C212yesmaximal, complemented
9C4×#3715C211yesmaximal, characteristic, complemented
10#10590283C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83713—31nomaximal
13#80319—31nomaximal
14C32×#127C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#936—21no—
17C3×#936C2212yes—
18C3×#935—22no—
19C3×D4×Dic3—21no—
20C3×D4×Dic3C2212yes—
21C2×C3×#213C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63869C2212yes—
29#63856—21no—
30C2×#3715C2211yescharacteristic
31#63659C2212yes—
32#63659C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#832C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63575C2212yes—
37#63574C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2212yes—
40#63565C2211yescharacteristic
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#559—31no—
44#5713D311yescharacteristic, complemented
45#5579—31no—
46#5543—31no—
47C3×#459—31no—
48#5153—32no—
49Dic3×D8—32no—
50#5072D311yescharacteristic
51#5070—31no—
52#5070—31no—
53#5070—61no—
54#5057—32no—
55#5056—32no—
56C4×#215—31no—
57Q8×C3⋊C8—31no—
58#5021—31no—
59C4×#214—31no—
60C4×#213—32no—
61#5009—32no—
62#4850—31no—
63#4830—31no—
64#4768—32no—
65#4766—32no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634—21no—
70C22×C3×Dic3—22no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C2×D3×Dic3—22no—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2312yes—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×#217—22no—
82C3×#217—22no—
83C3×#217—22no—
84C3×#213—24no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3715—22no—
98#3361—91noSylow
99C2×C3×D8—32no—
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—31no—
110C3×C4×D4—61no—
111#946—61no—
112C2×#215—31no—
113#936—21no—
114#936C2×D312yes—
115#935—22no—
116D4×Dic3—21no—
117D4×Dic3—32no—
118D4×Dic3C2×D312yes—
119C2×#214—31no—
120C2×#213C2×D312yes—
121C2×C4⋊Dic3—61no—
122#924—61no—
123#896—62no—
124D3×C4⋊C4—61no—
125#890—32no—
126#878—62no—
127C4×D12—32no—
128C4×D12C2×D311yescharacteristic
129#870—32no—
130#869—31no—
131#869—31no—
132#869—61no—
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×C4⋊C8—31no—
136C3×#102—32no—
137#835—31no—
138#835—32no—
139#832—32no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—31no—
144#832—62no—
145#832—62no—
146#832C2×D312yes—
147#818—32no—
148#816—32no—
149Dic3⋊C8—32no—
150C8×Dic3—32no—
151#810—31no—
152#809—31no—
153#808—31no—
154#808—31no—
155#807—32no—
156C4⋊(C3⋊C8)—32no—
157C4⋊(C3⋊C8)C2×D311yescharacteristic
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8—61no—
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—22no—
172#634—81no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—82no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—21no—
180C3×D12#4112yes—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—21no—
184C3×Dic6—21no—
185D3×Dic3—82no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8—22no—
189#559—31no—
190#554—91no—
191#488—92no—
192#486—91no—
193#478—92no—
194#477—91no—
195#463—92no—
196#459—31no—
197C8×Q8—91no—
198C4×SD16—91no—
199C4×D8—92no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—22no—
207C2×C3×D4—31no—
208C2×C3×D4—41no—
209C2×C3×D4—41no—
210C2×C3×D4C22×D312yes—
211C2×C3×D4C22×D312yes—
212C22×C3×C4—62no—
213C22×C3×C4—61no—
214C22×Dic3—22no—
215C22×Dic3—62no—
216C2×D12C22×D311yescharacteristic
217C2×C4×D3—21no—
218C2×C4×D3—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—121no—
222C2×Dic6#6711yescharacteristic
223C2×Dic6C22×D311yescharacteristic
224C3×D8—64no—
225C2×C3×C8—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—61no—
231C3×C22⋊C4—62no—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—61no—
235C3×C42—21no—
236C3×C42—32no—
237C3×C42—61no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—22no—
241#217—22no—
242#217—22no—
243#217—62no—
244#215—62no—
245#214—62no—
246#213—24no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—62no—
255C4⋊Dic3—121no—
256C4⋊Dic3#6711yescharacteristic
257C4⋊Dic3C22×D311yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259Dic3⋊C4—21no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4#6712yes—
264C4×Dic3—21no—
265C4×Dic3C22×D312yes—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8C22×D312yes—
273C22×C32—42no—
274C22×C32—42no—
275C22×C32—42no—
276C22×C32C22×D411yescharacteristic
277C2×C3×D3—22no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C32×C4—21no—
281C32×C4#13512yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C2×SD16—91no—
291C2×D8—32no—
292C4⋊Q8—91no—
293#127D3211yescharacteristic
294#125—92no—
295#124—32no—
296#124—61no—
297#123—62no—
298C22⋊Q8—182no—
299C22⋊Q8—181no—
300C4×Q8—31no—
301C4×Q8—31no—
302C4×D4—32no—
303C4×D4—31no—
304C4×D4—61no—
305C4×D4—92no—
306C2×C4⋊C4—181no—
307#107—92no—
308#106—91no—
309C4⋊C8—31no—
310C4⋊C8—92no—
311#103—91no—
312#103—92no—
313#102—32no—
314#102—91no—
315#102—92no—
316#102—92no—
317C4×C8—92no—
318C4×C8—91no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—42no—
322C23×C3—61no—
323C22×D3—21no—
324C3×Q8—62no—
325C3×Q8—61no—
326C3×Q8—61no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—32no—
332C3×D4—42no—
333C3×D4—42no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—61no—
337C3×D4—82no—
338C3×D4—81no—
339C3×D4—81no—
340C3×D4—82no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—122no—
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—21no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—82no—
363C2×Dic3—122no—
364C2×Dic3—242no—
365C2×Dic3C2×#6712yes—
366C2×Dic3C2×#6712yes—
367D12—21no—
368D12#23712yes—
369C4×D3—42no—
370C4×D3—242no—
371Dic6—22no—
372Dic6—21no—
373Dic6—21no—
374Dic6—241no—
375Dic6—241no—
376Dic6—242no—
377C3×C8—62no—
378C3⋊C8—22no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C3⋊C8—121no—
384C3⋊C8—121no—
385C2×C32—82no—
386C2×C32#54811yescharacteristic
387C2×C32C2×#13511yescharacteristic
388C2×C32#57611yescharacteristic
389C3×D3—42no—
390C2×Q8—31no—
391C2×Q8—31no—
392C2×Q8—181no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—31no—
396C2×D4C2×D3212yes—
397C22×C4—62no—
398C22×C4—61no—
399C22×C4—182no—
400SD16—182no—
401D8—64no—
402C2×C8—32no—
403C2×C8—91no—
404C2×C8—91no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—31no—
408C4⋊C4—31no—
409C4⋊C4—61no—
410C4⋊C4—92no—
411C4⋊C4—182no—
412C4⋊C4—182no—
413C4⋊C4—181no—
414C22⋊C4—62no—
415C22⋊C4—62no—
416C22⋊C4—62no—
417C22⋊C4—61no—
418C22⋊C4—182no—
419C42—32no—
420C42—61no—
421C42C2×D3211yescharacteristic
422C22×C3—21no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—62no—
430C22×C3—82no—
431C22×C3—82no—
432C22×C3—82no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C2×D3—22no—
438C2×D3—41no—
439C2×D3—41no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—22no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—121no—
449C3×C4—121no—
450C3×C4—121no—
451C3×C4#91212yes—
452C3×C4#95012yes—
453C3×C4C2×#23711yescharacteristic
454C3×C4D3×#4111yescharacteristic
455C3×C4#101011yescharacteristic
456C3×C4#101011yescharacteristic
457Dic3—22no—
458Dic3—22no—
459Dic3—41no—
460Dic3—41no—
461Dic3—41no—
462Dic3—122no—
463Dic3—122no—
464Dic3—242no—
465C32#336111yescharacteristic, complemented, Sylow
466C23—22no—
467C23—61no—
468Q8—62no—
469Q8—61no—
470Q8—61no—
471Q8—721no—
472D4—22no—
473D4—22no—
474D4—32no—
475D4—42no—
476D4—61no—
477D4—81no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—122no—
484C2×C4—182no—
485C2×C4—242no—
486C2×C4—722no—
487C2×C4D3×#6711yescharacteristic
488C2×C4D3×#6711yescharacteristic
489C2×C4C22×D3211yescharacteristic
490C8—62no—
491C8—181no—
492C8—181no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—82no—
497C2×C3—82no—
498C2×C3—122no—
499C2×C3—162no—
500C2×C3#559811yescharacteristic
501C2×C3C2×#91211yescharacteristic
502C2×C3#577411yescharacteristic
503C2×C3C2×#95011yescharacteristic
504C2×C3#583111yescharacteristic
505C2×C3#583511yescharacteristic
506D3—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—62no—
511C22—121no—
512C22—121no—
513C22C2×D3×#6711yescharacteristic
514C4—21no—
515C4—62no—
516C4—62no—
517C4—121no—
518C4—121no—
519C4—121no—
520C4—362no—
521C4#6393312yes—
522C4#6430911yescharacteristic
523C4D3×#23711yescharacteristic
524C3—21no—
525C3#8031911yescharacteristic, complemented
526C3#8371311yescharacteristic, complemented
527C2—82no—
528C2—122no—
529C2#1059509711yescharacteristic
530C2C2×#6393311yescharacteristic
531C2#1059515711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5072C2
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. #10593960C2semidirect
3. #10592769C2semidirect
5. #10591478C2semidirect
6. #10591431C2semidirect
7. Dic3×#213C2semidirect
8. #10591411C2semidirect
9. C4×#3715C2semidirect
10. #10590283C2semidirect
11. #10590250C2semidirect
44. #5713D3semidirect
465. C32#3361semidirect
525. C3#80319semidirect
526. C3#83713semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
#105939602
#105927692
C3×#50722
#105914782
#105914312
Dic3×#2132
#105914112
C4×#37152
#105902832
#105902502
#837133
#803193