Finite Group Databasebeta

← #11895250

Subgroups — #11895250

Order 1152.

754 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5542C211yesmaximal, characteristic, complemented
2#10593960C211yesmaximal, characteristic, complemented
3#10592707C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic
5#10591478C212yesmaximal, complemented
6#10591431C212yesmaximal
7#10590544C212yesmaximal, complemented
8#10590453C212yesmaximal, complemented
9#10590363C211yesmaximal, characteristic, complemented
10#10590287C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83667—31nomaximal
13#79568—31nomaximal
14C32×C4×D4C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#936C2212yes—
17C2×C3×#213C2211yescharacteristic
18C3×#926—21no—
19C3×#924—21no—
20C3×#887C2212yes—
21C3×#879—22no—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63869C2212yes—
29#63856—21no—
30C2×#3715C2212yes—
31#63659C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#832C2211yescharacteristic
35C3×#809C2211yescharacteristic
36C3×#807C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63565C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#556—31no—
44#5579—31no—
45#5543—31no—
46#5542D311yescharacteristic, complemented
47C3×C4×D8—31no—
48#5153—32no—
49#5083—31no—
50#5079—31no—
51#5057—32no—
52#5056—32no—
53C4×#215—32no—
54Q8×C3⋊C8—31no—
55#5022—32no—
56#5019—31no—
57C4×#213D311yescharacteristic
58#5008—31no—
59#5008—31no—
60#5008—61no—
61#4877—32no—
62#4768—32no—
63#4758—32no—
64#4681—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×D3×Dic3—22no—
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2312yes—
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×#217—22no—
81C3×#217—22no—
82C3×#213—22no—
83C3×(C2×D3)⋊C4—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3715—24no—
98#3360—91noSylow
99C2×C3×D8—31no—
100C3×C4⋊Q8—31no—
101C3×#126—62no—
102C3×#124—32no—
103C3×C22⋊Q8—61no—
104C3×C4×Q8—31no—
105C3×C4×Q8—32no—
106C3×C4×D4—21no—
107C3×C4×D4—31no—
108C3×C4×D4C2×D311yescharacteristic
109C3×C4×D4C2×D311yescharacteristic
110C3×#117—61no—
111#946—61no—
112C2×#215—32no—
113#936C2×D312yes—
114D4×Dic3—32no—
115C2×#214—32no—
116C2×#213C2×D311yescharacteristic
117#926—21no—
118C2×C4⋊Dic3—61no—
119#924—21no—
120#924—61no—
121#896—62no—
122D3×C4⋊C4—61no—
123#890—32no—
124#887C2×D312yes—
125#879—22no—
126#878—62no—
127C4×D12—32no—
128C4×D12C2×D311yescharacteristic
129#870—32no—
130#869—31no—
131#869—31no—
132#869—61no—
133#869C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#107—31no—
136C3×#102—31no—
137C3×#102—31no—
138C3×C4×C8—31no—
139#835—32no—
140#835—32no—
141#835—32no—
142#832—32no—
143#832—32no—
144#832—62no—
145#832C2×D311yescharacteristic
146#816—32no—
147#816—32no—
148Dic3⋊C8—32no—
149C8×Dic3—32no—
150#810—32no—
151#809C2×D311yescharacteristic
152#808—32no—
153#808—32no—
154#808—62no—
155#807C2×D311yescharacteristic
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—21no—
164C32×D4—21no—
165C32×D4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—42no—
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—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183D3×Dic3—82no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#556—31no—
188#554—91no—
189#488—92no—
190#487—91no—
191#479—92no—
192#476—91no—
193#463—92no—
194#461—91no—
195C8×Q8—91no—
196C4×SD16—92no—
197C4×D8—31no—
198C2×C3×Q8—31no—
199C2×C3×Q8—32no—
200C2×C3×D4—21no—
201C2×C3×D4—31no—
202C2×C3×D4C22×D311yescharacteristic
203C2×C3×D4C22×D311yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—41no—
207C22×C3×C4—61no—
208C22×Dic3—62no—
209C2×D12C22×D311yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—121no—
215C2×Dic6#6711yescharacteristic
216C2×Dic6C22×D312yes—
217C3×D8—62no—
218C2×C3×C8—31no—
219C2×C3×C8—31no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—31no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4C22×D311yescharacteristic
228C3×C4⋊C4C22×D311yescharacteristic
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—41no—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—61no—
235C3×C42—21no—
236C3×C42—32no—
237C3×C42—62no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—22no—
241#217—22no—
242#217—62no—
243#215—64no—
244#214—64no—
245#213—22no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C4⋊Dic3—32no—
251C4⋊Dic3—32no—
252C4⋊Dic3—62no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—62no—
256C4⋊Dic3—121no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259Dic3⋊C4—22no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4#6712yes—
264C4×Dic3—22no—
265C4×Dic3C22×D312yes—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271C22×C32—41no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—41no—
280C32×C4#13512yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C2×SD16—92no—
289C2×D8—31no—
290C4⋊Q8—31no—
291C4⋊Q8—91no—
292#126—62no—
293#125—92no—
294#124—32no—
295C22⋊Q8—61no—
296C22⋊Q8—182no—
297C22⋊Q8—181no—
298C4×Q8—31no—
299C4×Q8—32no—
300C4×D4—31no—
301C4×D4—92no—
302C4×D4D3211yescharacteristic
303#117—61no—
304C2×C4⋊C4—181no—
305#107—31no—
306#106—92no—
307C4⋊C8—92no—
308C4⋊C8—91no—
309#103—92no—
310#103—92no—
311#103—92no—
312#102—31no—
313#102—31no—
314#102—92no—
315C4×C8—31no—
316C4×C8—92no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—41no—
320C23×C3—61no—
321C22×D3—21no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—62no—
325C3×D4—22no—
326C3×D4—21no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—32no—
331C3×D4—41no—
332C3×D4—61no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4—82no—
346C2×C3×C4—122no—
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×Dic3—21no—
354C2×Dic3—22no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—122no—
358C2×Dic3—242no—
359C2×Dic3C2×#6712yes—
360C2×Dic3C2×#6712yes—
361D12—21no—
362D12#23512yes—
363C4×D3—42no—
364C4×D3—242no—
365Dic6—22no—
366Dic6—22no—
367Dic6—22no—
368Dic6—241no—
369Dic6—241no—
370Dic6—242no—
371C3×C8—61no—
372C3×C8—61no—
373C3⋊C8—21no—
374C3⋊C8—21no—
375C3⋊C8—62no—
376C3⋊C8—62no—
377C3⋊C8—122no—
378C2×C32—81no—
379C2×C32#54811yescharacteristic
380C2×C32C2×#13511yescharacteristic
381C2×C32#57711yescharacteristic
382C3×D3—42no—
383C2×Q8—31no—
384C2×Q8—32no—
385C2×Q8—181no—
386C2×D4—31no—
387C2×D4C2×D3211yescharacteristic
388C22×C4—21no—
389C22×C4—61no—
390C22×C4—182no—
391SD16—184no—
392D8—62no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8—92no—
396C4⋊C4—31no—
397C4⋊C4—32no—
398C4⋊C4—31no—
399C4⋊C4—62no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C4⋊C4—92no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—181no—
406C4⋊C4C2×D3211yescharacteristic
407C22⋊C4—21no—
408C22⋊C4—62no—
409C22⋊C4—62no—
410C22⋊C4—61no—
411C22⋊C4—182no—
412C42—32no—
413C42—62no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—42no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3—62no—
424C22×C3—81no—
425C22×C3—81no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C22×#6711yescharacteristic
430C2×D3—22no—
431C2×D3—41no—
432C2×D3—41no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—41no—
441C3×C4—62no—
442C3×C4—62no—
443C3×C4—81no—
444C3×C4—122no—
445C3×C4—121no—
446C3×C4#91212yes—
447C3×C4#95012yes—
448C3×C4C2×#23511yescharacteristic
449C3×C4D3×#4111yescharacteristic
450C3×C4#101011yescharacteristic
451C3×C4#101011yescharacteristic
452Dic3—22no—
453Dic3—22no—
454Dic3—41no—
455Dic3—42no—
456Dic3—122no—
457Dic3—122no—
458Dic3—242no—
459C32#336011yescharacteristic, complemented, Sylow
460C23—21no—
461C23—61no—
462Q8—62no—
463Q8—62no—
464Q8—62no—
465Q8—721no—
466D4—21no—
467D4—21no—
468D4—32no—
469D4—61no—
470C2×C4—21no—
471C2×C4—32no—
472C2×C4—32no—
473C2×C4—42no—
474C2×C4—62no—
475C2×C4—61no—
476C2×C4—122no—
477C2×C4—182no—
478C2×C4—722no—
479C2×C4D3×#6711yescharacteristic
480C2×C4D3×#6711yescharacteristic
481C2×C4C22×D3211yescharacteristic
482C8—61no—
483C8—61no—
484C8—182no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—82no—
489C2×C3—81no—
490C2×C3—81no—
491C2×C3—122no—
492C2×C3#555211yescharacteristic
493C2×C3C2×#91211yescharacteristic
494C2×C3#577011yescharacteristic
495C2×C3C2×#95011yescharacteristic
496C2×C3#583111yescharacteristic
497C2×C3#583711yescharacteristic
498D3—42no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—62no—
503C22—121no—
504C22—121no—
505C22C2×D3×#6711yescharacteristic
506C4—21no—
507C4—41no—
508C4—62no—
509C4—62no—
510C4—121no—
511C4—122no—
512C4—362no—
513C4#6393312yes—
514C4#6429811yescharacteristic
515C4D3×#23511yescharacteristic
516C3—21no—
517C3#7956811yescharacteristic, complemented
518C3#8366711yescharacteristic, complemented
519C2—81no—
520C2—122no—
521C2#1059489911yescharacteristic
522C2C2×#6393311yescharacteristic
523C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3360
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×#5542C2semidirect
2. #10593960C2semidirect
3. #10592707C2semidirect
5. #10591478C2semidirect
7. #10590544C2semidirect
8. #10590453C2semidirect
9. #10590363C2semidirect
10. #10590287C2semidirect
11. C3⋊C8×Dic6C2semidirect
46. #5542D3semidirect
459. C32#3360semidirect
517. C3#79568semidirect
518. C3#83667semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
#105939602
#105927072
C3×C4×#2132
#105914782
#105914312
#105905442
#105904532
#105903632
#105902872
C3⋊C8×Dic62
#836673
#795683