Finite Group Databasebeta

← #11898377

Subgroups — #11898377

Order 1152.

780 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5542C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic, complemented
3#10592718C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic
5#10591470C212yesmaximal
6#10591441C212yesmaximal, complemented
7#10590532C212yesmaximal, complemented
8#10590481C212yesmaximal, complemented
9#10590386C211yesmaximal, characteristic, complemented
10#10590363C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83670—31nomaximal
13#79579—31nomaximal
14C32×C4×D4C2211yescharacteristic
15C2×#3754C2212yes—
16#64078C2211yescharacteristic
17C3×#936C2212yes—
18C2×C3×#213C2211yescharacteristic
19C3×#926—21no—
20C3×#924—21no—
21C3×#887C2212yes—
22C3×#879—22no—
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63861—22no—
27#63860C2212yes—
28#63856—21no—
29#63844C2212yes—
30#63841—21no—
31C2×#3719C2212yes—
32C2×#3719C2212yes—
33C2×#3715C2212yes—
34#63637C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×#832C2211yescharacteristic
37C3×#809C2211yescharacteristic
38C3×#807C2211yescharacteristic
39C3×C4×C3⋊C8C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41#63565C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#556—31no—
44#5584—31no—
45#5542—31no—
46#5542D311yescharacteristic, complemented
47C3×C4×D8—31no—
48#5155—32no—
49#5092—31no—
50#5083—31no—
51#5059—32no—
52#5054—32no—
53C4×#216—32no—
54#5028—32no—
55Q8×C3⋊C8—31no—
56#5019—31no—
57#5019—31no—
58#5019—31no—
59#5019—61no—
60C4×#213D311yescharacteristic
61#4873—32no—
62#4767—32no—
63#4767—32no—
64#4699—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2312yes—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C32×C4⋊C4C2311yescharacteristic
74C32×C22⋊C4—21no—
75C32×C42C2311yescharacteristic
76#3754—42no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—21no—
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—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3719—24no—
99#3719—42no—
100#3715—42no—
101#3393—91noSylow
102C2×C3×D8—31no—
103C3×C4⋊Q8—31no—
104C3×#126—62no—
105C3×#124—32no—
106C3×C22⋊Q8—61no—
107C3×C4×Q8—31no—
108C3×C4×Q8—32no—
109C3×C4×D4—21no—
110C3×C4×D4—31no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113C3×#117—61no—
114#946—61no—
115C2×#216—32no—
116C2×#216—32no—
117C2×#215—32no—
118#936—32no—
119#936C2×D312yes—
120C2×#214—32no—
121C2×#214—32no—
122C2×#214—32no—
123C2×#214—62no—
124C2×#213C2×D311yescharacteristic
125#926—21no—
126#926—61no—
127#924—21no—
128#924—61no—
129C2×Dic12—32no—
130C2×Dic12—32no—
131#898—62no—
132#892—61no—
133#887—32no—
134#887C2×D312yes—
135#879—22no—
136#879—62no—
137#875—32no—
138C4×D12C2×D311yescharacteristic
139#869—31no—
140#869—31no—
141#869—61no—
142#869C2×D311yescharacteristic
143C4×Dic6—32no—
144C4×Dic6C2×D311yescharacteristic
145C3×#107—31no—
146C3×#102—31no—
147C3×#102—31no—
148C3×C4×C8—31no—
149#835—32no—
150#832C2×D311yescharacteristic
151Dic3⋊C8—32no—
152C8×Dic3—32no—
153#810—32no—
154#810—32no—
155#810—32no—
156#810—62no—
157#809C2×D311yescharacteristic
158#807C2×D311yescharacteristic
159C4⋊(C3⋊C8)—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—32no—
162C4⋊(C3⋊C8)—61no—
163C4×C3⋊C8—32no—
164C4×C3⋊C8C2×D311yescharacteristic
165C23×C32—21no—
166C22×C3×D3—21no—
167C32×D4—21no—
168C32×D4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—22no—
175#634—22no—
176#634—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—21no—
182C3×D12—21no—
183C3×C4×D3—42no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C3⋊(C3⋊C8)—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8#4112yes—
190#556—31no—
191#556—91no—
192#495—92no—
193#494—91no—
194#464—92no—
195#464—92no—
196#461—91no—
197#461—91no—
198C8×Q8—91no—
199C4×Q16—92no—
200C4×D8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—32no—
203C2×C3×D4—21no—
204C2×C3×D4—31no—
205C2×C3×D4C22×D311yescharacteristic
206C2×C3×D4C22×D311yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—41no—
210C22×C3×C4—61no—
211C2×D12C22×D311yescharacteristic
212C2×C4×D3—21no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6#6711yescharacteristic
217C2×Dic6C22×D312yes—
218C3×D8—62no—
219C2×C3×C8—31no—
220C2×C3×C8—31no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4C22×D311yescharacteristic
229C3×C4⋊C4C22×D311yescharacteristic
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—41no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—62no—
235C3×C22⋊C4—61no—
236C3×C42—21no—
237C3×C42—32no—
238C3×C42—62no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#217—22no—
242#217—22no—
243#217—62no—
244#217—62no—
245#216—64no—
246#216—122no—
247#215—122no—
248#214—122no—
249#214—122no—
250#214—122no—
251#214—124no—
252#213—22no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—121no—
263C4⋊Dic3—121no—
264C4⋊Dic3#6711yescharacteristic
265C4⋊Dic3C22×D311yescharacteristic
266Dic3⋊C4—22no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4#6712yes—
270C4×Dic3—22no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3C22×D312yes—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D311yescharacteristic
279Dic12—64no—
280Dic12—122no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—21no—
289C32×C4—41no—
290C32×C4#13512yes—
291C32×C4C2×#4111yescharacteristic
292C32×C4H(5,𝔽2)11yescharacteristic
293C3⋊Dic3—42no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C2×Q16—92no—
299C2×Q16—92no—
300C2×SD16—92no—
301C2×SD16—92no—
302C2×D8—31no—
303C4⋊Q8—31no—
304C4⋊Q8—91no—
305#126—62no—
306#126—182no—
307#124—32no—
308#124—92no—
309C22⋊Q8—61no—
310C22⋊Q8—181no—
311C4×Q8—31no—
312C4×Q8—32no—
313C4×Q8—92no—
314C4×D4—31no—
315C4×D4D3211yescharacteristic
316#117—61no—
317#117—181no—
318#107—31no—
319C4⋊C8—92no—
320C4⋊C8—91no—
321#103—92no—
322#103—92no—
323#102—31no—
324#102—31no—
325C4×C8—31no—
326C4×C8—92no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—41no—
330C23×C3—61no—
331C22×D3—21no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×D4—22no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—41no—
341C3×D4—61no—
342C3×D4—61no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—62no—
354C2×C3×C4—61no—
355C2×C3×C4—82no—
356C2×C3×C4—122no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×Dic3—21no—
364C2×Dic3—22no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—122no—
368C2×Dic3C2×#6712yes—
369C2×Dic3C2×#6712yes—
370D12—21no—
371D12—21no—
372C4×D3—42no—
373Dic6—22no—
374Dic6—22no—
375Dic6—22no—
376Dic6—62no—
377Dic6—62no—
378Dic6—62no—
379Dic6—62no—
380Dic6—122no—
381Dic6—122no—
382C3×C8—32no—
383C3×C8—61no—
384C3⋊C8—21no—
385C3⋊C8—62no—
386C3⋊C8—62no—
387C3⋊C8—122no—
388C3⋊C8#23512yes—
389C2×C32—81no—
390C2×C32#55011yescharacteristic
391C2×C32C2×#13511yescharacteristic
392C2×C32#57811yescharacteristic
393C3×D3—81no—
394C2×Q8—31no—
395C2×Q8—32no—
396C2×Q8—92no—
397C2×D4—31no—
398C2×D4C2×D3211yescharacteristic
399C22×C4—21no—
400C22×C4—61no—
401Q16—184no—
402Q16—362no—
403SD16—362no—
404SD16—362no—
405D8—62no—
406C2×C8—31no—
407C2×C8—31no—
408C2×C8—92no—
409C4⋊C4—31no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—62no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4—182no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4C2×D3211yescharacteristic
419C22⋊C4—21no—
420C22⋊C4—62no—
421C22⋊C4—62no—
422C22⋊C4—61no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C42—32no—
426C42—62no—
427C42—182no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—42no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—81no—
438C22×C3—81no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3C2×D3×D411yescharacteristic
443C22×C3C22×#6711yescharacteristic
444C2×D3—41no—
445C2×D3—41no—
446C2×D3—41no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—81no—
458C3×C4—122no—
459C3×C4—121no—
460C3×C4#91212yes—
461C3×C4#95012yes—
462C3×C4C2×#23511yescharacteristic
463C3×C4D3×#4111yescharacteristic
464C3×C4#100911yescharacteristic
465C3×C4#100911yescharacteristic
466Dic3—22no—
467Dic3—22no—
468Dic3—41no—
469Dic3—42no—
470Dic3—122no—
471Dic3—122no—
472Dic3—242no—
473C32#339311yescharacteristic, complemented, Sylow
474C23—21no—
475C23—61no—
476Q8—62no—
477Q8—62no—
478Q8—62no—
479Q8—182no—
480Q8—182no—
481D4—21no—
482D4—21no—
483D4—61no—
484D4—61no—
485C2×C4—21no—
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—42no—
489C2×C4—62no—
490C2×C4—61no—
491C2×C4—122no—
492C2×C4—182no—
493C2×C4D3×#6711yescharacteristic
494C2×C4D3×#6711yescharacteristic
495C2×C4C22×D3211yescharacteristic
496C8—32no—
497C8—61no—
498C8—182no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—82no—
503C2×C3—81no—
504C2×C3—81no—
505C2×C3—241no—
506C2×C3#555311yescharacteristic
507C2×C3C2×#91211yescharacteristic
508C2×C3#577111yescharacteristic
509C2×C3C2×#95011yescharacteristic
510C2×C3#583411yescharacteristic
511C2×C3#583811yescharacteristic
512D3—81no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22C2×D3×#6711yescharacteristic
520C4—21no—
521C4—41no—
522C4—62no—
523C4—62no—
524C4—121no—
525C4—122no—
526C4—362no—
527C4#6393312yes—
528C4D3×#23511yescharacteristic
529C4#6430811yescharacteristic
530C3—21no—
531C3#7957911yescharacteristic, complemented
532C3#8367011yescharacteristic, complemented
533C2—81no—
534C2—241no—
535C2#1059500711yescharacteristic
536C2C2×#6393311yescharacteristic
537C2#1059546711yescharacteristic
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#3393
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. #10593879C2semidirect
3. #10592718C2semidirect
6. #10591441C2semidirect
7. #10590532C2semidirect
8. #10590481C2semidirect
9. #10590386C2semidirect
10. #10590363C2semidirect
11. C3⋊C8×Dic6C2semidirect
46. #5542D3semidirect
473. C32#3393semidirect
531. C3#79579semidirect
532. C3#83670semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
#105938792
#105927182
C3×C4×#2132
#105914702
#105914412
#105905322
#105904812
#105903862
#105903632
C3⋊C8×Dic62
#836703
#795793