Finite Group Databasebeta

← #11895356

Subgroups — #11895356

Order 1152.

838 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic, complemented
3C3×C4×#214C211yesmaximal, characteristic, complemented
4C3×#5015C211yesmaximal, characteristic
5#10591476C212yesmaximal, complemented
6#10591435C212yesmaximal, complemented
7#10590539C212yesmaximal, complemented
8#10590474C212yesmaximal, complemented
9#10590283C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#80319—31nomaximal
13#79621—31nomaximal
14C32×C4×D4C2211yescharacteristic
15D4×C3⋊Dic3C2212yes—
16C2×C4⋊(C3⋊Dic3)—21no—
17#64133—21no—
18#64099C2212yes—
19#64087—22no—
20#64078C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C2×C3×#213C2212yes—
24C3×#874C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63898C2212yes—
27Dic3×D12—21no—
28#63884—22no—
29#63863C2212yes—
30#63860—21no—
31C3×#832C2211yescharacteristic
32C3×#810C2211yescharacteristic
33C3×#809C2212yes—
34C3×#808C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2212yes—
38#63572C2212yes—
39#63566C2212yes—
40#63563C2212yes—
41#63563C2212yes—
42#63553C2212yes—
43#5713—31no—
44#5585—31no—
45#5543—31no—
46#5543—31no—
47#5543—61no—
48C3×#459—31no—
49C3×C4×SD16—31no—
50#5165—32no—
51#5153—32no—
52Dic3×D8—32no—
53#5070—31no—
54#5021—31no—
55C4×#214D311yescharacteristic, complemented
56#5015D311yescharacteristic
57#4871—32no—
58#4850—31no—
59#4830—31no—
60#4800—32no—
61#4768—32no—
62#4766—32no—
63#4756—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C3⋊Dic3—22no—
69C2×#634—21no—
70C2×#634D411yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12C2312yes—
74C2×C3×Dic6C2311yescharacteristic
75C2×D3×Dic3—22no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3757—22no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83C4⋊(C3⋊Dic3)C2312yes—
84#3750—22no—
85#3750D412yes—
86C4×C3⋊Dic3C2312yes—
87C3×#214—22no—
88C3×#213—24no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3361—91noSylow
99C2×C3×SD16—31no—
100C2×C3×D8—32no—
101C3×#127—31no—
102C3×C4×Q8—31no—
103C3×C4×D4—21no—
104C3×C4×D4C2×D311yescharacteristic
105C3×C4×D4C2×D311yescharacteristic
106#947—32no—
107#936—32no—
108#936—61no—
109#935—62no—
110D4×Dic3—32no—
111D4×Dic3—32no—
112D4×Dic3—32no—
113D4×Dic3—62no—
114D4×Dic3—61no—
115C2×#214C2×D311yescharacteristic
116C2×#213C2×D312yes—
117C2×C4⋊Dic3—61no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3—62no—
120#924—61no—
121#924—61no—
122#924—62no—
123#894—62no—
124#893—32no—
125#890—32no—
126#890—32no—
127#890—62no—
128#878—62no—
129#878—62no—
130#878—64no—
131#875—61no—
132#874C2×D311yescharacteristic
133C4×D12—61no—
134#869—31no—
135#869—31no—
136#869—61no—
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×#106—31no—
142C3×C4⋊C8—31no—
143C3×#103—31no—
144C3×#102—31no—
145C3×#102—32no—
146C3×C4×C8—31no—
147#835—32no—
148#832—32no—
149#832—32no—
150#832C2×D311yescharacteristic
151#821—32no—
152#821—32no—
153#818—32no—
154#816—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157C8×Dic3—32no—
158C8×Dic3—32no—
159#810C2×D311yescharacteristic
160#809C2×D312yes—
161#808C2×D311yescharacteristic
162#807—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C23×C32—21no—
166C22×C3×D3—22no—
167C32×D4—21no—
168C32×D4#4112yes—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—82no—
176C2×C3⋊Dic3C2×D412yes—
177C2×C3⋊Dic3C2×D412yes—
178#634—22no—
179#634—81no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—42no—
185C3×D12—81no—
186C3×Dic6—21no—
187C3×Dic6—21no—
188D3×Dic3—82no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#559—91no—
193#554—91no—
194#488—92no—
195#486—91no—
196#478—92no—
197#477—91no—
198#463—92no—
199#459—31no—
200C8×Q8—91no—
201C4×SD16—31no—
202C4×D8—92no—
203C2×C3×Q8—31no—
204C2×C3×D4—21no—
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4C22×D311yescharacteristic
209C2×C3×D4C22×D311yescharacteristic
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×Dic3—62no—
214C22×Dic3—62no—
215C22×Dic3—62no—
216C22×Dic3—64no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12C22×D312yes—
220C2×C4×D3—62no—
221C2×Dic6—31no—
222C2×Dic6—31no—
223C2×Dic6—61no—
224C2×Dic6—62no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6C22×D311yescharacteristic
228C3×SD16—62no—
229C3×D8—64no—
230C2×C3×C8—31no—
231C2×C3×C8—32no—
232C2×C3×C8—31no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C22⋊C4—22no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C42—21no—
242C3×C42—61no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#217—62no—
246#217—62no—
247#217—62no—
248#217—62no—
249#217—62no—
250#217—64no—
251#214—22no—
252#213—24no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—32no—
259C4⋊Dic3—32no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—62no—
264C4⋊Dic3—62no—
265C4⋊Dic3—64no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3C22×D311yescharacteristic
269Dic3⋊C4—21no—
270Dic3⋊C4—32no—
271Dic3⋊C4—32no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—64no—
276C4×Dic3—21no—
277C4×Dic3—32no—
278C4×Dic3—32no—
279C4×Dic3—62no—
280C2×C3⋊C8C22×D311yescharacteristic
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D312yes—
283C22×C32—22no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4#13512yes—
293C32×C4C2×#4111yescharacteristic
294C32×C42−1+411yescharacteristic
295C3⋊Dic3—22no—
296C3⋊Dic3—22no—
297C3⋊Dic3—42no—
298C3×Dic3—41no—
299C3×Dic3—41no—
300C2×SD16—31no—
301C2×D8—32no—
302C4⋊Q8—91no—
303#127—31no—
304#125—92no—
305#124—92no—
306#124—181no—
307#123—182no—
308C22⋊Q8—182no—
309C22⋊Q8—181no—
310C4×Q8—31no—
311C4×Q8—91no—
312C4×D4—92no—
313C4×D4—92no—
314C4×D4—181no—
315C4×D4D3211yescharacteristic
316C2×C4⋊C4—181no—
317#107—92no—
318#106—31no—
319C4⋊C8—31no—
320C4⋊C8—92no—
321#103—31no—
322#103—92no—
323#102—31no—
324#102—32no—
325#102—92no—
326#102—92no—
327C4×C8—31no—
328C4×C8—92no—
329C23×C3—22no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—62no—
333C22×D3—22no—
334C3×Q8—61no—
335C3×Q8—61no—
336C3×D4—22no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—22no—
340C3×D4—62no—
341C3×D4—62no—
342C3×D4—122no—
343C3×D4—241no—
344C3×D4#23512yes—
345C3×D4#23712yes—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—44no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—242no—
375C2×Dic3—242no—
376C2×Dic3—242no—
377C2×Dic3—244no—
378D12—22no—
379D12—22no—
380D12—42no—
381D12—81no—
382C4×D3—242no—
383Dic6—21no—
384Dic6—21no—
385Dic6—62no—
386Dic6—62no—
387Dic6—122no—
388Dic6—241no—
389Dic6—241no—
390Dic6—242no—
391C3×C8—62no—
392C3×C8—61no—
393C3×C8—61no—
394C3⋊C8—21no—
395C3⋊C8—22no—
396C3⋊C8—21no—
397C2×C32—42no—
398C2×C32#54811yescharacteristic
399C2×C32C2×#13511yescharacteristic
400C2×C32#57611yescharacteristic
401C3×D3—82no—
402C2×Q8—31no—
403C2×Q8—91no—
404C2×Q8—181no—
405C2×D4—32no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4C2×D3211yescharacteristic
409C22×C4—21no—
410C22×C4—182no—
411C22×C4—182no—
412SD16—62no—
413D8—64no—
414C2×C8—31no—
415C2×C8—31no—
416C2×C8—32no—
417C4⋊C4—31no—
418C4⋊C4—61no—
419C4⋊C4—91no—
420C4⋊C4—92no—
421C4⋊C4—92no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4—181no—
425C4⋊C4C2×D3211yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—182no—
428C22⋊C4—182no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C42—61no—
432C42—92no—
433C42C2×D3211yescharacteristic
434C22×C3—24no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3C2×D3×D411yescharacteristic
448C22×C3C2×D3×D411yescharacteristic
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—42no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—41no—
458C3×C4—42no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4#91212yes—
464C3×C4#91612yes—
465C3×C4C2×#23511yescharacteristic
466C3×C4C2×#23711yescharacteristic
467C3×C4#101011yescharacteristic
468C3×C4#101011yescharacteristic
469Dic3—41no—
470Dic3—41no—
471Dic3—62no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—122no—
476Dic3—122no—
477Dic3—124no—
478Dic3—122no—
479Dic3—122no—
480C32#336111yescharacteristic, complemented, Sylow
481C23—21no—
482C23—62no—
483Q8—61no—
484Q8—61no—
485Q8—182no—
486Q8—721no—
487D4—21no—
488D4—62no—
489D4—62no—
490D4—122no—
491D4—241no—
492D4#379512yes—
493C2×C4—21no—
494C2×C4—42no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—92no—
498C2×C4—92no—
499C2×C4—182no—
500C2×C4—722no—
501C2×C4—722no—
502C2×C4#381111yescharacteristic
503C2×C4#381111yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—62no—
506C8—61no—
507C8—61no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—44no—
512C2×C3—42no—
513C2×C3—42no—
514C2×C3—242no—
515C2×C3#555211yescharacteristic
516C2×C3#559811yescharacteristic
517C2×C3C2×#91211yescharacteristic
518C2×C3C2×#91611yescharacteristic
519C2×C3#576911yescharacteristic
520C2×C3#577411yescharacteristic
521D3—82no—
522C22—22no—
523C22—41no—
524C22—41no—
525C22—122no—
526C22—122no—
527C22—122no—
528C22C2×#381111yescharacteristic
529C4—21no—
530C4—41no—
531C4—121no—
532C4—121no—
533C4—182no—
534C4—182no—
535C4—362no—
536C4#6393612yes—
537C4C2×#379511yescharacteristic
538C4#6429811yescharacteristic
539C3—21no—
540C3#7962111yescharacteristic, complemented
541C3#8031911yescharacteristic, complemented
542C2—42no—
543C2—242no—
544C2#1059491811yescharacteristic
545C2C2×#6393611yescharacteristic
546C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5015C2
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. #10596014C2semidirect
2. #10593951C2semidirect
3. C3×C4×#214C2semidirect
5. #10591476C2semidirect
6. #10591435C2semidirect
7. #10590539C2semidirect
8. #10590474C2semidirect
9. #10590283C2semidirect
10. #10590273C2semidirect
11. #10590254C2semidirect
55. C4×#214D3semidirect
480. C32#3361semidirect
540. C3#79621semidirect
541. C3#80319semidirect

Maximal subgroups

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

subgroupindex
#105960142
#105939512
C3×C4×#2142
C3×#50152
#105914762
#105914352
#105905392
#105904742
#105902832
#105902732
#105902542
#803193
#796213