Finite Group Databasebeta

← #11898376

Subgroups — #11898376

Order 1152.

787 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5542C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic
4C3×#5019C211yesmaximal, characteristic, complemented
5#10591473C212yesmaximal
6#10591442C212yesmaximal, complemented
7#10590536C212yesmaximal, complemented
8#10590476C212yesmaximal, complemented
9#10590387C211yesmaximal, characteristic, complemented
10#10590379C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83670—31nomaximal
13#80421—31nomaximal
14C32×C4×D4C2211yescharacteristic
15C2×#3753C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#936C2212yes—
18C2×C3×#214C2212yes—
19C3×#926—21no—
20C3×#924—21no—
21C3×#887C2212yes—
22C3×#879—22no—
23C3×#869C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63871—21no—
27#63864C2212yes—
28#63849—21no—
29#63848—22no—
30Dic3×Dic6C2212yes—
31C2×#3718C2212yes—
32C2×#3718C2212yes—
33C2×#3717C2212yes—
34#63659C2211yescharacteristic
35#63636C2211yescharacteristic
36#63634C2211yescharacteristic
37C4×C3⋊(C3⋊C8)C2211yescharacteristic
38C3×#810C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41#63566C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#556—31no—
44#5732—31no—
45#5584—31no—
46#5542D311yescharacteristic, complemented
47C3×#461—31no—
48#5168—32no—
49#5166—32no—
50#5092—31no—
51#5092—31no—
52#5083—31no—
53#5059—32no—
54#5054—32no—
55C4×#216—32no—
56#5028—32no—
57Q8×C3⋊C8—31no—
58#5019D311yescharacteristic, complemented
59C4×#213—31no—
60C4×#213—31no—
61C4×#213—61no—
62#4841—31no—
63#4830—31no—
64#4798—32no—
65#4790—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×C3×Dic6C2312yes—
73C32×C4⋊C4C2311yescharacteristic
74C32×C22⋊C4—21no—
75C32×C42C2311yescharacteristic
76#3753—22no—
77#3752—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×#217—22no—
82C3×#217—22no—
83C3×#214—42no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94Dic3⋊Dic3—22no—
95#3722—22no—
96#3722—22no—
97Dic32—22no—
98#3718—24no—
99#3718—42no—
100#3717—42no—
101#3393—91noSylow
102C2×C3×SD16—32no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—31no—
105C3×#126—62no—
106C3×#124—32no—
107C3×C22⋊Q8—61no—
108C3×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×D4—21no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113C3×#117—61no—
114#947—32no—
115#946—61no—
116Q8×Dic3—32no—
117C2×#216—32no—
118C2×#216—32no—
119C2×#216—32no—
120C2×#216—32no—
121C2×#215—32no—
122#936C2×D312yes—
123C2×#214C2×D312yes—
124C2×#213—31no—
125C2×#213—31no—
126C2×#213—61no—
127#926—21no—
128#924—21no—
129C2×#204—32no—
130#898—62no—
131#898—62no—
132#897—61no—
133#892—61no—
134#892—61no—
135#887C2×D312yes—
136#879—22no—
137#875—32no—
138C4×D12—31no—
139C4×D12—31no—
140C4×D12—61no—
141#869C2×D311yescharacteristic
142#869C2×D311yescharacteristic
143C4×Dic6—32no—
144C4×Dic6C2×D311yescharacteristic
145C3×C4⋊C8—31no—
146C3×#103—32no—
147#835—32no—
148#832—31no—
149#832—31no—
150#832—61no—
151#816—32no—
152Dic3⋊C8—32no—
153C8×Dic3—32no—
154#810C2×D312yes—
155#809—31no—
156#809—31no—
157#809—61no—
158#807—31no—
159#807—31no—
160#807—61no—
161C4⋊(C3⋊C8)—32no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4×C3⋊C8—31no—
164C4×C3⋊C8—31no—
165C4×C3⋊C8—32no—
166C4×C3⋊C8—61no—
167C23×C32—21no—
168C22×C3⋊D3—21no—
169C32×D4—21no—
170C32×D4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—42no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)—21no—
179C4×C3⋊D3—42no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C3×Dic6—22no—
188C3×Dic6—22no—
189C3⋊(C3⋊C8)—21no—
190C3⋊(C3⋊C8)#4112yes—
191C3×C3⋊C8—22no—
192#556—31no—
193#556—91no—
194#495—92no—
195#494—91no—
196#464—92no—
197#464—92no—
198#461—31no—
199#461—91no—
200C8×Q8—91no—
201C4×Q16—92no—
202C4×D8—91no—
203C2×C3×Q8—31no—
204C2×C3×Q8—32no—
205C2×C3×Q8—32no—
206C2×C3×D4—21no—
207C2×C3×D4C22×D311yescharacteristic
208C2×C3×D4C22×D311yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—41no—
212C2×D12—31no—
213C2×D12—31no—
214C2×D12—61no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—121no—
218C2×Dic6#6711yescharacteristic
219C2×Dic6C22×D312yes—
220C2×Dic6C22×D312yes—
221C3×SD16—122no—
222C2×C3×C8—32no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C22⋊C4—21no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—41no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—62no—
238C3×C42—21no—
239C3×C42—32no—
240C3×C42—62no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#217—22no—
244#217—22no—
245#216—64no—
246#216—64no—
247#216—122no—
248#216—122no—
249#215—122no—
250#214—42no—
251#213—62no—
252#213—62no—
253#213—64no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—121no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—21no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3#6711yescharacteristic
270Dic3⋊C4—22no—
271Dic3⋊C4—62no—
272Dic3⋊C4#6712yes—
273C4×Dic3—22no—
274C4×Dic3—62no—
275C4×Dic3—62no—
276C4×Dic3C22×D312yes—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—61no—
282C2×C3⋊C8—61no—
283C2×C3⋊C8C22×D312yes—
284#204—122no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C32×C4—21no—
293C32×C4—41no—
294C32×C4#13512yes—
295C32×C4C2×#4111yescharacteristic
296C32×C4H(5,𝔽2)11yescharacteristic
297C3⋊Dic3—41no—
298C3×Dic3—22no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C2×Q16—92no—
303C2×Q16—92no—
304C2×SD16—32no—
305C2×SD16—92no—
306C2×D8—91no—
307C4⋊Q8—31no—
308C4⋊Q8—31no—
309#126—62no—
310#126—182no—
311#124—32no—
312#124—92no—
313C22⋊Q8—61no—
314C22⋊Q8—181no—
315C4×Q8—31no—
316C4×Q8—32no—
317C4×Q8—92no—
318C4×D4—91no—
319C4×D4D3211yescharacteristic
320#117—61no—
321#117—181no—
322#107—91no—
323C4⋊C8—31no—
324C4⋊C8—92no—
325#103—32no—
326#103—92no—
327#102—91no—
328#102—91no—
329C4×C8—92no—
330C4×C8—91no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—41no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—121no—
337C3×Q8—62no—
338C3×Q8—62no—
339C3×Q8—62no—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×D4—22no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4—41no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—32no—
354C2×C3×C4—32no—
355C2×C3×C4—41no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—82no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—121no—
372C2×Dic3C2×#6712yes—
373C2×Dic3C2×#6712yes—
374D12—62no—
375D12—61no—
376D12—61no—
377D12—61no—
378D12—61no—
379D12—121no—
380C4×D3—122no—
381C4×D3—122no—
382C4×D3—242no—
383Dic6—22no—
384Dic6—22no—
385Dic6—22no—
386Dic6—22no—
387Dic6—22no—
388C3×C8—62no—
389C3⋊C8—22no—
390C3⋊C8—32no—
391C3⋊C8—32no—
392C3⋊C8—62no—
393C3⋊C8—61no—
394C3⋊C8—61no—
395C3⋊C8—121no—
396C2×C32—81no—
397C2×C32#55011yescharacteristic
398C2×C32C2×#13511yescharacteristic
399C2×C32#57811yescharacteristic
400C3⋊D3—81no—
401C2×Q8—31no—
402C2×Q8—32no—
403C2×Q8—32no—
404C2×D4—91no—
405C2×D4C2×D3211yescharacteristic
406C22×C4—21no—
407C22×C4—181no—
408Q16—184no—
409Q16—362no—
410SD16—122no—
411SD16—362no—
412D8—182no—
413C2×C8—32no—
414C2×C8—91no—
415C2×C8—91no—
416C4⋊C4—31no—
417C4⋊C4—32no—
418C4⋊C4—62no—
419C4⋊C4—61no—
420C4⋊C4—61no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C4⋊C4—91no—
424C4⋊C4—182no—
425C4⋊C4C2×D3211yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—62no—
428C22⋊C4—62no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C22⋊C4—181no—
432C42—32no—
433C42—62no—
434C42—182no—
435C42C2×D3211yescharacteristic
436C22×C3—21no—
437C22×C3—42no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—81no—
445C22×C3—81no—
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C22×#6711yescharacteristic
448C2×D3—122no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—241no—
456C2×D3—241no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—62no—
466C3×C4—62no—
467C3×C4—81no—
468C3×C4—122no—
469C3×C4—122no—
470C3×C4#91612yes—
471C3×C4#95012yes—
472C3×C4#100411yescharacteristic
473C3×C4D3×#4111yescharacteristic
474C3×C4D3×#4111yescharacteristic
475C3×C4#100911yescharacteristic
476Dic3—22no—
477Dic3—22no—
478Dic3—42no—
479Dic3—42no—
480Dic3—121no—
481Dic3—121no—
482Dic3—241no—
483C32#339311yescharacteristic, complemented, Sylow
484C23—21no—
485C23—181no—
486Q8—62no—
487Q8—62no—
488Q8—62no—
489Q8—62no—
490Q8—62no—
491D4—21no—
492D4—21no—
493D4—181no—
494D4—181no—
495C2×C4—21no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—42no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—181no—
502C2×C4—362no—
503C2×C4D3×#6711yescharacteristic
504C2×C4D3×#6711yescharacteristic
505C2×C4C22×D3211yescharacteristic
506C8—62no—
507C8—92no—
508C8—181no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—82no—
513C2×C3—81no—
514C2×C3—81no—
515C2×C3#559911yescharacteristic
516C2×C3C2×#91611yescharacteristic
517C2×C3#577911yescharacteristic
518C2×C3C2×#95011yescharacteristic
519C2×C3#583411yescharacteristic
520C2×C3#583811yescharacteristic
521D3—242no—
522D3—241no—
523D3—241no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—361no—
528C22—361no—
529C22—361no—
530C22C2×D3×#6711yescharacteristic
531C4—21no—
532C4—41no—
533C4—62no—
534C4—62no—
535C4—122no—
536C4—122no—
537C4—361no—
538C4#6393512yes—
539C4#6430611yescharacteristic
540C4#6430711yescharacteristic
541C3—21no—
542C3#8042111yescharacteristic, complemented
543C3#8367011yescharacteristic, complemented
544C2—81no—
545C2—721no—
546C2#1059500611yescharacteristic
547C2C2×#6393511yescharacteristic
548C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#3753C22
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. #10593865C2semidirect
4. C3×#5019C2semidirect
6. #10591442C2semidirect
7. #10590536C2semidirect
8. #10590476C2semidirect
9. #10590387C2semidirect
10. #10590379C2semidirect
11. #10590250C2semidirect
46. #5542D3semidirect
58. #5019D3semidirect
483. C32#3393semidirect
542. C3#80421semidirect
543. C3#83670semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
#105938652
C4×#37532
C3×#50192
#105914732
#105914422
#105905362
#105904762
#105903872
#105903792
#105902502
#836703
#804213