Finite Group Databasebeta

← #11895863

Subgroups — #11895863

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5542C211yesmaximal, characteristic, complemented
2#10593903C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591488C212yesmaximal, complemented
6#10591432C212yesmaximal
7#10590557C212yesmaximal, complemented
8#10590457C212yesmaximal, complemented
9#10590379C211yesmaximal, characteristic, complemented
10#10590290C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83668—31nomaximal
13#80993—31nomaximal
14C2×#3797—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3753C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#936C2212yes—
19C3×#926—21no—
20C3×#924—21no—
21C3×#887C2212yes—
22C3×#879—22no—
23C3×#869C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63918C2212yes—
27#63895—22no—
28#63894C2212yes—
29#63871—21no—
30C2×#3717C2212yes—
31#63659C2211yescharacteristic
32#63636C2211yescharacteristic
33#63634C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#832C2212yes—
36C3×#807C2212yes—
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2212yes—
40#63565C2212yes—
41#63565C2212yes—
42#63554C2212yes—
43C3×#556—31no—
44#5727—31no—
45Q8×D12—31no—
46#5542D311yescharacteristic, complemented
47C3×#474—31no—
48#5093—31no—
49#5083—31no—
50#5079—31no—
51#5057—32no—
52#5055—32no—
53#5026—32no—
54#5024—31no—
55#5021—32no—
56C4×#213—31no—
57C4×#213—31no—
58C4×#213—61no—
59#5007D311yescharacteristic, complemented
60#4889—32no—
61#4875—32no—
62#4841—31no—
63#4831—31no—
64#4787—32no—
65#4765—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×#627—22no—
74C2×#624—22no—
75#3797—44no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3753—22no—
80#3752—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×#217—22no—
85C3×#217—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96Dic3⋊Dic3—22no—
97#3722—22no—
98#3717—24no—
99#3367—91noSylow
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C3×C4⋊Q8—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×D4C2×D311yescharacteristic
111C3×C4×D4C2×D311yescharacteristic
112C3×#117—61no—
113#946—61no—
114C2×#215—32no—
115#936C2×D312yes—
116C2×#213—31no—
117C2×#213—31no—
118C2×#213—61no—
119#926—21no—
120#924—21no—
121C2×#204—32no—
122#897—62no—
123#897—61no—
124#896—62no—
125#893—32no—
126#888—32no—
127#887C2×D312yes—
128#879—22no—
129C4×D12—31no—
130C4×D12—31no—
131C4×D12—32no—
132C4×D12—61no—
133#869—32no—
134#869C2×D311yescharacteristic
135#869C2×D311yescharacteristic
136C4×Dic6C2×D311yescharacteristic
137C3×#107—32no—
138C3×C4⋊C8—31no—
139C3×#102—32no—
140#835—32no—
141#835—32no—
142#835—32no—
143#832—31no—
144#832—31no—
145#832—61no—
146#832C2×D312yes—
147#816—32no—
148#815—32no—
149Dic3⋊C8—32no—
150#810—32no—
151#810—32no—
152#809—31no—
153#809—31no—
154#809—61no—
155#807—31no—
156#807—31no—
157#807—61no—
158#807C2×D312yes—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161#803—32no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—61no—
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—21no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)#4112yes—
177C4×C3⋊D3—42no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—42no—
186#627—44no—
187#624—44no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190C3×C3⋊C8—22no—
191#556—31no—
192D4×Q8—91no—
193#489—92no—
194#487—91no—
195#477—92no—
196#474—31no—
197#463—92no—
198#461—91no—
199#446—91no—
200#440—92no—
201C4×D8—91no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8—61no—
205C2×C3×D4—21no—
206C2×C3×D4C22×D311yescharacteristic
207C2×C3×D4C22×D311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—41no—
211D3×Q8—124no—
212D3×Q8—124no—
213C2×D12—31no—
214C2×D12—31no—
215C2×D12—61no—
216C2×C4×D3—62no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—62no—
220C2×C4×D3—121no—
221C2×Dic6—21no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6#6711yescharacteristic
225C2×Dic6C22×D312yes—
226C2×C3×C8—32no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—41no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—62no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42—62no—
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247#217—22no—
248#217—22no—
249#215—64no—
250#213—62no—
251#213—62no—
252#213—64no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—121no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—61no—
264C4⋊Dic3—62no—
265C4⋊Dic3#6711yescharacteristic
266C4⋊Dic3C22×D312yes—
267Dic3⋊C4—22no—
268Dic3⋊C4—62no—
269Dic3⋊C4#6712yes—
270C4×Dic3—22no—
271C4×Dic3C22×D312yes—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8C22×D312yes—
279#204—64no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—22no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4AGL(1,ℤ/8)12yes—
290C32×C4C2×#4111yescharacteristic
291C32×C42−1+411yescharacteristic
292C3⋊Dic3—41no—
293C3×Dic3—22no—
294C3×Dic3—22no—
295C3×Dic3—42no—
296C3×Dic3—42no—
297C22×Q8—181no—
298C2×SD16—92no—
299C2×D8—91no—
300C4⋊Q8—31no—
301C4⋊Q8—31no—
302C4⋊Q8—92no—
303#126—62no—
304#124—32no—
305C22⋊Q8—61no—
306C22⋊Q8—182no—
307C22⋊Q8—181no—
308C4×Q8—31no—
309C4×Q8—32no—
310C4×D4—92no—
311C4×D4—91no—
312C4×D4D3211yescharacteristic
313#117—61no—
314#107—32no—
315#107—91no—
316C4⋊C8—31no—
317C4⋊C8—92no—
318#103—92no—
319#103—92no—
320#103—92no—
321#102—32no—
322#102—91no—
323#102—91no—
324#97—92no—
325C4×C8—91no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—41no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—121no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—122no—
336C3×D4—22no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—21no—
341C3×D4—41no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—41no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—82no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—121no—
366C2×Dic3C2×#6712yes—
367C2×Dic3C2×#6712yes—
368D12—32no—
369D12—32no—
370D12—62no—
371D12—61no—
372D12—61no—
373D12—121no—
374C4×D3—124no—
375C4×D3—124no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—242no—
379Dic6—22no—
380Dic6—22no—
381Dic6—22no—
382Dic6—42no—
383Dic6—124no—
384Dic6—124no—
385C3×C8—62no—
386C3⋊C8—22no—
387C3⋊C8—62no—
388C3⋊C8—61no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—61no—
392C3⋊C8—121no—
393C2×C32—81no—
394C2×C32#54811yescharacteristic
395C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
396C2×C32#57811yescharacteristic
397C3⋊D3—42no—
398C2×Q8—31no—
399C2×Q8—32no—
400C2×Q8—61no—
401C2×Q8—182no—
402C2×Q8—364no—
403C2×D4—91no—
404C2×D4C2×D3211yescharacteristic
405C22×C4—21no—
406C22×C4—182no—
407C22×C4—181no—
408SD16—184no—
409D8—182no—
410C2×C8—32no—
411C2×C8—91no—
412C2×C8—91no—
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—32no—
416C4⋊C4—62no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—61no—
420C4⋊C4—91no—
421C4⋊C4—182no—
422C4⋊C4C2×D3211yescharacteristic
423C22⋊C4—21no—
424C22⋊C4—62no—
425C22⋊C4—62no—
426C22⋊C4—182no—
427C22⋊C4—181no—
428C42—32no—
429C42—62no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—42no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—81no—
440C22×C3—81no—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C22×#6711yescharacteristic
443C2×D3—62no—
444C2×D3—62no—
445C2×D3—122no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—241no—
451C2×D3—241no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—81no—
463C3×C4—122no—
464C3×C4—122no—
465C3×C4#91112yes—
466C3×C4#94912yes—
467C3×C4#100711yescharacteristic
468C3×C4D3×#4111yescharacteristic
469C3×C4D3×#4111yescharacteristic
470C3×C4#101011yescharacteristic
471Dic3—22no—
472Dic3—22no—
473Dic3—42no—
474Dic3—42no—
475Dic3—121no—
476Dic3—121no—
477Dic3—241no—
478C32#336711yescharacteristic, complemented, Sylow
479C23—21no—
480C23—181no—
481Q8—62no—
482Q8—62no—
483Q8—62no—
484Q8—122no—
485Q8—364no—
486D4—21no—
487D4—21no—
488D4—92no—
489D4—181no—
490C2×C4—21no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—42no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—181no—
497C2×C4—364no—
498C2×C4—362no—
499C2×C4D3×#6711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—62no—
503C8—181no—
504C8—181no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—82no—
509C2×C3—81no—
510C2×C3—81no—
511C2×C3#563311yescharacteristic
512C2×C3C2×#91111yescharacteristic
513C2×C3#577911yescharacteristic
514C2×C3C2×#94911yescharacteristic
515C2×C3#583111yescharacteristic
516C2×C3#583811yescharacteristic
517D3—122no—
518D3—122no—
519D3—242no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—182no—
524C22—361no—
525C22—361no—
526C22C2×D3×#6711yescharacteristic
527C4—21no—
528C4—41no—
529C4—62no—
530C4—62no—
531C4—122no—
532C4—122no—
533C4—361no—
534C4#6392512yes—
535C4#6429711yescharacteristic
536C4#6430611yescharacteristic
537C3—21no—
538C3#8099311yescharacteristic, complemented
539C3#8366811yescharacteristic, complemented
540C2—81no—
541C2—362no—
542C2#1059483011yescharacteristic
543C2C2×#6392511yescharacteristic
544C2#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#3367
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. #10593903C2semidirect
4. C3×#5007C2semidirect
5. #10591488C2semidirect
7. #10590557C2semidirect
8. #10590457C2semidirect
9. #10590379C2semidirect
10. #10590290C2semidirect
11. #10590259C2semidirect
46. #5542D3semidirect
59. #5007D3semidirect
478. C32#3367semidirect
538. C3#80993semidirect
539. C3#83668semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
#105939032
C4×#37532
C3×#50072
#105914882
#105914322
#105905572
#105904572
#105903792
#105902902
#105902592
#836683
#809933