Finite Group Databasebeta

← #11895249

Subgroups — #11895249

Order 1152.

767 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5542C211yesmaximal, characteristic, complemented
2#10593958C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591478C212yesmaximal, complemented
6#10591432C212yesmaximal
7#10590543C212yesmaximal, complemented
8#10590458C212yesmaximal, complemented
9#10590379C211yesmaximal, characteristic, complemented
10#10590290C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83667—31nomaximal
13#81087—31nomaximal
14C32×C4×D4C2211yescharacteristic
15C2×#3753C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#936C2212yes—
18C3×#926—21no—
19C3×#924—21no—
20C3×#887C2212yes—
21C3×#879—22no—
22C3×#869C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63900—21no—
26#63894C2212yes—
27#63888—22no—
28#63871—21no—
29#63869C2212yes—
30C2×#3717C2212yes—
31#63659C2211yescharacteristic
32#63636C2211yescharacteristic
33#63634C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#832C2212yes—
36C3×#808C2212yes—
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2212yes—
40#63565C2212yes—
41#63565C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#556—31no—
44#5730—31no—
45#5579—31no—
46#5542D311yescharacteristic, complemented
47C3×#476—31no—
48#5093—31no—
49#5083—31no—
50#5079—31no—
51#5057—32no—
52#5056—32no—
53C4×#215—32no—
54Q8×C3⋊C8—31no—
55#5022—32no—
56C4×#213—31no—
57C4×#213—31no—
58C4×#213—61no—
59#5008D311yescharacteristic, complemented
60#4857—32no—
61#4852—32no—
62#4841—31no—
63#4830—31no—
64#4787—32no—
65#4768—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×#624—22no—
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3753—22no—
78#3752—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#217—22no—
83C3×#217—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97#3717—24no—
98#3360—91noSylow
99C3×C4⋊Q8—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×D4C2×D311yescharacteristic
108C3×C4×D4C2×D311yescharacteristic
109C3×#117—61no—
110#946—61no—
111#946—62no—
112C2×#215—32no—
113#936C2×D312yes—
114C2×#213—31no—
115C2×#213—31no—
116C2×#213—61no—
117#926—21no—
118#924—21no—
119C2×#204—32no—
120#897—61no—
121#896—62no—
122#893—32no—
123D3×C4⋊C4—61no—
124D3×C4⋊C4—61no—
125#890—32no—
126#887C2×D312yes—
127#879—22no—
128C4×D12—31no—
129C4×D12—31no—
130C4×D12—32no—
131C4×D12—61no—
132#870—32no—
133#869C2×D311yescharacteristic
134#869C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#106—32no—
137C3×C4⋊C8—31no—
138C3×#102—32no—
139#835—32no—
140#835—32no—
141#835—32no—
142#832—31no—
143#832—31no—
144#832—61no—
145#832C2×D312yes—
146#816—32no—
147Dic3⋊C8—32no—
148C8×Dic3—32no—
149#810—32no—
150#810—32no—
151#809—31no—
152#809—31no—
153#809—61no—
154#808C2×D312yes—
155#807—31no—
156#807—31no—
157#807—61no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)C2×D311yescharacteristic
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—32no—
163C4×C3⋊C8—61no—
164C23×C32—21no—
165C22×C3⋊D3—21no—
166C32×D4—21no—
167C32×D4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—42no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C4⋊(C3⋊D3)—21no—
175C4⋊(C3⋊D3)#4112yes—
176C4×C3⋊D3—42no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—81no—
185#624—82no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8—22no—
189#556—31no—
190#554—91no—
191#488—92no—
192#487—91no—
193#479—92no—
194#476—31no—
195#463—92no—
196#461—91no—
197C8×Q8—91no—
198C4×SD16—92no—
199C4×D8—91no—
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8—61no—
203C2×C3×D4—21no—
204C2×C3×D4C22×D311yescharacteristic
205C2×C3×D4C22×D311yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—41no—
209C2×D12—31no—
210C2×D12—31no—
211C2×D12—61no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—121no—
217C2×Dic6—21no—
218C2×Dic6#6711yescharacteristic
219C2×Dic6C22×D312yes—
220C2×C3×C8—32no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4C22×D311yescharacteristic
230C3×C4⋊C4C22×D311yescharacteristic
231C3×C22⋊C4—21no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—41no—
234C3×C22⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C42—21no—
237C3×C42—32no—
238C3×C42—62no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#217—22no—
242#217—22no—
243#215—64no—
244#213—62no—
245#213—62no—
246#213—64no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—121no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3#6711yescharacteristic
260C4⋊Dic3C22×D312yes—
261Dic3⋊C4—22no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4#6712yes—
266C4×Dic3—22no—
267C4×Dic3C22×D312yes—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8C22×D312yes—
275#204—64no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—22no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4#13512yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—41no—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C2×SD16—92no—
294C2×D8—91no—
295C4⋊Q8—31no—
296C4⋊Q8—31no—
297#126—62no—
298#125—92no—
299#124—32no—
300C22⋊Q8—61no—
301C22⋊Q8—182no—
302C22⋊Q8—181no—
303C4×Q8—31no—
304C4×Q8—32no—
305C4×D4—92no—
306C4×D4—91no—
307C4×D4D3211yescharacteristic
308#117—61no—
309C2×C4⋊C4—181no—
310#107—91no—
311#106—32no—
312C4⋊C8—31no—
313C4⋊C8—92no—
314#103—92no—
315#103—92no—
316#103—92no—
317#102—32no—
318#102—91no—
319#102—91no—
320C4×C8—92no—
321C4×C8—91no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—41no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—121no—
328C3×Q8—62no—
329C3×Q8—62no—
330C3×Q8—62no—
331C3×Q8—241no—
332C3×D4—22no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—41no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—41no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—82no—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—121no—
362C2×Dic3C2×#6712yes—
363C2×Dic3C2×#6712yes—
364D12—32no—
365D12—32no—
366D12—62no—
367D12—61no—
368D12—61no—
369D12—121no—
370C4×D3—122no—
371C4×D3—122no—
372C4×D3—242no—
373C4×D3—242no—
374C4×D3—242no—
375Dic6—22no—
376Dic6—22no—
377Dic6—22no—
378Dic6—81no—
379C3×C8—62no—
380C3⋊C8—22no—
381C3⋊C8—62no—
382C3⋊C8—61no—
383C3⋊C8—61no—
384C3⋊C8—61no—
385C3⋊C8—61no—
386C3⋊C8—121no—
387C2×C32—81no—
388C2×C32#54811yescharacteristic
389C2×C32C2×#13511yescharacteristic
390C2×C32#57711yescharacteristic
391C3⋊D3—42no—
392C2×Q8—31no—
393C2×Q8—32no—
394C2×Q8—61no—
395C2×D4—91no—
396C2×D4C2×D3211yescharacteristic
397C22×C4—21no—
398C22×C4—182no—
399C22×C4—181no—
400SD16—184no—
401D8—182no—
402C2×C8—32no—
403C2×C8—91no—
404C2×C8—91no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—32no—
408C4⋊C4—62no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—91no—
413C4⋊C4—182no—
414C4⋊C4—182no—
415C4⋊C4C2×D3211yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—62no—
418C22⋊C4—62no—
419C22⋊C4—182no—
420C22⋊C4—181no—
421C42—32no—
422C42—62no—
423C42C2×D3211yescharacteristic
424C22×C3—21no—
425C22×C3—42no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C22×#6711yescharacteristic
436C2×D3—62no—
437C2×D3—62no—
438C2×D3—122no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—241no—
444C2×D3—241no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—41no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—81no—
456C3×C4—122no—
457C3×C4—122no—
458C3×C4#91612yes—
459C3×C4#95012yes—
460C3×C4#100711yescharacteristic
461C3×C4D3×#4111yescharacteristic
462C3×C4D3×#4111yescharacteristic
463C3×C4#101011yescharacteristic
464Dic3—22no—
465Dic3—22no—
466Dic3—42no—
467Dic3—42no—
468Dic3—121no—
469Dic3—121no—
470Dic3—241no—
471C32#336011yescharacteristic, complemented, Sylow
472C23—21no—
473C23—181no—
474Q8—62no—
475Q8—62no—
476Q8—62no—
477Q8—241no—
478D4—21no—
479D4—21no—
480D4—92no—
481D4—181no—
482C2×C4—21no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—42no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—181no—
489C2×C4—362no—
490C2×C4—722no—
491C2×C4D3×#6711yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—62no—
495C8—181no—
496C8—181no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—82no—
501C2×C3—81no—
502C2×C3—81no—
503C2×C3#563311yescharacteristic
504C2×C3C2×#91611yescharacteristic
505C2×C3#577511yescharacteristic
506C2×C3C2×#95011yescharacteristic
507C2×C3#583111yescharacteristic
508C2×C3#583711yescharacteristic
509D3—122no—
510D3—122no—
511D3—242no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—182no—
516C22—361no—
517C22—361no—
518C22C2×D3×#6711yescharacteristic
519C4—21no—
520C4—41no—
521C4—62no—
522C4—62no—
523C4—122no—
524C4—122no—
525C4—361no—
526C4#6393512yes—
527C4#6429711yescharacteristic
528C4#6430611yescharacteristic
529C3—21no—
530C3#8108711yescharacteristic, complemented
531C3#8366711yescharacteristic, complemented
532C2—81no—
533C2—362no—
534C2#1059483011yescharacteristic
535C2C2×#6393511yescharacteristic
536C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#3753C22
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. #10593958C2semidirect
4. C3×#5008C2semidirect
5. #10591478C2semidirect
7. #10590543C2semidirect
8. #10590458C2semidirect
9. #10590379C2semidirect
10. #10590290C2semidirect
11. #10590250C2semidirect
46. #5542D3semidirect
59. #5008D3semidirect
471. C32#3360semidirect
530. C3#81087semidirect
531. C3#83667semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
#105939582
C4×#37532
C3×#50082
#105914782
#105914322
#105905432
#105904582
#105903792
#105902902
#105902502
#836673
#810873