Finite Group Databasebeta

← #11895165

Subgroups — #11895165

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5567C211yesmaximal, characteristic, complemented
2#10593903C211yesmaximal, characteristic
3C4×#3755C211yesmaximal, characteristic
4C3×#5020C211yesmaximal, characteristic, complemented
5#10591623C212yesmaximal, complemented
6#10591565C212yesmaximal
7#10590556C212yesmaximal, complemented
8#10590458C212yesmaximal
9#10590379C211yesmaximal, characteristic
10#10590290C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83688—31nomaximal
13#81037—31nomaximal
14C2×#3797—21no—
15C32×C4×Q8C2211yescharacteristic
16C2×#3755C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#944C2212yes—
19C3×#889—22no—
20C3×#887C2212yes—
21C3×#870—21no—
22C3×#869C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6—21no—
25C3×C4×Dic6C2211yescharacteristic
26#63918C2212yes—
27#63895—22no—
28#63894C2212yes—
29#63871—21no—
30C2×#3717C2212yes—
31#63662C2211yescharacteristic
32#63636C2211yescharacteristic
33#63635C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#835C2212yes—
36C3×#808C2212yes—
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2212yes—
40#63565C2212yes—
41#63565C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5727—31no—
45Q8×D12—31no—
46#5567D311yescharacteristic, complemented
47C3×#475—31no—
48#5093—31no—
49#5083—32no—
50#5083—31no—
51#5079—31no—
52#5079—32no—
53C4×#215—31no—
54C4×#215—31no—
55C4×#215—32no—
56C4×#215—61no—
57Q8×C3⋊C8—31no—
58#5020—32no—
59#5020D311yescharacteristic, complemented
60#4854—32no—
61#4852—32no—
62#4841—31no—
63#4830—31no—
64#4818—32no—
65#4792—32no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×#627—22no—
73C2×#624—22no—
74#3797—44no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C42—21no—
78C32×C42C2311yescharacteristic
79#3755—22no—
80#3752—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
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#3359—91noSylow
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C3×C4⋊Q8—32no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—31no—
105C3×#125—61no—
106C3×#125—62no—
107C3×C4×Q8—21no—
108C3×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×Q8—61no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C2×D311yescharacteristic
113#946—61no—
114#944C2×D312yes—
115C2×#215—31no—
116C2×#215—31no—
117C2×#215—32no—
118C2×#215—61no—
119C2×#204—32no—
120#897—62no—
121#897—61no—
122#896—62no—
123#893—32no—
124#889—22no—
125#888—32no—
126#887C2×D312yes—
127C4×D12—31no—
128C4×D12—31no—
129C4×D12—32no—
130C4×D12—61no—
131#870—21no—
132#869—32no—
133#869C2×D311yescharacteristic
134#869C2×D311yescharacteristic
135C4×Dic6—21no—
136C4×Dic6C2×D311yescharacteristic
137C3×#106—32no—
138C3×C4⋊C8—31no—
139C3×#103—32no—
140#835—31no—
141#835—31no—
142#835—32no—
143#835—32no—
144#835—32no—
145#835—61no—
146#835C2×D312yes—
147#816—32no—
148Dic3⋊C8—32no—
149C8×Dic3—32no—
150#810—32no—
151#810—32no—
152#809—31no—
153#809—31no—
154#809—61no—
155#808—31no—
156#808—31no—
157#808—61no—
158#808C2×D312yes—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161C4×C3⋊C8—31no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—32no—
164C4×C3⋊C8—61no—
165C22×C3⋊D3—21no—
166C32×Q8—21no—
167C32×Q8—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
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—42no—
184C3×Dic6SD1614yescomplemented
185#627—44no—
186#624—44no—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)—21no—
189C3×C3⋊C8—22no—
190#557—31no—
191D4×Q8—91no—
192#487—92no—
193#487—91no—
194#475—31no—
195#475—92no—
196#461—92no—
197#461—91no—
198C8×Q8—91no—
199C4×SD16—92no—
200C4×SD16—91no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8—61no—
205C2×C3×Q8C22×D311yescharacteristic
206C2×C3×Q8C22×D311yescharacteristic
207D3×Q8—124no—
208D3×Q8—124no—
209C2×D12—31no—
210C2×D12—31no—
211C2×D12—61no—
212C2×C4×D3—62no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—62no—
216C2×C4×D3—121no—
217C2×Dic6—21no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6#6711yescharacteristic
221C2×Dic6C22×D312yes—
222C2×C3×C8—32no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42—32no—
242C3×C42—41no—
243C3×C42—62no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#215—64no—
247#215—62no—
248#215—62no—
249#215—64no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—61no—
252(C2×D3)⋊C4—61no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—121no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3#6711yescharacteristic
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—22no—
265Dic3⋊C4—22no—
266Dic3⋊C4—22no—
267Dic3⋊C4—62no—
268Dic3⋊C4#6712yes—
269C4×Dic3—22no—
270C4×Dic3C22×D312yes—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8C22×D312yes—
278#204—64no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—22no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4C2×SD1612yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—41no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C3×Dic3C2×SD1614yes—
294C22×Q8—181no—
295C2×SD16—92no—
296C2×SD16—91no—
297C4⋊Q8—32no—
298C4⋊Q8—31no—
299C4⋊Q8—31no—
300C4⋊Q8—92no—
301#125—61no—
302#125—62no—
303C22⋊Q8—182no—
304C22⋊Q8—181no—
305C4×Q8—31no—
306C4×Q8—32no—
307C4×Q8—61no—
308C4×Q8D3211yescharacteristic
309C4×D4—92no—
310C4×D4—91no—
311#106—32no—
312#106—91no—
313C4⋊C8—31no—
314C4⋊C8—92no—
315#103—32no—
316#103—92no—
317#103—92no—
318#103—92no—
319#103—91no—
320#102—91no—
321C4×C8—92no—
322C4×C8—91no—
323C22×D3—61no—
324C22×D3—61no—
325C22×D3—121no—
326C3×Q8—22no—
327C3×Q8—21no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8—34no—
332C3×Q8—41no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—122no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
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—41no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—121no—
360C2×Dic3C2×#6712yes—
361C2×Dic3C2×#6712yes—
362D12—32no—
363D12—32no—
364D12—62no—
365D12—61no—
366D12—61no—
367D12—121no—
368C4×D3—124no—
369C4×D3—122no—
370C4×D3—122no—
371C4×D3—124no—
372C4×D3—242no—
373Dic6—22no—
374Dic6—22no—
375Dic6—42no—
376Dic6—124no—
377Dic6—124no—
378Dic6#21514yescomplemented
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#54811yescharacteristic
388C2×C32C22×SD1611yescharacteristic
389C2×C32#57811yescharacteristic
390C3⋊D3—42no—
391C2×Q8—31no—
392C2×Q8—32no—
393C2×Q8—61no—
394C2×Q8—182no—
395C2×Q8—364no—
396C2×Q8C2×D3211yescharacteristic
397C2×D4—91no—
398C22×C4—182no—
399C22×C4—181no—
400SD16—184no—
401SD16—182no—
402C2×C8—32no—
403C2×C8—91no—
404C2×C8—91no—
405C4⋊C4—21no—
406C4⋊C4—32no—
407C4⋊C4—31no—
408C4⋊C4—32no—
409C4⋊C4—62no—
410C4⋊C4—62no—
411C4⋊C4—62no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4—91no—
416C4⋊C4—182no—
417C4⋊C4C2×D3211yescharacteristic
418C22⋊C4—182no—
419C22⋊C4—181no—
420C42—21no—
421C42—32no—
422C42—62no—
423C42C2×D3211yescharacteristic
424C22×C3—21no—
425C22×C3C2×D3×D411yescharacteristic
426C22×C3C22×#6711yescharacteristic
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—122no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—241no—
435C2×D3—241no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—34no—
442C3×C4—41no—
443C3×C4—42no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—62no—
449C3×C4—81no—
450C3×C4—122no—
451C3×C4—122no—
452C3×C4D3×SD1612yes—
453C3×C4C2×#21512yes—
454C3×C4#100711yescharacteristic
455C3×C4D3×#4111yescharacteristic
456C3×C4D3×#4111yescharacteristic
457C3×C4#101011yescharacteristic
458Dic3—22no—
459Dic3—42no—
460Dic3—42no—
461Dic3—121no—
462Dic3—121no—
463Dic3—241no—
464Dic3C2×#21514yes—
465C32#335911yescharacteristic, complemented, Sylow
466C23—181no—
467Q8—21no—
468Q8—21no—
469Q8—34no—
470Q8—62no—
471Q8—62no—
472Q8—122no—
473Q8—364no—
474D4—92no—
475D4—181no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—181no—
483C2×C4—364no—
484C2×C4—362no—
485C2×C4D3×#6711yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—62no—
489C8—181no—
490C8—181no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3#563311yescharacteristic
495C2×C3C2×D3×SD1611yescharacteristic
496C2×C3#577911yescharacteristic
497C2×C3C22×#21511yescharacteristic
498C2×C3#583111yescharacteristic
499C2×C3#583811yescharacteristic
500D3—122no—
501D3—122no—
502D3—242no—
503C22—182no—
504C22—361no—
505C22—361no—
506C22C2×D3×#6711yescharacteristic
507C4—21no—
508C4—34no—
509C4—41no—
510C4—41no—
511C4—62no—
512C4—122no—
513C4—122no—
514C4—361no—
515C4D3×#21512yes—
516C4#6429711yescharacteristic
517C4#6430611yescharacteristic
518C3—21no—
519C3#8103711yescharacteristic, complemented
520C3#8368811yescharacteristic, complemented
521C2—362no—
522C2#1059483011yescharacteristic
523C2C2×D3×#21511yescharacteristic
524C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4×Q8D32
hypocenterC32#3359
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5567C2semidirect
4. C3×#5020C2semidirect
5. #10591623C2semidirect
7. #10590556C2semidirect
10. #10590290C2semidirect
11. #10590250C2semidirect
46. #5567D3semidirect
59. #5020D3semidirect
184. C3×Dic6SD16semidirect
378. Dic6#215semidirect
465. C32#3359semidirect
519. C3#81037semidirect
520. C3#83688semidirect

Maximal subgroups

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

subgroupindex
C3×#55672
#105939032
C4×#37552
C3×#50202
#105916232
#105915652
#105905562
#105904582
#105903792
#105902902
#105902502
#836883
#810373