Finite Group Databasebeta

← #11895167

Subgroups — #11895167

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5567C211yesmaximal, characteristic, complemented
2Dic6×D12C211yesmaximal, characteristic
3#10592719C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic
5#10591623C212yesmaximal, complemented
6#10591564C212yesmaximal
7#10590556C212yesmaximal, complemented
8#10590453C212yesmaximal
9#10590363C211yesmaximal, characteristic
10#10590287C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83688—31nomaximal
13#79619—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4×Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#944C2212yes—
18C2×C3×#215C2211yescharacteristic
19C3×#889—22no—
20C3×#887C2212yes—
21C3×C4×D12C2211yescharacteristic
22C3×#870—21no—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6—21no—
25C3×C4×Dic6C2211yescharacteristic
26#63918C2212yes—
27#63893—22no—
28Dic3×D12C2212yes—
29#63857—21no—
30C2×#3715C2212yes—
31#63662C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#835C2211yescharacteristic
35C3×#809C2211yescharacteristic
36C3×#808C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63565C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44Q8×D12—31no—
45#5567D311yescharacteristic, complemented
46D4×Dic6—31no—
47C3×C4×SD16—31no—
48#5162—32no—
49#5083—32no—
50#5083—31no—
51#5079—32no—
52#5079—31no—
53C4×#215—32no—
54C4×#215D311yescharacteristic
55Q8×C3⋊C8—31no—
56#5020—31no—
57#5020—31no—
58#5020—32no—
59#5020—61no—
60#5019—31no—
61#4854—32no—
62#4792—32no—
63#4758—32no—
64#4681—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×#627—22no—
73C2×D3×Dic3—22no—
74D3×Dic6—44no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C42—21no—
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×#215—22no—
83C3×(C2×D3)⋊C4—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—22no—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3715—24no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×SD16—31no—
103C3×C4⋊Q8—32no—
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
113C3×C4×D4—31no—
114#944C2×D312yes—
115C2×#215—32no—
116C2×#215C2×D311yescharacteristic
117D4×Dic3—32no—
118C2×#214—32no—
119#924—61no—
120#897—62no—
121#897—61no—
122#889—22no—
123#888—32no—
124#887C2×D312yes—
125#878—62no—
126C4×D12—32no—
127C4×D12C2×D311yescharacteristic
128#870—21no—
129#869—31no—
130#869—31no—
131#869—32no—
132#869—61no—
133#869C2×D311yescharacteristic
134C4×Dic6—21no—
135C4×Dic6C2×D311yescharacteristic
136C3×#106—31no—
137C3×#103—31no—
138C3×#102—31no—
139C3×C4×C8—31no—
140#835—32no—
141#835—32no—
142#835—32no—
143#835—32no—
144#835—32no—
145#835—62no—
146#835C2×D311yescharacteristic
147#816—32no—
148#816—32no—
149Dic3⋊C8—32no—
150C8×Dic3—32no—
151#810—32no—
152#809C2×D311yescharacteristic
153#808—32no—
154#808—32no—
155#808—62no—
156#808C2×D311yescharacteristic
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3×D3—21no—
164C32×Q8—21no—
165C32×Q8—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172#634—42no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6SD1614yescomplemented
183#627—44no—
184D3×Dic3—44no—
185C3⋊(C3⋊C8)—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—21no—
188#557—31no—
189D4×Q8—91no—
190#487—91no—
191#487—92no—
192#475—92no—
193#475—91no—
194#461—91no—
195#461—92no—
196C8×Q8—91no—
197C4×SD16—31no—
198C4×SD16—92no—
199C2×C3×Q8—21no—
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8C22×D311yescharacteristic
203C2×C3×Q8C22×D311yescharacteristic
204C2×C3×D4—31no—
205C22×C3×C4—61no—
206C22×Dic3—62no—
207D3×Q8—124no—
208C2×D12C22×D311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—62no—
211C2×Dic6—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×Dic6—121no—
216C2×Dic6—124no—
217C2×Dic6#6711yescharacteristic
218C2×Dic6C22×D312yes—
219C3×SD16—62no—
220C2×C3×C8—31no—
221C2×C3×C8—31no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—32no—
241C3×C42—41no—
242C3×C42—62no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#217—62no—
246#215—22no—
247#215—64no—
248#214—64no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—62no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—121no—
260C4⋊Dic3#6711yescharacteristic
261C4⋊Dic3C22×D311yescharacteristic
262Dic3⋊C4—22no—
263Dic3⋊C4—22no—
264Dic3⋊C4—22no—
265Dic3⋊C4—62no—
266Dic3⋊C4#6712yes—
267C4×Dic3—22no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—62no—
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D311yescharacteristic
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—41no—
280C32×C4—41no—
281C32×C4C2×SD1612yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—41no—
288C3×Dic3C2×SD1614yes—
289C22×Q8—181no—
290C2×SD16—31no—
291C2×SD16—92no—
292C4⋊Q8—32no—
293C4⋊Q8—31no—
294C4⋊Q8—92no—
295C4⋊Q8—91no—
296#125—61no—
297#125—62no—
298C22⋊Q8—182no—
299C22⋊Q8—181no—
300C4×Q8—31no—
301C4×Q8—32no—
302C4×Q8—61no—
303C4×Q8D3211yescharacteristic
304C4×D4—31no—
305C4×D4—92no—
306#106—31no—
307#106—92no—
308C4⋊C8—92no—
309C4⋊C8—91no—
310#103—31no—
311#103—92no—
312#103—92no—
313#103—92no—
314#103—92no—
315#102—31no—
316C4×C8—31no—
317C4×C8—92no—
318C23×C3—61no—
319C22×D3—21no—
320C3×Q8—22no—
321C3×Q8—21no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—21no—
325C3×Q8—34no—
326C3×Q8—41no—
327C3×Q8—62no—
328C3×Q8—62no—
329C3×D4—32no—
330C3×D4—61no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—62no—
343C2×C3×C4—61no—
344C2×C3×C4—122no—
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—122no—
356C2×Dic3—124no—
357C2×Dic3C2×#6712yes—
358C2×Dic3C2×#6712yes—
359D12—21no—
360D12#23512yes—
361C4×D3—42no—
362C4×D3—124no—
363Dic6—22no—
364Dic6—22no—
365Dic6—124no—
366Dic6—122no—
367Dic6—122no—
368Dic6—124no—
369Dic6—242no—
370Dic6#21514yescomplemented
371C3×C8—61no—
372C3×C8—61no—
373C3⋊C8—21no—
374C3⋊C8—21no—
375C3⋊C8—62no—
376C3⋊C8—62no—
377C3⋊C8—122no—
378C2×C32#54811yescharacteristic
379C2×C32C22×SD1611yescharacteristic
380C2×C32#57811yescharacteristic
381C3×D3—42no—
382C2×Q8—31no—
383C2×Q8—32no—
384C2×Q8—182no—
385C2×Q8—181no—
386C2×Q8—364no—
387C2×Q8C2×D3211yescharacteristic
388C2×D4—31no—
389C22×C4—61no—
390C22×C4—182no—
391SD16—62no—
392SD16—184no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8—92no—
396C4⋊C4—21no—
397C4⋊C4—32no—
398C4⋊C4—31no—
399C4⋊C4—31no—
400C4⋊C4—62no—
401C4⋊C4—62no—
402C4⋊C4—62no—
403C4⋊C4—61no—
404C4⋊C4—61no—
405C4⋊C4—92no—
406C4⋊C4—182no—
407C4⋊C4—181no—
408C4⋊C4C2×D3211yescharacteristic
409C22⋊C4—61no—
410C22⋊C4—182no—
411C42—21no—
412C42—32no—
413C42—62no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—62no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×#6711yescharacteristic
421C2×D3—22no—
422C2×D3—41no—
423C2×D3—41no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—34no—
430C3×C4—41no—
431C3×C4—42no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—62no—
437C3×C4—81no—
438C3×C4—121no—
439C3×C4—122no—
440C3×C4D3×SD1612yes—
441C3×C4C2×#21512yes—
442C3×C4C2×#23511yescharacteristic
443C3×C4D3×#4111yescharacteristic
444C3×C4#101011yescharacteristic
445C3×C4#101011yescharacteristic
446Dic3—22no—
447Dic3—41no—
448Dic3—42no—
449Dic3—122no—
450Dic3—122no—
451Dic3—242no—
452Dic3C2×#21514yes—
453C32#335911yescharacteristic, complemented, Sylow
454C23—61no—
455Q8—21no—
456Q8—21no—
457Q8—34no—
458Q8—62no—
459Q8—62no—
460Q8—364no—
461Q8—362no—
462D4—32no—
463D4—61no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—62no—
469C2×C4—61no—
470C2×C4—122no—
471C2×C4—182no—
472C2×C4—364no—
473C2×C4D3×#6711yescharacteristic
474C2×C4D3×#6711yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—61no—
477C8—61no—
478C8—182no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—122no—
483C2×C3#555211yescharacteristic
484C2×C3C2×D3×SD1611yescharacteristic
485C2×C3#577111yescharacteristic
486C2×C3C22×#21511yescharacteristic
487C2×C3#583111yescharacteristic
488C2×C3#583811yescharacteristic
489D3—42no—
490C22—62no—
491C22—121no—
492C22—121no—
493C22C2×D3×#6711yescharacteristic
494C4—21no—
495C4—34no—
496C4—41no—
497C4—41no—
498C4—62no—
499C4—122no—
500C4—121no—
501C4—362no—
502C4D3×#21512yes—
503C4#6429811yescharacteristic
504C4D3×#23511yescharacteristic
505C3—21no—
506C3#7961911yescharacteristic, complemented
507C3#8368811yescharacteristic, complemented
508C2—122no—
509C2#1059489911yescharacteristic
510C2C2×D3×#21511yescharacteristic
511C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
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
3. #10592719C2semidirect
5. #10591623C2semidirect
7. #10590556C2semidirect
10. #10590287C2semidirect
11. C3⋊C8×Dic6C2semidirect
45. #5567D3semidirect
182. C3×Dic6SD16semidirect
370. Dic6#215semidirect
453. C32#3359semidirect
506. C3#79619semidirect
507. C3#83688semidirect

Maximal subgroups

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

subgroupindex
C3×#55672
Dic6×D122
#105927192
C3×C4×#2152
#105916232
#105915642
#105905562
#105904532
#105903632
#105902872
C3⋊C8×Dic62
#836883
#796193