Finite Group Databasebeta

← #11895161

Subgroups — #11895161

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2Dic6×D12C211yesmaximal, characteristic
3#10592778C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic
5#10591623C212yesmaximal, complemented
6#10591564C212yesmaximal
7Dic3×#215C212yesmaximal
8#10591544C212yesmaximal, complemented
9C4×#3715C211yesmaximal, characteristic
10#10590301C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83688—31nomaximal
13#80414—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C3×#944C2212yes—
19C2×C3×#215C2212yes—
20C3×#890—21no—
21C3×#889—22no—
22C3×#887—21no—
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63918C2212yes—
27#63893—22no—
28Dic3×D12C2212yes—
29#63857—21no—
30C2×#3715C2211yescharacteristic
31#63662C2212yes—
32#63662C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#835C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63574C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2212yes—
40#63565C2211yescharacteristic
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5721D311yescharacteristic, complemented
45Q8×D12—31no—
46D4×Dic6—31no—
47C3×#461—31no—
48#5162—32no—
49Dic3×SD16—32no—
50#5083—32no—
51#5083D311yescharacteristic
52#5079—31no—
53#5079—31no—
54#5079—32no—
55#5079—61no—
56C4×#215—32no—
57C4×#215—31no—
58Q8×C3⋊C8—31no—
59#5020—32no—
60#5020—31no—
61C4×#214—31no—
62#4851—31no—
63#4830—31no—
64#4792—32no—
65#4791—32no—
66C2×C32×Q8C2312yes—
67C2×#634—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×D3×Dic3—22no—
74D3×Dic6—44no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#215—24no—
83C3×(C2×D3)⋊C4—21no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—21no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3715—22no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8—32no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×#125—62no—
108C3×#125—61no—
109C3×C4×Q8—31no—
110C3×C4×Q8—32no—
111C3×C4×Q8—31no—
112C3×C4×Q8—61no—
113C3×C4×D4—31no—
114Q8×Dic3C2×D312yes—
115#944C2×D312yes—
116C2×#215—31no—
117C2×#215C2×D312yes—
118D4×Dic3—32no—
119C2×#214—31no—
120#924—61no—
121#897—62no—
122#897—61no—
123#890—21no—
124#889—22no—
125#888—32no—
126#887—21no—
127#878—62no—
128C4×D12—32no—
129C4×D12C2×D311yescharacteristic
130#869—31no—
131#869—31no—
132#869—32no—
133#869—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—31no—
137C3×#103—32no—
138#835—32no—
139#835—32no—
140#835—32no—
141#835—32no—
142#835—31no—
143#835—32no—
144#835—62no—
145#835—62no—
146#835C2×D312yes—
147#832—31no—
148#817—32no—
149#816—32no—
150Dic3⋊C8—32no—
151C8×Dic3—32no—
152#810—31no—
153#809—31no—
154#808—31no—
155#808—31no—
156#808—32no—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8—61no—
163C22×C3×D3—21no—
164C32×Q8—22no—
165C32×Q8—22no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—22no—
171#634—42no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—42no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6SD1614yescomplemented
183#627—44no—
184D3×Dic3—44no—
185C3⋊(C3⋊C8)—21no—
186C3⋊(C3⋊C8)—21no—
187C3×C3⋊C8—22no—
188#557—31no—
189D4×Q8—91no—
190#487—92no—
191#487—91no—
192#475—92no—
193#475—91no—
194#461—31no—
195#461—92no—
196C8×Q8—91no—
197C4×SD16—91no—
198C4×SD16—92no—
199C2×C3×Q8—22no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8C22×D312yes—
203C2×C3×Q8C22×D312yes—
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×D311yescharacteristic
219C3×SD16—64no—
220C2×C3×C8—32no—
221C3×C4⋊C4—21no—
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—31no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—41no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—61no—
235C3×C22⋊C4—61no—
236C3×C42—21no—
237C3×C42—32no—
238C3×C42—62no—
239C3×C42—61no—
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D311yescharacteristic
242#217—62no—
243#215—24no—
244#215—62no—
245#214—62no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—22no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—121no—
256C4⋊Dic3#6711yescharacteristic
257C4⋊Dic3C22×D311yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259Dic3⋊C4—21no—
260Dic3⋊C4—22no—
261Dic3⋊C4—22no—
262Dic3⋊C4—62no—
263Dic3⋊C4#6712yes—
264C4×Dic3—21no—
265C4×Dic3—22no—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8C22×D312yes—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—42no—
280C32×C4C2×SD1612yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—41no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C3×Dic3C2×SD1614yes—
289C22×Q8—181no—
290C2×SD16—32no—
291C2×SD16—91no—
292C4⋊Q8—32no—
293C4⋊Q8—92no—
294C4⋊Q8—91no—
295C4⋊Q8D3211yescharacteristic
296#125—62no—
297#125—61no—
298C22⋊Q8—182no—
299C22⋊Q8—181no—
300C4×Q8—31no—
301C4×Q8—32no—
302C4×Q8—31no—
303C4×Q8—61no—
304C4×D4—31no—
305C4×D4—92no—
306#106—91no—
307#106—92no—
308C4⋊C8—31no—
309C4⋊C8—92no—
310#103—32no—
311#103—91no—
312#103—92no—
313#103—92no—
314#103—92no—
315#102—91no—
316C4×C8—92no—
317C4×C8—91no—
318C23×C3—61no—
319C22×D3—21no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—34no—
325C3×Q8—42no—
326C3×Q8—42no—
327C3×Q8—61no—
328C3×Q8—61no—
329C3×D4—32no—
330C3×D4—61no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—42no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—122no—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—124no—
356C2×Dic3C2×#6712yes—
357C2×Dic3C2×#6712yes—
358D12—21no—
359D12#23712yes—
360C4×D3—42no—
361C4×D3—124no—
362Dic6—21no—
363Dic6—21no—
364Dic6—124no—
365Dic6—122no—
366Dic6—122no—
367Dic6—124no—
368Dic6—242no—
369Dic6#21514yescomplemented
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—61no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—61no—
376C3⋊C8—121no—
377C3⋊C8—121no—
378C2×C32#54811yescharacteristic
379C2×C32C22×SD1611yescharacteristic
380C2×C32#57811yescharacteristic
381C3×D3—42no—
382C2×Q8—31no—
383C2×Q8—31no—
384C2×Q8—182no—
385C2×Q8—181no—
386C2×Q8—364no—
387C2×Q8C2×D3212yes—
388C2×D4—31no—
389C22×C4—61no—
390C22×C4—182no—
391SD16—64no—
392SD16—182no—
393C2×C8—32no—
394C2×C8—91no—
395C2×C8—91no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—32no—
399C4⋊C4—31no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—62no—
405C4⋊C4—61no—
406C4⋊C4—92no—
407C4⋊C4—182no—
408C4⋊C4—181no—
409C22⋊C4—61no—
410C22⋊C4—182no—
411C42—32no—
412C42—62no—
413C42—61no—
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—22no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—34no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—62no—
434C3×C4—82no—
435C3×C4—121no—
436C3×C4—121no—
437C3×C4—121no—
438C3×C4D3×SD1612yes—
439C3×C4C2×#21512yes—
440C3×C4C2×#23711yescharacteristic
441C3×C4D3×#4111yescharacteristic
442C3×C4#101011yescharacteristic
443C3×C4#101011yescharacteristic
444Dic3—22no—
445Dic3—41no—
446Dic3—41no—
447Dic3—41no—
448Dic3—122no—
449Dic3—122no—
450Dic3—242no—
451Dic3C2×#21514yes—
452C32#335911yescharacteristic, complemented, Sylow
453C23—61no—
454Q8—22no—
455Q8—22no—
456Q8—34no—
457Q8—61no—
458Q8—61no—
459Q8—364no—
460Q8—362no—
461D4—32no—
462D4—61no—
463C2×C4—22no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—122no—
470C2×C4—182no—
471C2×C4—364no—
472C2×C4D3×#6711yescharacteristic
473C2×C4D3×#6711yescharacteristic
474C2×C4C22×D3211yescharacteristic
475C8—62no—
476C8—181no—
477C8—181no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—122no—
482C2×C3#559811yescharacteristic
483C2×C3C2×D3×SD1611yescharacteristic
484C2×C3#577911yescharacteristic
485C2×C3C22×#21511yescharacteristic
486C2×C3#583111yescharacteristic
487C2×C3#583811yescharacteristic
488D3—42no—
489C22—62no—
490C22—121no—
491C22—121no—
492C22C2×D3×#6711yescharacteristic
493C4—21no—
494C4—34no—
495C4—42no—
496C4—62no—
497C4—121no—
498C4—121no—
499C4—121no—
500C4—362no—
501C4D3×#21512yes—
502C4#6430911yescharacteristic
503C4D3×#23711yescharacteristic
504C3—21no—
505C3#8041411yescharacteristic, complemented
506C3#8368811yescharacteristic, complemented
507C2—122no—
508C2#1059515711yescharacteristic
509C2C2×D3×#21511yescharacteristic
510C2#1059532811yescharacteristic
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×#5721C2semidirect
3. #10592778C2semidirect
5. #10591623C2semidirect
8. #10591544C2semidirect
10. #10590301C2semidirect
11. #10590250C2semidirect
44. #5721D3semidirect
182. C3×Dic6SD16semidirect
369. Dic6#215semidirect
452. C32#3359semidirect
505. C3#80414semidirect
506. C3#83688semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
Dic6×D122
#105927782
C3×#50832
#105916232
#105915642
Dic3×#2152
#105915442
C4×#37152
#105903012
#105902502
#836883
#804143