Finite Group Databasebeta

← #11897661

Subgroups — #11897661

Order 1152.

728 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2#10593960C211yesmaximal, characteristic
3#10592720C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic
5#10591566C212yesmaximal
6#10591547C212yesmaximal, complemented
7#10590463C212yesmaximal
8#10590421C212yesmaximal, complemented
9#10590311C211yesmaximal, characteristic, complemented
10#10590266C211yesmaximal, characteristic
11#10590258C211yesmaximal, characteristic, complemented
12#83706—31nomaximal
13#79634—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×Q8×Dic3C2212yes—
17C2×C3×#215C2211yescharacteristic
18C3×#888—22no—
19C3×#888C2212yes—
20C3×C4×D12C2211yescharacteristic
21C3×#869—21no—
22C3×#869C2211yescharacteristic
23C3×C4×Dic6—21no—
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63869C2212yes—
29#63856—21no—
30#63662C2212yes—
31#63634C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#835C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#808C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2212yes—
38#63575C2212yes—
39#63574C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×Q82—31no—
44#5579—31no—
45Q8×Dic6D311yescharacteristic, complemented
46#5543—31no—
47C3×C4×SD16—31no—
48#5164—32no—
49#5087—32no—
50#5084—31no—
51#5081—32no—
52#5078—31no—
53#5026—32no—
54C4×#215D311yescharacteristic
55#5024—31no—
56#5022—32no—
57#5021—31no—
58#5021—31no—
59#5021—61no—
60#5008—31no—
61#4856—32no—
62#4796—32no—
63#4759—32no—
64#4682—31no—
65#4679—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6D411yescharacteristic
73C2×D3×Dic3—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×#215Q814yescomplemented
82C3×(C2×D3)⋊C4—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3385—91noSylow
98C2×C3×SD16—31no—
99C3×C4⋊Q8—32no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—61no—
102C3×C4⋊Q8—62no—
103C3×C4×Q8—21no—
104C3×C4×Q8—31no—
105C3×C4×Q8—32no—
106C3×C4×Q8—61no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×D4—31no—
110#946—61no—
111Q8×Dic3C2×D312yes—
112C2×#215C2×D311yescharacteristic
113D4×Dic3—32no—
114C2×C4⋊Dic3—61no—
115#924—61no—
116#896—62no—
117D3×C4⋊C4—61no—
118#890—32no—
119#888—22no—
120#888C2×D312yes—
121#878—62no—
122C4×D12—32no—
123C4×D12C2×D311yescharacteristic
124#870—32no—
125#869—21no—
126#869—31no—
127#869—31no—
128#869—61no—
129#869C2×D311yescharacteristic
130C4×Dic6—21no—
131C4×Dic6C2×D311yescharacteristic
132C3×#106—31no—
133C3×#103—31no—
134C3×#102—31no—
135C3×C4×C8—31no—
136#835—32no—
137#835—32no—
138#835—62no—
139#835C2×D311yescharacteristic
140#832—32no—
141#818—32no—
142#818—32no—
143#815—32no—
144Dic3⋊C8—32no—
145#809—32no—
146#809C2×D311yescharacteristic
147#808—32no—
148#808—32no—
149#808C2×D311yescharacteristic
150#807—32no—
151#807—32no—
152#807—32no—
153#807—32no—
154#807—62no—
155C4⋊(C3⋊C8)—31no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—32no—
158C4⋊(C3⋊C8)—61no—
159#803—32no—
160C4×C3⋊C8C2×D311yescharacteristic
161C22×C3×D3—21no—
162C32×Q8—21no—
163C32×Q8C2×Q812yes—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170#634—81no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D412yes—
175C3×D12—21no—
176C3×D12C2×Q812yes—
177C3×C4×D3—42no—
178C3×Dic6—22no—
179C3×Dic6—82no—
180C3×Dic6—81no—
181D3×Dic3—82no—
182C3⋊(C3⋊C8)—22no—
183C3×C3⋊C8—21no—
184C3×C3⋊C8C2×Q812yes—
185Q82—31no—
186#554—91no—
187#501—92no—
188#500—91no—
189#479—92no—
190#477—91no—
191#476—91no—
192#474—92no—
193#446—91no—
194#440—92no—
195C4×SD16—31no—
196C2×C3×Q8—21no—
197C2×C3×Q8—31no—
198C2×C3×Q8—62no—
199C2×C3×Q8—61no—
200C2×C3×Q8C22×D311yescharacteristic
201C2×C3×Q8C22×D311yescharacteristic
202C2×C3×D4—31no—
203C22×C3×C4—61no—
204C22×Dic3—62no—
205C2×D12C22×D311yescharacteristic
206C2×C4×D3—21no—
207C2×C4×D3—62no—
208C2×Dic6—21no—
209C2×Dic6—22no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—121no—
213C2×Dic6#6711yescharacteristic
214C3×SD16—34no—
215C2×C3×C8—31no—
216C2×C3×C8—31no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4C22×D311yescharacteristic
229C3×C4⋊C4C22×D311yescharacteristic
230C3×C22⋊C4—61no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—32no—
235C3×C42—41no—
236C3×C42—62no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#217—62no—
240#215Dic614yescomplemented
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—21no—
244C4⋊Dic3—22no—
245C4⋊Dic3—32no—
246C4⋊Dic3—32no—
247C4⋊Dic3—62no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—62no—
251C4⋊Dic3—121no—
252C4⋊Dic3#6711yescharacteristic
253C4⋊Dic3C22×D311yescharacteristic
254C4⋊Dic3C22×D312yes—
255Dic3⋊C4—22no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4#6712yes—
260C4×Dic3—22no—
261C4×Dic3C22×D312yes—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267C22×C32C22×D411yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—41no—
270C2×C3×D3—41no—
271C32×C4—22no—
272C32×C4—21no—
273C32×C4—41no—
274C32×C4#13712yes—
275C32×C4C22×Q811yescharacteristic
276C32×C42−1+411yescharacteristic
277C3⋊Dic3—42no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—41no—
281C3×Dic3—42no—
282C2×SD16—31no—
283C4⋊Q8—32no—
284C4⋊Q8—31no—
285C4⋊Q8—61no—
286C4⋊Q8—62no—
287C4⋊Q8—91no—
288#125—92no—
289C22⋊Q8—182no—
290C22⋊Q8—181no—
291C4×Q8—31no—
292C4×Q8—32no—
293C4×Q8—61no—
294C4×Q8D3211yescharacteristic
295C4×D4—31no—
296C4×D4—92no—
297C2×C4⋊C4—181no—
298#107—92no—
299#107—92no—
300#107—92no—
301#106—31no—
302#106—92no—
303C4⋊C8—92no—
304C4⋊C8—91no—
305#103—31no—
306#103—92no—
307#102—31no—
308#102—92no—
309#97—92no—
310C4×C8—31no—
311C23×C3—61no—
312C22×D3—21no—
313C3×Q8—21no—
314C3×Q8—21no—
315C3×Q8—22no—
316C3×Q8—41no—
317C3×Q8—62no—
318C3×Q8—241no—
319C3×Q8—242no—
320C3×Q8C2×Dic612yes—
321C3×Q8D3×Q812yes—
322C3×D4—32no—
323C3×D4—61no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—62no—
336C2×C3×C4—61no—
337C2×C3×C4—122no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—122no—
349C2×Dic3—242no—
350C2×Dic3C2×#6712yes—
351C2×Dic3C2×#6712yes—
352D12—21no—
353D12C2×Dic612yes—
354C4×D3—42no—
355C4×D3—242no—
356Dic6—22no—
357Dic6—82no—
358Dic6—81no—
359Dic6—241no—
360Dic6—241no—
361Dic6—242no—
362C3×C8—32no—
363C3×C8—61no—
364C3⋊C8—21no—
365C3⋊C8—62no—
366C3⋊C8—62no—
367C3⋊C8—122no—
368C3⋊C8C2×Dic612yes—
369C2×C32D4×Q811yescharacteristic
370C2×C32C2×#13711yescharacteristic
371C2×C32#57611yescharacteristic
372C3×D3—42no—
373C2×Q8—31no—
374C2×Q8—62no—
375C2×Q8—61no—
376C2×Q8—181no—
377C2×Q8C2×D3211yescharacteristic
378C2×D4—31no—
379C22×C4—61no—
380C22×C4—182no—
381SD16—34no—
382C2×C8—31no—
383C2×C8—31no—
384C2×C8—92no—
385C4⋊C4—21no—
386C4⋊C4—31no—
387C4⋊C4—32no—
388C4⋊C4—32no—
389C4⋊C4—31no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—61no—
393C4⋊C4—92no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C4⋊C4—181no—
397C4⋊C4C2×D3211yescharacteristic
398C22⋊C4—61no—
399C22⋊C4—182no—
400C42—21no—
401C42—32no—
402C42—62no—
403C42C2×D3211yescharacteristic
404C22×C3—21no—
405C22×C3—62no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C22×#6711yescharacteristic
410C2×D3—22no—
411C2×D3—41no—
412C2×D3—41no—
413C3×C4—21no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—22no—
420C3×C4—41no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—62no—
425C3×C4—62no—
426C3×C4—81no—
427C3×C4—122no—
428C3×C4—121no—
429C3×C4#91512yes—
430C3×C4#94212yes—
431C3×C4C22×Dic611yescharacteristic
432C3×C4C2×D3×Q811yescharacteristic
433C3×C4#100711yescharacteristic
434C3×C4#101011yescharacteristic
435Dic3—22no—
436Dic3—22no—
437Dic3—41no—
438Dic3—42no—
439Dic3—122no—
440Dic3—122no—
441Dic3—242no—
442C32#338511yescharacteristic, complemented, Sylow
443C23—61no—
444Q8—21no—
445Q8—62no—
446Q8—241no—
447Q8—242no—
448Q8—721no—
449Q8D3×Dic612yes—
450D4—32no—
451D4—61no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—32no—
455C2×C4—32no—
456C2×C4—62no—
457C2×C4—61no—
458C2×C4—122no—
459C2×C4—182no—
460C2×C4—722no—
461C2×C4D3×#6711yescharacteristic
462C2×C4D3×#6711yescharacteristic
463C2×C4C22×D3211yescharacteristic
464C8—32no—
465C8—61no—
466C8—182no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—122no—
471C2×C3D4×Dic611yescharacteristic
472C2×C3C2×#91511yescharacteristic
473C2×C3#576911yescharacteristic
474C2×C3C2×#94211yescharacteristic
475C2×C3Q8×#6711yescharacteristic
476C2×C3#583511yescharacteristic
477D3—42no—
478C22—62no—
479C22—121no—
480C22—121no—
481C22C2×D3×#6711yescharacteristic
482C4—22no—
483C4—21no—
484C4—41no—
485C4—62no—
486C4—62no—
487C4—121no—
488C4—122no—
489C4—362no—
490C4#6394612yes—
491C4C2×D3×Dic611yescharacteristic
492C4#6429711yescharacteristic
493C3—21no—
494C3#7963411yescharacteristic, complemented
495C3#8370611yescharacteristic, complemented
496C2—122no—
497C2Dic6×#6711yescharacteristic
498C2C2×#6394611yescharacteristic
499C2#1059545611yescharacteristic
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#3385
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×Q8×Dic6C2semidirect
3. #10592720C2semidirect
6. #10591547C2semidirect
8. #10590421C2semidirect
9. #10590311C2semidirect
11. #10590258C2semidirect
45. Q8×Dic6D3semidirect
81. C3×#215Q8semidirect
240. #215Dic6semidirect
442. C32#3385semidirect
494. C3#79634semidirect
495. C3#83706semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
#105939602
#105927202
C3×C4×#2152
#105915662
#105915472
#105904632
#105904212
#105903112
#105902662
#105902582
#837063
#796343