Finite Group Databasebeta

← #11887641

Subgroups — #11887641

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic
2#10593960C211yesmaximal, characteristic
3#10592720C211yesmaximal, characteristic, complemented
4C3×C4×#216C211yesmaximal, characteristic, complemented
5#10591594C212yesmaximal, complemented
6D3×#835C212yesmaximal, complemented
7#10590518C212yesmaximal, complemented
8#10590440C212yesmaximal, complemented
9#10590384C211yesmaximal, characteristic, complemented
10C3⋊C8×D12C211yesmaximal, characteristic
11#10590287C211yesmaximal, characteristic, complemented
12#83551—31nomaximal
13#79735—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C32×C4×Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×#216C2211yescharacteristic
18C3×#897—22no—
19C3×#897C2212yes—
20C3×C4×D12—21no—
21C3×C4×D12C2211yescharacteristic
22C3×#869—21no—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12—21no—
27D3×C4⋊Dic3C2212yes—
28#63869—21no—
29#63856C2212yes—
30C2×#3718C2212yes—
31C2×D3×C3⋊C8C2212yes—
32#63662C2212yes—
33#63634C2212yes—
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
35C3×#835C2211yescharacteristic
36C3×#810C2211yescharacteristic
37C3×#807C2211yescharacteristic
38C3×C4×C3⋊C8C2211yescharacteristic
39#63566C2212yes—
40#63566C2212yes—
41#63565C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×D4×Q8—31no—
44#5579—31no—
45Q8×D12D311yescharacteristic
46#5543—31no—
47C3×C4×Q16—31no—
48#5228—32no—
49C2×#835—32no—
50#5186—32no—
51#5090—31no—
52#5079—31no—
53#5051—32no—
54#5044—32no—
55#5031—31no—
56C4×#216D311yescharacteristic, complemented
57#5021—31no—
58#5021—31no—
59#5021—61no—
60D4×C3⋊C8—31no—
61#4884—32no—
62#4813—32no—
63D3×#103—32no—
64C8×D12—31no—
65#4681—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634—21no—
68C3×D3×Q8—24no—
69C3×D3×Q8—42no—
70C2×C3×D12D411yescharacteristic
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3C2312yes—
73C2×C3×Dic6—22no—
74C2×C3×Dic6C2312yes—
75C2×C3×Dic6C2311yescharacteristic
76C2×D3×Dic3—22no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#216—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4D412yes—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×C4×Dic3—21no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96#3724—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99#3718—42no—
100D3×C3⋊C8—42no—
101#3299—91noSylow
102C22×C3×Q8—32no—
103C2×D3×Q8C2×D312yes—
104C2×C3×Q16—31no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8—61no—
107C3×C22⋊Q8—32no—
108C3×C22⋊Q8—62no—
109C3×C4×Q8—21no—
110C3×C4×Q8—31no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×D4—31no—
114C3×C4×D4—61no—
115#946—32no—
116C2×#216—32no—
117C2×#216—32no—
118C2×#216C2×D311yescharacteristic
119D4×Dic3—61no—
120C2×C4⋊Dic3—32no—
121#924—32no—
122C22×C3⋊C8—32no—
123C2×D3×C8—32no—
124#897—22no—
125#897C2×D312yes—
126#896—62no—
127D3×C4⋊C4—32no—
128#890—61no—
129#878—62no—
130C4×D12—21no—
131C4×D12—61no—
132C4×D12C2×D311yescharacteristic
133#870—61no—
134#869—21no—
135#869—31no—
136#869—31no—
137#869—61no—
138#869C2×D311yescharacteristic
139C4×Dic6C2×D311yescharacteristic
140C3×#107—31no—
141C3×#103—31no—
142C3×#103—31no—
143C3×C4×C8—31no—
144#835—32no—
145#835—32no—
146#835—32no—
147#835—32no—
148#835—32no—
149#835—62no—
150#835C2×D311yescharacteristic
151#830—32no—
152(C2×D3)⋊C8—32no—
153#816—32no—
154#816—32no—
155#810—32no—
156#810C2×D311yescharacteristic
157#807—32no—
158#807—32no—
159#807—62no—
160#807C2×D311yescharacteristic
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—61no—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3×D3C2×D412yes—
166C32×Q8—21no—
167C32×Q8#4112yes—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174#634—81no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C3×D12Q1614yescomplemented
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×C4×D3—44no—
183C3×Dic6—21no—
184C3×Dic6—22no—
185C3×Dic6—21no—
186C3×Dic6—22no—
187C3×Dic6—44no—
188D3×Dic3—82no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#554—91no—
193D4×Q8—31no—
194#487—91no—
195#484—92no—
196#477—91no—
197#467—92no—
198#462—91no—
199#451—92no—
200C4×Q16—31no—
201C8×D4—91no—
202C2×#103—92no—
203C2×C3×Q8—21no—
204C2×C3×Q8—32no—
205C2×C3×Q8—31no—
206C2×C3×Q8—62no—
207C2×C3×Q8—64no—
208C2×C3×Q8—122no—
209C2×C3×Q8C22×D311yescharacteristic
210C2×C3×Q8C22×D311yescharacteristic
211C2×C3×D4—31no—
212C22×C3×C4—32no—
213C22×C3×C4—62no—
214C22×Dic3—62no—
215D3×Q8—24no—
216D3×Q8—42no—
217C2×D12#6711yescharacteristic
218C2×C4×D3—22no—
219C2×C4×D3—62no—
220C2×C4×D3C22×D312yes—
221C2×Dic6—22no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—121no—
225C2×Dic6C22×D312yes—
226C2×Dic6C22×D311yescharacteristic
227C3×Q16—62no—
228C2×C3×C8—31no—
229C2×C3×C8—31no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C22⋊C4—32no—
243C3×C22⋊C4—62no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—41no—
248C3×C42—61no—
249C3×C42C22×D311yescharacteristic
250C3×C42C22×D311yescharacteristic
251#217—62no—
252#216—22no—
253#216—122no—
254#216—122no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4#6712yes—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—22no—
261C4⋊Dic3—32no—
262C4⋊Dic3—32no—
263C4⋊Dic3—62no—
264C4⋊Dic3—62no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3—121no—
268C4⋊Dic3#6711yescharacteristic
269C4⋊Dic3C22×D311yescharacteristic
270Dic3⋊C4—21no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274C4×Dic3—21no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—122no—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D311yescharacteristic
281D3×C8—122no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3C2×Q1614yes—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4C2×Q1612yes—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—42no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×Q8—32no—
298C2×Q16—31no—
299C2×Q16—92no—
300C22×C8—92no—
301C4⋊Q8—31no—
302C4⋊Q8—61no—
303C4⋊Q8—91no—
304#125—181no—
305C22⋊Q8—32no—
306C22⋊Q8—62no—
307C22⋊Q8—92no—
308C22⋊Q8—182no—
309C4×Q8—31no—
310C4×Q8D3211yescharacteristic
311C4×D4—31no—
312C4×D4—61no—
313C4×D4—181no—
314C2×C4⋊C4—92no—
315#107—31no—
316#107—92no—
317C4⋊C8—91no—
318#103—31no—
319#103—31no—
320#103—92no—
321#103—92no—
322#103—92no—
323#103—92no—
324C22⋊C8—92no—
325C4×C8—31no—
326C23×C3—32no—
327C22×D3C2×#6712yes—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—22no—
331C3×Q8—41no—
332C3×Q8—62no—
333C3×Q8—61no—
334C3×Q8—61no—
335C3×Q8—62no—
336C3×Q8—124no—
337C3×Q8#23512yes—
338C3×Q8#23712yes—
339C3×D4—34no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—32no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—124no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—22no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—122no—
368C2×Dic3—242no—
369C2×Dic3C2×#6712yes—
370D12#21614yescomplemented
371C4×D3—22no—
372C4×D3—22no—
373C4×D3—44no—
374C4×D3—242no—
375Dic6—21no—
376Dic6—22no—
377Dic6—22no—
378Dic6—21no—
379Dic6—44no—
380Dic6—241no—
381Dic6—241no—
382Dic6—242no—
383C3×C8—61no—
384C3×C8—61no—
385C3⋊C8—21no—
386C3⋊C8—21no—
387C3⋊C8—62no—
388C3⋊C8—62no—
389C3⋊C8—122no—
390C2×C32#54611yescharacteristic
391C2×C32C22×Q1611yescharacteristic
392C2×C32#57711yescharacteristic
393C3×D3—24no—
394C2×Q8—31no—
395C2×Q8—32no—
396C2×Q8—62no—
397C2×Q8—64no—
398C2×Q8—122no—
399C2×Q8—181no—
400C2×Q8C2×D3211yescharacteristic
401C2×D4—31no—
402C22×C4—32no—
403C22×C4—62no—
404C22×C4—182no—
405Q16—62no—
406Q16—362no—
407C2×C8—31no—
408C2×C8—31no—
409C2×C8—92no—
410C2×C8—362no—
411C4⋊C4—21no—
412C4⋊C4—31no—
413C4⋊C4—31no—
414C4⋊C4—62no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C4⋊C4—92no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C4⋊C4—181no—
422C4⋊C4C2×D3211yescharacteristic
423C22⋊C4—32no—
424C22⋊C4—62no—
425C22⋊C4—182no—
426C42—21no—
427C42—61no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—34no—
431C22×C3—62no—
432C22×C3—62no—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×#6711yescharacteristic
435C2×D3—22no—
436C2×D3—22no—
437C2×D3C2×#21614yes—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—62no—
450C3×C4—81no—
451C3×C4—122no—
452C3×C4—121no—
453C3×C4—121no—
454C3×C4D3×Q1612yes—
455C3×C4C2×#21612yes—
456C3×C4C2×#23511yescharacteristic
457C3×C4C2×#23711yescharacteristic
458C3×C4#100411yescharacteristic
459C3×C4#100911yescharacteristic
460Dic3—22no—
461Dic3—41no—
462Dic3—41no—
463Dic3—42no—
464Dic3—122no—
465Dic3—122no—
466Dic3—242no—
467C32#329911yescharacteristic, complemented, Sylow
468C23—32no—
469Q8—21no—
470Q8—61no—
471Q8—62no—
472Q8—61no—
473Q8—62no—
474Q8—124no—
475Q8—721no—
476Q8#379512yes—
477D4—34no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—32no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—124no—
487C2×C4—182no—
488C2×C4—722no—
489C2×C4D3×#6711yescharacteristic
490C2×C4D3×#6711yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—61no—
493C8—61no—
494C8—182no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—64no—
499C2×C3#555011yescharacteristic
500C2×C3C2×D3×Q1611yescharacteristic
501C2×C3#577011yescharacteristic
502C2×C3#580611yescharacteristic
503C2×C3C22×#21611yescharacteristic
504C2×C3#583711yescharacteristic
505D3—24no—
506C22—34no—
507C22—62no—
508C22—62no—
509C22C2×D3×#6711yescharacteristic
510C4—22no—
511C4—21no—
512C4—41no—
513C4—62no—
514C4—122no—
515C4—121no—
516C4—121no—
517C4—362no—
518C4D3×#21612yes—
519C4C2×#379511yescharacteristic
520C4#6430711yescharacteristic
521C3—21no—
522C3#7973511yescharacteristic, complemented
523C3#8355111yescharacteristic, complemented
524C2—64no—
525C2#1059488611yescharacteristic
526C2C2×D3×#21611yescharacteristic
527C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4×Q8D32
hypocenterC32#3299
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
3. #10592720C2semidirect
4. C3×C4×#216C2semidirect
5. #10591594C2semidirect
6. D3×#835C2semidirect
7. #10590518C2semidirect
8. #10590440C2semidirect
9. #10590384C2semidirect
11. #10590287C2semidirect
56. C4×#216D3semidirect
179. C3×D12Q16semidirect
370. D12#216semidirect
467. C32#3299semidirect
522. C3#79735semidirect
523. C3#83551semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
#105939602
#105927202
C3×C4×#2162
#105915942
D3×#8352
#105905182
#105904402
#105903842
C3⋊C8×D122
#105902872
#835513
#797353