Finite Group Databasebeta

← #11895427

Subgroups — #11895427

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593902C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592393C211yesmaximal, characteristic, complemented
4C3×C4×#204C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590878C212yesmaximal, complemented
7#10590799C212yesmaximal, complemented
8#10590792C212yesmaximal, complemented
9#10590759C212yesmaximal, complemented
10#10590367C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#79932—31nomaximal
13#79622—31nomaximal
14C2×#3799—21no—
15#64083C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×#204C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918—21no—
22#63918C2212yes—
23#63911C2212yes—
24#63910—22no—
25#63909—21no—
26#63894C2212yes—
27Dic3×Dic6—21no—
28Dic3×Dic6C2212yes—
29#63840—22no—
30C2×#3717C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2212yes—
33#63648C2212yes—
34C3×#821C2211yescharacteristic
35C3×#817C2211yescharacteristic
36C3×#816C2211yescharacteristic
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63564C2212yes—
42#63563C2212yes—
43#5577—31no—
44Q8×Dic6—31no—
45Q8×Dic6—31no—
46#5553—31no—
47C3×C8×Q8—31no—
48C3×C4×SD16—31no—
49#5163—32no—
50#5027—31no—
51#5008—31no—
52#4870—32no—
53#4848—32no—
54#4848—31no—
55#4842—31no—
56#4842—32no—
57#4788—32no—
58#4760—32no—
59#4694—31no—
60#4694—31no—
61#4694—32no—
62#4694—61no—
63C4×#204—32no—
64C4×#204D311yescharacteristic, complemented
65C8×Dic6D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×#634—21no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#627—22no—
75C2×#626—22no—
76C2×#626—22no—
77C2×#624—22no—
78#3799—44no—
79C2×C32×C8C2311yescharacteristic
80C2×C32×C8C2311yescharacteristic
81C32×C42C2311yescharacteristic
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C3×(C2×D3)⋊C4—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—21no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C3×#204—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97Dic32—22no—
98#3717—24no—
99#3362—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C2×C3×SD16—31no—
103C3×C4×Q8—31no—
104C3×C4×Q8—31no—
105C3×C4×D4—31no—
106Q8×Dic3—32no—
107Q8×Dic3—61no—
108C2×#215—32no—
109#940—32no—
110#930—61no—
111C2×#204—32no—
112C2×#204C2×D311yescharacteristic
113#895—62no—
114#895—61no—
115#893—32no—
116#888—32no—
117#888—61no—
118#888—62no—
119#888—62no—
120#884—62no—
121#874—32no—
122#874—31no—
123#874—31no—
124#874—61no—
125C4×D12—32no—
126C4×D12C2×D311yescharacteristic
127#869—31no—
128#869—31no—
129#869—32no—
130#869—61no—
131#869—61no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#106—31no—
137C3×C4⋊C8—32no—
138C3×C4⋊C8—31no—
139C3×#103—31no—
140C3×#102—31no—
141C3×C4×C8—21no—
142C3×C4×C8—32no—
143C3×C4×C8C2×D311yescharacteristic
144C3×C4×C8C2×D311yescharacteristic
145#832—32no—
146#821—32no—
147#821—32no—
148#821—32no—
149#821—32no—
150#821—32no—
151#821—32no—
152#821—62no—
153#821—62no—
154#821C2×D311yescharacteristic
155#817—32no—
156#817C2×D311yescharacteristic
157#816C2×D311yescharacteristic
158Dic3⋊C8C2×D312yes—
159C8×Dic3C2×D312yes—
160#809—32no—
161#808—32no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C4⋊(C3⋊D3)—22no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—42no—
172C4⋊(C3⋊D3)—81no—
173#634—81no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—21no—
180C3×D12—21no—
181C3×C4×D3—42no—
182C3×Dic6—21no—
183C3×Dic6SD1614yescomplemented
184C3×Dic6#4112yescomplemented
185#627—82no—
186#626—44no—
187#626—82no—
188#624—44no—
189C32×C8—21no—
190C32×C8—21no—
191C3×C3⋊C8—22no—
192Q82—91no—
193#550—91no—
194#486—92no—
195#486—91no—
196#476—92no—
197#476—91no—
198#460—91no—
199#460—92no—
200C8×Q8—31no—
201C4×SD16—31no—
202C4×SD16—92no—
203C2×C3×Q8—31no—
204C2×C3×Q8—31no—
205C2×C3×D4—31no—
206C22×C3×C4—61no—
207C2×#67—62no—
208C2×#67—62no—
209#239—124no—
210#235—124no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—121no—
221C2×D12—121no—
222C2×D12C22×D311yescharacteristic
223C2×C4×D3—21no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×Dic6—62no—
227C2×Dic6—61no—
228C2×Dic6—61no—
229C2×Dic6—62no—
230C2×Dic6—121no—
231C2×Dic6D1211yescharacteristic
232C2×Dic6C22×D311yescharacteristic
233C3×SD16—62no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—32no—
237C2×C3×C8C22×D311yescharacteristic
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C22×D311yescharacteristic
241C3×C4⋊C4—32no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—61no—
246C3×C22⋊C4—61no—
247C3×C42—21no—
248C3×C42—32no—
249C3×C42—61no—
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252#215—64no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—32no—
257C4⋊Dic3—32no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3—121no—
264C4⋊Dic3D1211yescharacteristic
265C4⋊Dic3C22×D311yescharacteristic
266C4⋊Dic3C22×D311yescharacteristic
267Dic3⋊C4—21no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4D1212yes—
271C4×Dic3—21no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C4×Dic3C22×D312yes—
275C2×C3⋊C8C22×D312yes—
276#204—22no—
277#204—64no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C32×C4—21no—
286C32×C4C2×SD1612yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—42no—
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—41no—
293C3×Dic3—41no—
294C3×Dic3C2×SD1614yes—
295C2×#41—181no—
296C2×SD16—31no—
297C2×SD16—92no—
298C4⋊Q8—92no—
299C4⋊Q8—91no—
300C4⋊Q8—181no—
301C4⋊Q8—182no—
302#127—92no—
303#127—91no—
304#121—182no—
305#121—181no—
306C4×Q8—31no—
307C4×Q8—31no—
308C4×Q8—92no—
309C4×Q8—181no—
310C4×D4—31no—
311C4×D4—92no—
312#106—31no—
313#106—92no—
314C4⋊C8—32no—
315C4⋊C8—31no—
316#103—31no—
317#102—31no—
318#102—92no—
319#102—92no—
320#102—92no—
321#102—92no—
322C4×C8—32no—
323C4×C8D3211yescharacteristic
324C23×C3—61no—
325C22×D3—21no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—122no—
329C3×Q8—34no—
330C3×Q8—32no—
331C3×Q8—61no—
332C3×D4—61no—
333C3×D4—61no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—122no—
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349#67—124no—
350#67—242no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—122no—
357C2×Dic3C2×D1212yes—
358C2×Dic3C2×D1212yes—
359D12—21no—
360D12—21no—
361D12—62no—
362D12—62no—
363D12—62no—
364D12—62no—
365D12—122no—
366D12—122no—
367D12—124no—
368D12—122no—
369D12—122no—
370D12—242no—
371D12—241no—
372D12—241no—
373D12—242no—
374D12—242no—
375C4×D3—42no—
376C4×D3—124no—
377C4×D3—124no—
378Dic6—21no—
379Dic6—242no—
380Dic6—242no—
381Dic6—241no—
382Dic6—241no—
383Dic6—242no—
384Dic6#20414yescomplemented
385Dic6#23512yescomplemented
386C3×C8—21no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—41no—
391C3×C8—41no—
392C3×C8—62no—
393C3⋊C8—22no—
394C2×C32#54811yescharacteristic
395C2×C32C22×SD1611yescharacteristic
396C2×C32#57611yescharacteristic
397C3⋊D3—82no—
398C3×D3—81no—
399#41—364no—
400C2×Q8—31no—
401C2×Q8—31no—
402C2×Q8—182no—
403C2×Q8—181no—
404C2×D4—31no—
405C2×D4—92no—
406C2×D4—182no—
407C2×D4—182no—
408C2×D4—181no—
409C2×D4—181no—
410C22×C4—61no—
411C22×C4—182no—
412SD16—62no—
413SD16—184no—
414C2×C8—32no—
415C2×C8C2×D3211yescharacteristic
416C2×C8C2×D3211yescharacteristic
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—61no—
422C4⋊C4—92no—
423C4⋊C4—182no—
424C4⋊C4—182no—
425C4⋊C4—181no—
426C22⋊C4—61no—
427C22⋊C4—182no—
428C42—32no—
429C42—61no—
430C42—182no—
431C42C2×D3211yescharacteristic
432C22×C3—21no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3C22×D1211yescharacteristic
437C22×C3C2×D3×D411yescharacteristic
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—41no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—242no—
448C2×D3—242no—
449C2×D3—242no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—22no—
455C3×C4—21no—
456C3×C4—34no—
457C3×C4—62no—
458C3×C4—62no—
459C3×C4—121no—
460C3×C4—121no—
461C3×C4C2×#20412yes—
462C3×C4D3×SD1612yes—
463C3×C4C2×#23511yescharacteristic
464C3×C4#100711yescharacteristic
465C3×C4D3×#4111yescharacteristic
466C3×C4#101011yescharacteristic
467Dic3—22no—
468Dic3—22no—
469Dic3—41no—
470Dic3—41no—
471Dic3—122no—
472Dic3—122no—
473Dic3—242no—
474Dic3C2×#20414yes—
475C32#336211yescharacteristic, complemented, Sylow
476C23—61no—
477C23—182no—
478Q8—34no—
479Q8—32no—
480Q8—61no—
481Q8—721no—
482Q8—722no—
483D4—61no—
484D4—61no—
485D4—182no—
486D4—182no—
487D4—364no—
488D4—362no—
489D4—721no—
490D4—722no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—122no—
497C2×C4—182no—
498C2×C4—364no—
499C2×C4D3×D1211yescharacteristic
500C2×C4D3×D1211yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—21no—
503C8—21no—
504C8—62no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—241no—
509C2×C3#555211yescharacteristic
510C2×C3#557611yescharacteristic
511C2×C3C22×#20411yescharacteristic
512C2×C3#575211yescharacteristic
513C2×C3C2×D3×SD1611yescharacteristic
514C2×C3#576911yescharacteristic
515D3—81no—
516D3—242no—
517D3—242no—
518D3—482no—
519C22—121no—
520C22—121no—
521C22—121no—
522C22—362no—
523C22—362no—
524C22—362no—
525C22C2×D3×D1211yescharacteristic
526C4—21no—
527C4—34no—
528C4—62no—
529C4—62no—
530C4—121no—
531C4—121no—
532C4—362no—
533C4D3×#20412yes—
534C4#6429711yescharacteristic
535C4D3×#23511yescharacteristic
536C3—21no—
537C3#7962211yescharacteristic, complemented
538C3#7993211yescharacteristic, complemented
539C2—241no—
540C2—722no—
541C2#1059389911yescharacteristic
542C2C2×D3×#20411yescharacteristic
543C2#1059468011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593902C2
hypercenterC4×C8D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. Dic62C2semidirect
3. #10592393C2semidirect
4. C3×C4×#204C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590878C2semidirect
7. #10590799C2semidirect
8. #10590792C2semidirect
9. #10590759C2semidirect
10. #10590367C2semidirect
11. #10590268C2semidirect
64. C4×#204D3semidirect
65. C8×Dic6D3semidirect
183. C3×Dic6SD16semidirect
184. C3×Dic6#41semidirect
384. Dic6#204semidirect
385. Dic6#235semidirect
475. C32#3362semidirect
537. C3#79622semidirect
538. C3#79932semidirect

Maximal subgroups

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

subgroupindex
#105939022
Dic622
#105923932
C3×C4×#2042
C3×C8×Dic62
#105908782
#105907992
#105907922
#105907592
#105903672
#105902682
#799323
#796223