Finite Group Databasebeta

← #11897565

Subgroups — #11897565

Order 1152.

802 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×#5543C211yesmaximal, characteristic, complemented
2Dic6×D12C211yesmaximal, characteristic, complemented
3#10592706C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic
5#10591430C212yesmaximal
6#10591408C212yesmaximal, complemented
7#10590467C212yesmaximal, complemented
8#10590418C212yesmaximal, complemented
9#10590303C211yesmaximal, characteristic, complemented
10#10590266C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83630—31nomaximal
13#79576—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4×D4C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×D4×Dic3C2212yes—
18C2×C3×#213C2211yescharacteristic
19C2×C3×C4⋊Dic3—21no—
20C3×#924—21no—
21C3×#890C2212yes—
22C3×#878—22no—
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63918C2212yes—
27#63893—22no—
28Dic3×D12C2212yes—
29#63857—21no—
30#63659C2212yes—
31#63634C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#807C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63574C2212yes—
38#63573C2212yes—
39#63573C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×#554—31no—
44Q8×D12—31no—
45#5543D311yescharacteristic, complemented
46D4×Dic6—31no—
47C3×C4×D8—31no—
48#5152—32no—
49#5084—31no—
50#5080—31no—
51#5066—32no—
52#5064—32no—
53#5024—31no—
54#5014—32no—
55C4×#213D311yescharacteristic
56#5008—31no—
57#5008—32no—
58#5007—31no—
59#5007—31no—
60#5007—61no—
61#4876—32no—
62#4763—32no—
63#4761—32no—
64#4680—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634—21no—
69C22×C3×Dic3—22no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×#627—22no—
75C2×D3×Dic3—22no—
76D3×Dic6—44no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×#217—22no—
84C3×#213Q814yescomplemented
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3384—91noSylow
99C2×D3×Q8—61no—
100C22×Dic6—61no—
101C2×C3×D8—31no—
102C3×C4⋊Q8—31no—
103C3×#125—32no—
104C3×C22⋊Q8—62no—
105C3×C22⋊Q8—61no—
106C3×C4×Q8—31no—
107C3×C4×D4—21no—
108C3×C4×D4—32no—
109C3×C4×D4—31no—
110C3×C4×D4C2×D311yescharacteristic
111C3×C4×D4C2×D311yescharacteristic
112C2×C3×C4⋊C4—61no—
113D4×Dic3—32no—
114D4×Dic3C2×D312yes—
115C2×#213C2×D311yescharacteristic
116C2×C4⋊Dic3—21no—
117#924—21no—
118#924—61no—
119#897—62no—
120#897—61no—
121#890C2×D312yes—
122#888—32no—
123#878—22no—
124#878—62no—
125C4×D12—32no—
126C4×D12C2×D311yescharacteristic
127#869—31no—
128#869—31no—
129#869—32no—
130#869—61no—
131#869C2×D311yescharacteristic
132C4×Dic6C2×D311yescharacteristic
133C3×#107—31no—
134C3×#102—31no—
135C3×#102—31no—
136C3×C4×C8—31no—
137#832—32no—
138#832—32no—
139#832—32no—
140#832—62no—
141#832C2×D311yescharacteristic
142#817—32no—
143#817—32no—
144#815—32no—
145Dic3⋊C8—32no—
146#809—32no—
147#809C2×D311yescharacteristic
148#808—32no—
149#808—32no—
150#808—32no—
151#808—32no—
152#807—32no—
153#807—32no—
154#807—62no—
155#807C2×D311yescharacteristic
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160#803—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C23×C32—21no—
163C22×C3×D3—21no—
164C32×D4—21no—
165C32×D4C2×Q812yescomplemented
166C2×C32×C4—21no—
167C2×C32×C4—42no—
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×Dic3—82no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—21no—
179C3×D12C2×Q812yes—
180C3×C4×D3—42no—
181C3×Dic6—22no—
182C3×Dic6—81no—
183#627—44no—
184D3×Dic3—44no—
185C3⋊(C3⋊C8)—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8C2×Q812yescomplemented
188#554—31no—
189D4×Q8—91no—
190#501—92no—
191#498—91no—
192#478—92no—
193#476—92no—
194#476—91no—
195#474—91no—
196#446—91no—
197#442—92no—
198C4×D8—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8—61no—
201C2×C3×D4—21no—
202C2×C3×D4—31no—
203C2×C3×D4C22×D311yescharacteristic
204C2×C3×D4C22×D311yescharacteristic
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—41no—
208C22×C3×C4—62no—
209C22×C3×C4—61no—
210C22×Dic3—22no—
211C22×Dic3—62no—
212D3×Q8—124no—
213C2×D12C22×D311yescharacteristic
214C2×C4×D3—21no—
215C2×C4×D3—62no—
216C2×Dic6—21no—
217C2×Dic6—62no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—62no—
221C2×Dic6—121no—
222C2×Dic6—124no—
223C2×Dic6#6711yescharacteristic
224C3×D8—34no—
225C2×C3×C8—31no—
226C2×C3×C8—31no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—41no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—61no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—22no—
247#217—62no—
248#213Dic614yescomplemented
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—62no—
251C4⋊Dic3—21no—
252C4⋊Dic3—22no—
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
262C4⋊Dic3C22×D312yes—
263Dic3⋊C4—22no—
264Dic3⋊C4—62no—
265Dic3⋊C4#6712yes—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8C22×D311yescharacteristic
271C2×C3⋊C8C22×D311yescharacteristic
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4—41no—
281C32×C4AGL(1,ℤ/8)12yes—
282C32×C4C22×Q811yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—42no—
289C22×Q8—181no—
290C2×D8—31no—
291C4⋊Q8—31no—
292C4⋊Q8—92no—
293C4⋊Q8—91no—
294#125—32no—
295C22⋊Q8—62no—
296C22⋊Q8—61no—
297C22⋊Q8—182no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×D4—32no—
301C4×D4—31no—
302C4×D4—92no—
303C4×D4D3211yescharacteristic
304C2×C4⋊C4—61no—
305#107—31no—
306#107—92no—
307#106—92no—
308#106—92no—
309#106—92no—
310C4⋊C8—92no—
311C4⋊C8—91no—
312#102—31no—
313#102—31no—
314#102—92no—
315#102—92no—
316#97—92no—
317C4×C8—31no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—41no—
321C23×C3—61no—
322C22×D3—21no—
323C3×Q8—62no—
324C3×Q8—241no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—22no—
328C3×D4—32no—
329C3×D4—41no—
330C3×D4—61no—
331C3×D4C2×Dic612yescomplemented
332C3×D4D3×Q812yescomplemented
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—42no—
342C2×C3×C4—42no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4—82no—
346C2×C3×C4—122no—
347C2×C3×C4—242no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—82no—
359C2×Dic3—122no—
360C2×Dic3—124no—
361C2×Dic3C2×#6712yes—
362C2×Dic3C2×#6712yes—
363D12—21no—
364D12C2×Dic612yes—
365C4×D3—42no—
366C4×D3—124no—
367Dic6—22no—
368Dic6—81no—
369Dic6—124no—
370Dic6—124no—
371Dic6—122no—
372Dic6—122no—
373Dic6—242no—
374C3×C8—32no—
375C3×C8—61no—
376C3⋊C8—21no—
377C3⋊C8—62no—
378C3⋊C8—62no—
379C3⋊C8—122no—
380C3⋊C8C2×Dic612yescomplemented
381C2×C32—42no—
382C2×C32D4×Q811yescharacteristic
383C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
384C2×C32#57711yescharacteristic
385C3×D3—42no—
386C2×Q8—31no—
387C2×Q8—61no—
388C2×Q8—182no—
389C2×Q8—181no—
390C2×Q8—364no—
391C2×D4—31no—
392C2×D4C2×D3211yescharacteristic
393C22×C4—21no—
394C22×C4—62no—
395C22×C4—61no—
396C22×C4—182no—
397D8—34no—
398C2×C8—31no—
399C2×C8—31no—
400C2×C8—92no—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—31no—
404C4⋊C4—32no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—61no—
408C4⋊C4—92no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C4⋊C4C2×D3211yescharacteristic
412C22⋊C4—21no—
413C22⋊C4—62no—
414C22⋊C4—61no—
415C22⋊C4—182no—
416C42—32no—
417C42C2×D3211yescharacteristic
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—42no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—62no—
427C22×C3—81no—
428C22×C3—81no—
429C22×C3—121no—
430C22×C3—121no—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C22×#6711yescharacteristic
433C2×D3—22no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—62no—
445C3×C4—62no—
446C3×C4—81no—
447C3×C4—122no—
448C3×C4—121no—
449C3×C4#91112yes—
450C3×C4#94912yes—
451C3×C4C22×Dic611yescharacteristic
452C3×C4C2×D3×Q811yescharacteristic
453C3×C4#100711yescharacteristic
454C3×C4#101011yescharacteristic
455Dic3—22no—
456Dic3—22no—
457Dic3—41no—
458Dic3—42no—
459Dic3—122no—
460Dic3—122no—
461Dic3—242no—
462C32#338411yescharacteristic, complemented, Sylow
463C23—21no—
464C23—61no—
465Q8—62no—
466Q8—241no—
467Q8—364no—
468Q8—362no—
469D4—21no—
470D4—32no—
471D4—61no—
472D4D3×Dic612yescomplemented
473C2×C4—21no—
474C2×C4—32no—
475C2×C4—32no—
476C2×C4—42no—
477C2×C4—62no—
478C2×C4—61no—
479C2×C4—122no—
480C2×C4—182no—
481C2×C4—242no—
482C2×C4—364no—
483C2×C4D3×#6711yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—32no—
487C8—61no—
488C8—182no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—42no—
493C2×C3—42no—
494C2×C3—82no—
495C2×C3—122no—
496C2×C3D4×Dic611yescharacteristic
497C2×C3C2×#91111yescharacteristic
498C2×C3#577011yescharacteristic
499C2×C3Q8×#6711yescharacteristic
500C2×C3C2×#94911yescharacteristic
501C2×C3#583611yescharacteristic
502D3—42no—
503C22—22no—
504C22—41no—
505C22—41no—
506C22—62no—
507C22—121no—
508C22—121no—
509C22C2×D3×#6711yescharacteristic
510C4—21no—
511C4—41no—
512C4—62no—
513C4—62no—
514C4—121no—
515C4—122no—
516C4—362no—
517C4#6392512yes—
518C4C2×D3×Dic611yescharacteristic
519C4#6429711yescharacteristic
520C3—21no—
521C3#7957611yescharacteristic, complemented
522C3#8363011yescharacteristic, complemented
523C2—42no—
524C2—122no—
525C2Dic6×#6711yescharacteristic
526C2C2×#6392511yescharacteristic
527C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5543C2semidirect
2. Dic6×D12C2semidirect
3. #10592706C2semidirect
6. #10591408C2semidirect
7. #10590467C2semidirect
8. #10590418C2semidirect
9. #10590303C2semidirect
10. #10590266C2semidirect
11. #10590258C2semidirect
45. #5543D3semidirect
84. C3×#213Q8semidirect
165. C32×D4C2×Q8semidirect
187. C3×C3⋊C8C2×Q8semidirect
248. #213Dic6semidirect
331. C3×D4C2×Dic6semidirect
332. C3×D4D3×Q8semidirect
380. C3⋊C8C2×Dic6semidirect
462. C32#3384semidirect
472. D4D3×Dic6semidirect
521. C3#79576semidirect
522. C3#83630semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
Dic6×D122
#105927062
C3×C4×#2132
#105914302
#105914082
#105904672
#105904182
#105903032
#105902662
#105902582
#836303
#795763