Finite Group Databasebeta

← #11895867

Subgroups — #11895867

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5584C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3#10592723C211yesmaximal, characteristic, complemented
4#10590363C211yesmaximal, characteristic, complemented
5#10590358C212yesmaximal, complemented
6#10590348C212yesmaximal
7C4×#3713C211yesmaximal, characteristic
8#10590310C212yesmaximal, complemented
9#10590290C211yesmaximal, characteristic, complemented
10#10590280C212yesmaximal, complemented
11#10590269C211yesmaximal, characteristic, complemented
12#83668—31nomaximal
13#83563—31nomaximal
14C2×C3×D3×Q8—21no—
15C32×C4×Q8C2211yescharacteristic
16C3×#946—21no—
17C3×#898—22no—
18C3×#897—21no—
19C3×#897—22no—
20C3×#892—21no—
21C3×#875C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2212yes—
25C3×#869C2211yescharacteristic
26C3×#869C2211yescharacteristic
27C3×#869C2212yes—
28C3×C4×Dic6C2212yes—
29C2×#3715C2212yes—
30C2×#3713C2211yescharacteristic
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
32C4⋊(C3⋊(C3⋊C8))C2212yes—
33#63630C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35#63576C2212yes—
36#63576C2211yescharacteristic
37#63565C2212yes—
38#63565C2212yes—
39#63565C2212yes—
40#63562C2212yes—
41#63562C2211yescharacteristic
42#63562C2211yescharacteristic
43C3×#556—31no—
44C3×D4×Q8—31no—
45#5584D311yescharacteristic, complemented
46Q8×D12D311yescharacteristic, complemented
47#5093—31no—
48#5091—32no—
49#5089—32no—
50#5087—31no—
51#5083—31no—
52#5079—31no—
53#5057—32no—
54#5055—32no—
55#5026—32no—
56#5024—31no—
57#5024—31no—
58#5024—61no—
59#5021—32no—
60#5019—31no—
61#5018—32no—
62#5016—32no—
63C4×#213—31no—
64C4×#213—31no—
65#5007—31no—
66C2×C32×Q8D411yescharacteristic
67C3×D3×Q8—44no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—21no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2312yes—
76C32×C4⋊C4D411yescharacteristic
77C32×C4⋊C4D412yes—
78C32×C42C2311yescharacteristic
79C32×C42C2312yes—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—21no—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—22no—
97#3715—24no—
98#3713—22no—
99#3367—91noSylow
100C22×C3×Q8—61no—
101C2×D3×Q8—21no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×#126—62no—
106C3×#124—32no—
107C3×C22⋊Q8—61no—
108C3×C22⋊Q8—61no—
109C3×C22⋊Q8—62no—
110C3×C4×Q8—21no—
111C3×C4×Q8—32no—
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×D4—31no—
115C3×C4×D4—31no—
116C3×C4×D4—32no—
117C3×#117—61no—
118#946—21no—
119C2×#215—32no—
120C2×#214—32no—
121C2×#213—31no—
122C2×#213—31no—
123#898—22no—
124#897—21no—
125#897—22no—
126#892—21no—
127#875C2×D312yes—
128C4×D12C2×D311yescharacteristic
129C4×D12C2×D311yescharacteristic
130C4×D12C2×D312yes—
131#869C2×D311yescharacteristic
132#869C2×D311yescharacteristic
133#869C2×D312yes—
134C4×Dic6C2×D312yes—
135#835—32no—
136#835—32no—
137#835—32no—
138#832—32no—
139#832—31no—
140#832—31no—
141#810—32no—
142#810—32no—
143#810—32no—
144#809—31no—
145#809—31no—
146#809—32no—
147#807—32no—
148#807—31no—
149#807—31no—
150#807—32no—
151C4⋊(C3⋊C8)—31no—
152C4⋊(C3⋊C8)—32no—
153C4⋊(C3⋊C8)—31no—
154C4⋊(C3⋊C8)—32no—
155C4⋊(C3⋊C8)—61no—
156C4⋊(C3⋊C8)—62no—
157#803—32no—
158#803—32no—
159#803—62no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C32×Q8—22no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C3×D12—21no—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12#4112yes—
179C3×C4×D3—44no—
180C3×C4×D3—42no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—44no—
185C3×Dic6—42no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)—22no—
189#556—31no—
190D4×Q8—31no—
191#489—92no—
192#487—91no—
193#477—92no—
194#474—91no—
195#463—92no—
196#461—91no—
197#446—91no—
198#440—92no—
199C4×D8—91no—
200C2×C3×Q8—21no—
201C2×C3×Q8—32no—
202C2×C3×Q8—62no—
203C2×C3×Q8—61no—
204C2×C3×Q8—124no—
205C2×C3×Q8#6711yescharacteristic
206C2×C3×Q8#6711yescharacteristic
207C2×C3×D4—31no—
208C2×C3×D4—31no—
209C22×C3×C4—61no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212D3×Q8—44no—
213C2×D12C22×D311yescharacteristic
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—22no—
217C2×C4×D3—21no—
218C2×Dic6—22no—
219C2×Dic6—21no—
220C2×Dic6C22×D312yes—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4#6711yescharacteristic
232C3×C4⋊C4#6711yescharacteristic
233C3×C4⋊C4#6712yes—
234C3×C4⋊C4#6712yes—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—61no—
238C3×C22⋊C4—61no—
239C3×C22⋊C4—62no—
240C3×C42—21no—
241C3×C42—22no—
242C3×C42—62no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D312yes—
246C3×C42C22×D312yes—
247#215—64no—
248#214—64no—
249#213—62no—
250#213—62no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—22no—
255(C2×D3)⋊C4—22no—
256C4⋊Dic3—21no—
257C4⋊Dic3—22no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3C22×D311yescharacteristic
261C4⋊Dic3C22×D312yes—
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—22no—
264C4×Dic3—22no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—62no—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C32×C4—22no—
282C32×C4—22no—
283C32×C4—21no—
284C32×C4AGL(1,ℤ/8)12yes—
285C32×C4C2×#4111yescharacteristic
286C32×C42−1+411yescharacteristic
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3—42no—
290C3×Dic3—41no—
291C22×Q8—61no—
292C2×SD16—92no—
293C2×D8—91no—
294C4⋊Q8—31no—
295C4⋊Q8—32no—
296C4⋊Q8—31no—
297#126—62no—
298#124—32no—
299C22⋊Q8—61no—
300C22⋊Q8—61no—
301C22⋊Q8—62no—
302C4×Q8—32no—
303C4×Q8D3211yescharacteristic
304C4×D4—31no—
305C4×D4—32no—
306C4×D4—31no—
307#117—61no—
308#107—91no—
309#107—92no—
310C4⋊C8—91no—
311C4⋊C8—92no—
312#103—92no—
313#103—92no—
314#103—92no—
315#102—91no—
316#102—91no—
317#102—92no—
318#97—92no—
319C4×C8—91no—
320C23×C3—61no—
321C23×C3—61no—
322C22×D3—21no—
323C22×D3—21no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—42no—
327C3×Q8—62no—
328C3×Q8—62no—
329C3×Q8—124no—
330C3×Q8—122no—
331C3×D4—32no—
332C3×D4—61no—
333C3×D4—61no—
334C3×D4—61no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—61no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—61no—
344C2×C3×C4—124no—
345C2×C3×C4—122no—
346C2×C3×C4—122no—
347C2×C3×C4C2×#6712yes—
348C2×C3×C4C2×#6712yes—
349C2×C3×C4C2×#6712yes—
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—22no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361D12—21no—
362D12—21no—
363D12—21no—
364D12#23912yes—
365C4×D3—44no—
366C4×D3—42no—
367C4×D3—42no—
368Dic6—22no—
369Dic6—22no—
370Dic6—44no—
371Dic6—42no—
372C3⋊C8—62no—
373C3⋊C8—61no—
374C3⋊C8—62no—
375C3⋊C8—61no—
376C3⋊C8—61no—
377C3⋊C8—62no—
378C3⋊C8—61no—
379C3⋊C8—121no—
380C3⋊C8—122no—
381C2×C32#54811yescharacteristic
382C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
383C2×C32#57811yescharacteristic
384C3×D3—42no—
385C3×D3—81no—
386C2×Q8—32no—
387C2×Q8—62no—
388C2×Q8—61no—
389C2×Q8—124no—
390C2×Q8#62511yescharacteristic
391C2×D4—31no—
392C2×D4—31no—
393C22×C4—61no—
394C22×C4—62no—
395C22×C4—61no—
396SD16—184no—
397D8—182no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8—92no—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—31no—
404C4⋊C4—61no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—61no—
408C4⋊C4—61no—
409C4⋊C4#62511yescharacteristic
410C4⋊C4#62512yes—
411C22⋊C4—62no—
412C22⋊C4—62no—
413C22⋊C4—61no—
414C22⋊C4—61no—
415C22⋊C4—62no—
416C42—62no—
417C42C2×D3211yescharacteristic
418C42C2×D3212yes—
419C22×C3—21no—
420C22×C3—62no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3C22×#6711yescharacteristic
427C22×C3C22×#6711yescharacteristic
428C2×D3—22no—
429C2×D3—41no—
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—41no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—41no—
446C3×C4—121no—
447C3×C4—122no—
448C3×C4—122no—
449C3×C4—121no—
450C3×C4#93212yes—
451C3×C4#94912yes—
452C3×C4C2×#23911yescharacteristic
453C3×C4#100711yescharacteristic
454C3×C4D3×#4111yescharacteristic
455C3×C4#101011yescharacteristic
456Dic3—41no—
457Dic3—42no—
458Dic3—41no—
459Dic3—42no—
460C32#336711yescharacteristic, complemented, Sylow
461C23—61no—
462C23—61no—
463Q8—22no—
464Q8—62no—
465Q8—62no—
466Q8—124no—
467Q8—122no—
468D4—32no—
469D4—61no—
470D4—61no—
471D4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—61no—
476C2×C4—124no—
477C2×C4—122no—
478C2×C4—122no—
479C2×C4C2×#62512yes—
480C2×C4C2×#62511yescharacteristic
481C2×C4C2×#62512yes—
482C2×C4C2×#62511yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—181no—
485C8—181no—
486C8—182no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—122no—
491C2×C3—241no—
492C2×C3C2×#93211yescharacteristic
493C2×C3#581711yescharacteristic
494C2×C3C2×#94911yescharacteristic
495C2×C3#583111yescharacteristic
496C2×C3#583811yescharacteristic
497C2×C3#583811yescharacteristic
498D3—42no—
499D3—81no—
500C22—62no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22C22×#62511yescharacteristic
507C4—22no—
508C4—21no—
509C4—22no—
510C4—122no—
511C4—122no—
512C4—121no—
513C4—121no—
514C4#6382312yes—
515C4#6431511yescharacteristic
516C4D3×#23911yescharacteristic
517C3—21no—
518C3#8356311yescharacteristic, complemented
519C3#8366811yescharacteristic, complemented
520C2—122no—
521C2—241no—
522C2C2×#6382311yescharacteristic
523C2#1059540911yescharacteristic
524C2#1059544511yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4×Q8D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5584C2semidirect
2. C3×Q8×D12C2semidirect
3. #10592723C2semidirect
4. #10590363C2semidirect
5. #10590358C2semidirect
8. #10590310C2semidirect
9. #10590290C2semidirect
10. #10590280C2semidirect
11. #10590269C2semidirect
45. #5584D3semidirect
46. Q8×D12D3semidirect
460. C32#3367semidirect
518. C3#83563semidirect
519. C3#83668semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C3×Q8×D122
#105927232
#105903632
#105903582
#105903482
C4×#37132
#105903102
#105902902
#105902802
#105902692
#836683
#835633