Finite Group Databasebeta

← #11786694

Subgroups — #11786694

Order 1152.

689 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5827C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic
3C3×#5232C211yesmaximal, characteristic
4#10591359C211yesmaximal, characteristic, complemented
5#10591139C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71664—31nomaximal
9#70297—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×Q8×Dic3—21no—
14C3×D4×Dic3—21no—
15C3×D4×Dic3—22no—
16C3×#926—21no—
17C3×#926C2211yescharacteristic
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×#3724—22no—
23#63664C414yescomplemented
24C3×#835—21no—
25C3×#832—21no—
26#63576—21no—
27#63574—21no—
28C3×#520—31no—
29#5827D311yescharacteristic
30C3×#417—31no—
31C2×#837—31no—
32C2×#837—31no—
33C2×#837—61no—
34#5232D311yescharacteristic
35#4995—31no—
36#4975—31no—
37#4975—31no—
38#4964—31no—
39#4555—31no—
40#4554—31no—
41#4532—31no—
42#4530—31no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41C2×C412yes—
46C32×#41Q812yes—
47C2×C32×Q8D411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3C2×C412yescomplemented
58#3748—21no—
59#3748C2×C412yescomplemented
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—22no—
62C3×#217—21no—
63C3×C4⋊Dic3—22no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×C4⋊Dic3D411yescharacteristic
70C3×C4×Dic3—22no—
71C3×C4×Dic3—21no—
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8—21no—
75#3724—44no—
76#1859—91noSylow
77C2×C3×#41—21no—
78C2×C3×#41C2×D311yescharacteristic
79C2×C3×#41C2×D311yescharacteristic
80C2×C3×M16—31no—
81C3×C4×Q8—61no—
82C3×C4×D4—62no—
83C3×C4×D4—61no—
84C3×#117—31no—
85C3×#117—61no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89Q8×Dic3—21no—
90D4×Dic3—21no—
91D4×Dic3—22no—
92#926—21no—
93#926C2×D311yescharacteristic
94C2×C4⋊Dic3—21no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×Dic3⋊C4—62no—
98C2×Dic3⋊C4—62no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—61no—
102C2×#208—31no—
103C2×#208—31no—
104C2×#208—61no—
105C2×#208C2×D311yescharacteristic
106C3×#103—61no—
107C3×#102—61no—
108#837—34no—
109#837—34no—
110#837—64no—
111#835—21no—
112#832—21no—
113#808—61no—
114#808—61no—
115#807—61no—
116#807—61no—
117C23×C32—21no—
118C23×C32C2×D411yescharacteristic
119C32×Q8—21no—
120C32×Q8C4⋊C412yescomplemented
121C32×D4—22no—
122C32×D4—22no—
123C32×D4—21no—
124C32×D4C4⋊C412yescomplemented
125C2×C32×C4—21no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×Q811yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—82no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—41no—
146#520—31no—
147#428—91no—
148C2×#104—91no—
149#417—31no—
150#384—91no—
151#343—91no—
152#339—91no—
153C3×#41—21no—
154C3×#41—21no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—22no—
158C3×#41—22no—
159C3×#41—41no—
160C3×#41—41no—
161C3×#41Dic612yes—
162C3×#41Dic612yes—
163C3×#41C4×D312yes—
164C3×#41C4×D312yes—
165C2×C3×Q8—21no—
166C2×C3×Q8#6711yescharacteristic
167C2×C3×Q8#6711yescharacteristic
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—41no—
172C2×C3×D4#6711yescharacteristic
173C2×C3×D4#6711yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—32no—
178C22×C3×C4—41no—
179C22×C3×C4—62no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—22no—
184C22×Dic3—21no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—121no—
188C22×Dic3#6712yes—
189C3×M16—61no—
190C3×M16—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—31no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—62no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C22⋊C4—62no—
200C3×C22⋊C4—61no—
201C3×C42—62no—
202C3×C42—61no—
203#217—22no—
204#217—21no—
205C4⋊Dic3—22no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C4⋊Dic3#6711yescharacteristic
211C4⋊Dic3#6711yescharacteristic
212Dic3⋊C4—124no—
213Dic3⋊C4—124no—
214C4×Dic3—22no—
215C4×Dic3—21no—
216C4×Dic3—32no—
217C4×Dic3—32no—
218C4×Dic3—62no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C4×Dic3—121no—
222#208—21no—
223#208—21no—
224#208—32no—
225#208—32no—
226#208—62no—
227#208—61no—
228#208—61no—
229#208—121no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—121no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32—22no—
237C22×C32—41no—
238C22×C32—41no—
239C22×C32C4×D411yescharacteristic
240C22×C32#12011yescharacteristic
241C22×C32C22⋊Q811yescharacteristic
242C32×C4—22no—
243C32×C4C2×C4⋊C411yescharacteristic
244C32×C4C4×D411yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C32×C4#12311yescharacteristic
247C3⋊Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—81no—
252C2×#41D3211yescharacteristic
253C2×M16—31no—
254C2×M16—91no—
255C4×Q8—61no—
256C4×D4—62no—
257C4×D4—61no—
258#117—31no—
259#117—61no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—61no—
263C2×C4⋊C4—182no—
264C2×C42—91no—
265#107—181no—
266#106—181no—
267#104—94no—
268#103—61no—
269#102—61no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—41no—
274C23×C3D3×D411yescharacteristic
275C23×C3C2×#6711yescharacteristic
276C3×Q8—21no—
277C3×Q8—21no—
278C3×Q8—22no—
279C3×Q8—41no—
280C3×Q8Dic3⋊C412yescomplemented
281C3×Q8Dic3⋊C412yescomplemented
282C3×D4—22no—
283C3×D4—22no—
284C3×D4—22no—
285C3×D4—22no—
286C3×D4—21no—
287C3×D4—21no—
288C3×D4—22no—
289C3×D4—41no—
290C3×D4—42no—
291C3×D4—42no—
292C3×D4Dic3⋊C412yescomplemented
293C3×D4Dic3⋊C412yescomplemented
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—41no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—62no—
312C2×C3×C4—122no—
313C2×C3×C4—122no—
314C2×C3×C4—121no—
315C2×C3×C4—242no—
316C2×C3×C4C2×Dic611yescharacteristic
317C2×C3×C4C2×Dic611yescharacteristic
318C2×C3×C4C2×C4×D311yescharacteristic
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4#23511yescharacteristic
321C2×C3×C4#23511yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4#23711yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328C2×Dic3—21no—
329C2×Dic3—22no—
330C2×Dic3—21no—
331C2×Dic3—42no—
332C2×Dic3—42no—
333C2×Dic3—41no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—82no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C3×C8—121no—
345C3⋊C8—41no—
346C3⋊C8—62no—
347C3⋊C8—62no—
348C3⋊C8—122no—
349C2×C32—21no—
350C2×C32—21no—
351C2×C32—42no—
352C2×C32#38511yescharacteristic
353C2×C32#45311yescharacteristic
354C2×C32#45611yescharacteristic
355#41—21no—
356#41—21no—
357#41#62412yes—
358#41#62712yes—
359C2×Q8#62511yescharacteristic
360C2×D4—21no—
361C2×D4#62511yescharacteristic
362C22×C4—21no—
363C22×C4—32no—
364C22×C4—62no—
365C22×C4—61no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368M16—61no—
369M16—61no—
370M16—92no—
371M16—181no—
372C2×C8—61no—
373C2×C8—181no—
374C4⋊C4—31no—
375C4⋊C4—31no—
376C4⋊C4—62no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4—364no—
382C22⋊C4—62no—
383C22⋊C4—61no—
384C42—62no—
385C42—61no—
386C42—92no—
387C42—181no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—42no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—81no—
405C22×C3—81no—
406C22×C3#87811yescharacteristic
407C22×C3#67⋊C411yescharacteristic
408C22×C3#92411yescharacteristic
409C22×C3C4×#6711yescharacteristic
410C22×C3#93711yescharacteristic
411C22×C3#95311yescharacteristic
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—42no—
419C3×C4—122no—
420C3×C4—121no—
421C3×C4—121no—
422C3×C4—241no—
423C3×C4#87811yescharacteristic
424C3×C4#67⋊C411yescharacteristic
425C3×C4C2×Dic3⋊C411yescharacteristic
426C3×C4C2×Dic3⋊C411yescharacteristic
427C3×C4#92411yescharacteristic
428C3×C4C4×#6711yescharacteristic
429C3×C4#92911yescharacteristic
430C3×C4#93511yescharacteristic
431Dic3—42no—
432Dic3—41no—
433Dic3—41no—
434Dic3—64no—
435Dic3—64no—
436Dic3—81no—
437Dic3—124no—
438C32#185911yescharacteristic, complemented, Sylow
439C23—21no—
440C23D3×#6711yescharacteristic
441Q8—21no—
442Q8#372412yescomplemented
443D4—22no—
444D4—22no—
445D4—21no—
446D4#372412yescomplemented
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—62no—
453C2×C4—122no—
454C2×C4—122no—
455C2×C4—121no—
456C2×C4—182no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—242no—
460C2×C4#380411yescharacteristic
461C2×C4#380411yescharacteristic
462C2×C4C2×#62411yescharacteristic
463C2×C4C2×#62511yescharacteristic
464C2×C4C2×#62711yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C8—121no—
467C8—182no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—41no—
476C2×C3—41no—
477C2×C3—42no—
478C2×C3—42no—
479C2×C3—82no—
480C2×C3#494611yescharacteristic
481C2×C3#519811yescharacteristic
482C2×C3#520511yescharacteristic
483C2×C3#521011yescharacteristic
484C2×C3#524111yescharacteristic
485C2×C3#524611yescharacteristic
486C22—21no—
487C22—21no—
488C22—22no—
489C22—41no—
490C22—41no—
491C22#6395211yescharacteristic
492C22#6396411yescharacteristic
493C22#6397611yescharacteristic
494C4—22no—
495C4—122no—
496C4—121no—
497C4—121no—
498C4—184no—
499C4—241no—
500C4#6395211yescharacteristic
501C4#6396111yescharacteristic
502C4#6396411yescharacteristic
503C4C2×#372411yescharacteristic
504C3—21no—
505C3#7029711yescharacteristic, complemented
506C3#7166411yescharacteristic, complemented
507C2—21no—
508C2—21no—
509C2—42no—
510C2#1059166511yescharacteristic
511C2#1059168711yescharacteristic
512C2#1059169311yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#120
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1859
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591359C2semidirect
5. #10591139C2semidirect
6. #10589167C2semidirect
7. #10589160C2semidirect
23. #63664C4semidirect
57. C4×C3⋊Dic3C2×C4semidirect
59. #3748C2×C4semidirect
120. C32×Q8C4⋊C4semidirect
124. C32×D4C4⋊C4semidirect
280. C3×Q8Dic3⋊C4semidirect
281. C3×Q8Dic3⋊C4semidirect
292. C3×D4Dic3⋊C4semidirect
293. C3×D4Dic3⋊C4semidirect
438. C32#1859semidirect
442. Q8#3724semidirect
446. D4#3724semidirect
505. C3#70297semidirect
506. C3#71664semidirect

Maximal subgroups

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

subgroupindex
C3×#58272
C2×#636642
C3×#52322
#105913592
#105911392
#105891672
#105891602
#716643
#702973