Finite Group Databasebeta

← #11788171

Subgroups — #11788171

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595023C211yesmaximal, characteristic
2C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×#63652C211yesmaximal, characteristic, complemented
4C3×#5126C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#69965—31nomaximal
9#68756—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C32×M16C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63977—21no—
19#63966—21no—
20C2×Dic32—21no—
21#63909C412yescomplemented
22C4×#626—22no—
23C4×D3×Dic3—22no—
24C4×D3×Dic3—22no—
25#63857C412yescomplemented
26#63652—22no—
27C3×(C2×D3)⋊C8—22no—
28#63570—22no—
29#5791—31no—
30C22×C4×Dic3—31no—
31#5524—31no—
32C2×C42×D3—31no—
33C3×#407—31no—
34C2×#825—31no—
35C2×#825—31no—
36C2×#825—31no—
37C2×#825—61no—
38#5126D311yescharacteristic, complemented
39C2×#805—31no—
40C3×#339—31no—
41#4555—31no—
42#4555D311yescharacteristic, complemented
43#4532—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
53C2×C4×C3⋊D3—21no—
54C2×#634C2×C411yescharacteristic, complemented
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3C2×C412yes—
62C2×C3×C4×D3D412yes—
63C2×#626—22no—
64C2×D3×Dic3—28no—
65C2×D3×Dic3—24no—
66C32×M16—21no—
67C32×M16—21no—
68C2×C32×C8—21no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3D412yescomplemented
71C3×#217—21no—
72C3×C4⋊Dic3C2×C412yescomplemented
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3D412yescomplemented
76C3×#208—21no—
77C3×#208—21no—
78C2×C3×C3⋊C8—21no—
79Dic3⋊Dic3—22no—
80#3722—22no—
81(C2×D3)⋊Dic3—22no—
82Dic32—24no—
83#1896—91noSylow
84C23×C3×C4—31no—
85C23×Dic3—61no—
86C2×#235—31no—
87C2×#235—31no—
88C2×#235—61no—
89C22×C4×D3—61no—
90C22×C4×D3C2×D311yescharacteristic
91C2×C3×M16—21no—
92C2×C3×M16—31no—
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×M16C2×D311yescharacteristic
95C3×#117—31no—
96C2×C3×C42—31no—
97#953—61no—
98#930—32no—
99#929—61no—
100C4×#67—62no—
101#926C2×D311yescharacteristic
102#924—32no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—31no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3—62no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—62no—
110C2×C4×Dic3C2×D311yescharacteristic
111C2×#208C2×D311yescharacteristic
112#897—32no—
113#895—32no—
114#886—61no—
115#882—61no—
116C4×D12—62no—
117C42×D3—62no—
118C42×D3—62no—
119C3×C22⋊C8—62no—
120#825—62no—
121#825—62no—
122#825—64no—
123#825—62no—
124(C2×D3)⋊C8—22no—
125#805—62no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—24no—
131C22×C3×D3C22⋊C412yes—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138#638—41no—
139#638—41no—
140C2×C3⋊Dic3—24no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—21no—
143C4⋊(C3⋊D3)—21no—
144C4⋊(C3⋊D3)—21no—
145C4×C3⋊D3—41no—
146C4×C3⋊D3—41no—
147#634—21no—
148#634—21no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3C22⋊C412yes—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159#626—44no—
160D3×Dic3—216no—
161C32×C8—41no—
162C3×C3⋊C8—41no—
163#525—91no—
164C22×C42—91no—
165C2×#104—91no—
166C2×#104—91no—
167#407—31no—
168#339—31no—
169#339—91no—
170C24×C3—31no—
171C23×D3D1211yescharacteristic
172C22×C3×C4—21no—
173C22×C3×C4—31no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—62no—
184C2×#67—61no—
185C2×#67—61no—
186C2×#67—121no—
187C22×Dic3—21no—
188C22×Dic3—64no—
189C22×Dic3—68no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3D1211yescharacteristic
194#235—62no—
195#235—62no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204#235—121no—
205#235—121no—
206C2×D12—31no—
207C2×D12—31no—
208C2×D12—61no—
209C2×D12—62no—
210C2×C4×D3—21no—
211C2×C4×D3—21no—
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C4×D3—64no—
215C2×C4×D3—68no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—121no—
219C2×C4×D3C4×D312yes—
220C2×C4×D3#6712yes—
221C2×Dic6—31no—
222C2×Dic6—31no—
223C2×Dic6—61no—
224C3×M16—22no—
225C3×M16—21no—
226C3×M16—21no—
227C3×M16—21no—
228C3×M16—21no—
229C3×M16—41no—
230C3×M16—61no—
231C3×M16—61no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—41no—
235C2×C3×C8—61no—
236C3×C4⋊C4—32no—
237C3×C22⋊C4—61no—
238C3×C42—32no—
239C3×C42—61no—
240C3×C42—61no—
241#217—21no—
242#217—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246C4⋊Dic3—62no—
247C4⋊Dic3C4×D312yescomplemented
248Dic3⋊C4—62no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—62no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—121no—
259C4×Dic3D1212yescomplemented
260#208—21no—
261#208—21no—
262C2×C3⋊C8—21no—
263C22×C32—22no—
264C22×C32C2×C22⋊C411yescharacteristic
265C22×C32#12011yescharacteristic
266C22×C32#12311yescharacteristic
267C2×C3⋊D3—41no—
268C2×C3⋊D3—42no—
269C2×C3×D3—24no—
270C2×C3×D3—24no—
271C2×C3×D3—22no—
272C2×C3×D3—22no—
273C2×C3×D3#10414yescomplemented
274C32×C4C4×D411yescharacteristic
275C32×C4C4×D411yescharacteristic
276C32×C4#12111yescharacteristic
277C32×C4#12111yescharacteristic
278C3⋊Dic3—24no—
279C3⋊Dic3—41no—
280C3×Dic3—24no—
281C3×Dic3—22no—
282C3×Dic3—42no—
283C2×#41—91no—
284C23×C4—31no—
285C23×C4—181no—
286C2×M16—31no—
287C2×M16D3211yescharacteristic
288#123—181no—
289C22⋊Q8—92no—
290#121—92no—
291#120—181no—
292C4×D4—182no—
293#117—31no—
294C2×C42—31no—
295C2×C42—91no—
296C2×C42—182no—
297C2×C42—182no—
298C2×C42—181no—
299#104—182no—
300#104—182no—
301C22⋊C8—62no—
302C23×C3—21no—
303C23×C3—32no—
304C23×C3—64no—
305C23×C3—61no—
306C23×C3—61no—
307C23×C3C2×D1211yescharacteristic
308C23×C3D3×D411yescharacteristic
309C22×D3—21no—
310C22×D3—21no—
311C22×D3—24no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—121no—
315C22×D3(C2×D3)⋊C412yes—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—32no—
323C2×C3×C4—64no—
324C2×C3×C4—61no—
325C2×C3×C4—62no—
326C2×C3×C4—61no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4C2×C4×D311yescharacteristic
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4#23511yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4#23711yescharacteristic
342C2×C3×C4#23911yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344#67—124no—
345#67—122no—
346#67—122no—
347#67—121no—
348#67—121no—
349#67—121no—
350#67—121no—
351C2×Dic3—24no—
352C2×Dic3—22no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—616no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—122no—
364C2×Dic3—121no—
365C2×Dic3—124no—
366C2×Dic3(C2×D3)⋊C412yes—
367D12—62no—
368D12—61no—
369D12—61no—
370D12—61no—
371D12—61no—
372D12—121no—
373D12—124no—
374C4×D3—22no—
375C4×D3—22no—
376C4×D3—22no—
377C4×D3—22no—
378C4×D3—616no—
379C4×D3—122no—
380C4×D3—122no—
381C4×D3—121no—
382C4×D3—121no—
383C4×D3—121no—
384C4×D3—121no—
385Dic6—62no—
386Dic6—61no—
387Dic6—61no—
388Dic6—61no—
389Dic6—61no—
390Dic6—121no—
391C3×C8—42no—
392C3×C8—41no—
393C3×C8—41no—
394C3×C8—121no—
395C3⋊C8—41no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32#38611yescharacteristic
399C2×C32C2×#10412yes—
400C3⋊D3—81no—
401C3×D3—24no—
402C24—31no—
403#41—181no—
404#41—181no—
405#41—181no—
406#41—181no—
407C2×Q8—91no—
408C2×D4—91no—
409C2×D4—182no—
410C2×D4—181no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—184no—
420C22×C4—188no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4C2×D3211yescharacteristic
424M16—21no—
425M16—21no—
426M16—61no—
427M16—61no—
428C2×C8—21no—
429C2×C8—61no—
430C4⋊C4—32no—
431C4⋊C4—182no—
432C22⋊C4—61no—
433C22⋊C4—182no—
434C22⋊C4—182no—
435C42—32no—
436C42—61no—
437C42—61no—
438C42—92no—
439C42—184no—
440C42—181no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—34no—
447C22×C3—42no—
448C22×C3—64no—
449C22×C3—64no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3D3×C22⋊C411yescharacteristic
453C22×C3#88211yescharacteristic
454C22×C3#88211yescharacteristic
455C22×C3#88611yescharacteristic
456C22×C3#89411yescharacteristic
457C22×C3C2×(C2×D3)⋊C411yescharacteristic
458C2×D3—24no—
459C2×D3—24no—
460C2×D3—22no—
461C2×D3—22no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—122no—
467C2×D3—242no—
468C2×D3#82514yescomplemented
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—64no—
474C3×C4—62no—
475C3×C4—122no—
476C3×C4C4×D1211yescharacteristic
477C3×C4#67⋊C411yescharacteristic
478C3×C4#67⋊C411yescharacteristic
479C3×C4#88411yescharacteristic
480C3×C4#89311yescharacteristic
481C3×C4#89511yescharacteristic
482C3×C4#93911yescharacteristic
483C3×C4#93911yescharacteristic
484Dic3—24no—
485Dic3—22no—
486Dic3—42no—
487Dic3—64no—
488Dic3—64no—
489Dic3—124no—
490Dic3—122no—
491Dic3—121no—
492Dic3—121no—
493C32#189611yescharacteristic, complemented, Sylow
494C23—32no—
495C23—64no—
496C23—61no—
497C23—61no—
498C23—181no—
499C23D3×D1211yescharacteristic
500Q8—181no—
501Q8—181no—
502D4—181no—
503D4—181no—
504D4—364no—
505D4—361no—
506D4—361no—
507C2×C4—32no—
508C2×C4—64no—
509C2×C4—61no—
510C2×C4—62no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—1816no—
518C2×C4—184no—
519C2×C4—182no—
520C2×C4—181no—
521C2×C4—361no—
522C2×C4—361no—
523C2×C4#379611yescharacteristic
524C2×C4C4×D3211yescharacteristic
525C2×C4D3×D1211yescharacteristic
526C2×C4#380411yescharacteristic
527C2×C4D3×#6711yescharacteristic
528C2×C4#381111yescharacteristic
529C8—41no—
530C8—121no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—41no—
538C2×C3—41no—
539C2×C3—64no—
540C2×C3#466511yescharacteristic
541C2×C3D3×#10412yes—
542C2×C3#495811yescharacteristic
543C2×C3C2×#82512yes—
544D3—24no—
545D3—242no—
546D3—241no—
547D3—241no—
548C22—22no—
549C22—34no—
550C22—64no—
551C22—64no—
552C22—62no—
553C22—62no—
554C22—362no—
555C22—361no—
556C22#6389011yescharacteristic
557C22D3×(C2×D3)⋊C411yescharacteristic
558C22#6392311yescharacteristic
559C4—64no—
560C4—62no—
561C4—122no—
562C4—184no—
563C4—361no—
564C4#6388011yescharacteristic
565C4#6388111yescharacteristic
566C4#6388611yescharacteristic
567C4#6397111yescharacteristic
568C3—21no—
569C3#6875611yescharacteristic, complemented
570C3#6996511yescharacteristic, complemented
571C2—21no—
572C2—21no—
573C2—64no—
574C2—721no—
575C2D3×#82512yes—
576C2#1059136411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595023C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×Dic3C2semidirect
3. C2×#63652C2semidirect
4. C3×#5126C2semidirect
5. C2×#63570C2semidirect
6. C3×#4555C2semidirect
7. #10589160C2semidirect
21. #63909C4semidirect
25. #63857C4semidirect
38. #5126D3semidirect
42. #4555D3semidirect
52. C2×C4⋊(C3⋊D3)C2×C4semidirect
54. C2×#634C2×C4semidirect
70. C4×C3⋊Dic3D4semidirect
72. C3×C4⋊Dic3C2×C4semidirect
75. C3×C4×Dic3D4semidirect
247. C4⋊Dic3C4×D3semidirect
259. C4×Dic3D12semidirect
273. C2×C3×D3#104semidirect
468. C2×D3#825semidirect
493. C32#1896semidirect
569. C3#68756semidirect
570. C3#69965semidirect

Maximal subgroups

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

subgroupindex
#105950232
C2×C4×D3×Dic32
C2×#636522
C3×#51262
C2×#635702
C3×#45552
#105891602
#699653
#687563