Finite Group Databasebeta

← #11788175

Subgroups — #11788175

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595034C211yesmaximal, characteristic
3C2×C3×#805C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic, complemented
5#10591074C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70382—31nomaximal
9#68756—31nomaximal
10C22×C4×C3⋊D3—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4×C3⋊Dic3—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C42×C3⋊D3—22no—
17C42×C3⋊D3—22no—
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63981—21no—
22#63962—21no—
23#63916C412yescomplemented
24C4×#626—22no—
25#63871C412yescomplemented
26C3×#805—22no—
27#63568—22no—
28#63557—22no—
29#5828—31no—
30#5524—31no—
31C2×C42×D3—31no—
32C2×C42×D3—31no—
33C2×C42×D3—61no—
34C2×C3×#104—31no—
35C2×#837—31no—
36C2×#825—31no—
37#5126—31no—
38#5126—31no—
39C2×#805D311yescharacteristic, complemented
40C3×#339—31no—
41#4555—31no—
42#4532—31no—
43#4523D311yescharacteristic, complemented
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3—28no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3—21no—
55C2×C4×C3⋊D3C2×C412yes—
56C2×C4×C3⋊D3D412yes—
57C2×C3×#67—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C2×C3×D12C2×C411yescharacteristic, complemented
63C2×C3×C4×D3—21no—
64C2×C3×Dic6C2×C411yescharacteristic, complemented
65C2×#626—22no—
66C32×C42—21no—
67C32×C42D412yescomplemented
68C4×C3⋊Dic3—24no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3D412yescomplemented
71C3×#217—21no—
72C3×C4⋊Dic3C2×C412yescomplemented
73C3×C4×Dic3—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80Dic3⋊Dic3—22no—
81#3722—22no—
82(C2×D3)⋊Dic3—22no—
83#1896—91noSylow
84C2×C3×#41—31no—
85C2×#235C2×D311yescharacteristic
86C22×C4×D3—31no—
87C22×C4×D3—31no—
88C22×C4×D3—61no—
89C22×C4×D3—61no—
90C22×C4×D3—61no—
91C22×C4×D3—62no—
92C2×C3×M16—31no—
93C2×C3×M16—31no—
94C3×#117—31no—
95C2×C3×C42—21no—
96C2×C3×C42C2×D311yescharacteristic
97C2×C3×C42C2×D311yescharacteristic
98#946—32no—
99#938—32no—
100#937—61no—
101#935—61no—
102C4×#67—62no—
103#926C2×D311yescharacteristic
104C2×C4×Dic3—31no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—62no—
110C2×#208C2×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—
119C42×D3—64no—
120C42×D3—64no—
121C42×D3—62no—
122C42×D3—62no—
123C3×#104—62no—
124#837—62no—
125#825—62no—
126(C2×D3)⋊C8—62no—
127(C2×D3)⋊C8—62no—
128#805—22no—
129C23×C32C2×D411yescharacteristic
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—24no—
133C22×C3⋊D3C22⋊C412yes—
134C22×C3×D3—21no—
135C2×C32×C4—24no—
136C2×C32×C4—22no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—24no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3C22⋊C412yes—
148C4×C3⋊D3—216no—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153C3×#67—41no—
154C3×#67—41no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—21no—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—41no—
160C3×C4×D3—41no—
161C3×Dic6—21no—
162C3×Dic6—21no—
163#626—44no—
164C3×C3⋊C8—41no—
165C3×C3⋊C8—41no—
166#525—91no—
167C22×C42—91no—
168C2×#104—31no—
169C2×#104—91no—
170#407—91no—
171#339—31no—
172#339—91no—
173C23×D3—31no—
174C23×D3—31no—
175C23×D3—61no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—31no—
181C2×C3×D4—31no—
182C2×C3×D4—61no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—21no—
191C2×#67—62no—
192C22×Dic3—31no—
193C22×Dic3—31no—
194C22×Dic3—61no—
195C22×Dic3—62no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198#235—21no—
199#235—21no—
200#235—21no—
201#235—21no—
202C2×D12—62no—
203C2×D12C4×D311yescharacteristic, complemented
204C2×C4×D3—21no—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—32no—
208C2×C4×D3—32no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—68no—
212C2×C4×D3—64no—
213C2×C4×D3—64no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—68no—
217C2×C4×D3—68no—
218C2×C4×D3—616no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×Dic6C4×D311yescharacteristic, complemented
230C3×M16—61no—
231C3×M16—61no—
232C3×M16—61no—
233C3×M16—61no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C3×C4⋊C4—32no—
237C3×C22⋊C4—61no—
238C3×C42—22no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42—22no—
242C3×C42—61no—
243C3×C42D1212yescomplemented
244C3×C42#6712yescomplemented
245#217—21no—
246#217—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3C4×D312yescomplemented
252Dic3⋊C4—62no—
253C4×Dic3—21no—
254C4×Dic3—32no—
255C4×Dic3—32no—
256C4×Dic3—62no—
257C4×Dic3—68no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—62no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263#208—21no—
264#208—21no—
265#208—21no—
266#208—21no—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
269C22×C32—22no—
270C22×C32C2×C22⋊C411yescharacteristic
271C22×C32#12011yescharacteristic
272C22×C32#12311yescharacteristic
273C2×C3⋊D3—24no—
274C2×C3⋊D3—24no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—22no—
277C2×C3⋊D3#10414yescomplemented
278C2×C3×D3—41no—
279C2×C3×D3—42no—
280C32×C4—24no—
281C32×C4C4×D411yescharacteristic
282C32×C4C4×D411yescharacteristic
283C32×C4#12111yescharacteristic
284C32×C4#12111yescharacteristic
285C3⋊Dic3—24no—
286C3⋊Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—42no—
289C2×#41—31no—
290C23×C4—91no—
291C23×C4—181no—
292C2×M16—31no—
293C2×M16—31no—
294#123—181no—
295C22⋊Q8—92no—
296#121—92no—
297#120—181no—
298C4×D4—182no—
299#117—31no—
300C2×C42—91no—
301C2×C42—182no—
302C2×C42—181no—
303C2×C42—182no—
304C2×C42D3211yescharacteristic
305#104—62no—
306#104—182no—
307C22⋊C8—182no—
308C23×C3—21no—
309C23×C3—61no—
310C23×C3D3×D411yescharacteristic
311C23×C3D3×D411yescharacteristic
312C22×D3—21no—
313C22×D3—32no—
314C22×D3—32no—
315C22×D3—62no—
316C22×D3—64no—
317C22×D3—64no—
318C22×D3—62no—
319C22×D3—68no—
320C22×D3—62no—
321C22×D3—61no—
322C22×D3—61no—
323C22×D3—61no—
324C22×D3—61no—
325C3×Q8—61no—
326C3×Q8—61no—
327C3×D4—61no—
328C3×D4—61no—
329C3×D4—121no—
330C3×D4—121no—
331C2×C3×C4—24no—
332C2×C3×C4—28no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—61no—
344C2×C3×C4—62no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C2×C4×D311yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4#23511yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4#23911yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359#67—41no—
360#67—41no—
361#67—124no—
362C2×Dic3—22no—
363C2×Dic3—21no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—62no—
367C2×Dic3—64no—
368C2×Dic3—62no—
369C2×Dic3—68no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—62no—
378C2×Dic3—61no—
379D12—21no—
380D12—21no—
381D12—124no—
382C4×D3—41no—
383C4×D3—41no—
384C4×D3—632no—
385C4×D3—616no—
386C4×D3—616no—
387C4×D3—64no—
388C4×D3—64no—
389C4×D3—64no—
390C4×D3—64no—
391C4×D3—62no—
392C4×D3—62no—
393C4×D3—62no—
394C4×D3—62no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—62no—
398C4×D3—62no—
399Dic6—21no—
400Dic6—21no—
401C3×C8—121no—
402C3×C8—121no—
403C3⋊C8—41no—
404C3⋊C8—41no—
405C2×C32—21no—
406C2×C32—21no—
407C2×C32#38611yescharacteristic
408C2×C32C2×#10412yes—
409C3⋊D3—24no—
410C3×D3—81no—
411C24—91no—
412#41—61no—
413#41—61no—
414#41—61no—
415#41—61no—
416C2×Q8—31no—
417C2×D4—31no—
418C2×D4—61no—
419C2×D4—182no—
420C22×C4—21no—
421C22×C4—61no—
422C22×C4—91no—
423C22×C4—92no—
424C22×C4—92no—
425C22×C4—184no—
426C22×C4—188no—
427C22×C4—181no—
428C22×C4—181no—
429C22×C4—181no—
430C22×C4—181no—
431C22×C4—181no—
432C22×C4C2×D3211yescharacteristic
433M16—61no—
434M16—61no—
435M16—61no—
436M16—61no—
437C2×C8—61no—
438C2×C8—61no—
439C4⋊C4—32no—
440C4⋊C4—182no—
441C22⋊C4—61no—
442C22⋊C4—182no—
443C22⋊C4—182no—
444C42—21no—
445C42—61no—
446C42—92no—
447C42—184no—
448C42—181no—
449C42#62612yescomplemented
450C22×C3—24no—
451C22×C3—22no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—121no—
457C22×C3—122no—
458C22×C3D3×C22⋊C411yescharacteristic
459C22×C3D3×C22⋊C411yescharacteristic
460C22×C3#88211yescharacteristic
461C22×C3#88311yescharacteristic
462C22×C3#89411yescharacteristic
463C22×C3#93711yescharacteristic
464C2×D3—34no—
465C2×D3—34no—
466C2×D3—41no—
467C2×D3—42no—
468C2×D3—64no—
469C2×D3—68no—
470C2×D3—64no—
471C2×D3—64no—
472C2×D3—64no—
473C2×D3—68no—
474C2×D3—64no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—62no—
480C2×D3—62no—
481C3×C4—28no—
482C3×C4—24no—
483C3×C4—24no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—121no—
489C3×C4—122no—
490C3×C4C4×D1211yescharacteristic
491C3×C4#67⋊C411yescharacteristic
492C3×C4#88411yescharacteristic
493C3×C4#88411yescharacteristic
494C3×C4#89311yescharacteristic
495C3×C4#89511yescharacteristic
496C3×C4C4×#6711yescharacteristic
497C3×C4#93811yescharacteristic
498Dic3—41no—
499Dic3—42no—
500Dic3—68no—
501Dic3—64no—
502Dic3—64no—
503Dic3—64no—
504Dic3—62no—
505Dic3—62no—
506C32#189611yescharacteristic, complemented, Sylow
507C23—61no—
508C23—92no—
509C23—184no—
510C23—181no—
511C23—181no—
512C23#381111yescharacteristic
513Q8—61no—
514Q8—61no—
515D4—61no—
516D4—61no—
517D4—121no—
518D4—121no—
519D4—364no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—92no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—1816no—
528C2×C4—184no—
529C2×C4—181no—
530C2×C4—182no—
531C2×C4—181no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—182no—
535C2×C4—182no—
536C2×C4#379611yescharacteristic
537C2×C4#379811yescharacteristic
538C2×C4C4×D3211yescharacteristic
539C2×C4#380211yescharacteristic
540C2×C4C2×#62611yescharacteristic
541C2×C4#381111yescharacteristic
542C8—121no—
543C8—121no—
544C2×C3—22no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—22no—
552C2×C3—241no—
553C2×C3#466511yescharacteristic
554C2×C3D3×#10412yes—
555C2×C3D3×#10412yes—
556C2×C3#495611yescharacteristic
557D3—68no—
558D3—64no—
559D3—64no—
560D3—81no—
561C22—22no—
562C22—94no—
563C22—121no—
564C22—122no—
565C22—184no—
566C22—184no—
567C22—182no—
568C22—182no—
569C22#6385311yescharacteristic
570C22#6392111yescharacteristic
571C22#6398111yescharacteristic
572C4—24no—
573C4—121no—
574C4—122no—
575C4—184no—
576C4—182no—
577C4#6388111yescharacteristic
578C4C4×#62611yescharacteristic
579C4#6391211yescharacteristic
580C4#6391611yescharacteristic
581C3—21no—
582C3#6875611yescharacteristic, complemented
583C3#7038211yescharacteristic, complemented
584C2—21no—
585C2—21no—
586C2—184no—
587C2—241no—
588C2#1059039312yes—
589C2#1059138711yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595034C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C42×C3⋊D3C2semidirect
3. C2×C3×#805C2semidirect
4. C2×#63568C2semidirect
5. #10591074C2semidirect
6. C3×#4523C2semidirect
7. #10589160C2semidirect
23. #63916C4semidirect
25. #63871C4semidirect
39. C2×#805D3semidirect
43. #4523D3semidirect
62. C2×C3×D12C2×C4semidirect
64. C2×C3×Dic6C2×C4semidirect
67. C32×C42D4semidirect
70. C4×C3⋊Dic3D4semidirect
72. C3×C4⋊Dic3C2×C4semidirect
203. C2×D12C4×D3semidirect
229. C2×Dic6C4×D3semidirect
243. C3×C42D12semidirect
244. C3×C42#67semidirect
251. C4⋊Dic3C4×D3semidirect
277. C2×C3⋊D3#104semidirect
449. C42#626semidirect
506. C32#1896semidirect
582. C3#68756semidirect
583. C3#70382semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
#105950342
C2×C3×#8052
C2×#635682
#105910742
C3×#45232
#105891602
#703823
#687563