Finite Group Databasebeta

← #11778182

Subgroups — #11778182

Order 1152.

765 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 765 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595965C211yesmaximal, characteristic, complemented
2C3×#4960C211yesmaximal, characteristic, complemented
3#10591172C211yesmaximal, characteristic, complemented
4#10591162C211yesmaximal, characteristic, complemented
5C3×#4525C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#69697—31nomaximal
9#68107—31nomaximal
10C22×C3×#67—21no—
11C22×C3×D12C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13#64162—21no—
14#64139C2211yescharacteristic
15C4×#638—21no—
16#64133C2211yescharacteristic
17#64094—21no—
18#64093—21no—
19#64092—21no—
20#64088—21no—
21C2×C3×(C2×D3)⋊C4—21no—
22C2×#3716—21no—
23C2×#3714—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63563—21no—
28#63563—21no—
29#5494—31no—
30#5494—31no—
31#5494—61no—
32C3×#392—31no—
33#5218—31no—
34#5217—31no—
35#4960D311yescharacteristic, complemented
36#4732—31no—
37#4731—31no—
38C3×#323—31no—
39#4525D311yescharacteristic, complemented
40#4470—31no—
41#4467—31no—
42#4452—31no—
43#4451—31no—
44C24×C32D411yescharacteristic
45C23×C3×D3—21no—
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C2×#638—21no—
49C2×#638—21no—
50C2×#638—21no—
51C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
52C2×C4×C3⋊D3—21no—
53C2×#634D411yescharacteristic, complemented
54C2×C3×#67—42no—
55C2×C3×#67—42no—
56C2×C3×#67—42no—
57C22×C3×Dic3—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—42no—
61C32×C22⋊C4—21no—
62C32×C22⋊C4—21no—
63#3757—21no—
64#3757—21no—
65#3757—21no—
66#3752—21no—
67#3752—21no—
68C4⋊(C3⋊Dic3)D411yescharacteristic, complemented
69C4⋊(C3⋊Dic3)D411yescharacteristic, complemented
70#3750—21no—
71#3750—21no—
72C4×C3⋊Dic3—21no—
73C3×(C2×D3)⋊C4—42no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#3716—42no—
77#3714—42no—
78#1600—91noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C22×#67—21no—
82C22×D12C2×D311yescharacteristic
83C2×C3×C22⋊C4—21no—
84C2×C3×C22⋊C4—61no—
85C2×C3×C22⋊C4C2×D311yescharacteristic
86C2×C3×C22⋊C4C2×D311yescharacteristic
87#953—62no—
88#953—61no—
89#953—61no—
90C2×#214—61no—
91C2×#213—61no—
92#930—31no—
93#930—31no—
94#930—61no—
95C4×#67—62no—
96C4×#67—61no—
97C4×#67—61no—
98C2×(C2×D3)⋊C4—21no—
99#924—31no—
100#924—31no—
101#924—61no—
102C2×D24—61no—
103C2×#204—61no—
104#885—61no—
105#885—61no—
106#885—62no—
107#884—61no—
108#884—61no—
109#884—62no—
110#883—61no—
111#883—61no—
112#883—62no—
113#879—61no—
114#879—61no—
115#879—62no—
116C3×C22⋊C8—31no—
117C3×C22⋊C8—31no—
118C3×#95—31no—
119#832—61no—
120#832—61no—
121C3⋊#95C2×D311yescharacteristic
122#830C2×D311yescharacteristic
123#830C2×D311yescharacteristic
124#821—61no—
125#821—61no—
126C23×C32—21no—
127C23×C32—21no—
128C23×C32—21no—
129C23×C32—41no—
130C23×C32—41no—
131C23×C32C2×D411yescharacteristic
132C22×C3⋊D3—21no—
133C22×C3×D3—22no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C22×C3×D3—41no—
139C22×C3×D3—41no—
140C2×C32×C4—21no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145#638—41no—
146#638—41no—
147#638—81no—
148#638—81no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C4⋊(C3⋊D3)—41no—
153C4×C3⋊D3—81no—
154#634—41no—
155C3×#67—48no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—41no—
162C3×D12—41no—
163C3×C3⋊C8—41no—
164C3×C3⋊C8—41no—
165#538—91no—
166#450—91no—
167#447—91no—
168#392—31no—
169#328—91no—
170#327—91no—
171#323—31no—
172C24×C3—21no—
173C24×C3—61no—
174C24×C3D1211yescharacteristic
175C24×C3#6711yescharacteristic
176C23×D3—21no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—122no—
180C2×C3×D4—122no—
181C2×C3×D4—122no—
182C2×C3×D4—122no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—61no—
186C22×C3×C4D1211yescharacteristic
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—42no—
191C2×#67—42no—
192C2×#67—42no—
193C2×#67—62no—
194C2×#67—61no—
195C2×#67—61no—
196C2×#67—62no—
197C2×#67—61no—
198C2×#67—61no—
199C2×#67—62no—
200C2×#67—61no—
201C2×#67—61no—
202C22×Dic3—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—42no—
208C2×D12—61no—
209C2×C4×D3—62no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×Dic6—31no—
213C2×Dic6—31no—
214C2×Dic6—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C22⋊C4—22no—
218C3×C22⋊C4—22no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—21no—
221C3×C22⋊C4—21no—
222C3×C22⋊C4—21no—
223C3×C22⋊C4—122no—
224#217—62no—
225#217—61no—
226#217—61no—
227#217—62no—
228#217—61no—
229#217—61no—
230#217—62no—
231#217—61no—
232#217—61no—
233#214—122no—
234#213—122no—
235(C2×D3)⋊C4—42no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—61no—
239(C2×D3)⋊C4—61no—
240(C2×D3)⋊C4—61no—
241(C2×D3)⋊C4—61no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248Dic3⋊C4—62no—
249Dic3⋊C4—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—62no—
252Dic3⋊C4—61no—
253Dic3⋊C4—61no—
254C4×Dic3—62no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259D24—122no—
260#204—122no—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32—41no—
264C22×C32—41no—
265C22×C32—41no—
266C22×C32—42no—
267C22×C32—81no—
268C22×C32#12011yescharacteristic
269C22×C32#13511yescharacteristic
270C22×C32AGL(1,ℤ/8)11yescharacteristic
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C2×C3⋊D3—41no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C2×C3×D3—81no—
278C2×C3×D3—81no—
279C2×C3×D3—81no—
280C2×C3×D3—81no—
281C32×C4—21no—
282C32×C4—21no—
283C32×C4—41no—
284C3⋊Dic3—41no—
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C3×Dic3—42no—
288C22×D4—31no—
289C22×D4—61no—
290C2×SD16—181no—
291C2×D8—181no—
292#126—181no—
293#124—181no—
294#123—181no—
295C22⋊Q8—91no—
296#121—91no—
297#121—181no—
298#120—181no—
299C4×D4—181no—
300C2×C22⋊C4—61no—
301C2×C22⋊C4D3211yescharacteristic
302#102—181no—
303#102—181no—
304C22⋊C8—31no—
305C22⋊C8—31no—
306#95—31no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—62no—
322C23×C3—81no—
323C23×C3—81no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3—121no—
327C23×C3—121no—
328C23×C3—121no—
329C23×C3—121no—
330C23×C3C2×D1211yescharacteristic
331C23×C3C2×#6711yescharacteristic
332C22×D3—22no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—41no—
337C22×D3—41no—
338C22×D3—41no—
339C22×D3—62no—
340C22×D3—61no—
341C22×D3—61no—
342C3×D4—62no—
343C3×D4—62no—
344C3×D4—121no—
345C3×D4—121no—
346C3×D4—128no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—62no—
357C2×C3×C4—81no—
358C2×C3×C4—81no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365#67—48no—
366#67—122no—
367#67—122no—
368#67—121no—
369#67—121no—
370#67—121no—
371#67—121no—
372#67—242no—
373#67—242no—
374#67—241no—
375#67—241no—
376#67—241no—
377#67—241no—
378C2×Dic3—22no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390D12—22no—
391D12—22no—
392D12—41no—
393D12—41no—
394D12—121no—
395D12—121no—
396D12—241no—
397C4×D3—242no—
398C4×D3—241no—
399C4×D3—241no—
400Dic6—121no—
401Dic6—121no—
402Dic6—241no—
403C3×C8—121no—
404C3×C8—121no—
405C3⋊C8—41no—
406C3⋊C8—41no—
407C2×C32—21no—
408C2×C32—21no—
409C2×C32—81no—
410C2×C32#44911yescharacteristic
411C2×C32#45311yescharacteristic
412C2×C32B(4,𝔽2)11yescharacteristic
413C3⋊D3—81no—
414C3×D3—82no—
415C24—61no—
416C24#62611yescharacteristic
417C2×Q8—91no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—91no—
421C2×D4—122no—
422C2×D4—122no—
423C2×D4—122no—
424C2×D4—122no—
425C2×D4—181no—
426C2×D4—181no—
427C2×D4—181no—
428C22×C4—61no—
429C22×C4—181no—
430C22×C4#62611yescharacteristic
431C22×C4C2×D3211yescharacteristic
432SD16—362no—
433D8—362no—
434C2×C8—61no—
435C2×C8—61no—
436C4⋊C4—91no—
437C4⋊C4—91no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—122no—
443C22⋊C4—181no—
444C22⋊C4—181no—
445C22⋊C4—181no—
446C22⋊C4—181no—
447C22⋊C4—181no—
448C42—181no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—82no—
470C22×C3—81no—
471C22×C3—81no—
472C22×C3—82no—
473C22×C3—122no—
474C22×C3—122no—
475C22×C3—122no—
476C22×C3—241no—
477C22×C3—241no—
478C22×C3—241no—
479C22×C3—241no—
480C22×C3#88211yescharacteristic
481C22×C3#90411yescharacteristic
482C22×C3#90811yescharacteristic
483C22×C3#93211yescharacteristic
484C22×C3#93711yescharacteristic
485C22×C3#95011yescharacteristic
486C2×D3—42no—
487C2×D3—42no—
488C2×D3—42no—
489C2×D3—81no—
490C2×D3—81no—
491C2×D3—81no—
492C2×D3—81no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—121no—
497C2×D3—121no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—41no—
507C3×C4—41no—
508C3×C4—42no—
509C3×C4—41no—
510C3×C4—41no—
511C3×C4—122no—
512Dic3—42no—
513Dic3—122no—
514Dic3—122no—
515Dic3—122no—
516Dic3—121no—
517Dic3—121no—
518Dic3—121no—
519Dic3—121no—
520Dic3—121no—
521Dic3—121no—
522C32#160011yescharacteristic, complemented, Sylow
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528C23—62no—
529C23—121no—
530C23—121no—
531C23—121no—
532C23—121no—
533C23—121no—
534C23—121no—
535C23—181no—
536C23C2×#62611yescharacteristic
537Q8—361no—
538D4—62no—
539D4—62no—
540D4—121no—
541D4—121no—
542D4—128no—
543D4—361no—
544D4—361no—
545D4—361no—
546D4—721no—
547D4—721no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—62no—
552C2×C4—121no—
553C2×C4—121no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—721no—
558C2×C4#381111yescharacteristic
559C2×C4#381111yescharacteristic
560C8—121no—
561C8—121no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—41no—
570C2×C3—41no—
571C2×C3—82no—
572C2×C3—81no—
573C2×C3—81no—
574C2×C3—242no—
575C2×C3#473411yescharacteristic
576C2×C3#474111yescharacteristic
577C2×C3#474711yescharacteristic
578C2×C3#503211yescharacteristic
579C2×C3#503711yescharacteristic
580C2×C3#507711yescharacteristic
581D3—82no—
582D3—242no—
583D3—241no—
584D3—241no—
585C22—21no—
586C22—21no—
587C22—42no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—122no—
593C22—122no—
594C22—122no—
595C22—241no—
596C22—241no—
597C22—241no—
598C22—241no—
599C22—361no—
600C22—361no—
601C22—361no—
602C22#6382911yescharacteristic
603C22#6383011yescharacteristic
604C22#6398111yescharacteristic
605C4—21no—
606C4—21no—
607C4—41no—
608C4—122no—
609C4—361no—
610C4—361no—
611C4—361no—
612C3—21no—
613C3#6810711yescharacteristic, complemented
614C3#6969711yescharacteristic, complemented
615C2—21no—
616C2—21no—
617C2—81no—
618C2—242no—
619C2—721no—
620C2#1059118211yescharacteristic
621C2#1059151111yescharacteristic
622C2#1059153211yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
hypercenterC2×C22⋊C4D32
hypocenterC32#1600
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595965C2semidirect
2. C3×#4960C2semidirect
3. #10591172C2semidirect
4. #10591162C2semidirect
5. C3×#4525C2semidirect
6. #10589154C2semidirect
7. #10589151C2semidirect
35. #4960D3semidirect
39. #4525D3semidirect
51. C2×C4⋊(C3⋊D3)D4semidirect
53. C2×#634D4semidirect
68. C4⋊(C3⋊Dic3)D4semidirect
69. C4⋊(C3⋊Dic3)D4semidirect
522. C32#1600semidirect
613. C3#68107semidirect
614. C3#69697semidirect

Maximal subgroups

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

subgroupindex
#105959652
C3×#49602
#105911722
#105911622
C3×#45252
#105891542
#105891512
#696973
#681073