Finite Group Databasebeta

← #11778181

Subgroups — #11778181

Order 1152.

801 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 801 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#5494C211yesmaximal, characteristic, complemented
2#10592659C211yesmaximal, characteristic, complemented
3#10591183C211yesmaximal, characteristic, complemented
4#10591168C211yesmaximal, characteristic, complemented
5C3×#4525C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#71884—31nomaximal
9#68107—31nomaximal
10C22×#638—21no—
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3752—21no—
14C3×#953—21no—
15C3×#930C2211yescharacteristic
16C3×C4×#67—21no—
17C3×#924C2211yescharacteristic
18C3×#885—21no—
19C3×#884—21no—
20C3×#883—21no—
21C3×#879—21no—
22C2×#3717—21no—
23C2×#3714—21no—
24#63658C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63564—21no—
28#63564—21no—
29C3×#538—31no—
30#5494D311yescharacteristic, complemented
31#5046—31no—
32#5036—31no—
33#4960—31no—
34#4960—31no—
35#4960—61no—
36#4732—31no—
37#4731—31no—
38C3×#323—31no—
39#4538—31no—
40#4537—31no—
41#4525D311yescharacteristic, complemented
42#4470—31no—
43#4467—31no—
44C24×C32D411yescharacteristic
45C23×C3⋊D3—21no—
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C2×#638—42no—
49C2×#638—42no—
50C2×#638—42no—
51C22×C3⋊Dic3—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—42no—
55C2×C3×#67—21no—
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C2×C3×D12D411yescharacteristic, complemented
59C2×C3×C4×D3—21no—
60C2×C3×Dic6D411yescharacteristic, complemented
61C32×C22⋊C4—21no—
62C32×C22⋊C4—21no—
63#3752—42no—
64C3×#217—21no—
65C3×#217—21no—
66C3×#217—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×C4⋊Dic3D411yescharacteristic, complemented
70C3×C4⋊Dic3D411yescharacteristic, complemented
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#3717—42no—
77#3714—42no—
78#1600—91noSylow
79C22×#67—62no—
80C22×#67—61no—
81C22×#67—61no—
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—61no—
85C3×#126—61no—
86C3×#124—61no—
87C3×#123—61no—
88C3×C22⋊Q8—31no—
89C3×#121—31no—
90C3×#121—61no—
91C3×#120—61no—
92C3×C4×D4—61no—
93C2×C3×C22⋊C4—21no—
94C2×C3×C22⋊C4C2×D311yescharacteristic
95C2×C3×C22⋊C4C2×D311yescharacteristic
96#953—21no—
97C2×#215—61no—
98C2×#213—61no—
99#930C2×D311yescharacteristic
100C4×#67—21no—
101C2×(C2×D3)⋊C4—62no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104#924C2×D311yescharacteristic
105C2×D24—61no—
106C2×#204—61no—
107#885—21no—
108#884—21no—
109#883—21no—
110#879—21no—
111C3×C22⋊C8—31no—
112C3×C22⋊C8—31no—
113C3⋊#95—31no—
114C3⋊#95—31no—
115C3⋊#95—61no—
116#830C2×D311yescharacteristic
117#830C2×D311yescharacteristic
118#821—61no—
119#821—61no—
120#809—61no—
121#809—61no—
122C23×C32—21no—
123C23×C32—21no—
124C23×C32—21no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3—41no—
132C22×C3⋊D3—41no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3—41no—
135C22×C3×D3—21no—
136C2×C32×C4—21no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141#638—48no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—41no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—41no—
148C4⋊(C3⋊D3)—41no—
149C3×#67—41no—
150C3×#67—41no—
151C3×#67—81no—
152C3×#67—81no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—21no—
156C3×D12—41no—
157C3×C4×D3—81no—
158C3×Dic6—41no—
159C3×C3⋊C8—41no—
160C3×C3⋊C8—41no—
161#538—31no—
162#450—91no—
163#447—91no—
164#392—91no—
165#328—91no—
166#327—91no—
167#323—31no—
168C24×C3—21no—
169C24×C3D1211yescharacteristic
170C24×C3#6711yescharacteristic
171C23×D3—62no—
172C23×D3—61no—
173C23×D3—61no—
174C2×C3×Q8—31no—
175C2×C3×D4—31no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—61no—
182C22×C3×C4D1211yescharacteristic
183C22×C3×C4#6711yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C2×#67—21no—
187C2×#67—21no—
188C2×#67—21no—
189C2×#67—122no—
190C2×#67—122no—
191C2×#67—124no—
192C2×#67—122no—
193C2×#67—122no—
194C2×#67—124no—
195C2×#67—124no—
196C2×#67—122no—
197C2×#67—122no—
198C22×Dic3—62no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—121no—
206C2×D12—121no—
207C2×D12—122no—
208C2×D12—122no—
209C2×D12—124no—
210C2×D12#6711yescharacteristic, complemented
211C2×C4×D3—21no—
212C2×Dic6#6711yescharacteristic, complemented
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C3×C4⋊C4—31no—
216C3×C4⋊C4—31no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—21no—
221C3×C22⋊C4—21no—
222C3×C22⋊C4—21no—
223C3×C22⋊C4—41no—
224C3×C22⋊C4—41no—
225C3×C22⋊C4—61no—
226C3×C22⋊C4—61no—
227C3×C22⋊C4—61no—
228C3×C22⋊C4—61no—
229C3×C22⋊C4—61no—
230C3×C42—61no—
231#217—21no—
232#217—21no—
233#217—21no—
234#215—122no—
235#213—122no—
236(C2×D3)⋊C4—21no—
237(C2×D3)⋊C4—21no—
238(C2×D3)⋊C4—122no—
239(C2×D3)⋊C4—122no—
240(C2×D3)⋊C4—124no—
241C4⋊Dic3#6711yescharacteristic, complemented
242C4⋊Dic3#6711yescharacteristic, complemented
243Dic3⋊C4—21no—
244Dic3⋊C4—21no—
245C4×Dic3—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248D24—122no—
249#204—122no—
250C22×C32—21no—
251C22×C32—21no—
252C22×C32—42no—
253C22×C32—41no—
254C22×C32—41no—
255C22×C32—41no—
256C22×C32—81no—
257C22×C32#12011yescharacteristic
258C22×C32#13511yescharacteristic
259C22×C32AGL(1,ℤ/8)11yescharacteristic
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—81no—
264C2×C3⋊D3—81no—
265C2×C3⋊D3—81no—
266C2×C3⋊D3—81no—
267C2×C3×D3—41no—
268C2×C3×D3—41no—
269C2×C3×D3—41no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—41no—
273C3⋊Dic3—42no—
274C3×Dic3—41no—
275C3×Dic3—41no—
276C3×Dic3—41no—
277C22×D4—91no—
278C22×D4—181no—
279C2×SD16—181no—
280C2×D8—181no—
281#126—61no—
282#124—61no—
283#123—61no—
284C22⋊Q8—31no—
285#121—31no—
286#121—61no—
287#120—61no—
288C4×D4—61no—
289C2×C22⋊C4—181no—
290C2×C22⋊C4D3211yescharacteristic
291#102—181no—
292#102—181no—
293C22⋊C8—31no—
294C22⋊C8—31no—
295#95—91no—
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—61no—
313C23×C3C2×D1211yescharacteristic
314C23×C3C2×#6711yescharacteristic
315C22×D3—21no—
316C22×D3—64no—
317C22×D3—62no—
318C22×D3—62no—
319C22×D3—122no—
320C22×D3—121no—
321C22×D3—121no—
322C22×D3—122no—
323C22×D3—121no—
324C22×D3—121no—
325C22×D3—122no—
326C22×D3—122no—
327C22×D3—121no—
328C22×D3—121no—
329C22×D3—122no—
330C22×D3—122no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—121no—
334C22×D3—121no—
335C22×D3—121no—
336C22×D3—121no—
337C3×Q8—121no—
338C3×D4—121no—
339C3×D4—121no—
340C3×D4—121no—
341C3×D4—241no—
342C3×D4—241no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—42no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—42no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—241no—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362#67—41no—
363#67—41no—
364#67—81no—
365#67—81no—
366#67—1216no—
367#67—128no—
368#67—128no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—64no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—122no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—122no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381D12—41no—
382D12—62no—
383D12—62no—
384D12—62no—
385D12—62no—
386D12—122no—
387D12—122no—
388D12—121no—
389D12—121no—
390D12—121no—
391D12—121no—
392D12—122no—
393D12—122no—
394C4×D3—81no—
395Dic6—41no—
396C3×C8—121no—
397C3×C8—121no—
398C3⋊C8—41no—
399C3⋊C8—41no—
400C2×C32—21no—
401C2×C32—21no—
402C2×C32—81no—
403C2×C32#44911yescharacteristic
404C2×C32#45311yescharacteristic
405C2×C32B(4,𝔽2)11yescharacteristic
406C3⋊D3—82no—
407C3×D3—81no—
408C24—181no—
409C24#62611yescharacteristic
410C2×Q8—31no—
411C2×D4—31no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—61no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4—362no—
418C2×D4—362no—
419C2×D4—362no—
420C2×D4—362no—
421C22×C4—61no—
422C22×C4—181no—
423C22×C4#62611yescharacteristic
424C22×C4C2×D3211yescharacteristic
425SD16—362no—
426D8—362no—
427C2×C8—61no—
428C2×C8—61no—
429C4⋊C4—31no—
430C4⋊C4—31no—
431C4⋊C4—61no—
432C4⋊C4—61no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—61no—
436C22⋊C4—61no—
437C22⋊C4—61no—
438C22⋊C4—61no—
439C22⋊C4—61no—
440C22⋊C4—362no—
441C42—61no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—44no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—41no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3—81no—
464C22×C3—81no—
465C22×C3—82no—
466C22×C3—121no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3#88211yescharacteristic
470C22×C3#90411yescharacteristic
471C22×C3#90811yescharacteristic
472C22×C3#94911yescharacteristic
473C22×C3#95011yescharacteristic
474C22×C3#95311yescharacteristic
475C2×D3—41no—
476C2×D3—41no—
477C2×D3—41no—
478C2×D3—124no—
479C2×D3—124no—
480C2×D3—122no—
481C2×D3—122no—
482C2×D3—124no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—122no—
487C2×D3—242no—
488C2×D3—242no—
489C2×D3—241no—
490C2×D3—241no—
491C2×D3—241no—
492C2×D3—241no—
493C2×D3—242no—
494C2×D3—242no—
495C2×D3—241no—
496C2×D3—241no—
497C2×D3—241no—
498C2×D3—241no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—41no—
504C3×C4—41no—
505C3×C4—41no—
506C3×C4—41no—
507C3×C4—81no—
508C3×C4—121no—
509C3×C4—121no—
510C3×C4—121no—
511Dic3—41no—
512Dic3—41no—
513Dic3—41no—
514Dic3—124no—
515Dic3—122no—
516Dic3—122no—
517C32#160011yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—61no—
524C23—182no—
525C23—361no—
526C23—361no—
527C23—361no—
528C23—361no—
529C23—361no—
530C23—361no—
531C23C2×#62611yescharacteristic
532Q8—121no—
533D4—121no—
534D4—121no—
535D4—121no—
536D4—182no—
537D4—182no—
538D4—241no—
539D4—241no—
540D4—361no—
541D4—361no—
542D4—368no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—182no—
550C2×C4—241no—
551C2×C4—361no—
552C2×C4—361no—
553C2×C4D3×#6711yescharacteristic
554C2×C4D3×#6711yescharacteristic
555C8—121no—
556C8—121no—
557C2×C3—22no—
558C2×C3—22no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—82no—
567C2×C3—81no—
568C2×C3—81no—
569C2×C3—241no—
570C2×C3#473411yescharacteristic
571C2×C3#474111yescharacteristic
572C2×C3#474711yescharacteristic
573C2×C3#523811yescharacteristic
574C2×C3#524111yescharacteristic
575C2×C3#524411yescharacteristic
576D3—81no—
577D3—244no—
578D3—242no—
579D3—242no—
580C22—21no—
581C22—21no—
582C22—42no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—81no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22—362no—
591C22—362no—
592C22—362no—
593C22—721no—
594C22—721no—
595C22—721no—
596C22—721no—
597C22#6382511yescharacteristic
598C22#6382911yescharacteristic
599C22#6397711yescharacteristic
600C4—21no—
601C4—21no—
602C4—41no—
603C4—121no—
604C4—121no—
605C4—121no—
606C4—362no—
607C3—21no—
608C3#6810711yescharacteristic, complemented
609C3#7188411yescharacteristic, complemented
610C2—21no—
611C2—21no—
612C2—81no—
613C2—241no—
614C2—722no—
615C2#1059116311yescharacteristic
616C2#1059151011yescharacteristic
617C2#1059153111yescharacteristic
subgroupG/H
centerC22#63977
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. C3×#5494C2semidirect
2. #10592659C2semidirect
3. #10591183C2semidirect
4. #10591168C2semidirect
5. C3×#4525C2semidirect
6. #10589152C2semidirect
7. #10589150C2semidirect
30. #5494D3semidirect
41. #4525D3semidirect
58. C2×C3×D12D4semidirect
60. C2×C3×Dic6D4semidirect
69. C3×C4⋊Dic3D4semidirect
70. C3×C4⋊Dic3D4semidirect
210. C2×D12#67semidirect
212. C2×Dic6#67semidirect
241. C4⋊Dic3#67semidirect
242. C4⋊Dic3#67semidirect
517. C32#1600semidirect
608. C3#68107semidirect
609. C3#71884semidirect

Maximal subgroups

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

subgroupindex
C3×#54942
#105926592
#105911832
#105911682
C3×#45252
#105891522
#105891502
#718843
#681073