Finite Group Databasebeta

← #11778183

Subgroups — #11778183

Order 1152.

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

normal subgroups only

This group has 689 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
2C3×#4960C211yesmaximal, characteristic, complemented
3#10591169C211yesmaximal, characteristic, complemented
4#10591160C211yesmaximal, characteristic, complemented
5#10589391C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#71884—31nomaximal
9#69697—31nomaximal
10C22×C3×#67—21no—
11C22×C3×D12C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C3×#953—21no—
14C3×#930C2211yescharacteristic
15C3×C4×#67—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C3×#924C2211yescharacteristic
18C3×#885—21no—
19C3×#884—21no—
20C3×#883—21no—
21C3×#879—21no—
22C2×#3715—21no—
23C2×#3713—21no—
24#63657C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27#63562—21no—
28#63562—21no—
29C3×#538—31no—
30#5494D311yescharacteristic, complemented
31C3×#392—31no—
32#5218—31no—
33#5217—31no—
34#5046—31no—
35#5036—31no—
36#4960D311yescharacteristic, complemented
37#4538—31no—
38#4537—31no—
39#4525—31no—
40#4525—31no—
41#4525—61no—
42#4452—31no—
43#4451—31no—
44C24×C32D411yescharacteristic
45C23×C3×D3—21no—
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C2×C3×#67—42no—
52C2×C3×#67—42no—
53C2×C3×#67—42no—
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—42no—
58C2×C3×D12D411yescharacteristic, complemented
59C2×C3×C4×D3—21no—
60C2×C3×Dic6D411yescharacteristic, complemented
61C32×C22⋊C4—21no—
62C32×C22⋊C4—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×#217—21no—
66C3×#217—21no—
67C3×#217—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—42no—
71C3×C4⋊Dic3D411yescharacteristic, complemented
72C3×C4⋊Dic3D411yescharacteristic, complemented
73C3×Dic3⋊C4—21no—
74C3×Dic3⋊C4—21no—
75C3×C4×Dic3—21no—
76#3715—42no—
77#3713—42no—
78#1600—91noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C22×#67—21no—
82C22×D12C2×D311yescharacteristic
83C3×#126—61no—
84C3×#124—61no—
85C3×#123—61no—
86C3×C22⋊Q8—31no—
87C3×#121—31no—
88C3×#121—61no—
89C3×#120—61no—
90C3×C4×D4—61no—
91C2×C3×C22⋊C4—21no—
92C2×C3×C22⋊C4—61no—
93C2×C3×C22⋊C4C2×D311yescharacteristic
94C2×C3×C22⋊C4C2×D311yescharacteristic
95#953—21no—
96C2×#215—61no—
97C2×#214—61no—
98C2×#213—61no—
99C2×#213—61no—
100#930C2×D311yescharacteristic
101C4×#67—21no—
102C2×(C2×D3)⋊C4—21no—
103#924C2×D311yescharacteristic
104#885—21no—
105#884—21no—
106#883—21no—
107#879—21no—
108C3×#95—31no—
109#832—61no—
110#832—61no—
111C3⋊#95C2×D311yescharacteristic
112#830—31no—
113#830—31no—
114#830—31no—
115#830—31no—
116#830—61no—
117#830—61no—
118#809—61no—
119#809—61no—
120C23×C32—21no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—21no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C2×C32×C4—21no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C3×#67—48no—
140C3×#67—41no—
141C3×#67—41no—
142C3×#67—81no—
143C3×#67—81no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×D12—22no—
151C3×D12—22no—
152C3×D12—41no—
153C3×D12—41no—
154C3×D12—41no—
155C3×C4×D3—81no—
156C3×Dic6—41no—
157C3⋊(C3⋊C8)—41no—
158C3⋊(C3⋊C8)—41no—
159#538—31no—
160#450—91no—
161#447—91no—
162#392—31no—
163#328—91no—
164#327—91no—
165#323—91no—
166C24×C3—21no—
167C24×C3—61no—
168C24×C3#6711yescharacteristic
169C24×C3#6711yescharacteristic
170C23×D3—21no—
171C2×C3×Q8—31no—
172C2×C3×D4—31no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—122no—
179C2×C3×D4—122no—
180C2×C3×D4—122no—
181C2×C3×D4—122no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4#6711yescharacteristic
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—21no—
191C2×#67—21no—
192C2×#67—21no—
193C2×#67—42no—
194C2×#67—42no—
195C2×#67—42no—
196C22×Dic3—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—42no—
200C2×D12#6711yescharacteristic, complemented
201C2×C4×D3—21no—
202C2×Dic6#6711yescharacteristic, complemented
203C3×C4⋊C4—31no—
204C3×C4⋊C4—31no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—21no—
211C3×C22⋊C4—41no—
212C3×C22⋊C4—41no—
213C3×C22⋊C4—61no—
214C3×C22⋊C4—61no—
215C3×C22⋊C4—61no—
216C3×C22⋊C4—61no—
217C3×C22⋊C4—61no—
218C3×C22⋊C4—122no—
219C3×C42—61no—
220#217—21no—
221#217—21no—
222#217—21no—
223#215—122no—
224#214—122no—
225#213—122no—
226#213—122no—
227(C2×D3)⋊C4—21no—
228(C2×D3)⋊C4—21no—
229(C2×D3)⋊C4—42no—
230C4⋊Dic3#6711yescharacteristic, complemented
231C4⋊Dic3#6711yescharacteristic, complemented
232Dic3⋊C4—21no—
233Dic3⋊C4—21no—
234C4×Dic3—21no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—121no—
240C2×C3⋊C8—121no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—41no—
244C22×C32—42no—
245C22×C32—41no—
246C22×C32—41no—
247C22×C32—81no—
248C22×C32#12011yescharacteristic
249C22×C32#13511yescharacteristic
250C22×C32AGL(1,ℤ/8)11yescharacteristic
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—41no—
254C2×C3×D3—41no—
255C2×C3×D3—42no—
256C2×C3×D3—41no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C2×C3×D3—81no—
260C2×C3×D3—81no—
261C32×C4—21no—
262C32×C4—21no—
263C32×C4—41no—
264C3×Dic3—42no—
265C3×Dic3—41no—
266C3×Dic3—41no—
267C3×Dic3—41no—
268C22×D4—31no—
269C22×D4—61no—
270C2×SD16—181no—
271C2×D8—181no—
272#126—61no—
273#124—61no—
274#123—61no—
275C22⋊Q8—31no—
276#121—31no—
277#121—61no—
278#120—61no—
279C4×D4—61no—
280C2×C22⋊C4—61no—
281C2×C22⋊C4D3211yescharacteristic
282#102—181no—
283#102—181no—
284C22⋊C8—91no—
285C22⋊C8—91no—
286#95—31no—
287C23×C3—22no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—41no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—62no—
302C23×C3—61no—
303C23×C3—81no—
304C23×C3—81no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3—121no—
308C23×C3—121no—
309C23×C3—121no—
310C23×C3—121no—
311C23×C3C2×#6711yescharacteristic
312C23×C3C2×#6711yescharacteristic
313C22×D3—22no—
314C22×D3—21no—
315C22×D3—41no—
316C22×D3—41no—
317C22×D3—41no—
318C22×D3—41no—
319C22×D3—41no—
320C22×D3—41no—
321C3×Q8—121no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—121no—
325C3×D4—121no—
326C3×D4—121no—
327C3×D4—128no—
328C3×D4—121no—
329C3×D4—121no—
330C3×D4—241no—
331C3×D4—241no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—81no—
346C2×C3×C4—81no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4—241no—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354#67—48no—
355#67—41no—
356#67—41no—
357#67—81no—
358#67—81no—
359C2×Dic3—22no—
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365D12—22no—
366D12—22no—
367D12—41no—
368D12—41no—
369D12—41no—
370C4×D3—81no—
371Dic6—41no—
372C3⋊C8—121no—
373C3⋊C8—121no—
374C3⋊C8—121no—
375C3⋊C8—121no—
376C3⋊C8—241no—
377C3⋊C8—241no—
378C2×C32—21no—
379C2×C32—21no—
380C2×C32—81no—
381C2×C32#44911yescharacteristic
382C2×C32#45311yescharacteristic
383C2×C32B(4,𝔽2)11yescharacteristic
384C3×D3—81no—
385C3×D3—82no—
386C24—61no—
387C24#62511yescharacteristic
388C2×Q8—31no—
389C2×D4—31no—
390C2×D4—61no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—122no—
396C2×D4—122no—
397C2×D4—122no—
398C2×D4—122no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4#62511yescharacteristic
402C22×C4C2×D3211yescharacteristic
403SD16—362no—
404D8—362no—
405C2×C8—181no—
406C2×C8—181no—
407C4⋊C4—31no—
408C4⋊C4—31no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—61no—
414C22⋊C4—61no—
415C22⋊C4—61no—
416C22⋊C4—61no—
417C22⋊C4—61no—
418C22⋊C4—122no—
419C42—61no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—81no—
439C22×C3—81no—
440C22×C3—82no—
441C22×C3—81no—
442C22×C3—81no—
443C22×C3—82no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3—241no—
451C22×C3—241no—
452C22×C3—241no—
453C22×C3—241no—
454C22×C3#93211yescharacteristic
455C22×C3#93711yescharacteristic
456C22×C3#94911yescharacteristic
457C22×C3#95011yescharacteristic
458C22×C3#95011yescharacteristic
459C22×C3#95311yescharacteristic
460C2×D3—42no—
461C2×D3—42no—
462C2×D3—41no—
463C2×D3—41no—
464C2×D3—41no—
465C2×D3—42no—
466C2×D3—81no—
467C2×D3—81no—
468C2×D3—81no—
469C2×D3—81no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4—81no—
479C3×C4—122no—
480C3×C4—121no—
481C3×C4—121no—
482C3×C4—121no—
483Dic3—42no—
484Dic3—41no—
485Dic3—41no—
486Dic3—41no—
487C32#160011yescharacteristic, complemented, Sylow
488C23—21no—
489C23—21no—
490C23—21no—
491C23—41no—
492C23—41no—
493C23—62no—
494C23—61no—
495C23—121no—
496C23—121no—
497C23—121no—
498C23—121no—
499C23—121no—
500C23—121no—
501C23C2×#62511yescharacteristic
502Q8—121no—
503D4—62no—
504D4—62no—
505D4—121no—
506D4—121no—
507D4—121no—
508D4—128no—
509D4—121no—
510D4—121no—
511D4—241no—
512D4—241no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—62no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4—241no—
523C2×C4D3×#6711yescharacteristic
524C2×C4D3×#6711yescharacteristic
525C8—361no—
526C8—361no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—41no—
535C2×C3—41no—
536C2×C3—82no—
537C2×C3—81no—
538C2×C3—81no—
539C2×C3—241no—
540C2×C3—242no—
541C2×C3#503211yescharacteristic
542C2×C3#503711yescharacteristic
543C2×C3#507711yescharacteristic
544C2×C3#523811yescharacteristic
545C2×C3#524111yescharacteristic
546C2×C3#524411yescharacteristic
547D3—82no—
548D3—81no—
549C22—21no—
550C22—21no—
551C22—42no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—122no—
557C22—122no—
558C22—121no—
559C22—122no—
560C22—121no—
561C22—121no—
562C22—241no—
563C22—241no—
564C22—241no—
565C22—241no—
566C22#6382211yescharacteristic
567C22#6382311yescharacteristic
568C22#6397611yescharacteristic
569C4—21no—
570C4—21no—
571C4—41no—
572C4—122no—
573C4—121no—
574C4—121no—
575C4—121no—
576C3—21no—
577C3#6969711yescharacteristic, complemented
578C3#7188411yescharacteristic, complemented
579C2—21no—
580C2—21no—
581C2—81no—
582C2—242no—
583C2—241no—
584C2#1059116111yescharacteristic
585C2#1059150911yescharacteristic
586C2#1059153011yescharacteristic
subgroupG/H
centerC22#63976
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. C3×#4960C2semidirect
3. #10591169C2semidirect
4. #10591160C2semidirect
5. #10589391C2semidirect
6. #10589153C2semidirect
7. #10589149C2semidirect
30. #5494D3semidirect
36. #4960D3semidirect
58. C2×C3×D12D4semidirect
60. C2×C3×Dic6D4semidirect
71. C3×C4⋊Dic3D4semidirect
72. C3×C4⋊Dic3D4semidirect
200. C2×D12#67semidirect
202. C2×Dic6#67semidirect
230. C4⋊Dic3#67semidirect
231. C4⋊Dic3#67semidirect
487. C32#1600semidirect
577. C3#69697semidirect
578. C3#71884semidirect

Maximal subgroups

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

subgroupindex
C3×#54942
C3×#49602
#105911692
#105911602
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