Finite Group Databasebeta

← #11778180

Subgroups — #11778180

Order 1152.

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

normal subgroups only

This group has 685 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×#5617C211yesmaximal, characteristic, complemented
2C3×#5036C211yesmaximal, characteristic, complemented
3#10591389C211yesmaximal, characteristic, complemented
4#10591169C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71884—31nomaximal
9#70969—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×#625—21no—
12C32×#121C2211yescharacteristic
13C3×#939—21no—
14C3×#937—21no—
15C3×D4×Dic3—21no—
16C2×C3×#213—21no—
17C2×C3×(C2×D3)⋊C4C2211yescharacteristic
18C3×#924C2211yescharacteristic
19C3×#898—21no—
20C3×#886—21no—
21C3×#885—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×#3715—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#809—21no—
28#63562—21no—
29C3×#538—31no—
30#5617D311yescharacteristic, complemented
31C3×#447—31no—
32#5223—31no—
33#5218—31no—
34#5046—31no—
35#5036D311yescharacteristic, complemented
36#4960—31no—
37#4538—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4525—31no—
42#4468—31no—
43#4467—31no—
44C23×C3×D3—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4D411yescharacteristic, complemented
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—42no—
57C2×C3×Dic6D411yescharacteristic, complemented
58C2×#625—42no—
59C2×#625—42no—
60C2×#625—42no—
61C32×C4⋊C4D411yescharacteristic, complemented
62C32×C22⋊C4—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×#217—21no—
66C3×#213—42no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3D411yescharacteristic, complemented
73C3×Dic3⋊C4—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76(C2×D3)⋊Dic3—42no—
77#3715—42no—
78#1600—91noSylow
79C22×C3×D4—31no—
80C22×#67—61no—
81C22×#67—61no—
82C22×D12C2×D311yescharacteristic
83C2×C3×D8—61no—
84C3×#126—61no—
85C3×#124—61no—
86C3×#123—61no—
87C3×C22⋊Q8—31no—
88C3×#121—21no—
89C3×#121—61no—
90C3×#121C2×D311yescharacteristic
91C3×#121C2×D311yescharacteristic
92C3×#120—61no—
93C3×C4×D4—61no—
94C2×C3×C22⋊C4—31no—
95C2×#217—61no—
96C2×#215—61no—
97#939—21no—
98#937—21no—
99D4×Dic3—21no—
100C2×#214—61no—
101C2×#213—21no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4C2×D311yescharacteristic
104#924C2×D311yescharacteristic
105#898—21no—
106#886—21no—
107#885—21no—
108C3×#102—61no—
109C3×C22⋊C8—31no—
110#832—61no—
111C3⋊#95—31no—
112C3⋊#95—31no—
113C3⋊#95—61no—
114#830—31no—
115#830—31no—
116#830—61no—
117#830C2×D311yescharacteristic
118#809—21no—
119#809—61no—
120C23×C32—21no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—22no—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—21no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C32×D4—41no—
135C32×D4—41no—
136C32×D4—41no—
137C2×C32×C4—21no—
138C2×C32×C4—41no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C3×#67—81no—
145C3×#67—81no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—81no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—41no—
154C3×D12—41no—
155C3×Dic6—41no—
156#625—48no—
157C3⋊(C3⋊C8)—41no—
158C3×C3⋊C8—41no—
159#538—31no—
160#450—91no—
161#447—31no—
162#392—91no—
163#328—91no—
164#327—91no—
165#323—91no—
166C24×C3—31no—
167C24×C3—61no—
168C23×D3—21no—
169C23×D3#6711yescharacteristic
170C2×C3×Q8—31no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—41no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—122no—
180C2×C3×D4#6711yescharacteristic, complemented
181C2×C3×D4#6711yescharacteristic, complemented
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—21no—
188C2×#67—21no—
189C2×#67—122no—
190C2×#67—122no—
191C2×#67—122no—
192C2×#67—122no—
193C2×#67—122no—
194C2×#67—122no—
195C22×Dic3—21no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—121no—
199C22×Dic3#6711yescharacteristic
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—42no—
203C2×Dic6#6711yescharacteristic, complemented
204C3×D8—122no—
205C2×C3×C8—61no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—31no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4#6711yescharacteristic, complemented
211C3×C4⋊C4#6711yescharacteristic, complemented
212C3×C22⋊C4—21no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—41no—
215C3×C22⋊C4—61no—
216C3×C22⋊C4—61no—
217C3×C22⋊C4—61no—
218C3×C22⋊C4—61no—
219C3×C22⋊C4—61no—
220C3×C22⋊C4—61no—
221C3×C42—61no—
222#217—21no—
223#217—21no—
224#217—122no—
225#215—122no—
226#214—122no—
227#213—42no—
228(C2×D3)⋊C4—21no—
229(C2×D3)⋊C4—21no—
230(C2×D3)⋊C4—21no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—122no—
233C4⋊Dic3—21no—
234C4⋊Dic3#6711yescharacteristic, complemented
235Dic3⋊C4—21no—
236C4×Dic3—21no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—121no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—41no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32#12011yescharacteristic
247C22×C32#13511yescharacteristic
248C22×C32AGL(1,ℤ/8)11yescharacteristic
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C2×C3×D3—42no—
255C2×C3×D3—41no—
256C2×C3×D3—81no—
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—181no—
270C2×SD16—181no—
271C2×D8—61no—
272#126—61no—
273#124—61no—
274#123—61no—
275C22⋊Q8—31no—
276#121—61no—
277#121D3211yescharacteristic
278#120—61no—
279C4×D4—61no—
280C2×C22⋊C4—31no—
281C2×C22⋊C4—181no—
282#102—61no—
283#102—181no—
284C22⋊C8—31no—
285C22⋊C8—91no—
286#95—91no—
287C23×C3—21no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—41no—
291C23×C3—62no—
292C23×C3—61no—
293C23×C3—61no—
294C23×C3—61no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3—121no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—22no—
306C22×D3—21no—
307C22×D3—21no—
308C22×D3—21no—
309C22×D3—41no—
310C22×D3—41no—
311C22×D3—41no—
312C22×D3—41no—
313C22×D3—41no—
314C22×D3—41no—
315C22×D3—41no—
316C22×D3—41no—
317C3×Q8—121no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—41no—
321C3×D4—41no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—81no—
327C3×D4—81no—
328C3×D4—81no—
329C3×D4—121no—
330C3×D4—121no—
331C3×D4—241no—
332C3×D4—241no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—81no—
344C2×C3×C4—121no—
345C2×C3×C4—241no—
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350#67—81no—
351#67—81no—
352#67—128no—
353#67—128no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—41no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—81no—
361C2×Dic3—122no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—241no—
367C2×Dic3—241no—
368D12—22no—
369D12—22no—
370D12—41no—
371D12—41no—
372Dic6—41no—
373C3×C8—121no—
374C3⋊C8—41no—
375C3⋊C8—121no—
376C3⋊C8—121no—
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—31no—
387C24—61no—
388C2×Q8—31no—
389C2×D4—21no—
390C2×D4—61no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C2×D4—122no—
395C2×D4—362no—
396C2×D4—362no—
397C2×D4—362no—
398C2×D4#62511yescharacteristic, complemented
399C22×C4—31no—
400C22×C4—61no—
401C22×C4—181no—
402C22×C4C2×D3211yescharacteristic
403SD16—362no—
404D8—122no—
405C2×C8—61no—
406C2×C8—181no—
407C4⋊C4—31no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4#62511yescharacteristic, complemented
411C22⋊C4—21no—
412C22⋊C4—61no—
413C22⋊C4—61no—
414C22⋊C4—61no—
415C22⋊C4—61no—
416C22⋊C4—61no—
417C22⋊C4—61no—
418C22⋊C4—362no—
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—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—81no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—122no—
444C22×C3—121no—
445C22×C3—241no—
446C22×C3—241no—
447C22×C3—241no—
448C22×C3—241no—
449C22×C3—241no—
450C22×C3#91111yescharacteristic
451C22×C3#91211yescharacteristic
452C22×C3#93711yescharacteristic
453C22×C3#94911yescharacteristic
454C22×C3#95011yescharacteristic
455C22×C3#95311yescharacteristic
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—41no—
460C2×D3—41no—
461C2×D3—41no—
462C2×D3—42no—
463C2×D3—81no—
464C2×D3—81no—
465C2×D3—81no—
466C2×D3—81no—
467C2×D3—81no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—41no—
473C3×C4—41no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—81no—
477C3×C4—121no—
478C3×C4—121no—
479C3×C4—121no—
480Dic3—41no—
481Dic3—41no—
482Dic3—41no—
483Dic3—122no—
484Dic3—122no—
485Dic3—242no—
486C32#160011yescharacteristic, complemented, Sylow
487C23—21no—
488C23—62no—
489C23—61no—
490C23—61no—
491C23—61no—
492C23—121no—
493C23—121no—
494C23—121no—
495C23—121no—
496C23—121no—
497C23—121no—
498C23—121no—
499C23—121no—
500C23D3×#6711yescharacteristic
501Q8—121no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—62no—
506D4—62no—
507D4—121no—
508D4—121no—
509D4—241no—
510D4—241no—
511D4—368no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—121no—
518C2×C4—182no—
519C2×C4—241no—
520C2×C4—361no—
521C2×C4—361no—
522C2×C4C2×#62511yescharacteristic
523C2×C4D3×#6711yescharacteristic
524C8—121no—
525C8—361no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—41no—
534C2×C3—41no—
535C2×C3—81no—
536C2×C3—81no—
537C2×C3—161no—
538C2×C3—241no—
539C2×C3—242no—
540C2×C3#503211yescharacteristic
541C2×C3#515811yescharacteristic
542C2×C3#519811yescharacteristic
543C2×C3#523811yescharacteristic
544C2×C3#524111yescharacteristic
545C2×C3#524411yescharacteristic
546D3—82no—
547D3—81no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—122no—
554C22—122no—
555C22—122no—
556C22—122no—
557C22—121no—
558C22—121no—
559C22—121no—
560C22—241no—
561C22—241no—
562C22—241no—
563C22—241no—
564C22—241no—
565C22#6392511yescharacteristic
566C22#6393311yescharacteristic
567C22#6397611yescharacteristic
568C4—21no—
569C4—21no—
570C4—41no—
571C4—121no—
572C4—121no—
573C4—121no—
574C4—362no—
575C3—21no—
576C3#7096911yescharacteristic, complemented
577C3#7188411yescharacteristic, complemented
578C2—21no—
579C2—21no—
580C2—81no—
581C2—241no—
582C2—242no—
583C2#1059145011yescharacteristic
584C2#1059153011yescharacteristic
585C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
hypercenter#121D32
hypocenterC32#1600
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5617C2semidirect
2. C3×#5036C2semidirect
3. #10591389C2semidirect
4. #10591169C2semidirect
5. #10589403C2semidirect
6. #10589152C2semidirect
7. #10589145C2semidirect
30. #5617D3semidirect
35. #5036D3semidirect
47. C2×C32×D4D4semidirect
57. C2×C3×Dic6D4semidirect
61. C32×C4⋊C4D4semidirect
72. C3×C4⋊Dic3D4semidirect
180. C2×C3×D4#67semidirect
181. C2×C3×D4#67semidirect
203. C2×Dic6#67semidirect
210. C3×C4⋊C4#67semidirect
211. C3×C4⋊C4#67semidirect
234. C4⋊Dic3#67semidirect
398. C2×D4#625semidirect
410. C4⋊C4#625semidirect
486. C32#1600semidirect
576. C3#70969semidirect
577. C3#71884semidirect

Maximal subgroups

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

subgroupindex
C3×#56172
C3×#50362
#105913892
#105911692
#105894032
#105891522
#105891452
#718843
#709693