Finite Group Databasebeta

← #11778184

Subgroups — #11778184

Order 1152.

739 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 739 conjugacy classes of subgroups — too many to draw. Only its 78 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#10595038C211yesmaximal, characteristic, complemented
2#10592431C211yesmaximal, characteristic, complemented
3#10591395C211yesmaximal, characteristic, complemented
4#10591183C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#68317—31nomaximal
9#68107—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#626—21no—
12#64139C2211yescharacteristic
13C2×#3745—21no—
14C2×C3×(C2×D3)⋊C4C2211yescharacteristic
15C3×#924C2211yescharacteristic
16#63977—21no—
17C2×#3722—21no—
18#63952—21no—
19#63910—21no—
20#63907—21no—
21#63861—21no—
22#63854—21no—
23C2×#3717—21no—
24C32×C22⋊C8C2211yescharacteristic
25#63648—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28#63564—21no—
29#5644—31no—
30#5494—31no—
31#5046—31no—
32#4960—31no—
33#4732—31no—
34#4732—31no—
35#4732—61no—
36#4731—31no—
37#4671—31no—
38C3×#328—31no—
39C3×#323—31no—
40#4470—31no—
41#4468D311yescharacteristic, complemented
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C23×C3⋊D3—21no—
45C23×C3×D3D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—42no—
51C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic, complemented
55C2×#626—21no—
56C2×#626—21no—
57C2×#626—42no—
58C2×#626—42no—
59C2×#626—42no—
60C2×#624—21no—
61C2×C32×C8—21no—
62#3752—21no—
63C4⋊(C3⋊Dic3)D411yescharacteristic, complemented
64#3745—42no—
65C3×#217—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3D411yescharacteristic, complemented
69C3×Dic3⋊C4—21no—
70C2×C3×C3⋊C8—21no—
71#3724—21no—
72#3722—21no—
73#3722—42no—
74(C2×D3)⋊Dic3—21no—
75(C2×D3)⋊Dic3—21no—
76Dic32—21no—
77#3717—42no—
78#1600—91noSylow
79C22×#67—61no—
80C22×D12—31no—
81C22×D12—31no—
82C22×D12—61no—
83C22×D12—61no—
84C3×C22⋊Q8—31no—
85C2×C3×C22⋊C4—31no—
86#953—61no—
87#947—61no—
88C2×#215—61no—
89#930—31no—
90#930—31no—
91#930—61no—
92C4×#67—61no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4C2×D311yescharacteristic
96#924C2×D311yescharacteristic
97C2×D24—61no—
98C2×D24—61no—
99C2×D24—62no—
100C2×#204—61no—
101#898—61no—
102#895—61no—
103#894—61no—
104#885—61no—
105#884—61no—
106#883—61no—
107#882—61no—
108#67⋊C4—61no—
109#879—61no—
110C3×C22⋊C8—21no—
111C3×C22⋊C8—31no—
112C3×C22⋊C8C2×D311yescharacteristic
113C3×C22⋊C8C2×D311yescharacteristic
114C3×#95—31no—
115C3⋊#95C2×D311yescharacteristic
116#830C2×D311yescharacteristic
117#821—61no—
118#821—61no—
119#821—62no—
120#821—61no—
121#809—61no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3×D3—21no—
132C22×C3×D3—21no—
133C22×C3×D3—21no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C2×C32×C4—41no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139#638—41no—
140#638—41no—
141C2×C3⋊Dic3—21no—
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—41no—
145C4⋊(C3⋊D3)—41no—
146C4⋊(C3⋊D3)—41no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×Dic6—41no—
155#626—48no—
156#626—81no—
157#626—81no—
158#624—81no—
159C32×C8—41no—
160C3×C3⋊C8—41no—
161#538—91no—
162#450—91no—
163#447—91no—
164#392—91no—
165#328—31no—
166#327—91no—
167#323—31no—
168C24×C3—31no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C23×D3D1211yescharacteristic
173C2×C3×Q8—31no—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C2×#67—61no—
180C2×#67—61no—
181C2×#67—61no—
182C2×#67—61no—
183C2×#67—121no—
184C2×#67—122no—
185C2×#67—122no—
186C2×#67—122no—
187C22×Dic3—21no—
188C22×Dic3D1211yescharacteristic
189C2×D12—31no—
190C2×D12—31no—
191C2×D12—61no—
192C2×D12—62no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—121no—
200C2×D12—122no—
201C2×D12—122no—
202C2×D12—124no—
203C2×D12—122no—
204C2×D12—122no—
205C2×D12—122no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×Dic6D1211yescharacteristic, complemented
209C2×C3×C8—22no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—61no—
213C3×C4⋊C4—31no—
214C3×C4⋊C4—61no—
215C3×C22⋊C4—61no—
216C3×C22⋊C4—61no—
217C3×C22⋊C4—61no—
218#217—21no—
219#217—61no—
220#217—61no—
221#215—122no—
222(C2×D3)⋊C4—21no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—61no—
225(C2×D3)⋊C4—61no—
226(C2×D3)⋊C4—61no—
227(C2×D3)⋊C4—61no—
228(C2×D3)⋊C4—61no—
229(C2×D3)⋊C4—61no—
230(C2×D3)⋊C4—121no—
231(C2×D3)⋊C4—122no—
232(C2×D3)⋊C4—122no—
233C4⋊Dic3—31no—
234C4⋊Dic3—31no—
235C4⋊Dic3—61no—
236C4⋊Dic3D1211yescharacteristic, complemented
237Dic3⋊C4—21no—
238Dic3⋊C4—61no—
239Dic3⋊C4—61no—
240C4×Dic3—61no—
241C4×Dic3—61no—
242C2×C3⋊C8—21no—
243D24—122no—
244D24—122no—
245D24—124no—
246#204—122no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32#12011yescharacteristic
250C22×C32#13511yescharacteristic
251C22×C32AGL(1,ℤ/8)11yescharacteristic
252C2×C3⋊D3—42no—
253C2×C3⋊D3—42no—
254C2×C3⋊D3—42no—
255C2×C3⋊D3—41no—
256C2×C3⋊D3—41no—
257C2×C3⋊D3—41no—
258C2×C3⋊D3—81no—
259C2×C3⋊D3—81no—
260C2×C3⋊D3—81no—
261C2×C3⋊D3—81no—
262C2×C3×D3—42no—
263C2×C3×D3—41no—
264C2×C3×D3—41no—
265C2×C3×D3—41no—
266C2×C3×D3—81no—
267C32×C4—21no—
268C32×C4—21no—
269C3⋊Dic3—41no—
270C3×Dic3—42no—
271C3×Dic3—41no—
272C3×Dic3—41no—
273C3×Dic3—41no—
274C22×D4—91no—
275C22×D4—181no—
276C2×SD16—181no—
277C2×D8—181no—
278#126—181no—
279#124—181no—
280#123—181no—
281C22⋊Q8—31no—
282#121—91no—
283#121—181no—
284#120—181no—
285C4×D4—181no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—181no—
288#102—181no—
289#102—181no—
290C22⋊C8—31no—
291C22⋊C8D3211yescharacteristic
292#95—31no—
293C23×C3—21no—
294C23×C3—61no—
295C23×C3—61no—
296C23×C3—61no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3C2×D1211yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—21no—
302C22×D3—21no—
303C22×D3—21no—
304C22×D3—41no—
305C22×D3—41no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—122no—
311C22×D3—121no—
312C22×D3—121no—
313C22×D3—121no—
314C22×D3—122no—
315C22×D3—121no—
316C22×D3—121no—
317C22×D3—121no—
318C22×D3—121no—
319C22×D3—122no—
320C22×D3—121no—
321C22×D3—121no—
322C22×D3—121no—
323C22×D3—121no—
324C22×D3—121no—
325C22×D3—121no—
326C22×D3—241no—
327C22×D3—241no—
328C22×D3—241no—
329C22×D3—241no—
330C3×Q8—121no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—42no—
336C2×C3×C4—62no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347#67—128no—
348#67—121no—
349#67—121no—
350#67—121no—
351#67—121no—
352#67—241no—
353#67—241no—
354#67—241no—
355#67—241no—
356C2×Dic3—22no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—41no—
361C2×Dic3—41no—
362C2×Dic3—41no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—121no—
366D12—62no—
367D12—64no—
368D12—62no—
369D12—62no—
370D12—62no—
371D12—122no—
372D12—121no—
373D12—121no—
374D12—122no—
375D12—121no—
376D12—121no—
377D12—121no—
378D12—121no—
379D12—122no—
380D12—122no—
381D12—128no—
382D12—241no—
383D12—241no—
384C4×D3—241no—
385C4×D3—241no—
386Dic6—41no—
387C3×C8—42no—
388C3×C8—41no—
389C3×C8—41no—
390C3×C8—121no—
391C3⋊C8—41no—
392C2×C32—21no—
393C2×C32—21no—
394C2×C32#44911yescharacteristic
395C2×C32#45311yescharacteristic
396C2×C32B(4,𝔽2)11yescharacteristic
397C3⋊D3—82no—
398C3⋊D3—81no—
399C3×D3—81no—
400C24—31no—
401C24—181no—
402C2×Q8—31no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4—181no—
409C2×D4—362no—
410C2×D4—362no—
411C2×D4—362no—
412C2×D4—362no—
413C22×C4—31no—
414C22×C4—61no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417SD16—362no—
418D8—362no—
419C2×C8—21no—
420C2×C8—61no—
421C4⋊C4—31no—
422C4⋊C4—61no—
423C4⋊C4—91no—
424C4⋊C4—181no—
425C22⋊C4—61no—
426C22⋊C4—61no—
427C22⋊C4—61no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—362no—
433C42—181no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—122no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3—121no—
447C22×C3—241no—
448C22×C3#88211yescharacteristic
449C22×C3#88211yescharacteristic
450C22×C3#90411yescharacteristic
451C22×C3#90811yescharacteristic
452C22×C3#91411yescharacteristic
453C22×C3#91911yescharacteristic
454C2×D3—42no—
455C2×D3—41no—
456C2×D3—41no—
457C2×D3—41no—
458C2×D3—81no—
459C2×D3—124no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—121no—
465C2×D3—122no—
466C2×D3—122no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—242no—
473C2×D3—242no—
474C2×D3—241no—
475C2×D3—241no—
476C2×D3—241no—
477C2×D3—241no—
478C2×D3—241no—
479C2×D3—241no—
480C2×D3—241no—
481C2×D3—242no—
482C2×D3—242no—
483C2×D3—242no—
484C2×D3—242no—
485C2×D3—241no—
486C2×D3—241no—
487C2×D3—241no—
488C2×D3—241no—
489C3×C4—22no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—41no—
495C3×C4—122no—
496C3×C4—121no—
497C3×C4—121no—
498C3×C4—121no—
499Dic3—42no—
500Dic3—41no—
501Dic3—41no—
502Dic3—41no—
503Dic3—121no—
504Dic3—121no—
505Dic3—241no—
506C32#160011yescharacteristic, complemented, Sylow
507C23—61no—
508C23—61no—
509C23—61no—
510C23—121no—
511C23—121no—
512C23—182no—
513C23—181no—
514C23—361no—
515C23—361no—
516C23—361no—
517C23—361no—
518C23—361no—
519C23—361no—
520C23D3×D1211yescharacteristic
521Q8—121no—
522D4—182no—
523D4—182no—
524D4—361no—
525D4—361no—
526D4—361no—
527D4—368no—
528D4—361no—
529D4—361no—
530D4—721no—
531D4—721no—
532C2×C4—41no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—121no—
538C2×C4—121no—
539C2×C4—121no—
540C2×C4—181no—
541C2×C4—721no—
542C2×C4D3×D1211yescharacteristic
543C2×C4#381111yescharacteristic
544C8—41no—
545C8—121no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—41no—
554C2×C3—41no—
555C2×C3—241no—
556C2×C3#473411yescharacteristic
557C2×C3#474111yescharacteristic
558C2×C3#474111yescharacteristic
559C2×C3#474711yescharacteristic
560C2×C3#481011yescharacteristic
561C2×C3#482211yescharacteristic
562D3—81no—
563D3—244no—
564D3—242no—
565D3—241no—
566D3—242no—
567D3—241no—
568D3—481no—
569C22—21no—
570C22—21no—
571C22—122no—
572C22—121no—
573C22—121no—
574C22—121no—
575C22—241no—
576C22—362no—
577C22—362no—
578C22—361no—
579C22—362no—
580C22—361no—
581C22—361no—
582C22—721no—
583C22—721no—
584C22—721no—
585C22—721no—
586C22#6379411yescharacteristic
587C22#6380811yescharacteristic
588C22#6392311yescharacteristic
589C4—21no—
590C4—21no—
591C4—122no—
592C4—121no—
593C4—121no—
594C4—121no—
595C4—361no—
596C3—21no—
597C3#6810711yescharacteristic, complemented
598C3#6831711yescharacteristic, complemented
599C2—21no—
600C2—21no—
601C2—241no—
602C2—722no—
603C2—721no—
604C2#1059041011yescharacteristic
605C2#1059096711yescharacteristic
606C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
hypercenterC22⋊C8D32
hypocenterC32#1600
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595038C2semidirect
2. #10592431C2semidirect
3. #10591395C2semidirect
4. #10591183C2semidirect
5. C3×#4468C2semidirect
6. C3×#4467C2semidirect
7. #10589151C2semidirect
41. #4468D3semidirect
42. #4467D3semidirect
51. C2×C4⋊(C3⋊D3)D4semidirect
54. C2×C3×Dic6D4semidirect
63. C4⋊(C3⋊Dic3)D4semidirect
68. C3×C4⋊Dic3D4semidirect
208. C2×Dic6D12semidirect
236. C4⋊Dic3D12semidirect
506. C32#1600semidirect
597. C3#68107semidirect
598. C3#68317semidirect

Maximal subgroups

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

subgroupindex
#105950382
#105924312
#105913952
#105911832
C3×#44682
C3×#44672
#105891512
#683173
#681073