Finite Group Databasebeta

← #11778669

Subgroups — #11778669

Order 1152.

633 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 633 conjugacy classes of subgroups — too many to draw. Only its 82 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#10595072C211yesmaximal, characteristic
2#10592667C211yesmaximal, characteristic, complemented
3C3×#4993C211yesmaximal, characteristic, complemented
4C3×#4968C211yesmaximal, characteristic, complemented
5#10589151C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71168—31nomaximal
9#69714—31nomaximal
10C2×D3×#67—21no—
11C2×C32×C4⋊C4C2211yescharacteristic, complemented
12#64139C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17#63978—21no—
18#63923—21no—
19#63922—21no—
20#63891—21no—
21#63890—21no—
22#63657C2211yescharacteristic, complemented
23#63636—21no—
24#63635—21no—
25C3×C3⋊#95C2211yescharacteristic, complemented
26C3×#830C2211yescharacteristic, complemented
27C3×#809—21no—
28C3×#808—21no—
29#5605—31no—
30#5493—31no—
31C3×#481—31no—
32C3×#399—31no—
33#4993D311yescharacteristic, complemented
34#4968—31no—
35#4968—31no—
36#4968—61no—
37#4968D311yescharacteristic, complemented
38#4537—31no—
39#4525—31no—
40#4470—31no—
41#4468—31no—
42#4451—31no—
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C22×D32—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×#638—21no—
49C2×C4⋊(C3⋊D3)D411yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C2×C3×D12D411yescharacteristic
54D3×#67—42no—
55D3×#67—42no—
56C2×#626—21no—
57C2×#626—21no—
58C2×#625—21no—
59C2×D3×Dic3—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62#3752—21no—
63C4⋊(C3⋊Dic3)D411yescharacteristic
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—42no—
69C3×C4⋊Dic3D411yescharacteristic
70C3×Dic3⋊C4—42no—
71C2×C3×C3⋊C8—21no—
72Dic3⋊Dic3—21no—
73#3722—21no—
74(C2×D3)⋊Dic3—21no—
75#1613—91noSylow
76C22×#67—61no—
77C2×D3×D4—61no—
78C3×#121—31no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—61no—
81C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
82C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
83C2×C3×C22⋊C4—31no—
84C2×C3×C22⋊C4—61no—
85#939—61no—
86#937—61no—
87#930—31no—
88#930—31no—
89#930—61no—
90#930—61no—
91#930C2×D311yescharacteristic
92C2×(C2×D3)⋊C4—21no—
93C2×(C2×D3)⋊C4C2×D311yescharacteristic
94C2×Dic3⋊C4—21no—
95#894—61no—
96#886—61no—
97#886—61no—
98#883—61no—
99#882—61no—
100#882—61no—
101#882—61no—
102C3×#106—61no—
103C3×#102—61no—
104C3×C22⋊C8—31no—
105C3×#95—31no—
106C3⋊#95C2×D311yescharacteristic, complemented
107#830—31no—
108#830—31no—
109#830—61no—
110#830C2×D311yescharacteristic, complemented
111#809—21no—
112#809—61no—
113#809—61no—
114#809—62no—
115#808—21no—
116#808—61no—
117#808—61no—
118#808—62no—
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3SD1612yes—
127C2×D32—42no—
128C2×D32—81no—
129C2×D32—81no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136#638—41no—
137#638—41no—
138C2×C3⋊Dic3—21no—
139C4⋊(C3⋊D3)—41no—
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C3×D12—41no—
149#626—42no—
150#626—81no—
151#625—42no—
152D3×Dic3—42no—
153C3⋊(C3⋊C8)—41no—
154C3×C3⋊C8—41no—
155#534—91no—
156#481—31no—
157#481—91no—
158#399—31no—
159#327—91no—
160#327—91no—
161#323—91no—
162C24×C3—31no—
163C23×D3—61no—
164C23×D3—61no—
165C23×D3#6711yescharacteristic
166C2×C3×D4—31no—
167C2×C3×D4—61no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—31no—
172C22×C3×C4—41no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C2×#67—21no—
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—61no—
180C2×#67—61no—
181C2×#67—61no—
182C2×#67—61no—
183C2×#67—121no—
184C2×#67—122no—
185C2×#67—122no—
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3#6711yescharacteristic
189D3×D4—122no—
190D3×D4—122no—
191C2×D12—31no—
192C2×D12—31no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12#6711yescharacteristic
197C2×C4×D3—61no—
198C2×C3×C8—61no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—31no—
205C3×C4⋊C4—41no—
206C3×C4⋊C4—122no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—61no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—122no—
211#217—61no—
212(C2×D3)⋊C4—21no—
213(C2×D3)⋊C4—21no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—42no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—121no—
222C4⋊Dic3—31no—
223C4⋊Dic3—31no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3#6711yescharacteristic
227Dic3⋊C4—42no—
228Dic3⋊C4—61no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32#12011yescharacteristic
236C22×C32C2×SD1611yescharacteristic
237C22×C32AGL(1,ℤ/8)11yescharacteristic
238C2×C3⋊D3—41no—
239C2×C3⋊D3—41no—
240C2×C3⋊D3—41no—
241C2×C3×D3—22no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—42no—
245C2×C3×D3—41no—
246C2×C3×D3—41no—
247C2×C3×D3—41no—
248C2×C3×D3—81no—
249D32—84no—
250C32×C4—21no—
251C32×C4—21no—
252C32×C4—81no—
253C3⋊Dic3—41no—
254C3×Dic3—42no—
255C3×Dic3—41no—
256C3×Dic3—41no—
257C22×D4—181no—
258#123—181no—
259#123—181no—
260#121—31no—
261#121—91no—
262#121—181no—
263#120—181no—
264#120—181no—
265C2×C4⋊C4—61no—
266C2×C4⋊C4D3211yescharacteristic, complemented
267C2×C22⋊C4—31no—
268C2×C22⋊C4—61no—
269#106—61no—
270#106—181no—
271#102—61no—
272#102—181no—
273C22⋊C8—31no—
274C22⋊C8—91no—
275#95—31no—
276C23×C3—21no—
277C23×C3—32no—
278C23×C3—61no—
279C23×C3—61no—
280C23×C3—61no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3D3×D411yescharacteristic
284C23×C3C2×#6711yescharacteristic
285C22×D3—21no—
286C22×D3—21no—
287C22×D3—21no—
288C22×D3—41no—
289C22×D3—41no—
290C22×D3—61no—
291C22×D3—61no—
292C22×D3—121no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—241no—
296C22×D3—241no—
297C22×D3—241no—
298C22×D3—241no—
299C22×D3#21512yes—
300C3×D4—121no—
301C3×D4—121no—
302C3×D4—121no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—42no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—42no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—62no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—81no—
319C2×C3×C4—81no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327#67—41no—
328#67—41no—
329#67—122no—
330#67—122no—
331#67—122no—
332#67—121no—
333#67—121no—
334#67—121no—
335#67—121no—
336#67—241no—
337#67—241no—
338#67—241no—
339C2×Dic3—22no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3—122no—
349D12—41no—
350D12—121no—
351D12—121no—
352D12—122no—
353D12—122no—
354D12—241no—
355C4×D3—122no—
356C3×C8—121no—
357C3⋊C8—41no—
358C3⋊C8—122no—
359C3⋊C8—121no—
360C3⋊C8—121no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32#45011yescharacteristic
364C2×C32#45311yescharacteristic
365C2×C32#45811yescharacteristic
366C3⋊D3—81no—
367C3×D3—42no—
368C3×D3—81no—
369C24—31no—
370C24—181no—
371C2×D4—31no—
372C2×D4—61no—
373C2×D4—91no—
374C2×D4—181no—
375C2×D4—181no—
376C2×D4—181no—
377C2×D4—181no—
378C2×D4—362no—
379C2×D4—362no—
380C22×C4—21no—
381C22×C4—31no—
382C22×C4—61no—
383C22×C4—181no—
384C22×C4C2×D3211yescharacteristic
385C2×C8—61no—
386C2×C8—181no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—31no—
390C4⋊C4—91no—
391C4⋊C4—122no—
392C4⋊C4—181no—
393C22⋊C4—61no—
394C22⋊C4—61no—
395C22⋊C4—61no—
396C22⋊C4—122no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—62no—
410C22×C3—122no—
411C22×C3—121no—
412C22×C3—121no—
413C22×C3—121no—
414C22×C3—121no—
415C22×C3—121no—
416C22×C3—241no—
417C22×C3D3×SD1611yescharacteristic
418C22×C3#91411yescharacteristic
419C22×C3#93711yescharacteristic
420C22×C3#93711yescharacteristic
421C22×C3C2×#21511yescharacteristic
422C22×C3#94911yescharacteristic
423C2×D3—22no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—42no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—81no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—121no—
436C2×D3—121no—
437C2×D3—241no—
438C2×D3—241no—
439C2×D3—241no—
440C2×D3—244no—
441C2×D3—244no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—82no—
449C3×C4—81no—
450C3×C4—81no—
451C3×C4—122no—
452C3×C4—121no—
453C3×C4—121no—
454Dic3—42no—
455Dic3—41no—
456Dic3—41no—
457Dic3—121no—
458Dic3—121no—
459Dic3—241no—
460C32#161311yescharacteristic, complemented, Sylow
461C23—32no—
462C23—61no—
463C23—61no—
464C23—61no—
465C23—121no—
466C23—121no—
467C23—181no—
468C23—362no—
469C23—721no—
470C23—721no—
471C23D3×#6711yescharacteristic
472D4—121no—
473D4—121no—
474D4—121no—
475D4—361no—
476D4—362no—
477D4—362no—
478D4—361no—
479D4—361no—
480D4—721no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4D3×#6711yescharacteristic
494C2×C4#381111yescharacteristic
495C8—121no—
496C8—361no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—41no—
505C2×C3—41no—
506C2×C3—122no—
507C2×C3—241no—
508C2×C3#504611yescharacteristic
509C2×C3#505311yescharacteristic
510C2×C3#505311yescharacteristic
511C2×C3#507711yescharacteristic
512C2×C3#516911yescharacteristic
513C2×C3#519811yescharacteristic
514D3—42no—
515D3—81no—
516D3—241no—
517D3—241no—
518D3—481no—
519C22—21no—
520C22—21no—
521C22—62no—
522C22—122no—
523C22—121no—
524C22—121no—
525C22—121no—
526C22—121no—
527C22—121no—
528C22—241no—
529C22—361no—
530C22—361no—
531C22—361no—
532C22—724no—
533C22D3×#21511yescharacteristic
534C22#6393911yescharacteristic
535C22#6398311yescharacteristic
536C4—21no—
537C4—21no—
538C4—81no—
539C4—122no—
540C4—121no—
541C4—121no—
542C4—361no—
543C3—21no—
544C3#6971411yescharacteristic, complemented
545C3#7116811yescharacteristic, complemented
546C2—21no—
547C2—21no—
548C2—122no—
549C2—241no—
550C2—721no—
551C2#1059139811yescharacteristic
552C2#1059152311yescharacteristic
553C2#1059165111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radical#10595072C2
hypercenterC2×C4⋊C4D32
hypocenterC32#1613
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592667C2semidirect
3. C3×#4993C2semidirect
4. C3×#4968C2semidirect
5. #10589151C2semidirect
6. #10589149C2semidirect
7. #10589145C2semidirect
11. C2×C32×C4⋊C4C22semidirect
22. #63657C22semidirect
25. C3×C3⋊#95C22semidirect
26. C3×#830C22semidirect
33. #4993D3semidirect
37. #4968D3semidirect
81. C2×C3×C4⋊C4C2×D3semidirect
82. C2×C3×C4⋊C4C2×D3semidirect
106. C3⋊#95C2×D3semidirect
110. #830C2×D3semidirect
266. C2×C4⋊C4D32semidirect
460. C32#1613semidirect
544. C3#69714semidirect
545. C3#71168semidirect

Maximal subgroups

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

subgroupindex
#105950722
#105926672
C3×#49932
C3×#49682
#105891512
#105891492
#105891452
#711683
#697143