Finite Group Databasebeta

← #11778443

Subgroups — #11778443

Order 1152.

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

normal subgroups only

This group has 617 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#10592666C211yesmaximal, characteristic, complemented
3C3×#4992C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic, complemented
5#10589151C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71164—31nomaximal
9#69708—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
16#63978—21no—
17#63923—21no—
18#63922—21no—
19#63891—21no—
20#63890—21no—
21#63657C2211yescharacteristic, complemented
22#63636—21no—
23#63634—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic, complemented
26C3×#830C2211yescharacteristic, complemented
27C3×#809—21no—
28C3×#807—21no—
29#5605—31no—
30#5493—31no—
31C3×#480—31no—
32C3×#397—31no—
33#4992D311yescharacteristic, complemented
34#4967—31no—
35#4967—31no—
36#4967—61no—
37#4967D311yescharacteristic, 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
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—21no—
72#3722—21no—
73(C2×D3)⋊Dic3—21no—
74#1607—91noSylow
75C22×#67—61no—
76C2×D3×D4—61no—
77C3×#121—31no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
80C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
81C2×C3×C22⋊C4—31no—
82C2×C3×C22⋊C4—61no—
83#939—61no—
84#937—61no—
85#930—31no—
86#930—31no—
87#930—61no—
88#930—61no—
89#930C2×D311yescharacteristic
90C2×(C2×D3)⋊C4—21no—
91C2×(C2×D3)⋊C4C2×D311yescharacteristic
92#894—61no—
93#886—61no—
94#886—61no—
95#883—61no—
96#882—61no—
97#882—61no—
98#882—61no—
99C3×#107—61no—
100C3×#102—61no—
101C3×C22⋊C8—31no—
102C3×#95—31no—
103C3×#95—61no—
104C3⋊#95—21no—
105C3⋊#95C2×D311yescharacteristic, complemented
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic, complemented
110#809—21no—
111#809—61no—
112#809—61no—
113#809—62no—
114#807—21no—
115#807—61no—
116#807—61no—
117#807—62no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3D812yes—
126C2×D32—42no—
127C2×D32—81no—
128C2×D32—81no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135#638—41no—
136#638—41no—
137C2×C3⋊Dic3—21no—
138C4⋊(C3⋊D3)—41no—
139C3×#67—41no—
140C3×#67—41no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×D12—41no—
148#626—42no—
149#626—81no—
150#625—42no—
151D3×Dic3—42no—
152C3⋊(C3⋊C8)—41no—
153C3×C3⋊C8—41no—
154#534—91no—
155#480—31no—
156#480—91no—
157#397—31no—
158#327—91no—
159#327—91no—
160#323—91no—
161C24×C3—31no—
162C23×D3—61no—
163C23×D3—61no—
164C23×D3#6711yescharacteristic
165C2×C3×D4—31no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—41no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—21no—
176C2×#67—61no—
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—61no—
180C2×#67—61no—
181C2×#67—61no—
182C2×#67—121no—
183C2×#67—122no—
184C2×#67—122no—
185C22×Dic3—21no—
186C22×Dic3—61no—
187C22×Dic3#6711yescharacteristic
188D3×D4—122no—
189D3×D4—122no—
190C2×D12—31no—
191C2×D12—31no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12#6711yescharacteristic
196C2×C4×D3—61no—
197C2×C3×C8—61no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—31no—
204C3×C4⋊C4—41no—
205C3×C22⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—122no—
209#217—61no—
210(C2×D3)⋊C4—21no—
211(C2×D3)⋊C4—21no—
212(C2×D3)⋊C4—21no—
213(C2×D3)⋊C4—42no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—121no—
220C4⋊Dic3—31no—
221C4⋊Dic3—31no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3#6711yescharacteristic
225Dic3⋊C4—61no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32#12011yescharacteristic
233C22×C32C2×D811yescharacteristic
234C22×C32AGL(1,ℤ/8)11yescharacteristic
235C2×C3⋊D3—41no—
236C2×C3⋊D3—41no—
237C2×C3⋊D3—41no—
238C2×C3×D3—22no—
239C2×C3×D3—41no—
240C2×C3×D3—41no—
241C2×C3×D3—42no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—81no—
246D32—84no—
247C32×C4—21no—
248C32×C4—21no—
249C32×C4—81no—
250C3⋊Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—81no—
254C22×D4—181no—
255#123—181no—
256#123—181no—
257#121—31no—
258#121—91no—
259#121—181no—
260#120—181no—
261#120—181no—
262C2×C4⋊C4D3211yescharacteristic, complemented
263C2×C22⋊C4—31no—
264C2×C22⋊C4—61no—
265#107—61no—
266#107—181no—
267#102—61no—
268#102—181no—
269C22⋊C8—31no—
270C22⋊C8—91no—
271#95—31no—
272#95—61no—
273C23×C3—21no—
274C23×C3—32no—
275C23×C3—61no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—121no—
279C23×C3—121no—
280C23×C3D3×D411yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3—41no—
286C22×D3—41no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—121no—
290C22×D3—122no—
291C22×D3—122no—
292C22×D3—241no—
293C22×D3—241no—
294C22×D3—241no—
295C22×D3—241no—
296C22×D3#21312yes—
297C3×D4—121no—
298C3×D4—121no—
299C3×D4—121no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—81no—
315C2×C3×C4—81no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324#67—41no—
325#67—41no—
326#67—122no—
327#67—122no—
328#67—122no—
329#67—121no—
330#67—121no—
331#67—121no—
332#67—121no—
333#67—241no—
334#67—241no—
335#67—241no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—41no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—121no—
345C2×Dic3—122no—
346D12—41no—
347D12—121no—
348D12—121no—
349D12—122no—
350D12—122no—
351D12—241no—
352C4×D3—122no—
353C3×C8—121no—
354C3⋊C8—41no—
355C3⋊C8—122no—
356C3⋊C8—121no—
357C3⋊C8—121no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32#44711yescharacteristic
361C2×C32#45511yescharacteristic
362C2×C32#45811yescharacteristic
363C3⋊D3—81no—
364C3×D3—42no—
365C3×D3—81no—
366C24—31no—
367C24—181no—
368C2×D4—31no—
369C2×D4—61no—
370C2×D4—91no—
371C2×D4—181no—
372C2×D4—181no—
373C2×D4—181no—
374C2×D4—181no—
375C2×D4—362no—
376C2×D4—362no—
377C22×C4—21no—
378C22×C4—31no—
379C22×C4—61no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382C2×C8—61no—
383C2×C8—181no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—31no—
387C4⋊C4—91no—
388C4⋊C4—181no—
389C22⋊C4—61no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—122no—
393C22⋊C4—181no—
394C22⋊C4—181no—
395C22⋊C4—181no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—62no—
406C22×C3—122no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3—241no—
413C22×C3D3×D811yescharacteristic
414C22×C3#91111yescharacteristic
415C22×C3C2×#21311yescharacteristic
416C22×C3#93711yescharacteristic
417C22×C3#93711yescharacteristic
418C22×C3#94911yescharacteristic
419C2×D3—22no—
420C2×D3—41no—
421C2×D3—41no—
422C2×D3—42no—
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—81no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—241no—
434C2×D3—241no—
435C2×D3—241no—
436C2×D3—244no—
437C2×D3—244no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—41no—
444C3×C4—82no—
445C3×C4—81no—
446C3×C4—81no—
447C3×C4—121no—
448C3×C4—121no—
449C3×C4—241no—
450Dic3—41no—
451Dic3—41no—
452Dic3—81no—
453Dic3—121no—
454Dic3—121no—
455Dic3—241no—
456C32#160711yescharacteristic, complemented, Sylow
457C23—32no—
458C23—61no—
459C23—61no—
460C23—61no—
461C23—121no—
462C23—121no—
463C23—181no—
464C23—362no—
465C23—721no—
466C23—721no—
467C23D3×#6711yescharacteristic
468D4—121no—
469D4—121no—
470D4—121no—
471D4—361no—
472D4—362no—
473D4—362no—
474D4—361no—
475D4—361no—
476D4—721no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4D3×#6711yescharacteristic
490C2×C4#381111yescharacteristic
491C8—121no—
492C8—361no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3—122no—
503C2×C3—241no—
504C2×C3#503611yescharacteristic
505C2×C3#505311yescharacteristic
506C2×C3#505311yescharacteristic
507C2×C3#506111yescharacteristic
508C2×C3#515611yescharacteristic
509C2×C3#520211yescharacteristic
510D3—42no—
511D3—81no—
512D3—241no—
513D3—241no—
514D3—481no—
515C22—21no—
516C22—21no—
517C22—62no—
518C22—122no—
519C22—121no—
520C22—121no—
521C22—121no—
522C22—121no—
523C22—121no—
524C22—241no—
525C22—361no—
526C22—361no—
527C22—361no—
528C22—724no—
529C22D3×#21311yescharacteristic
530C22#6392511yescharacteristic
531C22#6398311yescharacteristic
532C4—21no—
533C4—21no—
534C4—81no—
535C4—121no—
536C4—121no—
537C4—241no—
538C4—361no—
539C3—21no—
540C3#6970811yescharacteristic, complemented
541C3#7116411yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—122no—
545C2—241no—
546C2—721no—
547C2#1059139811yescharacteristic
548C2#1059151511yescharacteristic
549C2#1059165911yescharacteristic
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#1607
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. #10592666C2semidirect
3. C3×#4992C2semidirect
4. C3×#4967C2semidirect
5. #10589151C2semidirect
6. #10589149C2semidirect
7. #10589145C2semidirect
11. C2×C32×C4⋊C4C22semidirect
21. #63657C22semidirect
25. C3×C3⋊#95C22semidirect
26. C3×#830C22semidirect
33. #4992D3semidirect
37. #4967D3semidirect
79. C2×C3×C4⋊C4C2×D3semidirect
80. C2×C3×C4⋊C4C2×D3semidirect
105. C3⋊#95C2×D3semidirect
109. #830C2×D3semidirect
262. C2×C4⋊C4D32semidirect
456. C32#1607semidirect
540. C3#69708semidirect
541. C3#71164semidirect

Maximal subgroups

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

subgroupindex
#105950722
#105926662
C3×#49922
C3×#49672
#105891512
#105891492
#105891452
#711643
#697083