Finite Group Databasebeta

← #11778445

Subgroups — #11778445

Order 1152.

617 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 617 conjugacy classes of subgroups — too many to draw. Only its 88 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×#5605C211yesmaximal, characteristic
2#10592732C211yesmaximal, characteristic, complemented
3#10591315C211yesmaximal, characteristic, complemented
4#10591094C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71843—31nomaximal
9#68288—31nomaximal
10C2×C3×D3×D4—21no—
11C32×#121C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
13C3×#939—21no—
14C3×#937—21no—
15C3×#930C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4C2211yescharacteristic
17C3×#894—21no—
18C3×#883—21no—
19C3×#882—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63659—21no—
22#63657C2211yescharacteristic, complemented
23#63634—21no—
24C3×C3⋊#95C2211yescharacteristic, complemented
25C3×#830C2211yescharacteristic, complemented
26#63579—21no—
27#63575—21no—
28#63563—21no—
29C3×#534—31no—
30#5605D311yescharacteristic
31#5033—31no—
32#5033—31no—
33#5033—31no—
34#5033—61no—
35#4953—31no—
36#4736—31no—
37#4674—31no—
38C3×#327—31no—
39#4537—31no—
40#4537D311yescharacteristic, complemented
41#4525—31no—
42#4468—31no—
43#4451—31no—
44C23×C3×D3—21no—
45C23×C3×D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4D411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C3×D3×D4—42no—
56C3×D3×D4—42no—
57C2×C3×D12—21no—
58C2×C3×D12D411yescharacteristic
59C2×C3×C4×D3—21no—
60C32×C4⋊C4D411yescharacteristic
61C32×C22⋊C4—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×#217—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×C4⋊Dic3D411yescharacteristic
71C3×Dic3⋊C4—21no—
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—42no—
74#1607—91noSylow
75C22×C3×D4—61no—
76C2×D3×D4—21no—
77C3×#123—61no—
78C3×#123—61no—
79C3×#121—21no—
80C3×#121—31no—
81C3×#121—61no—
82C3×#121C2×D311yescharacteristic
83C3×#121C2×D311yescharacteristic
84C3×#120—61no—
85C3×#120—61no—
86C2×C3×C22⋊C4—31no—
87C2×#217—61no—
88#939—21no—
89#937—21no—
90#930C2×D311yescharacteristic
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4C2×D311yescharacteristic
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—61no—
96#894—21no—
97#883—21no—
98#882—21no—
99C3×C22⋊C8—31no—
100C3×#95—31no—
101#832—61no—
102#832—62no—
103#832—61no—
104#832—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107C3⋊#95C2×D311yescharacteristic, complemented
108#830—31no—
109#830—31no—
110#830—61no—
111#830C2×D311yescharacteristic, complemented
112#821—61no—
113#818—61no—
114#807—61no—
115#807—62no—
116#807—61no—
117#807—61no—
118C23×C32—21no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—42no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—81no—
127C22×C3×D3—81no—
128C22×C3×D3D812yes—
129C32×D4—41no—
130C32×D4—41no—
131C32×D4—41no—
132C2×C32×C4—21no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C3×#67—42no—
140C3×#67—41no—
141C3×#67—41no—
142C3×#67—81no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×D12—41no—
150C3×D12—42no—
151C3×C4×D3—42no—
152C3⋊(C3⋊C8)—41no—
153C3×C3⋊C8—41no—
154#534—31no—
155#480—91no—
156#480—91no—
157#397—91no—
158#327—31no—
159#327—91no—
160#323—91no—
161C24×C3—31no—
162C24×C3—61no—
163C23×D3—21no—
164C23×D3#6711yescharacteristic
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—31no—
169C2×C3×D4—41no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—122no—
175C2×C3×D4—122no—
176C2×C3×D4D1211yescharacteristic
177C2×C3×D4#6711yescharacteristic
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—21no—
185C2×#67—21no—
186C2×#67—21no—
187C22×Dic3—21no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—121no—
191C22×Dic3#6711yescharacteristic
192D3×D4—42no—
193D3×D4—42no—
194C2×D12—21no—
195C2×D12#6711yescharacteristic
196C2×C4×D3—21no—
197C2×C3×C8—61no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—31no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4D1211yescharacteristic
202C3×C4⋊C4#6711yescharacteristic
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—41no—
206C3×C22⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—61no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211#217—21no—
212#217—122no—
213(C2×D3)⋊C4—21no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—122no—
218C4⋊Dic3—62no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—121no—
224C4⋊Dic3#6711yescharacteristic
225Dic3⋊C4—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32—41no—
235C22×C32#12011yescharacteristic
236C22×C32C2×D811yescharacteristic
237C22×C32AGL(1,ℤ/8)11yescharacteristic
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—
246C2×C3×D3—84no—
247C32×C4—21no—
248C32×C4—21no—
249C32×C4—41no—
250C3⋊Dic3—81no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—81no—
254C22×D4—61no—
255#123—61no—
256#123—61no—
257#121—31no—
258#121—61no—
259#121D3211yescharacteristic
260#120—61no—
261#120—61no—
262C2×C4⋊C4—91no—
263C2×C22⋊C4—31no—
264C2×C22⋊C4—181no—
265#107—181no—
266#107—181no—
267#102—181no—
268#102—181no—
269C22⋊C8—31no—
270C22⋊C8—91no—
271#95—31no—
272#95—181no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—32no—
277C23×C3—41no—
278C23×C3—61no—
279C23×C3—61no—
280C23×C3—61no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3—122no—
284C23×C3—241no—
285C23×C3—241no—
286C23×C3D3×D411yescharacteristic
287C23×C3C2×#6711yescharacteristic
288C22×D3—21no—
289C22×D3—21no—
290C22×D3—21no—
291C22×D3—42no—
292C22×D3—41no—
293C22×D3—41no—
294C22×D3—81no—
295C22×D3—81no—
296C22×D3#21312yes—
297C3×D4—41no—
298C3×D4—41no—
299C3×D4—42no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—41no—
304C3×D4—81no—
305C3×D4—81no—
306C3×D4—121no—
307C3×D4—122no—
308C3×D4—122no—
309C3×D4—121no—
310C3×D4—121no—
311C3×D4—241no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—42no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—122no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331#67—42no—
332#67—41no—
333#67—41no—
334#67—81no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—122no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—121no—
348C2×Dic3—241no—
349C2×Dic3—241no—
350D12—41no—
351D12—42no—
352C4×D3—42no—
353C3×C8—121no—
354C3⋊C8—41no—
355C3⋊C8—122no—
356C3⋊C8—121no—
357C3⋊C8—121no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—81no—
361C2×C32#44711yescharacteristic
362C2×C32#45511yescharacteristic
363C2×C32#45811yescharacteristic
364C3×D3—42no—
365C3×D3—81no—
366C24—31no—
367C24—61no—
368C2×D4—21no—
369C2×D4—31no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—122no—
375C2×D4—122no—
376C2×D4#62611yescharacteristic
377C22×C4—31no—
378C22×C4—61no—
379C22×C4—61no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382C2×C8—61no—
383C2×C8—181no—
384C4⋊C4—31no—
385C4⋊C4—61no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4#62611yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—61no—
395C22⋊C4—362no—
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—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—62no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—81no—
415C22×C3—122no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3—241no—
422C22×C3—244no—
423C22×C3#88211yescharacteristic
424C22×C3D3×D811yescharacteristic
425C22×C3#91411yescharacteristic
426C22×C3C2×#21311yescharacteristic
427C22×C3#93211yescharacteristic
428C22×C3#95311yescharacteristic
429C2×D3—22no—
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—42no—
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C2×D3—81no—
437C2×D3—84no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—81no—
447C3×C4—121no—
448C3×C4—121no—
449C3×C4—241no—
450Dic3—41no—
451Dic3—41no—
452Dic3—81no—
453Dic3—242no—
454Dic3—241no—
455Dic3—241no—
456C32#160711yescharacteristic, complemented, Sylow
457C23—21no—
458C23—32no—
459C23—61no—
460C23—61no—
461C23—61no—
462C23—121no—
463C23—121no—
464C23—122no—
465C23—241no—
466C23—241no—
467C23D3×#6711yescharacteristic
468D4—41no—
469D4—41no—
470D4—41no—
471D4—121no—
472D4—122no—
473D4—122no—
474D4—121no—
475D4—121no—
476D4—241no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—122no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—361no—
487C2×C4—361no—
488C2×C4—361no—
489C2×C4C2×#62611yescharacteristic
490C2×C4D3×#6711yescharacteristic
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—81no—
503C2×C3—81no—
504C2×C3—122no—
505C2×C3—161no—
506C2×C3—241no—
507C2×C3#474211yescharacteristic
508C2×C3#477311yescharacteristic
509C2×C3#482511yescharacteristic
510C2×C3#521711yescharacteristic
511C2×C3#524211yescharacteristic
512C2×C3#524311yescharacteristic
513D3—42no—
514D3—81no—
515C22—21no—
516C22—21no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—62no—
521C22—122no—
522C22—121no—
523C22—121no—
524C22—121no—
525C22—121no—
526C22—121no—
527C22—241no—
528C22—244no—
529C22D3×#21311yescharacteristic
530C22#6393411yescharacteristic
531C22#6397711yescharacteristic
532C4—21no—
533C4—21no—
534C4—41no—
535C4—121no—
536C4—121no—
537C4—241no—
538C4—721no—
539C3—21no—
540C3#6828811yescharacteristic, complemented
541C3#7184311yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—81no—
545C2—122no—
546C2—241no—
547C2#1059144811yescharacteristic
548C2#1059153411yescharacteristic
549C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radicalC3×#5605C2
hypercenter#121D32
hypocenterC32#1607
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
2. #10592732C2semidirect
3. #10591315C2semidirect
4. #10591094C2semidirect
5. C3×#4537C2semidirect
6. #10589149C2semidirect
7. #10589145C2semidirect
12. C2×C4⋊(C3⋊Dic3)C22semidirect
22. #63657C22semidirect
24. C3×C3⋊#95C22semidirect
25. C3×#830C22semidirect
40. #4537D3semidirect
107. C3⋊#95C2×D3semidirect
111. #830C2×D3semidirect
456. C32#1607semidirect
540. C3#68288semidirect
541. C3#71843semidirect

Maximal subgroups

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

subgroupindex
C3×#56052
#105927322
#105913152
#105910942
C3×#45372
#105891492
#105891452
#718433
#682883