Finite Group Databasebeta

← #11778454

Subgroups — #11778454

Order 1152.

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

normal subgroups only

This group has 605 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
2C3×#4674C211yesmaximal, characteristic, complemented
3#10591133C211yesmaximal, characteristic, complemented
4#10591089C211yesmaximal, characteristic, complemented
5#10589317C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#69708—31nomaximal
9#68288—31nomaximal
10C2×D3×#67—21no—
11#64139C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4—21no—
14C2×C3×(C2×D3)⋊C4C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
16#63978—21no—
17#63923—21no—
18#63922—21no—
19#63891—21no—
20#63890—21no—
21C32×#95C2211yescharacteristic, complemented
22#63657C2211yescharacteristic, complemented
23C3×C3⋊#95—21no—
24C3×#830C2211yescharacteristic, complemented
25#63576—21no—
26#63575—21no—
27#63564—21no—
28#63562—21no—
29#5605—31no—
30#5493—31no—
31C3×#397—31no—
32#5033—31no—
33#4967—31no—
34#4967—31no—
35#4736—31no—
36#4674D311yescharacteristic, complemented
37C3×#327—31no—
38#4525—31no—
39#4468—31no—
40#4451—31no—
41#4451—31no—
42#4451—61no—
43#4451D311yescharacteristic, complemented
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—
60#3752—21no—
61C4⋊(C3⋊Dic3)D411yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—42no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
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—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—61no—
81#939—61no—
82#937—61no—
83#930—31no—
84#930—31no—
85#930—61no—
86#930—61no—
87#930C2×D311yescharacteristic
88C2×(C2×D3)⋊C4—21no—
89C2×(C2×D3)⋊C4C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic, complemented
91#894—61no—
92#886—61no—
93#886—61no—
94#883—61no—
95#882—61no—
96#882—61no—
97#882—61no—
98C3×C22⋊C8—31no—
99C3×#95—21no—
100C3×#95—61no—
101C3×#95C2×D311yescharacteristic, complemented
102C3×#95C2×D311yescharacteristic, complemented
103#832—61no—
104C3⋊#95—21no—
105#830—31no—
106#830—31no—
107#830—61no—
108#830C2×D311yescharacteristic, complemented
109#821—61no—
110#818—61no—
111#809—61no—
112#809—61no—
113#807—61no—
114#807—61no—
115#807—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3D812yes—
124C2×D32—42no—
125C2×D32—81no—
126C2×D32—81no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133#638—41no—
134#638—41no—
135C2×C3⋊Dic3—21no—
136C4⋊(C3⋊D3)—41no—
137C3×#67—41no—
138C3×#67—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C3×D12—41no—
146#626—42no—
147#626—81no—
148#625—42no—
149D3×Dic3—42no—
150C3⋊(C3⋊C8)—41no—
151C3×C3⋊C8—41no—
152#534—91no—
153#480—91no—
154#480—91no—
155#397—31no—
156#327—31no—
157#327—91no—
158#323—91no—
159C24×C3—31no—
160C23×D3—61no—
161C23×D3—61no—
162C23×D3#6711yescharacteristic
163C2×C3×D4—31no—
164C2×C3×D4—61no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—41no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C2×#67—21no—
174C2×#67—61no—
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—61no—
180C2×#67—121no—
181C2×#67—122no—
182C2×#67—122no—
183C22×Dic3—21no—
184C22×Dic3—61no—
185C22×Dic3#6711yescharacteristic
186D3×D4—122no—
187D3×D4—122no—
188C2×D12—31no—
189C2×D12—31no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12D1211yescharacteristic
194C2×C4×D3—61no—
195C2×C3×C8—61no—
196C3×C4⋊C4—31no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—122no—
203#217—61no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—42no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—121no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—31no—
217C4⋊Dic3—31no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3D1211yescharacteristic
221Dic3⋊C4—61no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32#12011yescharacteristic
229C22×C32C2×D811yescharacteristic
230C22×C32AGL(1,ℤ/8)11yescharacteristic
231C2×C3⋊D3—41no—
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C2×C3×D3—22no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C2×C3×D3—42no—
238C2×C3×D3—41no—
239C2×C3×D3—41no—
240C2×C3×D3—41no—
241C2×C3×D3—81no—
242D32—84no—
243C32×C4—21no—
244C32×C4—21no—
245C32×C4—81no—
246C3⋊Dic3—41no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C3×Dic3—81no—
250C22×D4—181no—
251#123—181no—
252#123—181no—
253#121—31no—
254#121—91no—
255#121—181no—
256#120—181no—
257#120—181no—
258C2×C4⋊C4—31no—
259C2×C22⋊C4—31no—
260C2×C22⋊C4—61no—
261#107—181no—
262#107—181no—
263#102—181no—
264#102—181no—
265C22⋊C8—31no—
266C22⋊C8—91no—
267#95—61no—
268#95D3211yescharacteristic, complemented
269C23×C3—21no—
270C23×C3—32no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3—61no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3D3×D411yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C22×D3—21no—
279C22×D3—21no—
280C22×D3—21no—
281C22×D3—41no—
282C22×D3—41no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—121no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—241no—
289C22×D3—241no—
290C22×D3—241no—
291C22×D3—241no—
292C22×D3#21312yes—
293C3×D4—121no—
294C3×D4—121no—
295C3×D4—121no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—42no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—81no—
310C2×C3×C4—81no—
311C2×C3×C4—81no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4C2×D1211yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320#67—41no—
321#67—41no—
322#67—122no—
323#67—122no—
324#67—122no—
325#67—121no—
326#67—121no—
327#67—121no—
328#67—121no—
329#67—241no—
330#67—241no—
331#67—241no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—121no—
341C2×Dic3—122no—
342D12—41no—
343D12—121no—
344D12—121no—
345D12—122no—
346D12—241no—
347D12—241no—
348C4×D3—122no—
349C3×C8—121no—
350C3⋊C8—41no—
351C3⋊C8—121no—
352C3⋊C8—121no—
353C3⋊C8—241no—
354C2×C32—21no—
355C2×C32—21no—
356C2×C32#44711yescharacteristic
357C2×C32#45511yescharacteristic
358C2×C32#45811yescharacteristic
359C3⋊D3—81no—
360C3×D3—42no—
361C3×D3—81no—
362C24—31no—
363C24—181no—
364C2×D4—31no—
365C2×D4—61no—
366C2×D4—91no—
367C2×D4—181no—
368C2×D4—181no—
369C2×D4—181no—
370C2×D4—181no—
371C2×D4—362no—
372C2×D4—362no—
373C22×C4—21no—
374C22×C4—31no—
375C22×C4—61no—
376C22×C4—181no—
377C22×C4C2×D3211yescharacteristic
378C2×C8—61no—
379C2×C8—181no—
380C4⋊C4—31no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4—91no—
384C4⋊C4—181no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—122no—
389C22⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—62no—
402C22×C3—122no—
403C22×C3—121no—
404C22×C3—121no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—241no—
409C22×C3#88211yescharacteristic
410C22×C3D3×D811yescharacteristic
411C22×C3#91411yescharacteristic
412C22×C3C2×#21311yescharacteristic
413C22×C3#93711yescharacteristic
414C22×C3#94911yescharacteristic
415C2×D3—22no—
416C2×D3—41no—
417C2×D3—41no—
418C2×D3—42no—
419C2×D3—41no—
420C2×D3—41no—
421C2×D3—41no—
422C2×D3—81no—
423C2×D3—121no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—241no—
430C2×D3—241no—
431C2×D3—241no—
432C2×D3—244no—
433C2×D3—244no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—81no—
441C3×C4—81no—
442C3×C4—82no—
443C3×C4—121no—
444C3×C4—121no—
445C3×C4—241no—
446Dic3—41no—
447Dic3—41no—
448Dic3—81no—
449Dic3—121no—
450Dic3—121no—
451Dic3—241no—
452C32#160711yescharacteristic, complemented, Sylow
453C23—32no—
454C23—61no—
455C23—61no—
456C23—61no—
457C23—121no—
458C23—121no—
459C23—181no—
460C23—362no—
461C23—721no—
462C23—721no—
463C23D3×#6711yescharacteristic
464D4—121no—
465D4—121no—
466D4—121no—
467D4—361no—
468D4—362no—
469D4—362no—
470D4—361no—
471D4—361no—
472D4—721no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—181no—
484C2×C4—362no—
485C2×C4D3×D1211yescharacteristic
486C2×C4#380211yescharacteristic
487C8—121no—
488C8—361no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—41no—
497C2×C3—41no—
498C2×C3—122no—
499C2×C3—241no—
500C2×C3#474211yescharacteristic
501C2×C3#477311yescharacteristic
502C2×C3#482511yescharacteristic
503C2×C3#503611yescharacteristic
504C2×C3#505311yescharacteristic
505C2×C3#506111yescharacteristic
506D3—42no—
507D3—81no—
508D3—241no—
509D3—241no—
510D3—481no—
511C22—21no—
512C22—21no—
513C22—62no—
514C22—122no—
515C22—121no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22—121no—
520C22—241no—
521C22—361no—
522C22—361no—
523C22—361no—
524C22—724no—
525C22#6392211yescharacteristic
526C22D3×#21311yescharacteristic
527C22#6393911yescharacteristic
528C4—21no—
529C4—21no—
530C4—81no—
531C4—121no—
532C4—121no—
533C4—241no—
534C4—361no—
535C3—21no—
536C3#6828811yescharacteristic, complemented
537C3#6970811yescharacteristic, complemented
538C2—21no—
539C2—21no—
540C2—122no—
541C2—241no—
542C2—721no—
543C2#1059039611yescharacteristic
544C2#1059040811yescharacteristic
545C2#1059059511yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#10595072C2
hypercenter#95D32
hypocenterC32#1607
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#4674C2semidirect
3. #10591133C2semidirect
4. #10591089C2semidirect
5. #10589317C2semidirect
6. C3×#4451C2semidirect
7. #10589145C2semidirect
15. C2×C3×C4⋊Dic3C22semidirect
21. C32×#95C22semidirect
22. #63657C22semidirect
24. C3×#830C22semidirect
36. #4674D3semidirect
43. #4451D3semidirect
90. C2×C4⋊Dic3C2×D3semidirect
101. C3×#95C2×D3semidirect
102. C3×#95C2×D3semidirect
108. #830C2×D3semidirect
268. #95D32semidirect
452. C32#1607semidirect
536. C3#68288semidirect
537. C3#69708semidirect

Maximal subgroups

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

subgroupindex
#105950722
C3×#46742
#105911332
#105910892
#105893172
C3×#44512
#105891452
#697083
#682883