Finite Group Databasebeta

← #11778642

Subgroups — #11778642

Order 1152.

516 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 84 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×#5644C211yesmaximal, characteristic
2#10592742C211yesmaximal, characteristic, complemented
3#10591315C211yesmaximal, characteristic, complemented
4#10591094C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71882—31nomaximal
9#68321—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#947—21no—
13C3×#930C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C2211yescharacteristic
15C3×#898—21no—
16C3×#895—21no—
17C3×#894—21no—
18C3×#882—21no—
19C3×#67⋊C4—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63662—21no—
22#63657C2211yescharacteristic
23#63635—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27#63575—21no—
28#63563—21no—
29C3×#538—31no—
30#5644D311yescharacteristic
31#5043—31no—
32#5043—31no—
33#5043—61no—
34#5033—31no—
35#4953—31no—
36#4736—31no—
37#4674—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4537—31no—
41#4525—31no—
42#4468—31no—
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12D411yescharacteristic
54C2×C3×C4×D3—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×C4⋊Dic3D411yescharacteristic
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71(C2×D3)⋊Dic3—42no—
72#1612—91noSylow
73C3×#126—61no—
74C3×#124—61no—
75C3×#123—61no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8C2×D311yescharacteristic
78C3×C22⋊Q8C2×D311yescharacteristic
79C3×#121—31no—
80C3×#121—61no—
81C3×#120—61no—
82C3×C4×D4—61no—
83C2×C3×C22⋊C4—31no—
84C2×#217—61no—
85#947—21no—
86#930C2×D311yescharacteristic
87C2×(C2×D3)⋊C4—61no—
88C2×(C2×D3)⋊C4C2×D311yescharacteristic
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92#898—21no—
93#895—21no—
94#894—21no—
95#882—21no—
96#67⋊C4—21no—
97C3×C22⋊C8—31no—
98C3×#95—31no—
99#835—62no—
100#835—61no—
101#835—61no—
102#832—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#821—61no—
111#818—61no—
112#808—62no—
113#808—61no—
114#808—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—
123C32×Q8—41no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C3×#67—41no—
133C3×#67—41no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C3×D12—41no—
141C3×D12—81no—
142C3×D12—81no—
143C3×C4×D3—81no—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—41no—
146#538—31no—
147#483—91no—
148#480—91no—
149#397—91no—
150#328—31no—
151#327—91no—
152#323—91no—
153C24×C3—31no—
154C23×D3#6711yescharacteristic
155C2×C3×Q8—21no—
156C2×C3×Q8D1211yescharacteristic
157C2×C3×Q8#6711yescharacteristic
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—21no—
169C22×Dic3—21no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—121no—
173C22×Dic3#6711yescharacteristic
174C2×D12—21no—
175C2×D12—21no—
176C2×D12#6711yescharacteristic
177C2×C4×D3—21no—
178C2×C3×C8—61no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—41no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4D1211yescharacteristic
186C3×C4⋊C4#6711yescharacteristic
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C42—61no—
197#217—122no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—122no—
205C4⋊Dic3—62no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—121no—
211C4⋊Dic3#6711yescharacteristic
212Dic3⋊C4—21no—
213C4×Dic3—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—62no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—61no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32#12011yescharacteristic
221C22×C32#13511yescharacteristic
222C22×C32AGL(1,ℤ/8)11yescharacteristic
223C2×C3×D3—42no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C2×C3×D3—41no—
230C2×C3×D3—81no—
231C32×C4—21no—
232C32×C4—21no—
233C32×C4—41no—
234C32×C4—41no—
235C3⋊Dic3—81no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C3×Dic3—81no—
239#126—61no—
240#124—61no—
241#123—61no—
242C22⋊Q8D3211yescharacteristic
243#121—31no—
244#121—61no—
245#120—61no—
246C4×D4—61no—
247C2×C4⋊C4—91no—
248C2×C22⋊C4—31no—
249C2×C22⋊C4—181no—
250#107—181no—
251#106—181no—
252#103—181no—
253#102—181no—
254C22⋊C8—31no—
255C22⋊C8—91no—
256#95—31no—
257#95—181no—
258C23×C3—21no—
259C23×C3—61no—
260C23×C3—61no—
261C23×C3—61no—
262C23×C3—61no—
263C23×C3—121no—
264C23×C3—121no—
265C23×C3D3×D411yescharacteristic
266C23×C3C2×#6711yescharacteristic
267C22×D3—21no—
268C22×D3—21no—
269C22×D3—21no—
270C22×D3—21no—
271C22×D3—41no—
272C22×D3—41no—
273C3×Q8—41no—
274C3×Q8—41no—
275C3×Q8—42no—
276C3×D4—121no—
277C3×D4—121no—
278C3×D4—121no—
279C3×D4—241no—
280C3×D4—241no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—42no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—241no—
299C2×C3×C4C2×D1211yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303#67—41no—
304#67—41no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—122no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—241no—
319C2×Dic3—241no—
320D12—41no—
321D12—81no—
322D12—81no—
323C4×D3—81no—
324C3×C8—121no—
325C3⋊C8—41no—
326C3⋊C8—122no—
327C3⋊C8—121no—
328C3⋊C8—121no—
329C2×C32—21no—
330C2×C32—21no—
331C2×C32#44911yescharacteristic
332C2×C32#45511yescharacteristic
333C2×C32#45811yescharacteristic
334C3×D3—81no—
335C3×D3—81no—
336C24—31no—
337C2×Q8#62611yescharacteristic
338C2×D4—31no—
339C2×D4—61no—
340C2×D4—61no—
341C2×D4—61no—
342C22×C4—31no—
343C22×C4—61no—
344C22×C4—61no—
345C22×C4—181no—
346C22×C4C2×D3211yescharacteristic
347C2×C8—61no—
348C2×C8—181no—
349C4⋊C4—21no—
350C4⋊C4—31no—
351C4⋊C4—61no—
352C4⋊C4—181no—
353C4⋊C4—181no—
354C4⋊C4#62611yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—61no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C22⋊C4—61no—
362C22⋊C4—362no—
363C42—61no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—122no—
374C22×C3—121no—
375C22×C3—121no—
376C22×C3—121no—
377C22×C3—121no—
378C22×C3—121no—
379C22×C3—121no—
380C22×C3—241no—
381C22×C3#88211yescharacteristic
382C22×C3#91411yescharacteristic
383C22×C3#91911yescharacteristic
384C22×C3#94911yescharacteristic
385C22×C3#95011yescharacteristic
386C22×C3#95311yescharacteristic
387C2×D3—42no—
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—41no—
391C2×D3—41no—
392C2×D3—41no—
393C2×D3—41no—
394C2×D3—81no—
395C3×C4—22no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—41no—
405C3×C4—81no—
406C3×C4—81no—
407C3×C4—121no—
408C3×C4—121no—
409C3×C4—241no—
410Dic3—41no—
411Dic3—41no—
412Dic3—81no—
413Dic3—242no—
414Dic3—241no—
415Dic3—241no—
416C32#161211yescharacteristic, complemented, Sylow
417C23—61no—
418C23—61no—
419C23—61no—
420C23—61no—
421C23—121no—
422C23—121no—
423C23D3×#6711yescharacteristic
424Q8—41no—
425D4—121no—
426D4—121no—
427D4—121no—
428D4—241no—
429D4—241no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—41no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4—121no—
438C2×C4—121no—
439C2×C4—241no—
440C2×C4—361no—
441C2×C4—361no—
442C2×C4—361no—
443C2×C4C2×#62611yescharacteristic
444C2×C4D3×#6711yescharacteristic
445C8—121no—
446C8—361no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—41no—
455C2×C3—41no—
456C2×C3—241no—
457C2×C3—241no—
458C2×C3#474211yescharacteristic
459C2×C3#481011yescharacteristic
460C2×C3#482511yescharacteristic
461C2×C3#523811yescharacteristic
462C2×C3#524211yescharacteristic
463C2×C3#524311yescharacteristic
464D3—81no—
465D3—81no—
466C22—21no—
467C22—21no—
468C22—122no—
469C22—121no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22—121no—
475C22—241no—
476C22#6393911yescharacteristic
477C22#6394911yescharacteristic
478C22#6397711yescharacteristic
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—121no—
484C4—121no—
485C4—241no—
486C4—721no—
487C3—21no—
488C3#6832111yescharacteristic, complemented
489C3#7188211yescharacteristic, complemented
490C2—21no—
491C2—21no—
492C2—241no—
493C2—241no—
494C2#1059153411yescharacteristic
495C2#1059158811yescharacteristic
496C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC3×#5644C2
hypercenterC22⋊Q8D32
hypocenterC32#1612
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592742C2semidirect
3. #10591315C2semidirect
4. #10591094C2semidirect
5. C3×#4538C2semidirect
6. #10589149C2semidirect
7. #10589145C2semidirect
39. #4538D3semidirect
416. C32#1612semidirect
488. C3#68321semidirect
489. C3#71882semidirect

Maximal subgroups

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

subgroupindex
C3×#56442
#105927422
#105913152
#105910942
C3×#45382
#105891492
#105891452
#718823
#683213