Finite Group Databasebeta

← #11778644

Subgroups — #11778644

Order 1152.

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

normal subgroups only

This group has 504 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
2C3×#5043C211yesmaximal, characteristic, complemented
3#10591314C211yesmaximal, characteristic, complemented
4#10591089C211yesmaximal, characteristic, complemented
5#10589404C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71882—31nomaximal
9#71173—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C3×#947—21no—
12C3×#930C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C3×#898—21no—
16C3×#895—21no—
17C3×#894—21no—
18C3×#882—21no—
19C3×#67⋊C4—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63658C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×#835—21no—
24C3×#830C2211yescharacteristic
25C3×#808—21no—
26#63579—21no—
27#63576—21no—
28#63562—21no—
29C3×#538—31no—
30#5644D311yescharacteristic
31C3×#483—31no—
32#5043D311yescharacteristic, complemented
33#5033—31no—
34#4992—31no—
35#4967—31no—
36#4953—31no—
37#4538—31no—
38#4538—31no—
39#4538—61no—
40#4537—31no—
41#4525—31no—
42#4470—31no—
43#4468—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—
58C2×C3⋊(C3⋊C8)—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—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×C4⋊C4—31no—
84C2×C3×C22⋊C4—31no—
85C2×#217—61no—
86#947—21no—
87#930C2×D311yescharacteristic
88C2×(C2×D3)⋊C4—61no—
89C2×(C2×D3)⋊C4C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91#898—21no—
92#895—21no—
93#894—21no—
94#882—21no—
95#67⋊C4—21no—
96C3×#106—61no—
97C3×#103—61no—
98C3×C22⋊C8—31no—
99#835—21no—
100#832—61no—
101C3⋊#95—31no—
102C3⋊#95—31no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#809—61no—
111#808—21no—
112#807—61no—
113#807—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C32×Q8—41no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C3×#67—41no—
131C3×#67—41no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C3×D12—41no—
139C3×D12—81no—
140C3×D12—81no—
141C3×C4×D3—81no—
142C3⋊(C3⋊C8)—41no—
143C3×C3⋊C8—41no—
144#538—31no—
145#483—31no—
146#480—91no—
147#397—91no—
148#328—91no—
149#327—91no—
150#323—91no—
151C24×C3—31no—
152C23×D3#6711yescharacteristic
153C2×C3×Q8—21no—
154C2×C3×Q8#6711yescharacteristic
155C2×C3×Q8#6711yescharacteristic
156C2×C3×D4—31no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C2×#67—21no—
167C22×Dic3—21no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—121no—
171C22×Dic3#6711yescharacteristic
172C2×D12—21no—
173C2×D12—21no—
174C2×D12#6711yescharacteristic
175C2×C4×D3—21no—
176C2×C3×C8—61no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—31no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4#6711yescharacteristic
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—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3#6711yescharacteristic
208Dic3⋊C4—21no—
209C4×Dic3—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—121no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32#12011yescharacteristic
217C22×C32#13511yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C2×C3×D3—42no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—81no—
227C32×C4—21no—
228C32×C4—21no—
229C32×C4—41no—
230C32×C4—41no—
231C3⋊Dic3—81no—
232C3×Dic3—41no—
233C3×Dic3—41no—
234C3×Dic3—81no—
235#126—61no—
236#124—61no—
237#123—61no—
238C22⋊Q8D3211yescharacteristic
239#121—31no—
240#121—61no—
241#120—61no—
242C4×D4—61no—
243C2×C4⋊C4—31no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—181no—
246#107—181no—
247#106—61no—
248#103—61no—
249#102—181no—
250C22⋊C8—31no—
251C22⋊C8—91no—
252#95—91no—
253#95—181no—
254C23×C3—21no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—61no—
258C23×C3—61no—
259C23×C3—121no—
260C23×C3—121no—
261C23×C3D3×D411yescharacteristic
262C23×C3C2×#6711yescharacteristic
263C22×D3—21no—
264C22×D3—21no—
265C22×D3—21no—
266C22×D3—21no—
267C22×D3—41no—
268C22×D3—41no—
269C3×Q8—41no—
270C3×Q8—41no—
271C3×Q8—81no—
272C3×D4—121no—
273C3×D4—121no—
274C3×D4—121no—
275C3×D4—241no—
276C3×D4—241no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—81no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4—241no—
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299#67—41no—
300#67—41no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—121no—
311C2×Dic3—122no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—241no—
315C2×Dic3—241no—
316D12—41no—
317D12—81no—
318D12—81no—
319C4×D3—81no—
320C3×C8—121no—
321C3⋊C8—41no—
322C3⋊C8—121no—
323C3⋊C8—121no—
324C3⋊C8—241no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32#44911yescharacteristic
328C2×C32#45511yescharacteristic
329C2×C32#45811yescharacteristic
330C3×D3—81no—
331C3×D3—81no—
332C24—31no—
333C2×Q8#62511yescharacteristic
334C2×D4—31no—
335C2×D4—61no—
336C2×D4—61no—
337C2×D4—61no—
338C22×C4—31no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—181no—
342C22×C4C2×D3211yescharacteristic
343C2×C8—61no—
344C2×C8—181no—
345C4⋊C4—21no—
346C4⋊C4—31no—
347C4⋊C4—61no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4#62511yescharacteristic
351C22⋊C4—21no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—61no—
357C22⋊C4—61no—
358C22⋊C4—362no—
359C42—61no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—122no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3—121no—
373C22×C3—121no—
374C22×C3—121no—
375C22×C3—121no—
376C22×C3—241no—
377C22×C3#91411yescharacteristic
378C22×C3#91611yescharacteristic
379C22×C3#93711yescharacteristic
380C22×C3#94911yescharacteristic
381C22×C3#95011yescharacteristic
382C22×C3#95311yescharacteristic
383C2×D3—42no—
384C2×D3—41no—
385C2×D3—41no—
386C2×D3—41no—
387C2×D3—41no—
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—81no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—41no—
401C3×C4—81no—
402C3×C4—81no—
403C3×C4—121no—
404C3×C4—121no—
405C3×C4—241no—
406Dic3—41no—
407Dic3—41no—
408Dic3—81no—
409Dic3—241no—
410Dic3—241no—
411Dic3—242no—
412C32#161211yescharacteristic, complemented, Sylow
413C23—61no—
414C23—61no—
415C23—61no—
416C23—61no—
417C23—121no—
418C23—121no—
419C23D3×#6711yescharacteristic
420Q8—41no—
421D4—121no—
422D4—121no—
423D4—121no—
424D4—241no—
425D4—241no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—121no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—241no—
436C2×C4—361no—
437C2×C4—361no—
438C2×C4—361no—
439C2×C4C2×#62511yescharacteristic
440C2×C4D3×#6711yescharacteristic
441C8—121no—
442C8—361no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—241no—
453C2×C3—241no—
454C2×C3#505311yescharacteristic
455C2×C3#517211yescharacteristic
456C2×C3#520211yescharacteristic
457C2×C3#523811yescharacteristic
458C2×C3#524211yescharacteristic
459C2×C3#524311yescharacteristic
460D3—81no—
461D3—81no—
462C22—21no—
463C22—21no—
464C22—122no—
465C22—121no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22—241no—
472C22#6393911yescharacteristic
473C22#6394711yescharacteristic
474C22#6397611yescharacteristic
475C4—21no—
476C4—21no—
477C4—41no—
478C4—41no—
479C4—121no—
480C4—121no—
481C4—241no—
482C4—721no—
483C3—21no—
484C3#7117311yescharacteristic, complemented
485C3#7188211yescharacteristic, complemented
486C2—21no—
487C2—21no—
488C2—241no—
489C2—241no—
490C2#1059153311yescharacteristic
491C2#1059158611yescharacteristic
492C2#1059166411yescharacteristic
subgroupG/H
centerC22#63976
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. C3×#5043C2semidirect
3. #10591314C2semidirect
4. #10591089C2semidirect
5. #10589404C2semidirect
6. #10589150C2semidirect
7. #10589145C2semidirect
32. #5043D3semidirect
412. C32#1612semidirect
484. C3#71173semidirect
485. C3#71882semidirect

Maximal subgroups

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

subgroupindex
C3×#56442
C3×#50432
#105913142
#105910892
#105894042
#105891502
#105891452
#718823
#711733