Finite Group Databasebeta

← #11778529

Subgroups — #11778529

Order 1152.

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

normal subgroups only

This group has 484 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×#5645C211yesmaximal, characteristic
2#10592742C211yesmaximal, characteristic, complemented
3#10591353C211yesmaximal, characteristic, complemented
4#10591094C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#71886—31nomaximal
9#68328—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#946—21no—
13C3×#930C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C3×#898—21no—
16C3×#894—21no—
17C3×#890—21no—
18C3×#886—21no—
19C3×#67⋊C4—21no—
20C2×Dic3⋊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×#539—31no—
30#5645D311yescharacteristic
31#5043—31no—
32#5043—31no—
33#5043—61no—
34#5033—31no—
35#4981—31no—
36#4736—31no—
37#4661—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4537—31no—
41#4528—31no—
42#4469—31no—
43#4451—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—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×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—42no—
72#1609—91noSylow
73C3×#126—61no—
74C3×#125—61no—
75C3×#123—61no—
76C3×#123—61no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8C2×D311yescharacteristic
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×#121—31no—
82C3×C4×D4—61no—
83C2×C3×C4⋊C4—31no—
84#946—21no—
85#930C2×D311yescharacteristic
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—61no—
89C2×C4⋊Dic3—61no—
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4C2×D311yescharacteristic
92#898—21no—
93#894—21no—
94#890—21no—
95#886—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—
118C32×Q8—41no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C3×#67—41no—
128C3×#67—41no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C3×D12—41no—
139C3×C4×D3—81no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142#539—31no—
143#483—91no—
144#480—91no—
145#398—91no—
146#328—31no—
147#327—91no—
148#324—91no—
149C2×C3×Q8—21no—
150C2×C3×Q8D1211yescharacteristic
151C2×C3×Q8#6711yescharacteristic
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—21no—
162C22×Dic3—21no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166C22×Dic3#6711yescharacteristic
167C22×Dic3#6711yescharacteristic
168C2×D12#6711yescharacteristic
169C2×C4×D3—21no—
170C2×C3×C8—61no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4D1211yescharacteristic
182C3×C4⋊C4#6711yescharacteristic
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—41no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C42—61no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—62no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—121no—
203C4⋊Dic3—122no—
204C4⋊Dic3#6711yescharacteristic
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—122no—
209C4×Dic3—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32#12011yescharacteristic
217C22×C32#13511yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4—41no—
226C3⋊Dic3—81no—
227C3×Dic3—42no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231#126—61no—
232#125—61no—
233#123—61no—
234#123—61no—
235C22⋊Q8—61no—
236C22⋊Q8D3211yescharacteristic
237#121—31no—
238C4×D4—61no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—91no—
241C2×C4⋊C4—181no—
242#107—181no—
243#106—181no—
244#103—181no—
245#102—181no—
246C22⋊C8—31no—
247C22⋊C8—91no—
248#95—31no—
249#95—181no—
250C23×C3—21no—
251C23×C3—61no—
252C23×C3D3×D411yescharacteristic
253C23×C3C2×#6711yescharacteristic
254C22×D3—21no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×Q8—42no—
258C3×D4—121no—
259C3×D4—121no—
260C3×D4—121no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—42no—
272C2×C3×C4—62no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4—241no—
282C2×C3×C4C2×D1211yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286#67—41no—
287#67—41no—
288C2×Dic3—22no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—41no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3—122no—
298C2×Dic3—121no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303C2×Dic3—121no—
304C2×Dic3—241no—
305C2×Dic3—241no—
306D12—41no—
307C4×D3—81no—
308C3×C8—121no—
309C3⋊C8—41no—
310C3⋊C8—122no—
311C3⋊C8—121no—
312C3⋊C8—121no—
313C2×C32—21no—
314C2×C32—21no—
315C2×C32#44911yescharacteristic
316C2×C32#45611yescharacteristic
317C2×C32#45811yescharacteristic
318C3×D3—81no—
319C2×Q8#62611yescharacteristic
320C2×D4—31no—
321C2×D4—61no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—61no—
325C22×C4—61no—
326C22×C4—181no—
327C22×C4C2×D3211yescharacteristic
328C2×C8—61no—
329C2×C8—181no—
330C4⋊C4—21no—
331C4⋊C4—31no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—181no—
338C4⋊C4—181no—
339C4⋊C4—362no—
340C4⋊C4#62611yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C42—61no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—121no—
357C22×C3—121no—
358C22×C3—121no—
359C22×C3#88211yescharacteristic
360C22×C3#91411yescharacteristic
361C22×C3#91911yescharacteristic
362C22×C3#94911yescharacteristic
363C22×C3#95011yescharacteristic
364C22×C3#95311yescharacteristic
365C2×D3—41no—
366C2×D3—41no—
367C2×D3—41no—
368C3×C4—22no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—81no—
379C3×C4—81no—
380C3×C4—122no—
381C3×C4—121no—
382C3×C4—121no—
383C3×C4—121no—
384Dic3—42no—
385Dic3—41no—
386Dic3—41no—
387Dic3—41no—
388Dic3—242no—
389Dic3—241no—
390Dic3—241no—
391C32#160911yescharacteristic, complemented, Sylow
392C23—61no—
393C23D3×#6711yescharacteristic
394Q8—41no—
395D4—121no—
396D4—121no—
397D4—121no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—62no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4—241no—
411C2×C4—361no—
412C2×C4—361no—
413C2×C4—361no—
414C2×C4C2×#62611yescharacteristic
415C2×C4D3×#6711yescharacteristic
416C8—121no—
417C8—361no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—241no—
428C2×C3#474211yescharacteristic
429C2×C3#481011yescharacteristic
430C2×C3#482611yescharacteristic
431C2×C3#523811yescharacteristic
432C2×C3#524311yescharacteristic
433C2×C3#524611yescharacteristic
434D3—81no—
435C22—21no—
436C22—21no—
437C22—121no—
438C22—121no—
439C22—121no—
440C22#6393911yescharacteristic
441C22#6394911yescharacteristic
442C22#6397711yescharacteristic
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—122no—
448C4—121no—
449C4—121no—
450C4—121no—
451C4—721no—
452C3—21no—
453C3#6832811yescharacteristic, complemented
454C3#7188611yescharacteristic, complemented
455C2—21no—
456C2—21no—
457C2—241no—
458C2#1059153411yescharacteristic
459C2#1059158811yescharacteristic
460C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC22⋊Q8D32
hypocenterC32#1609
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. #10591353C2semidirect
5. C3×#4538C2semidirect
7. #10589147C2semidirect
39. #4538D3semidirect
391. C32#1609semidirect
453. C3#68328semidirect
454. C3#71886semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
#105927422
#105913532
#105910942
C3×#45382
#105891492
#105891472
#718863
#683283