Finite Group Databasebeta

← #11779384

Subgroups — #11779384

Order 1152.

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

normal subgroups only

This group has 547 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
1#10593906C211yesmaximal, characteristic
2C3×#4693C211yesmaximal, characteristic, complemented
3#10590284C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic, complemented
5#10589322C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71271—31nomaximal
9#68188—31nomaximal
10C2×#3795—21no—
11C4×#634C2211yescharacteristic
12C2×C3×#204—22no—
13C3×#874C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×#869C2211yescharacteristic
16#63914—21no—
17#63908—21no—
18#63898—21no—
19#63885—22no—
20C32×C4×C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63575—21no—
24#63574—21no—
25#63567—21no—
26#63562—21no—
27#5718—31no—
28#5553—31no—
29C3×#492—31no—
30#5091—31no—
31#5084—31no—
32#5008—31no—
33#4850—31no—
34#4693D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36#4544—31no—
37#4485—31no—
38#4459D311yescharacteristic, complemented
39#4456—31no—
40#4456—31no—
41#4456—61no—
42C2×#634D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×D12D412yes—
47C2×C3×C4×D3—21no—
48C2×C3×Dic6—21no—
49C2×#625—22no—
50C2×#625—22no—
51C2×D3×Dic3—22no—
52#3795—42no—
53#3795—42no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58C4×C3⋊Dic3—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C2×C3×C3⋊C8—21no—
65C3×#204—44no—
66(C2×D3)⋊Dic3—22no—
67#1631—91noSylow
68C2×#237—61no—
69C2×#235—61no—
70C2×C3×SD16—62no—
71C3×C4⋊Q8—31no—
72C3×#127—31no—
73C3×C4×D4—31no—
74#940—61no—
75#940—61no—
76#939—62no—
77#938—61no—
78D4×Dic3—61no—
79#930—61no—
80C2×#204—22no—
81#893—61no—
82#884—62no—
83#874C2×D311yescharacteristic
84C4×D12C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86C4×Dic6—31no—
87C4×Dic6—31no—
88C4×Dic6—61no—
89C3×C4⋊C8—31no—
90C3×C4×C8—21no—
91C3×C4×C8C2×D311yescharacteristic
92C3×C4×C8C2×D311yescharacteristic
93#832—61no—
94#818—61no—
95#816—61no—
96#810—61no—
97#809—61no—
98#808—61no—
99#808—61no—
100#807—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C22×C3×D3—22no—
106C22×C3×D3—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112#634—21no—
113#634SD1612yescomplemented
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×Dic6—42no—
126#625—44no—
127#625—82no—
128D3×Dic3—44no—
129C32×C8—22no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—41no—
132#550—91no—
133#492—31no—
134#477—91no—
135#476—91no—
136#331—91no—
137Q8⋊C8—91no—
138D4⋊C8—31no—
139C2×C3×Q8—61no—
140C2×C3×D4—31no—
141C2×C3×D4—32no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C22×C3×C4—61no—
145C2×#67—62no—
146C2×#67—62no—
147C2×#67—62no—
148C2×#67—62no—
149C22×Dic3—62no—
150#237—122no—
151#237—122no—
152#235—122no—
153#235—122no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12D1211yescharacteristic
157C2×D12#6712yes—
158C2×C4×D3—21no—
159C2×C4×D3—62no—
160C2×Dic6—21no—
161C2×Dic6—31no—
162C2×Dic6—31no—
163C2×Dic6—61no—
164C3×SD16—124no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—41no—
168C2×C3×C8—61no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C42—21no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176#217—62no—
177(C2×D3)⋊C4—21no—
178(C2×D3)⋊C4—62no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—61no—
184C4⋊Dic3D1211yescharacteristic
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—121no—
188C4×Dic3—61no—
189C4×Dic3—61no—
190C4×Dic3—121no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195#204—44no—
196C22×C32#12011yescharacteristic
197C2×C3×D3—42no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—42no—
201C2×C3×D3—41no—
202C2×C3×D3—42no—
203C32×C4—21no—
204C32×C4C2×SD1611yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4#13711yescharacteristic
208C3⋊Dic3—22no—
209C3⋊Dic3—41no—
210C3×Dic3—41no—
211C3×Dic3—81no—
212C2×#41—181no—
213C2×SD16—62no—
214C4⋊Q8—31no—
215#127—31no—
216#127—181no—
217#121—182no—
218#121—181no—
219C4×Q8—91no—
220C4×D4—31no—
221C4×D4—181no—
222#107—181no—
223#106—181no—
224C4⋊C8—31no—
225C4⋊C8—91no—
226#103—181no—
227#102—181no—
228C4×C8D3211yescharacteristic
229C23×C3—62no—
230C23×C3—61no—
231C22×D3—21no—
232C22×D3—22no—
233C3×Q8—122no—
234C3×D4—61no—
235C3×D4—61no—
236C3×D4—122no—
237C3×D4—121no—
238C3×D4—121no—
239C3×D4—121no—
240C3×D4—121no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—61no—
245C2×C3×C4—121no—
246C2×C3×C4—121no—
247C2×C3×C4—121no—
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4C2×#6711yescharacteristic
254#67—124no—
255#67—124no—
256#67—242no—
257#67—242no—
258C2×Dic3—21no—
259C2×Dic3—41no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—121no—
265C2×Dic3—121no—
266C2×Dic3—124no—
267D12—21no—
268D12—21no—
269D12—42no—
270D12—41no—
271D12—41no—
272D12—41no—
273D12—41no—
274C4×D3—41no—
275C4×D3—41no—
276C4×D3—124no—
277Dic6—32no—
278Dic6—32no—
279Dic6—42no—
280Dic6—62no—
281Dic6—61no—
282Dic6—61no—
283Dic6—121no—
284C3×C8—22no—
285C3×C8—22no—
286C3×C8—42no—
287C3×C8—121no—
288C3⋊C8—41no—
289C3⋊C8—121no—
290C3⋊C8—121no—
291C3⋊C8—241no—
292C2×C32#45011yescharacteristic
293C2×C32#45211yescharacteristic
294C2×C32#45311yescharacteristic
295C3×D3—81no—
296C3×D3—82no—
297#41—362no—
298#41—362no—
299C2×Q8—61no—
300C2×Q8—91no—
301C2×D4—31no—
302C2×D4—32no—
303C2×D4—61no—
304C2×D4—61no—
305C2×D4—182no—
306C2×D4—182no—
307C22×C4—61no—
308C22×C4—182no—
309SD16—124no—
310C2×C8—21no—
311C2×C8—61no—
312C2×C8—181no—
313C4⋊C4—31no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—91no—
317C4⋊C4—181no—
318C22⋊C4—61no—
319C22⋊C4—182no—
320C42—181no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3—122no—
326C22×C3—122no—
327C22×C3—121no—
328C22×C3—122no—
329C22×C3#88211yescharacteristic
330C22×C3#93711yescharacteristic
331C2×D3—42no—
332C2×D3—42no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—42no—
336C2×D3—41no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—41no—
344C3×C4—121no—
345C3×C4—241no—
346C3×C4#90411yescharacteristic
347C3×C4#90911yescharacteristic
348C3×C4#91111yescharacteristic
349C3×C4D3×SD1611yescharacteristic
350C3×C4D3×SD1611yescharacteristic
351C3×C4#91411yescharacteristic
352C3×C4#91511yescharacteristic
353C3×C4#91611yescharacteristic
354Dic3—41no—
355Dic3—62no—
356Dic3—62no—
357Dic3—81no—
358Dic3—122no—
359Dic3—121no—
360Dic3—121no—
361Dic3—241no—
362C32#163111yescharacteristic, complemented, Sylow
363C23—61no—
364C23—62no—
365Q8—92no—
366Q8—122no—
367Q8—181no—
368D4—61no—
369D4—61no—
370D4—122no—
371D4—121no—
372D4—121no—
373D4—121no—
374D4—121no—
375D4—364no—
376D4—722no—
377C2×C4—61no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4—121no—
381C2×C4—181no—
382C2×C4—181no—
383C2×C4—364no—
384C2×C4D3×D1211yescharacteristic
385C2×C4#380211yescharacteristic
386C2×C4D3×#6711yescharacteristic
387C8—22no—
388C8—121no—
389C8—361no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—242no—
394C2×C3—241no—
395C2×C3#473311yescharacteristic
396C2×C3#477611yescharacteristic
397C2×C3#482211yescharacteristic
398C2×C3#507711yescharacteristic
399C2×C3#516911yescharacteristic
400C2×C3#517311yescharacteristic
401D3—81no—
402D3—82no—
403C22—122no—
404C22—121no—
405C22—121no—
406C22—122no—
407C22—121no—
408C22—122no—
409C22#6392211yescharacteristic
410C4—21no—
411C4—121no—
412C4—182no—
413C4—241no—
414C4—361no—
415C4#6379611yescharacteristic
416C4#6379811yescharacteristic
417C4#6380011yescharacteristic
418C4#6380611yescharacteristic
419C3—21no—
420C3#6818811yescharacteristic, complemented
421C3#7127111yescharacteristic, complemented
422C2—242no—
423C2—241no—
424C2#1059039511yescharacteristic
425C2#1059094311yescharacteristic
426C2#1059096011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10593906C2
hypercenterC4×C8D32
hypocenterC32#1631
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×#4693C2semidirect
3. #10590284C2semidirect
4. #10590266C2semidirect
5. #10589322C2semidirect
6. C3×#4459C2semidirect
7. #10589090C2semidirect
34. #4693D3semidirect
38. #4459D3semidirect
113. #634SD16semidirect
362. C32#1631semidirect
420. C3#68188semidirect
421. C3#71271semidirect

Maximal subgroups

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

subgroupindex
#105939062
C3×#46932
#105902842
#105902662
#105893222
C3×#44592
#105890902
#712713
#681883