Finite Group Databasebeta

← #11779871

Subgroups — #11779871

Order 1152.

541 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 541 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5553C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic, complemented
3#10590285C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71921—31nomaximal
9#71045—31nomaximal
10C2×C3×#235—21no—
11C32×C4×D4C2211yescharacteristic
12C3×#940—21no—
13C2×C3×#214—21no—
14C3×#930—21no—
15C3×#893—21no—
16C3×#884—22no—
17C3×#874C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#810—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63574—21no—
25#63565—21no—
26#63562—22no—
27C3×#550—31no—
28#5553D311yescharacteristic
29C3×#461—31no—
30#5094—31no—
31#5088—31no—
32#5070—31no—
33#5020—31no—
34#5019D311yescharacteristic, complemented
35#4544—31no—
36#4535—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—61no—
40#4485—31no—
41#4484—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C3×#67—22no—
45C2×C3×#67—22no—
46C3×#235—42no—
47C3×#235—42no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12D412yes—
51C2×C3×C4×D3—22no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42C2311yescharacteristic
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#214—42no—
60C3×(C2×D3)⋊C4—22no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67#1642—91noSylow
68C2×C3×#41—61no—
69C2×#235—21no—
70C2×C3×SD16—61no—
71C3×C4⋊Q8—31no—
72C3×#127—31no—
73C3×#127—61no—
74C3×#121—62no—
75C3×#121—61no—
76C3×C4×Q8—31no—
77C3×C4×D4—21no—
78C3×C4×D4—61no—
79C3×C4×D4C2×D311yescharacteristic
80C3×C4×D4C2×D311yescharacteristic
81#940—21no—
82C2×#214—21no—
83#930—21no—
84#893—21no—
85#884—22no—
86#874C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C4×Dic6C2×D311yescharacteristic
89C3×C4⋊C8—31no—
90C3×#103—61no—
91#835—61no—
92#832—62no—
93#810—21no—
94#810—61no—
95#809—62no—
96#808—61no—
97#808—61no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C23×C32—21no—
106C22×C3×D3—22no—
107C32×D4—21no—
108C32×D4—21no—
109C2×C32×C4—21no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C3×#67—44no—
116C3×#67—82no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—41no—
120C3×D12—42no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×D12—41no—
125C3×C4×D3—44no—
126C3×Dic6—21no—
127C3×Dic6—41no—
128C3×Dic6—41no—
129C3×Dic6SD1612yescomplemented
130C3⋊(C3⋊C8)—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133#550—31no—
134#486—91no—
135#475—91no—
136#461—31no—
137#331—91no—
138Q8⋊C8—91no—
139D4⋊C8—91no—
140C3×#41—122no—
141C3×#41—122no—
142C2×C3×Q8—31no—
143C2×C3×Q8—61no—
144C2×C3×D4—21no—
145C2×C3×D4—32no—
146C2×C3×D4—62no—
147C2×C3×D4—62no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4#6711yescharacteristic
151C2×C3×D4#6711yescharacteristic
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—41no—
155C22×C3×C4—62no—
156C2×#67—22no—
157C2×#67—22no—
158#235—42no—
159#235—42no—
160C2×D12—21no—
161C2×D12—21no—
162C2×D12#6712yes—
163C2×C4×D3—22no—
164C2×Dic6—21no—
165C2×Dic6#6711yescharacteristic
166C3×SD16—122no—
167C2×C3×C8—61no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4#6711yescharacteristic
174C3×C4⋊C4#6711yescharacteristic
175C3×C22⋊C4—21no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—41no—
178C3×C22⋊C4—62no—
179C3×C42—21no—
180C3×C42—61no—
181C3×C42C22×D311yescharacteristic
182C3×C42C22×D311yescharacteristic
183#214—42no—
184(C2×D3)⋊C4—22no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3#6711yescharacteristic
188Dic3⋊C4—21no—
189C4×Dic3—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—121no—
196C2×C3⋊C8—121no—
197C22×C32—41no—
198C22×C32—41no—
199C22×C32—41no—
200C22×C32#12011yescharacteristic
201C2×C3×D3—42no—
202C2×C3×D3—42no—
203C2×C3×D3—42no—
204C32×C4—21no—
205C32×C4—41no—
206C32×C4C2×SD1611yescharacteristic
207C32×C4#13511yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C3×Dic3—22no—
211C3×Dic3—41no—
212C3×Dic3—81no—
213C2×#41—61no—
214C2×SD16—61no—
215C4⋊Q8—31no—
216#127—31no—
217#127—61no—
218#121—62no—
219#121—61no—
220C4×Q8—31no—
221C4×D4—61no—
222C4×D4D3211yescharacteristic
223#106—181no—
224C4⋊C8—31no—
225C4⋊C8—91no—
226#103—61no—
227#103—181no—
228#102—182no—
229C4×C8—91no—
230C23×C3—21no—
231C23×C3—21no—
232C23×C3—41no—
233C23×C3—62no—
234C22×D3—22no—
235C3×Q8—32no—
236C3×Q8—61no—
237C3×Q8—121no—
238C3×Q8—121no—
239C3×D4—22no—
240C3×D4—21no—
241C3×D4—21no—
242C3×D4—21no—
243C3×D4—21no—
244C3×D4—41no—
245C3×D4—122no—
246C3×D4—124no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C3×D4—242no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—81no—
265C2×C3×C4—81no—
266C2×C3×C4—124no—
267C2×C3×C4—121no—
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274#67—44no—
275#67—82no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—41no—
279D12—42no—
280D12—41no—
281D12—41no—
282D12—41no—
283D12—41no—
284C4×D3—44no—
285Dic6—21no—
286Dic6—41no—
287Dic6—41no—
288Dic6#21412yescomplemented
289C3×C8—121no—
290C3⋊C8—41no—
291C3⋊C8—121no—
292C3⋊C8—121no—
293C3⋊C8—122no—
294C3⋊C8—121no—
295C3⋊C8—121no—
296C3⋊C8—241no—
297C2×C32—81no—
298C2×C32#44911yescharacteristic
299C2×C32#45011yescharacteristic
300C2×C32#45511yescharacteristic
301C3×D3—82no—
302#41—122no—
303#41—122no—
304C2×Q8—31no—
305C2×Q8—61no—
306C2×D4—32no—
307C2×D4—62no—
308C2×D4—62no—
309C2×D4—61no—
310C2×D4—61no—
311C2×D4#62511yescharacteristic
312C22×C4—21no—
313C22×C4—62no—
314SD16—122no—
315C2×C8—61no—
316C2×C8—181no—
317C2×C8—181no—
318C4⋊C4—31no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4#62511yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—62no—
325C42—61no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—42no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3—122no—
338C22×C3—122no—
339C22×C3—122no—
340C22×C3#93711yescharacteristic
341C22×C3#95311yescharacteristic
342C2×D3—42no—
343C2×D3—42no—
344C2×D3—42no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—62no—
355C3×C4—81no—
356C3×C4—121no—
357C3×C4—241no—
358C3×C4D3×SD1611yescharacteristic
359C3×C4#91411yescharacteristic
360C3×C4#93211yescharacteristic
361C3×C4#93211yescharacteristic
362C3×C4C2×#21411yescharacteristic
363C3×C4#94911yescharacteristic
364C3×C4#95011yescharacteristic
365C3×C4#95011yescharacteristic
366Dic3—22no—
367Dic3—41no—
368Dic3—81no—
369C32#164211yescharacteristic, complemented, Sylow
370C23—21no—
371C23—62no—
372Q8—32no—
373Q8—61no—
374Q8—121no—
375Q8—121no—
376D4—21no—
377D4—21no—
378D4—122no—
379D4—124no—
380D4—121no—
381D4—121no—
382D4—121no—
383D4—121no—
384D4—242no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—124no—
391C2×C4—121no—
392C2×C4C2×#62511yescharacteristic
393C2×C4D3×#6711yescharacteristic
394C2×C4D3×#6711yescharacteristic
395C8—121no—
396C8—361no—
397C8—361no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—82no—
402C2×C3—81no—
403C2×C3—81no—
404C2×C3—242no—
405C2×C3#503711yescharacteristic
406C2×C3#516911yescharacteristic
407C2×C3#520211yescharacteristic
408C2×C3#521811yescharacteristic
409C2×C3#523811yescharacteristic
410C2×C3#524211yescharacteristic
411D3—82no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—122no—
416C22—122no—
417C22—122no—
418C22#6397611yescharacteristic
419C4—21no—
420C4—41no—
421C4—62no—
422C4—121no—
423C4—241no—
424C4#6382211yescharacteristic
425C4#6382311yescharacteristic
426C4D3×#21411yescharacteristic
427C4#6393411yescharacteristic
428C3—21no—
429C3#7104511yescharacteristic, complemented
430C3#7192111yescharacteristic, complemented
431C2—81no—
432C2—242no—
433C2#1059116111yescharacteristic
434C2#1059145811yescharacteristic
435C2#1059166411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC3×#5553C2
hypercenterC4×D4D32
hypocenterC32#1642
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5019C2semidirect
3. #10590285C2semidirect
4. #10590277C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589090C2semidirect
7. #10589083C2semidirect
34. #5019D3semidirect
129. C3×Dic6SD16semidirect
288. Dic6#214semidirect
369. C32#1642semidirect
429. C3#71045semidirect
430. C3#71921semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
C3×#50192
#105902852
#105902772
D4⋊(C3⋊(C3⋊C8))2
#105890902
#105890832
#719213
#710453