Finite Group Databasebeta

← #11779869

Subgroups — #11779869

Order 1152.

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

normal subgroups only

This group has 560 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
2#10592718C211yesmaximal, characteristic, complemented
3#10590301C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71921—31nomaximal
9#68197—31nomaximal
10C2×C3×#235—21no—
11C32×C4×D4C2211yescharacteristic
12C2×#3754—21no—
13#64078C2211yescharacteristic
14C3×#940—21no—
15C3×#930—21no—
16C3×#893—21no—
17C3×#884—22no—
18C3×#874C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63637—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63573—21no—
25#63566—21no—
26#63563—22no—
27C3×#550—31no—
28#5553D311yescharacteristic
29#5070—31no—
30#5020—31no—
31#5019—31no—
32#5019—31no—
33#5019—61no—
34#4851—31no—
35#4694—31no—
36C3×D4⋊C8—31no—
37#4544—31no—
38#4535—31no—
39D4⋊(C3⋊C8)D311yescharacteristic, complemented
40#4485—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#634—21no—
45C2×C3×#67—22no—
46C2×C3×#67—22no—
47C3×#235—42no—
48C3×#235—42no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12D412yes—
52C2×C3×C4×D3—22no—
53C2×C3×Dic6D411yescharacteristic
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42C2311yescharacteristic
57#3754—42no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—22no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1642—91noSylow
68C2×C3×#41—61no—
69C2×#235—21no—
70C3×#127—31no—
71C3×#127—61no—
72C3×#121—62no—
73C3×#121—61no—
74C3×C4×Q8—31no—
75C3×C4×D4—21no—
76C3×C4×D4—61no—
77C3×C4×D4C2×D311yescharacteristic
78C3×C4×D4C2×D311yescharacteristic
79#940—21no—
80C2×#214—62no—
81C2×#214—61no—
82C2×#214—61no—
83#930—21no—
84#893—21no—
85#884—22no—
86#874C2×D311yescharacteristic
87#869—31no—
88#869—31no—
89#869—61no—
90C4×Dic6C2×D311yescharacteristic
91C3×C4⋊C8—31no—
92C3×C4×C8—31no—
93#835—61no—
94#832—62no—
95#821—62no—
96#817—61no—
97#816—61no—
98#810—62no—
99#810—61no—
100#810—61no—
101#808—61no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C23×C32—21no—
108C22×C3×D3—22no—
109C32×D4—21no—
110C32×D4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—41no—
118#634—41no—
119#634—41no—
120C3×#67—44no—
121C3×#67—82no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C3×D12—42no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—41no—
128C3×D12—41no—
129C3×C4×D3—44no—
130C3×Dic6—21no—
131C3×Dic6SD1612yescomplemented
132C3⋊(C3⋊C8)—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135#550—31no—
136#486—91no—
137#475—91no—
138#461—91no—
139#331—91no—
140Q8⋊C8—91no—
141D4⋊C8—31no—
142C3×#41—122no—
143C3×#41—122no—
144C2×C3×Q8—31no—
145C2×C3×D4—21no—
146C2×C3×D4—32no—
147C2×C3×D4—62no—
148C2×C3×D4—62no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C2×C3×D4D1211yescharacteristic
152C2×C3×D4#6711yescharacteristic
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—41no—
156C22×C3×C4—62no—
157C2×#67—22no—
158C2×#67—22no—
159#235—42no—
160#235—42no—
161C2×D12—21no—
162C2×D12—21no—
163C2×D12#6712yes—
164C2×C4×D3—22no—
165C2×Dic6—62no—
166C2×Dic6—61no—
167C2×Dic6—61no—
168C2×Dic6#6711yescharacteristic
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4D1211yescharacteristic
175C3×C4⋊C4#6711yescharacteristic
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C22⋊C4—41no—
179C3×C22⋊C4—62no—
180C3×C42—21no—
181C3×C42—61no—
182C3×C42C22×D311yescharacteristic
183C3×C42C22×D311yescharacteristic
184#214—124no—
185#214—122no—
186#214—122no—
187(C2×D3)⋊C4—22no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—121no—
193C4⋊Dic3—121no—
194C4⋊Dic3#6711yescharacteristic
195Dic3⋊C4—21no—
196C4×Dic3—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—62no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C22×C32—41no—
203C22×C32—41no—
204C22×C32—41no—
205C22×C32#12011yescharacteristic
206C2×C3×D3—42no—
207C2×C3×D3—42no—
208C2×C3×D3—42no—
209C32×C4—21no—
210C32×C4—41no—
211C32×C4C2×SD1611yescharacteristic
212C32×C4#13511yescharacteristic
213C32×C4AGL(1,ℤ/8)11yescharacteristic
214C32×C4AGL(1,ℤ/8)11yescharacteristic
215C3⋊Dic3—81no—
216C3×Dic3—22no—
217C3×Dic3—41no—
218C2×#41—61no—
219C2×SD16—181no—
220C4⋊Q8—91no—
221#127—31no—
222#127—61no—
223#121—62no—
224#121—61no—
225C4×Q8—31no—
226C4×D4—61no—
227C4×D4D3211yescharacteristic
228#106—181no—
229C4⋊C8—31no—
230C4⋊C8—91no—
231#103—181no—
232#103—181no—
233#102—182no—
234C4×C8—31no—
235C23×C3—21no—
236C23×C3—21no—
237C23×C3—41no—
238C23×C3—62no—
239C22×D3—22no—
240C3×Q8—32no—
241C3×Q8—61no—
242C3×D4—22no—
243C3×D4—21no—
244C3×D4—21no—
245C3×D4—21no—
246C3×D4—21no—
247C3×D4—41no—
248C3×D4—122no—
249C3×D4—124no—
250C3×D4—121no—
251C3×D4—121no—
252C3×D4—121no—
253C3×D4—121no—
254C3×D4—242no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—81no—
268C2×C3×C4—81no—
269C2×C3×C4—124no—
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276#67—44no—
277#67—82no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—122no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283D12—42no—
284D12—41no—
285D12—41no—
286D12—41no—
287D12—41no—
288C4×D3—44no—
289Dic6—21no—
290Dic6—122no—
291Dic6—122no—
292Dic6—121no—
293Dic6—121no—
294Dic6—121no—
295Dic6—121no—
296Dic6#21412yescomplemented
297C3×C8—121no—
298C3×C8—121no—
299C3⋊C8—41no—
300C3⋊C8—41no—
301C3⋊C8—122no—
302C3⋊C8—121no—
303C3⋊C8—121no—
304C2×C32—81no—
305C2×C32#44911yescharacteristic
306C2×C32#45011yescharacteristic
307C2×C32#45511yescharacteristic
308C3×D3—82no—
309#41—122no—
310#41—122no—
311C2×Q8—31no—
312C2×Q8—181no—
313C2×D4—32no—
314C2×D4—62no—
315C2×D4—62no—
316C2×D4—61no—
317C2×D4—61no—
318C2×D4#62611yescharacteristic
319C22×C4—21no—
320C22×C4—62no—
321SD16—362no—
322C2×C8—61no—
323C2×C8—61no—
324C2×C8—181no—
325C4⋊C4—31no—
326C4⋊C4—61no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C4⋊C4#62611yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—62no—
332C42—61no—
333C42C2×D3211yescharacteristic
334C22×C3—21no—
335C22×C3—42no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—81no—
343C22×C3—81no—
344C22×C3—122no—
345C22×C3—122no—
346C22×C3—122no—
347C22×C3#88211yescharacteristic
348C22×C3#95311yescharacteristic
349C2×D3—42no—
350C2×D3—42no—
351C2×D3—42no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—62no—
362C3×C4—81no—
363C3×C4—121no—
364C3×C4#90411yescharacteristic
365C3×C4#90811yescharacteristic
366C3×C4#91111yescharacteristic
367C3×C4D3×SD1611yescharacteristic
368C3×C4#93211yescharacteristic
369C3×C4C2×#21411yescharacteristic
370C3×C4#94911yescharacteristic
371C3×C4#95011yescharacteristic
372Dic3—22no—
373Dic3—41no—
374Dic3—242no—
375Dic3—241no—
376Dic3—241no—
377C32#164211yescharacteristic, complemented, Sylow
378C23—21no—
379C23—62no—
380Q8—32no—
381Q8—61no—
382Q8—361no—
383Q8—361no—
384D4—21no—
385D4—21no—
386D4—122no—
387D4—124no—
388D4—121no—
389D4—121no—
390D4—121no—
391D4—121no—
392D4—242no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—124no—
399C2×C4—361no—
400C2×C4C2×#62611yescharacteristic
401C2×C4D3×#6711yescharacteristic
402C2×C4D3×#6711yescharacteristic
403C8—121no—
404C8—121no—
405C8—361no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—82no—
410C2×C3—81no—
411C2×C3—81no—
412C2×C3—242no—
413C2×C3#473411yescharacteristic
414C2×C3#477611yescharacteristic
415C2×C3#482511yescharacteristic
416C2×C3#521811yescharacteristic
417C2×C3#523811yescharacteristic
418C2×C3#524211yescharacteristic
419D3—82no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—122no—
424C22—122no—
425C22—122no—
426C22#6397711yescharacteristic
427C4—21no—
428C4—41no—
429C4—62no—
430C4—121no—
431C4—721no—
432C4#6382511yescharacteristic
433C4#6382911yescharacteristic
434C4D3×#21411yescharacteristic
435C4#6393211yescharacteristic
436C3—21no—
437C3#6819711yescharacteristic, complemented
438C3#7192111yescharacteristic, complemented
439C2—81no—
440C2—242no—
441C2#1059116311yescharacteristic
442C2#1059145911yescharacteristic
443C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
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. #10592718C2semidirect
3. #10590301C2semidirect
4. #10590273C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589090C2semidirect
7. #10589084C2semidirect
39. D4⋊(C3⋊C8)D3semidirect
131. C3×Dic6SD16semidirect
296. Dic6#214semidirect
377. C32#1642semidirect
437. C3#68197semidirect
438. C3#71921semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105927182
#105903012
#105902732
C3×D4⋊(C3⋊C8)2
#105890902
#105890842
#719213
#681973