Finite Group Databasebeta

← #11779226

Subgroups — #11779226

Order 1152.

535 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 535 conjugacy classes of subgroups — too many to draw. Only its 92 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#10593904C211yesmaximal, characteristic, complemented
2C3×#4694C211yesmaximal, characteristic, complemented
3#10590377C211yesmaximal, characteristic, complemented
4#10590347C211yesmaximal, characteristic
5#10589322C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#71205—31nomaximal
9#68187—31nomaximal
10C2×D3×Dic6—21no—
11C4×#634C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63919—21no—
16#63899—22no—
17#63898—21no—
18#63856—21no—
19C2×#3716—21no—
20C2×#3713—21no—
21C32×C4×C8C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#821—22no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63563—21no—
26#63562—21no—
27#5727—31no—
28D4×Dic6—31no—
29C3×#486—31no—
30#5075—31no—
31#5072—31no—
32#5015—31no—
33#4848—31no—
34#4694D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36#4547—31no—
37#4482—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×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6—21no—
49C2×#627—22no—
50C2×D3×Dic3—22no—
51D3×Dic6—42no—
52D3×Dic6—42no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)D411yescharacteristic
56#3750—21no—
57C4×C3⋊Dic3—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D412yes—
63C2×C3×C3⋊C8—21no—
64#3724—22no—
65(C2×D3)⋊Dic3—22no—
66#3716—42no—
67#3713—42no—
68#1627—91noSylow
69C2×D3×Q8—61no—
70C22×Dic6—61no—
71C3×C4⋊Q8—31no—
72C3×#127—31no—
73C3×C4×D4—31no—
74#946—61no—
75D4×Dic3—61no—
76C2×#214—61no—
77C2×#213—61no—
78C2×#213—61no—
79#924—61no—
80C2×#204—61no—
81#896—62no—
82#893—61no—
83#888—61no—
84#888—61no—
85#878—62no—
86#874C2×D311yescharacteristic
87C4×D12C2×D311yescharacteristic
88#869C2×D311yescharacteristic
89C4×Dic6—31no—
90C4×Dic6—31no—
91C4×Dic6—61no—
92C3×C4⋊C8—31no—
93C3×#102—62no—
94C3×C4×C8—21no—
95C3×C4×C8C2×D311yescharacteristic
96C3×C4×C8C2×D311yescharacteristic
97#832—61no—
98#832—61no—
99#821—22no—
100#821—61no—
101#809—61no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C22×C3×D3—21no—
107C22×C3×D3—41no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113#634—21no—
114#634D812yescomplemented
115C2×C3×Dic3—22no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12SD1612yescomplemented
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128#627—44no—
129D3×Dic3—44no—
130C32×C8—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133D4×Q8—91no—
134#486—31no—
135#460—91no—
136#459—91no—
137#332—91no—
138Q8⋊C8—91no—
139D4⋊C8—31no—
140C2×C3×Q8—61no—
141C2×C3×D4—31no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C22×C3×C4—61no—
146C22×Dic3—62no—
147D3×Q8—122no—
148D3×Q8—122no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12D1211yescharacteristic
153C2×C4×D3—21no—
154C2×C4×D3—62no—
155C2×Dic6—21no—
156C2×Dic6—31no—
157C2×Dic6—31no—
158C2×Dic6—61no—
159C2×Dic6—62no—
160C2×Dic6—62no—
161C2×Dic6—122no—
162C2×Dic6—122no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—41no—
166C2×C3×C8—61no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—32no—
169C3×C4⋊C4—61no—
170C3×C22⋊C4—61no—
171C3×C42—21no—
172C3×C42C22×D311yescharacteristic
173C3×C42C22×D311yescharacteristic
174#217—62no—
175#214—122no—
176#213—122no—
177#213—122no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—62no—
180C4⋊Dic3—21no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—61no—
184C4⋊Dic3D1211yescharacteristic
185C4⋊Dic3#6712yes—
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—121no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—121no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—121no—
198#204—122no—
199C22×C32#12011yescharacteristic
200C2×C3×D3—22no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C2×C3×D3—81no—
206C32×C4—21no—
207C32×C4C2×D811yescharacteristic
208C32×C4C2×SD1611yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4#13711yescharacteristic
211C3⋊Dic3—22no—
212C3⋊Dic3—41no—
213C3×Dic3—42no—
214C3×Dic3—41no—
215C22×Q8—181no—
216C2×SD16—181no—
217C2×D8—181no—
218C4⋊Q8—31no—
219C4⋊Q8—181no—
220#127—31no—
221C22⋊Q8—182no—
222C22⋊Q8—181no—
223C4×Q8—91no—
224C4×D4—31no—
225C4×D4—181no—
226C4⋊C8—31no—
227C4⋊C8—91no—
228#102—62no—
229#102—181no—
230#102—181no—
231C4×C8D3211yescharacteristic
232C23×C3—61no—
233C23×C3—121no—
234C22×D3—21no—
235C22×D3—41no—
236C3×Q8—121no—
237C3×Q8—121no—
238C3×D4—32no—
239C3×D4—61no—
240C3×D4—122no—
241C3×D4—121no—
242C3×D4—121no—
243C3×D4—121no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—62no—
249C2×C3×C4—61no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×Dic3—21no—
259C2×Dic3—22no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—121no—
265C2×Dic3—121no—
266C2×Dic3—124no—
267D12—21no—
268D12—42no—
269D12—41no—
270D12—41no—
271D12—41no—
272D12—41no—
273D12#20412yescomplemented
274C4×D3—41no—
275C4×D3—41no—
276C4×D3—124no—
277Dic6—32no—
278Dic6—32no—
279Dic6—41no—
280Dic6—41no—
281Dic6—62no—
282Dic6—61no—
283Dic6—61no—
284Dic6—121no—
285Dic6—124no—
286Dic6—124no—
287C3×C8—41no—
288C3×C8—41no—
289C3×C8—42no—
290C3×C8—121no—
291C3⋊C8—41no—
292C3⋊C8—121no—
293C3⋊C8—121no—
294C3⋊C8—241no—
295C2×C32#44711yescharacteristic
296C2×C32#44811yescharacteristic
297C2×C32#45411yescharacteristic
298C3×D3—42no—
299C3×D3—161no—
300C2×Q8—61no—
301C2×Q8—91no—
302C2×Q8—182no—
303C2×Q8—362no—
304C2×Q8—362no—
305C2×D4—31no—
306C2×D4—61no—
307C2×D4—61no—
308C2×D4—61no—
309C22×C4—61no—
310C22×C4—182no—
311SD16—362no—
312D8—362no—
313C2×C8—21no—
314C2×C8—61no—
315C2×C8—181no—
316C4⋊C4—31no—
317C4⋊C4—32no—
318C4⋊C4—61no—
319C4⋊C4—91no—
320C4⋊C4—182no—
321C4⋊C4—181no—
322C22⋊C4—61no—
323C22⋊C4—182no—
324C42—181no—
325C42C2×D3211yescharacteristic
326C22×C3—21no—
327C22×C3—62no—
328C22×C3—121no—
329C22×C3—121no—
330C22×C3—241no—
331C22×C3—241no—
332C22×C3—241no—
333C22×C3#88211yescharacteristic
334C22×C3#93711yescharacteristic
335C2×D3—22no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—81no—
339C2×D3—81no—
340C2×D3—81no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—41no—
348C3×C4—121no—
349C3×C4—122no—
350C3×C4C2×#20411yescharacteristic
351C3×C4#90911yescharacteristic
352C3×C4D3×D811yescharacteristic
353C3×C4D3×D811yescharacteristic
354C3×C4#91111yescharacteristic
355C3×C4D3×SD1611yescharacteristic
356C3×C4#91411yescharacteristic
357C3×C4#91511yescharacteristic
358Dic3—42no—
359Dic3—41no—
360Dic3—62no—
361Dic3—62no—
362Dic3—122no—
363Dic3—121no—
364Dic3—121no—
365Dic3—241no—
366C32#162711yescharacteristic, complemented, Sylow
367C23—61no—
368C23—121no—
369Q8—92no—
370Q8—121no—
371Q8—121no—
372Q8—181no—
373Q8—364no—
374D4—32no—
375D4—61no—
376D4—122no—
377D4—121no—
378D4—121no—
379D4—121no—
380D4—121no—
381C2×C4—61no—
382C2×C4—62no—
383C2×C4—121no—
384C2×C4—121no—
385C2×C4—181no—
386C2×C4—181no—
387C2×C4—364no—
388C2×C4D3×D1211yescharacteristic
389C2×C4#380211yescharacteristic
390C2×C4D3×#6711yescharacteristic
391C8—41no—
392C8—121no—
393C8—361no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—122no—
398C2×C3—481no—
399C2×C3#473811yescharacteristic
400C2×C3#477311yescharacteristic
401C2×C3#482711yescharacteristic
402C2×C3#506211yescharacteristic
403C2×C3#515611yescharacteristic
404C2×C3#517011yescharacteristic
405D3—42no—
406D3—161no—
407C22—62no—
408C22—121no—
409C22—121no—
410C22—241no—
411C22—241no—
412C22—241no—
413C22#6392211yescharacteristic
414C4—21no—
415C4—121no—
416C4—122no—
417C4—182no—
418C4—361no—
419C4D3×#20411yescharacteristic
420C4#6379711yescharacteristic
421C4#6379811yescharacteristic
422C4#6380011yescharacteristic
423C3—21no—
424C3#6818711yescharacteristic, complemented
425C3#7120511yescharacteristic, complemented
426C2—122no—
427C2—481no—
428C2#1059040011yescharacteristic
429C2#1059082211yescharacteristic
430C2#1059094511yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10590347C2
hypercenterC4×C8D32
hypocenterC32#1627
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
1. #10593904C2semidirect
2. C3×#4694C2semidirect
3. #10590377C2semidirect
5. #10589322C2semidirect
6. C3×#4459C2semidirect
7. #10589093C2semidirect
34. #4694D3semidirect
38. #4459D3semidirect
114. #634D8semidirect
123. C3×D12SD16semidirect
273. D12#204semidirect
366. C32#1627semidirect
424. C3#68187semidirect
425. C3#71205semidirect

Maximal subgroups

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

subgroupindex
#105939042
C3×#46942
#105903772
#105903472
#105893222
C3×#44592
#105890932
#712053
#681873