Finite Group Databasebeta

← #11779224

Subgroups — #11779224

Order 1152.

535 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 535 conjugacy classes of subgroups — too many to draw. Only its 104 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×Q8×D12C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic
4#10590277C211yesmaximal, characteristic, complemented
5#10589401C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71914—31nomaximal
9#71035—31nomaximal
10C2×C3×D3×Q8—21no—
11C32×C4×Q8C2211yescharacteristic
12C2×C3×#215—21no—
13C3×#897—21no—
14C3×#897—22no—
15C3×#874C2211yescharacteristic
16C3×C4×D12—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869—21no—
19C3×#869C2211yescharacteristic
20C2×#3713—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#809—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63562—22no—
26#63562—21no—
27C3×D4×Q8—31no—
28Q8×D12D311yescharacteristic, complemented
29C3×#460—31no—
30#5088—31no—
31#5072—31no—
32#5070—31no—
33#5027D311yescharacteristic, complemented
34#5015—31no—
35#4547—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39D4⋊(C3⋊C8)—31no—
40#4483—31no—
41#4482—31no—
42C2×C32×Q8D411yescharacteristic
43C3×D3×Q8—42no—
44C3×D3×Q8—42no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—22no—
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—22no—
52C2×C3×Dic6—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C42—21no—
56C32×C42C2311yescharacteristic
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#215—42no—
60C3×(C2×D3)⋊C4—22no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D412yes—
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67#3713—42no—
68#1627—91noSylow
69C22×C3×Q8—61no—
70C2×D3×Q8—21no—
71C2×C3×SD16—61no—
72C3×C4⋊Q8—31no—
73C3×C4⋊Q8—61no—
74C3×#127—31no—
75C3×C22⋊Q8—62no—
76C3×C22⋊Q8—61no—
77C3×C4×Q8—21no—
78C3×C4×Q8C2×D311yescharacteristic
79C3×C4×Q8C2×D311yescharacteristic
80C3×C4×D4—31no—
81C3×C4×D4—61no—
82C2×#215—21no—
83C2×#213—61no—
84C2×#213—61no—
85#897—21no—
86#897—22no—
87#874C2×D311yescharacteristic
88C4×D12—21no—
89C4×D12C2×D311yescharacteristic
90#869—21no—
91#869C2×D311yescharacteristic
92C3×C4⋊C8—31no—
93C3×#102—61no—
94#832—62no—
95#832—61no—
96#809—21no—
97#809—61no—
98#809—62no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—31no—
104C4×C3⋊C8—31no—
105C4×C3⋊C8—61no—
106C22×C3×D3—21no—
107C22×C3×D3—41no—
108C32×Q8—21no—
109C32×Q8D812yescomplemented
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12SD1612yescomplemented
124C3×C4×D3—44no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—44no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130C3⋊(C3⋊C8)—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133D4×Q8—31no—
134#486—91no—
135#460—31no—
136#459—91no—
137#332—91no—
138Q8⋊C8—91no—
139D4⋊C8—91no—
140C2×C3×Q8—21no—
141C2×C3×Q8—62no—
142C2×C3×Q8—61no—
143C2×C3×Q8—122no—
144C2×C3×Q8—122no—
145C2×C3×Q8#6711yescharacteristic
146C2×C3×Q8#6711yescharacteristic
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C22×C3×C4—62no—
152C22×C3×C4—61no—
153D3×Q8—42no—
154D3×Q8—42no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12#6711yescharacteristic
159C2×C4×D3—22no—
160C2×C4×D3—21no—
161C2×Dic6—22no—
162C2×Dic6—21no—
163C3×SD16—122no—
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—32no—
170C3×C4⋊C4—41no—
171C3×C4⋊C4—62no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4#6711yescharacteristic
174C3×C4⋊C4#6711yescharacteristic
175C3×C22⋊C4—62no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42—21no—
180C3×C42—41no—
181C3×C42C22×D311yescharacteristic
182C3×C42C22×D311yescharacteristic
183#215—42no—
184#213—122no—
185#213—122no—
186(C2×D3)⋊C4—22no—
187(C2×D3)⋊C4—21no—
188C4⋊Dic3—22no—
189C4⋊Dic3—21no—
190C4⋊Dic3#6711yescharacteristic
191C4⋊Dic3#6712yes—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—121no—
198C2×C3⋊C8—121no—
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—22no—
207C32×C4—21no—
208C32×C4—41no—
209C32×C4C2×D811yescharacteristic
210C32×C4C2×SD1611yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C32×C4#13711yescharacteristic
213C3×Dic3—41no—
214C3×Dic3—42no—
215C22×Q8—61no—
216C2×SD16—61no—
217C2×D8—181no—
218C4⋊Q8—31no—
219C4⋊Q8—61no—
220#127—31no—
221C22⋊Q8—62no—
222C22⋊Q8—61no—
223C4×Q8D3211yescharacteristic
224C4×D4—31no—
225C4×D4—61no—
226C4⋊C8—31no—
227C4⋊C8—91no—
228#102—61no—
229#102—181no—
230#102—182no—
231C4×C8—91no—
232C23×C3—61no—
233C23×C3—121no—
234C22×D3—21no—
235C22×D3—41no—
236C3×Q8—21no—
237C3×Q8—21no—
238C3×Q8—22no—
239C3×Q8—41no—
240C3×Q8—124no—
241C3×Q8—121no—
242C3×Q8—121no—
243C3×Q8#21312yescomplemented
244C3×Q8#21312yescomplemented
245C3×D4—32no—
246C3×D4—61no—
247C3×D4—122no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C3×D4—121no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—62no—
262C2×C3×C4—61no—
263C2×C3×C4—124no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—21no—
273C2×Dic3—22no—
274D12—21no—
275D12—42no—
276D12—41no—
277D12—41no—
278D12—41no—
279D12—41no—
280D12#21512yescomplemented
281C4×D3—44no—
282C4×D3—41no—
283C4×D3—41no—
284Dic6—44no—
285Dic6—41no—
286Dic6—41no—
287C3×C8—121no—
288C3⋊C8—41no—
289C3⋊C8—121no—
290C3⋊C8—121no—
291C3⋊C8—122no—
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—62no—
301C2×Q8—61no—
302C2×Q8—122no—
303C2×Q8—122no—
304C2×Q8#62511yescharacteristic
305C2×D4—31no—
306C2×D4—61no—
307C2×D4—61no—
308C2×D4—61no—
309C22×C4—62no—
310C22×C4—61no—
311SD16—122no—
312D8—362no—
313C2×C8—61no—
314C2×C8—181no—
315C2×C8—181no—
316C4⋊C4—21no—
317C4⋊C4—31no—
318C4⋊C4—32no—
319C4⋊C4—62no—
320C4⋊C4—61no—
321C4⋊C4#62511yescharacteristic
322C22⋊C4—62no—
323C22⋊C4—61no—
324C42—21no—
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#93711yescharacteristic
334C22×C3#95311yescharacteristic
335C2×D3—22no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—81no—
339C2×D3—81no—
340C2×D3—81no—
341C3×C4—21no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—22no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—42no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—81no—
354C3×C4—122no—
355C3×C4—121no—
356C3×C4D3×SD1611yescharacteristic
357C3×C4#91511yescharacteristic
358C3×C4C2×#21311yescharacteristic
359C3×C4C2×#21311yescharacteristic
360C3×C4#93211yescharacteristic
361C3×C4C2×#21511yescharacteristic
362C3×C4#94211yescharacteristic
363C3×C4#94911yescharacteristic
364Dic3—41no—
365Dic3—42no—
366C32#162711yescharacteristic, complemented, Sylow
367C23—61no—
368C23—121no—
369Q8—21no—
370Q8—124no—
371Q8—121no—
372Q8—121no—
373Q8#371312yescomplemented
374D4—32no—
375D4—61no—
376D4—122no—
377D4—121no—
378D4—121no—
379D4—121no—
380D4—121no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—62no—
384C2×C4—61no—
385C2×C4—124no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4C2×#62511yescharacteristic
389C2×C4D3×#6711yescharacteristic
390C2×C4D3×#6711yescharacteristic
391C8—121no—
392C8—361no—
393C8—361no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—122no—
398C2×C3—481no—
399C2×C3#503611yescharacteristic
400C2×C3#517011yescharacteristic
401C2×C3#520111yescharacteristic
402C2×C3#521711yescharacteristic
403C2×C3#522711yescharacteristic
404C2×C3#524511yescharacteristic
405D3—42no—
406D3—161no—
407C22—62no—
408C22—121no—
409C22—121no—
410C22—241no—
411C22—241no—
412C22—241no—
413C22#6397611yescharacteristic
414C4—22no—
415C4—21no—
416C4—41no—
417C4—122no—
418C4—121no—
419C4C2×#371311yescharacteristic
420C4#6382311yescharacteristic
421C4D3×#21511yescharacteristic
422C4#6394611yescharacteristic
423C3—21no—
424C3#7103511yescharacteristic, complemented
425C3#7191411yescharacteristic, complemented
426C2—122no—
427C2—481no—
428C2#1059116011yescharacteristic
429C2#1059158311yescharacteristic
430C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radical#10590347C2
hypercenterC4×Q8D32
hypocenterC32#1627
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×Q8×D12C2semidirect
2. C3×#5027C2semidirect
4. #10590277C2semidirect
5. #10589401C2semidirect
6. #10589093C2semidirect
7. #10589080C2semidirect
28. Q8×D12D3semidirect
33. #5027D3semidirect
109. C32×Q8D8semidirect
123. C3×D12SD16semidirect
243. C3×Q8#213semidirect
244. C3×Q8#213semidirect
280. D12#215semidirect
366. C32#1627semidirect
373. Q8#3713semidirect
424. C3#71035semidirect
425. C3#71914semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
C3×#50272
#105903472
#105902772
#105894012
#105890932
#105890802
#719143
#710353