Finite Group Databasebeta

← #11779880

Subgroups — #11779880

Order 1152.

535 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 535 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5577C211yesmaximal, characteristic
2C3×#5020C211yesmaximal, characteristic, complemented
3#10590363C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic, complemented
5#10589401C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71921—31nomaximal
9#71124—31nomaximal
10C2×C3×#239—21no—
11C32×C4×Q8C2211yescharacteristic
12C3×#895—22no—
13C3×#895—21no—
14C3×#874—21no—
15C3×#874C2211yescharacteristic
16C3×C4×D12—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3715—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#835—21no—
23C3×#808—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63565—21no—
26#63562—22no—
27C3×#550—31no—
28#5577D311yescharacteristic
29C3×#475—31no—
30#5088—31no—
31#5083—31no—
32#5070—31no—
33#5020D311yescharacteristic, complemented
34#5019—31no—
35#4544—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39D4⋊(C3⋊C8)—31no—
40#4485—31no—
41#4483—31no—
42C2×C32×Q8D411yescharacteristic
43C3×#239—42no—
44C3×#239—42no—
45C2×C3×D12—22no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—22no—
49C2×C3×D12D411yescharacteristic
50C2×C3×D12D412yes—
51C2×C3×C4×D3—22no—
52C2×C3×C4×D3—21no—
53C2×C3×Dic6—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C42—21no—
57C32×C42C2311yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×(C2×D3)⋊C4—22no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66#3715—42no—
67#1642—91noSylow
68C2×C3×#41—61no—
69C2×#239—21no—
70C3×C4⋊Q8—31no—
71C3×#127—31no—
72C3×#127—61no—
73C3×#121—62no—
74C3×#121—61no—
75C3×C4×Q8—21no—
76C3×C4×Q8C2×D311yescharacteristic
77C3×C4×Q8C2×D311yescharacteristic
78C3×C4×D4—31no—
79C3×C4×D4—61no—
80C2×#215—61no—
81C2×#214—61no—
82#895—22no—
83#895—21no—
84#874—21no—
85#874C2×D311yescharacteristic
86C4×D12—21no—
87C4×D12C2×D311yescharacteristic
88#869C2×D311yescharacteristic
89C3×#106—61no—
90C3×C4⋊C8—31no—
91C3×#103—61no—
92#835—21no—
93#835—61no—
94#832—62no—
95#810—61no—
96#809—62no—
97#808—21no—
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—
105C22×C3×D3—21no—
106C22×C3×D3—22no—
107C32×Q8—21no—
108C32×Q8SD1612yescomplemented
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—44no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×D12—82no—
125C3×C4×D3—44no—
126C3×C4×D3—41no—
127C3×C4×D3—41no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130C3⋊(C3⋊C8)—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133#550—31no—
134#486—91no—
135#475—31no—
136#461—91no—
137#331—91no—
138Q8⋊C8—91no—
139D4⋊C8—91no—
140C3×#41—122no—
141C3×#41—122no—
142C2×C3×Q8—21no—
143C2×C3×Q8—61no—
144C2×C3×Q8#6711yescharacteristic
145C2×C3×Q8#6711yescharacteristic
146C2×C3×D4—31no—
147C2×C3×D4—32no—
148C2×C3×D4—62no—
149C2×C3×D4—62no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C22×C3×C4—62no—
153C22×C3×C4—61no—
154#239—42no—
155#239—42no—
156C2×D12—22no—
157C2×D12—21no—
158C2×D12—21no—
159C2×D12—22no—
160C2×D12#6711yescharacteristic
161C2×D12#6712yes—
162C2×C4×D3—22no—
163C2×C4×D3—21no—
164C2×Dic6—21no—
165C2×C3×C8—61no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—41no—
171C3×C4⋊C4—61no—
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—122no—
184#214—122no—
185(C2×D3)⋊C4—22no—
186(C2×D3)⋊C4—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C4⋊Dic3#6711yescharacteristic
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#12011yescharacteristic
198C2×C3×D3—41no—
199C2×C3×D3—42no—
200C2×C3×D3—42no—
201C2×C3×D3—41no—
202C2×C3×D3—42no—
203C2×C3×D3—41no—
204C32×C4—22no—
205C32×C4—21no—
206C32×C4—41no—
207C32×C4C2×SD1611yescharacteristic
208C32×C4#13511yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4AGL(1,ℤ/8)11yescharacteristic
211C3×Dic3—41no—
212C3×Dic3—81no—
213C2×#41—61no—
214C2×SD16—181no—
215C4⋊Q8—31no—
216#127—31no—
217#127—61no—
218#121—62no—
219#121—61no—
220C4×Q8D3211yescharacteristic
221C4×D4—31no—
222C4×D4—61no—
223#106—61no—
224C4⋊C8—31no—
225C4⋊C8—91no—
226#103—61no—
227#103—181no—
228#102—182no—
229C4×C8—91no—
230C23×C3—61no—
231C23×C3—62no—
232C22×D3—21no—
233C22×D3—22no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—22no—
237C3×Q8—41no—
238C3×Q8—121no—
239C3×Q8—121no—
240C3×Q8#21412yescomplemented
241C3×Q8#21512yescomplemented
242C3×D4—61no—
243C3×D4—61no—
244C3×D4—122no—
245C3×D4—124no—
246C3×D4—121no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—242no—
251C2×C3×C4—21no—
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—41no—
259C2×C3×C4—41no—
260C2×C3×C4—61no—
261C2×C3×C4—124no—
262C2×C3×C4—121no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—41no—
273D12—21no—
274D12—21no—
275D12—42no—
276D12—44no—
277D12—41no—
278D12—41no—
279D12—41no—
280D12—41no—
281D12—82no—
282C4×D3—44no—
283C4×D3—41no—
284C4×D3—41no—
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#44911yescharacteristic
296C2×C32#45011yescharacteristic
297C2×C32#45511yescharacteristic
298C3×D3—81no—
299C3×D3—82no—
300#41—122no—
301#41—122no—
302C2×Q8—61no—
303C2×Q8#62511yescharacteristic
304C2×D4—31no—
305C2×D4—32no—
306C2×D4—62no—
307C2×D4—62no—
308C2×D4—61no—
309C2×D4—61no—
310C22×C4—62no—
311C22×C4—61no—
312SD16—362no—
313C2×C8—61no—
314C2×C8—181no—
315C2×C8—181no—
316C4⋊C4—21no—
317C4⋊C4—31no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4#62511yescharacteristic
321C22⋊C4—62no—
322C22⋊C4—61no—
323C42—21no—
324C42C2×D3211yescharacteristic
325C22×C3—21no—
326C22×C3—121no—
327C22×C3—122no—
328C22×C3—122no—
329C22×C3—121no—
330C22×C3—122no—
331C22×C3—121no—
332C22×C3#93711yescharacteristic
333C22×C3#95311yescharacteristic
334C2×D3—42no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—42no—
338C2×D3—42no—
339C2×D3—41no—
340C3×C4—21no—
341C3×C4—22no—
342C3×C4—21no—
343C3×C4—22no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—41no—
349C3×C4—42no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—81no—
353C3×C4—121no—
354C3×C4—241no—
355C3×C4#91411yescharacteristic
356C3×C4#91611yescharacteristic
357C3×C4#93211yescharacteristic
358C3×C4C2×#21411yescharacteristic
359C3×C4C2×#21511yescharacteristic
360C3×C4#94911yescharacteristic
361C3×C4#94911yescharacteristic
362C3×C4#95011yescharacteristic
363Dic3—41no—
364Dic3—81no—
365C32#164211yescharacteristic, complemented, Sylow
366C23—61no—
367C23—62no—
368Q8—21no—
369Q8—121no—
370Q8—121no—
371Q8#371512yescomplemented
372D4—61no—
373D4—61no—
374D4—122no—
375D4—124no—
376D4—121no—
377D4—121no—
378D4—121no—
379D4—121no—
380D4—242no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—61no—
384C2×C4—124no—
385C2×C4—121no—
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—241no—
398C2×C3—242no—
399C2×C3#504611yescharacteristic
400C2×C3#517211yescharacteristic
401C2×C3#520211yescharacteristic
402C2×C3#521811yescharacteristic
403C2×C3#523811yescharacteristic
404C2×C3#524211yescharacteristic
405D3—81no—
406D3—82no—
407C22—121no—
408C22—122no—
409C22—122no—
410C22—121no—
411C22—122no—
412C22—121no—
413C22#6397611yescharacteristic
414C4—21no—
415C4—22no—
416C4—41no—
417C4—121no—
418C4—241no—
419C4#6382311yescharacteristic
420C4C2×#371511yescharacteristic
421C4#6393911yescharacteristic
422C4#6394711yescharacteristic
423C3—21no—
424C3#7112411yescharacteristic, complemented
425C3#7192111yescharacteristic, complemented
426C2—241no—
427C2—242no—
428C2#1059116911yescharacteristic
429C2#1059158611yescharacteristic
430C2#1059166411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC3×#5577C2
hypercenterC4×Q8D32
hypocenterC32#1642
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
2. C3×#5020C2semidirect
3. #10590363C2semidirect
4. #10590277C2semidirect
5. #10589401C2semidirect
6. #10589090C2semidirect
7. #10589080C2semidirect
33. #5020D3semidirect
108. C32×Q8SD16semidirect
240. C3×Q8#214semidirect
241. C3×Q8#215semidirect
365. C32#1642semidirect
371. Q8#3715semidirect
424. C3#71124semidirect
425. C3#71921semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
C3×#50202
#105903632
#105902772
#105894012
#105890902
#105890802
#719213
#711243