Finite Group Databasebeta

← #11779094

Subgroups — #11779094

Order 1152.

512 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593988C211yesmaximal, characteristic, complemented
2C3×#4843C211yesmaximal, characteristic, complemented
3#10590369C211yesmaximal, characteristic, complemented
4#10590347C211yesmaximal, characteristic, complemented
5#10589347C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71017—31nomaximal
9#68199—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×D24—21no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15#63913—22no—
16#63908—21no—
17#63908—21no—
18#63841—21no—
19#63841—21no—
20C2×#3716—22no—
21C2×#3713—21no—
22C32×C4⋊C8C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#821—21no—
25C3×C4×C3⋊C8C2211yescharacteristic
26#63562—21no—
27#5563—31no—
28#5563—31no—
29C3×#459—31no—
30#5076—31no—
31#5072—31no—
32#5015—31no—
33#4843D311yescharacteristic, complemented
34#4693—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4483D311yescharacteristic, complemented
38#4481—31no—
39#4481—31no—
40#4481—61no—
41#4459—31no—
42C2×#634D412yes—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×D12D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×#625—22no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61C3×D24—42no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64Dic32—22no—
65#3716—44no—
66#3713—42no—
67#1624—91noSylow
68C2×C3×D8—61no—
69C3×#127—31no—
70C3×C4×D4—31no—
71C3×C4×D4—31no—
72#938—61no—
73#938—61no—
74C2×#214—62no—
75C2×#213—61no—
76C2×#213—61no—
77#930—61no—
78#930—61no—
79#926—61no—
80#926—61no—
81C2×D24—21no—
82C2×#204—62no—
83#892—61no—
84#892—61no—
85#885—62no—
86#885—62no—
87#874C2×D311yescharacteristic
88C4×D12C2×D311yescharacteristic
89C4×D12C2×D311yescharacteristic
90#869—31no—
91#869—31no—
92#869—61no—
93C3×C4⋊C8—21no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C2×D311yescharacteristic
96C3×#102—61no—
97C3×C4×C8—31no—
98#832—61no—
99#821—21no—
100#809—61no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—21no—
107C22×C3×D3—41no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—22no—
112#634—42no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C3×D12—21no—
116C3×D12—21no—
117C3×D12—21no—
118C3×D12—21no—
119C3×D12—42no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×C4×D3—41no—
128#625—82no—
129C32×C8—41no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—22no—
132#555—91no—
133#492—91no—
134#459—31no—
135#459—91no—
136#333—91no—
137D4⋊C8—31no—
138D4⋊C8—91no—
139C2×C3×D4—31no—
140C2×C3×D4—31no—
141C2×C3×D4—61no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C22×C3×C4—61no—
145C22×C3×C4—61no—
146C2×#67—62no—
147C2×#67—62no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12D1211yescharacteristic
152C2×D12#6711yescharacteristic
153C2×C4×D3—21no—
154C2×C4×D3—21no—
155C2×Dic6—32no—
156C2×Dic6—32no—
157C2×Dic6—62no—
158C3×D8—122no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—41no—
162C2×C3×C8—61no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—31no—
165C3×C22⋊C4—61no—
166C3×C22⋊C4—61no—
167C3×C42—21no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#217—62no—
171#217—62no—
172#214—124no—
173#213—122no—
174#213—122no—
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—121no—
184C4⋊Dic3—121no—
185C4⋊Dic3D1211yescharacteristic
186C4⋊Dic3#6711yescharacteristic
187C4×Dic3—62no—
188C4×Dic3—62no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—121no—
193D24—42no—
194#204—124no—
195C22×C32#12011yescharacteristic
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—81no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C32×C4—21no—
206C32×C4#13511yescharacteristic
207C32×C4#13511yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C3⋊Dic3—42no—
211C3×Dic3—41no—
212C3×Dic3—41no—
213C2×SD16—182no—
214C2×D8—61no—
215C2×D8—181no—
216C4⋊Q8—91no—
217#127—31no—
218#124—182no—
219#121—181no—
220#121—181no—
221C4×D4—31no—
222C4×D4—31no—
223#117—181no—
224#117—181no—
225C4⋊C8—91no—
226C4⋊C8D3211yescharacteristic
227#102—61no—
228#102—181no—
229C4×C8—31no—
230C23×C3—61no—
231C23×C3—61no—
232C23×C3—121no—
233C22×D3—21no—
234C22×D3—21no—
235C22×D3—41no—
236C3×D4—61no—
237C3×D4—61no—
238C3×D4—61no—
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—61no—
249C2×C3×C4—61no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4—121no—
254C2×C3×C4C2×D1211yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260#67—242no—
261#67—242no—
262C2×Dic3—21no—
263C2×Dic3—21no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—122no—
267D12—21no—
268D12—21no—
269D12—21no—
270D12—21no—
271D12—42no—
272D12—41no—
273D12—41no—
274D12—41no—
275D12—41no—
276C4×D3—41no—
277C4×D3—41no—
278C4×D3—41no—
279C4×D3—41no—
280Dic6—122no—
281Dic6—122no—
282Dic6—242no—
283C3×C8—41no—
284C3×C8—41no—
285C3×C8—62no—
286C3×C8—81no—
287C3⋊C8—22no—
288C3⋊C8—121no—
289C3⋊C8—121no—
290C3⋊C8—241no—
291C2×C32#44911yescharacteristic
292C2×C32#44911yescharacteristic
293C2×C32#45311yescharacteristic
294C3×D3—81no—
295C3×D3—81no—
296C3×D3—161no—
297C2×Q8—92no—
298C2×D4—31no—
299C2×D4—31no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—182no—
304C22×C4—61no—
305C22×C4—61no—
306SD16—364no—
307D8—122no—
308D8—362no—
309C2×C8—21no—
310C2×C8—61no—
311C2×C8—181no—
312C4⋊C4—31no—
313C4⋊C4—31no—
314C4⋊C4—181no—
315C4⋊C4—181no—
316C22⋊C4—61no—
317C22⋊C4—61no—
318C22⋊C4—182no—
319C22⋊C4—182no—
320C42—182no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3—121no—
326C22×C3—121no—
327C22×C3—121no—
328C22×C3—121no—
329C22×C3—241no—
330C22×C3—241no—
331C22×C3—241no—
332C22×C3#88211yescharacteristic
333C22×C3#93711yescharacteristic
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—81no—
341C2×D3—81no—
342C2×D3—81no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—121no—
351C3×C4—121no—
352C3×C4#90411yescharacteristic
353C3×C4#90811yescharacteristic
354C3×C4#91111yescharacteristic
355C3×C4#91111yescharacteristic
356C3×C4#91211yescharacteristic
357C3×C4#91611yescharacteristic
358C3×C4#93211yescharacteristic
359C3×C4#95011yescharacteristic
360Dic3—41no—
361Dic3—41no—
362Dic3—122no—
363Dic3—122no—
364Dic3—242no—
365C32#162411yescharacteristic, complemented, Sylow
366C23—61no—
367C23—61no—
368C23—121no—
369Q8—362no—
370D4—61no—
371D4—61no—
372D4—61no—
373D4—61no—
374D4—122no—
375D4—121no—
376D4—121no—
377D4—121no—
378D4—121no—
379D4—722no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—182no—
387C2×C4D3×D1211yescharacteristic
388C2×C4#380211yescharacteristic
389C2×C4D3×#6711yescharacteristic
390C8—41no—
391C8—62no—
392C8—361no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—241no—
397C2×C3—241no—
398C2×C3—481no—
399C2×C3#473411yescharacteristic
400C2×C3#478111yescharacteristic
401C2×C3#482211yescharacteristic
402C2×C3#503711yescharacteristic
403C2×C3#515811yescharacteristic
404C2×C3#519811yescharacteristic
405D3—81no—
406D3—81no—
407D3—161no—
408C22—121no—
409C22—121no—
410C22—121no—
411C22—121no—
412C22—121no—
413C22—121no—
414C22—241no—
415C22—241no—
416C22—241no—
417C22#6392211yescharacteristic
418C4—21no—
419C4—121no—
420C4—121no—
421C4—362no—
422C4#6379511yescharacteristic
423C4#6380711yescharacteristic
424C4#6393211yescharacteristic
425C4#6394711yescharacteristic
426C3—21no—
427C3#6819911yescharacteristic, complemented
428C3#7101711yescharacteristic, complemented
429C2—241no—
430C2—241no—
431C2—481no—
432C2#1059061311yescharacteristic
433C2#1059096211yescharacteristic
434C2#1059101311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1624
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. #10593988C2semidirect
2. C3×#4843C2semidirect
3. #10590369C2semidirect
4. #10590347C2semidirect
5. #10589347C2semidirect
6. C3×#4483C2semidirect
7. #10589081C2semidirect
33. #4843D3semidirect
37. #4483D3semidirect
365. C32#1624semidirect
427. C3#68199semidirect
428. C3#71017semidirect

Maximal subgroups

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

subgroupindex
#105939882
C3×#48432
#105903692
#105903472
#105893472
C3×#44832
#105890812
#710173
#681993