Finite Group Databasebeta

← #11780451

Subgroups — #11780451

Order 1152.

512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593895C211yesmaximal, characteristic
2C3×#4846C211yesmaximal, characteristic, complemented
3#10590363C211yesmaximal, characteristic, complemented
4#10590303C211yesmaximal, characteristic, complemented
5#10589348C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71111—31nomaximal
9#68211—31nomaximal
10C2×#3795—21no—
11#64078C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63908—21no—
16#63891—22no—
17D3×C4⋊Dic3—21no—
18#63857—21no—
19C2×#3715—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#821—21no—
23C3×#818—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63573—22no—
26#63565—21no—
27#5555—31no—
28#5551—31no—
29C3×#474—31no—
30#5083—31no—
31#5080—31no—
32#5019—31no—
33#4846D311yescharacteristic, complemented
34#4680—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4483D311yescharacteristic, complemented
38#4482—31no—
39#4482—31no—
40#4482—61no—
41#4459—31no—
42C2×#634—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×Dic6—21no—
48C2×#625—22no—
49C2×D3×Dic3—22no—
50#3795—42no—
51#3795—42no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)D412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66#3715—42no—
67#1654—91noSylow
68C2×#237—61no—
69C2×#235—61no—
70C3×C4⋊Q8—31no—
71C3×C4×D4—31no—
72C3×C4×D4—31no—
73C2×#215—61no—
74#938—61no—
75C2×#214—61no—
76#930—61no—
77C2×C4⋊Dic3—61no—
78#924—61no—
79#897—61no—
80D3×C4⋊C4—61no—
81#886—62no—
82#883—62no—
83C4×D12C2×D311yescharacteristic
84C4×D12C2×D311yescharacteristic
85#869—31no—
86#869—31no—
87#869—61no—
88#869C2×D311yescharacteristic
89C3×#107—61no—
90C3×C4⋊C8—21no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×#102—61no—
94C3×C4×C8—31no—
95#835—61no—
96#821—21no—
97#818—21no—
98#817—62no—
99#810—61no—
100#808—62no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—22no—
111#634—41no—
112#634—41no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12—21no—
118C3×D12—21no—
119C3×D12SD1612yescomplemented
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126#625—44no—
127D3×Dic3—44no—
128C32×C8—41no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—22no—
131#547—91no—
132#498—91no—
133#474—31no—
134#461—91no—
135#332—91no—
136D4⋊C8—31no—
137D4⋊C8—91no—
138C2×C3×Q8—61no—
139C2×C3×D4—31no—
140C2×C3×D4—31no—
141C22×C3×C4—61no—
142C22×C3×C4—61no—
143C2×#67—62no—
144C2×#67—62no—
145C22×Dic3—62no—
146#237—122no—
147#237—122no—
148#235—122no—
149#235—122no—
150C2×D12D1211yescharacteristic
151C2×D12#6711yescharacteristic
152C2×C4×D3—21no—
153C2×C4×D3—21no—
154C2×C4×D3—62no—
155C2×Dic6—21no—
156C2×Dic6—61no—
157C2×Dic6—61no—
158C2×Dic6—121no—
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×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C22⋊C4—61no—
168C3×C22⋊C4—61no—
169C3×C42—21no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172#217—62no—
173#215—122no—
174#214—122no—
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—62no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—32no—
181C4⋊Dic3—32no—
182C4⋊Dic3—62no—
183C4⋊Dic3—62no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—121no—
187C4⋊Dic3D1211yescharacteristic
188C4⋊Dic3#6711yescharacteristic
189Dic3⋊C4—62no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—121no—
194C22×C32#12011yescharacteristic
195C2×C3×D3—22no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C32×C4—21no—
202C32×C4C2×SD1611yescharacteristic
203C32×C4#13511yescharacteristic
204C32×C4AGL(1,ℤ/8)11yescharacteristic
205C32×C4AGL(1,ℤ/8)11yescharacteristic
206C3⋊Dic3—42no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—81no—
210C2×#41—181no—
211C2×SD16—181no—
212C4⋊Q8—31no—
213C4⋊Q8—91no—
214#123—182no—
215C22⋊Q8—181no—
216#121—181no—
217C4×D4—31no—
218C4×D4—31no—
219C2×C4⋊C4—181no—
220#107—61no—
221#106—182no—
222C4⋊C8—91no—
223C4⋊C8D3211yescharacteristic
224#103—181no—
225#102—61no—
226C4×C8—31no—
227C23×C3—61no—
228C23×C3—61no—
229C22×D3—21no—
230C22×D3—21no—
231C3×Q8—121no—
232C3×Q8—121no—
233C3×D4—32no—
234C3×D4—61no—
235C3×D4—61no—
236C3×D4—61no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4—121no—
245C2×C3×C4—121no—
246C2×C3×C4—121no—
247C2×C3×C4C2×D1211yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253#67—124no—
254#67—124no—
255C2×Dic3—21no—
256C2×Dic3—21no—
257C2×Dic3—41no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—122no—
261C2×Dic3—124no—
262D12—21no—
263D12—21no—
264D12—21no—
265D12#21512yescomplemented
266C4×D3—41no—
267C4×D3—41no—
268C4×D3—41no—
269C4×D3—41no—
270C4×D3—124no—
271Dic6—41no—
272Dic6—41no—
273Dic6—121no—
274Dic6—121no—
275Dic6—121no—
276Dic6—121no—
277Dic6—241no—
278Dic6—241no—
279C3×C8—41no—
280C3×C8—41no—
281C3×C8—62no—
282C3×C8—81no—
283C3⋊C8—22no—
284C3⋊C8—121no—
285C3⋊C8—121no—
286C3⋊C8—241no—
287C2×C32#44911yescharacteristic
288C2×C32#45011yescharacteristic
289C2×C32#45611yescharacteristic
290C3×D3—42no—
291C3×D3—81no—
292#41—362no—
293#41—362no—
294C2×Q8—61no—
295C2×Q8—181no—
296C2×D4—31no—
297C2×D4—31no—
298C2×D4—182no—
299C22×C4—61no—
300C22×C4—61no—
301C22×C4—182no—
302SD16—362no—
303C2×C8—21no—
304C2×C8—61no—
305C2×C8—181no—
306C4⋊C4—31no—
307C4⋊C4—31no—
308C4⋊C4—61no—
309C4⋊C4—61no—
310C4⋊C4—92no—
311C4⋊C4—182no—
312C4⋊C4—181no—
313C22⋊C4—61no—
314C22⋊C4—61no—
315C22⋊C4—182no—
316C42C2×D3211yescharacteristic
317C22×C3—21no—
318C22×C3—62no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3—121no—
322C22×C3—121no—
323C22×C3—121no—
324C22×C3#88211yescharacteristic
325C22×C3#93711yescharacteristic
326C2×D3—22no—
327C2×D3—41no—
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—41no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—121no—
340C3×C4—121no—
341C3×C4—241no—
342C3×C4#90411yescharacteristic
343C3×C4#90811yescharacteristic
344C3×C4#91111yescharacteristic
345C3×C4#91111yescharacteristic
346C3×C4#91211yescharacteristic
347C3×C4D3×SD1611yescharacteristic
348C3×C4C2×#21511yescharacteristic
349C3×C4#94911yescharacteristic
350Dic3—41no—
351Dic3—41no—
352Dic3—81no—
353Dic3—122no—
354Dic3—122no—
355Dic3—242no—
356C32#165411yescharacteristic, complemented, Sylow
357C23—61no—
358C23—61no—
359Q8—121no—
360Q8—121no—
361Q8—361no—
362Q8—361no—
363D4—32no—
364D4—61no—
365D4—61no—
366D4—61no—
367D4—364no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—121no—
371C2×C4—121no—
372C2×C4—121no—
373C2×C4—121no—
374C2×C4—121no—
375C2×C4—182no—
376C2×C4—364no—
377C2×C4D3×D1211yescharacteristic
378C2×C4#380211yescharacteristic
379C2×C4D3×#6711yescharacteristic
380C8—41no—
381C8—62no—
382C8—361no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—122no—
387C2×C3—241no—
388C2×C3#473411yescharacteristic
389C2×C3#477611yescharacteristic
390C2×C3#482611yescharacteristic
391C2×C3#504611yescharacteristic
392C2×C3#515811yescharacteristic
393C2×C3#520511yescharacteristic
394D3—42no—
395D3—81no—
396C22—62no—
397C22—121no—
398C22—121no—
399C22—121no—
400C22—121no—
401C22—121no—
402C22#6392211yescharacteristic
403C4—21no—
404C4—121no—
405C4—121no—
406C4—241no—
407C4—362no—
408C4#6379511yescharacteristic
409C4#6380711yescharacteristic
410C4#6392511yescharacteristic
411C4D3×#21511yescharacteristic
412C3—21no—
413C3#6821111yescharacteristic, complemented
414C3#7111111yescharacteristic, complemented
415C2—122no—
416C2—241no—
417C2#1059059611yescharacteristic
418C2#1059096211yescharacteristic
419C2#1059101711yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593895C2
hypercenterC4⋊C8D32
hypocenterC32#1654
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
2. C3×#4846C2semidirect
3. #10590363C2semidirect
4. #10590303C2semidirect
5. #10589348C2semidirect
6. C3×#4483C2semidirect
7. #10589081C2semidirect
33. #4846D3semidirect
37. #4483D3semidirect
119. C3×D12SD16semidirect
265. D12#215semidirect
356. C32#1654semidirect
413. C3#68211semidirect
414. C3#71111semidirect

Maximal subgroups

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

subgroupindex
#105938952
C3×#48462
#105903632
#105903032
#105893482
C3×#44832
#105890812
#711113
#682113