Finite Group Databasebeta

← #11779877

Subgroups — #11779877

Order 1152.

535 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 535 conjugacy classes of subgroups — too many to draw. Only its 88 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#10593906C211yesmaximal, characteristic
2C3×#4841C211yesmaximal, characteristic, complemented
3#10590307C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic, complemented
5#10589350C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71045—31nomaximal
9#68393—31nomaximal
10C2×#3795—21no—
11C4×#634C2211yescharacteristic
12C2×C3×#204—21no—
13C3×#874C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×#869C2211yescharacteristic
16#63914—21no—
17#63908—21no—
18#63898—21no—
19#63885—22no—
20C32×C4⋊C8C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#816—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63573—21no—
25#63567—21no—
26#63562—22no—
27#5718—31no—
28#5553—31no—
29C3×#461—31no—
30#5094—31no—
31#5088—31no—
32#5070—31no—
33#4851—31no—
34#4841D311yescharacteristic, complemented
35C3×#331—31no—
36D4⋊(C3⋊C8)—31no—
37#4485D311yescharacteristic, complemented
38#4484—31no—
39#4484—31no—
40#4484—61no—
41#4483—31no—
42C2×#634D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×D12D412yes—
47C2×C3×C4×D3—21no—
48C2×C3×Dic6—21no—
49C2×#625—22no—
50C2×#625—22no—
51C2×D3×Dic3—22no—
52#3795—42no—
53#3795—42no—
54C2×C32×C8—21no—
55C32×C42C2311yescharacteristic
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58C4×C3⋊Dic3—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C2×C3×C3⋊C8—21no—
65C3×#204—42no—
66(C2×D3)⋊Dic3—22no—
67#1642—91noSylow
68C2×#237—61no—
69C2×#235—61no—
70C2×C3×SD16—61no—
71C3×C4⋊Q8—31no—
72C3×#127—31no—
73C3×C4×D4—31no—
74#940—61no—
75#940—61no—
76#939—62no—
77#938—61no—
78D4×Dic3—61no—
79#930—61no—
80C2×#204—21no—
81#893—61no—
82#884—62no—
83#874C2×D311yescharacteristic
84C4×D12C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86C4×Dic6—31no—
87C4×Dic6—31no—
88C4×Dic6—61no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×#103—61no—
94#832—62no—
95#817—61no—
96#816—21no—
97#816—61no—
98#810—61no—
99#809—62no—
100#808—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C22×C3×D3—22no—
106C22×C3×D3—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112#634—21no—
113#634SD1612yescomplemented
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12—21no—
118C3×D12—42no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12—41no—
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127#625—44no—
128#625—82no—
129D3×Dic3—44no—
130C32×C8—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133#550—91no—
134#486—91no—
135#475—91no—
136#461—31no—
137#331—31no—
138Q8⋊C8—91no—
139D4⋊C8—91no—
140C2×C3×Q8—61no—
141C2×C3×D4—31no—
142C2×C3×D4—32no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C22×C3×C4—61no—
146C2×#67—62no—
147C2×#67—62no—
148C2×#67—62no—
149C2×#67—62no—
150C22×Dic3—62no—
151#237—122no—
152#237—122no—
153#235—122no—
154#235—122no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12D1212yes—
158C2×D12#6711yescharacteristic
159C2×C4×D3—21no—
160C2×C4×D3—62no—
161C2×Dic6—21no—
162C2×Dic6—31no—
163C2×Dic6—31no—
164C2×Dic6—61no—
165C3×SD16—122no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—41no—
169C2×C3×C8—61no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C42—21no—
175C3×C42C22×D311yescharacteristic
176C3×C42C22×D311yescharacteristic
177#217—62no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—62no—
180C4⋊Dic3—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3#6711yescharacteristic
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—121no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C4×Dic3—121no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—121no—
196#204—42no—
197C22×C32#12011yescharacteristic
198C2×C3×D3—41no—
199C2×C3×D3—42no—
200C2×C3×D3—42no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C2×C3×D3—42no—
204C32×C4—21no—
205C32×C4C2×SD1611yescharacteristic
206C32×C4#13511yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C32×C4AGL(1,ℤ/8)11yescharacteristic
209C3⋊Dic3—22no—
210C3⋊Dic3—41no—
211C3×Dic3—41no—
212C3×Dic3—81no—
213C2×#41—181no—
214C2×SD16—61no—
215C4⋊Q8—31no—
216#127—31no—
217#127—181no—
218#121—182no—
219#121—181no—
220C4×Q8—91no—
221C4×D4—31no—
222C4×D4—181no—
223#106—181no—
224C4⋊C8—31no—
225C4⋊C8D3211yescharacteristic
226#103—61no—
227#103—181no—
228#102—182no—
229C4×C8—91no—
230C23×C3—61no—
231C23×C3—62no—
232C22×D3—22no—
233C22×D3—21no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×D4—61no—
237C3×D4—61no—
238C3×D4—122no—
239C3×D4—121no—
240C3×D4—121no—
241C3×D4—121no—
242C3×D4—121no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—61no—
247C2×C3×C4—121no—
248C2×C3×C4—121no—
249C2×C3×C4—121no—
250C2×C3×C4C2×D1211yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256#67—124no—
257#67—124no—
258#67—242no—
259#67—242no—
260C2×Dic3—21no—
261C2×Dic3—41no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—121no—
267C2×Dic3—121no—
268C2×Dic3—124no—
269D12—21no—
270D12—21no—
271D12—42no—
272D12—41no—
273D12—41no—
274D12—41no—
275D12—41no—
276C4×D3—41no—
277C4×D3—41no—
278C4×D3—124no—
279Dic6—32no—
280Dic6—32no—
281Dic6—41no—
282Dic6—41no—
283Dic6—62no—
284Dic6—61no—
285Dic6—61no—
286Dic6—121no—
287C3×C8—41no—
288C3×C8—41no—
289C3×C8—81no—
290C3×C8—121no—
291C3⋊C8—41no—
292C3⋊C8—121no—
293C3⋊C8—121no—
294C3⋊C8—122no—
295C2×C32#44911yescharacteristic
296C2×C32#45011yescharacteristic
297C2×C32#45511yescharacteristic
298C3×D3—82no—
299C3×D3—81no—
300#41—362no—
301#41—362no—
302C2×Q8—61no—
303C2×Q8—91no—
304C2×D4—32no—
305C2×D4—31no—
306C2×D4—61no—
307C2×D4—61no—
308C2×D4—182no—
309C2×D4—182no—
310C22×C4—61no—
311C22×C4—182no—
312SD16—122no—
313C2×C8—21no—
314C2×C8—61no—
315C2×C8—181no—
316C4⋊C4—31no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—91no—
320C4⋊C4—181no—
321C22⋊C4—61no—
322C22⋊C4—182no—
323C42—181no—
324C42C2×D3211yescharacteristic
325C22×C3—21no—
326C22×C3—122no—
327C22×C3—122no—
328C22×C3—121no—
329C22×C3—121no—
330C22×C3—121no—
331C22×C3—122no—
332C22×C3#88211yescharacteristic
333C22×C3#93711yescharacteristic
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—42no—
337C2×D3—42no—
338C2×D3—42no—
339C2×D3—41no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—121no—
348C3×C4—241no—
349C3×C4#91111yescharacteristic
350C3×C4#91111yescharacteristic
351C3×C4D3×SD1611yescharacteristic
352C3×C4D3×SD1611yescharacteristic
353C3×C4#91411yescharacteristic
354C3×C4#91611yescharacteristic
355C3×C4#93211yescharacteristic
356C3×C4#95011yescharacteristic
357Dic3—41no—
358Dic3—62no—
359Dic3—62no—
360Dic3—81no—
361Dic3—122no—
362Dic3—121no—
363Dic3—121no—
364Dic3—241no—
365C32#164211yescharacteristic, complemented, Sylow
366C23—61no—
367C23—62no—
368Q8—92no—
369Q8—121no—
370Q8—121no—
371Q8—181no—
372D4—61no—
373D4—61no—
374D4—122no—
375D4—121no—
376D4—121no—
377D4—121no—
378D4—121no—
379D4—364no—
380D4—722no—
381C2×C4—61no—
382C2×C4—121no—
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—241no—
398C2×C3—242no—
399C2×C3#474611yescharacteristic
400C2×C3#477611yescharacteristic
401C2×C3#478111yescharacteristic
402C2×C3#503711yescharacteristic
403C2×C3#516911yescharacteristic
404C2×C3#520211yescharacteristic
405D3—82no—
406D3—81no—
407C22—122no—
408C22—121no—
409C22—121no—
410C22—122no—
411C22—121no—
412C22—122no—
413C22#6392211yescharacteristic
414C4—21no—
415C4—121no—
416C4—182no—
417C4—241no—
418C4—361no—
419C4#6379611yescharacteristic
420C4#6379811yescharacteristic
421C4#6393211yescharacteristic
422C4#6394711yescharacteristic
423C3—21no—
424C3#6839311yescharacteristic, complemented
425C3#7104511yescharacteristic, complemented
426C2—242no—
427C2—241no—
428C2#1059061311yescharacteristic
429C2#1059094311yescharacteristic
430C2#1059101211yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593906C2
hypercenterC4⋊C8D32
hypocenterC32#1642
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×#4841C2semidirect
3. #10590307C2semidirect
4. #10590277C2semidirect
5. #10589350C2semidirect
6. C3×#4485C2semidirect
7. #10589080C2semidirect
34. #4841D3semidirect
37. #4485D3semidirect
113. #634SD16semidirect
365. C32#1642semidirect
424. C3#68393semidirect
425. C3#71045semidirect

Maximal subgroups

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

subgroupindex
#105939062
C3×#48412
#105903072
#105902772
#105893502
C3×#44852
#105890802
#710453
#683933