Finite Group Databasebeta

← #11779271

Subgroups — #11779271

Order 1152.

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

normal subgroups only

This group has 538 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#10596013C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic
3#10590377C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#71019—31nomaximal
9#68201—31nomaximal
10C32×C4×D4C2211yescharacteristic
11#64145—21no—
12#64135—21no—
13#64133—21no—
14#64096—21no—
15#64088—22no—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×#213—21no—
19C3×#874C2211yescharacteristic
20C2×#3716—21no—
21C3×#809—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63563—22no—
26#63563—21no—
27#5542—31no—
28#5542—31no—
29#5542—61no—
30C3×#459—31no—
31#5075—31no—
32#5070—31no—
33#5015D311yescharacteristic
34#4848—31no—
35#4694—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic, complemented
38#4486—31no—
39#4484—31no—
40#4482—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#634—21no—
45C2×#634D411yescharacteristic
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C22⋊C4—21no—
51C32×C42C2311yescharacteristic
52#3757—22no—
53#3757—22no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56C4⋊(C3⋊Dic3)D412yes—
57#3750—22no—
58#3750—21no—
59C4×C3⋊Dic3—22no—
60C4×C3⋊Dic3—21no—
61C3×#213—42no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3716—42no—
66#1628—91noSylow
67C2×C3×D8—61no—
68C3×#127—31no—
69C3×C4×D4—21no—
70C3×C4×D4C2×D311yescharacteristic
71C3×C4×D4C2×D311yescharacteristic
72#936—62no—
73#936—61no—
74#936—61no—
75C2×#214—61no—
76C2×#213—21no—
77#926—61no—
78#926—61no—
79#926—62no—
80#924—61no—
81#924—61no—
82#924—62no—
83C2×#204—61no—
84#887—62no—
85#887—61no—
86#887—61no—
87#879—62no—
88#879—62no—
89#879—64no—
90#874C2×D311yescharacteristic
91#869—31no—
92#869—31no—
93#869—61no—
94C4×Dic6—31no—
95C4×Dic6—31no—
96C4×Dic6—61no—
97C3×C4⋊C8—31no—
98C3×C4⋊C8—31no—
99C3×#102—61no—
100C3×C4×C8—31no—
101#832—62no—
102#832—61no—
103#821—62no—
104#821—61no—
105#809—21no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4×C3⋊C8C2×D311yescharacteristic
109C23×C32—21no—
110C22×C3×D3—41no—
111C32×D4—21no—
112C32×D4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—22no—
122#634—21no—
123#634—21no—
124#634—41no—
125#634—41no—
126C3×D12—42no—
127C3×D12—41no—
128C3×D12—41no—
129C3×D12—41no—
130C3×D12—41no—
131C3×C3⋊C8—41no—
132C3×C3⋊C8—41no—
133C3×C3⋊C8—41no—
134#556—91no—
135#486—91no—
136#460—91no—
137#459—31no—
138#332—91no—
139Q8⋊C8—91no—
140D4⋊C8—31no—
141C2×C3×D4—21no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4D1211yescharacteristic
146C2×C3×D4#6711yescharacteristic
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—21no—
153C2×Dic6—31no—
154C2×Dic6—31no—
155C2×Dic6—61no—
156C2×Dic6—62no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C3×D8—122no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4D1211yescharacteristic
165C3×C4⋊C4#6711yescharacteristic
166C3×C22⋊C4—22no—
167C3×C22⋊C4—21no—
168C3×C22⋊C4—21no—
169C3×C42—21no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172#217—64no—
173#217—62no—
174#217—62no—
175#217—64no—
176#217—62no—
177#217—62no—
178#214—122no—
179#213—42no—
180C4⋊Dic3—31no—
181C4⋊Dic3—32no—
182C4⋊Dic3—31no—
183C4⋊Dic3—32no—
184C4⋊Dic3—61no—
185C4⋊Dic3—62no—
186C4⋊Dic3—62no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189Dic3⋊C4—62no—
190Dic3⋊C4—64no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195C4×Dic3—62no—
196C4×Dic3—64no—
197C4×Dic3—62no—
198C4×Dic3—62no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204#204—122no—
205C22×C32—41no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32#12011yescharacteristic
209C2×C3×D3—81no—
210C2×C3×D3—81no—
211C2×C3×D3—81no—
212C32×C4—21no—
213C32×C4—41no—
214C32×C4#13511yescharacteristic
215C32×C4#13511yescharacteristic
216C32×C4AGL(1,ℤ/8)11yescharacteristic
217C32×C4AGL(1,ℤ/8)11yescharacteristic
218C3⋊Dic3—41no—
219C3⋊Dic3—42no—
220C3⋊Dic3—41no—
221C2×SD16—181no—
222C2×D8—61no—
223C4⋊Q8—91no—
224#127—31no—
225#126—182no—
226#124—181no—
227C22⋊Q8—181no—
228C4×Q8—91no—
229C4×Q8—181no—
230C4×D4D3211yescharacteristic
231#117—181no—
232C4⋊C8—31no—
233C4⋊C8—31no—
234#102—61no—
235#102—181no—
236#102—182no—
237C4×C8—31no—
238C23×C3—22no—
239C23×C3—21no—
240C23×C3—21no—
241C23×C3—121no—
242C22×D3—41no—
243C3×D4—21no—
244C3×D4—21no—
245C3×D4—21no—
246C3×D4—21no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—122no—
250C3×D4—121no—
251C3×D4—121no—
252C3×D4—121no—
253C3×D4—121no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4C2×D1211yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—64no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—62no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—62no—
281D12—42no—
282D12—41no—
283D12—41no—
284D12—41no—
285D12—41no—
286Dic6—61no—
287Dic6—61no—
288Dic6—61no—
289Dic6—61no—
290Dic6—121no—
291Dic6—121no—
292Dic6—122no—
293Dic6—122no—
294Dic6—121no—
295Dic6—121no—
296Dic6—121no—
297Dic6—121no—
298C3×C8—121no—
299C3×C8—121no—
300C3×C8—121no—
301C3⋊C8—41no—
302C3⋊C8—41no—
303C3⋊C8—41no—
304C2×C32—81no—
305C2×C32#44911yescharacteristic
306C2×C32#44911yescharacteristic
307C2×C32#45411yescharacteristic
308C3×D3—161no—
309C2×Q8—91no—
310C2×Q8—181no—
311C2×D4—61no—
312C2×D4—61no—
313C2×D4—61no—
314C2×D4#62611yescharacteristic
315C22×C4—21no—
316SD16—362no—
317D8—122no—
318C2×C8—61no—
319C2×C8—61no—
320C2×C8—61no—
321C4⋊C4—91no—
322C4⋊C4—92no—
323C4⋊C4—182no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C4⋊C4#62611yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—182no—
329C22⋊C4—182no—
330C42—182no—
331C42—181no—
332C42C2×D3211yescharacteristic
333C22×C3—21no—
334C22×C3—42no—
335C22×C3—42no—
336C22×C3—42no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—241no—
344C22×C3—241no—
345C22×C3—241no—
346C22×C3#88211yescharacteristic
347C22×C3#93711yescharacteristic
348C2×D3—81no—
349C2×D3—81no—
350C2×D3—81no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—41no—
358C3×C4—42no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4#90411yescharacteristic
362C3×C4#90811yescharacteristic
363C3×C4#91111yescharacteristic
364C3×C4#91111yescharacteristic
365C3×C4#91211yescharacteristic
366C3×C4#91611yescharacteristic
367C3×C4#93211yescharacteristic
368C3×C4#95011yescharacteristic
369Dic3—124no—
370Dic3—122no—
371Dic3—122no—
372Dic3—121no—
373Dic3—121no—
374Dic3—122no—
375Dic3—121no—
376Dic3—122no—
377Dic3—121no—
378C32#162811yescharacteristic, complemented, Sylow
379C23—21no—
380C23—121no—
381Q8—181no—
382Q8—181no—
383Q8—361no—
384Q8—361no—
385D4—21no—
386D4—21no—
387D4—122no—
388D4—121no—
389D4—121no—
390D4—121no—
391D4—121no—
392C2×C4—21no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—181no—
396C2×C4—182no—
397C2×C4—181no—
398C2×C4C2×#62611yescharacteristic
399C2×C4#381111yescharacteristic
400C2×C4#381111yescharacteristic
401C8—121no—
402C8—121no—
403C8—121no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—82no—
408C2×C3—81no—
409C2×C3—81no—
410C2×C3—481no—
411C2×C3#473411yescharacteristic
412C2×C3#478111yescharacteristic
413C2×C3#482711yescharacteristic
414C2×C3#503711yescharacteristic
415C2×C3#515811yescharacteristic
416C2×C3#520111yescharacteristic
417D3—161no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—241no—
422C22—241no—
423C22—241no—
424C22#6398111yescharacteristic
425C4—21no—
426C4—41no—
427C4—361no—
428C4—362no—
429C4—361no—
430C4#6382911yescharacteristic
431C4#6383011yescharacteristic
432C4#6392711yescharacteristic
433C4#6393611yescharacteristic
434C3—21no—
435C3#6820111yescharacteristic, complemented
436C3#7101911yescharacteristic, complemented
437C2—81no—
438C2—481no—
439C2#1059118211yescharacteristic
440C2#1059145711yescharacteristic
441C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#1628
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596013C2semidirect
3. #10590377C2semidirect
4. #10590273C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589094C2semidirect
7. #10589085C2semidirect
37. D4⋊(C3⋊C8)D3semidirect
378. C32#1628semidirect
435. C3#68201semidirect
436. C3#71019semidirect

Maximal subgroups

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

subgroupindex
#105960132
C3×#50152
#105903772
#105902732
C3×D4⋊(C3⋊C8)2
#105890942
#105890852
#710193
#682013