Finite Group Databasebeta

← #11779012

Subgroups — #11779012

Order 1152.

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

normal subgroups only

This group has 536 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#10593956C211yesmaximal, characteristic, complemented
2#10592774C211yesmaximal, characteristic, complemented
3C3×#5076C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic
5#10589095C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71264—31nomaximal
9#71016—31nomaximal
10C32×#127C2211yescharacteristic
11C2×#3754—21no—
12C4×#634C2211yescharacteristic
13C2×C3×#214—22no—
14C2×C3×#213—21no—
15C3×C4×D12C2211yescharacteristic
16C3×#869C2211yescharacteristic
17#63898—21no—
18D3×C4⋊Dic3—21no—
19#63887—22no—
20#63872—21no—
21#63857—21no—
22#63659—21no—
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#832—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5730—31no—
28#5543—31no—
29C3×#492—31no—
30C3×#459—31no—
31#5076D311yescharacteristic, complemented
32#5075—31no—
33#5075—31no—
34#5075—61no—
35#5072D311yescharacteristic
36#4546—31no—
37D4⋊(C3⋊C8)—31no—
38#4484—31no—
39#4481—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×#634D411yescharacteristic
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D412yes—
49C2×D3×Dic3—22no—
50C32×C42C2311yescharacteristic
51#3754—42no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—21no—
54C4×C3⋊Dic3—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#214—44no—
57C3×#213—42no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65Dic3⋊Dic3—22no—
66(C2×D3)⋊Dic3—22no—
67#1622—91noSylow
68C2×C3×SD16—62no—
69C2×C3×D8—61no—
70C3×C4⋊Q8—31no—
71C3×#127—21no—
72C3×#127C2×D311yescharacteristic
73C3×#127C2×D311yescharacteristic
74C3×C4×D4—31no—
75#946—62no—
76D4×Dic3—61no—
77C2×#214—22no—
78C2×#214—61no—
79C2×#214—61no—
80C2×#214—62no—
81C2×#213—21no—
82C2×C4⋊Dic3—61no—
83#924—61no—
84#897—61no—
85#893—61no—
86D3×C4⋊C4—61no—
87#890—61no—
88#890—61no—
89#878—62no—
90C4×D12C2×D311yescharacteristic
91#869C2×D311yescharacteristic
92C4×Dic6—31no—
93C4×Dic6—31no—
94C4×Dic6—61no—
95C3×C4⋊C8—31no—
96C3×#102—61no—
97C3×C4×C8—31no—
98#832—21no—
99#832—61no—
100#832—61no—
101#832—62no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C23×C32—41no—
108C22×C3×D3—21no—
109C32×D4—41no—
110C32×D4—41no—
111C32×D4—42no—
112C32×D4—41no—
113C32×D4—41no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119#634—21no—
120#634—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—21no—
123C3×D12—21no—
124C3×D12SD1612yescomplemented
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—42no—
128D3×Dic3—82no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—41no—
132#554—91no—
133#492—31no—
134#460—91no—
135#459—31no—
136#333—91no—
137Q8⋊C8—91no—
138D4⋊C8—91no—
139C2×C3×Q8—32no—
140C2×C3×D4—22no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—31no—
148C2×C3×D4—41no—
149C2×C3×D4—41no—
150C22×C3×C4—61no—
151C22×Dic3—62no—
152C2×D12#6711yescharacteristic
153C2×C4×D3—21no—
154C2×C4×D3—62no—
155C2×Dic6—31no—
156C2×Dic6—31no—
157C2×Dic6—61no—
158C2×Dic6#6712yes—
159C3×SD16—124no—
160C3×D8—122no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C22⋊C4—61no—
167C3×C42—21no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#217—62no—
171#214—44no—
172#214—124no—
173#214—122no—
174#214—122no—
175#213—42no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—62no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—61no—
183C4⋊Dic3—62no—
184C4⋊Dic3—62no—
185C4⋊Dic3#6711yescharacteristic
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—121no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—121no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—62no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C22×C32—81no—
200C22×C32—81no—
201C22×C32—81no—
202C22×C32#12011yescharacteristic
203C2×C3×D3—22no—
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C32×C4—21no—
207C32×C4C2×SD1611yescharacteristic
208C32×C4#13511yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4#13711yescharacteristic
211C3⋊Dic3—41no—
212C3⋊Dic3—41no—
213C3×Dic3—41no—
214C3×Dic3—42no—
215C2×SD16—62no—
216C2×SD16—181no—
217C2×D8—61no—
218C4⋊Q8—31no—
219#127D3211yescharacteristic
220#125—181no—
221C22⋊Q8—182no—
222C22⋊Q8—181no—
223C4×Q8—91no—
224C4×D4—31no—
225C4×D4—181no—
226C2×C4⋊C4—181no—
227C4⋊C8—31no—
228C4⋊C8—91no—
229#102—61no—
230#102—181no—
231C4×C8—31no—
232C23×C3—42no—
233C23×C3—41no—
234C23×C3—41no—
235C23×C3—61no—
236C22×D3—21no—
237C3×Q8—122no—
238C3×D4—32no—
239C3×D4—42no—
240C3×D4—42no—
241C3×D4—42no—
242C3×D4—42no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—61no—
252C3×D4—81no—
253C3×D4—81no—
254C3×D4—82no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—61no—
259C2×C3×C4—62no—
260C2×C3×C4—121no—
261C2×C3×C4—121no—
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×Dic3—21no—
269C2×Dic3—22no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—121no—
275C2×Dic3—121no—
276C2×Dic3—242no—
277D12—21no—
278D12#21412yescomplemented
279C4×D3—41no—
280C4×D3—41no—
281C4×D3—242no—
282Dic6—42no—
283Dic6—62no—
284Dic6—61no—
285Dic6—61no—
286Dic6—61no—
287Dic6—61no—
288Dic6—121no—
289C3×C8—62no—
290C3×C8—121no—
291C3⋊C8—22no—
292C3⋊C8—41no—
293C3⋊C8—122no—
294C3⋊C8—121no—
295C3⋊C8—121no—
296C2×C32—161no—
297C2×C32#44811yescharacteristic
298C2×C32#44911yescharacteristic
299C2×C32#45311yescharacteristic
300C3×D3—42no—
301C2×Q8—32no—
302C2×Q8—91no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—31no—
307C22×C4—61no—
308C22×C4—182no—
309SD16—124no—
310SD16—362no—
311D8—122no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—181no—
315C4⋊C4—31no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—91no—
319C4⋊C4—182no—
320C4⋊C4—182no—
321C4⋊C4—181no—
322C22⋊C4—61no—
323C22⋊C4—182no—
324C42—181no—
325C42C2×D3211yescharacteristic
326C22×C3—21no—
327C22×C3—62no—
328C22×C3—82no—
329C22×C3—82no—
330C22×C3—82no—
331C22×C3—81no—
332C22×C3—81no—
333C22×C3—81no—
334C22×C3—81no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3—121no—
338C22×C3—121no—
339C22×C3#93711yescharacteristic
340C22×C3#93711yescharacteristic
341C2×D3—22no—
342C2×D3—41no—
343C2×D3—41no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—121no—
352C3×C4—122no—
353C3×C4#91111yescharacteristic
354C3×C4#91211yescharacteristic
355C3×C4D3×SD1611yescharacteristic
356C3×C4#91411yescharacteristic
357C3×C4#91511yescharacteristic
358C3×C4#91611yescharacteristic
359C3×C4C2×#21411yescharacteristic
360C3×C4#95111yescharacteristic
361Dic3—41no—
362Dic3—42no—
363Dic3—122no—
364Dic3—121no—
365Dic3—121no—
366Dic3—121no—
367Dic3—121no—
368Dic3—241no—
369C32#162211yescharacteristic, complemented, Sylow
370C23—41no—
371C23—61no—
372Q8—122no—
373Q8—181no—
374Q8—181no—
375D4—32no—
376D4—42no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—41no—
381D4—61no—
382C2×C4—61no—
383C2×C4—62no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—181no—
387C2×C4—181no—
388C2×C4—722no—
389C2×C4D3×#6711yescharacteristic
390C2×C4D3×#6711yescharacteristic
391C2×C4#381111yescharacteristic
392C8—62no—
393C8—121no—
394C8—361no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—122no—
399C2×C3—162no—
400C2×C3—161no—
401C2×C3—161no—
402C2×C3#504011yescharacteristic
403C2×C3#507711yescharacteristic
404C2×C3#515811yescharacteristic
405C2×C3#517011yescharacteristic
406C2×C3#517211yescharacteristic
407C2×C3#519811yescharacteristic
408D3—42no—
409C22—62no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—121no—
414C22—121no—
415C22#6398311yescharacteristic
416C4—21no—
417C4—121no—
418C4—122no—
419C4—361no—
420C4—361no—
421C4D3×#21411yescharacteristic
422C4#6392911yescharacteristic
423C4#6393611yescharacteristic
424C4#6393711yescharacteristic
425C3—21no—
426C3#7101611yescharacteristic, complemented
427C3#7126411yescharacteristic, complemented
428C2—122no—
429C2—161no—
430C2#1059151711yescharacteristic
431C2#1059152011yescharacteristic
432C2#1059152311yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#120
prime radicalC3×#5072C2
hypercenter#127D32
hypocenterC32#1622
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10593956C2semidirect
2. #10592774C2semidirect
3. C3×#5076C2semidirect
5. #10589095C2semidirect
6. #10589085C2semidirect
7. #10589081C2semidirect
31. #5076D3semidirect
124. C3×D12SD16semidirect
278. D12#214semidirect
369. C32#1622semidirect
426. C3#71016semidirect
427. C3#71264semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105927742
C3×#50762
C3×#50722
#105890952
#105890852
#105890812
#712643
#710163