Finite Group Databasebeta

← #11779010

Subgroups — #11779010

Order 1152.

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

normal subgroups only

This group has 543 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#10593960C211yesmaximal, characteristic, complemented
2#10592775C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic
5#10589096C211yesmaximal, characteristic, complemented
6#10589083C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71028—31nomaximal
9#71016—31nomaximal
10C32×#127C2211yescharacteristic
11C2×#3754—22no—
12#64078C2211yescharacteristic
13C2×C3×#214—21no—
14C2×C3×#213—21no—
15C3×C4×D12C2211yescharacteristic
16C3×C4×Dic6C2211yescharacteristic
17#63896—22no—
18Dic3×D12—21no—
19D3×C4⋊Dic3—21no—
20#63869—21no—
21#63856—21no—
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#832—21no—
24C3×#832—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27#5579—31no—
28#5543—31no—
29C3×#460—31no—
30C3×#459—31no—
31#5076—31no—
32#5076—31no—
33#5076—61no—
34#5075D311yescharacteristic, complemented
35#5072D311yescharacteristic
36#4535—31no—
37D4⋊(C3⋊C8)—31no—
38#4484—31no—
39#4483—31no—
40#4481—31no—
41#4481—31no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×#634D412yes—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×D3×Dic3—22no—
50C32×C42C2311yescharacteristic
51#3754—44no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#214—42no—
56C3×#213—42no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3724—22no—
65Dic3⋊Dic3—22no—
66(C2×D3)⋊Dic3—22no—
67#1622—91noSylow
68C2×C3×SD16—61no—
69C2×C3×D8—61no—
70C3×#127—21no—
71C3×#127C2×D311yescharacteristic
72C3×#127C2×D311yescharacteristic
73C3×C4×Q8—31no—
74C3×C4×D4—31no—
75#946—61no—
76D4×Dic3—61no—
77C2×#214—21no—
78C2×#214—62no—
79C2×#214—62no—
80C2×#214—64no—
81C2×#213—21no—
82C2×C4⋊Dic3—61no—
83#924—61no—
84#896—62no—
85D3×C4⋊C4—61no—
86#890—61no—
87#878—62no—
88C4×D12—61no—
89C4×D12C2×D311yescharacteristic
90#870—61no—
91#869—31no—
92#869—31no—
93#869—61no—
94C4×Dic6C2×D311yescharacteristic
95C3×C4⋊C8—31no—
96C3×C4⋊C8—31no—
97C3×#102—61no—
98C3×#102—61no—
99#832—21no—
100#832—21no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—31no—
104C4×C3⋊C8—31no—
105C4×C3⋊C8—61no—
106C23×C32—41no—
107C22×C3×D3—21no—
108C32×D4—42no—
109C32×D4—41no—
110C32×D4—41no—
111C32×D4—41no—
112C32×D4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3—22no—
117#634—42no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C3×D12—21no—
122C3×D12SD1612yescomplemented
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×Dic6—21no—
126C3×Dic6—21no—
127D3×Dic3—82no—
128C3⋊(C3⋊C8)—22no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#554—91no—
132#492—91no—
133#460—31no—
134#459—31no—
135#333—91no—
136Q8⋊C8—91no—
137D4⋊C8—91no—
138C2×C3×Q8—31no—
139C2×C3×D4—22no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—31no—
147C2×C3×D4—41no—
148C2×C3×D4—41no—
149C22×C3×C4—61no—
150C22×Dic3—62no—
151C2×D12#6711yescharacteristic
152C2×C4×D3—21no—
153C2×C4×D3—62no—
154C2×Dic6—32no—
155C2×Dic6—32no—
156C2×Dic6—62no—
157C2×Dic6#6711yescharacteristic
158C3×SD16—122no—
159C3×D8—122no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C3×C4⋊C4—31no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—61no—
165C3×C22⋊C4—61no—
166C3×C42—21no—
167C3×C42—61no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#217—62no—
171#214—42no—
172#214—124no—
173#214—124no—
174#214—128no—
175#213—42no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—62no—
178C4⋊Dic3—62no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—121no—
184C4⋊Dic3—121no—
185C4⋊Dic3#6711yescharacteristic
186C4⋊Dic3#6711yescharacteristic
187Dic3⋊C4—21no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191C4×Dic3—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—62no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C22×C32—81no—
198C22×C32—81no—
199C22×C32—81no—
200C22×C32#12011yescharacteristic
201C2×C3×D3—22no—
202C2×C3×D3—41no—
203C2×C3×D3—41no—
204C32×C4—21no—
205C32×C4C2×SD1611yescharacteristic
206C32×C4#13511yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C32×C4#13711yescharacteristic
209C3⋊Dic3—42no—
210C3×Dic3—41no—
211C3×Dic3—41no—
212C3×Dic3—41no—
213C2×SD16—61no—
214C2×SD16—182no—
215C2×D8—61no—
216C4⋊Q8—91no—
217#127D3211yescharacteristic
218#125—181no—
219C22⋊Q8—182no—
220C22⋊Q8—181no—
221C4×Q8—31no—
222C4×D4—31no—
223C4×D4—181no—
224C2×C4⋊C4—181no—
225C4⋊C8—31no—
226C4⋊C8—31no—
227#102—61no—
228#102—61no—
229C4×C8—91no—
230C23×C3—42no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3—61no—
234C22×D3—21no—
235C3×Q8—61no—
236C3×Q8—61no—
237C3×D4—32no—
238C3×D4—44no—
239C3×D4—42no—
240C3×D4—42no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—61no—
250C3×D4—81no—
251C3×D4—81no—
252C3×D4—81no—
253C3×D4—81no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
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—21no—
270C2×Dic3—21no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—122no—
274C2×Dic3—242no—
275D12—21no—
276D12#21412yescomplemented
277C4×D3—41no—
278C4×D3—41no—
279C4×D3—242no—
280Dic6—21no—
281Dic6—21no—
282Dic6—122no—
283Dic6—122no—
284Dic6—124no—
285C3×C8—121no—
286C3×C8—121no—
287C3⋊C8—41no—
288C3⋊C8—41no—
289C3⋊C8—64no—
290C3⋊C8—62no—
291C3⋊C8—62no—
292C2×C32—161no—
293C2×C32#44811yescharacteristic
294C2×C32#44911yescharacteristic
295C2×C32#45311yescharacteristic
296C3×D3—42no—
297C2×Q8—31no—
298C2×Q8—92no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—31no—
303C22×C4—61no—
304C22×C4—182no—
305SD16—122no—
306SD16—364no—
307D8—122no—
308C2×C8—61no—
309C2×C8—61no—
310C2×C8—181no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4—61no—
314C4⋊C4—182no—
315C4⋊C4—182no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C22⋊C4—61no—
319C22⋊C4—182no—
320C42—61no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—62no—
324C22×C3—82no—
325C22×C3—82no—
326C22×C3—82no—
327C22×C3—81no—
328C22×C3—81no—
329C22×C3—81no—
330C22×C3—81no—
331C22×C3—81no—
332C22×C3—81no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3#93711yescharacteristic
336C22×C3#93711yescharacteristic
337C2×D3—22no—
338C2×D3—41no—
339C2×D3—41no—
340C3×C4—22no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—121no—
348C3×C4—121no—
349C3×C4—121no—
350C3×C4#91111yescharacteristic
351C3×C4#91211yescharacteristic
352C3×C4D3×SD1611yescharacteristic
353C3×C4#91511yescharacteristic
354C3×C4#93211yescharacteristic
355C3×C4C2×#21411yescharacteristic
356C3×C4#95011yescharacteristic
357C3×C4#95111yescharacteristic
358Dic3—41no—
359Dic3—41no—
360Dic3—41no—
361Dic3—122no—
362Dic3—122no—
363Dic3—242no—
364C32#162211yescharacteristic, complemented, Sylow
365C23—41no—
366C23—61no—
367Q8—61no—
368Q8—61no—
369Q8—362no—
370D4—32no—
371D4—42no—
372D4—41no—
373D4—41no—
374D4—41no—
375D4—41no—
376D4—61no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—121no—
381C2×C4—121no—
382C2×C4—182no—
383C2×C4—722no—
384C2×C4D3×#6711yescharacteristic
385C2×C4D3×#6711yescharacteristic
386C2×C4#381111yescharacteristic
387C8—121no—
388C8—121no—
389C8—182no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—122no—
394C2×C3—162no—
395C2×C3—161no—
396C2×C3—161no—
397C2×C3#503711yescharacteristic
398C2×C3#504011yescharacteristic
399C2×C3#515811yescharacteristic
400C2×C3#517011yescharacteristic
401C2×C3#519811yescharacteristic
402C2×C3#519811yescharacteristic
403D3—42no—
404C22—62no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—121no—
409C22—121no—
410C22#6398311yescharacteristic
411C4—21no—
412C4—121no—
413C4—121no—
414C4—121no—
415C4—362no—
416C4D3×#21411yescharacteristic
417C4#6392911yescharacteristic
418C4#6393211yescharacteristic
419C4#6393311yescharacteristic
420C3—21no—
421C3#7101611yescharacteristic, complemented
422C3#7102811yescharacteristic, complemented
423C2—122no—
424C2—161no—
425C2#1059151711yescharacteristic
426C2#1059151911yescharacteristic
427C2#1059152211yescharacteristic
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. #10593960C2semidirect
2. #10592775C2semidirect
3. C3×#5075C2semidirect
5. #10589096C2semidirect
6. #10589083C2semidirect
7. #10589080C2semidirect
34. #5075D3semidirect
122. C3×D12SD16semidirect
276. D12#214semidirect
364. C32#1622semidirect
421. C3#71016semidirect
422. C3#71028semidirect

Maximal subgroups

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

subgroupindex
#105939602
#105927752
C3×#50752
C3×#50722
#105890962
#105890832
#105890802
#710283
#710163