Finite Group Databasebeta

← #11779216

Subgroups — #11779216

Order 1152.

559 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 559 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic6×D12C211yesmaximal, characteristic, complemented
2#10592769C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic
5#10589094C211yesmaximal, characteristic, complemented
6#10589083C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71035—31nomaximal
9#71014—31nomaximal
10C2×D3×Dic6—21no—
11C32×#127C2211yescharacteristic
12#64078C2211yescharacteristic
13C2×C3×#214—21no—
14C2×C3×#213—21no—
15C3×C4×D12C2211yescharacteristic
16C3×C4×Dic6C2211yescharacteristic
17#63918—21no—
18#63893—22no—
19Dic3×D12—21no—
20#63857—21no—
21#63659—22no—
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#832—21no—
24C3×#832—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27Q8×D12—31no—
28D4×Dic6—31no—
29C3×#460—31no—
30C3×#459—31no—
31#5075D311yescharacteristic, complemented
32#5072D311yescharacteristic
33#5070—31no—
34#5070—31no—
35#5070—61no—
36#4535—31no—
37D4⋊(C3⋊C8)—31no—
38#4486—31no—
39#4484—31no—
40#4483—31no—
41#4482—31no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×#634—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#627—22no—
50C2×D3×Dic3—22no—
51D3×Dic6—42no—
52D3×Dic6—42no—
53C32×C42C2311yescharacteristic
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)D412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#214—42no—
58C3×#213—42no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66Dic3⋊Dic3—22no—
67(C2×D3)⋊Dic3—22no—
68#1627—91noSylow
69C2×D3×Q8—61no—
70C22×Dic6—61no—
71C2×C3×SD16—61no—
72C2×C3×D8—61no—
73C3×#127—21no—
74C3×#127C2×D311yescharacteristic
75C3×#127C2×D311yescharacteristic
76C3×C4×Q8—31no—
77C3×C4×D4—31no—
78D4×Dic3—61no—
79C2×#214—21no—
80C2×#213—21no—
81#924—61no—
82#897—62no—
83#897—61no—
84#888—61no—
85#878—62no—
86C4×D12—61no—
87C4×D12C2×D311yescharacteristic
88#869—31no—
89#869—31no—
90#869—61no—
91#869—61no—
92C4×Dic6C2×D311yescharacteristic
93C3×C4⋊C8—31no—
94C3×C4⋊C8—31no—
95C3×#102—61no—
96C3×#102—61no—
97#832—21no—
98#832—21no—
99#832—62no—
100#832—62no—
101#832—64no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8—31no—
105C4×C3⋊C8—31no—
106C4×C3⋊C8—61no—
107C23×C32—41no—
108C22×C3×D3—21no—
109C32×D4—42no—
110C32×D4—41no—
111C32×D4—41no—
112C32×D4—41no—
113C32×D4—41no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—22no—
118#634—41no—
119#634—41no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C3×D12—21no—
124C3×D12SD1612yescomplemented
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—21no—
128C3×Dic6D812yescomplemented
129#627—44no—
130D3×Dic3—44no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133C3×C3⋊C8—41no—
134D4×Q8—91no—
135#486—91no—
136#460—31no—
137#459—31no—
138#332—91no—
139Q8⋊C8—91no—
140D4⋊C8—91no—
141C2×C3×Q8—31no—
142C2×C3×D4—22no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—31no—
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C22×C3×C4—61no—
153C22×Dic3—62no—
154D3×Q8—122no—
155D3×Q8—122no—
156C2×D12#6711yescharacteristic
157C2×C4×D3—21no—
158C2×C4×D3—62no—
159C2×Dic6—62no—
160C2×Dic6—62no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×Dic6—121no—
164C2×Dic6—122no—
165C2×Dic6—122no—
166C2×Dic6#6711yescharacteristic
167C3×SD16—122no—
168C3×D8—122no—
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—61no—
174C3×C22⋊C4—61no—
175C3×C42—21no—
176C3×C42—61no—
177C3×C42C22×D311yescharacteristic
178C3×C42C22×D311yescharacteristic
179#217—62no—
180#214—42no—
181#213—42no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—62no—
184C4⋊Dic3—32no—
185C4⋊Dic3—32no—
186C4⋊Dic3—62no—
187C4⋊Dic3—62no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—121no—
191C4⋊Dic3#6711yescharacteristic
192C4⋊Dic3#6711yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—62no—
195C4×Dic3—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—62no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C22×C32—81no—
202C22×C32—81no—
203C22×C32—81no—
204C22×C32#12011yescharacteristic
205C2×C3×D3—22no—
206C2×C3×D3—41no—
207C2×C3×D3—41no—
208C32×C4—21no—
209C32×C4C2×D811yescharacteristic
210C32×C4C2×SD1611yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C32×C4#13711yescharacteristic
213C3⋊Dic3—42no—
214C3×Dic3—22no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C22×Q8—181no—
218C2×SD16—61no—
219C2×D8—61no—
220C4⋊Q8—91no—
221C4⋊Q8—181no—
222#127D3211yescharacteristic
223C22⋊Q8—182no—
224C22⋊Q8—181no—
225C4×Q8—31no—
226C4×D4—31no—
227C4×D4—181no—
228C4⋊C8—31no—
229C4⋊C8—31no—
230#102—61no—
231#102—61no—
232#102—182no—
233C4×C8—91no—
234C23×C3—42no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3—61no—
238C22×D3—21no—
239C3×Q8—32no—
240C3×Q8—61no—
241C3×D4—32no—
242C3×D4—44no—
243C3×D4—42no—
244C3×D4—42no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—61no—
254C3×D4—81no—
255C3×D4—81no—
256C3×D4—81no—
257C3×D4—81no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—122no—
278C2×Dic3—124no—
279D12—21no—
280D12#21412yescomplemented
281C4×D3—41no—
282C4×D3—41no—
283C4×D3—124no—
284Dic6—21no—
285Dic6—124no—
286Dic6—124no—
287Dic6—121no—
288Dic6—121no—
289Dic6—121no—
290Dic6—121no—
291Dic6—241no—
292Dic6—241no—
293Dic6#21312yescomplemented
294C3×C8—121no—
295C3×C8—121no—
296C3⋊C8—41no—
297C3⋊C8—41no—
298C3⋊C8—122no—
299C3⋊C8—121no—
300C3⋊C8—121no—
301C2×C32—161no—
302C2×C32#44711yescharacteristic
303C2×C32#44811yescharacteristic
304C2×C32#45411yescharacteristic
305C3×D3—42no—
306C2×Q8—31no—
307C2×Q8—182no—
308C2×Q8—181no—
309C2×Q8—362no—
310C2×Q8—362no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—31no—
315C22×C4—61no—
316C22×C4—182no—
317SD16—122no—
318D8—122no—
319C2×C8—61no—
320C2×C8—61no—
321C2×C8—181no—
322C4⋊C4—31no—
323C4⋊C4—31no—
324C4⋊C4—61no—
325C4⋊C4—92no—
326C4⋊C4—182no—
327C4⋊C4—181no—
328C22⋊C4—61no—
329C22⋊C4—182no—
330C42—61no—
331C42C2×D3211yescharacteristic
332C22×C3—21no—
333C22×C3—62no—
334C22×C3—82no—
335C22×C3—82no—
336C22×C3—82no—
337C22×C3—81no—
338C22×C3—81no—
339C22×C3—81no—
340C22×C3—81no—
341C22×C3—81no—
342C22×C3—81no—
343C22×C3—121no—
344C22×C3—121no—
345C22×C3#93711yescharacteristic
346C22×C3#93711yescharacteristic
347C2×D3—22no—
348C2×D3—41no—
349C2×D3—41no—
350C3×C4—22no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—62no—
358C3×C4—121no—
359C3×C4—121no—
360C3×C4D3×D811yescharacteristic
361C3×C4#91111yescharacteristic
362C3×C4D3×SD1611yescharacteristic
363C3×C4#91511yescharacteristic
364C3×C4C2×#21311yescharacteristic
365C3×C4C2×#21411yescharacteristic
366C3×C4#94911yescharacteristic
367C3×C4#95111yescharacteristic
368Dic3—22no—
369Dic3—41no—
370Dic3—41no—
371Dic3—122no—
372Dic3—122no—
373Dic3—242no—
374C32#162711yescharacteristic, complemented, Sylow
375C23—41no—
376C23—61no—
377Q8—32no—
378Q8—61no—
379Q8—364no—
380Q8—361no—
381Q8—361no—
382D4—32no—
383D4—42no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—41no—
388D4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—182no—
395C2×C4—364no—
396C2×C4D3×#6711yescharacteristic
397C2×C4D3×#6711yescharacteristic
398C2×C4#381111yescharacteristic
399C8—121no—
400C8—121no—
401C8—361no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—122no—
406C2×C3—162no—
407C2×C3—161no—
408C2×C3—161no—
409C2×C3#503611yescharacteristic
410C2×C3#504011yescharacteristic
411C2×C3#515611yescharacteristic
412C2×C3#517011yescharacteristic
413C2×C3#520111yescharacteristic
414C2×C3#520111yescharacteristic
415D3—42no—
416C22—62no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—121no—
421C22—121no—
422C22#6398311yescharacteristic
423C4—21no—
424C4—62no—
425C4—121no—
426C4—121no—
427C4—362no—
428C4D3×#21311yescharacteristic
429C4#6392511yescharacteristic
430C4D3×#21411yescharacteristic
431C4#6392911yescharacteristic
432C3—21no—
433C3#7101411yescharacteristic, complemented
434C3#7103511yescharacteristic, complemented
435C2—122no—
436C2—161no—
437C2#1059151511yescharacteristic
438C2#1059151711yescharacteristic
439C2#1059152411yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#120
prime radicalC3×#5072C2
hypercenter#127D32
hypocenterC32#1627
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. Dic6×D12C2semidirect
2. #10592769C2semidirect
3. C3×#5075C2semidirect
5. #10589094C2semidirect
6. #10589083C2semidirect
7. #10589080C2semidirect
31. #5075D3semidirect
124. C3×D12SD16semidirect
128. C3×Dic6D8semidirect
280. D12#214semidirect
293. Dic6#213semidirect
374. C32#1627semidirect
433. C3#71014semidirect
434. C3#71035semidirect

Maximal subgroups

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

subgroupindex
Dic6×D122
#105927692
C3×#50752
C3×#50722
#105890942
#105890832
#105890802
#710353
#710143