Finite Group Databasebeta

← #11779129

Subgroups — #11779129

Order 1152.

553 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 553 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#5555C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71910—31nomaximal
9#71018—31nomaximal
10C2×C3×#237—21no—
11C32×C4×D4C2211yescharacteristic
12C2×C3×#213—21no—
13C3×#930—21no—
14C2×C3×C4⋊Dic3—21no—
15C3×#897—21no—
16C3×#886—22no—
17C3×#874C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C2×#3713—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#809—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63562—22no—
26#63562—21no—
27C3×#547—31no—
28#5555D311yescharacteristic, complemented
29C3×#459—31no—
30#5088—31no—
31#5072—31no—
32#5070—31no—
33#5015—31no—
34#5015D311yescharacteristic, complemented
35#4547—31no—
36D4⋊(C3⋊C8)—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—61no—
40#4483—31no—
41#4482—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C3×#67—22no—
45C22×C3×Dic3—22no—
46C3×#237—42no—
47C3×#237—42no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42C2311yescharacteristic
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#213—42no—
60C3×(C2×D3)⋊C4—22no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D412yes—
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67#3713—42no—
68#1625—91noSylow
69C2×C3×#41—61no—
70C2×#237—21no—
71C2×C3×D8—61no—
72C3×C4⋊Q8—31no—
73C3×#127—31no—
74C3×#123—62no—
75C3×C22⋊Q8—61no—
76C3×#121—61no—
77C3×C4×D4—21no—
78C3×C4×D4—31no—
79C3×C4×D4C2×D311yescharacteristic
80C3×C4×D4C2×D311yescharacteristic
81C2×C3×C4⋊C4—61no—
82C2×#213—21no—
83C2×#213—61no—
84C2×#213—61no—
85#930—21no—
86C2×C4⋊Dic3—21no—
87#897—21no—
88#886—22no—
89#874C2×D311yescharacteristic
90C4×D12C2×D311yescharacteristic
91#869C2×D311yescharacteristic
92C3×C4⋊C8—31no—
93C3×#102—61no—
94#832—62no—
95#832—61no—
96#809—21no—
97#809—61no—
98#809—62no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—31no—
104C4×C3⋊C8—31no—
105C4×C3⋊C8—61no—
106C23×C32—21no—
107C22×C3×D3—21no—
108C22×C3×D3—41no—
109C32×D4—21no—
110C32×D4D812yescomplemented
111C2×C32×C4—21no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C3×#67—44no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—44no—
121C3×D12—21no—
122C3×D12—21no—
123C3×D12—42no—
124C3×D12—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—41no—
128C3×C4×D3—41no—
129C3×C4×D3—41no—
130C3×Dic6—41no—
131C3×Dic6—41no—
132C3⋊(C3⋊C8)—41no—
133C3⋊(C3⋊C8)—41no—
134C3×C3⋊C8—41no—
135#547—31no—
136#486—91no—
137#459—31no—
138#459—91no—
139#332—91no—
140D4⋊C8—91no—
141D4⋊C8—91no—
142C3×#41—122no—
143C3×#41—122no—
144C2×C3×Q8—61no—
145C2×C3×D4—21no—
146C2×C3×D4—31no—
147C2×C3×D4—62no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C2×C3×D4#6711yescharacteristic
152C2×C3×D4#6711yescharacteristic
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—41no—
156C22×C3×C4—62no—
157C22×C3×C4—61no—
158C2×#67—22no—
159C22×Dic3—22no—
160#237—42no—
161#237—42no—
162C2×D12—21no—
163C2×D12—21no—
164C2×D12—21no—
165C2×D12#6711yescharacteristic
166C2×C4×D3—21no—
167C2×Dic6—21no—
168C3×D8—122no—
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—32no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4#6711yescharacteristic
176C3×C4⋊C4#6711yescharacteristic
177C3×C22⋊C4—21no—
178C3×C22⋊C4—21no—
179C3×C22⋊C4—41no—
180C3×C22⋊C4—62no—
181C3×C22⋊C4—61no—
182C3×C42—21no—
183C3×C42C22×D311yescharacteristic
184C3×C42C22×D311yescharacteristic
185#213—42no—
186#213—122no—
187#213—122no—
188(C2×D3)⋊C4—22no—
189(C2×D3)⋊C4—21no—
190C4⋊Dic3—22no—
191C4⋊Dic3—21no—
192C4⋊Dic3#6712yes—
193C4⋊Dic3#6711yescharacteristic
194C2×C3⋊C8—21no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—121no—
200C2×C3⋊C8—121no—
201C22×C32—22no—
202C22×C32—41no—
203C22×C32—41no—
204C22×C32#12011yescharacteristic
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C2×C3×D3—41no—
208C2×C3×D3—81no—
209C2×C3×D3—81no—
210C2×C3×D3—81no—
211C32×C4—21no—
212C32×C4—41no—
213C32×C4C2×D811yescharacteristic
214C32×C4#13511yescharacteristic
215C32×C4AGL(1,ℤ/8)11yescharacteristic
216C32×C4AGL(1,ℤ/8)11yescharacteristic
217C3×Dic3—42no—
218C3×Dic3—41no—
219C2×#41—61no—
220C2×D8—61no—
221C2×D8—181no—
222C4⋊Q8—31no—
223#127—31no—
224#123—62no—
225C22⋊Q8—61no—
226#121—61no—
227C4×D4—31no—
228C4×D4D3211yescharacteristic
229C2×C4⋊C4—61no—
230C4⋊C8—31no—
231C4⋊C8—91no—
232#102—61no—
233#102—181no—
234#102—182no—
235C4×C8—91no—
236C23×C3—21no—
237C23×C3—21no—
238C23×C3—41no—
239C23×C3—61no—
240C23×C3—121no—
241C22×D3—21no—
242C22×D3—41no—
243C3×Q8—121no—
244C3×Q8—121no—
245C3×D4—21no—
246C3×D4—21no—
247C3×D4—22no—
248C3×D4—41no—
249C3×D4—61no—
250C3×D4—61no—
251C3×D4—122no—
252C3×D4—124no—
253C3×D4—121no—
254C3×D4—121no—
255C3×D4—121no—
256C3×D4—121no—
257C3×D4#21312yescomplemented
258C3×D4#21312yescomplemented
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—61no—
270C2×C3×C4—62no—
271C2×C3×C4—81no—
272C2×C3×C4—81no—
273C2×C3×C4—124no—
274C2×C3×C4—121no—
275C2×C3×C4—121no—
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282#67—44no—
283C2×Dic3—22no—
284C2×Dic3—21no—
285C2×Dic3—44no—
286D12—21no—
287D12—21no—
288D12—42no—
289D12—41no—
290D12—41no—
291D12—41no—
292D12—41no—
293C4×D3—41no—
294C4×D3—41no—
295Dic6—41no—
296Dic6—41no—
297C3×C8—121no—
298C3⋊C8—41no—
299C3⋊C8—121no—
300C3⋊C8—121no—
301C3⋊C8—122no—
302C3⋊C8—121no—
303C3⋊C8—121no—
304C3⋊C8—241no—
305C2×C32—42no—
306C2×C32#44711yescharacteristic
307C2×C32#44911yescharacteristic
308C2×C32#45411yescharacteristic
309C3×D3—81no—
310C3×D3—161no—
311#41—122no—
312#41—122no—
313C2×Q8—61no—
314C2×D4—31no—
315C2×D4—62no—
316C2×D4—61no—
317C2×D4—61no—
318C2×D4—61no—
319C2×D4#62511yescharacteristic
320C22×C4—21no—
321C22×C4—62no—
322C22×C4—61no—
323D8—122no—
324D8—362no—
325C2×C8—61no—
326C2×C8—181no—
327C2×C8—181no—
328C4⋊C4—31no—
329C4⋊C4—32no—
330C4⋊C4—62no—
331C4⋊C4—61no—
332C4⋊C4#62511yescharacteristic
333C22⋊C4—21no—
334C22⋊C4—62no—
335C22⋊C4—61no—
336C42C2×D3211yescharacteristic
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—42no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—81no—
346C22×C3—81no—
347C22×C3—121no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—241no—
351C22×C3—241no—
352C22×C3—241no—
353C22×C3#93711yescharacteristic
354C22×C3#95311yescharacteristic
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—41no—
358C2×D3—81no—
359C2×D3—81no—
360C2×D3—81no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—81no—
371C3×C4—121no—
372C3×C4—122no—
373C3×C4#91111yescharacteristic
374C3×C4#91211yescharacteristic
375C3×C4C2×#21311yescharacteristic
376C3×C4C2×#21311yescharacteristic
377C3×C4#93211yescharacteristic
378C3×C4#94911yescharacteristic
379C3×C4#94911yescharacteristic
380C3×C4#95011yescharacteristic
381Dic3—42no—
382Dic3—41no—
383C32#162511yescharacteristic, complemented, Sylow
384C23—21no—
385C23—61no—
386C23—121no—
387Q8—121no—
388Q8—121no—
389D4—21no—
390D4—61no—
391D4—61no—
392D4—122no—
393D4—124no—
394D4—121no—
395D4—121no—
396D4—121no—
397D4—121no—
398D4#371312yescomplemented
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—61no—
403C2×C4—62no—
404C2×C4—124no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4C2×#62511yescharacteristic
408C2×C4D3×#6711yescharacteristic
409C2×C4D3×#6711yescharacteristic
410C8—121no—
411C8—361no—
412C8—361no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—42no—
417C2×C3—42no—
418C2×C3—82no—
419C2×C3—241no—
420C2×C3—481no—
421C2×C3#503611yescharacteristic
422C2×C3#515811yescharacteristic
423C2×C3#520111yescharacteristic
424C2×C3#521711yescharacteristic
425C2×C3#523811yescharacteristic
426C2×C3#524511yescharacteristic
427D3—81no—
428D3—161no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22—121no—
433C22—121no—
434C22—121no—
435C22—241no—
436C22—241no—
437C22—241no—
438C22#6397611yescharacteristic
439C4—21no—
440C4—41no—
441C4—121no—
442C4—122no—
443C4C2×#371311yescharacteristic
444C4#6382311yescharacteristic
445C4#6392511yescharacteristic
446C4#6393311yescharacteristic
447C3—21no—
448C3#7101811yescharacteristic, complemented
449C3#7191011yescharacteristic, complemented
450C2—42no—
451C2—241no—
452C2—481no—
453C2#1059116011yescharacteristic
454C2#1059145011yescharacteristic
455C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
hypercenterC4×D4D32
hypocenterC32#1625
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. C3×#5555C2semidirect
2. C3×#5015C2semidirect
3. #10590347C2semidirect
4. #10590277C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589093C2semidirect
7. #10589080C2semidirect
28. #5555D3semidirect
34. #5015D3semidirect
110. C32×D4D8semidirect
257. C3×D4#213semidirect
258. C3×D4#213semidirect
383. C32#1625semidirect
398. D4#3713semidirect
448. C3#71018semidirect
449. C3#71910semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C3×#50152
#105903472
#105902772
D4⋊(C3⋊(C3⋊C8))2
#105890932
#105890802
#719103
#710183