Finite Group Databasebeta

← #11779231

Subgroups — #11779231

Order 1152.

570 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 104 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×D4×Dic6C211yesmaximal, characteristic, complemented
2#10592714C211yesmaximal, characteristic
3#10590367C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71914—31nomaximal
9#68187—31nomaximal
10C22×C3×Dic6—21no—
11C32×C4×D4C2211yescharacteristic
12C2×#3753—21no—
13#64083C2211yescharacteristic
14C3×D4×Dic3—21no—
15C3×#924—21no—
16C3×#888—21no—
17C3×#878—22no—
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C2×#3717—21no—
21#63636—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63564—22no—
26#63564—21no—
27C3×D4×Q8—31no—
28D4×Dic6D311yescharacteristic, complemented
29#5088—31no—
30#5027—31no—
31#5015—31no—
32#5015—31no—
33#5015—61no—
34#4848—31no—
35#4694—31no—
36C3×D4⋊C8—31no—
37#4547—31no—
38#4535—31no—
39D4⋊(C3⋊C8)D311yescharacteristic, complemented
40#4482—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C22×C3×Dic3—22no—
48C2×C3×Dic6—22no—
49C2×C3×Dic6—21no—
50C2×C3×Dic6—42no—
51C2×C3×Dic6—42no—
52C2×C3×Dic6D411yescharacteristic
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55C32×C42C2311yescharacteristic
56#3753—42no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—22no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D412yes—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3717—42no—
68#1627—91noSylow
69C22×C3×Q8—61no—
70C22×Dic6—21no—
71C3×C4⋊Q8—31no—
72C3×C4⋊Q8—61no—
73C3×C22⋊Q8—62no—
74C3×C22⋊Q8—61no—
75C3×C4×Q8—31no—
76C3×C4×D4—21no—
77C3×C4×D4—61no—
78C3×C4×D4C2×D311yescharacteristic
79C3×C4×D4C2×D311yescharacteristic
80C2×#215—61no—
81D4×Dic3—21no—
82C2×#213—62no—
83C2×#213—61no—
84C2×#213—61no—
85#924—21no—
86C2×#204—61no—
87#888—21no—
88#878—22no—
89#874—31no—
90#874—31no—
91#874—61no—
92#869C2×D311yescharacteristic
93C4×Dic6C2×D311yescharacteristic
94C3×C4⋊C8—31no—
95C3×C4×C8—31no—
96#821—62no—
97#821—61no—
98#809—61no—
99#809—62no—
100#809—62no—
101#809—61no—
102#809—61no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—31no—
105C4⋊(C3⋊C8)—61no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C23×C32—21no—
109C22×C3⋊D3—41no—
110C32×D4—21no—
111C32×D4SD1612yescomplemented
112C2×C32×C4—21no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—42no—
121C4⋊(C3⋊D3)—41no—
122C4⋊(C3⋊D3)—41no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—44no—
127C3×Dic6—21no—
128C3×Dic6—44no—
129C3×Dic6—41no—
130C3×Dic6—41no—
131C3×Dic6D812yescomplemented
132C3⋊(C3⋊C8)—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135D4×Q8—31no—
136#486—91no—
137#460—91no—
138#459—91no—
139#332—91no—
140Q8⋊C8—91no—
141D4⋊C8—31no—
142C2×C3×Q8—31no—
143C2×C3×Q8—62no—
144C2×C3×Q8—61no—
145C2×C3×Q8—122no—
146C2×C3×Q8—122no—
147C2×C3×D4—21no—
148C2×C3×D4D1211yescharacteristic
149C2×C3×D4#6711yescharacteristic
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—41no—
153C22×C3×C4—62no—
154C22×Dic3—22no—
155C2×D12—62no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12—61no—
161C2×D12—61no—
162C2×D12—121no—
163C2×D12—121no—
164C2×Dic6—22no—
165C2×Dic6—21no—
166C2×Dic6—42no—
167C2×Dic6—42no—
168C2×Dic6#6711yescharacteristic
169C2×C3×C8—61no—
170C2×C3×C8—61no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—32no—
174C3×C4⋊C4—62no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4D1211yescharacteristic
178C3×C4⋊C4#6711yescharacteristic
179C3×C22⋊C4—21no—
180C3×C22⋊C4—21no—
181C3×C22⋊C4—41no—
182C3×C22⋊C4—62no—
183C3×C42—21no—
184C3×C42—61no—
185C3×C42C22×D311yescharacteristic
186C3×C42C22×D311yescharacteristic
187#217—22no—
188#215—122no—
189#213—124no—
190#213—122no—
191#213—122no—
192C4⋊Dic3—21no—
193C4⋊Dic3#6711yescharacteristic
194C4⋊Dic3#6712yes—
195Dic3⋊C4—22no—
196Dic3⋊C4—21no—
197C4×Dic3—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203#204—122no—
204C22×C32—22no—
205C22×C32—41no—
206C22×C32—41no—
207C22×C32#12011yescharacteristic
208C2×C3⋊D3—81no—
209C2×C3⋊D3—81no—
210C2×C3⋊D3—81no—
211C32×C4—21no—
212C32×C4—41no—
213C32×C4C2×D811yescharacteristic
214C32×C4C2×SD1611yescharacteristic
215C32×C4AGL(1,ℤ/8)11yescharacteristic
216C32×C4#13711yescharacteristic
217C3×Dic3—22no—
218C3×Dic3—42no—
219C3×Dic3—41no—
220C22×Q8—61no—
221C2×SD16—181no—
222C2×D8—181no—
223C4⋊Q8—31no—
224C4⋊Q8—61no—
225#127—91no—
226C22⋊Q8—62no—
227C22⋊Q8—61no—
228C4×Q8—31no—
229C4×D4—61no—
230C4×D4D3211yescharacteristic
231C4⋊C8—31no—
232C4⋊C8—91no—
233#102—181no—
234#102—182no—
235#102—181no—
236C4×C8—31no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—41no—
240C22×D3—122no—
241C22×D3—121no—
242C22×D3—121no—
243C3×Q8—32no—
244C3×Q8—61no—
245C3×Q8—124no—
246C3×Q8—121no—
247C3×Q8—121no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—22no—
251C3×D4—41no—
252C3×D4#20412yescomplemented
253C3×D4#21512yescomplemented
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—62no—
267C2×C3×C4—81no—
268C2×C3×C4—81no—
269C2×C3×C4—124no—
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—22no—
279C2×Dic3—44no—
280D12—122no—
281D12—122no—
282D12—122no—
283D12—122no—
284D12—121no—
285D12—121no—
286D12—121no—
287D12—121no—
288D12—121no—
289D12—121no—
290D12—121no—
291D12—121no—
292D12—241no—
293D12—241no—
294D12—242no—
295Dic6—21no—
296Dic6—44no—
297Dic6—41no—
298Dic6—41no—
299Dic6#21312yescomplemented
300C3×C8—121no—
301C3×C8—121no—
302C3⋊C8—41no—
303C3⋊C8—41no—
304C3⋊C8—122no—
305C3⋊C8—121no—
306C3⋊C8—121no—
307C2×C32—42no—
308C2×C32#44711yescharacteristic
309C2×C32#44811yescharacteristic
310C2×C32#45411yescharacteristic
311C3⋊D3—161no—
312C2×Q8—31no—
313C2×Q8—62no—
314C2×Q8—61no—
315C2×Q8—122no—
316C2×Q8—122no—
317C2×D4—181no—
318C2×D4—181no—
319C2×D4—181no—
320C2×D4#62611yescharacteristic
321C22×C4—21no—
322C22×C4—62no—
323SD16—362no—
324D8—362no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—181no—
328C4⋊C4—31no—
329C4⋊C4—32no—
330C4⋊C4—62no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4#62611yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—62no—
336C42—61no—
337C42C2×D3211yescharacteristic
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—42no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—81no—
347C22×C3—81no—
348C22×C3#88211yescharacteristic
349C22×C3#95311yescharacteristic
350C2×D3—242no—
351C2×D3—242no—
352C2×D3—242no—
353C2×D3—241no—
354C2×D3—241no—
355C2×D3—241no—
356C2×D3—241no—
357C2×D3—241no—
358C2×D3—241no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—62no—
369C3×C4—81no—
370C3×C4—122no—
371C3×C4—121no—
372C3×C4C2×#20411yescharacteristic
373C3×C4#90911yescharacteristic
374C3×C4D3×D811yescharacteristic
375C3×C4#91411yescharacteristic
376C3×C4C2×#21311yescharacteristic
377C3×C4#93211yescharacteristic
378C3×C4C2×#21511yescharacteristic
379C3×C4#94211yescharacteristic
380Dic3—22no—
381Dic3—42no—
382Dic3—41no—
383C32#162711yescharacteristic, complemented, Sylow
384C23—21no—
385C23—361no—
386Q8—32no—
387Q8—61no—
388Q8—124no—
389Q8—121no—
390Q8—121no—
391D4—21no—
392D4—362no—
393D4—361no—
394D4—361no—
395D4—361no—
396D4—361no—
397D4#371712yescomplemented
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—62no—
404C2×C4—124no—
405C2×C4C2×#62611yescharacteristic
406C2×C4D3×#6711yescharacteristic
407C2×C4D3×#6711yescharacteristic
408C8—121no—
409C8—121no—
410C8—361no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—42no—
415C2×C3—42no—
416C2×C3—82no—
417C2×C3#473811yescharacteristic
418C2×C3#477311yescharacteristic
419C2×C3#482711yescharacteristic
420C2×C3#521711yescharacteristic
421C2×C3#522711yescharacteristic
422C2×C3#524511yescharacteristic
423D3—482no—
424D3—481no—
425D3—481no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—721no—
430C22—721no—
431C22—721no—
432C22#6397711yescharacteristic
433C4—21no—
434C4—41no—
435C4—62no—
436C4—121no—
437C4—122no—
438C4C2×#371711yescharacteristic
439C4#6383311yescharacteristic
440C4D3×#21311yescharacteristic
441C4#6393411yescharacteristic
442C3—21no—
443C3#6818711yescharacteristic, complemented
444C3#7191411yescharacteristic, complemented
445C2—42no—
446C2—1441no—
447C2#1059117411yescharacteristic
448C2#1059144811yescharacteristic
449C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radical#10592714C2
hypercenterC4×D4D32
hypocenterC32#1627
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×D4×Dic6C2semidirect
3. #10590367C2semidirect
4. #10590281C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589093C2semidirect
7. #10589084C2semidirect
28. D4×Dic6D3semidirect
39. D4⋊(C3⋊C8)D3semidirect
111. C32×D4SD16semidirect
131. C3×Dic6D8semidirect
252. C3×D4#204semidirect
253. C3×D4#215semidirect
299. Dic6#213semidirect
383. C32#1627semidirect
397. D4#3717semidirect
443. C3#68187semidirect
444. C3#71914semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
#105927142
#105903672
#105902812
C3×D4⋊(C3⋊C8)2
#105890932
#105890842
#719143
#681873