Finite Group Databasebeta

← #11778969

Subgroups — #11778969

Order 1152.

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

normal subgroups only

This group has 620 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×#5577C211yesmaximal, characteristic, complemented
2#10592726C211yesmaximal, characteristic, complemented
3#10590350C211yesmaximal, characteristic, complemented
4#10590349C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71918—31nomaximal
9#68259—31nomaximal
10C2×C3×#239—21no—
11C32×C4×Q8C2211yescharacteristic
12C2×#3755—21no—
13#64083C2211yescharacteristic
14C3×#895—22no—
15C3×#895—21no—
16C3×#874—21no—
17C3×#874C2211yescharacteristic
18C3×C4×D12—21no—
19C3×C4×D12C2211yescharacteristic
20C2×#3714—21no—
21C2×#3714—22no—
22#63636—21no—
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26#63564—21no—
27C3×#550—31no—
28#5577D311yescharacteristic, complemented
29#5073—31no—
30#5027—31no—
31#5027—31no—
32#5027—61no—
33#5015—31no—
34#4843—31no—
35#4695—31no—
36C3×Q8⋊C8—31no—
37#4544—31no—
38#4535D311yescharacteristic, complemented
39D4⋊(C3⋊C8)—31no—
40#4485—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C3×#239—42no—
47C3×#239—42no—
48C2×C3×D12—22no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—22no—
52C2×C3×D12D411yescharacteristic
53C2×C3×D12D412yes—
54C2×C3×C4×D3—22no—
55C2×C3×C4×D3—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D411yescharacteristic
58C32×C42—21no—
59C32×C42C2311yescharacteristic
60#3755—42no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×(C2×D3)⋊C4—22no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3714—44no—
68#3714—42no—
69#1621—91noSylow
70C2×C3×#41—61no—
71C2×#239—21no—
72C3×#127—31no—
73C3×#127—61no—
74C3×#121—62no—
75C3×#121—61no—
76C3×C4×Q8—21no—
77C3×C4×Q8C2×D311yescharacteristic
78C3×C4×Q8C2×D311yescharacteristic
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81C2×#215—62no—
82C2×#215—61no—
83C2×#215—61no—
84C2×#213—61no—
85C2×#213—62no—
86C2×D24—62no—
87C2×D24—61no—
88#895—22no—
89#895—21no—
90#874—21no—
91#874—31no—
92#874—31no—
93#874—61no—
94#874C2×D311yescharacteristic
95C4×D12—21no—
96C4×D12C2×D311yescharacteristic
97C3×C4⋊C8—31no—
98C3×C4×C8—31no—
99#821—61no—
100#809—61no—
101#809—62no—
102#809—61no—
103#809—61no—
104C4⋊(C3⋊C8)—31no—
105C4⋊(C3⋊C8)—31no—
106C4⋊(C3⋊C8)—61no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊D3—41no—
110C22×C3×D3—21no—
111C22×C3×D3—22no—
112C32×Q8—21no—
113C32×Q8D812yescomplemented
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C4⋊(C3⋊D3)—42no—
122C4⋊(C3⋊D3)—41no—
123C4⋊(C3⋊D3)—41no—
124C2×C3×Dic3—21no—
125C3×D12—21no—
126C3×D12—21no—
127C3×D12—42no—
128C3×D12—44no—
129C3×D12—41no—
130C3×D12—41no—
131C3×D12—41no—
132C3×D12—41no—
133C3×D12—82no—
134C3×C4×D3—44no—
135C3×C4×D3—41no—
136C3×C4×D3—41no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—41no—
140#550—31no—
141#493—91no—
142#460—91no—
143#459—91no—
144#331—91no—
145Q8⋊C8—31no—
146D4⋊C8—91no—
147C3×#41—122no—
148C3×#41—122no—
149C2×C3×Q8—21no—
150C2×C3×Q8D1211yescharacteristic
151C2×C3×Q8#6711yescharacteristic
152C2×C3×D4—31no—
153C2×C3×D4—32no—
154C2×C3×D4—62no—
155C2×C3×D4—62no—
156C2×C3×D4—61no—
157C2×C3×D4—61no—
158C22×C3×C4—62no—
159C22×C3×C4—61no—
160#239—42no—
161#239—42no—
162C2×D12—22no—
163C2×D12—21no—
164C2×D12—21no—
165C2×D12—22no—
166C2×D12—62no—
167C2×D12—61no—
168C2×D12—61no—
169C2×D12—61no—
170C2×D12—61no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—121no—
174C2×D12—121no—
175C2×D12#6711yescharacteristic
176C2×D12#6712yes—
177C2×C4×D3—22no—
178C2×C4×D3—21no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—41no—
186C3×C4⋊C4D1211yescharacteristic
187C3×C4⋊C4#6711yescharacteristic
188C3×C22⋊C4—62no—
189C3×C22⋊C4—61no—
190C3×C42—21no—
191C3×C42—21no—
192C3×C42—21no—
193C3×C42—41no—
194C3×C42C22×D311yescharacteristic
195C3×C42C22×D311yescharacteristic
196#215—124no—
197#215—122no—
198#215—122no—
199#213—124no—
200#213—122no—
201(C2×D3)⋊C4—22no—
202(C2×D3)⋊C4—21no—
203C4⋊Dic3#6711yescharacteristic
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—62no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209D24—124no—
210D24—122no—
211C22×C32#12011yescharacteristic
212C2×C3⋊D3—81no—
213C2×C3⋊D3—81no—
214C2×C3⋊D3—81no—
215C2×C3×D3—42no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C2×C3×D3—42no—
219C2×C3×D3—42no—
220C2×C3×D3—41no—
221C32×C4—22no—
222C32×C4—21no—
223C32×C4—41no—
224C32×C4C2×D811yescharacteristic
225C32×C4#13511yescharacteristic
226C32×C4AGL(1,ℤ/8)11yescharacteristic
227C32×C4AGL(1,ℤ/8)11yescharacteristic
228C3×Dic3—41no—
229C2×#41—61no—
230C2×SD16—181no—
231C2×D8—181no—
232C2×D8—182no—
233#127—31no—
234#127—61no—
235#127—91no—
236#121—62no—
237#121—61no—
238C4×Q8D3211yescharacteristic
239C4×D4—31no—
240C4×D4—61no—
241C4⋊C8—31no—
242C4⋊C8—91no—
243#102—181no—
244#102—181no—
245C4×C8—31no—
246C23×C3—61no—
247C23×C3—62no—
248C22×D3—21no—
249C22×D3—22no—
250C22×D3—122no—
251C22×D3—121no—
252C22×D3—121no—
253C3×Q8—21no—
254C3×Q8—21no—
255C3×Q8—22no—
256C3×Q8—41no—
257C3×Q8D2412yescomplemented
258C3×Q8#21312yescomplemented
259C3×D4—61no—
260C3×D4—61no—
261C3×D4—122no—
262C3×D4—124no—
263C3×D4—121no—
264C3×D4—121no—
265C3×D4—121no—
266C3×D4—121no—
267C3×D4—242no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—61no—
278C2×C3×C4—124no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4C2×D1211yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×Dic3—21no—
288D12—21no—
289D12—21no—
290D12—42no—
291D12—44no—
292D12—41no—
293D12—41no—
294D12—41no—
295D12—41no—
296D12—82no—
297D12—122no—
298D12—122no—
299D12—122no—
300D12—122no—
301D12—121no—
302D12—121no—
303D12—121no—
304D12—121no—
305D12—121no—
306D12—121no—
307D12—121no—
308D12—121no—
309D12—241no—
310D12—241no—
311D12—242no—
312C4×D3—44no—
313C4×D3—41no—
314C4×D3—41no—
315C3×C8—62no—
316C3×C8—121no—
317C3⋊C8—22no—
318C3⋊C8—41no—
319C3⋊C8—122no—
320C3⋊C8—121no—
321C3⋊C8—121no—
322C2×C32#44711yescharacteristic
323C2×C32#44911yescharacteristic
324C2×C32#45311yescharacteristic
325C3⋊D3—161no—
326C3×D3—81no—
327C3×D3—82no—
328#41—122no—
329#41—122no—
330C2×Q8#62611yescharacteristic
331C2×D4—31no—
332C2×D4—32no—
333C2×D4—62no—
334C2×D4—62no—
335C2×D4—61no—
336C2×D4—61no—
337C2×D4—181no—
338C2×D4—181no—
339C2×D4—181no—
340C22×C4—62no—
341C22×C4—61no—
342SD16—362no—
343D8—364no—
344D8—362no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—181no—
348C4⋊C4—21no—
349C4⋊C4—31no—
350C4⋊C4#62611yescharacteristic
351C22⋊C4—62no—
352C22⋊C4—61no—
353C42—21no—
354C42C2×D3211yescharacteristic
355C22×C3—21no—
356C22×C3—122no—
357C22×C3—121no—
358C22×C3—121no—
359C22×C3—122no—
360C22×C3—122no—
361C22×C3—121no—
362C22×C3#88211yescharacteristic
363C22×C3#95311yescharacteristic
364C2×D3—42no—
365C2×D3—41no—
366C2×D3—41no—
367C2×D3—42no—
368C2×D3—42no—
369C2×D3—41no—
370C2×D3—242no—
371C2×D3—242no—
372C2×D3—242no—
373C2×D3—241no—
374C2×D3—241no—
375C2×D3—241no—
376C2×D3—241no—
377C2×D3—241no—
378C2×D3—241no—
379C3×C4—22no—
380C3×C4—21no—
381C3×C4—22no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—41no—
388C3×C4—42no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—81no—
392C3×C4—121no—
393C3×C4C2×D2411yescharacteristic
394C3×C4#90811yescharacteristic
395C3×C4#91411yescharacteristic
396C3×C4#91911yescharacteristic
397C3×C4C2×#21311yescharacteristic
398C3×C4#93211yescharacteristic
399C3×C4#94911yescharacteristic
400C3×C4#95011yescharacteristic
401Dic3—41no—
402C32#162111yescharacteristic, complemented, Sylow
403C23—61no—
404C23—62no—
405C23—361no—
406Q8—21no—
407Q8#371412yescomplemented
408D4—61no—
409D4—61no—
410D4—122no—
411D4—124no—
412D4—121no—
413D4—121no—
414D4—121no—
415D4—121no—
416D4—242no—
417D4—362no—
418D4—361no—
419D4—361no—
420D4—361no—
421D4—361no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—61no—
425C2×C4—124no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4C2×#62611yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C2×C4D3×#6711yescharacteristic
431C8—62no—
432C8—121no—
433C8—361no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—241no—
438C2×C3—242no—
439C2×C3#473211yescharacteristic
440C2×C3#481011yescharacteristic
441C2×C3#482211yescharacteristic
442C2×C3#521711yescharacteristic
443C2×C3#523811yescharacteristic
444C2×C3#524111yescharacteristic
445D3—81no—
446D3—82no—
447D3—482no—
448D3—481no—
449D3—481no—
450C22—121no—
451C22—122no—
452C22—122no—
453C22—121no—
454C22—122no—
455C22—121no—
456C22—721no—
457C22—721no—
458C22—721no—
459C22#6397711yescharacteristic
460C4—21no—
461C4—22no—
462C4—41no—
463C4—121no—
464C4C2×#371411yescharacteristic
465C4#6383011yescharacteristic
466C4#6393911yescharacteristic
467C4#6394911yescharacteristic
468C3—21no—
469C3#6825911yescharacteristic, complemented
470C3#7191811yescharacteristic, complemented
471C2—241no—
472C2—242no—
473C2—1441no—
474C2#1059116211yescharacteristic
475C2#1059158811yescharacteristic
476C2#1059166611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
hypercenterC4×Q8D32
hypocenterC32#1621
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5577C2semidirect
2. #10592726C2semidirect
3. #10590350C2semidirect
4. #10590349C2semidirect
5. C3×#4535C2semidirect
6. #10589090C2semidirect
7. #10589081C2semidirect
28. #5577D3semidirect
38. #4535D3semidirect
113. C32×Q8D8semidirect
257. C3×Q8D24semidirect
258. C3×Q8#213semidirect
402. C32#1621semidirect
407. Q8#3714semidirect
469. C3#68259semidirect
470. C3#71918semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
#105927262
#105903502
#105903492
C3×#45352
#105890902
#105890812
#719183
#682593