Finite Group Databasebeta

← #11779727

Subgroups — #11779727

Order 1152.

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

normal subgroups only

This group has 676 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×D12C211yesmaximal, characteristic
2#10592718C211yesmaximal, characteristic, complemented
3#10590273C211yesmaximal, characteristic, complemented
4#10590272C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71908—31nomaximal
9#68196—31nomaximal
10C2×C3×D3×D4—21no—
11C22×C3×D12—21no—
12C32×C4×D4C2211yescharacteristic
13C2×#3754—21no—
14#64078C2211yescharacteristic, complemented
15C3×#930—21no—
16C3×#895—21no—
17C3×#882—22no—
18C3×#874C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20#63637—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
22C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×C4×C3⋊C8C2211yescharacteristic, complemented
24#63575—21no—
25#63563—21no—
26#63563—22no—
27C3×D42—31no—
28D4×D12D311yescharacteristic
29#5070—31no—
30#5019—31no—
31#5019—31no—
32#5019—61no—
33#5007—31no—
34#4846—31no—
35#4694—31no—
36C3×D4⋊C8—31no—
37#4544—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)D311yescharacteristic, complemented
40#4485—31no—
41#4459—31no—
42C23×C3×D3—22no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C2×#634—21no—
46C2×C3×#67—22no—
47C3×D3×D4—42no—
48C3×D3×D4—42no—
49C2×C3×D12—22no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—42no—
53C2×C3×D12—42no—
54C2×C3×D12D411yescharacteristic
55C2×C3×D12D412yes—
56C2×C3×C4×D3—21no—
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C42C2311yescharacteristic
60#3754—42no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×(C2×D3)⋊C4—22no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#1639—91noSylow
70C22×C3×D4—61no—
71C22×C3×D4—61no—
72C2×D3×D4—21no—
73C22×D12—21no—
74C3×#127—31no—
75C3×#121—61no—
76C3×#121—61no—
77C3×#120—62no—
78C3×C4×D4—21no—
79C3×C4×D4—31no—
80C3×C4×D4C2×D311yescharacteristic
81C3×C4×D4C2×D311yescharacteristic
82C2×#214—62no—
83C2×#214—61no—
84C2×#214—61no—
85#930—21no—
86#895—21no—
87#882—22no—
88#874C2×D311yescharacteristic
89C4×D12C2×D311yescharacteristic
90#869—31no—
91#869—31no—
92#869—61no—
93C3×C4⋊C8—31no—
94C3×C4×C8—31no—
95#832—61no—
96#832—62no—
97#821—62no—
98#821—61no—
99#818—61no—
100#810—62no—
101#810—61no—
102#810—61no—
103#807—61no—
104C4⋊(C3⋊C8)—31no—
105C4⋊(C3⋊C8)—31no—
106C4⋊(C3⋊C8)—61no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
108C4×C3⋊C8C2×D311yescharacteristic, complemented
109C23×C32—21no—
110C22×C3×D3—21no—
111C22×C3×D3—22no—
112C22×C3×D3—44no—
113C22×C3×D3—44no—
114C22×C3×D3—82no—
115C32×D4—21no—
116C32×D4D812yes—
117C2×C32×C4—21no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—41no—
124#634—41no—
125#634—41no—
126C3×#67—44no—
127C2×C3×Dic3—21no—
128C3×D12—21no—
129C3×D12—42no—
130C3×D12—44no—
131C3×D12—41no—
132C3×D12—41no—
133C3×D12—41no—
134C3×D12—41no—
135C3×D12SD1612yescomplemented
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141D42—31no—
142#486—91no—
143#474—91no—
144#461—91no—
145#331—91no—
146D4⋊C8—31no—
147D4⋊C8—91no—
148C24×C3—62no—
149C23×D3—22no—
150C2×C3×D4—21no—
151C2×C3×D4—31no—
152C2×C3×D4—32no—
153C2×C3×D4—62no—
154C2×C3×D4—62no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C2×C3×D4—122no—
158C2×C3×D4—122no—
159C2×C3×D4—122no—
160C2×C3×D4—122no—
161C2×C3×D4D1211yescharacteristic
162C2×C3×D4#6711yescharacteristic
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—41no—
166C22×C3×C4—61no—
167C2×#67—22no—
168D3×D4—42no—
169D3×D4—42no—
170C2×D12—22no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—42no—
174C2×D12—42no—
175C2×D12#6711yescharacteristic
176C2×D12#6712yes—
177C2×C4×D3—21no—
178C2×Dic6—62no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4D1211yescharacteristic
186C3×C4⋊C4#6711yescharacteristic
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—62no—
191C3×C22⋊C4—61no—
192C3×C42—21no—
193C3×C42C22×D311yescharacteristic
194C3×C42C22×D311yescharacteristic
195#214—124no—
196#214—122no—
197#214—122no—
198(C2×D3)⋊C4—22no—
199(C2×D3)⋊C4—21no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—121no—
205C4⋊Dic3—121no—
206C4⋊Dic3#6711yescharacteristic
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—62no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C22×C32—22no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32#12011yescharacteristic
216C2×C3×D3—22no—
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—42no—
220C2×C3×D3—42no—
221C2×C3×D3—42no—
222C2×C3×D3—88no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4C2×D811yescharacteristic
226C32×C4C2×SD1611yescharacteristic
227C32×C4AGL(1,ℤ/8)11yescharacteristic
228C32×C4AGL(1,ℤ/8)11yescharacteristic
229C3⋊Dic3—81no—
230C3×Dic3—41no—
231C22×D4—61no—
232C22×D4—61no—
233C2×SD16—181no—
234C4⋊Q8—91no—
235#127—31no—
236#121—61no—
237#121—61no—
238#120—62no—
239C4×D4—31no—
240C4×D4D3211yescharacteristic
241#107—181no—
242C4⋊C8—31no—
243C4⋊C8—91no—
244#103—181no—
245#102—181no—
246#102—182no—
247C4×C8—31no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—41no—
251C23×C3—61no—
252C23×C3—62no—
253C23×C3—124no—
254C23×C3—124no—
255C23×C3—242no—
256C22×D3—21no—
257C22×D3—22no—
258C22×D3—44no—
259C22×D3—44no—
260C22×D3—82no—
261C3×D4—21no—
262C3×D4—21no—
263C3×D4—22no—
264C3×D4—32no—
265C3×D4—41no—
266C3×D4—61no—
267C3×D4—122no—
268C3×D4—124no—
269C3×D4—124no—
270C3×D4—121no—
271C3×D4—121no—
272C3×D4—121no—
273C3×D4—121no—
274C3×D4D2412yes—
275C3×D4#21312yes—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—61no—
287C2×C3×C4—81no—
288C2×C3×C4—81no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4C2×D1211yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297#67—44no—
298C2×Dic3—21no—
299C2×Dic3—122no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302D12—21no—
303D12—42no—
304D12—44no—
305D12—41no—
306D12—41no—
307D12—41no—
308D12—41no—
309D12#21412yescomplemented
310C4×D3—41no—
311C4×D3—41no—
312Dic6—122no—
313Dic6—122no—
314Dic6—121no—
315Dic6—121no—
316Dic6—121no—
317Dic6—121no—
318C3×C8—121no—
319C3×C8—121no—
320C3⋊C8—41no—
321C3⋊C8—41no—
322C3⋊C8—122no—
323C3⋊C8—121no—
324C3⋊C8—121no—
325C2×C32—42no—
326C2×C32#44711yescharacteristic
327C2×C32#45011yescharacteristic
328C2×C32#45511yescharacteristic
329C3×D3—42no—
330C3×D3—82no—
331C24—62no—
332C2×Q8—181no—
333C2×D4—31no—
334C2×D4—32no—
335C2×D4—62no—
336C2×D4—62no—
337C2×D4—61no—
338C2×D4—61no—
339C2×D4—122no—
340C2×D4—122no—
341C2×D4—122no—
342C2×D4—122no—
343C2×D4#62611yescharacteristic
344C22×C4—21no—
345C22×C4—61no—
346SD16—362no—
347C2×C8—61no—
348C2×C8—61no—
349C2×C8—181no—
350C4⋊C4—31no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C4⋊C4#62611yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—62no—
356C22⋊C4—61no—
357C42C2×D3211yescharacteristic
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—21no—
361C22×C3—42no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—62no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3—121no—
370C22×C3—121no—
371C22×C3—122no—
372C22×C3—122no—
373C22×C3—122no—
374C22×C3—248no—
375C22×C3#88211yescharacteristic
376C22×C3#95311yescharacteristic
377C2×D3—22no—
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—42no—
381C2×D3—42no—
382C2×D3—42no—
383C2×D3—88no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—81no—
394C3×C4—121no—
395C3×C4C2×D2411yescharacteristic
396C3×C4#90811yescharacteristic
397C3×C4#91111yescharacteristic
398C3×C4D3×SD1611yescharacteristic
399C3×C4C2×#21311yescharacteristic
400C3×C4#93211yescharacteristic
401C3×C4#93211yescharacteristic
402C3×C4C2×#21411yescharacteristic
403Dic3—41no—
404Dic3—242no—
405Dic3—241no—
406Dic3—241no—
407C32#163911yescharacteristic, complemented, Sylow
408C23—21no—
409C23—61no—
410C23—62no—
411C23—124no—
412C23—124no—
413C23—242no—
414Q8—361no—
415Q8—361no—
416D4—21no—
417D4—32no—
418D4—61no—
419D4—122no—
420D4—124no—
421D4—124no—
422D4—121no—
423D4—121no—
424D4—121no—
425D4—121no—
426D4#371412yes—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—61no—
431C2×C4—121no—
432C2×C4—121no—
433C2×C4—361no—
434C2×C4C2×#62611yescharacteristic
435C2×C4D3×#6711yescharacteristic
436C2×C4D3×#6711yescharacteristic
437C8—121no—
438C8—121no—
439C8—361no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—42no—
444C2×C3—42no—
445C2×C3—82no—
446C2×C3—122no—
447C2×C3—242no—
448C2×C3#473211yescharacteristic
449C2×C3#477611yescharacteristic
450C2×C3#482511yescharacteristic
451C2×C3#521711yescharacteristic
452C2×C3#521811yescharacteristic
453C2×C3#524211yescharacteristic
454D3—42no—
455D3—82no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—62no—
460C22—121no—
461C22—121no—
462C22—122no—
463C22—122no—
464C22—122no—
465C22—248no—
466C22#6397711yescharacteristic
467C4—21no—
468C4—41no—
469C4—121no—
470C4—721no—
471C4C2×#371411yescharacteristic
472C4#6383011yescharacteristic
473C4D3×#21411yescharacteristic
474C4#6393211yescharacteristic
475C3—21no—
476C3#6819611yescharacteristic, complemented
477C3#7190811yescharacteristic, complemented
478C2—42no—
479C2—122no—
480C2—242no—
481C2#1059116211yescharacteristic
482C2#1059145911yescharacteristic
483C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC3×D4×D12C2
hypercenterC4×D4D32
hypocenterC32#1639
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
2. #10592718C2semidirect
3. #10590273C2semidirect
4. #10590272C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589090C2semidirect
7. #10589081C2semidirect
14. #64078C22semidirect
21. C4⋊(C3⋊(C3⋊C8))C22semidirect
22. C3×C4⋊(C3⋊C8)C22semidirect
23. C3×C4×C3⋊C8C22semidirect
39. D4⋊(C3⋊C8)D3semidirect
107. C4⋊(C3⋊C8)C2×D3semidirect
108. C4×C3⋊C8C2×D3semidirect
135. C3×D12SD16semidirect
309. D12#214semidirect
407. C32#1639semidirect
476. C3#68196semidirect
477. C3#71908semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D122
#105927182
#105902732
#105902722
C3×D4⋊(C3⋊C8)2
#105890902
#105890812
#719083
#681963