Finite Group Databasebeta

← #11779722

Subgroups — #11779722

Order 1152.

676 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 92 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
1#10594004C211yesmaximal, characteristic
2#10592782C211yesmaximal, characteristic, complemented
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10589090C211yesmaximal, characteristic, complemented
6#10589082C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71198—31nomaximal
9#71108—31nomaximal
10C2×#3802—21no—
11C2×D3×D12—21no—
12C32×C4⋊Q8C2211yescharacteristic, complemented
13C2×#3755—21no—
14C4×C4⋊(C3⋊D3)C2211yescharacteristic
15C3×#874C2211yescharacteristic
16C3×C4×D12C2211yescharacteristic
17#63922—22no—
18#63916—21no—
19#63908—21no—
20#63662—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
22C3×#809—21no—
23C3×#809—22no—
24C3×#807—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×C4×C3⋊C8C2211yescharacteristic, complemented
27#5717—31no—
28D4×D12—31no—
29C3×#486—31no—
30C3×#474—31no—
31#5088D311yescharacteristic, complemented
32#5087D311yescharacteristic, complemented
33#5083—31no—
34#5083—31no—
35#5083—61no—
36#4544—31no—
37D4⋊(C3⋊C8)—31no—
38#4485—31no—
39#4483—31no—
40#4459—31no—
41#4459—31no—
42C22×D32—22no—
43C2×C32×Q8—21no—
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12D411yescharacteristic
49C2×C3×D12D412yes—
50C2×C3×C4×D3—21no—
51C2×#626—22no—
52C2×#625—22no—
53#3802—42no—
54#3802—42no—
55D3×D12—42no—
56D3×D12—42no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C32×C42C2311yescharacteristic
60#3755—42no—
61#3752—21no—
62C4⋊(C3⋊Dic3)D411yescharacteristic
63C2×C3⋊(C3⋊C8)—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68(C2×D3)⋊Dic3—22no—
69#1639—91noSylow
70C2×D3×D4—61no—
71C2×D3×D4—61no—
72C2×D3×D4—61no—
73C22×D12—61no—
74C3×C4⋊Q8—21no—
75C3×C4⋊Q8C2×D311yescharacteristic, complemented
76C3×C4⋊Q8C2×D311yescharacteristic, complemented
77C3×#127—31no—
78C3×C4×D4—31no—
79C2×#215—61no—
80C2×#215—61no—
81C2×#215—62no—
82#938—61no—
83#938—61no—
84#937—62no—
85#930—61no—
86#895—61no—
87#882—62no—
88#874C2×D311yescharacteristic
89C4×D12—31no—
90C4×D12—31no—
91C4×D12—61no—
92C4×D12C2×D311yescharacteristic
93C3×#107—61no—
94C3×C4⋊C8—31no—
95C3×#102—61no—
96C3×#102—62no—
97C3×C4×C8—31no—
98#835—61no—
99#835—61no—
100#835—62no—
101#809—21no—
102#809—22no—
103#807—21no—
104C4⋊(C3⋊C8)—31no—
105C4⋊(C3⋊C8)—31no—
106C4⋊(C3⋊C8)—61no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
108C4×C3⋊C8C2×D311yescharacteristic, complemented
109C22×C3⋊D3—21no—
110C22×C3×D3—21no—
111C22×C3×D3—22no—
112C2×D32—44no—
113C2×D32—44no—
114C2×D32—82no—
115C32×Q8—41no—
116C32×Q8—41no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)D812yes—
124C4×C3⋊D3—41no—
125C4×C3⋊D3—41no—
126C2×C3×Dic3—21no—
127C3×D12—21no—
128C3×D12—42no—
129C3×D12—41no—
130C3×D12—41no—
131C3×D12—41no—
132C3×D12—41no—
133C3×D12SD1612yescomplemented
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136#626—44no—
137#625—44no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141D42—91no—
142#486—31no—
143#474—31no—
144#461—91no—
145#331—91no—
146D4⋊C8—91no—
147D4⋊C8—91no—
148C23×D3—62no—
149C23×D3—62no—
150C2×C3×Q8—22no—
151C2×C3×Q8—21no—
152C2×C3×Q8—21no—
153C2×C3×D4—31no—
154C2×C3×D4—32no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C22×C3×C4—61no—
158C2×#67—62no—
159C2×#67—62no—
160C2×#67—62no—
161D3×D4—122no—
162D3×D4—122no—
163D3×D4—122no—
164D3×D4—122no—
165D3×D4—122no—
166D3×D4—122no—
167C2×D12—21no—
168C2×D12—21no—
169C2×D12—31no—
170C2×D12—31no—
171C2×D12—61no—
172C2×D12—62no—
173C2×D12—122no—
174C2×D12—122no—
175C2×D12#6711yescharacteristic
176C2×D12#6712yes—
177C2×C4×D3—21no—
178C2×C4×D3—61no—
179C2×C4×D3—61no—
180C2×C4×D3—121no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—41no—
189C3×C4⋊C4—41no—
190C3×C22⋊C4—61no—
191C3×C42—21no—
192C3×C42C22×D311yescharacteristic
193C3×C42C22×D311yescharacteristic
194#217—62no—
195#215—122no—
196#215—122no—
197#215—124no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—62no—
200(C2×D3)⋊C4—61no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—121no—
203C4⋊Dic3—31no—
204C4⋊Dic3—31no—
205C4⋊Dic3—61no—
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#12011yescharacteristic
213C2×C3⋊D3—22no—
214C2×C3⋊D3—41no—
215C2×C3⋊D3—41no—
216C2×C3×D3—22no—
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—42no—
220C2×C3×D3—42no—
221C2×C3×D3—42no—
222D32—88no—
223C32×C4—21no—
224C32×C4—81no—
225C32×C4C2×D811yescharacteristic
226C32×C4C2×SD1611yescharacteristic
227C32×C4AGL(1,ℤ/8)11yescharacteristic
228C32×C4AGL(1,ℤ/8)11yescharacteristic
229C3⋊Dic3—41no—
230C3×Dic3—41no—
231C22×D4—181no—
232C22×D4—181no—
233C2×SD16—181no—
234C4⋊Q8D3211yescharacteristic, complemented
235#127—31no—
236#121—181no—
237#121—181no—
238#120—182no—
239C4×D4—31no—
240C4×D4—91no—
241#107—61no—
242C4⋊C8—31no—
243C4⋊C8—91no—
244#103—181no—
245#102—61no—
246#102—62no—
247C4×C8—31no—
248C23×C3—61no—
249C23×C3—62no—
250C22×D3—21no—
251C22×D3—22no—
252C22×D3—61no—
253C22×D3—61no—
254C22×D3—121no—
255C22×D3—124no—
256C22×D3—124no—
257C22×D3—124no—
258C22×D3—124no—
259C22×D3—242no—
260C22×D3—242no—
261C3×Q8—42no—
262C3×Q8—42no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×Q8—41no—
266C3×Q8—41no—
267C3×D4—32no—
268C3×D4—61no—
269C3×D4—122no—
270C3×D4—121no—
271C3×D4—121no—
272C3×D4—121no—
273C3×D4—121no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—42no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—61no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289#67—124no—
290#67—124no—
291#67—124no—
292C2×Dic3—21no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—121no—
296D12—21no—
297D12—32no—
298D12—32no—
299D12—42no—
300D12—41no—
301D12—41no—
302D12—41no—
303D12—41no—
304D12—62no—
305D12—61no—
306D12—61no—
307D12—121no—
308D12—124no—
309D12#21512yescomplemented
310C4×D3—41no—
311C4×D3—41no—
312C4×D3—121no—
313C4×D3—121no—
314C4×D3—121no—
315C4×D3—121no—
316C4×D3—241no—
317C4×D3—241no—
318C3×C8—121no—
319C3×C8—121no—
320C3⋊C8—41no—
321C3⋊C8—41no—
322C3⋊C8—122no—
323C3⋊C8—121no—
324C3⋊C8—121no—
325C2×C32#44711yescharacteristic
326C2×C32#45011yescharacteristic
327C2×C32#45511yescharacteristic
328C3⋊D3—42no—
329C3×D3—42no—
330C3×D3—82no—
331C24—182no—
332C2×Q8—21no—
333C2×D4—31no—
334C2×D4—32no—
335C2×D4—61no—
336C2×D4—61no—
337C2×D4—91no—
338C2×D4—182no—
339C2×D4—182no—
340C2×D4—362no—
341C2×D4—362no—
342C2×D4—362no—
343C2×D4—362no—
344C22×C4—61no—
345C22×C4—181no—
346SD16—362no—
347C2×C8—61no—
348C2×C8—61no—
349C2×C8—181no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—31no—
353C4⋊C4—91no—
354C22⋊C4—61no—
355C22⋊C4—182no—
356C22⋊C4—181no—
357C42C2×D3211yescharacteristic
358C22×C3—21no—
359C22×C3—62no—
360C22×C3—121no—
361C22×C3—121no—
362C22×C3—122no—
363C22×C3—122no—
364C22×C3—122no—
365C22×C3#93711yescharacteristic
366C22×C3#93711yescharacteristic
367C2×D3—22no—
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—42no—
371C2×D3—42no—
372C2×D3—42no—
373C2×D3—62no—
374C2×D3—62no—
375C2×D3—122no—
376C2×D3—121no—
377C2×D3—121no—
378C2×D3—121no—
379C2×D3—121no—
380C2×D3—241no—
381C2×D3—241no—
382C2×D3—248no—
383C2×D3—248no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—41no—
391C3×C4—82no—
392C3×C4—81no—
393C3×C4—81no—
394C3×C4—121no—
395C3×C4D3×D811yescharacteristic
396C3×C4D3×D811yescharacteristic
397C3×C4#91111yescharacteristic
398C3×C4#91111yescharacteristic
399C3×C4D3×SD1611yescharacteristic
400C3×C4#91411yescharacteristic
401C3×C4C2×#21511yescharacteristic
402C3×C4#94911yescharacteristic
403Dic3—41no—
404Dic3—121no—
405Dic3—121no—
406Dic3—241no—
407C32#163911yescharacteristic, complemented, Sylow
408C23—61no—
409C23—62no—
410C23—181no—
411C23—364no—
412C23—364no—
413C23—722no—
414Q8—41no—
415Q8—41no—
416D4—32no—
417D4—61no—
418D4—92no—
419D4—122no—
420D4—121no—
421D4—121no—
422D4—121no—
423D4—121no—
424D4—181no—
425D4—364no—
426D4—364no—
427C2×C4—41no—
428C2×C4—61no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—181no—
432C2×C4—361no—
433C2×C4—361no—
434C2×C4D3×#6711yescharacteristic
435C2×C4D3×#6711yescharacteristic
436C2×C4#381111yescharacteristic
437C8—121no—
438C8—121no—
439C8—361no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—122no—
444C2×C3—242no—
445C2×C3#504611yescharacteristic
446C2×C3#506111yescharacteristic
447C2×C3#515611yescharacteristic
448C2×C3#515611yescharacteristic
449C2×C3#516911yescharacteristic
450C2×C3#520211yescharacteristic
451D3—42no—
452D3—82no—
453D3—122no—
454D3—122no—
455D3—242no—
456C22—62no—
457C22—121no—
458C22—121no—
459C22—122no—
460C22—122no—
461C22—122no—
462C22—182no—
463C22—361no—
464C22—361no—
465C22—728no—
466C22#6398311yescharacteristic
467C4—21no—
468C4—81no—
469C4—121no—
470C4—361no—
471C4#6392611yescharacteristic
472C4#6392711yescharacteristic
473C4D3×#21511yescharacteristic
474C4#6393911yescharacteristic
475C3—21no—
476C3#7110811yescharacteristic, complemented
477C3#7119811yescharacteristic, complemented
478C2—122no—
479C2—242no—
480C2—362no—
481C2#1059151611yescharacteristic
482C2#1059165111yescharacteristic
483C2#1059165911yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10594004C2
hypercenterC4⋊Q8D32
hypocenterC32#1639
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
2. #10592782C2semidirect
3. C3×#5088C2semidirect
4. C3×#5087C2semidirect
5. #10589090C2semidirect
6. #10589082C2semidirect
7. #10589081C2semidirect
12. C32×C4⋊Q8C22semidirect
21. C4⋊(C3⋊(C3⋊C8))C22semidirect
25. C3×C4⋊(C3⋊C8)C22semidirect
26. C3×C4×C3⋊C8C22semidirect
31. #5088D3semidirect
32. #5087D3semidirect
75. C3×C4⋊Q8C2×D3semidirect
76. C3×C4⋊Q8C2×D3semidirect
107. C4⋊(C3⋊C8)C2×D3semidirect
108. C4×C3⋊C8C2×D3semidirect
133. C3×D12SD16semidirect
234. C4⋊Q8D32semidirect
309. D12#215semidirect
407. C32#1639semidirect
476. C3#71108semidirect
477. C3#71198semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105927822
C3×#50882
C3×#50872
#105890902
#105890822
#105890812
#711983
#711083