Finite Group Databasebeta

← #11779547

Subgroups — #11779547

Order 1152.

614 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 90 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#10596022C211yesmaximal, characteristic
2C3×#5008C211yesmaximal, characteristic, complemented
3#10590300C211yesmaximal, characteristic, complemented
4#10590287C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#71140—31nomaximal
9#68181—31nomaximal
10C2×#3828—21no—
11C32×C4×D4C2211yescharacteristic
12#64147—21no—
13#64133—21no—
14C4⋊C4×C3⋊D3—21no—
15#64092—22no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#832—21no—
20C3×#808—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63573—21no—
25#63566—22no—
26#63564—21no—
27#5551—31no—
28#5551—31no—
29#5551—61no—
30C3×#476—31no—
31#5084—31no—
32#5079—31no—
33#5008D311yescharacteristic, complemented
34#4842—31no—
35#4681—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic, complemented
38#4486—31no—
39#4483—31no—
40#4482—31no—
41#4459—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#638—22no—
45#3828—42no—
46#3828—42no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3—21no—
50C2×#634—21no—
51C2×C3×Dic6—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C22⋊C4—21no—
54C32×C42C2311yescharacteristic
55#3757—22no—
56#3752—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)D412yes—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60#3750—22no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#1635—91noSylow
67C2×#235—61no—
68C2×#235—61no—
69C2×#235—62no—
70C3×C4⋊Q8—31no—
71C3×C4×D4—21no—
72C3×C4×D4C2×D311yescharacteristic
73C3×C4×D4C2×D311yescharacteristic
74#938—62no—
75#938—61no—
76#938—61no—
77#924—61no—
78#924—61no—
79#924—62no—
80D3×C4⋊C4—62no—
81D3×C4⋊C4—61no—
82D3×C4⋊C4—61no—
83#883—62no—
84#883—62no—
85#883—64no—
86C4×D12—31no—
87C4×D12—31no—
88C4×D12—61no—
89#869—31no—
90#869—31no—
91#869—61no—
92#869C2×D311yescharacteristic
93C3×#106—61no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8—31no—
96C3×#102—61no—
97C3×C4×C8—31no—
98#835—62no—
99#832—21no—
100#821—61no—
101#817—61no—
102#816—62no—
103#809—61no—
104#808—21no—
105#808—61no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4×C3⋊C8C2×D311yescharacteristic
109C23×C32—21no—
110C22×C3⋊D3—21no—
111C32×D4—21no—
112C32×D4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119#638—44no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—22no—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)SD1612yes—
124C4×C3⋊D3—44no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127#634—41no—
128#634—41no—
129C2×C3×Dic3—41no—
130C3×Dic6—42no—
131C3×C3⋊C8—41no—
132C3×C3⋊C8—41no—
133C3×C3⋊C8—41no—
134#547—91no—
135#487—91no—
136#476—31no—
137#476—91no—
138#332—91no—
139D4⋊C8—31no—
140D4⋊C8—91no—
141C2×C3×Q8—61no—
142C2×C3×D4—21no—
143C2×C3×D4D1211yescharacteristic
144C2×C3×D4#6711yescharacteristic
145C22×C3×C4—22no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C2×#67—64no—
149C2×#67—62no—
150C2×#67—62no—
151#235—122no—
152#235—122no—
153#235—124no—
154#235—124no—
155#235—122no—
156#235—122no—
157C2×D12—31no—
158C2×D12—31no—
159C2×D12—61no—
160C2×C4×D3—62no—
161C2×C4×D3—64no—
162C2×C4×D3—62no—
163C2×C4×D3—62no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×Dic6—21no—
167C2×Dic6—62no—
168C2×Dic6—61no—
169C2×Dic6—61no—
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4D1211yescharacteristic
177C3×C4⋊C4#6711yescharacteristic
178C3×C22⋊C4—22no—
179C3×C22⋊C4—21no—
180C3×C22⋊C4—21no—
181C3×C42—21no—
182C3×C42C22×D311yescharacteristic
183C3×C42C22×D311yescharacteristic
184#217—64no—
185#217—62no—
186#217—62no—
187(C2×D3)⋊C4—62no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3—31no—
193C4⋊Dic3—32no—
194C4⋊Dic3—31no—
195C4⋊Dic3—32no—
196C4⋊Dic3—62no—
197C4⋊Dic3—61no—
198C4⋊Dic3—62no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201Dic3⋊C4—64no—
202Dic3⋊C4—62no—
203Dic3⋊C4—62no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C22×C32—41no—
208C22×C32—41no—
209C22×C32—41no—
210C22×C32#12011yescharacteristic
211C2×C3⋊D3—22no—
212C2×C3⋊D3—41no—
213C2×C3⋊D3—41no—
214C32×C4—21no—
215C32×C4—41no—
216C32×C4C2×SD1611yescharacteristic
217C32×C4#13511yescharacteristic
218C32×C4AGL(1,ℤ/8)11yescharacteristic
219C32×C4#13711yescharacteristic
220C3⋊Dic3—42no—
221C3⋊Dic3—41no—
222C3×Dic3—81no—
223C2×#41—181no—
224C4⋊Q8—31no—
225C4⋊Q8—91no—
226#123—182no—
227C22⋊Q8—181no—
228#121—181no—
229C4×D4—91no—
230C4×D4D3211yescharacteristic
231C2×C4⋊C4—181no—
232#106—61no—
233#106—181no—
234C4⋊C8—31no—
235C4⋊C8—31no—
236#103—182no—
237#102—61no—
238#102—181no—
239C4×C8—31no—
240C23×C3—22no—
241C23×C3—21no—
242C23×C3—21no—
243C22×D3—62no—
244C22×D3—61no—
245C22×D3—61no—
246C3×Q8—122no—
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—41no—
252C3×D4—41no—
253C2×C3×C4—22no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—121no—
266C2×C3×C4C2×D1211yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272#67—128no—
273#67—124no—
274#67—124no—
275C2×Dic3—41no—
276C2×Dic3—62no—
277C2×Dic3—64no—
278C2×Dic3—61no—
279C2×Dic3—62no—
280C2×Dic3—61no—
281C2×Dic3—62no—
282D12—32no—
283D12—32no—
284D12—62no—
285D12—62no—
286D12—61no—
287D12—61no—
288C4×D3—122no—
289C4×D3—122no—
290C4×D3—128no—
291C4×D3—124no—
292C4×D3—124no—
293C4×D3—121no—
294C4×D3—121no—
295C4×D3—121no—
296C4×D3—121no—
297Dic6—42no—
298Dic6—122no—
299Dic6—122no—
300Dic6—121no—
301Dic6—121no—
302Dic6—121no—
303Dic6—121no—
304C3×C8—121no—
305C3×C8—121no—
306C3×C8—121no—
307C3⋊C8—41no—
308C3⋊C8—41no—
309C3⋊C8—41no—
310C2×C32—81no—
311C2×C32#45011yescharacteristic
312C2×C32#45211yescharacteristic
313C2×C32#45411yescharacteristic
314C3⋊D3—42no—
315#41—362no—
316#41—362no—
317C2×Q8—61no—
318C2×Q8—181no—
319C2×D4—91no—
320C2×D4—182no—
321C2×D4#62611yescharacteristic
322C22×C4—21no—
323C22×C4—182no—
324C22×C4—181no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—92no—
331C4⋊C4—91no—
332C4⋊C4—182no—
333C4⋊C4—181no—
334C4⋊C4#62611yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—182no—
337C22⋊C4—181no—
338C42C2×D3211yescharacteristic
339C22×C3—21no—
340C22×C3—42no—
341C22×C3—42no—
342C22×C3—42no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3#88211yescharacteristic
350C22×C3#93711yescharacteristic
351C2×D3—64no—
352C2×D3—62no—
353C2×D3—62no—
354C2×D3—122no—
355C2×D3—122no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—121no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—41no—
367C3×C4—42no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—241no—
371C3×C4#90411yescharacteristic
372C3×C4#90911yescharacteristic
373C3×C4#91111yescharacteristic
374C3×C4D3×SD1611yescharacteristic
375C3×C4D3×SD1611yescharacteristic
376C3×C4#91411yescharacteristic
377C3×C4#94211yescharacteristic
378C3×C4#95011yescharacteristic
379Dic3—81no—
380Dic3—124no—
381Dic3—122no—
382Dic3—122no—
383Dic3—121no—
384Dic3—122no—
385Dic3—121no—
386C32#163511yescharacteristic, complemented, Sylow
387C23—21no—
388C23—181no—
389Q8—122no—
390Q8—361no—
391Q8—361no—
392D4—21no—
393D4—21no—
394D4—92no—
395D4—181no—
396D4—364no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—121no—
401C2×C4—181no—
402C2×C4—182no—
403C2×C4—364no—
404C2×C4—361no—
405C2×C4—361no—
406C2×C4C2×#62611yescharacteristic
407C2×C4#381111yescharacteristic
408C2×C4#381111yescharacteristic
409C8—121no—
410C8—121no—
411C8—121no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—82no—
416C2×C3—81no—
417C2×C3—81no—
418C2×C3#473311yescharacteristic
419C2×C3#477611yescharacteristic
420C2×C3#482711yescharacteristic
421C2×C3#504711yescharacteristic
422C2×C3#516911yescharacteristic
423C2×C3#520111yescharacteristic
424D3—124no—
425D3—122no—
426D3—122no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—182no—
431C22—361no—
432C22—361no—
433C22#6398111yescharacteristic
434C4—21no—
435C4—41no—
436C4—241no—
437C4—361no—
438C4—362no—
439C4#6382911yescharacteristic
440C4#6383311yescharacteristic
441C4#6393011yescharacteristic
442C4#6393711yescharacteristic
443C3—21no—
444C3#6818111yescharacteristic, complemented
445C3#7114011yescharacteristic, complemented
446C2—81no—
447C2—362no—
448C2#1059118411yescharacteristic
449C2#1059146711yescharacteristic
450C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radical#10596022C2
hypercenterC4×D4D32
hypocenterC32#1635
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. C3×#5008C2semidirect
3. #10590300C2semidirect
4. #10590287C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589094C2semidirect
7. #10589082C2semidirect
33. #5008D3semidirect
37. D4⋊(C3⋊C8)D3semidirect
386. C32#1635semidirect
444. C3#68181semidirect
445. C3#71140semidirect

Maximal subgroups

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

subgroupindex
#105960222
C3×#50082
#105903002
#105902872
C3×D4⋊(C3⋊C8)2
#105890942
#105890822
#711403
#681813