Finite Group Databasebeta

← #11779870

Subgroups — #11779870

Order 1152.

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

normal subgroups only

This group has 656 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#10596024C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic, complemented
3#10590307C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589091C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#71045—31nomaximal
9#68197—31nomaximal
10C2×#3828—21no—
11C32×C4×D4C2211yescharacteristic
12#64149—21no—
13#64139—21no—
14#64102—21no—
15#64093—22no—
16#64083C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×#214—21no—
19C3×#869C2211yescharacteristic
20C3×#810—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63573—21no—
25#63567—21no—
26#63564—22no—
27#5553—31no—
28#5553—31no—
29#5553—61no—
30C3×#461—31no—
31#5094—31no—
32#5088—31no—
33#5019D311yescharacteristic, complemented
34#4851—31no—
35#4694—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic, complemented
38#4485—31no—
39#4485—31no—
40#4484—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#638—22no—
45C2×#638—22no—
46#3828—42no—
47#3828—42no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)D412yes—
51C2×C4×C3⋊D3—22no—
52C2×#634D411yescharacteristic
53C2×C3×Dic6—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42C2311yescharacteristic
57#3752—22no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60C4×C3⋊Dic3—21no—
61C3×#214—42no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1642—91noSylow
68C2×#235—61no—
69C2×#235—61no—
70C2×#235—62no—
71C2×C3×SD16—61no—
72C3×C4⋊Q8—31no—
73C3×C4×D4—21no—
74C3×C4×D4C2×D311yescharacteristic
75C3×C4×D4C2×D311yescharacteristic
76#940—62no—
77#940—61no—
78#940—61no—
79C2×#214—21no—
80#930—61no—
81#930—61no—
82#930—62no—
83#893—62no—
84#893—61no—
85#893—61no—
86#884—62no—
87#884—62no—
88#884—64no—
89#874—31no—
90#874—31no—
91#874—61no—
92#869C2×D311yescharacteristic
93C4×Dic6—31no—
94C4×Dic6—31no—
95C4×Dic6—61no—
96C3×C4⋊C8—31no—
97C3×C4⋊C8—31no—
98C3×#103—61no—
99C3×C4×C8—31no—
100#821—62no—
101#817—61no—
102#816—61no—
103#810—21no—
104#810—61no—
105#809—62no—
106#808—61no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4⋊(C3⋊C8)C2×D311yescharacteristic
109C4×C3⋊C8C2×D311yescharacteristic
110C23×C32—21no—
111C22×C3⋊D3—22no—
112C32×D4—21no—
113C32×D4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120#638—44no—
121#638—82no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C4⋊(C3⋊D3)—41no—
125C4⋊(C3⋊D3)—41no—
126C4⋊(C3⋊D3)—41no—
127C4⋊(C3⋊D3)—41no—
128C4⋊(C3⋊D3)—42no—
129C4×C3⋊D3—44no—
130#634—21no—
131#634SD1612yescomplemented
132C2×C3×Dic3—41no—
133C3×Dic6—41no—
134C3×Dic6—41no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137C3×C3⋊C8—41no—
138#550—91no—
139#486—91no—
140#475—91no—
141#461—31no—
142#331—91no—
143Q8⋊C8—91no—
144D4⋊C8—31no—
145C2×C3×Q8—61no—
146C2×C3×D4—21no—
147C2×C3×D4D1211yescharacteristic
148C2×C3×D4#6711yescharacteristic
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C2×#67—64no—
153C2×#67—62no—
154C2×#67—62no—
155C2×#67—64no—
156C2×#67—62no—
157C2×#67—62no—
158#235—122no—
159#235—122no—
160#235—124no—
161#235—124no—
162#235—122no—
163#235—122no—
164C2×D12—32no—
165C2×D12—32no—
166C2×D12—62no—
167C2×D12—62no—
168C2×D12—62no—
169C2×D12—61no—
170C2×D12—61no—
171C2×D12—61no—
172C2×D12—61no—
173C2×C4×D3—64no—
174C2×C4×D3—62no—
175C2×C4×D3—62no—
176C2×Dic6—21no—
177C2×Dic6—31no—
178C2×Dic6—31no—
179C2×Dic6—61no—
180C3×SD16—122no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4D1211yescharacteristic
188C3×C4⋊C4#6711yescharacteristic
189C3×C22⋊C4—22no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—21no—
192C3×C42—21no—
193C3×C42C22×D311yescharacteristic
194C3×C42C22×D311yescharacteristic
195#214—42no—
196(C2×D3)⋊C4—64no—
197(C2×D3)⋊C4—62no—
198(C2×D3)⋊C4—62no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—31no—
202C4⋊Dic3—31no—
203C4⋊Dic3—61no—
204Dic3⋊C4—62no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207C4×Dic3—62no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32#12011yescharacteristic
217C2×C3⋊D3—42no—
218C2×C3⋊D3—42no—
219C2×C3⋊D3—42no—
220C32×C4—21no—
221C32×C4—41no—
222C32×C4C2×SD1611yescharacteristic
223C32×C4#13511yescharacteristic
224C32×C4AGL(1,ℤ/8)11yescharacteristic
225C32×C4AGL(1,ℤ/8)11yescharacteristic
226C3⋊Dic3—22no—
227C3⋊Dic3—41no—
228C3×Dic3—81no—
229C2×#41—181no—
230C2×SD16—61no—
231C4⋊Q8—31no—
232#127—91no—
233#127—181no—
234#121—182no—
235#121—181no—
236C4×Q8—91no—
237C4×D4—181no—
238C4×D4D3211yescharacteristic
239#106—181no—
240C4⋊C8—31no—
241C4⋊C8—31no—
242#103—61no—
243#103—181no—
244#102—182no—
245C4×C8—31no—
246C23×C3—22no—
247C23×C3—21no—
248C23×C3—21no—
249C22×D3—64no—
250C22×D3—62no—
251C22×D3—62no—
252C3×Q8—121no—
253C3×Q8—121no—
254C3×D4—21no—
255C3×D4—21no—
256C3×D4—21no—
257C3×D4—21no—
258C3×D4—41no—
259C3×D4—41no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—121no—
273C2×C3×C4C2×D1211yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279#67—128no—
280#67—124no—
281#67—124no—
282#67—244no—
283#67—242no—
284#67—242no—
285C2×Dic3—41no—
286C2×Dic3—62no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—62no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292D12—122no—
293D12—122no—
294D12—122no—
295D12—122no—
296D12—122no—
297D12—122no—
298D12—121no—
299D12—121no—
300D12—121no—
301D12—121no—
302D12—121no—
303D12—121no—
304D12—121no—
305D12—121no—
306D12—242no—
307C4×D3—128no—
308C4×D3—124no—
309C4×D3—124no—
310Dic6—32no—
311Dic6—32no—
312Dic6—41no—
313Dic6—41no—
314Dic6—62no—
315Dic6—62no—
316Dic6—61no—
317Dic6—61no—
318C3×C8—121no—
319C3×C8—121no—
320C3×C8—121no—
321C3⋊C8—41no—
322C3⋊C8—41no—
323C3⋊C8—41no—
324C2×C32—81no—
325C2×C32#44911yescharacteristic
326C2×C32#45011yescharacteristic
327C2×C32#45511yescharacteristic
328C3⋊D3—82no—
329#41—362no—
330#41—362no—
331C2×Q8—61no—
332C2×Q8—91no—
333C2×D4—92no—
334C2×D4—182no—
335C2×D4—182no—
336C2×D4—181no—
337C2×D4—181no—
338C2×D4#62611yescharacteristic
339C22×C4—21no—
340C22×C4—182no—
341SD16—122no—
342C2×C8—61no—
343C2×C8—61no—
344C2×C8—61no—
345C4⋊C4—61no—
346C4⋊C4—61no—
347C4⋊C4—91no—
348C4⋊C4—181no—
349C4⋊C4#62611yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—182no—
352C42—181no—
353C42C2×D3211yescharacteristic
354C22×C3—21no—
355C22×C3—42no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3#88211yescharacteristic
365C22×C3#93711yescharacteristic
366C2×D3—124no—
367C2×D3—124no—
368C2×D3—124no—
369C2×D3—122no—
370C2×D3—122no—
371C2×D3—122no—
372C2×D3—122no—
373C2×D3—122no—
374C2×D3—122no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—41no—
382C3×C4—42no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—241no—
386C3×C4#90411yescharacteristic
387C3×C4#90811yescharacteristic
388C3×C4#91111yescharacteristic
389C3×C4D3×SD1611yescharacteristic
390C3×C4D3×SD1611yescharacteristic
391C3×C4#91411yescharacteristic
392C3×C4#93211yescharacteristic
393C3×C4#95011yescharacteristic
394Dic3—64no—
395Dic3—62no—
396Dic3—62no—
397Dic3—81no—
398Dic3—122no—
399Dic3—121no—
400Dic3—121no—
401C32#164211yescharacteristic, complemented, Sylow
402C23—21no—
403C23—182no—
404Q8—92no—
405Q8—121no—
406Q8—121no—
407Q8—181no—
408D4—21no—
409D4—21no—
410D4—362no—
411D4—364no—
412D4—361no—
413D4—361no—
414D4—361no—
415D4—361no—
416D4—722no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—121no—
421C2×C4—181no—
422C2×C4—181no—
423C2×C4—364no—
424C2×C4C2×#62611yescharacteristic
425C2×C4#381111yescharacteristic
426C2×C4#381111yescharacteristic
427C8—121no—
428C8—121no—
429C8—121no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—82no—
434C2×C3—81no—
435C2×C3—81no—
436C2×C3#473411yescharacteristic
437C2×C3#477611yescharacteristic
438C2×C3#482511yescharacteristic
439C2×C3#503711yescharacteristic
440C2×C3#516911yescharacteristic
441C2×C3#520211yescharacteristic
442D3—244no—
443D3—242no—
444D3—242no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—362no—
449C22—362no—
450C22—362no—
451C22#6398111yescharacteristic
452C4—21no—
453C4—41no—
454C4—182no—
455C4—241no—
456C4—361no—
457C4#6382911yescharacteristic
458C4#6383011yescharacteristic
459C4#6393011yescharacteristic
460C4#6393711yescharacteristic
461C3—21no—
462C3#6819711yescharacteristic, complemented
463C3#7104511yescharacteristic, complemented
464C2—81no—
465C2—722no—
466C2#1059118211yescharacteristic
467C2#1059146711yescharacteristic
468C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radical#10596024C2
hypercenterC4×D4D32
hypocenterC32#1642
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×#5019C2semidirect
3. #10590307C2semidirect
4. #10590281C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589091C2semidirect
7. #10589085C2semidirect
33. #5019D3semidirect
37. D4⋊(C3⋊C8)D3semidirect
131. #634SD16semidirect
401. C32#1642semidirect
462. C3#68197semidirect
463. C3#71045semidirect

Maximal subgroups

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

subgroupindex
#105960242
C3×#50192
#105903072
#105902812
C3×D4⋊(C3⋊C8)2
#105890912
#105890852
#710453
#681973