Finite Group Databasebeta

← #11779314

Subgroups — #11779314

Order 1152.

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

normal subgroups only

This group has 669 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
2C3×#4693C211yesmaximal, characteristic, complemented
3#10590300C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic, complemented
5#10589325C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71266—31nomaximal
9#68195—31nomaximal
10C2×#3802—21no—
11C2×D3×D12—21no—
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#204—22no—
14C3×#874C2211yescharacteristic
15C3×C4×D12C2211yescharacteristic
16C3×#869C2211yescharacteristic, complemented
17#63922—22no—
18#63916—21no—
19#63908—21no—
20C32×C4×C8C2211yescharacteristic, complemented
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
22C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
23#63574—21no—
24#63573—21no—
25#63564—21no—
26#63562—21no—
27#5717—31no—
28D4×D12—31no—
29C3×#492—31no—
30#5084—31no—
31#5084—31no—
32#5008—31no—
33#4842—31no—
34#4693D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36#4544—31no—
37#4485—31no—
38#4459—31no—
39#4459—31no—
40#4459—61no—
41#4459D311yescharacteristic, complemented
42C22×D32—22no—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12D411yescharacteristic
48C2×C3×D12D412yes—
49C2×C3×C4×D3—21no—
50C2×C3×Dic6—21no—
51C2×#626—22no—
52C2×#625—22no—
53#3802—42no—
54#3802—42no—
55D3×D12—42no—
56D3×D12—42no—
57C2×C32×C8—21no—
58C32×C42C2311yescharacteristic
59#3752—21no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61C2×C3⋊(C3⋊C8)—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C3×#204—44no—
68(C2×D3)⋊Dic3—22no—
69#1629—91noSylow
70C2×D3×D4—61no—
71C2×D3×D4—61no—
72C2×D3×D4—61no—
73C22×D12—61no—
74C2×C3×SD16—62no—
75C3×C4⋊Q8—31no—
76C3×#127—31no—
77C3×C4×D4—31no—
78#938—61no—
79#938—61no—
80#937—62no—
81#930—61no—
82C2×#204—22no—
83#895—61no—
84#882—62no—
85#874C2×D311yescharacteristic
86C4×D12—31no—
87C4×D12—31no—
88C4×D12—61no—
89C4×D12C2×D311yescharacteristic
90#869C2×D311yescharacteristic, complemented
91C3×C4⋊C8—31no—
92C3×C4×C8—21no—
93C3×C4×C8C2×D311yescharacteristic, complemented
94C3×C4×C8C2×D311yescharacteristic, complemented
95#832—61no—
96#821—61no—
97#817—61no—
98#809—61no—
99#809—61no—
100#808—61no—
101#808—61no—
102#808—61no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—31no—
105C4⋊(C3⋊C8)—61no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
107C22×C3⋊D3—21no—
108C22×C3×D3—21no—
109C22×C3×D3—22no—
110C2×D32—44no—
111C2×D32—44no—
112C2×D32—82no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3—21no—
117C4⋊(C3⋊D3)—21no—
118C4⋊(C3⋊D3)SD1612yescomplemented
119C4×C3⋊D3—41no—
120C4×C3⋊D3—41no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—41no—
123C3×D12—21no—
124C3×D12—42no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—41no—
128C3×D12—41no—
129C3×D12SD1612yescomplemented
130C3×C4×D3—41no—
131C3×C4×D3—41no—
132C3×Dic6—42no—
133#626—44no—
134#625—44no—
135C32×C8—22no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—41no—
138D42—91no—
139#492—31no—
140#476—91no—
141#476—91no—
142#331—91no—
143D4⋊C8—31no—
144D4⋊C8—91no—
145C23×D3—62no—
146C23×D3—62no—
147C2×C3×Q8—61no—
148C2×C3×D4—31no—
149C2×C3×D4—32no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C22×C3×C4—61no—
153C2×#67—62no—
154C2×#67—62no—
155C2×#67—62no—
156D3×D4—122no—
157D3×D4—122no—
158D3×D4—122no—
159D3×D4—122no—
160D3×D4—122no—
161D3×D4—122no—
162C2×D12—21no—
163C2×D12—21no—
164C2×D12—31no—
165C2×D12—31no—
166C2×D12—61no—
167C2×D12—62no—
168C2×D12—122no—
169C2×D12—122no—
170C2×D12D1211yescharacteristic
171C2×D12#6712yes—
172C2×C4×D3—21no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—121no—
176C2×Dic6—21no—
177C3×SD16—124no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—41no—
181C2×C3×C8—61no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C42—21no—
187C3×C42C22×D311yescharacteristic
188C3×C42C22×D311yescharacteristic
189#217—62no—
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—121no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—31no—
198C4⋊Dic3—31no—
199C4⋊Dic3—61no—
200C4⋊Dic3D1211yescharacteristic
201C2×C3⋊C8—21no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—121no—
205#204—44no—
206C22×C32#12011yescharacteristic
207C2×C3⋊D3—22no—
208C2×C3⋊D3—41no—
209C2×C3⋊D3—41no—
210C2×C3×D3—22no—
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—42no—
214C2×C3×D3—42no—
215C2×C3×D3—42no—
216D32—88no—
217C32×C4—21no—
218C32×C4C2×SD1611yescharacteristic
219C32×C4C2×SD1611yescharacteristic
220C32×C4AGL(1,ℤ/8)11yescharacteristic
221C32×C4AGL(1,ℤ/8)11yescharacteristic
222C3⋊Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—81no—
225C22×D4—181no—
226C22×D4—181no—
227C2×SD16—62no—
228C4⋊Q8—31no—
229#127—31no—
230#121—181no—
231#121—181no—
232#120—182no—
233C4×D4—31no—
234C4×D4—91no—
235#106—181no—
236#106—181no—
237C4⋊C8—31no—
238C4⋊C8—91no—
239#102—181no—
240#102—181no—
241C4×C8D3211yescharacteristic, complemented
242C23×C3—61no—
243C23×C3—62no—
244C22×D3—21no—
245C22×D3—22no—
246C22×D3—61no—
247C22×D3—61no—
248C22×D3—121no—
249C22×D3—124no—
250C22×D3—124no—
251C22×D3—124no—
252C22×D3—124no—
253C22×D3—242no—
254C22×D3—242no—
255C3×Q8—122no—
256C3×D4—32no—
257C3×D4—61no—
258C3×D4—122no—
259C3×D4—121no—
260C3×D4—121no—
261C3×D4—121no—
262C3×D4—121no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—61no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276#67—124no—
277#67—124no—
278#67—124no—
279C2×Dic3—21no—
280C2×Dic3—41no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—121no—
284D12—21no—
285D12—32no—
286D12—32no—
287D12—42no—
288D12—41no—
289D12—41no—
290D12—41no—
291D12—41no—
292D12—62no—
293D12—61no—
294D12—61no—
295D12—121no—
296D12—124no—
297D12#20412yescomplemented
298C4×D3—41no—
299C4×D3—41no—
300C4×D3—121no—
301C4×D3—121no—
302C4×D3—121no—
303C4×D3—121no—
304C4×D3—241no—
305C4×D3—241no—
306Dic6—42no—
307C3×C8—22no—
308C3×C8—22no—
309C3×C8—42no—
310C3×C8—121no—
311C3⋊C8—41no—
312C3⋊C8—121no—
313C3⋊C8—121no—
314C3⋊C8—241no—
315C2×C32#45011yescharacteristic
316C2×C32#45011yescharacteristic
317C2×C32#45311yescharacteristic
318C3⋊D3—42no—
319C3×D3—42no—
320C3×D3—82no—
321C24—182no—
322C2×Q8—61no—
323C2×D4—31no—
324C2×D4—32no—
325C2×D4—61no—
326C2×D4—61no—
327C2×D4—91no—
328C2×D4—182no—
329C2×D4—182no—
330C2×D4—362no—
331C2×D4—362no—
332C2×D4—362no—
333C2×D4—362no—
334C22×C4—61no—
335C22×C4—181no—
336SD16—124no—
337C2×C8—21no—
338C2×C8—61no—
339C2×C8—181no—
340C4⋊C4—31no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C4⋊C4—91no—
344C22⋊C4—61no—
345C22⋊C4—182no—
346C22⋊C4—181no—
347C42C2×D3211yescharacteristic
348C22×C3—21no—
349C22×C3—62no—
350C22×C3—121no—
351C22×C3—121no—
352C22×C3—122no—
353C22×C3—122no—
354C22×C3—122no—
355C22×C3#88211yescharacteristic
356C22×C3#93711yescharacteristic
357C2×D3—22no—
358C2×D3—41no—
359C2×D3—41no—
360C2×D3—42no—
361C2×D3—42no—
362C2×D3—42no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—122no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—241no—
371C2×D3—241no—
372C2×D3—248no—
373C2×D3—248no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—121no—
382C3×C4—241no—
383C3×C4C2×#20411yescharacteristic
384C3×C4#90811yescharacteristic
385C3×C4#91111yescharacteristic
386C3×C4D3×SD1611yescharacteristic
387C3×C4D3×SD1611yescharacteristic
388C3×C4D3×SD1611yescharacteristic
389C3×C4#91411yescharacteristic
390C3×C4#91411yescharacteristic
391Dic3—41no—
392Dic3—81no—
393Dic3—121no—
394Dic3—121no—
395Dic3—241no—
396C32#162911yescharacteristic, complemented, Sylow
397C23—61no—
398C23—62no—
399C23—181no—
400C23—364no—
401C23—364no—
402C23—722no—
403Q8—122no—
404D4—32no—
405D4—61no—
406D4—92no—
407D4—122no—
408D4—121no—
409D4—121no—
410D4—121no—
411D4—121no—
412D4—181no—
413D4—364no—
414D4—364no—
415C2×C4—61no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—121no—
419C2×C4—181no—
420C2×C4—361no—
421C2×C4—361no—
422C2×C4D3×D1211yescharacteristic
423C2×C4#380211yescharacteristic
424C2×C4D3×#6711yescharacteristic
425C8—22no—
426C8—121no—
427C8—361no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—122no—
432C2×C3—242no—
433C2×C3#473111yescharacteristic
434C2×C3#477611yescharacteristic
435C2×C3#482211yescharacteristic
436C2×C3#507711yescharacteristic
437C2×C3#516911yescharacteristic
438C2×C3#516911yescharacteristic
439D3—42no—
440D3—82no—
441D3—122no—
442D3—122no—
443D3—242no—
444C22—62no—
445C22—121no—
446C22—121no—
447C22—122no—
448C22—122no—
449C22—122no—
450C22—182no—
451C22—361no—
452C22—361no—
453C22—728no—
454C22#6392211yescharacteristic
455C4—21no—
456C4—121no—
457C4—241no—
458C4—361no—
459C4D3×#20411yescharacteristic
460C4#6379411yescharacteristic
461C4#6379611yescharacteristic
462C4#6379811yescharacteristic
463C3—21no—
464C3#6819511yescharacteristic, complemented
465C3#7126611yescharacteristic, complemented
466C2—122no—
467C2—242no—
468C2—362no—
469C2#1059039511yescharacteristic
470C2#1059094211yescharacteristic
471C2#1059094311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10594004C2
hypercenterC4×C8D32
hypocenterC32#1629
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×#4693C2semidirect
3. #10590300C2semidirect
4. #10590266C2semidirect
5. #10589325C2semidirect
6. C3×#4459C2semidirect
7. #10589090C2semidirect
16. C3×#869C22semidirect
20. C32×C4×C8C22semidirect
21. C4⋊(C3⋊(C3⋊C8))C22semidirect
22. C3×C4⋊(C3⋊C8)C22semidirect
34. #4693D3semidirect
41. #4459D3semidirect
90. #869C2×D3semidirect
93. C3×C4×C8C2×D3semidirect
94. C3×C4×C8C2×D3semidirect
106. C4⋊(C3⋊C8)C2×D3semidirect
118. C4⋊(C3⋊D3)SD16semidirect
129. C3×D12SD16semidirect
241. C4×C8D32semidirect
297. D12#204semidirect
396. C32#1629semidirect
464. C3#68195semidirect
465. C3#71266semidirect

Maximal subgroups

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

subgroupindex
#105940042
C3×#46932
#105903002
#105902662
#105893252
C3×#44592
#105890902
#712663
#681953