Finite Group Databasebeta

← #11776581

Subgroups — #11776581

Order 1152.

706 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#874C211yesmaximal, characteristic
2C3×#4835C211yesmaximal, characteristic, complemented
3#10590263C211yesmaximal, characteristic, complemented
4#10589351C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6#10589091C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#70818—31nomaximal
9#68387—31nomaximal
10C2×D3×D12—21no—
11C2×D3×D12—21no—
12C2×D3×D12C412yes—
13#64083C2211yescharacteristic
14C3×#874C2211yescharacteristic
15C3×C42×D3C2211yescharacteristic
16#63911—21no—
17#63911—21no—
18#63911C412yes—
19C32×C4⋊C8C2211yescharacteristic, complemented
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
21C3×(C2×D3)⋊C8—21no—
22C3×#815—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
25(C2×D3)⋊(C3⋊C8)—21no—
26#63554—21no—
27D3×#127—31no—
28C2×#874—31no—
29C3×#432—31no—
30#4926—31no—
31#4835—31no—
32#4835D311yescharacteristic, complemented
33C3×#331—31no—
34#4544—31no—
35#4485—31no—
36#4485—31no—
37#4485—31no—
38#4485—31no—
39#4485—31no—
40#4485—61no—
41#4485D311yescharacteristic, complemented
42C22×D32—22no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)C2×C412yes—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12C2×C412yes—
49C2×C3×C4×D3C2×C411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C2×C3×C4×D3D411yescharacteristic
52C2×#626—22no—
53C2×#626—22no—
54C2×#626—22no—
55D3×D12—42no—
56D3×D12—42no—
57D3×D12—42no—
58D3×D12—42no—
59D3×D12—44no—
60C2×C32×C8—21no—
61C32×C42C2311yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C3×C4×Dic3C2×C411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1555—91noSylow
69C2×D3×D4—32no—
70C2×D3×D4—61no—
71C2×D3×D4—61no—
72C22×D12—32no—
73C22×D12—61no—
74C22×D12—61no—
75C3×#127—31no—
76C2×C3×C42—31no—
77#940—32no—
78#940—61no—
79#940—61no—
80#874—32no—
81#874—31no—
82#874—31no—
83#874—61no—
84#874—61no—
85#874—61no—
86#874C2×D311yescharacteristic
87C42×D3C2×D311yescharacteristic
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic, complemented
92C3×C4⋊C8C2×D311yescharacteristic, complemented
93C3×C22⋊C8—61no—
94C3×#97—61no—
95#830—61no—
96(C2×D3)⋊C8—21no—
97(C2×D3)⋊C8—61no—
98#815—21no—
99#815—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
104C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
105#803—61no—
106C22×C3⋊D3—22no—
107C22×C3×D3—22no—
108C22×C3×D3C22⋊C411yescharacteristic
109C2×D32—44no—
110C2×D32—44no—
111C2×D32—44no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C4⋊(C3⋊D3)—42no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)—41no—
120C2×C3×Dic3C22⋊C411yescharacteristic
121C2×C3×Dic3C22⋊C411yescharacteristic
122C2×C3×Dic3C22⋊C411yescharacteristic
123C3×D12—42no—
124C3×D12—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—41no—
128C3×C4×D3—22no—
129C3×C4×D3—21no—
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133#626—44no—
134#626—44no—
135#626—44no—
136C32×C8—41no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—41no—
139C3×C3⋊C8—41no—
140C2×#127—91no—
141#432—31no—
142#432—91no—
143#331—31no—
144#331—91no—
145#331—91no—
146#331—91no—
147C23×D3—62no—
148C23×D3—62no—
149C2×C3×D4—32no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C2×#67—62no—
156C2×#67—62no—
157C2×#67—62no—
158D3×D4—124no—
159D3×D4—122no—
160D3×D4—122no—
161D3×D4—122no—
162D3×D4—122no—
163C2×D12—21no—
164C2×D12—21no—
165C2×D12—32no—
166C2×D12—32no—
167C2×D12—62no—
168C2×D12—62no—
169C2×D12—62no—
170C2×D12—62no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—121no—
176C2×D12—121no—
177C2×D12—124no—
178C2×D12—122no—
179C2×D12—122no—
180C2×D12—122no—
181C2×D12—122no—
182C2×D12C4×D312yes—
183C2×C4×D3C4×D311yescharacteristic
184C2×C4×D3D1211yescharacteristic
185C2×C4×D3#6711yescharacteristic
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—41no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C3×C42—21no—
192C3×C42—31no—
193C3×C42—31no—
194C3×C42—31no—
195C3×C42C22×D311yescharacteristic
196C3×C42C22×D311yescharacteristic
197C4×Dic3C4×D311yescharacteristic
198C4×Dic3D1211yescharacteristic
199C4×Dic3#6711yescharacteristic
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—121no—
205C22×C32C2×C22⋊C411yescharacteristic
206C2×C3⋊D3—42no—
207C2×C3⋊D3—42no—
208C2×C3⋊D3—42no—
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C2×C3×D3—42no—
212C2×C3×D3—42no—
213C2×C3×D3—42no—
214C2×C3×D3#10012yes—
215D32—88no—
216C32×C4—21no—
217C32×C4AGL(1,ℤ/8)11yescharacteristic
218C32×C4AGL(1,ℤ/8)11yescharacteristic
219C32×C4AGL(1,ℤ/8)11yescharacteristic
220C32×C4AGL(1,ℤ/8)11yescharacteristic
221C3×Dic3—21no—
222C3×Dic3—21no—
223C3×Dic3—21no—
224C22×D4—92no—
225C22×D4—181no—
226C22×D4—181no—
227#127—31no—
228#127—92no—
229#127—91no—
230#127—181no—
231#127—181no—
232C2×C42—31no—
233C4⋊C8—31no—
234C4⋊C8—31no—
235C4⋊C8—91no—
236C4⋊C8D3211yescharacteristic, complemented
237C22⋊C8—61no—
238C22⋊C8—181no—
239#97—61no—
240#97—181no—
241C23×C3—31no—
242C23×C3—62no—
243C22×D3—22no—
244C22×D3—62no—
245C22×D3—62no—
246C22×D3—122no—
247C22×D3—124no—
248C22×D3—124no—
249C22×D3—124no—
250C22×D3—124no—
251C22×D3—124no—
252C22×D3—124no—
253C22×D3(C2×D3)⋊C411yescharacteristic
254C3×D4—122no—
255C3×D4—121no—
256C3×D4—121no—
257C3×D4—121no—
258C3×D4—121no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—31no—
263C2×C3×C4—31no—
264C2×C3×C4—31no—
265C2×C3×C4—62no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4C2×D1211yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276#67—124no—
277#67—124no—
278#67—124no—
279C2×Dic3(C2×D3)⋊C411yescharacteristic
280C2×Dic3(C2×D3)⋊C411yescharacteristic
281C2×Dic3(C2×D3)⋊C411yescharacteristic
282D12—42no—
283D12—41no—
284D12—41no—
285D12—41no—
286D12—41no—
287D12—122no—
288D12—122no—
289D12—124no—
290D12—124no—
291D12—124no—
292D12—121no—
293D12—121no—
294D12—121no—
295D12—121no—
296D12—121no—
297D12—121no—
298D12—121no—
299D12—121no—
300D12—241no—
301D12—241no—
302D12—241no—
303D12—241no—
304D12—242no—
305C4×D3—22no—
306C4×D3—21no—
307C4×D3—21no—
308C4×D3—21no—
309C4×D3—21no—
310C3×C8—41no—
311C3×C8—41no—
312C3×C8—81no—
313C3×C8—121no—
314C3×C8—121no—
315C3⋊C8—41no—
316C3⋊C8—41no—
317C3⋊C8—121no—
318C3⋊C8—121no—
319C3⋊C8—241no—
320C2×C32C2×#10011yescharacteristic
321C2×C32#41811yescharacteristic
322C2×C32#41811yescharacteristic
323C3⋊D3—82no—
324C3×D3—22no—
325C3×D3—82no—
326C24—182no—
327C2×D4—32no—
328C2×D4—61no—
329C2×D4—61no—
330C2×D4—92no—
331C2×D4—182no—
332C2×D4—182no—
333C2×D4—182no—
334C2×D4—181no—
335C2×D4—181no—
336C2×D4—364no—
337C2×D4—362no—
338C2×D4—362no—
339C2×D4—362no—
340C2×D4—362no—
341C22×C4—31no—
342C22×C4—31no—
343C22×C4—31no—
344C2×C8—21no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—181no—
348C42—31no—
349C42—31no—
350C42—31no—
351C42C2×D3211yescharacteristic
352C22×C3—21no—
353C22×C3—32no—
354C22×C3—61no—
355C22×C3—61no—
356C22×C3—122no—
357C22×C3—122no—
358C22×C3—122no—
359C22×C3D3×C22⋊C411yescharacteristic
360C22×C3C2×(C2×D3)⋊C411yescharacteristic
361C2×D3—21no—
362C2×D3—21no—
363C2×D3—42no—
364C2×D3—42no—
365C2×D3—42no—
366C2×D3—122no—
367C2×D3—122no—
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—122no—
371C2×D3—122no—
372C2×D3—242no—
373C2×D3—242no—
374C2×D3—242no—
375C2×D3—248no—
376C2×D3—248no—
377C2×D3#82312yes—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—41no—
385C3×C4—61no—
386C3×C4—61no—
387C3×C4—61no—
388C3×C4#90811yescharacteristic
389C3×C4#90811yescharacteristic
390C3×C4#91111yescharacteristic
391C3×C4#91111yescharacteristic
392C3×C4#91411yescharacteristic
393C3×C4#91411yescharacteristic
394C3×C4#94911yescharacteristic
395C3×C4#94911yescharacteristic
396Dic3—21no—
397Dic3—21no—
398Dic3—21no—
399C32#155511yescharacteristic, complemented, Sylow
400C23—31no—
401C23—62no—
402C23—182no—
403C23—364no—
404C23—364no—
405C23—364no—
406D4—122no—
407D4—121no—
408D4—121no—
409D4—121no—
410D4—121no—
411D4—362no—
412D4—364no—
413D4—364no—
414D4—364no—
415D4—361no—
416D4—361no—
417D4—361no—
418D4—361no—
419C2×C4—31no—
420C2×C4—31no—
421C2×C4—31no—
422C2×C4—62no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4C4×D3211yescharacteristic
428C2×C4D3×D1211yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C8—41no—
431C8—121no—
432C8—121no—
433C8—361no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—62no—
438C2×C3—242no—
439C2×C3D3×#10011yescharacteristic
440C2×C3#477011yescharacteristic
441C2×C3#477011yescharacteristic
442C2×C3#500111yescharacteristic
443C2×C3C2×#82311yescharacteristic
444C2×C3#513111yescharacteristic
445D3—22no—
446D3—82no—
447D3—242no—
448D3—242no—
449D3—482no—
450C22—32no—
451C22—61no—
452C22—61no—
453C22—122no—
454C22—122no—
455C22—122no—
456C22—362no—
457C22—362no—
458C22—362no—
459C22—728no—
460C22D3×(C2×D3)⋊C411yescharacteristic
461C4—21no—
462C4—61no—
463C4—61no—
464C4—61no—
465C4#6379411yescharacteristic
466C4#6379511yescharacteristic
467C4#6392511yescharacteristic
468C4#6393911yescharacteristic
469C3—21no—
470C3#6838711yescharacteristic, complemented
471C3#7081811yescharacteristic, complemented
472C2—62no—
473C2—242no—
474C2—722no—
475C2#1059059211yescharacteristic
476C2#1059093911yescharacteristic
477C2D3×#82311yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalD3×#874C2
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1555
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4835C2semidirect
3. #10590263C2semidirect
4. #10589351C2semidirect
5. C3×#4485C2semidirect
6. #10589091C2semidirect
7. #10589090C2semidirect
19. C32×C4⋊C8C22semidirect
20. C4⋊(C3⋊(C3⋊C8))C22semidirect
23. C3×C4⋊(C3⋊C8)C22semidirect
24. C3×C4⋊(C3⋊C8)C22semidirect
32. #4835D3semidirect
41. #4485D3semidirect
91. C3×C4⋊C8C2×D3semidirect
92. C3×C4⋊C8C2×D3semidirect
103. C4⋊(C3⋊C8)C2×D3semidirect
104. C4⋊(C3⋊C8)C2×D3semidirect
236. C4⋊C8D32semidirect
399. C32#1555semidirect
470. C3#68387semidirect
471. C3#70818semidirect

Maximal subgroups

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

subgroupindex
D3×#8742
C3×#48352
#105902632
#105893512
C3×#44852
#105890912
#105890902
#708183
#683873