Finite Group Databasebeta

← #11774620

Subgroups — #11774620

Order 1152.

533 conjugacy classes of subgroups.

The subgroup lattice has 473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#237C211yesmaximal, characteristic
2#10590263C211yesmaximal, characteristic, complemented
3#10590261C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71640—31nomaximal
9#68173—31nomaximal
10C2×C3×#237C411yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C3×D4×Dic3C411yescharacteristic
13C3×C4×#67—21no—
14C2×C3×C4×Dic3—21no—
15C3×#892C411yescharacteristic
16C3×#887C411yescharacteristic
17C3×#67⋊C4—21no—
18C3×#877—21no—
19C3×C42×D3C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25Dic3⋊(C3⋊C8)—21no—
26(C2×D3)⋊(C3⋊C8)—21no—
27(C2×D3)⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×C4×#41—31no—
30C4×#237D311yescharacteristic
31#4926—31no—
32#4925—31no—
33#4835—31no—
34#4685—31no—
35C3×D4⋊C8—31no—
36#4535—31no—
37#4535—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—31no—
40D4⋊(C3⋊C8)—61no—
41D4⋊(C3⋊C8)D311yescharacteristic, complemented
42#4484—31no—
43#4456—31no—
44C2×C32×D4C2×C411yescharacteristic
45C22×C32×C4—21no—
46C2×C3×#67—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C3×#237—22no—
50C3×#237—22no—
51C2×C3×C4×D3C2×C411yescharacteristic
52C2×C3×C4×D3D411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×Dic6C2×C411yescharacteristic
55C32×C4⋊C4C2×C411yescharacteristic
56C32×C22⋊C4—21no—
57C32×C42C2311yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#1488—91noSylow
74C2×C3×#41—31no—
75C2×#237Dic311yescharacteristic
76C3×C4×Q8—31no—
77C3×C4×Q8—31no—
78C3×C4×D4—21no—
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81C3×C4×D4—61no—
82C3×C4×D4C2×D311yescharacteristic
83C3×C4×D4C2×D311yescharacteristic
84C3×#117—31no—
85C3×#117—61no—
86C2×C3×C42—31no—
87C2×C3×C42—61no—
88D4×Dic3Dic311yescharacteristic
89C4×#67—21no—
90C2×C4×Dic3—21no—
91#892Dic311yescharacteristic
92#887Dic311yescharacteristic
93#67⋊C4—21no—
94#877—21no—
95C42×D3C2×D311yescharacteristic
96C4×Dic6C2×D311yescharacteristic
97C3×C4⋊C8—31no—
98C3×C4×C8—31no—
99#830—61no—
100#830—61no—
101(C2×D3)⋊C8—61no—
102(C2×D3)⋊C8—61no—
103#815—61no—
104Dic3⋊C8—61no—
105C4⋊(C3⋊C8)—31no—
106C4⋊(C3⋊C8)—31no—
107C4⋊(C3⋊C8)—61no—
108C4⋊(C3⋊C8)—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110#803—61no—
111C4×C3⋊C8—31no—
112C4×C3⋊C8—31no—
113C4×C3⋊C8—61no—
114C4×C3⋊C8C2×D311yescharacteristic
115C23×C32—21no—
116C22×C3×D3C22⋊C411yescharacteristic
117C32×D4—21no—
118C32×D4M1612yes—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C3×#67—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3C22⋊C411yescharacteristic
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—21no—
137C3×C4×D3—41no—
138C3×Dic6—21no—
139C3×Dic6M1612yes—
140C3⋊(C3⋊C8)—41no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144C4×#41—31no—
145#432—91no—
146#431—91no—
147Q8⋊C8—91no—
148Q8⋊C8—91no—
149D4⋊C8—31no—
150D4⋊C8—91no—
151C3×#41—62no—
152C3×#41—62no—
153C2×C3×Q8—31no—
154C2×C3×D4—21no—
155C2×C3×D4—61no—
156C2×C3×D4C4×D311yescharacteristic
157C2×C3×D4C2×Dic311yescharacteristic
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—41no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C2×#67—21no—
167C22×Dic3—21no—
168C22×Dic3—21no—
169#237—22no—
170#237—22no—
171C2×C4×D3C2×Dic311yescharacteristic
172C2×C4×D3#6711yescharacteristic
173C2×C4×D3#6711yescharacteristic
174C2×Dic6C2×Dic311yescharacteristic
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—31no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4C4×D311yescharacteristic
182C3×C4⋊C4C2×Dic311yescharacteristic
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—41no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—21no—
189C3×C42—31no—
190C3×C42—31no—
191C3×C42—31no—
192C3×C42—61no—
193C3×C42—61no—
194C3×C42—61no—
195C3×C42C22×D311yescharacteristic
196C3×C42C22×D311yescharacteristic
197#217—21no—
198(C2×D3)⋊C4—21no—
199C4⋊Dic3C2×Dic311yescharacteristic
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C4×Dic3—21no—
205C4×Dic3C2×Dic311yescharacteristic
206C4×Dic3#6711yescharacteristic
207C4×Dic3#6711yescharacteristic
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—121no—
215C2×C3⋊C8—121no—
216C22×C32—22no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32C2×C22⋊C411yescharacteristic
220C2×C3×D3—21no—
221C2×C3×D3—21no—
222C2×C3×D3—21no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4C2×M1611yescharacteristic
226C32×C4C2×M1611yescharacteristic
227C32×C4#13511yescharacteristic
228C32×C4#13511yescharacteristic
229C3×Dic3—22no—
230C3×Dic3—21no—
231C3×Dic3—21no—
232C3×Dic3—21no—
233C3×Dic3—41no—
234C2×#41—31no—
235C4×Q8—31no—
236C4×Q8—31no—
237C4×D4—31no—
238C4×D4—61no—
239C4×D4—61no—
240C4×D4D3211yescharacteristic
241#117—31no—
242#117—61no—
243C2×C42—31no—
244C2×C42—61no—
245C4⋊C8—31no—
246C4⋊C8—91no—
247C4⋊C8—181no—
248C22⋊C8—181no—
249C22⋊C8—181no—
250#97—181no—
251C4×C8—31no—
252C4×C8—91no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—31no—
256C23×C3—41no—
257C22×D3#21711yescharacteristic
258C3×Q8—32no—
259C3×Q8—61no—
260C3×D4—21no—
261C3×D4—21no—
262C3×D4—22no—
263C3×D4—41no—
264C3×D4—64no—
265C3×D4ΓL(1,𝔽25)12yes—
266C3×D4#20812yes—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—64no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—81no—
288C2×C3×C4—81no—
289C2×C3×C4—121no—
290C2×C3×C4—122no—
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4C22×Dic311yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297#67—24no—
298C2×Dic3—24no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—42no—
302C2×Dic3#21711yescharacteristic
303C2×Dic3#21711yescharacteristic
304C2×Dic3#21711yescharacteristic
305C4×D3—21no—
306C4×D3—21no—
307C4×D3—21no—
308C4×D3—21no—
309C4×D3—41no—
310Dic6—21no—
311Dic6#20812yes—
312C3×C8—121no—
313C3×C8—121no—
314C3⋊C8—41no—
315C3⋊C8—41no—
316C3⋊C8—121no—
317C3⋊C8—121no—
318C3⋊C8—122no—
319C3⋊C8—121no—
320C3⋊C8—121no—
321C3⋊C8—241no—
322C2×C32—42no—
323C2×C32#40711yescharacteristic
324C2×C32#41611yescharacteristic
325C2×C32#42111yescharacteristic
326C3×D3—41no—
327#41—62no—
328#41—62no—
329C2×Q8—31no—
330C2×D4—61no—
331C2×D4D3×Dic311yescharacteristic
332C22×C4—21no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—61no—
337C22×C4—61no—
338C2×C8—61no—
339C2×C8—61no—
340C2×C8—181no—
341C2×C8—181no—
342C4⋊C4—31no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C4⋊C4D3×Dic311yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C42—31no—
350C42—31no—
351C42—31no—
352C42—61no—
353C42—61no—
354C42—61no—
355C42C2×D3211yescharacteristic
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—42no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—61no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3D3×C22⋊C411yescharacteristic
370C22×C3C2×#21711yescharacteristic
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—61no—
384C3×C4—62no—
385C3×C4—61no—
386C3×C4—61no—
387C3×C4—81no—
388C3×C4—121no—
389C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
390C3×C4D3×M1611yescharacteristic
391C3×C4#91211yescharacteristic
392C3×C4#91611yescharacteristic
393C3×C4C2×#20811yescharacteristic
394C3×C4C2×#20811yescharacteristic
395C3×C4#95011yescharacteristic
396C3×C4#95011yescharacteristic
397Dic3—22no—
398Dic3—21no—
399Dic3—21no—
400Dic3—21no—
401Dic3—41no—
402C32#148811yescharacteristic, complemented, Sylow
403C23—21no—
404C23—31no—
405Q8—32no—
406Q8—61no—
407D4—21no—
408D4—64no—
409D4#371112yes—
410C2×C4—21no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—64no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—121no—
424C2×C4—122no—
425C2×C4C2×D3×Dic311yescharacteristic
426C2×C4D3×#6711yescharacteristic
427C2×C4D3×#6711yescharacteristic
428C8—121no—
429C8—121no—
430C8—361no—
431C8—361no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—42no—
436C2×C3—42no—
437C2×C3—82no—
438C2×C3—121no—
439C2×C3#472611yescharacteristic
440C2×C3#477211yescharacteristic
441C2×C3#482111yescharacteristic
442C2×C3#520711yescharacteristic
443C2×C3#523311yescharacteristic
444C2×C3#523611yescharacteristic
445D3—41no—
446C22—22no—
447C22—41no—
448C22—41no—
449C22—61no—
450C22—61no—
451C22—61no—
452C22D3×#21711yescharacteristic
453C4—21no—
454C4—41no—
455C4—61no—
456C4—62no—
457C4—61no—
458C4—61no—
459C4—121no—
460C4D3×#20811yescharacteristic
461C4C2×#371111yescharacteristic
462C4#6393311yescharacteristic
463C4#6393511yescharacteristic
464C3—21no—
465C3#6817311yescharacteristic, complemented
466C3#7164011yescharacteristic, complemented
467C2—42no—
468C2—121no—
469C2#1059115411yescharacteristic
470C2#1059142011yescharacteristic
471C2#1059167011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#237C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10590263C2semidirect
3. #10590261C2semidirect
4. D4⋊(C3⋊(C3⋊C8))C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589084C2semidirect
7. #10589083C2semidirect
41. D4⋊(C3⋊C8)D3semidirect
402. C32#1488semidirect
465. C3#68173semidirect
466. C3#71640semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2372
#105902632
#105902612
D4⋊(C3⋊(C3⋊C8))2
C3×D4⋊(C3⋊C8)2
#105890842
#105890832
#716403
#681733