Finite Group Databasebeta

← #11774470

Subgroups — #11774470

Order 1152.

509 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5557C211yesmaximal, characteristic
2C4×#3711C211yesmaximal, characteristic, complemented
3D3×C4⋊(C3⋊C8)C211yesmaximal, 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#71751—31nomaximal
9#68170—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C3×#938C411yescharacteristic
12C3×#936C411yescharacteristic
13C3×C4×#67—21no—
14C3×#926—21no—
15C3×#897C411yescharacteristic
16C3×#890C411yescharacteristic
17C3×#883—21no—
18C3×#879—21no—
19C3×C42×D3C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C2×#3711—21no—
22C2×D3×C3⋊C8—21no—
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×#529—31no—
30#5557D311yescharacteristic
31C2×C4⋊(C3⋊C8)—31no—
32C4×#208—31no—
33D3×C4⋊C8—31no—
34C4×ΓL(1,𝔽25)—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—
47C2×C3×C4×D3C2×C411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×C3×Dic6C2×C411yescharacteristic
51C32×C4⋊C4C2×C411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2311yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×#217—21no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#3711—24no—
72D3×C3⋊C8—42no—
73#1483—91noSylow
74C3×#126—61no—
75C3×#125—31no—
76C3×#124—31no—
77C3×#123—61no—
78C3×C22⋊Q8—31no—
79C3×#121—31no—
80C3×C4×Q8—31no—
81C3×C4×D4—21no—
82C3×C4×D4—61no—
83C3×C4×D4C2×D311yescharacteristic
84C3×C4×D4C2×D311yescharacteristic
85C3×#117—61no—
86C2×C3×C42—31no—
87#938Dic311yescharacteristic
88#936Dic311yescharacteristic
89C4×#67—21no—
90#926—21no—
91C2×#208—61no—
92C22×C3⋊C8—61no—
93C2×ΓL(1,𝔽25)—61no—
94C2×D3×C8—61no—
95#897Dic311yescharacteristic
96#890Dic311yescharacteristic
97#883—21no—
98#879—21no—
99C42×D3C2×D311yescharacteristic
100C4×Dic6C2×D311yescharacteristic
101C3×C4⋊C8—31no—
102C3×C4×C8—31no—
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×D4—21no—
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—42no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3C22⋊C411yescharacteristic
129C2×C3×Dic3C22⋊C411yescharacteristic
130C2×C3×Dic3C22⋊C411yescharacteristic
131C3×C4×D3—22no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×Dic6—21no—
137C3×Dic6—21no—
138C3⋊(C3⋊C8)—22no—
139C3⋊(C3⋊C8)—41no—
140C3×C3⋊C8—22no—
141C3×C3⋊C8—41no—
142#529—31no—
143C2×C4⋊C8—91no—
144C4×M16—91no—
145Q8⋊C8—91no—
146Q8⋊C8—91no—
147D4⋊C8—31no—
148D4⋊C8—91no—
149C2×C3×Q8—31no—
150C2×C3×D4—21no—
151C2×C3×D4—61no—
152C2×C3×D4C4×D311yescharacteristic
153C2×C3×D4C2×Dic311yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—41no—
160C2×#67—21no—
161C2×C4×D3C2×Dic311yescharacteristic
162C2×C4×D3#6711yescharacteristic
163C2×C4×D3#6711yescharacteristic
164C2×Dic6C2×Dic311yescharacteristic
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4C4×D311yescharacteristic
174C3×C4⋊C4C2×Dic311yescharacteristic
175C3×C22⋊C4—21no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—41no—
178C3×C22⋊C4—61no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C42—21no—
183C3×C42—31no—
184C3×C42—31no—
185C3×C42—31no—
186C3×C42—61no—
187C3×C42C22×D311yescharacteristic
188C3×C42C22×D311yescharacteristic
189#217—21no—
190#217—21no—
191#217—21no—
192(C2×D3)⋊C4—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3C2×Dic311yescharacteristic
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198C4×Dic3—21no—
199C4×Dic3C2×Dic311yescharacteristic
200C4×Dic3#6711yescharacteristic
201C4×Dic3#6711yescharacteristic
202#208—64no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C2×C3⋊C8—121no—
211C2×C3⋊C8—122no—
212ΓL(1,𝔽25)—64no—
213D3×C8—122no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32C2×C22⋊C411yescharacteristic
218C2×C3×D3—21no—
219C2×C3×D3—21no—
220C2×C3×D3#10412yes—
221C32×C4—21no—
222C32×C4—41no—
223C32×C4#13111yescharacteristic
224C32×C4#13111yescharacteristic
225C32×C4AGL(1,ℤ/8)11yescharacteristic
226C32×C4#13711yescharacteristic
227C3×Dic3—21no—
228C3×Dic3—21no—
229C3×Dic3—21no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232C2×M16—181no—
233C22×C8—181no—
234#126—61no—
235#125—31no—
236#124—31no—
237#123—61no—
238C22⋊Q8—31no—
239#121—31no—
240C4×Q8—31no—
241C4×D4—61no—
242C4×D4D3211yescharacteristic
243#117—61no—
244C2×C42—31no—
245C4⋊C8—31no—
246C4⋊C8—91no—
247C4⋊C8—181no—
248#97—181no—
249C4×C8—31no—
250C4×C8—91no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—31no—
254C23×C3—41no—
255C22×D3#21711yescharacteristic
256C3×Q8—61no—
257C3×Q8—61no—
258C3×D4—22no—
259C3×D4—21no—
260C3×D4—21no—
261C3×D4—21no—
262C3×D4—21no—
263C3×D4—41no—
264C3×D4—122no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—62no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—81no—
286C2×C3×C4—81no—
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4C22×Dic311yescharacteristic
291C2×C3×C4C2×#6711yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293#67—42no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3#21711yescharacteristic
297C2×Dic3#21711yescharacteristic
298C2×Dic3#21711yescharacteristic
299C4×D3—22no—
300C4×D3—21no—
301C4×D3—21no—
302C4×D3—21no—
303C4×D3—21no—
304Dic6—21no—
305Dic6—21no—
306C3×C8—62no—
307C3×C8—121no—
308C3⋊C8—22no—
309C3⋊C8—41no—
310C3⋊C8—62no—
311C3⋊C8—62no—
312C3⋊C8—122no—
313C3⋊C8—121no—
314C3⋊C8—121no—
315C3⋊C8—241no—
316C2×C32—81no—
317C2×C32#40811yescharacteristic
318C2×C32#41711yescharacteristic
319C2×C32C2×#10411yescharacteristic
320C3×D3—22no—
321C2×Q8—31no—
322C2×D4—61no—
323C2×D4D3×Dic311yescharacteristic
324C22×C4—21no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—31no—
328M16—184no—
329C2×C8—61no—
330C2×C8—61no—
331C2×C8—181no—
332C2×C8—181no—
333C2×C8—362no—
334C4⋊C4—31no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4D3×Dic311yescharacteristic
340C22⋊C4—21no—
341C22⋊C4—61no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C42—31no—
346C42—31no—
347C42—31no—
348C42—61no—
349C42C2×D3211yescharacteristic
350C22×C3—21no—
351C22×C3—32no—
352C22×C3—42no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—61no—
360C22×C3—61no—
361C22×C3—81no—
362C22×C3—81no—
363C22×C3D3×C22⋊C411yescharacteristic
364C22×C3C2×#21711yescharacteristic
365C2×D3—21no—
366C2×D3—21no—
367C2×D3#83712yes—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—61no—
378C3×C4—61no—
379C3×C4—61no—
380C3×C4—81no—
381C3×C4—121no—
382C3×C4—121no—
383C3×C4#90111yescharacteristic
384C3×C4#90711yescharacteristic
385C3×C4#91111yescharacteristic
386C3×C4#91511yescharacteristic
387C3×C4#94811yescharacteristic
388C3×C4#94811yescharacteristic
389C3×C4#94911yescharacteristic
390C3×C4#95111yescharacteristic
391Dic3—21no—
392Dic3—21no—
393Dic3—21no—
394Dic3—41no—
395Dic3—41no—
396C32#148311yescharacteristic, complemented, Sylow
397C23—21no—
398C23—31no—
399Q8—61no—
400Q8—61no—
401D4—21no—
402D4—21no—
403D4—122no—
404C2×C4—21no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—62no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4C2×D3×Dic311yescharacteristic
418C2×C4D3×#6711yescharacteristic
419C2×C4D3×#6711yescharacteristic
420C8—62no—
421C8—121no—
422C8—182no—
423C8—361no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—62no—
428C2×C3—82no—
429C2×C3—81no—
430C2×C3—81no—
431C2×C3#472711yescharacteristic
432C2×C3#477111yescharacteristic
433C2×C3D3×#10411yescharacteristic
434C2×C3#523211yescharacteristic
435C2×C3#523411yescharacteristic
436C2×C3C2×#83711yescharacteristic
437D3—22no—
438C22—32no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—61no—
443C22—61no—
444C22D3×#21711yescharacteristic
445C4—21no—
446C4—41no—
447C4—61no—
448C4—61no—
449C4—61no—
450C4—121no—
451C4—121no—
452C4#6381411yescharacteristic
453C4#6381511yescharacteristic
454C4#6392511yescharacteristic
455C4#6392911yescharacteristic
456C3—21no—
457C3#6817011yescharacteristic, complemented
458C3#7175111yescharacteristic, complemented
459C2—62no—
460C2—81no—
461C2#1059114511yescharacteristic
462C2#1059141411yescharacteristic
463C2D3×#83711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#938C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1483
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. C4×#3711C2semidirect
3. D3×C4⋊(C3⋊C8)C2semidirect
4. D4⋊(C3⋊(C3⋊C8))C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589084C2semidirect
7. #10589083C2semidirect
41. D4⋊(C3⋊C8)D3semidirect
396. C32#1483semidirect
457. C3#68170semidirect
458. C3#71751semidirect

Maximal subgroups

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

subgroupindex
C3×#55572
C4×#37112
D3×C4⋊(C3⋊C8)2
D4⋊(C3⋊(C3⋊C8))2
C3×D4⋊(C3⋊C8)2
#105890842
#105890832
#717513
#681703