Finite Group Databasebeta

← #11774619

Subgroups — #11774619

Order 1152.

527 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3795C211yesmaximal, characteristic
2C3×#4835C211yesmaximal, characteristic, complemented
3#10590261C211yesmaximal, characteristic, complemented
4#10589350C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#70798—31nomaximal
9#68173—31nomaximal
10C2×#3795C411yescharacteristic
11C4×#634C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×C42×D3C2211yescharacteristic
14C4×#625—21no—
15Dic3×D12C411yescharacteristic
16#63879—21no—
17#63877—21no—
18C4×D3×Dic3—21no—
19#63844C411yescharacteristic
20#63841C411yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×(C2×D3)⋊C8—21no—
24C3×#815—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C4×#237—31no—
30C4×#235—31no—
31C3×#432—31no—
32#4925—31no—
33#4835D311yescharacteristic, complemented
34#4685—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4484—31no—
38#4484—31no—
39#4484—31no—
40#4484—61no—
41#4483—31no—
42#4483D311yescharacteristic, complemented
43#4456—31no—
44C2×#634C2×C411yescharacteristic
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3C2×C411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×#625—21no—
51C2×D3×Dic3—21no—
52C2×D3×Dic3—21no—
53#3795—22no—
54#3795—22no—
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58#3750—21no—
59C4×C3⋊Dic3—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×C4×Dic3C2×C411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72Dic32—21no—
73#1488—91noSylow
74C2×#237—31no—
75C2×#235—31no—
76C3×C4×D4—31no—
77C2×C3×C42—31no—
78D4×Dic3—31no—
79C4×#67—61no—
80C4×#67—61no—
81C4×#67—61no—
82#926—31no—
83C2×C4×Dic3—61no—
84#892—31no—
85#887—31no—
86#67⋊C4—61no—
87#877—61no—
88C4×D12—31no—
89C4×D12C2×D311yescharacteristic
90#872—61no—
91C42×D3—61no—
92C42×D3C2×D311yescharacteristic
93C4×Dic6—31no—
94C4×Dic6—31no—
95C4×Dic6—31no—
96C4×Dic6—61no—
97C3×C4⋊C8—21no—
98C3×C4⋊C8—31no—
99C3×C4⋊C8C2×D311yescharacteristic
100C3×C4⋊C8C2×D311yescharacteristic
101C3×C22⋊C8—61no—
102C3×#97—61no—
103C3×C4×C8—31no—
104#830—61no—
105(C2×D3)⋊C8—21no—
106(C2×D3)⋊C8—61no—
107#815—21no—
108Dic3⋊C8—61no—
109C4⋊(C3⋊C8)—61no—
110C4⋊(C3⋊C8)C2×D311yescharacteristic
111C4×C3⋊C8—31no—
112C4×C3⋊C8—31no—
113C4×C3⋊C8—61no—
114C4×C3⋊C8C2×D311yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3C22⋊C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122#634—21no—
123#634M1612yes—
124C2×C3×Dic3—21no—
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C3×D12—21no—
129C3×D12M1612yes—
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136C3×C4×D3—41no—
137#625—24no—
138D3×Dic3—24no—
139D3×Dic3—42no—
140C32×C8—41no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144C4×#41—91no—
145#432—31no—
146#431—91no—
147Q8⋊C8—91no—
148Q8⋊C8—91no—
149D4⋊C8—31no—
150D4⋊C8—91no—
151C2×C3×D4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C2×#67—61no—
157C2×#67—61no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160#237—62no—
161#237—62no—
162#235—62no—
163#235—62no—
164C2×D12C4×D311yescharacteristic
165C2×C4×D3—21no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3C4×D311yescharacteristic
169C2×C4×D3D1211yescharacteristic
170C2×C4×D3#6711yescharacteristic
171C2×Dic6—31no—
172C2×Dic6—31no—
173C2×Dic6—61no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—41no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179C3×C4⋊C4—31no—
180C3×C22⋊C4—61no—
181C3×C42—21no—
182C3×C42—31no—
183C3×C42—31no—
184C3×C42—31no—
185C3×C42C22×D311yescharacteristic
186C3×C42C22×D311yescharacteristic
187#217—61no—
188#217—61no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192C4⋊Dic3—31no—
193C4⋊Dic3—31no—
194C4⋊Dic3—61no—
195C4⋊Dic3C4×D311yescharacteristic
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—121no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—121no—
208C4×Dic3C4×D311yescharacteristic
209C4×Dic3D1211yescharacteristic
210C4×Dic3#6711yescharacteristic
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—121no—
216C22×C32C2×C22⋊C411yescharacteristic
217C2×C3×D3—22no—
218C2×C3×D3—21no—
219C2×C3×D3—21no—
220C2×C3×D3—21no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C32×C4—21no—
224C32×C4C2×M1611yescharacteristic
225C32×C4C2×M1611yescharacteristic
226C32×C4#13511yescharacteristic
227C32×C4#13511yescharacteristic
228C3⋊Dic3—22no—
229C3⋊Dic3—41no—
230C3×Dic3—21no—
231C3×Dic3—21no—
232C3×Dic3—21no—
233C3×Dic3—41no—
234C2×#41—91no—
235C4×Q8—91no—
236C4×Q8—91no—
237C4×D4—31no—
238C4×D4—91no—
239C4×D4—181no—
240C4×D4—181no—
241#117—91no—
242#117—181no—
243C2×C42—31no—
244C2×C42—181no—
245C4⋊C8—31no—
246C4⋊C8—181no—
247C4⋊C8D3211yescharacteristic
248C22⋊C8—61no—
249C22⋊C8—181no—
250#97—61no—
251C4×C8—31no—
252C4×C8—91no—
253C23×C3—31no—
254C23×C3—61no—
255C22×D3—21no—
256C22×D3(C2×D3)⋊C411yescharacteristic
257C3×D4—32no—
258C3×D4—61no—
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—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4C2×C4×D311yescharacteristic
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4C2×D1211yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279#67—64no—
280#67—64no—
281C2×Dic3—21no—
282C2×Dic3—64no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289C2×Dic3—122no—
290C2×Dic3(C2×D3)⋊C411yescharacteristic
291C2×Dic3(C2×D3)⋊C411yescharacteristic
292C2×Dic3(C2×D3)⋊C411yescharacteristic
293D12—21no—
294D12ΓL(1,𝔽25)12yes—
295C4×D3—21no—
296C4×D3—21no—
297C4×D3—21no—
298C4×D3—21no—
299C4×D3—41no—
300C4×D3—41no—
301C4×D3—41no—
302C4×D3—64no—
303C4×D3—122no—
304Dic6—32no—
305Dic6—32no—
306Dic6—62no—
307Dic6—61no—
308Dic6—61no—
309Dic6—121no—
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—122no—
320C2×C32#40711yescharacteristic
321C2×C32#41611yescharacteristic
322C2×C32#42111yescharacteristic
323C3×D3—41no—
324C3×D3—42no—
325#41—182no—
326#41—182no—
327C2×Q8—91no—
328C2×D4—31no—
329C2×D4—181no—
330C22×C4—31no—
331C22×C4—31no—
332C22×C4—31no—
333C22×C4—61no—
334C22×C4—181no—
335C22×C4—181no—
336C2×C8—21no—
337C2×C8—61no—
338C2×C8—61no—
339C2×C8—181no—
340C4⋊C4—31no—
341C4⋊C4—91no—
342C4⋊C4—181no—
343C4⋊C4—181no—
344C22⋊C4—61no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C42—31no—
348C42—31no—
349C42—31no—
350C42—181no—
351C42—181no—
352C42—181no—
353C42C2×D3211yescharacteristic
354C22×C3—21no—
355C22×C3—62no—
356C22×C3—61no—
357C22×C3—61no—
358C22×C3—61no—
359C22×C3—121no—
360C22×C3—121no—
361C22×C3D3×C22⋊C411yescharacteristic
362C22×C3C2×(C2×D3)⋊C411yescharacteristic
363C2×D3—21no—
364C2×D3—21no—
365C2×D3—22no—
366C2×D3—21no—
367C2×D3—41no—
368C2×D3—41no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—41no—
376C3×C4—61no—
377C3×C4—61no—
378C3×C4—61no—
379C3×C4—121no—
380C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
381C3×C4D3×M1611yescharacteristic
382C3×C4D3×M1611yescharacteristic
383C3×C4D3×M1611yescharacteristic
384C3×C4#91211yescharacteristic
385C3×C4#91611yescharacteristic
386C3×C4#95011yescharacteristic
387C3×C4#95011yescharacteristic
388Dic3—21no—
389Dic3—21no—
390Dic3—21no—
391Dic3—41no—
392Dic3—62no—
393Dic3—62no—
394Dic3—122no—
395Dic3—121no—
396Dic3—121no—
397Dic3—241no—
398C32#148811yescharacteristic, complemented, Sylow
399C23—31no—
400C23—61no—
401Q8—92no—
402Q8—181no—
403D4—32no—
404D4—61no—
405D4—184no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—184no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4—362no—
421C2×C4C4×D3211yescharacteristic
422C2×C4D3×D1211yescharacteristic
423C2×C4D3×#6711yescharacteristic
424C8—41no—
425C8—121no—
426C8—121no—
427C8—361no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—121no—
432C2×C3—122no—
433C2×C3#472611yescharacteristic
434C2×C3#477211yescharacteristic
435C2×C3#482111yescharacteristic
436C2×C3#500211yescharacteristic
437C2×C3#512611yescharacteristic
438C2×C3#513911yescharacteristic
439D3—42no—
440D3—41no—
441C22—61no—
442C22—61no—
443C22—61no—
444C22—62no—
445C22—121no—
446C22—121no—
447C22D3×(C2×D3)⋊C411yescharacteristic
448C4—21no—
449C4—61no—
450C4—61no—
451C4—61no—
452C4—121no—
453C4—182no—
454C4—361no—
455C4D3×ΓL(1,𝔽25)11yescharacteristic
456C4#6379111yescharacteristic
457C4#6393311yescharacteristic
458C4#6394711yescharacteristic
459C3—21no—
460C3#6817311yescharacteristic, complemented
461C3#7079811yescharacteristic, complemented
462C2—121no—
463C2—122no—
464C2#1059060811yescharacteristic
465C2#1059093611yescharacteristic
466C2#1059100511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3795C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4835C2semidirect
3. #10590261C2semidirect
4. #10589350C2semidirect
5. C3×#4483C2semidirect
6. #10589085C2semidirect
7. #10589080C2semidirect
33. #4835D3semidirect
42. #4483D3semidirect
398. C32#1488semidirect
460. C3#68173semidirect
461. C3#70798semidirect

Maximal subgroups

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

subgroupindex
C4×#37952
C3×#48352
#105902612
#105893502
C3×#44832
#105890852
#105890802
#707983
#681733