Finite Group Databasebeta

← #11774617

Subgroups — #11774617

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
1C4×#3799C211yesmaximal, characteristic
2C3×#4835C211yesmaximal, characteristic, complemented
3#10590261C211yesmaximal, characteristic, complemented
4#10589349C211yesmaximal, characteristic, complemented
5C3×#4484C211yesmaximal, characteristic, complemented
6#10589083C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#70798—31nomaximal
9#68237—31nomaximal
10C2×#3799C411yescharacteristic
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×C42×D3C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63904—21no—
15C4×#626—21no—
16#63894C411yescharacteristic
17C4×#624—21no—
18Dic3×Dic6C411yescharacteristic
19#63841C411yescharacteristic
20#63836—21no—
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×#239—31no—
30C4×#235—31no—
31C3×#432—31no—
32#4925—31no—
33#4835D311yescharacteristic, complemented
34#4685—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4484—31no—
38#4484D311yescharacteristic, complemented
39#4483—31no—
40#4483—31no—
41#4483—31no—
42#4483—61no—
43#4459—31no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×Dic6C2×C411yescharacteristic
50C2×#626—21no—
51C2×#624—21no—
52C2×#624—21no—
53#3799—22no—
54#3799—22no—
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57#3752—21no—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59C2×C3⋊(C3⋊C8)—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3C2×C411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68Dic3⋊Dic3—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72Dic32—21no—
73#1488—91noSylow
74C2×#239—31no—
75C2×#235—31no—
76C3×C4×Q8—31no—
77C2×C3×C42—31no—
78Q8×Dic3—31no—
79C4×#67—61no—
80C4×#67—61no—
81#926—31no—
82#893—31no—
83#893—61no—
84#892—31no—
85#892—61no—
86C4×D12—31no—
87C4×D12—31no—
88C4×D12—31no—
89C4×D12—61no—
90C4×D12—61no—
91#872—61no—
92C42×D3—61no—
93C42×D3—61no—
94C42×D3C2×D311yescharacteristic
95C4×Dic6—31no—
96C4×Dic6C2×D311yescharacteristic
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—
121C4⋊(C3⋊D3)—21no—
122C4⋊(C3⋊D3)M1612yes—
123C4×C3⋊D3—41no—
124C4×C3⋊D3—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C2×C3×Dic3C22⋊C411yescharacteristic
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—41no—
135C3×Dic6—21no—
136C3×Dic6M1612yes—
137#626—24no—
138#624—24no—
139#624—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—31no—
148Q8⋊C8—91no—
149D4⋊C8—91no—
150D4⋊C8—91no—
151C2×C3×Q8—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C2×#67—61no—
156#239—62no—
157#239—62no—
158#235—62no—
159#235—62no—
160C2×D12—31no—
161C2×D12—31no—
162C2×D12—61no—
163C2×D12—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3—121no—
171C2×C4×D3C4×D311yescharacteristic
172C2×C4×D3D1211yescharacteristic
173C2×C4×D3#6711yescharacteristic
174C2×Dic6C4×D311yescharacteristic
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—41no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C3×C4⋊C4—31no—
181C3×C4⋊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—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—121no—
196C4⋊Dic3—31no—
197C4⋊Dic3—31no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3C4×D311yescharacteristic
201Dic3⋊C4—21no—
202Dic3⋊C4—61no—
203C4×Dic3—21no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
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—41no—
219C2×C3⋊D3—41no—
220C2×C3×D3—21no—
221C2×C3×D3—21no—
222C2×C3×D3—21no—
223C32×C4—21no—
224C32×C4C2×M1611yescharacteristic
225C32×C4C2×M1611yescharacteristic
226C32×C4#13511yescharacteristic
227C32×C4#13511yescharacteristic
228C3⋊Dic3—41no—
229C3×Dic3—21no—
230C3×Dic3—22no—
231C3×Dic3—21no—
232C3×Dic3—21no—
233C3×Dic3—41no—
234C2×#41—91no—
235C4×Q8—31no—
236C4×Q8—91no—
237C4×D4—91no—
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—
254C22×D3—61no—
255C22×D3—61no—
256C22×D3—121no—
257C22×D3(C2×D3)⋊C411yescharacteristic
258C3×Q8—32no—
259C3×Q8—61no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—31no—
264C2×C3×C4—31no—
265C2×C3×C4—31no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
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—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—121no—
285C2×Dic3(C2×D3)⋊C411yescharacteristic
286C2×Dic3(C2×D3)⋊C411yescharacteristic
287C2×Dic3(C2×D3)⋊C411yescharacteristic
288D12—32no—
289D12—32no—
290D12—62no—
291D12—64no—
292D12—61no—
293D12—61no—
294D12—121no—
295C4×D3—21no—
296C4×D3—21no—
297C4×D3—21no—
298C4×D3—21no—
299C4×D3—41no—
300C4×D3—64no—
301C4×D3—64no—
302C4×D3—122no—
303C4×D3—122no—
304C4×D3—121no—
305C4×D3—121no—
306C4×D3—121no—
307C4×D3—121no—
308C4×D3—241no—
309C4×D3—241no—
310Dic6—21no—
311Dic6ΓL(1,𝔽25)12yes—
312C3×C8—41no—
313C3×C8—41no—
314C3×C8—81no—
315C3×C8—121no—
316C3×C8—121no—
317C3⋊C8—41no—
318C3⋊C8—41no—
319C3⋊C8—121no—
320C3⋊C8—121no—
321C3⋊C8—122no—
322C2×C32#40711yescharacteristic
323C2×C32#41611yescharacteristic
324C2×C32#42111yescharacteristic
325C3⋊D3—42no—
326C3×D3—41no—
327#41—182no—
328#41—182no—
329C2×Q8—31no—
330C2×D4—91no—
331C2×D4—181no—
332C22×C4—31no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—181no—
336C22×C4—181no—
337C22×C4—181no—
338C2×C8—21no—
339C2×C8—61no—
340C2×C8—61no—
341C2×C8—181no—
342C4⋊C4—31no—
343C4⋊C4—61no—
344C4⋊C4—91no—
345C4⋊C4—181no—
346C22⋊C4—181no—
347C22⋊C4—181no—
348C22⋊C4—181no—
349C42—31no—
350C42—31no—
351C42—31no—
352C42—61no—
353C42—181no—
354C42—181no—
355C42C2×D3211yescharacteristic
356C22×C3—21no—
357C22×C3—61no—
358C22×C3—61no—
359C22×C3—61no—
360C22×C3D3×C22⋊C411yescharacteristic
361C22×C3C2×(C2×D3)⋊C411yescharacteristic
362C2×D3—21no—
363C2×D3—21no—
364C2×D3—21no—
365C2×D3—62no—
366C2×D3—62no—
367C2×D3—122no—
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—121no—
371C2×D3—121no—
372C2×D3—241no—
373C2×D3—241no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—62no—
382C3×C4—61no—
383C3×C4—61no—
384C3×C4—61no—
385C3×C4—121no—
386C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
387C3×C4D3×M1611yescharacteristic
388C3×C4D3×M1611yescharacteristic
389C3×C4D3×M1611yescharacteristic
390C3×C4#91611yescharacteristic
391C3×C4#91911yescharacteristic
392C3×C4#95011yescharacteristic
393C3×C4#95011yescharacteristic
394Dic3—21no—
395Dic3—21no—
396Dic3—22no—
397Dic3—21no—
398Dic3—41no—
399Dic3—121no—
400Dic3—121no—
401Dic3—241no—
402C32#148811yescharacteristic, complemented, Sylow
403C23—31no—
404C23—181no—
405Q8—32no—
406Q8—61no—
407D4—92no—
408D4—184no—
409D4—181no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—121no—
420C2×C4—184no—
421C2×C4—181no—
422C2×C4—362no—
423C2×C4—361no—
424C2×C4—361no—
425C2×C4C4×D3211yescharacteristic
426C2×C4D3×D1211yescharacteristic
427C2×C4D3×#6711yescharacteristic
428C8—41no—
429C8—121no—
430C8—121no—
431C8—361no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—121no—
436C2×C3#472611yescharacteristic
437C2×C3#480411yescharacteristic
438C2×C3#482111yescharacteristic
439C2×C3#500211yescharacteristic
440C2×C3#512611yescharacteristic
441C2×C3#513911yescharacteristic
442D3—41no—
443D3—122no—
444D3—122no—
445D3—242no—
446C22—61no—
447C22—61no—
448C22—61no—
449C22—182no—
450C22—361no—
451C22—361no—
452C22D3×(C2×D3)⋊C411yescharacteristic
453C4—21no—
454C4—61no—
455C4—61no—
456C4—61no—
457C4—62no—
458C4—121no—
459C4—361no—
460C4D3×ΓL(1,𝔽25)11yescharacteristic
461C4#6379111yescharacteristic
462C4#6393511yescharacteristic
463C4#6394911yescharacteristic
464C3—21no—
465C3#6823711yescharacteristic, complemented
466C3#7079811yescharacteristic, complemented
467C2—121no—
468C2—362no—
469C2#1059061011yescharacteristic
470C2#1059093611yescharacteristic
471C2#1059100511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3799C4
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. #10589349C2semidirect
5. C3×#4484C2semidirect
6. #10589083C2semidirect
7. #10589082C2semidirect
33. #4835D3semidirect
38. #4484D3semidirect
402. C32#1488semidirect
465. C3#68237semidirect
466. C3#70798semidirect

Maximal subgroups

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

subgroupindex
C4×#37992
C3×#48352
#105902612
#105893492
C3×#44842
#105890832
#105890822
#707983
#682373