Finite Group Databasebeta

← C2×#10590694 #11858287

Subgroups — C2×#10590694 #11858287

Order 1152.

1093 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2C2×#63855C211yesmaximal, characteristic
3C22×#3711C211yesmaximal, characteristic
4C2×#63641C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C2×#63572C211yesmaximal, characteristic, complemented
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590694C218yesmaximal, direct product factor
9C2×#5102—31nomaximal
10C2×#4839—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×D3×C8—24no—
19C2×C3×D3×C8C2214yes—
20C2×Dic3⋊Dic3C411yescharacteristic
21C2×Dic3⋊Dic3C411yescharacteristic
22C2×(C2×D3)⋊Dic3C411yescharacteristic
23C2×(C2×D3)⋊Dic3C411yescharacteristic
24#63855C414yes—
25#63855C2214yes—
26C2×#3711—24no—
27C2×#3711C2214yes—
28#63641C2214yescomplemented
29C3×Dic3⋊C8C2214yescomplemented
30#63572C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32C23×C3×C8—31no—
33C2×#926—31no—
34C22×#208—31no—
35C22×ΓL(1,𝔽25)—31no—
36C22×D3×C8D311yescharacteristic
37C2×#872—31no—
38C2×C3×C4⋊C8—31no—
39#5102—38no—
40C2×Dic3⋊C8—31no—
41C2×Dic3⋊C8—31no—
42C2×Dic3⋊C8—31no—
43C2×Dic3⋊C8—31no—
44C2×Dic3⋊C8—31no—
45C2×Dic3⋊C8—61no—
46C2×Dic3⋊C8D311yescharacteristic, complemented
47C2×C4⋊(C3⋊C8)—31no—
48#4839—38no—
49C23×C3×D3C2×C411yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2×C411yescharacteristic
52C22×C3⋊Dic3C2×C411yescharacteristic
53C22×C3×Dic3C2×C411yescharacteristic
54C22×C3×Dic3C2×C411yescharacteristic
55C22×C3×Dic3C2×C411yescharacteristic
56C2×C3×C4×D3C2×C412yes—
57C2×C3×C4×D3D414yes—
58C2×C3×C4×D3Q814yes—
59C2×C3×C4×D3C2312yes—
60C2×C32×C8—22no—
61C2×C32×C8C2312yes—
62C4×C3⋊Dic3C2×C412yes—
63C4×C3⋊Dic3C2312yes—
64C2×C3⋊(C3⋊C8)—22no—
65C2×C3⋊(C3⋊C8)C2312yes—
66C3×C4×Dic3C2×C412yes—
67C3×C4×Dic3C2312yes—
68C2×C3×C3⋊C8—22no—
69C2×C3×C3⋊C8—22no—
70C2×C3×C3⋊C8C2312yes—
71C2×C3×C3⋊C8C2312yes—
72C3×D3×C8—28no—
73Dic3⋊Dic3C2×C414yes—
74Dic3⋊Dic3C2×C414yes—
75(C2×D3)⋊Dic3C2×C414yes—
76(C2×D3)⋊Dic3C2×C414yes—
77#3711—28no—
78C2×#424—91noSylow
79C23×C3×C4—31no—
80C22×C4×D3C2×D311yescharacteristic
81C22×C3×C8—21no—
82C22×C3×C8—31no—
83C22×C3×C8—31no—
84C22×C3×C8—34no—
85C22×C3×C8—64no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C2×C3×C42—31no—
89C2×#217—31no—
90C2×#217—31no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—31no—
93#926—34no—
94#926—34no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—61no—
102C2×C4×Dic3C2×D311yescharacteristic
103C2×#208—34no—
104C2×#208—64no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110C2×ΓL(1,𝔽25)—34no—
111C2×ΓL(1,𝔽25)—64no—
112C2×D3×C8—24no—
113C2×D3×C8C2×D314yes—
114#872—34no—
115#872—34no—
116C3×C4⋊C8—34no—
117Dic3⋊C8—34no—
118Dic3⋊C8—34no—
119Dic3⋊C8—34no—
120Dic3⋊C8—34no—
121Dic3⋊C8—34no—
122Dic3⋊C8—64no—
123Dic3⋊C8C2×D314yescomplemented
124C4⋊(C3⋊C8)—34no—
125C23×C32C22×C411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3C4⋊C414yes—
129C22×C3×D3C22×C412yes—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D412yes—
132C2×C32×C4C2×Q812yes—
133C2×C32×C4C2411yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3C22×C412yes—
137C2×C3⋊Dic3C22×C412yes—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3C4⋊C414yes—
141C2×C3×Dic3C22×C412yes—
142C2×C3×Dic3C22×C412yes—
143C2×C3×Dic3C22×C412yes—
144C3×C4×D3C4⋊C418yes—
145C3×C4×D3C2×D414yes—
146C3×C4×D3C2×Q814yes—
147C32×C8—22no—
148C3⋊(C3⋊C8)—22no—
149C3×C3⋊C8—22no—
150C3×C3⋊C8—22no—
151C22×M16—91no—
152C23×C8—31no—
153C2×#117—91no—
154#424—98no—
155C2×C4⋊C8—31no—
156C2×C4⋊C8—91no—
157C2×C4⋊C8—91no—
158C2×C4⋊C8—91no—
159C24×C3—31no—
160C23×D3C4×D311yescharacteristic
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—32no—
164C22×C3×C4—34no—
165C22×C3×C4—34no—
166C22×C3×C4—32no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3C4×D311yescharacteristic
178C22×Dic3C4×D311yescharacteristic
179C22×Dic3C4×D311yescharacteristic
180C2×C4×D3Dic614yes—
181C2×C4×D3C4×D312yes—
182C2×C4×D3#6714yes—
183C2×C4×D3C22×D312yes—
184C2×C3×C8—22no—
185C2×C3×C8—22no—
186C2×C3×C8—22no—
187C2×C3×C8—32no—
188C2×C3×C8—32no—
189C2×C3×C8—42no—
190C2×C3×C8—68no—
191C2×C3×C8—62no—
192C2×C3×C8—62no—
193C2×C3×C8C22×D312yes—
194C2×C3×C8C22×D312yes—
195C3×C42—32no—
196C3×C42—32no—
197#217—34no—
198#217—34no—
199(C2×D3)⋊C4—34no—
200(C2×D3)⋊C4—34no—
201C4⋊Dic3—34no—
202C4⋊Dic3—34no—
203Dic3⋊C4—34no—
204Dic3⋊C4—34no—
205C4×Dic3—32no—
206C4×Dic3—32no—
207C4×Dic3—32no—
208C4×Dic3—32no—
209C4×Dic3—62no—
210C4×Dic3—62no—
211C4×Dic3C4×D312yes—
212C4×Dic3C22×D312yes—
213#208—68no—
214C2×C3⋊C8—22no—
215C2×C3⋊C8—22no—
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—122no—
222C2×C3⋊C8C22×D312yes—
223C2×C3⋊C8C22×D312yes—
224ΓL(1,𝔽25)—68no—
225D3×C8—28no—
226C22×C32C2×C4⋊C412yes—
227C22×C32#13112yes—
228C22×C32#13112yes—
229C22×C32C23×C411yescharacteristic
230C2×C3×D3—22no—
231C2×C3×D3—22no—
232C2×C3×D3—28no—
233C2×C3×D3C2×C4⋊C414yes—
234C32×C4C2×C4⋊C412yes—
235C32×C4C22×D411yescharacteristic
236C32×C4C22×Q811yescharacteristic
237C3⋊Dic3—22no—
238C3⋊Dic3—22no—
239C3×Dic3—22no—
240C3×Dic3—22no—
241C3×Dic3C2×C4⋊C414yes—
242C23×C4—31no—
243C2×M16—94no—
244C2×M16—184no—
245C22×C8—31no—
246C22×C8—31no—
247C22×C8—34no—
248C22×C8—64no—
249C22×C8—91no—
250C22×C8D3211yescharacteristic
251#117—94no—
252#117—94no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4—91no—
255C2×C22⋊C4—91no—
256C2×C22⋊C4—91no—
257C2×C42—31no—
258C2×C42—91no—
259C4⋊C8—34no—
260C4⋊C8—94no—
261C4⋊C8—94no—
262C4⋊C8—94no—
263C23×C3—21no—
264C23×C3—34no—
265C23×C3—32no—
266C23×C3—62no—
267C23×C3—62no—
268C23×C3C2×C4×D311yescharacteristic
269C23×C3C2×C4×D311yescharacteristic
270C22×D3—22no—
271C22×D3—22no—
272C22×D3Dic3⋊C414yes—
273C22×D3C2×C4×D312yes—
274C2×C3×C4—21no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—22no—
278C2×C3×C4—34no—
279C2×C3×C4—32no—
280C2×C3×C4—38no—
281C2×C3×C4—34no—
282C2×C3×C4—34no—
283C2×C3×C4—32no—
284C2×C3×C4—32no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4C2×Dic612yes—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4D3×D412yes—
291C2×C3×C4D3×Q812yes—
292C2×C3×C4C2×#6712yes—
293C2×C3×C4C23×D311yescharacteristic
294C2×C3×C4C23×D311yescharacteristic
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—32no—
298C2×Dic3—32no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—64no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—122no—
309C2×Dic3Dic3⋊C414yes—
310C2×Dic3C2×C4×D312yes—
311C2×Dic3C2×C4×D312yes—
312C2×Dic3C2×C4×D312yes—
313C4×D3Dic3⋊C418yes—
314C4×D3C2×Dic614yes—
315C4×D3C2×#6714yes—
316C3×C8—22no—
317C3×C8—22no—
318C3×C8—42no—
319C3×C8—62no—
320C3×C8—62no—
321C3⋊C8—22no—
322C3⋊C8—22no—
323C3⋊C8—62no—
324C3⋊C8—62no—
325C3⋊C8—122no—
326C2×C32#42414yescomplemented
327C2×C32C22×C4⋊C411yescharacteristic
328C2×C32C2×#13111yescharacteristic
329C2×C32C2×#13111yescharacteristic
330C3×D3—24no—
331C24—31no—
332C22×C4—31no—
333C22×C4—32no—
334C22×C4—34no—
335C22×C4—32no—
336C22×C4—34no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4C2×D3211yescharacteristic
342M16—188no—
343C2×C8—22no—
344C2×C8—32no—
345C2×C8—32no—
346C2×C8—68no—
347C2×C8—62no—
348C2×C8—62no—
349C2×C8—92no—
350C2×C8—182no—
351C2×C8C2×D3212yes—
352C4⋊C4—94no—
353C4⋊C4—94no—
354C22⋊C4—94no—
355C22⋊C4—94no—
356C42—32no—
357C42—32no—
358C42—92no—
359C42—92no—
360C22×C3—21no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—34no—
365C22×C3—62no—
366C22×C3—62no—
367C22×C3—68no—
368C22×C3D3×C4⋊C412yes—
369C22×C3#90112yes—
370C22×C3#90112yes—
371C22×C3#90112yes—
372C22×C3#90712yes—
373C22×C3C2×Dic3⋊C412yes—
374C22×C3C22×C4×D311yescharacteristic
375C22×C3C22×C4×D311yescharacteristic
376C2×D3—22no—
377C2×D3—22no—
378C2×D3—28no—
379C2×D3C2×Dic3⋊C414yes—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—22no—
383C3×C4—34no—
384C3×C4—62no—
385C3×C4—62no—
386C3×C4D3×C4⋊C412yes—
387C3×C4C2×Dic3⋊C412yes—
388C3×C4C22×Dic611yescharacteristic
389C3×C4C2×D3×D411yescharacteristic
390C3×C4C2×D3×Q811yescharacteristic
391C3×C4C22×#6711yescharacteristic
392Dic3—22no—
393Dic3—22no—
394Dic3—64no—
395Dic3—62no—
396Dic3—62no—
397Dic3—62no—
398Dic3—62no—
399Dic3—122no—
400Dic3C2×Dic3⋊C414yes—
401C32C2×#42411yescharacteristic, complemented, Sylow
402C23—32no—
403C23—34no—
404C23—62no—
405C23—62no—
406C23C4×D3211yescharacteristic
407C2×C4—32no—
408C2×C4—34no—
409C2×C4—34no—
410C2×C4—34no—
411C2×C4—38no—
412C2×C4—32no—
413C2×C4—32no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—92no—
417C2×C4—92no—
418C2×C4—182no—
419C2×C4—182no—
420C2×C4D3×Dic612yes—
421C2×C4C4×D3211yescharacteristic
422C2×C4D3×#6712yes—
423C2×C4C22×D3211yescharacteristic
424C8—22no—
425C8—62no—
426C8—62no—
427C8—182no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—24no—
432C2×C3—64no—
433C2×C3#483914yescomplemented
434C2×C3#510214yescomplemented
435C2×C3C2×D3×C4⋊C411yescharacteristic
436C2×C3C2×#90111yescharacteristic
437C2×C3C2×#90111yescharacteristic
438C2×C3C2×#90111yescharacteristic
439C2×C3C2×#90711yescharacteristic
440C2×C3C22×Dic3⋊C411yescharacteristic
441D3—24no—
442C22—34no—
443C22—62no—
444C22—62no—
445C22—68no—
446C22#6380312yes—
447C22#6380412yes—
448C22D3×Dic3⋊C412yes—
449C22C2×C4×D3211yescharacteristic
450C4—34no—
451C4—62no—
452C4—62no—
453C4—182no—
454C4—182no—
455C4D3×Dic3⋊C412yes—
456C4C2×D3×Dic611yescharacteristic
457C4C2×D3×#6711yescharacteristic
458C3—21no—
459C3C2×#483911yescharacteristic, complemented
460C3C2×#510211yescharacteristic, complemented
461C2—64no—
462C2#1059069414yesdirect product factor
463C2C2×#6380311yescharacteristic
464C2C2×#6380411yescharacteristic
465C2C2×D3×Dic3⋊C411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#424
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×#63641C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. C2×#63572C2semidirect
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590694C2direct (N × H)
28. #63641C22semidirect
29. C3×Dic3⋊C8C22semidirect
30. #63572C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
46. C2×Dic3⋊C8D3semidirect
123. Dic3⋊C8C2×D3semidirect
326. C2×C32#424semidirect
401. C32C2×#424semidirect
433. C2×C3#4839semidirect
434. C2×C3#5102semidirect
459. C3C2×#4839semidirect
460. C3C2×#5102semidirect
462. C2#10590694direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×#638552
C22×#37112
C2×#636412
C2×C3×Dic3⋊C82
C2×#635722
C2×Dic3⋊(C3⋊C8)2
#105906942
C2×#51023
C2×#48393