Finite Group Databasebeta

← C2×#10590045 #11783143

Subgroups — C2×#10590045 #11783143

Order 1152.

718 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64286C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic
3C2×#63818C211yesmaximal, characteristic
4#10590045C214yesmaximal, direct product factor
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×C22⋊#157—21no—
7#64286—21no—
8#64286—21no—
9#64286C412yescomplemented
10#64286C2212yes—
11C2×C4⋊#157—21no—
12C2×C4×#157C412yescomplemented
13C2×C3×C4⋊Dic3—21no—
14C2×C3×#208—21no—
15C2×#3722—21no—
16C2×Dic32C412yescomplemented
17#63849—21no—
18#63849—21no—
19#63849C412yescomplemented
20#63849C2212yes—
21C2×#3712—21no—
22#63818—21no—
23#63818—21no—
24#63818C412yescomplemented
25#63818C2212yes—
26C2×#3710C412yescomplemented
27C2×D3×M16—61no—
28C2×#892—61no—
29C23×C3⋊D3D411yescharacteristic
30C22×#157—22no—
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3Q811yescharacteristic
43C2×C4×C3⋊D3Q811yescharacteristic
44C2×C4×C3⋊D3C2311yescharacteristic
45C22×C3×Dic3—22no—
46C22⋊#157—22no—
47C22⋊#157—22no—
48C4⋊#157—22no—
49C4⋊#157—22no—
50C4×#157—22no—
51C4×#157C2×C414yescomplemented
52C3×C4⋊Dic3—22no—
53C3×C4⋊Dic3—22no—
54C3×#208—22no—
55C3×#208—22no—
56C2×C3×C3⋊C8—22no—
57#3722—22no—
58#3722—22no—
59Dic32—22no—
60Dic32C2×C414yescomplemented
61#3712—22no—
62#3712—22no—
63#3710—22no—
64#3710C2×C414yescomplemented
65C2×H(3,ℤ/4)—91nomaximal, Sylow
66C22×C4×D3—61no—
67C22×C4×D3—61no—
68C2×C3×M16—61no—
69C2×C3×C4⋊C4—61no—
70C2×(C2×D3)⋊C4—62no—
71C2×C4⋊Dic3—21no—
72C2×C4×Dic3—62no—
73C2×#208—21no—
74D3×M16—62no—
75D3×M16—62no—
76D3×M16—62no—
77D3×M16—62no—
78C2×ΓL(1,𝔽25)—62no—
79C2×D3×C8—62no—
80#892—62no—
81#892—62no—
82#892—62no—
83#892—62no—
84C23×C32C22⋊C411yescharacteristic
85C22×C3⋊D3—42no—
86C22×C3⋊D3C22⋊C411yescharacteristic
87C22×C3⋊D3C22⋊C411yescharacteristic
88C22×C3⋊D3C22⋊C411yescharacteristic
89C22×C3⋊D3C4⋊C411yescharacteristic
90C22×C3⋊D3C4⋊C411yescharacteristic
91C22×C3⋊D3C2×D411yescharacteristic
92C2×#157—24no—
93C2×#157—44no—
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C4⋊C411yescharacteristic
98C2×C32×C4C4⋊C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C3⋊Dic3C4211yescharacteristic
101C2×C3⋊Dic3C4211yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C4⋊C411yescharacteristic
104C2×C3⋊Dic3C4⋊C411yescharacteristic
105C2×C3⋊Dic3C22×C411yescharacteristic
106C4×C3⋊D3C4211yescharacteristic
107C4×C3⋊D3C4211yescharacteristic
108C4×C3⋊D3C22⋊C411yescharacteristic
109C4×C3⋊D3C22⋊C411yescharacteristic
110C4×C3⋊D3C22⋊C411yescharacteristic
111C4×C3⋊D3C22⋊C411yescharacteristic
112C4×C3⋊D3C4⋊C411yescharacteristic
113C4×C3⋊D3C4⋊C411yescharacteristic
114C4×C3⋊D3C4⋊C411yescharacteristic
115C4×C3⋊D3C4⋊C411yescharacteristic
116C4×C3⋊D3C4⋊C411yescharacteristic
117C4×C3⋊D3C4⋊C411yescharacteristic
118C4×C3⋊D3C22×C411yescharacteristic
119C4×C3⋊D3C22×C411yescharacteristic
120C4×C3⋊D3C2×D411yescharacteristic
121C4×C3⋊D3C2×Q811yescharacteristic
122C2×C3×Dic3—24no—
123C2×C3×Dic3—44no—
124C3×C3⋊C8—24no—
125C22×M16—91no—
126C2×#117—91no—
127C2×#117—91no—
128H(3,ℤ/4)—94no—
129C23×D3—61no—
130C23×D3—61no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—62no—
134C22×Dic3—22no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—61no—
139C2×C4×D3—61no—
140C2×C4×D3—61no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—61no—
161C3×M16—62no—
162C3×M16—62no—
163C2×C3×C8—62no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—62no—
166(C2×D3)⋊C4—64no—
167(C2×D3)⋊C4—64no—
168C4⋊Dic3—22no—
169C4⋊Dic3—22no—
170C4×Dic3—64no—
171C4×Dic3—64no—
172#208—22no—
173#208—22no—
174C2×C3⋊C8—22no—
175ΓL(1,𝔽25)—64no—
176ΓL(1,𝔽25)—64no—
177D3×C8—64no—
178D3×C8—64no—
179C22×C32—22no—
180C22×C32#9511yescharacteristic
181C22×C32#9511yescharacteristic
182C22×C32C2×C22⋊C411yescharacteristic
183C2×C3⋊D3—22no—
184C2×C3⋊D3—22no—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3#9511yescharacteristic
190C2×C3⋊D3#9511yescharacteristic
191C2×C3⋊D3C2×C22⋊C411yescharacteristic
192C2×C3⋊D3C2×C4⋊C411yescharacteristic
193#157—44no—
194C32×C4#9511yescharacteristic
195C32×C4#9511yescharacteristic
196C32×C4C2×C22⋊C411yescharacteristic
197C32×C4C2×C4⋊C411yescharacteristic
198C3⋊Dic3#9511yescharacteristic
199C3⋊Dic3#9511yescharacteristic
200C3⋊Dic3C2×C4211yescharacteristic
201C3⋊Dic3C2×C4⋊C411yescharacteristic
202C3×Dic3—44no—
203C23×C4—91no—
204C2×M16—61no—
205C2×M16—92no—
206C2×M16—92no—
207C2×M16—181no—
208C2×M16—181no—
209C2×M16—181no—
210C22×C8—92no—
211#117—92no—
212#117—92no—
213#117—92no—
214#117—92no—
215#117—181no—
216#117—181no—
217#117—181no—
218#117—181no—
219C2×C4⋊C4—61no—
220C2×C4⋊C4—181no—
221C2×C22⋊C4—181no—
222C2×C22⋊C4—181no—
223C2×C42—92no—
224C2×C42—92no—
225C23×C3—21no—
226C23×C3—21no—
227C22×D3—61no—
228C22×D3—61no—
229C22×D3—61no—
230C22×D3—61no—
231C22×D3—61no—
232C22×D3—61no—
233C22×D3—61no—
234C22×D3—61no—
235C22×D3—61no—
236C22×D3—61no—
237C22×D3—61no—
238C22×D3—61no—
239C22×D3—124no—
240C22×D3—122no—
241C22×D3—122no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—64no—
255C2×C3×C4—124no—
256C2×Dic3—24no—
257C2×Dic3—44no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C4×D3—61no—
271C4×D3—61no—
272C4×D3—61no—
273C4×D3—61no—
274C4×D3—61no—
275C4×D3—61no—
276C4×D3—61no—
277C4×D3—61no—
278C4×D3—61no—
279C4×D3—61no—
280C4×D3—61no—
281C4×D3—61no—
282C4×D3—61no—
283C4×D3—61no—
284C4×D3—61no—
285C4×D3—61no—
286C4×D3—61no—
287C4×D3—61no—
288C4×D3—61no—
289C4×D3—61no—
290C4×D3—61no—
291C4×D3—61no—
292C4×D3—61no—
293C4×D3—61no—
294C4×D3—61no—
295C4×D3—61no—
296C4×D3—61no—
297C4×D3—61no—
298C4×D3—61no—
299C4×D3—61no—
300C4×D3—61no—
301C4×D3—61no—
302C3×C8—64no—
303C3⋊C8—24no—
304C2×C32—21no—
305C2×C32—21no—
306C2×C32H(3,ℤ/4)12yescomplemented
307C2×C32C2×#9511yescharacteristic
308C3⋊D3—21no—
309C3⋊D3—21no—
310C3⋊D3—21no—
311C3⋊D3—21no—
312C24—91no—
313C22×C4—62no—
314C22×C4—91no—
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—91no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—91no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—91no—
327C22×C4—182no—
328C22×C4GO+(4,𝔽2)11yescharacteristic
329M16—62no—
330M16—62no—
331M16—182no—
332M16—182no—
333C2×C8—62no—
334C2×C8—94no—
335C2×C8—182no—
336C4⋊C4—62no—
337C4⋊C4—62no—
338C4⋊C4—182no—
339C4⋊C4—182no—
340C22⋊C4—182no—
341C22⋊C4—182no—
342C22⋊C4—182no—
343C22⋊C4—182no—
344C42—94no—
345C42—94no—
346C42—182no—
347C42—182no—
348C22×C3—22no—
349C22×C3—22no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—42no—
357C2×D3—61no—
358C2×D3—61no—
359C2×D3—61no—
360C2×D3—61no—
361C2×D3—61no—
362C2×D3—61no—
363C2×D3—61no—
364C2×D3—61no—
365C2×D3—64no—
366C2×D3—122no—
367C2×D3—122no—
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—122no—
371C2×D3—122no—
372C2×D3—122no—
373C2×D3—121no—
374C2×D3—121no—
375C2×D3—121no—
376C2×D3—121no—
377C2×D3—122no—
378C2×D3—122no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—124no—
388Dic3—44no—
389Dic3—61no—
390Dic3—61no—
391Dic3—61no—
392Dic3—61no—
393Dic3—61no—
394Dic3—61no—
395Dic3—61no—
396Dic3—61no—
397C32C2×H(3,ℤ/4)11yescharacteristic, complemented, Sylow
398C23—91no—
399C23—91no—
400C23—91no—
401C23—91no—
402C23—91no—
403C23—91no—
404C23—362no—
405C23D32⋊C411yescharacteristic
406C2×C4—64no—
407C2×C4—91no—
408C2×C4—91no—
409C2×C4—91no—
410C2×C4—91no—
411C2×C4—91no—
412C2×C4—91no—
413C2×C4—91no—
414C2×C4—91no—
415C2×C4—91no—
416C2×C4—91no—
417C2×C4—91no—
418C2×C4—91no—
419C2×C4—91no—
420C2×C4—91no—
421C2×C4—91no—
422C2×C4—91no—
423C2×C4—91no—
424C2×C4—91no—
425C2×C4—91no—
426C2×C4—91no—
427C2×C4—91no—
428C2×C4—91no—
429C2×C4—124no—
430C2×C4—184no—
431C2×C4—364no—
432C2×C4D32⋊C411yescharacteristic
433C2×C4D32⋊C411yescharacteristic
434C2×C4D32⋊C411yescharacteristic
435C2×C4#377311yescharacteristic
436C2×C4#377311yescharacteristic
437C2×C4C2×GO+(4,𝔽2)11yescharacteristic
438C8—64no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—22no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—41no—
447C2×C3—41no—
448D3—62no—
449D3—62no—
450D3—121no—
451D3—121no—
452D3—121no—
453D3—121no—
454D3—121no—
455D3—121no—
456C22—22no—
457C22—91no—
458C22—91no—
459C22—91no—
460C22—91no—
461C22—182no—
462C22—182no—
463C22—361no—
464C22—361no—
465C22—361no—
466C22—361no—
467C22#6373711yescharacteristic
468C22#6373711yescharacteristic
469C22C2×D32⋊C411yescharacteristic
470C4—91no—
471C4—91no—
472C4—91no—
473C4—91no—
474C4—124no—
475C4—364no—
476C4#6373711yescharacteristic
477C4#6373711yescharacteristic
478C4C2×D32⋊C411yescharacteristic
479C4C2×#377311yescharacteristic
480C3—21no—
481C3—21no—
482C2—21no—
483C2—21no—
484C2—181no—
485C2—181no—
486C2—181no—
487C2—181no—
488C2#1059004512yesdirect product factor
489C2C2×#6373711yescharacteristic
subgroupG/H
centerC22#63737
commutatorC3⋊Dic3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×H(3,ℤ/4)
LCSG ▷ C3⋊Dic3 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590045C2direct (N × H)
9. #64286C4semidirect
12. C2×C4×#157C4semidirect
16. C2×Dic32C4semidirect
19. #63849C4semidirect
24. #63818C4semidirect
26. C2×#3710C4semidirect
51. C4×#157C2×C4semidirect
60. Dic32C2×C4semidirect
64. #3710C2×C4semidirect
306. C2×C32H(3,ℤ/4)semidirect
397. C32C2×H(3,ℤ/4)semidirect
488. C2#10590045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642862
C2×#638492
C2×#638182
#105900452
C2×H(3,ℤ/4)9