Finite Group Databasebeta

← C2×#10589180 #11796349

Subgroups — C2×#10589180 #11796349

Order 1152.

673 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#936C211yesmaximal, characteristic
2C2×#63661C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4#10589180C214yesmaximal, direct product factor
5C2×#4541—31nomaximal
6C2×#4473—31nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×C3×Dic6C411yescharacteristic, complemented
9C2×#3757—21no—
10C2×C3×#217—21no—
11C2×C3×#217—21no—
12C2×C3×#217—21no—
13C3×#936—21no—
14C3×#936—21no—
15C3×#936C412yescomplemented
16C3×#936C2212yes—
17C2×C3×C4×Dic3C411yescharacteristic, complemented
18#63661—21no—
19#63661C2212yes—
20C3×#834—21no—
21C3×#834C2212yes—
22C2×C3×#124—31no—
23C2×#936D311yescharacteristic
24C2×C3×#99—31no—
25C2×#834—31no—
26C2×#834—31no—
27C2×#834—61no—
28C2×#834D311yescharacteristic
29#4541—34no—
30#4473—34no—
31C24×C32D411yescharacteristic
32C24×C32D411yescharacteristic
33C2×C32×D4—41no—
34C2×C32×D4—41no—
35C2×C32×D4C2×C411yescharacteristic
36C2×C32×D4D411yescharacteristic
37C2×C32×D4D411yescharacteristic
38C2×C32×D4C2311yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C3⋊Dic3—41no—
41C22×C3×Dic3—21no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3—41no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6—41no—
46C2×C3×Dic6—41no—
47C2×C3×Dic6C2×C412yescomplemented
48#3757—22no—
49#3757—41no—
50C3×#217—22no—
51C3×#217—22no—
52C3×#217—22no—
53C3×#217—22no—
54C3×#217—22no—
55C3×#217—41no—
56C3×C4×Dic3—21no—
57C3×C4×Dic3C2×C412yescomplemented
58C2×#354—91noSylow
59C22×C3×Q8—31no—
60C22×C3×D4—21no—
61C22×C3×D4C2×D311yescharacteristic
62C22×C3×D4C2×D311yescharacteristic
63C22×Dic6Dic311yescharacteristic, complemented
64C3×#124—32no—
65C3×#124—32no—
66C3×#124—61no—
67C3×#124—61no—
68C2×C3×C22⋊C4—61no—
69C2×C3×C22⋊C4—61no—
70C2×C3×C22⋊C4—61no—
71C2×C3×C42—31no—
72C2×#217—21no—
73C2×#217—21no—
74C2×#217—21no—
75C2×#217—62no—
76C2×#217—61no—
77C2×#217—61no—
78#936—21no—
79#936—21no—
80#936Dic312yescomplemented
81#936C2×D312yes—
82C2×C4×Dic3Dic311yescharacteristic, complemented
83C3×#99—32no—
84C3×#99—61no—
85#834—21no—
86#834—32no—
87#834—32no—
88#834—62no—
89#834—62no—
90#834—61no—
91#834—61no—
92#834C2×D312yes—
93C23×C32—21no—
94C23×C32—21no—
95C23×C32—21no—
96C23×C32—21no—
97C23×C32—42no—
98C23×C32—42no—
99C23×C32C22⋊C411yescharacteristic
100C23×C32C22⋊C411yescharacteristic
101C23×C32C22⋊C411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×D411yescharacteristic
104C32×D4—41no—
105C32×D4—41no—
106C32×D4—41no—
107C32×D4—41no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C3⋊Dic3—42no—
113C2×C3⋊Dic3—82no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—82no—
121C3×Dic6—42no—
122C3×Dic6—42no—
123C2×#124—31no—
124C2×#99—31no—
125C2×#99—91no—
126#354—94no—
127C24×C3—21no—
128C24×C3—21no—
129C24×C3D1211yescharacteristic
130C24×C3#6711yescharacteristic
131C24×C3#6711yescharacteristic
132C24×C3#6711yescharacteristic
133C2×C3×Q8—32no—
134C2×C3×Q8—61no—
135C2×C3×Q8—121no—
136C2×C3×Q8—121no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—41no—
142C2×C3×D4—41no—
143C2×C3×D4—41no—
144C2×C3×D4—41no—
145C2×C3×D4—42no—
146C2×C3×D4—42no—
147C2×C3×D4C4×D311yescharacteristic
148C2×C3×D4D1211yescharacteristic
149C2×C3×D4C2×Dic311yescharacteristic
150C2×C3×D4#6711yescharacteristic
151C2×C3×D4#6711yescharacteristic
152C2×C3×D4#6711yescharacteristic
153C2×C3×D4C22×D311yescharacteristic
154C2×C3×D4C22×D311yescharacteristic
155C22×C3×C4—21no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4—121no—
159C22×C3×C4C4×D311yescharacteristic
160C22×C3×C4C2×Dic311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—41no—
164C22×Dic3—122no—
165C22×Dic3—121no—
166C22×Dic3—121no—
167C2×Dic6—21no—
168C2×Dic6—41no—
169C2×Dic6—41no—
170C2×Dic6C2×Dic312yescomplemented
171C3×C22⋊C4—62no—
172C3×C22⋊C4—62no—
173C3×C22⋊C4—62no—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—121no—
177C3×C42—32no—
178C3×C42—61no—
179#217—22no—
180#217—22no—
181#217—22no—
182#217—22no—
183#217—22no—
184#217—41no—
185#217—64no—
186#217—62no—
187#217—62no—
188#217—122no—
189#217—121no—
190#217—121no—
191C4×Dic3—21no—
192C4×Dic3C2×Dic312yescomplemented
193C22×C32—21no—
194C22×C32—21no—
195C22×C32—22no—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32—42no—
199C22×C32—41no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32—41no—
203C22×C32—42no—
204C22×C32—81no—
205C22×C32—81no—
206C22×C32#9911yescharacteristic
207C22×C32#9911yescharacteristic
208C22×C32C2×C22⋊C411yescharacteristic
209C32×C4—21no—
210C32×C4—21no—
211C3⋊Dic3—82no—
212C3×Dic3—42no—
213C3×Dic3—42no—
214C3×Dic3—82no—
215C22×Q8—31no—
216C22×D4D3211yescharacteristic
217#124—32no—
218#124—32no—
219#124—61no—
220#124—61no—
221C2×C22⋊C4—61no—
222C2×C22⋊C4—61no—
223C2×C22⋊C4—61no—
224C2×C22⋊C4—181no—
225C2×C42—31no—
226#99—32no—
227#99—61no—
228#99—92no—
229#99—181no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—21no—
236C23×C3—21no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—21no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—41no—
246C23×C3—41no—
247C23×C3—42no—
248C23×C3—42no—
249C23×C3—42no—
250C23×C3—42no—
251C23×C3—82no—
252C23×C3—82no—
253C23×C3(C2×D3)⋊C411yescharacteristic
254C23×C3(C2×D3)⋊C411yescharacteristic
255C23×C3(C2×D3)⋊C411yescharacteristic
256C23×C3#21711yescharacteristic
257C23×C3#21711yescharacteristic
258C23×C3#21711yescharacteristic
259C23×C3C2×D1211yescharacteristic
260C23×C3C2×#6711yescharacteristic
261C23×C3C2×#6711yescharacteristic
262C23×C3C2×#6711yescharacteristic
263C3×Q8—122no—
264C3×Q8—122no—
265C3×D4—41no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—41no—
270C3×D4—41no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—42no—
274C3×D4—42no—
275C3×D4—42no—
276C3×D4—42no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—122no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4—122no—
291C2×C3×C4—242no—
292C2×C3×C4(C2×D3)⋊C411yescharacteristic
293C2×C3×C4#21711yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C22×Dic311yescharacteristic
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—42no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—42no—
302C2×Dic3—82no—
303C2×Dic3—124no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—244no—
307C2×Dic3—242no—
308C2×Dic3—242no—
309Dic6—42no—
310Dic6—42no—
311C2×C32—21no—
312C2×C32—21no—
313C2×C32—41no—
314C2×C32—41no—
315C2×C32—41no—
316C2×C32—41no—
317C2×C32#35412yescomplemented
318C2×C32C2×#9911yescharacteristic
319C24#62511yescharacteristic
320C24#62611yescharacteristic
321C2×Q8—32no—
322C2×Q8—61no—
323C2×Q8—121no—
324C2×Q8—121no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4D3×Dic311yescharacteristic
328C2×D4#62511yescharacteristic
329C2×D4#62611yescharacteristic
330C2×D4C2×D3211yescharacteristic
331C22×C4—61no—
332C22×C4—61no—
333C22×C4—121no—
334C22×C4—361no—
335C22×C4D3×Dic311yescharacteristic
336C22⋊C4—62no—
337C22⋊C4—62no—
338C22⋊C4—62no—
339C22⋊C4—62no—
340C22⋊C4—62no—
341C22⋊C4—121no—
342C22⋊C4—182no—
343C22⋊C4—361no—
344C42—32no—
345C42—61no—
346C22×C3—22no—
347C22×C3—22no—
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—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—42no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—44no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3—82no—
378C22×C3—81no—
379C22×C3—81no—
380C22×C3—81no—
381C22×C3—81no—
382C22×C3—81no—
383C22×C3—81no—
384C22×C3—81no—
385C22×C3—81no—
386C22×C3—82no—
387C22×C3—82no—
388C22×C3#80611yescharacteristic
389C22×C3#80611yescharacteristic
390C22×C3#83411yescharacteristic
391C22×C3#83411yescharacteristic
392C22×C3C2×(C2×D3)⋊C411yescharacteristic
393C22×C3C2×#21711yescharacteristic
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—122no—
401C3×C4—122no—
402C3×C4—242no—
403Dic3—42no—
404Dic3—42no—
405Dic3—82no—
406Dic3—244no—
407Dic3—242no—
408Dic3—242no—
409C32C2×#35411yescharacteristic, complemented, Sylow
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—42no—
415C23—42no—
416C23(C2×D3)⋊Dic311yescharacteristic
417C23(C2×D3)⋊Dic311yescharacteristic
418C23(C2×D3)⋊Dic311yescharacteristic
419C23C2×#62511yescharacteristic
420C23C2×#62611yescharacteristic
421Q8—122no—
422Q8—122no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—122no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—122no—
435C2×C4—242no—
436C2×C4—362no—
437C2×C4—722no—
438C2×C4(C2×D3)⋊Dic311yescharacteristic
439C2×C4C2×D3×Dic311yescharacteristic
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—22no—
446C2×C3—41no—
447C2×C3—41no—
448C2×C3—42no—
449C2×C3—42no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3—41no—
455C2×C3—41no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3—81no—
459C2×C3—81no—
460C2×C3#447312yescomplemented
461C2×C3#454112yescomplemented
462C2×C3C2×#80611yescharacteristic
463C2×C3C2×#83411yescharacteristic
464C22—22no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—42no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22#6358011yescharacteristic
478C22#6358011yescharacteristic
479C22C2×(C2×D3)⋊Dic311yescharacteristic
480C4—21no—
481C4—21no—
482C4—122no—
483C4—122no—
484C4—242no—
485C4—722no—
486C3—21no—
487C3C2×#447311yescharacteristic, complemented
488C3C2×#454111yescharacteristic, complemented
489C2—21no—
490C2—21no—
491C2—41no—
492C2—41no—
493C2—41no—
494C2—41no—
495C2#1058918012yesdirect product factor
496C2C2×#6358011yescharacteristic
subgroupG/H
centerC22#63580
commutatorC2×C32×C4C22×C4
FrattiniC2×D4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#99
cosocleC2×C32×D4C23
hypercenterC22×D4D32
hypocenterC32C2×#354
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10589180C2direct (N × H)
8. C22×C3×Dic6C4semidirect
15. C3×#936C4semidirect
17. C2×C3×C4×Dic3C4semidirect
47. C2×C3×Dic6C2×C4semidirect
57. C3×C4×Dic3C2×C4semidirect
63. C22×Dic6Dic3semidirect
80. #936Dic3semidirect
82. C2×C4×Dic3Dic3semidirect
170. C2×Dic6C2×Dic3semidirect
192. C4×Dic3C2×Dic3semidirect
317. C2×C32#354semidirect
409. C32C2×#354semidirect
460. C2×C3#4473semidirect
461. C2×C3#4541semidirect
487. C3C2×#4473semidirect
488. C3C2×#4541semidirect
495. C2#10589180direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9362
C2×#636612
C2×C3×#8342
#105891802
C2×#45413
C2×#44733