Finite Group Databasebeta

← C2×#10590525 #11866802

Subgroups — C2×#10590525 #11866802

Order 1152.

1185 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3710C211yesmaximal, characteristic
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C2×C3×#807C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590525C218yesmaximal, direct product factor
9C2×#4887—31nomaximal
10C2×#4813—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)—21no—
17#64106—22no—
18#64106C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C2×#3722—21no—
24#63871—22no—
25#63871C2214yes—
26C2×#3719—24no—
27C2×#3719C2214yescomplemented
28C2×#3710—24no—
29C2×#3710C2214yes—
30C3×#810C2214yescomplemented
31C3×#807C2214yescomplemented
32#63567C2214yescomplemented
33C2×#946—31no—
34C22×#216—31no—
35C22×Dic12—31no—
36C22×D3×C8—31no—
37C22×D3×C8—31no—
38C2×#897—31no—
39C2×#897—31no—
40C2×#897—31no—
41C2×#897—61no—
42C2×C3×#107—31no—
43C2×C3×#103—31no—
44C2×#816—31no—
45C2×#810—31no—
46C2×#810D311yescharacteristic, complemented
47C2×#807D311yescharacteristic, complemented
48#4887—38no—
49#4813—38no—
50C23×C3⋊D3D411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3D411yescharacteristic
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3D412yes—
58C2×C4×C3⋊D3C2312yes—
59C2×#634—22no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634C2312yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71#3752—24no—
72C4⋊(C3⋊Dic3)—24no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8D414yes—
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2312yes—
79Dic3⋊Dic3—24no—
80#3722—24no—
81#3719—28no—
82#3710—28no—
83C2×#467—91noSylow
84C22×C3×Q8—31no—
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C22×Dic6C2×D311yescharacteristic
92C22×C3×C8—31no—
93C22×C3×C8—31no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C4⋊C4C2×D311yescharacteristic
98#946—34no—
99#946—62no—
100C2×#216—34no—
101C2×#216—64no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—62no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3—62no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×Dic3⋊C4—61no—
113C22×C3⋊C8C2×D311yescharacteristic
114C22×C3⋊C8C2×D311yescharacteristic
115C2×Dic12—34no—
116C2×Dic12—64no—
117C2×D3×C8—34no—
118C2×D3×C8—34no—
119C2×D3×C8—64no—
120C2×D3×C8—64no—
121#897—34no—
122#897—34no—
123#897—34no—
124#897—64no—
125#897—62no—
126#897—62no—
127#897—64no—
128#897—62no—
129C3×#107—34no—
130C3×#103—34no—
131#816—34no—
132#810—34no—
133#810C2×D314yescomplemented
134#807C2×D314yescomplemented
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3Q1614yescomplemented
139C22×C3⋊D3C2×D412yes—
140C2×C32×C4—22no—
141C2×C32×C4—42no—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—42no—
149C2×C3⋊Dic3C2×D412yes—
150C4×C3⋊D3—24no—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153#634—22no—
154#634—22no—
155#634—42no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3—42no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8C2×D414yes—
165C22×Q16—91no—
166C23×C8—91no—
167C2×C22⋊Q8—91no—
168C2×C22⋊Q8—91no—
169#467—98no—
170C2×#107—31no—
171C2×#103—31no—
172C2×#103—91no—
173C23×D3—31no—
174C23×D3—31no—
175C23×D3—61no—
176C2×C3×Q8—32no—
177C2×C3×Q8—61no—
178C2×C3×Q8—62no—
179C2×C3×Q8—62no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—61no—
193C22×Dic3—62no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—122no—
207C2×C4×D3—122no—
208C2×Dic6—22no—
209C2×Dic6—22no—
210C2×Dic6—21no—
211C2×Dic6—32no—
212C2×Dic6—32no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—122no—
222C2×Dic6—122no—
223C2×Dic6C22×D312yes—
224C2×C3×C8—34no—
225C2×C3×C8—32no—
226C2×C3×C8—32no—
227C2×C3×C8—62no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4C22×D312yes—
235C3×C4⋊C4C22×D312yes—
236#216—68no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—68no—
242C4⋊Dic3—21no—
243C4⋊Dic3—64no—
244C4⋊Dic3—64no—
245C4⋊Dic3—64no—
246C4⋊Dic3—68no—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—64no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8D1214yes—
251C2×C3⋊C8C22×D312yes—
252C2×C3⋊C8C22×D312yes—
253Dic12—68no—
254D3×C8—68no—
255D3×C8—68no—
256C22×C32#12112yes—
257C22×C32C2×Q1612yes—
258C22×C32#13512yes—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—22no—
261C2×C3⋊D3—22no—
262C2×C3⋊D3—28no—
263C2×C3⋊D3C2×Q1614yescomplemented
264C32×C4—42no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—22no—
269C3⋊Dic3—42no—
270C3×Dic3—42no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×Q8—91no—
274C23×C4—91no—
275C2×Q16—94no—
276C2×Q16—184no—
277C22×C8—31no—
278C22×C8—31no—
279C22×C8—94no—
280C22×C8—184no—
281C22⋊Q8—94no—
282C22⋊Q8—94no—
283C22⋊Q8—182no—
284C22⋊Q8—182no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—181no—
287C2×C4⋊C4—181no—
288C2×C4⋊C4D3211yescharacteristic
289C2×C22⋊C4—181no—
290C2×C22⋊C4—181no—
291#107—34no—
292#103—34no—
293#103—94no—
294C23×C3—21no—
295C23×C3D3×D411yescharacteristic
296C23×C3D3×D411yescharacteristic
297C22×D3—34no—
298C22×D3—34no—
299C22×D3—32no—
300C22×D3—32no—
301C22×D3—64no—
302C22×D3—62no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—122no—
308C22×D3—122no—
309C3×Q8—62no—
310C3×Q8—62no—
311C3×Q8—122no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—44no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—122no—
325C2×C3×C4—122no—
326C2×C3×C4C2×D1212yes—
327C2×C3×C4#23512yes—
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4#23912yes—
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—32no—
337C2×Dic3—32no—
338C2×Dic3—42no—
339C2×Dic3—42no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—64no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3—124no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C4×D3—64no—
351C4×D3—64no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—62no—
355C4×D3—62no—
356C4×D3—122no—
357C4×D3—122no—
358C4×D3—124no—
359Dic6—22no—
360Dic6—22no—
361Dic6—42no—
362Dic6—62no—
363Dic6—62no—
364Dic6—62no—
365Dic6—62no—
366Dic6—122no—
367Dic6—122no—
368Dic6—124no—
369Dic6—122no—
370Dic6—122no—
371C3×C8—34no—
372C3×C8—62no—
373C3⋊C8—22no—
374C3⋊C8C2×D1214yes—
375C2×C32#46714yescomplemented
376C2×C32C2×#12111yescharacteristic
377C2×C32C22×Q1611yescharacteristic
378C2×C32C2×#13511yescharacteristic
379C3⋊D3—24no—
380C24—91no—
381C2×Q8—32no—
382C2×Q8—61no—
383C2×Q8—62no—
384C2×Q8—62no—
385C2×Q8—92no—
386C2×Q8—181no—
387C2×Q8—182no—
388C2×Q8—182no—
389C22×C4—21no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—91no—
393C22×C4—92no—
394C22×C4—92no—
395C22×C4—182no—
396C22×C4—182no—
397C22×C4—181no—
398C22×C4C2×D3211yescharacteristic
399Q16—188no—
400C2×C8—32no—
401C2×C8—34no—
402C2×C8—32no—
403C2×C8—62no—
404C2×C8—188no—
405C4⋊C4—21no—
406C4⋊C4—32no—
407C4⋊C4—61no—
408C4⋊C4—184no—
409C4⋊C4—184no—
410C4⋊C4C2×D3212yes—
411C22⋊C4—184no—
412C22⋊C4—184no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3#88412yes—
418C22×C3#89512yes—
419C22×C3#91212yes—
420C22×C3#91612yes—
421C22×C3D3×Q1612yes—
422C22×C3D3×Q1612yes—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C2×D3×D411yescharacteristic
425C2×D3—34no—
426C2×D3—34no—
427C2×D3—64no—
428C2×D3—68no—
429C2×D3—62no—
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—68no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—128no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—44no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—122no—
444C3×C4—122no—
445C3×C4#88412yes—
446C3×C4#89512yes—
447C3×C4C22×D1211yescharacteristic
448C3×C4C2×#23511yescharacteristic
449C3×C4C2×D3×D411yescharacteristic
450C3×C4C2×#23911yescharacteristic
451Dic3—42no—
452Dic3—42no—
453Dic3—62no—
454Dic3—62no—
455Dic3—122no—
456Dic3—124no—
457Dic3—122no—
458Dic3—122no—
459C32C2×#46711yescharacteristic, complemented, Sylow
460C23—92no—
461C23—94no—
462C23—182no—
463C23—182no—
464C23#381111yescharacteristic
465Q8—62no—
466Q8—62no—
467Q8—122no—
468Q8—182no—
469Q8—182no—
470Q8—362no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—92no—
476C2×C4—122no—
477C2×C4—122no—
478C2×C4—182no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—184no—
482C2×C4—182no—
483C2×C4—362no—
484C2×C4#379912yes—
485C2×C4D3×D1212yes—
486C2×C4#381111yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—34no—
489C8—62no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—24no—
493C2×C3—21no—
494C2×C3#481314yescomplemented
495C2×C3#488714yescomplemented
496C2×C3C2×#88411yescharacteristic
497C2×C3C2×#89511yescharacteristic
498C2×C3C2×#91211yescharacteristic
499C2×C3C2×#91611yescharacteristic
500C2×C3C2×D3×Q1611yescharacteristic
501C2×C3C2×D3×Q1611yescharacteristic
502D3—64no—
503D3—64no—
504D3—124no—
505C22—94no—
506C22—182no—
507C22—188no—
508C22—182no—
509C22#6391012yes—
510C22#6393612yes—
511C22#6394412yes—
512C22C2×#381111yescharacteristic
513C4—42no—
514C4—122no—
515C4—122no—
516C4—182no—
517C4—362no—
518C4#6391012yes—
519C4C2×#379911yescharacteristic
520C4C2×D3×D1211yescharacteristic
521C3—21no—
522C3C2×#481311yescharacteristic, complemented
523C3C2×#488711yescharacteristic, complemented
524C2—184no—
525C2#1059052514yesdirect product factor
526C2C2×#6391011yescharacteristic
527C2C2×#6393611yescharacteristic
528C2C2×#6394411yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#3719C2semidirect
5. C2×C3×#810C2semidirect
6. C2×C3×#807C2semidirect
7. C2×#63567C2semidirect
8. #10590525C2direct (N × H)
27. C2×#3719C22semidirect
30. C3×#810C22semidirect
31. C3×#807C22semidirect
32. #63567C22semidirect
46. C2×#810D3semidirect
47. C2×#807D3semidirect
133. #810C2×D3semidirect
134. #807C2×D3semidirect
138. C22×C3⋊D3Q16semidirect
263. C2×C3⋊D3C2×Q16semidirect
375. C2×C32#467semidirect
459. C32C2×#467semidirect
494. C2×C3#4813semidirect
495. C2×C3#4887semidirect
522. C3C2×#4813semidirect
523. C3C2×#4887semidirect
525. C2#10590525direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×#638712
C22×#37192
C22×#37102
C2×C3×#8102
C2×C3×#8072
C2×#635672
#105905252
C2×#48873
C2×#48133