Finite Group Databasebeta

← C2×#10591489 #11865494

Subgroups — C2×#10591489 #11865494

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic
3C22×C3×#214C211yesmaximal, characteristic
4C2×#63866C211yesmaximal, characteristic, complemented
5#10591489C218yesmaximal, direct product factor
6C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C2×#5162—31nomaximal
10C2×#5019—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C23×C3×Dic3—21no—
14C22×C3×Dic6C2211yescharacteristic
15C2×#3754—24no—
16C2×#3754C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—21no—
19C3×D4×Dic3—22no—
20C3×D4×Dic3C2214yes—
21C2×C3×#214—24no—
22C2×C3×#214C2214yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×Dic3⋊Dic3—21no—
27C2×Dic3⋊Dic3—21no—
28#63866—22no—
29#63866C2214yescomplemented
30Dic3⋊(C3⋊C8)C2214yescomplemented
31#63567C2214yescomplemented
32#63565C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×C4×D4—31no—
35C2×#944—31no—
36C2×D4×Dic3D311yescharacteristic
37C22×#214—31no—
38C22×#214—31no—
39C22×#214—61no—
40C22×#214D311yescharacteristic
41C2×#869—31no—
42C2×#835—31no—
43#5162—38no—
44C2×#816—31no—
45C2×Dic3⋊C8—31no—
46#5019—38no—
47C2×#810—31no—
48C2×#810—31no—
49C2×C4⋊(C3⋊C8)—31no—
50C24×C32—21no—
51C2×C32×D4—21no—
52C2×C32×D4—22no—
53C2×C32×D4D414yes—
54C2×C32×D4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634—21no—
60C2×#634C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—24no—
64C22×C3×Dic3—44no—
65C22×C3×Dic3D411yescharacteristic
66C22×C3×Dic3D411yescharacteristic
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71#3754—28no—
72C2×C3⋊(C3⋊C8)—22no—
73C2×C3⋊(C3⋊C8)C2312yes—
74C3×#217—24no—
75C3×#214—28no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82Dic3⋊Dic3—24no—
83Dic3⋊Dic3—24no—
84C2×#461—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C23×C3×C4—61no—
90C23×Dic3—21no—
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C22×C3×C8—31no—
98C3×C4×D4—34no—
99C3×C4×D4—62no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C22⋊C4—61no—
102C2×C3×C42—31no—
103C2×#217—21no—
104#944—34no—
105#944—62no—
106D4×Dic3—22no—
107D4×Dic3C2×D314yes—
108C2×#214—24no—
109C2×#214—34no—
110C2×#214—34no—
111C2×#214—64no—
112C2×#214—68no—
113C2×#214—64no—
114C2×#214—64no—
115C2×#214C2×D314yes—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3—61no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×Dic3⋊C4—61no—
120C2×Dic3⋊C4—61no—
121C2×C4×Dic3C2×D311yescharacteristic
122C22×C3⋊C8—31no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—61no—
125C22×C3⋊C8C2×D311yescharacteristic
126#869—34no—
127#869—62no—
128#835—34no—
129#816—34no—
130Dic3⋊C8—34no—
131#810—34no—
132#810—34no—
133C4⋊(C3⋊C8)—34no—
134C23×C32—24no—
135C23×C32—22no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32C2×D411yescharacteristic
139C32×D4—24no—
140C32×D4—22no—
141C32×D4C2×D414yes—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—42no—
148#634—22no—
149#634—22no—
150#634—42no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3—48no—
157C2×C3×Dic3SD1614yescomplemented
158C2×C3×Dic3C2×D412yes—
159C2×C3×Dic3C2×D412yes—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163C3⋊(C3⋊C8)—22no—
164C3×C3⋊C8—22no—
165C22×SD16—31no—
166C22×SD16—91no—
167C2×C4⋊Q8—91no—
168C2×C4×D4—31no—
169#461—98no—
170C2×C4⋊C8—91no—
171C2×#103—91no—
172C2×#103—91no—
173C24×C3—21no—
174C24×C3—21no—
175C24×C3—41no—
176C2×C3×Q8—32no—
177C2×C3×Q8—61no—
178C2×C3×Q8—62no—
179C2×C3×Q8—62no—
180C2×C3×D4—22no—
181C2×C3×D4—21no—
182C2×C3×D4—22no—
183C2×C3×D4—21no—
184C2×C3×D4—24no—
185C2×C3×D4—22no—
186C2×C3×D4—42no—
187C2×C3×D4—41no—
188C2×C3×D4D1214yes—
189C2×C3×D4#6714yes—
190C2×C3×D4C22×D312yes—
191C2×C3×D4C22×D312yes—
192C22×C3×C4—21no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—64no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4—124no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—24no—
204C22×Dic3—44no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—121no—
208C22×Dic3#6711yescharacteristic
209C22×Dic3#6711yescharacteristic
210C2×Dic6—22no—
211C2×Dic6—22no—
212C2×Dic6—21no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6—64no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—121no—
224C2×Dic6—122no—
225C2×Dic6C22×D312yes—
226C3×SD16—68no—
227C2×C3×C8—32no—
228C2×C3×C8—62no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—61no—
231C3×C22⋊C4—64no—
232C3×C42—32no—
233C3×C42—32no—
234#217—24no—
235#214—28no—
236#214—616no—
237#214—68no—
238#214—68no—
239C4⋊Dic3—21no—
240C4⋊Dic3—64no—
241C4⋊Dic3—64no—
242C4⋊Dic3C22×D312yes—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245C4×Dic3#6712yes—
246C4×Dic3C22×D312yes—
247C2×C3⋊C8—22no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8—64no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8C22×D312yes—
255C22×C32—24no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32—48no—
259C22×C32#12112yes—
260C22×C32C2×SD1612yes—
261C22×C32#13712yes—
262C22×C32C22×D411yescharacteristic
263C32×C4#12112yes—
264C32×C4C22×D411yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—42no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C3×Dic3C2×SD1614yescomplemented
271C22×Q8—31no—
272C22×Q8—91no—
273C22×D4D3211yescharacteristic
274C23×C4—61no—
275C2×SD16—34no—
276C2×SD16—64no—
277C2×SD16—94no—
278C2×SD16—184no—
279C22×C8—31no—
280C22×C8—91no—
281C4⋊Q8—94no—
282C4⋊Q8—182no—
283C4×D4—34no—
284C4×D4—62no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—181no—
287C2×C4⋊C4—181no—
288C2×C22⋊C4—61no—
289C2×C42—31no—
290C4⋊C8—94no—
291#103—94no—
292#103—94no—
293C23×C3—24no—
294C23×C3—24no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—42no—
299C23×C3—44no—
300C23×C3—42no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—82no—
305C23×C3—82no—
306C23×C3D3×D411yescharacteristic
307C23×C3C2×#6711yescharacteristic
308C3×Q8—62no—
309C3×Q8—62no—
310C3×Q8—122no—
311C3×D4—24no—
312C3×D4—24no—
313C3×D4—22no—
314C3×D4—22no—
315C3×D4—24no—
316C3×D4—42no—
317C3×D4—44no—
318C3×D4C2×D1214yes—
319C3×D4C2×#6714yes—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—34no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—128no—
331C2×C3×C4—122no—
332C2×C3×C4—122no—
333C2×C3×C4C2×D1212yes—
334C2×C3×C4#23512yes—
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4#23712yes—
337C2×C3×C4C2×#6712yes—
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—42no—
345C2×Dic3—42no—
346C2×Dic3—48no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—122no—
350C2×Dic3—124no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3#21414yescomplemented
354C2×Dic3C2×#6712yes—
355C2×Dic3C2×#6712yes—
356Dic6—22no—
357Dic6—22no—
358Dic6—42no—
359Dic6—64no—
360Dic6—62no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—122no—
365Dic6—124no—
366Dic6—122no—
367Dic6—122no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—64no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C2×C32—44no—
374C2×C32#46114yescomplemented
375C2×C32C2×#12111yescharacteristic
376C2×C32C22×SD1611yescharacteristic
377C2×C32C2×#13711yescharacteristic
378C24—21no—
379C2×Q8—32no—
380C2×Q8—61no—
381C2×Q8—62no—
382C2×Q8—62no—
383C2×Q8—92no—
384C2×Q8—181no—
385C2×Q8—182no—
386C2×Q8—182no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4#62614yes—
390C2×D4C2×D3212yes—
391C22×C4—31no—
392C22×C4—31no—
393C22×C4—64no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—124no—
397C22×C4—181no—
398C22×C4C2×D3211yescharacteristic
399SD16—68no—
400SD16—188no—
401C2×C8—32no—
402C2×C8—62no—
403C2×C8—92no—
404C2×C8—182no—
405C4⋊C4—32no—
406C4⋊C4—61no—
407C4⋊C4—184no—
408C4⋊C4—184no—
409C22⋊C4—64no—
410C42—32no—
411C42—32no—
412C22×C3—24no—
413C22×C3—24no—
414C22×C3—21no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—44no—
419C22×C3—48no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—48no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—88no—
426C22×C3—82no—
427C22×C3—82no—
428C22×C3D3×SD1612yes—
429C22×C3#91512yes—
430C22×C3#93012yes—
431C22×C3C2×#21412yes—
432C22×C3#93912yes—
433C22×C3#95112yes—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C22×#6711yescharacteristic
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—34no—
440C3×C4—62no—
441C3×C4—122no—
442C3×C4—122no—
443C3×C4#93012yes—
444C3×C4#93912yes—
445C3×C4C22×D1211yescharacteristic
446C3×C4C2×#23511yescharacteristic
447C3×C4C2×#23711yescharacteristic
448C3×C4C22×#6711yescharacteristic
449Dic3—22no—
450Dic3—42no—
451Dic3—42no—
452Dic3—124no—
453Dic3—122no—
454Dic3—122no—
455Dic3C2×#21414yescomplemented
456C32C2×#46111yescharacteristic, complemented, Sylow
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23D3×#6711yescharacteristic
462Q8—62no—
463Q8—62no—
464Q8—122no—
465Q8—182no—
466Q8—182no—
467Q8—362no—
468D4—22no—
469D4—24no—
470D4C2×#62614yes—
471C2×C4—32no—
472C2×C4—34no—
473C2×C4—32no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—128no—
478C2×C4—122no—
479C2×C4—122no—
480C2×C4—182no—
481C2×C4—362no—
482C2×C4#380412yes—
483C2×C4C2×#62612yes—
484C2×C4D3×#6711yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—62no—
487C8—182no—
488C2×C3—24no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—44no—
493C2×C3—44no—
494C2×C3—84no—
495C2×C3#501914yescomplemented
496C2×C3#516214yescomplemented
497C2×C3C2×D3×SD1611yescharacteristic
498C2×C3C2×#91511yescharacteristic
499C2×C3C2×#93011yescharacteristic
500C2×C3C22×#21411yescharacteristic
501C2×C3C2×#93911yescharacteristic
502C2×C3C2×#95111yescharacteristic
503C22—24no—
504C22—48no—
505C22—42no—
506C22—42no—
507C22D3×#21412yes—
508C22#6392912yes—
509C22#6397812yes—
510C22C2×D3×#6711yescharacteristic
511C4—34no—
512C4—62no—
513C4—122no—
514C4—122no—
515C4—362no—
516C4#6397812yes—
517C4C2×#380411yescharacteristic
518C4C22×#62611yescharacteristic
519C3—21no—
520C3C2×#501911yescharacteristic, complemented
521C3C2×#516211yescharacteristic, complemented
522C2—44no—
523C2#1059148914yesdirect product factor
524C2C2×D3×#21411yescharacteristic
525C2C2×#6392911yescharacteristic
526C2C2×#6397811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#461
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. C2×#63866C2semidirect
5. #10591489C2direct (N × H)
6. C2×Dic3⋊(C3⋊C8)C2semidirect
7. C2×#63567C2semidirect
8. C2×#63565C2semidirect
29. #63866C22semidirect
30. Dic3⋊(C3⋊C8)C22semidirect
31. #63567C22semidirect
32. #63565C22semidirect
157. C2×C3×Dic3SD16semidirect
270. C3×Dic3C2×SD16semidirect
353. C2×Dic3#214semidirect
374. C2×C32#461semidirect
455. Dic3C2×#214semidirect
456. C32C2×#461semidirect
495. C2×C3#5019semidirect
496. C2×C3#5162semidirect
520. C3C2×#5019semidirect
521. C3C2×#5162semidirect
523. C2#10591489direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×D4×Dic32
C22×C3×#2142
C2×#638662
#105914892
C2×Dic3⋊(C3⋊C8)2
C2×#635672
C2×#635652
C2×#51623
C2×#50193