Finite Group Databasebeta

← C2×#10591612 #11865703

Subgroups — C2×#10591612 #11865703

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C22×C3×#215C211yesmaximal, characteristic
4C2×#63863C211yesmaximal, characteristic
5#10591612C218yesmaximal, direct product factor
6C2×#63572C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic
9C2×#5185—31nomaximal
10C2×#5166—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14Q8×C3⋊Dic3—22no—
15Q8×C3⋊Dic3C2214yescomplemented
16C2×C4⋊(C3⋊Dic3)—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#216—24no—
21C2×C3×#216C2214yescomplemented
22C2×C3×#215—24no—
23C2×C3×#215C2214yes—
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×(C2×D3)⋊Dic3—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63863—22no—
29#63863C2214yes—
30#63572C2214yescomplemented
31#63566C2214yescomplemented
32#63563C2214yes—
33C22×C3×Q16—31no—
34C22×C3×SD16—31no—
35C2×#947—31no—
36C2×Q8×Dic3—31no—
37C2×Q8×Dic3—31no—
38C2×Q8×Dic3—61no—
39C22×#216D311yescharacteristic, complemented
40C22×#215D311yescharacteristic
41C2×#936—31no—
42C2×#835—31no—
43C2×#832—31no—
44#5185—38no—
45#5166—38no—
46C2×#821—31no—
47C2×#816—31no—
48C2×Dic3⋊C8—31no—
49C2×Dic3⋊C8—31no—
50C23×C3×D3—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8D414yes—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3D411yescharacteristic
59C22×C3⋊Dic3D411yescharacteristic
60C22×C3×Dic3—21no—
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—24no—
71C4⋊(C3⋊Dic3)C2312yes—
72C4×C3⋊Dic3—24no—
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2312yes—
75C3×#216—28no—
76C3×#215—28no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81(C2×D3)⋊Dic3—24no—
82(C2×D3)⋊Dic3—24no—
83C2×#464—91noSylow
84C22×C3×Q8—21no—
85C22×C3×Q8—31no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×D4—31no—
89C22×D12C2×D311yescharacteristic
90C22×Dic6C2×D311yescharacteristic
91C2×C3×Q16—34no—
92C2×C3×Q16—64no—
93C2×C3×SD16—34no—
94C2×C3×SD16—64no—
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C2×#217—61no—
98C2×#217—61no—
99#947—34no—
100#947—62no—
101Q8×Dic3—34no—
102Q8×Dic3—34no—
103Q8×Dic3—64no—
104Q8×Dic3—62no—
105Q8×Dic3—62no—
106Q8×Dic3—64no—
107C2×#216—24no—
108C2×#216C2×D314yescomplemented
109C2×#215—24no—
110C2×#215C2×D314yes—
111#936—34no—
112#936—62no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—61no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3—62no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—61no—
124C2×C4×Dic3—61no—
125C2×C4×Dic3—61no—
126C2×C4×Dic3—62no—
127C22×C3⋊C8C2×D311yescharacteristic
128C22×C3⋊C8C2×D311yescharacteristic
129#835—34no—
130#832—34no—
131#821—34no—
132#816—34no—
133Dic3⋊C8—34no—
134Dic3⋊C8—34no—
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C32×Q8—24no—
141C32×Q8—22no—
142C32×Q8C2×D414yes—
143C2×C32×C4—24no—
144C2×C32×C4—22no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—42no—
153C2×C3⋊Dic3C2×D412yes—
154C2×C3⋊Dic3C2×D412yes—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—42no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—42no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—22no—
165C22×Q16—31no—
166C22×SD16—31no—
167C2×#124—91no—
168C2×C4×Q8—91no—
169#464—98no—
170C2×C4⋊C8—91no—
171C2×#103—91no—
172C2×#102—91no—
173C24×C3—61no—
174C23×D3—21no—
175C2×C3×Q8—22no—
176C2×C3×Q8—24no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—24no—
182C2×C3×Q8—22no—
183C2×C3×Q8—32no—
184C2×C3×Q8—61no—
185C2×C3×Q8—62no—
186C2×C3×Q8—62no—
187C2×C3×Q8#6714yes—
188C2×C3×Q8#6714yes—
189C2×C3×Q8C22×D312yes—
190C2×C3×Q8C22×D312yes—
191C2×C3×D4—32no—
192C2×C3×D4—61no—
193C2×C3×D4—62no—
194C2×C3×D4—62no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—62no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C2×D12—22no—
213C2×D12—22no—
214C2×D12—21no—
215C2×D12C22×D312yes—
216C2×Dic6—22no—
217C2×Dic6—22no—
218C2×Dic6—21no—
219C2×Dic6C22×D312yes—
220C3×Q16—68no—
221C3×SD16—68no—
222C2×C3×C8—32no—
223C2×C3×C8—32no—
224C2×C3×C8—62no—
225C2×C3×C8—62no—
226#217—64no—
227#217—64no—
228#216—28no—
229#215—28no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—62no—
235C4⋊Dic3—64no—
236C4⋊Dic3—64no—
237C4⋊Dic3—68no—
238C4⋊Dic3—62no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4×Dic3—32no—
242C4×Dic3—32no—
243C4×Dic3—32no—
244C4×Dic3—32no—
245C4×Dic3—62no—
246C4×Dic3—62no—
247C4×Dic3—64no—
248C4×Dic3—64no—
249C4×Dic3—68no—
250C2×C3⋊C8—22no—
251C2×C3⋊C8—22no—
252C2×C3⋊C8C22×D312yes—
253C2×C3⋊C8C22×D312yes—
254C22×C32#12112yes—
255C22×C32#13512yes—
256C22×C32#13712yes—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—84no—
262C32×C4—24no—
263C32×C4#12112yes—
264C32×C4C22×D411yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—22no—
267C3⋊Dic3—22no—
268C3⋊Dic3—42no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×Q8D3211yescharacteristic
272C22×D4—31no—
273C2×Q16—34no—
274C2×Q16—64no—
275C2×SD16—34no—
276C2×SD16—64no—
277C22×C8—31no—
278C22×C8—31no—
279#124—94no—
280#124—182no—
281C4×Q8—94no—
282C4×Q8—182no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—181no—
285C2×C22⋊C4—181no—
286C2×C22⋊C4—181no—
287C2×C42—91no—
288C2×C42—181no—
289C4⋊C8—94no—
290#103—94no—
291#102—94no—
292C23×C3—21no—
293C23×C3—62no—
294C23×C3—122no—
295C23×C3—122no—
296C23×C3—122no—
297C23×C3D3×D411yescharacteristic
298C23×C3D3×D411yescharacteristic
299C22×D3—22no—
300C22×D3—42no—
301C22×D3—42no—
302C22×D3—42no—
303C3×Q8—24no—
304C3×Q8—28no—
305C3×Q8—24no—
306C3×Q8—24no—
307C3×Q8—22no—
308C3×Q8—22no—
309C3×Q8—24no—
310C3×Q8—62no—
311C3×Q8—62no—
312C3×Q8—122no—
313C3×Q8C2×#6714yes—
314C3×Q8C2×#6714yes—
315C3×D4—62no—
316C3×D4—62no—
317C3×D4—122no—
318C2×C3×C4—24no—
319C2×C3×C4—28no—
320C2×C3×C4—24no—
321C2×C3×C4—24no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—62no—
329C2×C3×C4—122no—
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23712yes—
333C2×C3×C4#23712yes—
334C2×C3×C4C2×#6712yes—
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×Dic3—22no—
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—32no—
343C2×Dic3—42no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—64no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—64no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—124no—
356C2×Dic3—122no—
357C2×Dic3—122no—
358D12—22no—
359D12—22no—
360D12—42no—
361Dic6—22no—
362Dic6—22no—
363Dic6—42no—
364C3×C8—62no—
365C3×C8—62no—
366C3⋊C8—22no—
367C3⋊C8—22no—
368C2×C32#46414yescomplemented
369C2×C32C2×#12111yescharacteristic
370C2×C32C2×#13511yescharacteristic
371C2×C32C2×#13711yescharacteristic
372C3×D3—82no—
373C24—61no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—32no—
377C2×Q8—61no—
378C2×Q8—62no—
379C2×Q8—62no—
380C2×Q8#62514yes—
381C2×Q8C2×D3212yes—
382C2×D4—32no—
383C2×D4—62no—
384C2×D4—62no—
385C2×D4—61no—
386C22×C4—21no—
387C22×C4—61no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392Q16—68no—
393SD16—68no—
394C2×C8—32no—
395C2×C8—32no—
396C2×C8—62no—
397C2×C8—62no—
398C4⋊C4—92no—
399C4⋊C4—184no—
400C4⋊C4—181no—
401C22⋊C4—184no—
402C22⋊C4—184no—
403C42—92no—
404C42—92no—
405C42—184no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3—244no—
414C22×C3#91512yes—
415C22×C3#91612yes—
416C22×C3#91812yes—
417C22×C3#91912yes—
418C22×C3#93912yes—
419C22×C3#93912yes—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—84no—
426C3×C4—28no—
427C3×C4—24no—
428C3×C4—24no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—122no—
433C3×C4#93912yes—
434C3×C4#93912yes—
435C3×C4C2×#23711yescharacteristic
436C3×C4C2×#23711yescharacteristic
437C3×C4C22×#6711yescharacteristic
438C3×C4C22×#6711yescharacteristic
439Dic3—42no—
440Dic3—64no—
441Dic3—62no—
442Dic3—62no—
443Dic3—62no—
444Dic3—62no—
445Dic3—122no—
446Dic3—124no—
447Dic3—122no—
448Dic3—122no—
449C32C2×#46411yescharacteristic, complemented, Sylow
450C23—62no—
451C23—122no—
452C23—122no—
453C23—122no—
454C23#381111yescharacteristic
455Q8—22no—
456Q8—24no—
457Q8—62no—
458Q8—62no—
459Q8—122no—
460Q8C2×#62514yes—
461D4—62no—
462D4—62no—
463D4—122no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—62no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—122no—
470C2×C4—182no—
471C2×C4—182no—
472C2×C4—182no—
473C2×C4—362no—
474C2×C4#380512yes—
475C2×C4C2×#62512yes—
476C2×C4#381111yescharacteristic
477C2×C4C22×D3211yescharacteristic
478C8—62no—
479C8—62no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—24no—
483C2×C3—21no—
484C2×C3—242no—
485C2×C3#516614yescomplemented
486C2×C3#518514yescomplemented
487C2×C3C2×#91511yescharacteristic
488C2×C3C2×#91611yescharacteristic
489C2×C3C2×#91811yescharacteristic
490C2×C3C2×#91911yescharacteristic
491C2×C3C2×#93911yescharacteristic
492C2×C3C2×#93911yescharacteristic
493D3—82no—
494C22—122no—
495C22—122no—
496C22—122no—
497C22—244no—
498C22#6395012yes—
499C22#6395112yes—
500C22#6398012yes—
501C22C2×#381111yescharacteristic
502C4—24no—
503C4—122no—
504C4—182no—
505C4—182no—
506C4—362no—
507C4#6398012yes—
508C4C2×#380511yescharacteristic
509C4C22×#62511yescharacteristic
510C3—21no—
511C3C2×#516611yescharacteristic, complemented
512C3C2×#518511yescharacteristic, complemented
513C2—242no—
514C2#1059161214yesdirect product factor
515C2C2×#6395011yescharacteristic
516C2C2×#6395111yescharacteristic
517C2C2×#6398011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
2. C22×C3×#216C2semidirect
5. #10591612C2direct (N × H)
6. C2×#63572C2semidirect
7. C2×#63566C2semidirect
15. Q8×C3⋊Dic3C22semidirect
21. C2×C3×#216C22semidirect
30. #63572C22semidirect
31. #63566C22semidirect
39. C22×#216D3semidirect
108. C2×#216C2×D3semidirect
368. C2×C32#464semidirect
449. C32C2×#464semidirect
485. C2×C3#5166semidirect
486. C2×C3#5185semidirect
511. C3C2×#5166semidirect
512. C3C2×#5185semidirect
514. C2#10591612direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C22×C3×#2162
C22×C3×#2152
C2×#638632
#105916122
C2×#635722
C2×#635662
C2×#635632
C2×#51853
C2×#51663