Finite Group Databasebeta

← C2×#10591608 #11874397

Subgroups — C2×#10591608 #11874397

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic
2C2×C3×#944C211yesmaximal, characteristic, complemented
3C22×C3×#216C211yesmaximal, characteristic, complemented
4C2×#63864C211yesmaximal, characteristic
5C22×#3718C211yesmaximal, characteristic, complemented
6C22×#3717C211yesmaximal, characteristic
7#10591608C218yesmaximal, direct product factor
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5190—31nomaximal
10C2×#5086—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3755—24no—
16C2×#3755C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#944—22no—
19C3×#944C2214yescomplemented
20C2×C3×#216—24no—
21C2×C3×#216C2214yescomplemented
22C2×C3×Dic3⋊C4—22no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—22no—
26#63864—22no—
27#63864C2214yes—
28C2×#3718—24no—
29C2×#3718C2214yescomplemented
30C2×#3717—24no—
31C2×#3717C2214yes—
32#63554C2214yescomplemented
33C22×C3×Q16—31no—
34C2×C3×C4⋊Q8—31no—
35C2×#947—31no—
36C2×#944D311yescharacteristic, complemented
37C22×#216—31no—
38C22×#216—31no—
39C22×#216D311yescharacteristic, complemented
40C22×#215—31no—
41C22×#215—31no—
42C22×#215—31no—
43C22×#215—61no—
44C22×#204—31no—
45C2×#875—31no—
46#5190—38no—
47C2×#815—31no—
48#5086—38no—
49C2×#803—31no—
50C23×C3⋊D3—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2312yes—
72#3755—28no—
73C2×C3⋊(C3⋊C8)D414yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#216—28no—
76C3×Dic3⋊C4—28no—
77C3×C4×Dic3D412yes—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8D414yes—
80C2×C3×C3⋊C8C2312yes—
81#3722—28no—
82#3718—28no—
83#3717—28no—
84C2×#497—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8—31no—
87C22×C3×Q8—31no—
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×Q8C2×D311yescharacteristic
90C22×D12—31no—
91C22×D12—31no—
92C22×D12—61no—
93C22×Dic6C2×D311yescharacteristic
94C22×Dic6C2×D311yescharacteristic
95C2×C3×Q16—34no—
96C2×C3×Q16—64no—
97C22×C3×C8—31no—
98C3×C4⋊Q8—34no—
99C3×C4⋊Q8—62no—
100C2×C3×C4⋊C4—62no—
101C2×C3×C42—31no—
102#947—34no—
103#947—62no—
104#944—22no—
105#944C2×D314yescomplemented
106C2×#216—24no—
107C2×#216—34no—
108C2×#216—34no—
109C2×#216—64no—
110C2×#216—64no—
111C2×#216C2×D314yescomplemented
112C2×#215—34no—
113C2×#215—34no—
114C2×#215—34no—
115C2×#215—64no—
116C2×#215—64no—
117C2×#215—64no—
118C2×#215—68no—
119C2×#215—64no—
120C2×(C2×D3)⋊C4—62no—
121C2×(C2×D3)⋊C4—62no—
122C2×Dic3⋊C4—22no—
123C2×C4×Dic3C2×D311yescharacteristic
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127C22×C3⋊C8C2×D311yescharacteristic
128C2×#204—34no—
129C2×#204—64no—
130#875—34no—
131#875—62no—
132#815—34no—
133#803—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—44no—
138C32×Q8—22no—
139C32×Q8—22no—
140C32×Q8—42no—
141C2×C32×C4—22no—
142C2×C32×C4—42no—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2411yescharacteristic
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—42no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—42no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3C2×D414yes—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—42no—
161C3×Dic6—42no—
162C3⋊(C3⋊C8)C2×D414yes—
163C3×C3⋊C8C2×D414yes—
164C22×Q16—31no—
165C22×Q16—91no—
166C22×SD16—91no—
167C22×SD16—91no—
168C2×C4⋊Q8—31no—
169C2×#124—91no—
170#497—98no—
171C2×#97—91no—
172C23×D3—61no—
173C23×D3—61no—
174C23×D3—121no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—24no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—32no—
184C2×C3×Q8—32no—
185C2×C3×Q8—41no—
186C2×C3×Q8—42no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—62no—
190C2×C3×Q8—62no—
191C2×C3×Q8—62no—
192C2×C3×Q8—62no—
193C2×C3×Q8C22×D312yes—
194C2×C3×Q8C22×D312yes—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—32no—
199C22×C3×C4—41no—
200C22×C3×C4—61no—
201C22×C3×C4—61no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3#6712yes—
207C2×D12—32no—
208C2×D12—32no—
209C2×D12—62no—
210C2×D12—64no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—122no—
218C2×D12—121no—
219C2×Dic6—22no—
220C2×Dic6—22no—
221C2×Dic6—22no—
222C2×Dic6—22no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6C22×D312yes—
226C2×Dic6C22×D312yes—
227C3×Q16—68no—
228C2×C3×C8—34no—
229C2×C3×C8—32no—
230C3×C4⋊C4—68no—
231C3×C42—32no—
232C3×C42—32no—
233#216—28no—
234#216—68no—
235#216—68no—
236#215—68no—
237#215—68no—
238#215—616no—
239#215—68no—
240(C2×D3)⋊C4—68no—
241(C2×D3)⋊C4—68no—
242Dic3⋊C4—28no—
243C4×Dic3#6712yes—
244C4×Dic3C22×D312yes—
245C2×C3⋊C8—34no—
246C2×C3⋊C8—34no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—64no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8#6714yes—
252C2×C3⋊C8C22×D312yes—
253#204—68no—
254C22×C32#12712yes—
255C22×C32#13714yes—
256C22×C32C22×D411yescharacteristic
257C2×C3⋊D3—42no—
258C2×C3⋊D3—44no—
259C2×C3⋊D3—84no—
260C32×C4—42no—
261C32×C4#12712yes—
262C32×C4C22×D411yescharacteristic
263C32×C4C22×D411yescharacteristic
264C3×Dic3—24no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C22×Q8—31no—
268C22×Q8—31no—
269C22×Q8D3211yescharacteristic
270C22×D4—91no—
271C2×Q16—34no—
272C2×Q16—64no—
273C2×Q16—94no—
274C2×Q16—184no—
275C2×SD16—94no—
276C2×SD16—94no—
277C2×SD16—184no—
278C2×SD16—184no—
279C22×C8—31no—
280C22×C8—91no—
281C4⋊Q8—34no—
282C4⋊Q8—62no—
283#124—94no—
284#124—182no—
285C2×C4⋊C4—62no—
286C2×C22⋊C4—182no—
287C2×C42—31no—
288#97—94no—
289C23×C3—21no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—122no—
295C22×D3—124no—
296C22×D3—124no—
297C22×D3—122no—
298C22×D3—122no—
299C22×D3—124no—
300C22×D3—244no—
301C3×Q8—24no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—42no—
307C3×Q8—44no—
308C3×Q8—42no—
309C3×Q8—42no—
310C3×Q8—62no—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—62no—
314C3×Q8—122no—
315C3×Q8—122no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—34no—
323C2×C3×C4—42no—
324C2×C3×C4—44no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—64no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—122no—
331C2×C3×C4—122no—
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D412yes—
334C2×C3×C4D3×D412yes—
335C2×C3×C4D3×D412yes—
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6712yes—
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×Dic3—24no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—42no—
344C2×Dic3—42no—
345C2×Dic3C2×#6714yes—
346D12—64no—
347D12—62no—
348D12—62no—
349D12—62no—
350D12—62no—
351D12—122no—
352D12—124no—
353D12—122no—
354D12—122no—
355Dic6—22no—
356Dic6—22no—
357Dic6—22no—
358Dic6—22no—
359Dic6—42no—
360Dic6—42no—
361C3×C8—34no—
362C3⋊C8—34no—
363C3⋊C8—34no—
364C3⋊C8—64no—
365C3⋊C8C2×#6714yes—
366C2×C32#49714yescomplemented
367C2×C32C2×#12711yescharacteristic
368C2×C32C2×#13712yes—
369C3⋊D3—82no—
370C24—181no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—32no—
375C2×Q8—32no—
376C2×Q8—61no—
377C2×Q8—61no—
378C2×Q8—62no—
379C2×Q8—62no—
380C2×Q8—62no—
381C2×Q8—62no—
382C2×Q8C2×D3212yes—
383C2×D4—92no—
384C2×D4—182no—
385C2×D4—181no—
386C2×D4—182no—
387C22×C4—21no—
388C22×C4—32no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4C2×D3211yescharacteristic
392Q16—68no—
393Q16—188no—
394SD16—188no—
395SD16—188no—
396C2×C8—32no—
397C2×C8—34no—
398C2×C8—92no—
399C2×C8—94no—
400C4⋊C4—68no—
401C22⋊C4—188no—
402C42—32no—
403C42—32no—
404C22×C3—21no—
405C22×C3—24no—
406C22×C3—22no—
407C22×C3#91814yes—
408C22×C3#94012yes—
409C22×C3#94012yes—
410C22×C3#94214yes—
411C22×C3C2×D3×D411yescharacteristic
412C22×C3C22×#6711yescharacteristic
413C2×D3—124no—
414C2×D3—124no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—124no—
418C2×D3—244no—
419C2×D3—248no—
420C2×D3—244no—
421C2×D3—244no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—44no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4—64no—
429C3×C4—122no—
430C3×C4—122no—
431C3×C4#94012yes—
432C3×C4#94012yes—
433C3×C4C2×D3×D411yescharacteristic
434C3×C4C2×D3×D411yescharacteristic
435C3×C4C2×D3×D411yescharacteristic
436C3×C4C22×#6711yescharacteristic
437Dic3—24no—
438Dic3—42no—
439Dic3—42no—
440C32C2×#49711yescharacteristic, complemented, Sylow
441C23—182no—
442C23—364no—
443C23—362no—
444C23D3×#6711yescharacteristic
445Q8—22no—
446Q8—22no—
447Q8—42no—
448Q8—62no—
449Q8—62no—
450Q8—62no—
451Q8—62no—
452Q8—122no—
453Q8—122no—
454D4—182no—
455D4—182no—
456D4—362no—
457C2×C4—22no—
458C2×C4—34no—
459C2×C4—42no—
460C2×C4—64no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—122no—
464C2×C4—122no—
465C2×C4D3×#6712yes—
466C2×C4D3×#6711yescharacteristic
467C2×C4#381112yes—
468C2×C4C22×D3211yescharacteristic
469C8—34no—
470C8—94no—
471C2×C3—22no—
472C2×C3—24no—
473C2×C3—21no—
474C2×C3#508614yescomplemented
475C2×C3#519014yescomplemented
476C2×C3C2×#91812yes—
477C2×C3C2×#94011yescharacteristic
478C2×C3C2×#94011yescharacteristic
479C2×C3C2×#94212yes—
480D3—244no—
481D3—242no—
482D3—242no—
483C22—364no—
484C22—362no—
485C22—724no—
486C22#6394814yes—
487C22#6397912yes—
488C22C2×D3×#6711yescharacteristic
489C4—42no—
490C4—64no—
491C4—122no—
492C4—122no—
493C4#6397912yes—
494C4C2×D3×#6711yescharacteristic
495C4C2×#381111yescharacteristic
496C3—21no—
497C3C2×#508611yescharacteristic, complemented
498C3C2×#519011yescharacteristic, complemented
499C2—722no—
500C2#1059160814yesdirect product factor
501C2C2×#6394812yes—
502C2C2×#6397911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q8D32
hypocenterC32C2×#497
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
2. C2×C3×#944C2semidirect
3. C22×C3×#216C2semidirect
5. C22×#3718C2semidirect
7. #10591608C2direct (N × H)
8. C2×#63554C2semidirect
19. C3×#944C22semidirect
21. C2×C3×#216C22semidirect
29. C2×#3718C22semidirect
32. #63554C22semidirect
36. C2×#944D3semidirect
39. C22×#216D3semidirect
105. #944C2×D3semidirect
111. C2×#216C2×D3semidirect
366. C2×C32#497semidirect
440. C32C2×#497semidirect
474. C2×C3#5086semidirect
475. C2×C3#5190semidirect
497. C3C2×#5086semidirect
498. C3C2×#5190semidirect
500. C2#10591608direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C3×#9442
C22×C3×#2162
C2×#638642
C22×#37182
C22×#37172
#105916082
C2×#635542
C2×#51903
C2×#50863