Finite Group Databasebeta

← C2×#10591611 #11874398

Subgroups — C2×#10591611 #11874398

Order 1152.

1273 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
1C2×#64153C211yesmaximal, characteristic, complemented
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C22×C3×#215C211yesmaximal, characteristic
4C2×#63863C211yesmaximal, characteristic
5C22×#3719C211yesmaximal, characteristic, complemented
6C22×#3716C211yesmaximal, characteristic
7#10591611C218yesmaximal, direct product factor
8C2×#63555C211yesmaximal, characteristic, complemented
9C2×#5190—31nomaximal
10C2×#5167—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15#64153—22no—
16#64153C2214yescomplemented
17C2×#3750—22no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#216—24no—
20C2×C3×#216C2214yescomplemented
21C2×C3×#215—24no—
22C2×C3×#215C2214yes—
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—22no—
26#63863—22no—
27#63863C2214yes—
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yes—
32#63555C2214yescomplemented
33C22×C3×Q16—31no—
34C22×C3×SD16—31no—
35C2×#947—31no—
36C2×#944—31no—
37C2×#944—31no—
38C2×#944—61no—
39C22×#216—31no—
40C22×#216D311yescharacteristic, complemented
41C22×#215D311yescharacteristic
42C2×#936—31no—
43C22×#214—31no—
44C22×Dic12—31no—
45C22×#204—31no—
46#5190—38no—
47#5167—38no—
48C2×#815—31no—
49C2×#815—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
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3D412yes—
59C2×#634—22no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634C2312yes—
63C22×C3×Dic3—21no—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72#3750—28no—
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2312yes—
75C3×#216—28no—
76C3×#215—28no—
77C2×C3×C3⋊C8D414yes—
78C2×C3×C3⋊C8D414yes—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81(C2×D3)⋊Dic3—28no—
82#3719—28no—
83#3716—28no—
84C2×#497—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8—31no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×D4—31no—
90C22×D12C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C2×C3×Q16—34no—
96C2×C3×Q16—64no—
97C2×C3×SD16—34no—
98C2×C3×SD16—64no—
99C22×C3×C8—31no—
100C22×C3×C8—31no—
101C2×#217—62no—
102#947—34no—
103#947—62no—
104#944—34no—
105#944—34no—
106#944—64no—
107#944—62no—
108#944—62no—
109#944—64no—
110C2×#216—24no—
111C2×#216—34no—
112C2×#216—64no—
113C2×#216C2×D314yescomplemented
114C2×#215—24no—
115C2×#215C2×D314yes—
116#936—34no—
117#936—62no—
118C2×#214—34no—
119C2×#214—64no—
120C2×(C2×D3)⋊C4—62no—
121C2×Dic3⋊C4—62no—
122C2×Dic3⋊C4—62no—
123C2×Dic3⋊C4—64no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—61no—
127C22×C3⋊C8C2×D311yescharacteristic
128C22×C3⋊C8C2×D311yescharacteristic
129C2×Dic12—34no—
130C2×Dic12—64no—
131C2×#204—34no—
132C2×#204—64no—
133#815—34no—
134#815—34no—
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—44no—
139C32×Q8—22no—
140C32×Q8—22no—
141C32×Q8—42no—
142C2×C32×C4—22no—
143C2×C32×C4—42no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—24no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—42no—
151C2×C3⋊Dic3C2×D414yes—
152#634—22no—
153#634—22no—
154#634—42no—
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⋊C8C2×D414yes—
164C3×C3⋊C8C2×D414yes—
165C22×Q16—31no—
166C22×Q16—91no—
167C22×SD16—31no—
168C22×SD16—91no—
169C2×C4⋊Q8—91no—
170C2×#124—91no—
171#497—98no—
172C2×#97—91no—
173C24×C3—61no—
174C23×D3—21no—
175C2×C3×Q8—22no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
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—42no—
185C2×C3×Q8—42no—
186C2×C3×Q8—61no—
187C2×C3×Q8—62no—
188C2×C3×Q8—62no—
189C2×C3×Q8C22×D312yes—
190C2×C3×Q8C22×D312yes—
191C2×C3×D4—32no—
192C2×C3×D4—62no—
193C2×C3×D4—61no—
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—32no—
204C22×Dic3—32no—
205C22×Dic3—62no—
206C22×Dic3—62no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C2×D12—22no—
210C2×D12—22no—
211C2×D12—21no—
212C2×D12C22×D312yes—
213C2×Dic6—22no—
214C2×Dic6—22no—
215C2×Dic6—21no—
216C2×Dic6—32no—
217C2×Dic6—32no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—122no—
227C2×Dic6—122no—
228C2×Dic6C22×D312yes—
229C3×Q16—68no—
230C3×SD16—68no—
231C2×C3×C8—34no—
232C2×C3×C8—34no—
233C2×C3×C8—32no—
234C2×C3×C8—32no—
235#217—68no—
236#216—28no—
237#216—68no—
238#215—28no—
239#214—68no—
240(C2×D3)⋊C4—68no—
241Dic3⋊C4—68no—
242Dic3⋊C4—68no—
243Dic3⋊C4—616no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—32no—
247C4×Dic3—32no—
248C4×Dic3—62no—
249C4×Dic3—62no—
250C2×C3⋊C8#6714yes—
251C2×C3⋊C8#6714yes—
252C2×C3⋊C8C22×D312yes—
253C2×C3⋊C8C22×D312yes—
254Dic12—68no—
255#204—68no—
256C22×C32#12712yes—
257C22×C32#13714yes—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—42no—
260C2×C3×D3—44no—
261C2×C3×D3—84no—
262C32×C4—42no—
263C32×C4#12712yes—
264C32×C4C22×D411yescharacteristic
265C32×C4C22×D411yescharacteristic
266C3⋊Dic3—24no—
267C3⋊Dic3—42no—
268C3×Dic3—42no—
269C22×Q8—31no—
270C22×Q8—91no—
271C22×Q8D3211yescharacteristic
272C22×D4—31no—
273C2×Q16—34no—
274C2×Q16—64no—
275C2×Q16—94no—
276C2×Q16—184no—
277C2×SD16—34no—
278C2×SD16—64no—
279C2×SD16—94no—
280C2×SD16—184no—
281C22×C8—31no—
282C22×C8—31no—
283C4⋊Q8—94no—
284C4⋊Q8—182no—
285#124—94no—
286#124—182no—
287C2×C4⋊C4—182no—
288C2×C22⋊C4—182no—
289C2×C42—91no—
290#97—94no—
291C23×C3—21no—
292C23×C3—62no—
293C23×C3—124no—
294C23×C3—122no—
295C23×C3D3×D411yescharacteristic
296C23×C3D3×D411yescharacteristic
297C22×D3—22no—
298C22×D3—44no—
299C22×D3—42no—
300C3×Q8—22no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—42no—
305C3×Q8—42no—
306C3×Q8—44no—
307C3×Q8—42no—
308C3×Q8—42no—
309C3×Q8—62no—
310C3×Q8—62no—
311C3×Q8—122no—
312C3×D4—62no—
313C3×D4—62no—
314C3×D4—122no—
315C2×C3×C4—24no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—44no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4D3×D412yes—
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4C2×#6712yes—
332C2×C3×C4C2×#6712yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—34no—
337C2×Dic3—34no—
338C2×Dic3—42no—
339C2×Dic3—64no—
340C2×Dic3—68no—
341C2×Dic3—64no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—124no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349D12—22no—
350D12—22no—
351D12—42no—
352Dic6—22no—
353Dic6—22no—
354Dic6—42no—
355Dic6—62no—
356Dic6—62no—
357Dic6—62no—
358Dic6—62no—
359Dic6—122no—
360Dic6—122no—
361Dic6—124no—
362Dic6—122no—
363Dic6—122no—
364C3×C8—34no—
365C3×C8—34no—
366C3⋊C8C2×#6714yes—
367C3⋊C8C2×#6714yes—
368C2×C32#49714yescomplemented
369C2×C32C2×#12711yescharacteristic
370C2×C32C2×#13712yes—
371C3×D3—82no—
372C24—61no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—32no—
377C2×Q8—61no—
378C2×Q8—62no—
379C2×Q8—62no—
380C2×Q8—92no—
381C2×Q8—181no—
382C2×Q8—182no—
383C2×Q8—182no—
384C2×Q8C2×D3212yes—
385C2×D4—32no—
386C2×D4—62no—
387C2×D4—62no—
388C2×D4—61no—
389C22×C4—21no—
390C22×C4—61no—
391C22×C4—92no—
392C22×C4—181no—
393C22×C4C2×D3211yescharacteristic
394Q16—68no—
395Q16—188no—
396SD16—68no—
397SD16—188no—
398C2×C8—32no—
399C2×C8—32no—
400C2×C8—34no—
401C2×C8—34no—
402C4⋊C4—188no—
403C22⋊C4—188no—
404C42—92no—
405C42—92no—
406C22×C3—21no—
407C22×C3—24no—
408C22×C3—22no—
409C22×C3—124no—
410C22×C3—122no—
411C22×C3—244no—
412C22×C3#91514yes—
413C22×C3#91814yes—
414C22×C3#94012yes—
415C22×C3#94012yes—
416C22×C3C2×D3×D411yescharacteristic
417C22×C3C2×D3×D411yescharacteristic
418C2×D3—44no—
419C2×D3—42no—
420C2×D3—84no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—22no—
424C3×C4—44no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—122no—
428C3×C4#94012yes—
429C3×C4#94012yes—
430C3×C4C2×D3×D411yescharacteristic
431C3×C4C2×D3×D411yescharacteristic
432C3×C4C22×#6711yescharacteristic
433C3×C4C22×#6711yescharacteristic
434Dic3—42no—
435Dic3—68no—
436Dic3—64no—
437Dic3—64no—
438Dic3—124no—
439Dic3—122no—
440Dic3—122no—
441C32C2×#49711yescharacteristic, complemented, Sylow
442C23—62no—
443C23—124no—
444C23—122no—
445C23#381111yescharacteristic
446Q8—22no—
447Q8—22no—
448Q8—42no—
449Q8—62no—
450Q8—62no—
451Q8—122no—
452Q8—182no—
453Q8—182no—
454Q8—362no—
455D4—62no—
456D4—62no—
457D4—122no—
458C2×C4—22no—
459C2×C4—42no—
460C2×C4—62no—
461C2×C4—94no—
462C2×C4—122no—
463C2×C4—184no—
464C2×C4—182no—
465C2×C4—362no—
466C2×C4D3×#6712yes—
467C2×C4D3×#6712yes—
468C2×C4#381111yescharacteristic
469C2×C4C22×D3211yescharacteristic
470C8—34no—
471C8—34no—
472C2×C3—22no—
473C2×C3—24no—
474C2×C3—21no—
475C2×C3—242no—
476C2×C3#516714yescomplemented
477C2×C3#519014yescomplemented
478C2×C3C2×#91512yes—
479C2×C3C2×#91812yes—
480C2×C3C2×#94011yescharacteristic
481C2×C3C2×#94011yescharacteristic
482D3—82no—
483C22—124no—
484C22—122no—
485C22—244no—
486C22#6395114yes—
487C22#6397912yes—
488C22C2×#381111yescharacteristic
489C4—42no—
490C4—122no—
491C4—184no—
492C4—362no—
493C4#6397912yes—
494C4C2×D3×#6711yescharacteristic
495C4C2×D3×#6711yescharacteristic
496C3—21no—
497C3C2×#516711yescharacteristic, complemented
498C3C2×#519011yescharacteristic, complemented
499C2—242no—
500C2#1059161114yesdirect product factor
501C2C2×#6395112yes—
502C2C2×#6397911yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
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
1. C2×#64153C2semidirect
2. C22×C3×#216C2semidirect
5. C22×#3719C2semidirect
7. #10591611C2direct (N × H)
8. C2×#63555C2semidirect
16. #64153C22semidirect
20. C2×C3×#216C22semidirect
29. C2×#3719C22semidirect
32. #63555C22semidirect
40. C22×#216D3semidirect
113. C2×#216C2×D3semidirect
368. C2×C32#497semidirect
441. C32C2×#497semidirect
476. C2×C3#5167semidirect
477. C2×C3#5190semidirect
497. C3C2×#5167semidirect
498. C3C2×#5190semidirect
500. C2#10591611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C22×C3×#2162
C22×C3×#2152
C2×#638632
C22×#37192
C22×#37162
#105916112
C2×#635552
C2×#51903
C2×#51673