Finite Group Databasebeta

← C2×#10591609 #11874257

Subgroups — C2×#10591609 #11874257

Order 1152.

1333 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic, complemented
3C22×C3×#216C211yesmaximal, characteristic, complemented
4C2×#63864C211yesmaximal, characteristic, complemented
5C22×#3715C211yesmaximal, characteristic, complemented
6C22×#3714C211yesmaximal, characteristic
7#10591609C218yesmaximal, direct product factor
8C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
9C2×#5191—31nomaximal
10C2×#5059—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3755—24no—
16C2×#3755C2214yescomplemented
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#947—22no—
19C3×#947C2214yescomplemented
20C2×C3×#216—24no—
21C2×C3×#216C2214yescomplemented
22C2×C3×(C2×D3)⋊C4—22no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—22no—
26#63864—22no—
27#63864C2214yescomplemented
28C2×#3715—24no—
29C2×#3715C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yes—
32Dic3×C3⋊C8C2214yescomplemented
33C22×C3×Q16—31no—
34C2×C3×#124—31no—
35C2×#947—31no—
36C2×#947D311yescharacteristic, complemented
37C22×#216D311yescharacteristic, complemented
38C22×#215—31no—
39C22×#215—31no—
40C22×#215—31no—
41C22×#215—61no—
42C22×#214—31no—
43C22×#213—31no—
44C22×D24—31no—
45C2×#875—31no—
46#5191—38no—
47C2×C8×Dic3—31no—
48#5059—38no—
49C2×C4×C3⋊C8—31no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—22no—
54C2×C32×Q8—22no—
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
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#3755—28no—
73C2×C3⋊(C3⋊C8)D414yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#216—28no—
76C3×(C2×D3)⋊C4—28no—
77C3×C4×Dic3D412yes—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8D414yes—
80C2×C3×C3⋊C8C2312yes—
81#3722—28no—
82#3715—28no—
83#3714—28no—
84C2×#495—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8—31no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×D4—31no—
90C22×D12—31no—
91C22×D12—31no—
92C22×D12—61no—
93C22×D12C2×D311yescharacteristic
94C22×Dic6C2×D311yescharacteristic
95C2×C3×Q16—34no—
96C2×C3×Q16—64no—
97C22×C3×C8—31no—
98C3×#124—34no—
99C3×#124—62no—
100C2×C3×C22⋊C4—62no—
101C2×C3×C42—31no—
102#947—22no—
103#947—34no—
104#947—62no—
105#947C2×D314yescomplemented
106C2×#216—24no—
107C2×#216C2×D314yescomplemented
108C2×#215—34no—
109C2×#215—34no—
110C2×#215—34no—
111C2×#215—64no—
112C2×#215—64no—
113C2×#215—64no—
114C2×#215—64no—
115C2×#215—68no—
116C2×#214—34no—
117C2×#214—64no—
118C2×#213—34no—
119C2×#213—64no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—62no—
122C2×(C2×D3)⋊C4—62no—
123C2×C4×Dic3C2×D311yescharacteristic
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127C22×C3⋊C8C2×D311yescharacteristic
128C2×D24—34no—
129C2×D24—64no—
130#875—34no—
131#875—62no—
132C8×Dic3—34no—
133C4×C3⋊C8—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—44no—
138C22×C3×D3—22no—
139C22×C3×D3—42no—
140C22×C3×D3—44no—
141C32×Q8—22no—
142C32×Q8—22no—
143C32×Q8—42no—
144C2×C32×C4—22no—
145C2×C32×C4—42no—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2411yescharacteristic
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)—42no—
153C2×C3×Dic3—24no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C2×D414yes—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—42no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163C3⋊(C3⋊C8)C2×D414yes—
164C3×C3⋊C8C2×D414yes—
165C22×Q16—31no—
166C22×SD16—91no—
167C22×SD16—91no—
168C22×D8—91no—
169C2×#124—31no—
170C2×#124—91no—
171#495—98no—
172C2×C4×C8—91no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—121no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—24no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—22no—
186C2×C3×Q8—32no—
187C2×C3×Q8—41no—
188C2×C3×Q8—42no—
189C2×C3×Q8—61no—
190C2×C3×Q8—62no—
191C2×C3×Q8—62no—
192C2×C3×Q8C22×D312yes—
193C2×C3×Q8C22×D312yes—
194C2×C3×D4—32no—
195C2×C3×D4—62no—
196C2×C3×D4—61no—
197C2×C3×D4—62no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—32no—
202C22×C3×C4—41no—
203C22×C3×C4—61no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×Dic3—21no—
207C22×Dic3#6712yes—
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—21no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—62no—
214C2×D12—64no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—122no—
222C2×D12—121no—
223C2×D12C22×D312yes—
224C2×Dic6—22no—
225C2×Dic6—22no—
226C2×Dic6—21no—
227C2×Dic6C22×D312yes—
228C3×Q16—68no—
229C2×C3×C8—34no—
230C2×C3×C8—32no—
231C3×C22⋊C4—68no—
232C3×C42—32no—
233C3×C42—32no—
234#216—28no—
235#215—68no—
236#215—68no—
237#215—68no—
238#215—616no—
239#214—68no—
240#213—68no—
241(C2×D3)⋊C4—28no—
242(C2×D3)⋊C4—68no—
243(C2×D3)⋊C4—68no—
244C4×Dic3#6712yes—
245C4×Dic3C22×D312yes—
246C2×C3⋊C8—34no—
247C2×C3⋊C8—34no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8#6714yes—
253C2×C3⋊C8C22×D312yes—
254D24—68no—
255C22×C32#12712yes—
256C22×C32#13514yes—
257C22×C32C22×D411yescharacteristic
258C2×C3⋊D3—42no—
259C2×C3⋊D3—44no—
260C2×C3⋊D3—84no—
261C2×C3×D3—42no—
262C2×C3×D3—44no—
263C2×C3×D3—84no—
264C32×C4—42no—
265C32×C4#12712yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C22×D411yescharacteristic
268C3×Dic3—24no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×Q8D3211yescharacteristic
272C22×D4—31no—
273C22×D4—91no—
274C2×Q16—34no—
275C2×Q16—64no—
276C2×SD16—94no—
277C2×SD16—94no—
278C2×SD16—184no—
279C2×SD16—184no—
280C2×D8—94no—
281C2×D8—184no—
282C22×C8—31no—
283C22×C8—91no—
284#124—34no—
285#124—62no—
286#124—94no—
287#124—182no—
288C2×C22⋊C4—62no—
289C2×C22⋊C4—182no—
290C2×C42—31no—
291C4×C8—94no—
292C23×C3—21no—
293C23×C3—62no—
294C23×C3—124no—
295C23×C3—122no—
296C23×C3D3×D411yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C22×D3—22no—
299C22×D3—42no—
300C22×D3—44no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—122no—
304C22×D3—124no—
305C22×D3—124no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—124no—
309C22×D3—244no—
310C3×Q8—24no—
311C3×Q8—22no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—42no—
316C3×Q8—44no—
317C3×Q8—42no—
318C3×Q8—42no—
319C3×Q8—62no—
320C3×Q8—62no—
321C3×Q8—122no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—122no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—34no—
332C2×C3×C4—42no—
333C2×C3×C4—44no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—64no—
337C2×C3×C4—62no—
338C2×C3×C4—122no—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D412yes—
341C2×C3×C4D3×D412yes—
342C2×C3×C4D3×D412yes—
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6712yes—
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×Dic3—24no—
348C2×Dic3—22no—
349C2×Dic3—42no—
350C2×Dic3C2×#6714yes—
351D12—22no—
352D12—22no—
353D12—42no—
354D12—64no—
355D12—62no—
356D12—62no—
357D12—62no—
358D12—62no—
359D12—122no—
360D12—124no—
361D12—122no—
362D12—122no—
363Dic6—22no—
364Dic6—22no—
365Dic6—42no—
366C3×C8—34no—
367C3⋊C8—34no—
368C3⋊C8—34no—
369C3⋊C8—64no—
370C3⋊C8C2×#6714yes—
371C2×C32#49514yescomplemented
372C2×C32C2×#12711yescharacteristic
373C2×C32C2×#13512yes—
374C3⋊D3—82no—
375C3×D3—82no—
376C24—61no—
377C24—181no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—32no—
382C2×Q8—61no—
383C2×Q8—62no—
384C2×Q8—62no—
385C2×Q8C2×D3212yes—
386C2×D4—32no—
387C2×D4—62no—
388C2×D4—61no—
389C2×D4—62no—
390C2×D4—92no—
391C2×D4—182no—
392C2×D4—181no—
393C2×D4—182no—
394C22×C4—21no—
395C22×C4—32no—
396C22×C4—61no—
397C22×C4C2×D3211yescharacteristic
398Q16—68no—
399SD16—188no—
400SD16—188no—
401D8—188no—
402C2×C8—32no—
403C2×C8—34no—
404C2×C8—92no—
405C2×C8—94no—
406C22⋊C4—68no—
407C22⋊C4—188no—
408C42—32no—
409C42—32no—
410C22×C3—21no—
411C22×C3—24no—
412C22×C3—22no—
413C22×C3—124no—
414C22×C3—122no—
415C22×C3—244no—
416C22×C3#91914yes—
417C22×C3#94012yes—
418C22×C3#94012yes—
419C22×C3#95014yes—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C22×#6711yescharacteristic
422C2×D3—42no—
423C2×D3—44no—
424C2×D3—84no—
425C2×D3—124no—
426C2×D3—124no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—124no—
430C2×D3—244no—
431C2×D3—248no—
432C2×D3—244no—
433C2×D3—244no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—44no—
438C3×C4—42no—
439C3×C4—42no—
440C3×C4—64no—
441C3×C4—122no—
442C3×C4#94012yes—
443C3×C4#94012yes—
444C3×C4C2×D3×D411yescharacteristic
445C3×C4C2×D3×D411yescharacteristic
446C3×C4C2×D3×D411yescharacteristic
447C3×C4C22×#6711yescharacteristic
448Dic3—24no—
449Dic3—42no—
450C32C2×#49511yescharacteristic, complemented, Sylow
451C23—62no—
452C23—124no—
453C23—122no—
454C23—182no—
455C23—364no—
456C23—362no—
457C23D3×#6711yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—42no—
461Q8—62no—
462Q8—62no—
463Q8—122no—
464D4—62no—
465D4—62no—
466D4—122no—
467D4—182no—
468D4—182no—
469D4—362no—
470C2×C4—22no—
471C2×C4—34no—
472C2×C4—42no—
473C2×C4—64no—
474C2×C4—62no—
475C2×C4—122no—
476C2×C4D3×#6712yes—
477C2×C4D3×#6711yescharacteristic
478C2×C4#381112yes—
479C2×C4C22×D3211yescharacteristic
480C8—34no—
481C8—94no—
482C2×C3—22no—
483C2×C3—24no—
484C2×C3—21no—
485C2×C3—242no—
486C2×C3#505914yescomplemented
487C2×C3#519114yescomplemented
488C2×C3C2×#91912yes—
489C2×C3C2×#94011yescharacteristic
490C2×C3C2×#94011yescharacteristic
491C2×C3C2×#95012yes—
492D3—82no—
493D3—244no—
494D3—242no—
495D3—242no—
496C22—124no—
497C22—122no—
498C22—244no—
499C22—364no—
500C22—362no—
501C22—724no—
502C22#6394914yes—
503C22#6397912yes—
504C22C2×D3×#6711yescharacteristic
505C4—42no—
506C4—64no—
507C4—122no—
508C4#6397912yes—
509C4C2×D3×#6711yescharacteristic
510C4C2×#381111yescharacteristic
511C3—21no—
512C3C2×#505911yescharacteristic, complemented
513C3C2×#519111yescharacteristic, complemented
514C2—242no—
515C2—722no—
516C2#1059160914yesdirect product factor
517C2C2×#6394912yes—
518C2C2×#6397911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
hypercenterC22×Q8D32
hypocenterC32C2×#495
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. C22×#3755C2semidirect
2. C2×C3×#947C2semidirect
3. C22×C3×#216C2semidirect
4. C2×#63864C2semidirect
5. C22×#3715C2semidirect
7. #10591609C2direct (N × H)
8. C2×Dic3×C3⋊C8C2semidirect
16. C2×#3755C22semidirect
19. C3×#947C22semidirect
21. C2×C3×#216C22semidirect
27. #63864C22semidirect
29. C2×#3715C22semidirect
32. Dic3×C3⋊C8C22semidirect
36. C2×#947D3semidirect
37. C22×#216D3semidirect
105. #947C2×D3semidirect
107. C2×#216C2×D3semidirect
371. C2×C32#495semidirect
450. C32C2×#495semidirect
486. C2×C3#5059semidirect
487. C2×C3#5191semidirect
512. C3C2×#5059semidirect
513. C3C2×#5191semidirect
516. C2#10591609direct (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×#9472
C22×C3×#2162
C2×#638642
C22×#37152
C22×#37142
#105916092
C2×Dic3×C3⋊C82
C2×#51913
C2×#50593