Finite Group Databasebeta

← C2×#10591606 #11874259

Subgroups — C2×#10591606 #11874259

Order 1152.

1313 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3756C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic, complemented
3C22×C3×#215C211yesmaximal, characteristic, complemented
4C2×#63860C211yesmaximal, characteristic, complemented
5C22×#3716C211yesmaximal, characteristic, complemented
6C22×#3713C211yesmaximal, characteristic
7#10591606C218yesmaximal, direct product factor
8C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
9C2×#5168—31nomaximal
10C2×#5059—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×#3756—24no—
16C2×#3756C2214yescomplemented
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#947—22no—
19C3×#947C2214yescomplemented
20C2×C3×#215—24no—
21C2×C3×#215C2214yescomplemented
22C2×C3×(C2×D3)⋊C4—22no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—22no—
26#63860—22no—
27#63860C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yescomplemented
30C2×#3713—24no—
31C2×#3713C2214yes—
32Dic3×C3⋊C8C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×#124—31no—
35C2×#947D311yescharacteristic, complemented
36C22×#216—31no—
37C22×#216—31no—
38C22×#216—61no—
39C22×#215D311yescharacteristic, complemented
40C2×#936—31no—
41C22×#214—31no—
42C22×#213—31no—
43C22×#213—31no—
44C22×#204—31no—
45C2×#875—31no—
46#5168—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
58C22×C3⋊Dic3—21no—
59C2×#634—22no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634C2312yes—
63C22×C3×Dic3D412yes—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—22no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×D12C2312yes—
72#3756—28no—
73C2×C3⋊(C3⋊C8)D414yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#215—28no—
76C3×(C2×D3)⋊C4—28no—
77C3×C4×Dic3D412yes—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8D414yes—
80C2×C3×C3⋊C8C2312yes—
81(C2×D3)⋊Dic3—28no—
82#3716—28no—
83#3713—28no—
84C2×#495—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×D4—31no—
89C22×C3×D4—31no—
90C22×D12C2×D311yescharacteristic
91C22×D12C2×D311yescharacteristic
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C22×C3×C8—31no—
98C3×#124—34no—
99C3×#124—62no—
100C2×C3×C22⋊C4—62no—
101C2×C3×C42—31no—
102C2×#217—62no—
103#947—22no—
104#947C2×D314yescomplemented
105C2×#216—34no—
106C2×#216—34no—
107C2×#216—64no—
108C2×#216—64no—
109C2×#216—64no—
110C2×#216—68no—
111C2×#215—24no—
112C2×#215C2×D314yescomplemented
113#936—34no—
114#936—62no—
115C2×#214—34no—
116C2×#214—64no—
117C2×#213—34no—
118C2×#213—34no—
119C2×#213—64no—
120C2×#213—64no—
121C2×(C2×D3)⋊C4—22no—
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×#204—34no—
129C2×#204—64no—
130#875—34no—
131#875—62no—
132C8×Dic3—34no—
133C4×C3⋊C8—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—44no—
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
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—42no—
152#634—22no—
153#634—22no—
154#634—42no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3C2×D414yes—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—42no—
162C3×D12—42no—
163C3⋊(C3⋊C8)C2×D414yes—
164C3×C3⋊C8C2×D414yes—
165C22×Q16—91no—
166C22×SD16—31no—
167C22×SD16—91no—
168C22×D8—91no—
169C2×#124—31no—
170C2×#124—91no—
171#495—98no—
172C2×C4×C8—91no—
173C24×C3—61no—
174C24×C3—61no—
175C23×D3—21no—
176C23×D3—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—24no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—41no—
186C2×C3×Q8—42no—
187C2×C3×Q8C22×D312yes—
188C2×C3×Q8C22×D312yes—
189C2×C3×D4—32no—
190C2×C3×D4—32no—
191C2×C3×D4—62no—
192C2×C3×D4—62no—
193C2×C3×D4—62no—
194C2×C3×D4—61no—
195C2×C3×D4—62no—
196C2×C3×D4—61no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—32no—
201C22×C3×C4—41no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3—121no—
207C22×Dic3#6712yes—
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—22no—
211C2×D12—22no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12C22×D312yes—
215C2×D12C22×D312yes—
216C2×Dic6—32no—
217C2×Dic6—32no—
218C2×Dic6—62no—
219C2×Dic6—64no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—121no—
227C2×Dic6—122no—
228C3×SD16—68no—
229C2×C3×C8—34no—
230C2×C3×C8—32no—
231C3×C22⋊C4—68no—
232C3×C42—32no—
233C3×C42—32no—
234#217—68no—
235#216—68no—
236#216—68no—
237#216—616no—
238#215—28no—
239#214—68no—
240#213—68no—
241#213—68no—
242(C2×D3)⋊C4—28no—
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—
254#204—68no—
255C22×C32#12712yes—
256C22×C32#13514yes—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—44no—
261C2×C3×D3—44no—
262C2×C3×D3—84no—
263C2×C3×D3—84no—
264C32×C4—42no—
265C32×C4#12712yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C22×D411yescharacteristic
268C3⋊Dic3—42no—
269C3×Dic3—24no—
270C22×Q8—91no—
271C22×Q8D3211yescharacteristic
272C22×D4—31no—
273C22×D4—31no—
274C2×Q16—94no—
275C2×Q16—184no—
276C2×SD16—34no—
277C2×SD16—64no—
278C2×SD16—94no—
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—62no—
295C23×C3—124no—
296C23×C3—122no—
297C23×C3—122no—
298C23×C3—124no—
299C23×C3D3×D411yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C22×D3—22no—
302C22×D3—22no—
303C22×D3—44no—
304C22×D3—42no—
305C22×D3—42no—
306C22×D3—44no—
307C3×Q8—24no—
308C3×Q8—22no—
309C3×Q8—22no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—42no—
313C3×Q8—44no—
314C3×Q8—42no—
315C3×Q8—42no—
316C3×D4—62no—
317C3×D4—62no—
318C3×D4—62no—
319C3×D4—62no—
320C3×D4—122no—
321C3×D4—122no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—34no—
329C2×C3×C4—42no—
330C2×C3×C4—44no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—64no—
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D412yes—
336C2×C3×C4D3×D412yes—
337C2×C3×C4D3×D412yes—
338C2×C3×C4C2×#6711yescharacteristic
339C2×C3×C4C2×#6712yes—
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—24no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—122no—
346C2×Dic3—124no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3C2×#6714yes—
350D12—22no—
351D12—22no—
352D12—22no—
353D12—22no—
354D12—42no—
355D12—42no—
356Dic6—64no—
357Dic6—62no—
358Dic6—62no—
359Dic6—62no—
360Dic6—62no—
361Dic6—122no—
362Dic6—124no—
363Dic6—122no—
364Dic6—122no—
365C3×C8—34no—
366C3⋊C8—34no—
367C3⋊C8—34no—
368C3⋊C8—64no—
369C3⋊C8C2×#6714yes—
370C2×C32#49514yescomplemented
371C2×C32C2×#12711yescharacteristic
372C2×C32C2×#13512yes—
373C3×D3—82no—
374C3×D3—82no—
375C24—61no—
376C24—61no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—92no—
381C2×Q8—181no—
382C2×Q8—182no—
383C2×Q8—182no—
384C2×Q8C2×D3212yes—
385C2×D4—32no—
386C2×D4—32no—
387C2×D4—62no—
388C2×D4—62no—
389C2×D4—61no—
390C2×D4—61no—
391C2×D4—62no—
392C2×D4—62no—
393C22×C4—21no—
394C22×C4—32no—
395C22×C4—181no—
396C22×C4C2×D3211yescharacteristic
397Q16—188no—
398SD16—68no—
399SD16—188no—
400D8—188no—
401C2×C8—32no—
402C2×C8—34no—
403C2×C8—92no—
404C2×C8—94no—
405C22⋊C4—68no—
406C22⋊C4—188no—
407C42—32no—
408C42—32no—
409C22×C3—21no—
410C22×C3—24no—
411C22×C3—22no—
412C22×C3—124no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3—124no—
416C22×C3—244no—
417C22×C3—244no—
418C22×C3#91614yes—
419C22×C3#94012yes—
420C22×C3#94012yes—
421C22×C3#95014yes—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C22×#6711yescharacteristic
424C2×D3—44no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—44no—
428C2×D3—84no—
429C2×D3—84no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—44no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—64no—
437C3×C4#94012yes—
438C3×C4#94012yes—
439C3×C4C2×D3×D411yescharacteristic
440C3×C4C2×D3×D411yescharacteristic
441C3×C4C2×D3×D411yescharacteristic
442C3×C4C22×#6711yescharacteristic
443Dic3—24no—
444Dic3—124no—
445Dic3—122no—
446Dic3—122no—
447C32C2×#49511yescharacteristic, complemented, Sylow
448C23—62no—
449C23—62no—
450C23—124no—
451C23—124no—
452C23—122no—
453C23—122no—
454C23D3×#6711yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—42no—
458Q8—182no—
459Q8—182no—
460Q8—362no—
461D4—62no—
462D4—62no—
463D4—62no—
464D4—62no—
465D4—122no—
466D4—122no—
467C2×C4—22no—
468C2×C4—34no—
469C2×C4—42no—
470C2×C4—64no—
471C2×C4—182no—
472C2×C4—362no—
473C2×C4D3×#6712yes—
474C2×C4D3×#6711yescharacteristic
475C2×C4#381112yes—
476C2×C4C22×D3211yescharacteristic
477C8—34no—
478C8—94no—
479C2×C3—22no—
480C2×C3—24no—
481C2×C3—21no—
482C2×C3—242no—
483C2×C3—242no—
484C2×C3#505914yescomplemented
485C2×C3#516814yescomplemented
486C2×C3C2×#91612yes—
487C2×C3C2×#94011yescharacteristic
488C2×C3C2×#94011yescharacteristic
489C2×C3C2×#95012yes—
490D3—82no—
491D3—82no—
492C22—124no—
493C22—124no—
494C22—122no—
495C22—122no—
496C22—244no—
497C22—244no—
498C22#6394714yes—
499C22#6397912yes—
500C22C2×D3×#6711yescharacteristic
501C4—42no—
502C4—64no—
503C4—362no—
504C4#6397912yes—
505C4C2×D3×#6711yescharacteristic
506C4C2×#381111yescharacteristic
507C3—21no—
508C3C2×#505911yescharacteristic, complemented
509C3C2×#516811yescharacteristic, complemented
510C2—242no—
511C2—242no—
512C2#1059160614yesdirect product factor
513C2C2×#6394712yes—
514C2C2×#6397911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
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×#3756C2semidirect
2. C2×C3×#947C2semidirect
3. C22×C3×#215C2semidirect
4. C2×#63860C2semidirect
5. C22×#3716C2semidirect
7. #10591606C2direct (N × H)
8. C2×Dic3×C3⋊C8C2semidirect
16. C2×#3756C22semidirect
19. C3×#947C22semidirect
21. C2×C3×#215C22semidirect
27. #63860C22semidirect
29. C2×#3716C22semidirect
32. Dic3×C3⋊C8C22semidirect
35. C2×#947D3semidirect
39. C22×#215D3semidirect
104. #947C2×D3semidirect
112. C2×#215C2×D3semidirect
370. C2×C32#495semidirect
447. C32C2×#495semidirect
484. C2×C3#5059semidirect
485. C2×C3#5168semidirect
508. C3C2×#5059semidirect
509. C3C2×#5168semidirect
512. C2#10591606direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37562
C2×C3×#9472
C22×C3×#2152
C2×#638602
C22×#37162
C22×#37132
#105916062
C2×Dic3×C3⋊C82
C2×#51683
C2×#50593