Finite Group Databasebeta

← C2×#10591502 #11866917

Subgroups — C2×#10591502 #11866917

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic, complemented
4C22×#3711C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6#10591502C218yesmaximal, direct product factor
7C2×#63575C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C2×#5174—31nomaximal
10C2×#5042—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#217—21no—
18C3×#938—22no—
19C3×#938C2214yes—
20C2×C3×#214—24no—
21C2×C3×#214C2214yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3724—21no—
25C2×(C2×D3)⋊Dic3—21no—
26#63856—22no—
27#63856C2214yescomplemented
28C2×#3711—24no—
29C2×#3711C2214yescomplemented
30#63659C2214yescomplemented
31#63575C2214yescomplemented
32#63565C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×#121—31no—
35C2×#946—31no—
36C2×#938D311yescharacteristic
37C22×#214D311yescharacteristic, complemented
38C2×#924—31no—
39C22×#208—31no—
40C22×ΓL(1,𝔽25)—31no—
41C2×#835—31no—
42C2×#832—31no—
43C2×#832—31no—
44C2×#832—61no—
45#5174—38no—
46C2×#818—31no—
47#5042—38no—
48C2×#810—31no—
49C2×#807—31no—
50C24×C32—21no—
51C23×C3×D3D411yescharacteristic
52C2×C32×D4—22no—
53C2×C32×D4—21no—
54C2×C32×D4—22no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×C3×#67—24no—
59C2×C3×#67—44no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2312yes—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#217—24no—
76C3×#214—28no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C2×C3×C3⋊C8D414yescomplemented
80C2×C3×C3⋊C8C2312yes—
81#3724—24no—
82(C2×D3)⋊Dic3—24no—
83#3711—28no—
84C2×#468—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4—61no—
88C22×C3×D4C2×D311yescharacteristic
89C22×C3×D4C2×D311yescharacteristic
90C23×C3×C4—31no—
91C22×#67—21no—
92C22×C4×D3C2×D311yescharacteristic
93C22×Dic6C2×D311yescharacteristic
94C2×C3×SD16—34no—
95C2×C3×SD16—64no—
96C22×C3×C8—31no—
97C3×#121—34no—
98C3×#121—62no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C22⋊C4—61no—
101C2×#217—21no—
102C2×#217—61no—
103#946—34no—
104#946—62no—
105#938—22no—
106#938C2×D314yes—
107C2×#214—24no—
108C2×#214C2×D314yescomplemented
109C2×(C2×D3)⋊C4—61no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—61no—
113C2×C4⋊Dic3C2×D311yescharacteristic
114#924—34no—
115#924—62no—
116C2×Dic3⋊C4—61no—
117C2×Dic3⋊C4—61no—
118C2×#208—34no—
119C2×#208—64no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—61no—
123C22×C3⋊C8C2×D311yescharacteristic
124C2×ΓL(1,𝔽25)—34no—
125C2×ΓL(1,𝔽25)—64no—
126#835—34no—
127#832—34no—
128#832—34no—
129#832—64no—
130#818—34no—
131#810—34no—
132#807—34no—
133C23×C32—22no—
134C23×C32—42no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32C2×D411yescharacteristic
138C22×C3×D3—22no—
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3C2×D412yes—
142C32×D4—22no—
143C32×D4—22no—
144C32×D4—42no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—42no—
151C3×#67—48no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3—42no—
157C2×C3×Dic3C2×D412yes—
158C3×C4×D3—24no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164C3⋊(C3⋊C8)—22no—
165C3×C3⋊C8C2×D414yescomplemented
166C22×SD16—31no—
167C22×M16—91no—
168C2×C22⋊Q8—91no—
169C2×#121—31no—
170#468—98no—
171C2×#107—91no—
172C2×#103—91no—
173C2×#102—91no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—31no—
177C24×C3—41no—
178C23×D3#6711yescharacteristic
179C2×C3×Q8—32no—
180C2×C3×Q8—61no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C2×C3×D4—24no—
184C2×C3×D4—22no—
185C2×C3×D4—21no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—42no—
192C2×C3×D4—41no—
193C2×C3×D4—64no—
194C2×C3×D4—124no—
195C2×C3×D4C22×D312yes—
196C2×C3×D4C22×D312yes—
197C22×C3×C4—21no—
198C22×C3×C4—31no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4—62no—
202C22×C3×C4—62no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—24no—
208C2×#67—44no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—121no—
214C22×Dic3#6711yescharacteristic
215C2×C4×D3—22no—
216C2×C4×D3—22no—
217C2×C4×D3#6712yes—
218C2×C4×D3C22×D312yes—
219C2×Dic6—22no—
220C2×Dic6—22no—
221C2×Dic6—21no—
222C2×Dic6C22×D312yes—
223C3×SD16—68no—
224C2×C3×C8—34no—
225C2×C3×C8—32no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—61no—
228C3×C22⋊C4—64no—
229#217—24no—
230#217—64no—
231#214—28no—
232(C2×D3)⋊C4—64no—
233C4⋊Dic3—21no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—62no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—121no—
240C4⋊Dic3C22×D312yes—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243#208—68no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—122no—
250C2×C3⋊C8#6714yescomplemented
251C2×C3⋊C8C22×D312yes—
252ΓL(1,𝔽25)—68no—
253C22×C32—42no—
254C22×C32—42no—
255C22×C32—42no—
256C22×C32—84no—
257C22×C32#12112yes—
258C22×C32AGL(1,ℤ/8)12yes—
259C22×C32#13712yes—
260C22×C32C22×D411yescharacteristic
261C2×C3×D3—22no—
262C2×C3×D3—22no—
263C2×C3×D3—22no—
264C2×C3×D3—44no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—42no—
269C3×Dic3—22no—
270C3×Dic3—42no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×D4—61no—
274C22×D4D3211yescharacteristic
275C23×C4—31no—
276C2×SD16—34no—
277C2×SD16—64no—
278C2×M16—94no—
279C2×M16—184no—
280C22×C8—31no—
281C22×C8—91no—
282C22⋊Q8—94no—
283C22⋊Q8—182no—
284#121—34no—
285#121—62no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—181no—
289C2×C22⋊C4—61no—
290C2×C22⋊C4—181no—
291#107—94no—
292#103—94no—
293#102—94no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—21no—
297C23×C3—32no—
298C23×C3—42no—
299C23×C3—44no—
300C23×C3—42no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3—62no—
309C23×C3—82no—
310C23×C3—82no—
311C23×C3D3×D411yescharacteristic
312C23×C3C2×#6711yescharacteristic
313C22×D3—22no—
314C22×D3—22no—
315C22×D3—22no—
316C22×D3C2×#6712yes—
317C3×Q8—62no—
318C3×Q8—62no—
319C3×Q8—122no—
320C3×D4—24no—
321C3×D4—22no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—42no—
326C3×D4—44no—
327C3×D4—42no—
328C3×D4—42no—
329C3×D4—128no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—32no—
335C2×C3×C4—62no—
336C2×C3×C4—64no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—122no—
342C2×C3×C4—122no—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D412yes—
345C2×C3×C4#23712yes—
346C2×C3×C4#23712yes—
347C2×C3×C4C2×#6712yes—
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351#67—48no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—42no—
356C2×Dic3—42no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—122no—
360C2×Dic3—122no—
361C2×Dic3—122no—
362C2×Dic3—242no—
363C2×Dic3C2×#6712yes—
364C4×D3—24no—
365C4×D3—22no—
366C4×D3—22no—
367Dic6—22no—
368Dic6—22no—
369Dic6—42no—
370C3×C8—34no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C3⋊C8—122no—
374C3⋊C8C2×#6714yescomplemented
375C2×C32—82no—
376C2×C32#46814yescomplemented
377C2×C32C2×#12111yescharacteristic
378C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
379C2×C32C2×#13711yescharacteristic
380C3×D3—42no—
381C24—21no—
382C24—31no—
383C2×Q8—32no—
384C2×Q8—61no—
385C2×Q8—62no—
386C2×Q8—62no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—64no—
391C2×D4—124no—
392C2×D4C2×D3212yes—
393C22×C4—31no—
394C22×C4—32no—
395C22×C4—32no—
396C22×C4—62no—
397C22×C4—62no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—181no—
401C22×C4C2×D3211yescharacteristic
402SD16—68no—
403M16—188no—
404C2×C8—32no—
405C2×C8—34no—
406C2×C8—92no—
407C2×C8—182no—
408C4⋊C4—32no—
409C4⋊C4—61no—
410C4⋊C4—92no—
411C4⋊C4—184no—
412C4⋊C4—181no—
413C22⋊C4—64no—
414C22⋊C4—184no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—44no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—62no—
427C22×C3—62no—
428C22×C3—62no—
429C22×C3—82no—
430C22×C3—82no—
431C22×C3—88no—
432C22×C3—84no—
433C22×C3—84no—
434C22×C3—124no—
435C22×C3#91412yes—
436C22×C3#91512yes—
437C22×C3#93212yes—
438C22×C3#93812yes—
439C22×C3#93912yes—
440C22×C3#95112yes—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C22×#6711yescharacteristic
443C2×D3—22no—
444C2×D3—22no—
445C2×D3—22no—
446C2×D3—44no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—62no—
451C3×C4—122no—
452C3×C4—122no—
453C3×C4#93812yes—
454C3×C4#93912yes—
455C3×C4C2×D3×D411yescharacteristic
456C3×C4C2×#23711yescharacteristic
457C3×C4C2×#23711yescharacteristic
458C3×C4C22×#6711yescharacteristic
459Dic3—22no—
460Dic3—42no—
461Dic3—42no—
462Dic3—122no—
463Dic3—122no—
464Dic3—242no—
465C32C2×#46811yescharacteristic, complemented, Sylow
466C23—22no—
467C23—32no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—62no—
472C23—62no—
473C23—62no—
474C23D3×#6711yescharacteristic
475Q8—62no—
476Q8—62no—
477Q8—122no—
478D4—22no—
479D4—22no—
480D4—42no—
481D4—128no—
482C2×C4—32no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—64no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—122no—
490C2×C4—122no—
491C2×C4—182no—
492C2×C4—362no—
493C2×C4#380512yes—
494C2×C4D3×#6712yes—
495C2×C4D3×#6711yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—34no—
498C8—182no—
499C2×C3—24no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—84no—
504C2×C3—82no—
505C2×C3—82no—
506C2×C3—122no—
507C2×C3#504214yescomplemented
508C2×C3#517414yescomplemented
509C2×C3C2×#91411yescharacteristic
510C2×C3C2×#91511yescharacteristic
511C2×C3C2×#93211yescharacteristic
512C2×C3C2×#93811yescharacteristic
513C2×C3C2×#93911yescharacteristic
514C2×C3C2×#95111yescharacteristic
515D3—42no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—62no—
520C22—62no—
521C22—62no—
522C22—84no—
523C22—124no—
524C22#6392912yes—
525C22#6393412yes—
526C22#6397012yes—
527C22C2×D3×#6711yescharacteristic
528C4—62no—
529C4—122no—
530C4—122no—
531C4—362no—
532C4#6397012yes—
533C4C2×#380511yescharacteristic
534C4C2×D3×#6711yescharacteristic
535C3—21no—
536C3C2×#504211yescharacteristic, complemented
537C3C2×#517411yescharacteristic, complemented
538C2—82no—
539C2—122no—
540C2#1059150214yesdirect product factor
541C2C2×#6392911yescharacteristic
542C2C2×#6393411yescharacteristic
543C2C2×#6397011yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32C2×#468
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. C2×#63856C2semidirect
4. C22×#3711C2semidirect
5. C2×#63659C2semidirect
6. #10591502C2direct (N × H)
7. C2×#63575C2semidirect
8. C2×#63565C2semidirect
21. C2×C3×#214C22semidirect
27. #63856C22semidirect
29. C2×#3711C22semidirect
30. #63659C22semidirect
31. #63575C22semidirect
32. #63565C22semidirect
37. C22×#214D3semidirect
79. C2×C3×C3⋊C8D4semidirect
108. C2×#214C2×D3semidirect
165. C3×C3⋊C8C2×D4semidirect
250. C2×C3⋊C8#67semidirect
374. C3⋊C8C2×#67semidirect
376. C2×C32#468semidirect
465. C32C2×#468semidirect
507. C2×C3#5042semidirect
508. C2×C3#5174semidirect
536. C3C2×#5042semidirect
537. C3C2×#5174semidirect
540. C2#10591502direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C22×C3×#2142
C2×#638562
C22×#37112
C2×#636592
#105915022
C2×#635752
C2×#635652
C2×#51743
C2×#50423