Finite Group Databasebeta

← C2×#10590610 #11857793

Subgroups — C2×#10590610 #11857793

Order 1152.

1685 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C2×C3×#892C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590610C218yesmaximal, direct product factor
9C2×#5002—31nomaximal
10C2×#4804—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#626—21no—
15C22×#624—21no—
16C2×#3799—22no—
17C2×#3799—24no—
18C2×#3799C418yescomplemented
19C2×#3799C2214yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#892—22no—
27C3×#892C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63636C2214yescomplemented
31C3×#810C2214yescomplemented
32#63565C2214yescomplemented
33#63564C2214yescomplemented
34C22×#239—31no—
35C22×#235—31no—
36C2×C3×#117—31no—
37C23×C3⋊C8—31no—
38C22×D3×C8—31no—
39C2×#892D311yescharacteristic, complemented
40C2×C3×#103—31no—
41C2×#835—31no—
42C2×#821—31no—
43#5002—38no—
44C2×#810—31no—
45C2×#810D311yescharacteristic, complemented
46C2×#809—31no—
47C2×#809—31no—
48C2×#809—31no—
49C2×#809—61no—
50#4804—38no—
51C23×C3⋊D3—21no—
52C23×C3×D3D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)C2×C414yes—
58C2×C4⋊(C3⋊D3)C2312yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C2×C3×C4×D3C2×C414yes—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3D414yes—
65C2×C3×C4×D3C2312yes—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6C2×C414yes—
69C2×C3×Dic6C2312yes—
70C2×#626—28no—
71C2×#626—24no—
72C2×#624—28no—
73C2×#624—24no—
74#3799—216no—
75#3799—28no—
76#3799C2×C4116yescomplemented
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C2×C3⋊(C3⋊C8)—22no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3—24no—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8C2312yes—
87D3×C3⋊C8—28no—
88C2×#416—91noSylow
89C22×C3×Q8—31no—
90C23×C3×C4—31no—
91C22×#67—61no—
92C2×#239—38no—
93C2×#239—34no—
94C2×#239—64no—
95C2×#239—62no—
96C2×#235—38no—
97C2×#235—34no—
98C2×#235—64no—
99C2×#235—62no—
100C22×D12—31no—
101C22×D12—31no—
102C22×D12—61no—
103C22×D12—61no—
104C22×C4×D3—61no—
105C22×C4×D3—61no—
106C22×C4×D3C2×D311yescharacteristic
107C22×Dic6C2×D311yescharacteristic
108C22×C3×C8—31no—
109C3×#117—34no—
110C3×#117—62no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4—61no—
116C2×C3×C42—61no—
117C2×(C2×D3)⋊C4—21no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×C4×Dic3—21no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—34no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8—64no—
125C22×C3⋊C8C2×D311yescharacteristic
126C2×D3×C8—34no—
127C2×D3×C8—64no—
128#892—22no—
129#892C2×D314yescomplemented
130C3×#103—34no—
131#835—34no—
132#821—34no—
133#810—34no—
134#810C2×D314yescomplemented
135#809—34no—
136#809—34no—
137#809—34no—
138#809—64no—
139C23×C32C2×D411yescharacteristic
140C22×C3⋊D3—24no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—42no—
143C22×C3⋊D3—42no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3C22⋊C414yes—
147C22×C3×D3C2×D412yes—
148C2×C32×C4—22no—
149C2×C32×C4—42no—
150C2×C32×C4C22×C412yes—
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2411yescharacteristic
154C4⋊(C3⋊D3)—24no—
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)C22×C414yes—
157C2×C3×Dic3—24no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3C22⋊C414yes—
162C2×C3×Dic3C2×D412yes—
163C3×C4×D3C22⋊C418yes—
164C3×C4×D3C22×C414yes—
165C3×C4×D3C2×D414yes—
166C3×Dic6—24no—
167C3×Dic6—22no—
168C3×Dic6C22×C414yes—
169#626—216no—
170#624—216no—
171C3⋊(C3⋊C8)—22no—
172C3×C3⋊C8—22no—
173C22×#41—91no—
174C23×C8—91no—
175C2×#117—31no—
176#416—98no—
177C2×#103—31no—
178C2×#103—91no—
179C2×#102—91no—
180C2×#102—91no—
181C24×C3—31no—
182C23×D3—61no—
183C23×D3—61no—
184C23×D3—121no—
185C23×D3#6711yescharacteristic
186C2×C3×Q8—34no—
187C2×C3×Q8—32no—
188C2×C3×Q8—62no—
189C2×C3×Q8—61no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—31no—
194C22×C3×C4—34no—
195C22×C3×C4—34no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—41no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—68no—
204C2×#67—64no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3#6711yescharacteristic
208#239—316no—
209#239—616no—
210#239—68no—
211#235—316no—
212#235—616no—
213#235—68no—
214C2×D12—34no—
215C2×D12—34no—
216C2×D12—32no—
217C2×D12—32no—
218C2×D12—62no—
219C2×D12—64no—
220C2×D12—68no—
221C2×D12—64no—
222C2×D12—62no—
223C2×D12—62no—
224C2×D12—61no—
225C2×D12—61no—
226C2×D12—122no—
227C2×D12—121no—
228C2×C4×D3—68no—
229C2×C4×D3—64no—
230C2×C4×D3—68no—
231C2×C4×D3—64no—
232C2×C4×D3C4×D314yes—
233C2×C4×D3D1214yes—
234C2×C4×D3#6712yes—
235C2×C4×D3C22×D312yes—
236C2×Dic6—22no—
237C2×Dic6—21no—
238C2×Dic6C4×D314yes—
239C2×Dic6C22×D312yes—
240C2×C3×C8—32no—
241C2×C3×C8—62no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—41no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D312yes—
249C3×C4⋊C4C22×D312yes—
250C3×C22⋊C4—64no—
251C3×C42—64no—
252(C2×D3)⋊C4—24no—
253C4⋊Dic3—21no—
254C4⋊Dic3C22×D312yes—
255C4×Dic3—24no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8—32no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8—68no—
261C2×C3⋊C8—62no—
262C2×C3⋊C8—62no—
263C2×C3⋊C8—122no—
264C2×C3⋊C8C22×D312yes—
265D3×C8—68no—
266C22×C32C2×C22⋊C412yes—
267C22×C32#13512yes—
268C22×C32#13512yes—
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—24no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—48no—
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—28no—
277C2×C3×D3C2×C22⋊C414yes—
278C32×C4—42no—
279C32×C4C2×C22⋊C412yes—
280C32×C4C23×C411yescharacteristic
281C32×C4C22×D411yescharacteristic
282C3×Dic3—24no—
283C3×Dic3—42no—
284C3×Dic3C2×C22⋊C414yes—
285C2×#41—94no—
286C2×#41—98no—
287C2×#41—184no—
288C2×#41—182no—
289C22×Q8—31no—
290C22×D4—91no—
291C22×D4—181no—
292C23×C4—31no—
293C23×C4—181no—
294C22×C8—31no—
295C22×C8—94no—
296C22×C8—91no—
297C22×C8—184no—
298#117—34no—
299#117—62no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4D3211yescharacteristic
302C2×C22⋊C4—61no—
303C2×C42—61no—
304#103—34no—
305#103—94no—
306#102—94no—
307#102—94no—
308C23×C3—21no—
309C23×C3—34no—
310C23×C3—32no—
311C23×C3—62no—
312C23×C3—62no—
313C23×C3D3×D411yescharacteristic
314C23×C3C2×#6711yescharacteristic
315C22×D3—22no—
316C22×D3—22no—
317C22×D3—64no—
318C22×D3—64no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—122no—
322C22×D3—124no—
323C22×D3—122no—
324C22×D3—122no—
325C22×D3—122no—
326C22×D3—122no—
327C22×D3—242no—
328C22×D3—242no—
329C22×D3(C2×D3)⋊C414yes—
330C22×D3C2×#6712yes—
331C3×Q8—34no—
332C3×Q8—64no—
333C3×Q8—62no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—34no—
341C2×C3×C4—32no—
342C2×C3×C4—38no—
343C2×C3×C4—34no—
344C2×C3×C4—34no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—64no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—82no—
352C2×C3×C4—122no—
353C2×C3×C4C2×C4×D312yes—
354C2×C3×C4C2×C4×D312yes—
355C2×C3×C4C2×D1212yes—
356C2×C3×C4D3×D412yes—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—616no—
362C2×Dic3—24no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—42no—
366C2×Dic3(C2×D3)⋊C414yes—
367C2×Dic3C2×#6712yes—
368D12—34no—
369D12—34no—
370D12—64no—
371D12—616no—
372D12—64no—
373D12—64no—
374D12—62no—
375D12—62no—
376D12—122no—
377D12—124no—
378C4×D3—616no—
379C4×D3—616no—
380C4×D3(C2×D3)⋊C418yes—
381C4×D3C2×C4×D314yes—
382C4×D3C2×D1214yes—
383Dic6—24no—
384Dic6—22no—
385Dic6C2×C4×D314yes—
386C3×C8—62no—
387C3⋊C8—22no—
388C3⋊C8—62no—
389C3⋊C8—62no—
390C3⋊C8—122no—
391C2×C32#41614yescomplemented
392C2×C32C22×C22⋊C411yescharacteristic
393C2×C32C2×#13511yescharacteristic
394C2×C32C2×#13511yescharacteristic
395C3⋊D3—44no—
396C3×D3—24no—
397C24—31no—
398C24—181no—
399#41—916no—
400#41—188no—
401#41—1816no—
402C2×Q8—32no—
403C2×Q8—34no—
404C2×Q8—62no—
405C2×Q8—61no—
406C2×D4—92no—
407C2×D4—94no—
408C2×D4—184no—
409C2×D4—188no—
410C2×D4—182no—
411C2×D4—181no—
412C22×C4—21no—
413C22×C4—31no—
414C22×C4—32no—
415C22×C4—34no—
416C22×C4—34no—
417C22×C4—32no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—184no—
421C22×C4—188no—
422C22×C4C2×D3211yescharacteristic
423C2×C8—32no—
424C2×C8—62no—
425C2×C8—92no—
426C2×C8—188no—
427C2×C8—182no—
428C4⋊C4—21no—
429C4⋊C4—32no—
430C4⋊C4—61no—
431C4⋊C4C2×D3212yes—
432C22⋊C4—64no—
433C42—64no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—34no—
439C22×C3—62no—
440C22×C3—62no—
441C22×C3—68no—
442C22×C3D3×C22⋊C412yes—
443C22×C3#91612yes—
444C22×C3#91912yes—
445C22×C3C2×(C2×D3)⋊C412yes—
446C22×C3#95012yes—
447C22×C3#95012yes—
448C22×C3C2×D3×D411yescharacteristic
449C22×C3C22×#6711yescharacteristic
450C2×D3—28no—
451C2×D3—22no—
452C2×D3—22no—
453C2×D3—64no—
454C2×D3—64no—
455C2×D3—124no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—128no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—128no—
462C2×D3—242no—
463C2×D3—242no—
464C2×D3—248no—
465C2×D3C2×(C2×D3)⋊C414yes—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—22no—
469C3×C4—34no—
470C3×C4—42no—
471C3×C4—42no—
472C3×C4—64no—
473C3×C4—82no—
474C3×C4—122no—
475C3×C4D3×C22⋊C412yes—
476C3×C4C2×(C2×D3)⋊C412yes—
477C3×C4C22×C4×D311yescharacteristic
478C3×C4C22×C4×D311yescharacteristic
479C3×C4C22×D1211yescharacteristic
480C3×C4C2×D3×D411yescharacteristic
481Dic3—24no—
482Dic3—42no—
483Dic3C2×(C2×D3)⋊C414yes—
484C32C2×#41611yescharacteristic, complemented, Sylow
485C23—32no—
486C23—34no—
487C23—62no—
488C23—62no—
489C23—182no—
490C23—184no—
491C23—362no—
492C23—362no—
493C23D3×#6711yescharacteristic
494Q8—34no—
495Q8—62no—
496Q8—64no—
497D4—94no—
498D4—1816no—
499D4—182no—
500D4—184no—
501C2×C4—22no—
502C2×C4—32no—
503C2×C4—34no—
504C2×C4—34no—
505C2×C4—34no—
506C2×C4—38no—
507C2×C4—42no—
508C2×C4—62no—
509C2×C4—64no—
510C2×C4—62no—
511C2×C4—122no—
512C2×C4—1816no—
513C2×C4C4×D3212yes—
514C2×C4D3×D1212yes—
515C2×C4D3×#6711yescharacteristic
516C2×C4C22×D3211yescharacteristic
517C8—62no—
518C8—182no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—24no—
522C2×C3—21no—
523C2×C3—64no—
524C2×C3#480414yescomplemented
525C2×C3#500214yescomplemented
526C2×C3C2×D3×C22⋊C411yescharacteristic
527C2×C3C2×#91611yescharacteristic
528C2×C3C2×#91911yescharacteristic
529C2×C3C22×(C2×D3)⋊C411yescharacteristic
530C2×C3C2×#95011yescharacteristic
531C2×C3C2×#95011yescharacteristic
532D3—24no—
533D3—124no—
534D3—124no—
535D3—244no—
536C22—34no—
537C22—62no—
538C22—62no—
539C22—68no—
540C22—184no—
541C22—362no—
542C22—362no—
543C22—368no—
544C22D3×(C2×D3)⋊C412yes—
545C22#6393512yes—
546C22#6394912yes—
547C22C2×D3×#6711yescharacteristic
548C4—34no—
549C4—42no—
550C4—64no—
551C4—122no—
552C4D3×(C2×D3)⋊C412yes—
553C4C2×C4×D3211yescharacteristic
554C4C2×D3×D1211yescharacteristic
555C3—21no—
556C3C2×#480411yescharacteristic, complemented
557C3C2×#500211yescharacteristic, complemented
558C2—64no—
559C2—364no—
560C2#1059061014yesdirect product factor
561C2C2×D3×(C2×D3)⋊C411yescharacteristic
562C2C2×#6393511yescharacteristic
563C2C2×#6394911yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3799C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#892C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. C2×#63636C2semidirect
5. C2×C3×#810C2semidirect
6. C2×#63565C2semidirect
7. C2×#63564C2semidirect
8. #10590610C2direct (N × H)
18. C2×#3799C4semidirect
27. C3×#892C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63636C22semidirect
31. C3×#810C22semidirect
32. #63565C22semidirect
33. #63564C22semidirect
39. C2×#892D3semidirect
45. C2×#810D3semidirect
76. #3799C2×C4semidirect
129. #892C2×D3semidirect
134. #810C2×D3semidirect
391. C2×C32#416semidirect
484. C32C2×#416semidirect
524. C2×C3#4804semidirect
525. C2×C3#5002semidirect
556. C3C2×#4804semidirect
557. C3C2×#5002semidirect
560. C2#10590610direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C2×C3×#8922
C22×D3×C3⋊C82
C2×#636362
C2×C3×#8102
C2×#635652
C2×#635642
#105906102
C2×#50023
C2×#48043