Finite Group Databasebeta

← C2×#10591145 #11857402

Subgroups — C2×#10591145 #11857402

Order 1152.

1685 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C22×#3711C211yesmaximal, characteristic, complemented
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×#63657C211yesmaximal, characteristic, complemented
5C2×C3×#830C211yesmaximal, characteristic, complemented
6#10591145C218yesmaximal, direct product factor
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5234—31nomaximal
10C2×#4727—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×#67C411yescharacteristic
13C22×C3×#67C411yescharacteristic
14C2×C3×#235—24no—
15C2×C3×#235—24no—
16C2×C3×#235C414yes—
17C2×C3×#235C2214yes—
18C22×C3×D12C411yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C411yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×#3711—24no—
27C2×#3711C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63657C2214yescomplemented
31C3×#830C2214yescomplemented
32(C2×D3)⋊(C3⋊C8)C2214yescomplemented
33(C2×D3)⋊(C3⋊C8)C2214yescomplemented
34C22×C3×#41—31no—
35C22×#235D311yescharacteristic
36C22×#208—31no—
37C23×C3⋊C8—31no—
38C22×ΓL(1,𝔽25)—31no—
39C22×D3×C8—31no—
40C2×C3×C22⋊C8—31no—
41#5234—38no—
42C2×#830—31no—
43C2×#830—31no—
44C2×#830—31no—
45C2×#830—31no—
46C2×#830—61no—
47C2×#830D311yescharacteristic, complemented
48C2×(C2×D3)⋊C8—31no—
49C2×(C2×D3)⋊C8—31no—
50#4727—38no—
51C24×C32C2×C411yescharacteristic
52C23×C3×D3C2×C411yescharacteristic
53C23×C3×D3C2×C411yescharacteristic
54C22×C32×C4—22no—
55C22×C32×C4—22no—
56C22×C32×C4C2×C411yescharacteristic
57C22×C32×C4C2×C412yes—
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—24no—
61C2×C3×#67—24no—
62C2×C3×#67C2×C414yes—
63C2×C3×#67C2×C414yes—
64C22×C3×Dic3C2×C411yescharacteristic
65C22×C3×Dic3C2×C411yescharacteristic
66C3×#235—216no—
67C3×#235—28no—
68C3×#235—28no—
69C2×C3×D12—24no—
70C2×C3×D12C2×C414yes—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2×C412yes—
74C2×C3×C4×D3C2×C412yes—
75C2×C3×C4×D3D414yes—
76C2×C3×C4×D3D414yes—
77C2×C3×C4×D3C2312yes—
78C2×C3×C4×D3C2312yes—
79C2×C3×Dic6—24no—
80C2×C3×Dic6C2×C414yes—
81C2×C3⋊(C3⋊C8)—22no—
82C2×C3⋊(C3⋊C8)—22no—
83C2×C3⋊(C3⋊C8)C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88C2×C3×C3⋊C8C2312yes—
89#3711—28no—
90D3×C3⋊C8—28no—
91C2×#408—91noSylow
92C2×C3×#41—34no—
93C2×C3×#41—34no—
94C2×C3×#41—64no—
95C2×C3×#41—64no—
96C22×C3×Q8—31no—
97C22×C3×D4—31no—
98C22×C3×D4—31no—
99C22×C3×D4—31no—
100C23×C3×C4—21no—
101C23×C3×C4—31no—
102C23×C3×C4—31no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C22×#67Dic311yescharacteristic
106C22×#67Dic311yescharacteristic
107C2×#235—24no—
108C2×#235—24no—
109C2×#235Dic314yes—
110C2×#235C2×D314yes—
111C22×D12Dic311yescharacteristic
112C22×C4×D3C2×D311yescharacteristic
113C22×C4×D3C2×D311yescharacteristic
114C22×Dic6Dic311yescharacteristic
115C22×C3×C8—31no—
116C22×C3×C8—31no—
117C2×#208—34no—
118C2×#208—64no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—34no—
124C22×C3⋊C8—61no—
125C22×C3⋊C8—61no—
126C22×C3⋊C8—64no—
127C22×C3⋊C8C2×D311yescharacteristic
128C22×C3⋊C8C2×D311yescharacteristic
129C2×ΓL(1,𝔽25)—34no—
130C2×ΓL(1,𝔽25)—64no—
131C2×D3×C8—34no—
132C2×D3×C8—64no—
133C3×C22⋊C8—34no—
134#830—34no—
135#830—34no—
136#830—34no—
137#830—34no—
138#830—64no—
139#830C2×D314yescomplemented
140(C2×D3)⋊C8—34no—
141(C2×D3)⋊C8—34no—
142C23×C32—22no—
143C23×C32—22no—
144C23×C32—22no—
145C23×C32C22×C412yes—
146C23×C32C22×C411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3C22⋊C414yes—
153C22×C3×D3C22×C412yes—
154C22×C3×D3C22×C412yes—
155C2×C32×C4—22no—
156C2×C32×C4—24no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C22×C411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
164C3×#67—28no—
165C3×#67—28no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3C22⋊C414yes—
168C2×C3×Dic3C22×C412yes—
169C2×C3×Dic3C22×C412yes—
170C3×D12—28no—
171C3×C4×D3—24no—
172C3×C4×D3—22no—
173C3×C4×D3—22no—
174C3×C4×D3C22⋊C418yes—
175C3×C4×D3C2×D414yes—
176C3×C4×D3C2×D414yes—
177C3×Dic6—28no—
178C3⋊(C3⋊C8)—22no—
179C3⋊(C3⋊C8)—22no—
180C3×C3⋊C8—22no—
181C3×C3⋊C8—22no—
182C22×#41—31no—
183C22×M16—91no—
184C23×C8—91no—
185#408—98no—
186C2×C22⋊C8—31no—
187C2×C22⋊C8—91no—
188C2×C22⋊C8—91no—
189C2×C22⋊C8—91no—
190C24×C3—21no—
191C24×C3—31no—
192C24×C3—31no—
193C24×C3C4×D311yescharacteristic
194C24×C3C2×Dic311yescharacteristic
195C23×D3C2×Dic311yescharacteristic
196C23×D3C2×Dic311yescharacteristic
197C3×#41—616no—
198C3×#41—68no—
199C3×#41—68no—
200C2×C3×Q8—34no—
201C2×C3×Q8—64no—
202C2×C3×D4—34no—
203C2×C3×D4—34no—
204C2×C3×D4—34no—
205C2×C3×D4—64no—
206C2×C3×D4—64no—
207C2×C3×D4—64no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—21no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—31no—
217C22×C3×C4—32no—
218C22×C3×C4—34no—
219C22×C3×C4—34no—
220C22×C3×C4—32no—
221C22×C3×C4—31no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—42no—
225C22×C3×C4—42no—
226C22×C3×C4—62no—
227C22×C3×C4—62no—
228C22×C3×C4C4×D311yescharacteristic
229C22×C3×C4C4×D312yes—
230C22×C3×C4C2×Dic311yescharacteristic
231C22×C3×C4C2×Dic312yes—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—24no—
237C2×#67—24no—
238C2×#67C2×Dic314yes—
239C2×#67C2×Dic314yes—
240C22×Dic3C2×Dic311yescharacteristic
241C22×Dic3C2×Dic311yescharacteristic
242#235—216no—
243#235—28no—
244#235—28no—
245C2×D12—24no—
246C2×D12C2×Dic314yes—
247C2×C4×D3—22no—
248C2×C4×D3—22no—
249C2×C4×D3C2×Dic312yes—
250C2×C4×D3C2×Dic312yes—
251C2×C4×D3#6714yes—
252C2×C4×D3#6714yes—
253C2×C4×D3C22×D312yes—
254C2×C4×D3C22×D312yes—
255C2×Dic6—24no—
256C2×Dic6C2×Dic314yes—
257C2×C3×C8—32no—
258C2×C3×C8—32no—
259C2×C3×C8—62no—
260C2×C3×C8—62no—
261#208—68no—
262C2×C3⋊C8—22no—
263C2×C3⋊C8—22no—
264C2×C3⋊C8—32no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8—68no—
271C2×C3⋊C8—62no—
272C2×C3⋊C8—62no—
273C2×C3⋊C8—62no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8—122no—
276C2×C3⋊C8—122no—
277C2×C3⋊C8C22×D312yes—
278C2×C3⋊C8C22×D312yes—
279ΓL(1,𝔽25)—68no—
280D3×C8—68no—
281C22×C32—22no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—44no—
285C22×C32C2×C22⋊C412yes—
286C22×C32#13112yes—
287C22×C32#13112yes—
288C22×C32C23×C411yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—28no—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—44no—
296C2×C3×D3C2×C22⋊C414yes—
297C32×C4—22no—
298C32×C4C2×C22⋊C412yes—
299C32×C4C22×D411yescharacteristic
300C32×C4C22×D411yescharacteristic
301C3×Dic3—22no—
302C3×Dic3C2×C22⋊C414yes—
303C2×#41—34no—
304C2×#41—34no—
305C2×#41—64no—
306C2×#41—64no—
307C22×Q8—31no—
308C22×D4—31no—
309C22×D4—31no—
310C22×D4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4D3211yescharacteristic
314C2×M16—94no—
315C2×M16—184no—
316C22×C8—31no—
317C22×C8—31no—
318C22×C8—94no—
319C22×C8—91no—
320C22×C8—91no—
321C22×C8—184no—
322C22⋊C8—34no—
323C22⋊C8—94no—
324C22⋊C8—94no—
325C22⋊C8—94no—
326C23×C3—24no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—21no—
334C23×C3—22no—
335C23×C3—34no—
336C23×C3—32no—
337C23×C3—32no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—62no—
341C23×C3—62no—
342C23×C3—62no—
343C23×C3—62no—
344C23×C3—62no—
345C23×C3C2×C4×D312yes—
346C23×C3C2×C4×D311yescharacteristic
347C23×C3C22×Dic312yes—
348C23×C3C22×Dic311yescharacteristic
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3#21714yes—
355C22×D3C22×Dic312yes—
356C22×D3C22×Dic312yes—
357C3×Q8—68no—
358C3×D4—68no—
359C3×D4—68no—
360C3×D4—68no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—34no—
375C2×C3×C4—32no—
376C2×C3×C4—38no—
377C2×C3×C4—34no—
378C2×C3×C4—34no—
379C2×C3×C4—32no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—44no—
383C2×C3×C4—42no—
384C2×C3×C4—62no—
385C2×C3×C4—64no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4C2×C4×D311yescharacteristic
390C2×C3×C4D3×D412yes—
391C2×C3×C4D3×D412yes—
392C2×C3×C4C22×Dic312yes—
393C2×C3×C4C22×Dic311yescharacteristic
394C2×C3×C4C2×#6712yes—
395C2×C3×C4C2×#6712yes—
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398#67—28no—
399#67—28no—
400C2×Dic3—22no—
401C2×Dic3#21714yes—
402C2×Dic3C22×Dic312yes—
403C2×Dic3C22×Dic312yes—
404D12—28no—
405C4×D3—24no—
406C4×D3—22no—
407C4×D3—22no—
408C4×D3#21718yes—
409C4×D3C2×#6714yes—
410C4×D3C2×#6714yes—
411Dic6—28no—
412C3×C8—62no—
413C3×C8—62no—
414C3⋊C8—22no—
415C3⋊C8—22no—
416C3⋊C8—62no—
417C3⋊C8—62no—
418C3⋊C8—62no—
419C3⋊C8—62no—
420C3⋊C8—122no—
421C3⋊C8—122no—
422C2×C32—42no—
423C2×C32#40814yescomplemented
424C2×C32C22×C22⋊C411yescharacteristic
425C2×C32C2×#13111yescharacteristic
426C2×C32C2×#13111yescharacteristic
427C3×D3—24no—
428C3×D3—42no—
429C24—31no—
430C24—31no—
431C24D3×Dic311yescharacteristic
432#41—68no—
433#41—68no—
434#41—616no—
435C2×Q8—34no—
436C2×Q8—64no—
437C2×D4—34no—
438C2×D4—34no—
439C2×D4—34no—
440C2×D4—64no—
441C2×D4—64no—
442C2×D4—64no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—31no—
446C22×C4—32no—
447C22×C4—32no—
448C22×C4—34no—
449C22×C4—34no—
450C22×C4—31no—
451C22×C4—32no—
452C22×C4—32no—
453C22×C4—62no—
454C22×C4—62no—
455C22×C4D3×Dic311yescharacteristic
456C22×C4D3×Dic312yes—
457C22×C4C2×D3212yes—
458C22×C4C2×D3211yescharacteristic
459M16—188no—
460C2×C8—32no—
461C2×C8—32no—
462C2×C8—62no—
463C2×C8—62no—
464C2×C8—92no—
465C2×C8—92no—
466C2×C8—188no—
467C2×C8—182no—
468C2×C8—182no—
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—21no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—34no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—48no—
484C22×C3—44no—
485C22×C3—44no—
486C22×C3—62no—
487C22×C3—62no—
488C22×C3—68no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—62no—
492C22×C3—124no—
493C22×C3D3×C22⋊C412yes—
494C22×C3#90112yes—
495C22×C3#90712yes—
496C22×C3#94812yes—
497C22×C3#94812yes—
498C22×C3C2×#21712yes—
499C22×C3C22×C4×D311yescharacteristic
500C22×C3C23×Dic311yescharacteristic
501C2×D3—28no—
502C2×D3—22no—
503C2×D3—22no—
504C2×D3—22no—
505C2×D3—22no—
506C2×D3—22no—
507C2×D3—44no—
508C2×D3C2×#21714yes—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—22no—
514C3×C4—34no—
515C3×C4—42no—
516C3×C4—62no—
517C3×C4D3×C22⋊C412yes—
518C3×C4C2×#21712yes—
519C3×C4C2×D3×D411yescharacteristic
520C3×C4C2×D3×D411yescharacteristic
521C3×C4C22×#6711yescharacteristic
522C3×C4C22×#6711yescharacteristic
523Dic3—22no—
524Dic3C2×#21714yes—
525C32C2×#40811yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—22no—
529C23—32no—
530C23—34no—
531C23—32no—
532C23—62no—
533C23—62no—
534C23—62no—
535C23—62no—
536C23—62no—
537C23C2×D3×Dic312yes—
538C23C2×D3×Dic311yescharacteristic
539Q8—68no—
540D4—68no—
541D4—68no—
542D4—68no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—32no—
548C2×C4—34no—
549C2×C4—34no—
550C2×C4—34no—
551C2×C4—38no—
552C2×C4—32no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—64no—
557C2×C4C2×D3×Dic312yes—
558C2×C4C2×D3×Dic311yescharacteristic
559C2×C4D3×#6712yes—
560C2×C4D3×#6712yes—
561C2×C4C22×D3211yescharacteristic
562C8—62no—
563C8—62no—
564C8—182no—
565C8—182no—
566C2×C3—21no—
567C2×C3—24no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—44no—
571C2×C3—42no—
572C2×C3—42no—
573C2×C3—64no—
574C2×C3—122no—
575C2×C3#472714yescomplemented
576C2×C3#523414yescomplemented
577C2×C3C2×D3×C22⋊C411yescharacteristic
578C2×C3C2×#90111yescharacteristic
579C2×C3C2×#90711yescharacteristic
580C2×C3C2×#94811yescharacteristic
581C2×C3C2×#94811yescharacteristic
582C2×C3C22×#21711yescharacteristic
583D3—24no—
584D3—42no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—34no—
589C22—44no—
590C22—68no—
591C22—62no—
592C22—62no—
593C22—62no—
594C22—62no—
595C22—62no—
596C22—124no—
597C22#6381412yes—
598C22#6381512yes—
599C22D3×#21712yes—
600C22C22×D3×Dic311yescharacteristic
601C4—22no—
602C4—34no—
603C4—62no—
604C4D3×#21712yes—
605C4C2×D3×#6711yescharacteristic
606C4C2×D3×#6711yescharacteristic
607C3—21no—
608C3C2×#472711yescharacteristic, complemented
609C3C2×#523411yescharacteristic, complemented
610C2—42no—
611C2—64no—
612C2—122no—
613C2#1059114514yesdirect product factor
614C2C2×#6381411yescharacteristic
615C2C2×#6381511yescharacteristic
616C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC22×C3×#235C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#408
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3711C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. C2×#63657C2semidirect
5. C2×C3×#830C2semidirect
6. #10591145C2direct (N × H)
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
27. C2×#3711C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63657C22semidirect
31. C3×#830C22semidirect
32. (C2×D3)⋊(C3⋊C8)C22semidirect
33. (C2×D3)⋊(C3⋊C8)C22semidirect
47. C2×#830D3semidirect
139. #830C2×D3semidirect
423. C2×C32#408semidirect
525. C32C2×#408semidirect
575. C2×C3#4727semidirect
576. C2×C3#5234semidirect
608. C3C2×#4727semidirect
609. C3C2×#5234semidirect
613. C2#10591145direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#37112
C22×D3×C3⋊C82
C2×#636572
C2×C3×#8302
#105911452
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52343
C2×#47273