Finite Group Databasebeta

← C2×#10590953 #11857400

Subgroups — C2×#10590953 #11857400

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×#3798C211yesmaximal, characteristic
2C22×C3×D3×C8C211yesmaximal, characteristic, complemented
3C22×#3711C211yesmaximal, characteristic, complemented
4C2×#63647C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×#63557C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590953C218yesmaximal, direct product factor
9C2×#5110—31nomaximal
10C2×#4727—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×#627C411yescharacteristic
15C22×#626C411yescharacteristic
16C22×#626C411yescharacteristic
17C22×#625C411yescharacteristic
18C2×#3798—24no—
19C2×#3798—24no—
20C2×#3798C414yes—
21C2×#3798C2214yes—
22C22×C32×C8C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×C3×D3×C8—24no—
27C2×C3×D3×C8C2214yescomplemented
28C2×#3711—24no—
29C2×#3711C2214yescomplemented
30#63647C2214yescomplemented
31C3×(C2×D3)⋊C8C2214yescomplemented
32#63557C2214yescomplemented
33(C2×D3)⋊(C3⋊C8)C2214yescomplemented
34C22×#235—31no—
35C22×#235—31no—
36C23×C3×C8—31no—
37C22×#208—31no—
38C22×ΓL(1,𝔽25)—31no—
39C22×D3×C8D311yescharacteristic, complemented
40C2×C3×C22⋊C8—31no—
41C2×#830—31no—
42#5110—38no—
43C2×(C2×D3)⋊C8—31no—
44C2×(C2×D3)⋊C8—31no—
45C2×(C2×D3)⋊C8—31no—
46C2×(C2×D3)⋊C8—31no—
47C2×(C2×D3)⋊C8—31no—
48C2×(C2×D3)⋊C8—61no—
49C2×(C2×D3)⋊C8D311yescharacteristic, complemented
50#4727—38no—
51C23×C3⋊D3C2×C411yescharacteristic
52C23×C3×D3C2×C411yescharacteristic
53C23×C3×D3C2×C411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3C2×C411yescharacteristic
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3C2×C412yes—
59C2×C4×C3⋊D3C2312yes—
60C22×C3×Dic3C2×C411yescharacteristic
61C22×C3×Dic3C2×C411yescharacteristic
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3C2×C412yes—
65C2×C3×C4×D3C2×C412yes—
66C2×C3×C4×D3D414yes—
67C2×C3×C4×D3D414yes—
68C2×C3×C4×D3C2312yes—
69C2×C3×C4×D3C2312yes—
70C2×#627—24no—
71C2×#627C2×C414yes—
72C2×#626—24no—
73C2×#626—24no—
74C2×#626C2×C414yes—
75C2×#626C2×C414yes—
76C2×#625—24no—
77C2×#625C2×C414yes—
78#3798—216no—
79#3798—28no—
80#3798—28no—
81C2×C32×C8—22no—
82C2×C32×C8C2312yes—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88C2×C3×C3⋊C8C2312yes—
89C3×D3×C8—28no—
90#3711—28no—
91C2×#408—91noSylow
92C23×C3×C4—31no—
93C23×C3×C4—31no—
94C22×#67—31no—
95C22×#67—31no—
96C22×#67—31no—
97C22×#67—31no—
98C2×#235—34no—
99C2×#235—34no—
100C2×#235—34no—
101C2×#235—34no—
102C2×#235—64no—
103C2×#235—64no—
104C2×#235—64no—
105C2×#235—64no—
106C22×D12—31no—
107C22×D12—31no—
108C22×C4×D3—31no—
109C22×C4×D3—31no—
110C22×C4×D3—61no—
111C22×C4×D3C2×D311yescharacteristic
112C22×C4×D3C2×D311yescharacteristic
113C22×Dic6—31no—
114C22×Dic6—31no—
115C22×C3×C8—21no—
116C22×C3×C8—31no—
117C22×C3×C8—31no—
118C22×C3×C8—34no—
119C22×C3×C8—64no—
120C22×C3×C8C2×D311yescharacteristic
121C22×C3×C8C2×D311yescharacteristic
122C2×#208—34no—
123C2×#208—64no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127C22×C3⋊C8C2×D311yescharacteristic
128C22×C3⋊C8C2×D311yescharacteristic
129C2×ΓL(1,𝔽25)—34no—
130C2×ΓL(1,𝔽25)—64no—
131C2×D3×C8—24no—
132C2×D3×C8C2×D314yescomplemented
133C3×C22⋊C8—34no—
134#830—34no—
135(C2×D3)⋊C8—34no—
136(C2×D3)⋊C8—34no—
137(C2×D3)⋊C8—34no—
138(C2×D3)⋊C8—34no—
139(C2×D3)⋊C8—34no—
140(C2×D3)⋊C8—64no—
141(C2×D3)⋊C8C2×D314yescomplemented
142C23×C32C22×C411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3C22×C412yes—
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×C4C22×C411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3C22×C412yes—
161C4×C3⋊D3—24no—
162C4×C3⋊D3—22no—
163C4×C3⋊D3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C22⋊C414yes—
166C2×C3×Dic3C22×C412yes—
167C2×C3×Dic3C22×C412yes—
168C3×C4×D3—24no—
169C3×C4×D3—22no—
170C3×C4×D3—22no—
171C3×C4×D3C22⋊C418yes—
172C3×C4×D3C2×D414yes—
173C3×C4×D3C2×D414yes—
174#627—28no—
175#626—28no—
176#626—28no—
177#625—28no—
178C32×C8—22no—
179C3⋊(C3⋊C8)—22no—
180C3×C3⋊C8—22no—
181C3×C3⋊C8—22no—
182C22×#41—91no—
183C22×M16—91no—
184C23×C8—31no—
185#408—98no—
186C2×C22⋊C8—31no—
187C2×C22⋊C8—91no—
188C2×C22⋊C8—91no—
189C2×C22⋊C8—91no—
190C24×C3—31no—
191C24×C3—31no—
192C23×D3—31no—
193C23×D3—31no—
194C23×D3—61no—
195C23×D3C4×D311yescharacteristic
196C23×D3C4×D311yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—31no—
199C22×C3×C4—32no—
200C22×C3×C4—34no—
201C22×C3×C4—34no—
202C22×C3×C4—32no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—34no—
211C2×#67—34no—
212C2×#67—34no—
213C2×#67—34no—
214C2×#67—64no—
215C2×#67—64no—
216C2×#67—64no—
217C2×#67—64no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—61no—
221C22×Dic3C4×D311yescharacteristic
222C22×Dic3C4×D311yescharacteristic
223#235—616no—
224#235—68no—
225#235—68no—
226#235—616no—
227#235—68no—
228#235—68no—
229C2×D12—34no—
230C2×D12—34no—
231C2×D12—64no—
232C2×D12—64no—
233C2×C4×D3—22no—
234C2×C4×D3—22no—
235C2×C4×D3—32no—
236C2×C4×D3—32no—
237C2×C4×D3—32no—
238C2×C4×D3—32no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—122no—
246C2×C4×D3—122no—
247C2×C4×D3C4×D312yes—
248C2×C4×D3C4×D312yes—
249C2×C4×D3D1214yes—
250C2×C4×D3#6714yes—
251C2×C4×D3C22×D312yes—
252C2×C4×D3C22×D312yes—
253C2×Dic6—34no—
254C2×Dic6—34no—
255C2×Dic6—64no—
256C2×Dic6—64no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8—22no—
260C2×C3×C8—32no—
261C2×C3×C8—32no—
262C2×C3×C8—42no—
263C2×C3×C8—68no—
264C2×C3×C8—62no—
265C2×C3×C8—62no—
266C2×C3×C8C22×D312yes—
267C2×C3×C8C22×D312yes—
268#208—68no—
269C2×C3⋊C8—22no—
270C2×C3⋊C8—22no—
271C2×C3⋊C8—32no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—62no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8—122no—
277C2×C3⋊C8C22×D312yes—
278C2×C3⋊C8C22×D312yes—
279ΓL(1,𝔽25)—68no—
280D3×C8—28no—
281C22×C32C2×C22⋊C412yes—
282C22×C32#13112yes—
283C22×C32#13112yes—
284C22×C32C23×C411yescharacteristic
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—44no—
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×C4C2×C22⋊C412yes—
298C32×C4C22×D411yescharacteristic
299C32×C4C22×D411yescharacteristic
300C3⋊Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3C2×C22⋊C414yes—
303C2×#41—94no—
304C2×#41—94no—
305C2×#41—184no—
306C2×#41—184no—
307C22×Q8—91no—
308C22×D4—91no—
309C22×D4—91no—
310C22×D4—91no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—91no—
314C2×M16—94no—
315C2×M16—184no—
316C22×C8—31no—
317C22×C8—31no—
318C22×C8—34no—
319C22×C8—64no—
320C22×C8—91no—
321C22×C8D3211yescharacteristic
322C22⋊C8—34no—
323C22⋊C8—94no—
324C22⋊C8—94no—
325C22⋊C8—94no—
326C23×C3—21no—
327C23×C3—34no—
328C23×C3—32no—
329C23×C3—32no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3C2×C4×D311yescharacteristic
336C23×C3C2×C4×D311yescharacteristic
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—32no—
343C22×D3—32no—
344C22×D3—62no—
345C22×D3—64no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—122no—
353C22×D3—122no—
354C22×D3(C2×D3)⋊C414yes—
355C22×D3C2×C4×D312yes—
356C22×D3C2×C4×D312yes—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—34no—
362C2×C3×C4—32no—
363C2×C3×C4—38no—
364C2×C3×C4—34no—
365C2×C3×C4—34no—
366C2×C3×C4—32no—
367C2×C3×C4—62no—
368C2×C3×C4—64no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4C2×C4×D311yescharacteristic
372C2×C3×C4C2×C4×D311yescharacteristic
373C2×C3×C4C2×D1212yes—
374C2×C3×C4D3×D412yes—
375C2×C3×C4D3×D412yes—
376C2×C3×C4C2×#6712yes—
377C2×C3×C4C23×D311yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379#67—68no—
380#67—68no—
381#67—68no—
382#67—68no—
383C2×Dic3—22no—
384C2×Dic3—32no—
385C2×Dic3—32no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—122no—
390C2×Dic3(C2×D3)⋊C414yes—
391C2×Dic3C2×C4×D312yes—
392C2×Dic3C2×C4×D312yes—
393D12—68no—
394D12—68no—
395C4×D3—24no—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—64no—
399C4×D3—64no—
400C4×D3—62no—
401C4×D3—62no—
402C4×D3—62no—
403C4×D3—62no—
404C4×D3—122no—
405C4×D3—122no—
406C4×D3—124no—
407C4×D3(C2×D3)⋊C418yes—
408C4×D3C2×D1214yes—
409C4×D3C2×#6714yes—
410Dic6—68no—
411Dic6—68no—
412C3×C8—22no—
413C3×C8—22no—
414C3×C8—42no—
415C3×C8—62no—
416C3×C8—62no—
417C3⋊C8—22no—
418C3⋊C8—22no—
419C3⋊C8—62no—
420C3⋊C8—62no—
421C3⋊C8—122no—
422C2×C32#40814yescomplemented
423C2×C32C22×C22⋊C411yescharacteristic
424C2×C32C2×#13111yescharacteristic
425C2×C32C2×#13111yescharacteristic
426C3⋊D3—42no—
427C3×D3—24no—
428C3×D3—42no—
429C24—31no—
430C24—31no—
431C24—91no—
432#41—188no—
433#41—188no—
434#41—1816no—
435C2×Q8—94no—
436C2×Q8—184no—
437C2×D4—94no—
438C2×D4—94no—
439C2×D4—94no—
440C2×D4—184no—
441C2×D4—184no—
442C2×D4—184no—
443C22×C4—31no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—34no—
447C22×C4—34no—
448C22×C4—31no—
449C22×C4—32no—
450C22×C4—32no—
451C22×C4—62no—
452C22×C4—62no—
453C22×C4—91no—
454C22×C4—92no—
455C22×C4—92no—
456C22×C4—182no—
457C22×C4—182no—
458C22×C4C2×D3211yescharacteristic
459M16—188no—
460C2×C8—22no—
461C2×C8—32no—
462C2×C8—32no—
463C2×C8—68no—
464C2×C8—62no—
465C2×C8—62no—
466C2×C8—92no—
467C2×C8—182no—
468C2×C8C2×D3212yes—
469C22×C3—21no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—34no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3—68no—
477C22×C3—62no—
478C22×C3—62no—
479C22×C3—62no—
480C22×C3—124no—
481C22×C3D3×C22⋊C412yes—
482C22×C3#90112yes—
483C22×C3#90112yes—
484C22×C3#90112yes—
485C22×C3#90712yes—
486C22×C3C2×(C2×D3)⋊C412yes—
487C22×C3C22×C4×D311yescharacteristic
488C22×C3C22×C4×D311yescharacteristic
489C2×D3—22no—
490C2×D3—22no—
491C2×D3—28no—
492C2×D3—22no—
493C2×D3—22no—
494C2×D3—22no—
495C2×D3—44no—
496C2×D3—64no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—128no—
506C2×D3—124no—
507C2×D3—124no—
508C2×D3C2×(C2×D3)⋊C414yes—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—22no—
512C3×C4—34no—
513C3×C4—62no—
514C3×C4D3×C22⋊C412yes—
515C3×C4C2×(C2×D3)⋊C412yes—
516C3×C4C22×D1211yescharacteristic
517C3×C4C2×D3×D411yescharacteristic
518C3×C4C2×D3×D411yescharacteristic
519C3×C4C22×#6711yescharacteristic
520Dic3—22no—
521Dic3—62no—
522Dic3—62no—
523Dic3—122no—
524Dic3C2×(C2×D3)⋊C414yes—
525C32C2×#40811yescharacteristic, complemented, Sylow
526C23—32no—
527C23—34no—
528C23—32no—
529C23—62no—
530C23—62no—
531C23—62no—
532C23—62no—
533C23—62no—
534C23—92no—
535C23—182no—
536C23—182no—
537C23—182no—
538C23C4×D3211yescharacteristic
539Q8—188no—
540D4—188no—
541D4—188no—
542D4—188no—
543C2×C4—32no—
544C2×C4—34no—
545C2×C4—34no—
546C2×C4—34no—
547C2×C4—38no—
548C2×C4—32no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—64no—
553C2×C4—92no—
554C2×C4—182no—
555C2×C4—182no—
556C2×C4—182no—
557C2×C4—184no—
558C2×C4C4×D3211yescharacteristic
559C2×C4D3×D1212yes—
560C2×C4D3×#6712yes—
561C2×C4C22×D3211yescharacteristic
562C8—22no—
563C8—62no—
564C8—62no—
565C8—182no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—24no—
569C2×C3—21no—
570C2×C3—64no—
571C2×C3—122no—
572C2×C3#472714yescomplemented
573C2×C3#511014yescomplemented
574C2×C3C2×D3×C22⋊C411yescharacteristic
575C2×C3C2×#90111yescharacteristic
576C2×C3C2×#90111yescharacteristic
577C2×C3C2×#90111yescharacteristic
578C2×C3C2×#90711yescharacteristic
579C2×C3C22×(C2×D3)⋊C411yescharacteristic
580D3—24no—
581D3—42no—
582D3—124no—
583D3—122no—
584D3—122no—
585C22—34no—
586C22—62no—
587C22—62no—
588C22—68no—
589C22—62no—
590C22—62no—
591C22—62no—
592C22—124no—
593C22—182no—
594C22—182no—
595C22—182no—
596C22—364no—
597C22#6380312yes—
598C22#6380412yes—
599C22D3×(C2×D3)⋊C412yes—
600C22C2×C4×D3211yescharacteristic
601C4—34no—
602C4—62no—
603C4—182no—
604C4D3×(C2×D3)⋊C412yes—
605C4C2×D3×D1211yescharacteristic
606C4C2×D3×#6711yescharacteristic
607C3—21no—
608C3C2×#472711yescharacteristic, complemented
609C3C2×#511011yescharacteristic, complemented
610C2—64no—
611C2—122no—
612C2—362no—
613C2#1059095314yesdirect product factor
614C2C2×#6380311yescharacteristic
615C2C2×#6380411yescharacteristic
616C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC22×#3798C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#408
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×C3×D3×C8C2semidirect
3. C22×#3711C2semidirect
4. C2×#63647C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×#63557C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. #10590953C2direct (N × H)
27. C2×C3×D3×C8C22semidirect
29. C2×#3711C22semidirect
30. #63647C22semidirect
31. C3×(C2×D3)⋊C8C22semidirect
32. #63557C22semidirect
33. (C2×D3)⋊(C3⋊C8)C22semidirect
39. C22×D3×C8D3semidirect
49. C2×(C2×D3)⋊C8D3semidirect
132. C2×D3×C8C2×D3semidirect
141. (C2×D3)⋊C8C2×D3semidirect
422. C2×C32#408semidirect
525. C32C2×#408semidirect
572. C2×C3#4727semidirect
573. C2×C3#5110semidirect
608. C3C2×#4727semidirect
609. C3C2×#5110semidirect
613. C2#10590953direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37982
C22×C3×D3×C82
C22×#37112
C2×#636472
C2×C3×(C2×D3)⋊C82
C2×#635572
C2×(C2×D3)⋊(C3⋊C8)2
#105909532
C2×#51103
C2×#47273