Finite Group Databasebeta

← C2×#10594911 #11901148

Subgroups — C2×#10594911 #11901148

Order 1152.

3493 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C212yesmaximal, complemented
2C2×#64139C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×#63978C212yesmaximal, complemented
6C2×#63910C212yesmaximal, complemented
7C2×#63895C212yesmaximal, complemented
8#10594911C2116yesmaximal, direct product factor
9C2×#63893C212yesmaximal, complemented
10C2×#63886C212yesmaximal, complemented
11C2×#5597—31nomaximal
12C2×#5510—31nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2212yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C3×#67C2212yes—
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×#627C2212yes—
21C22×#626C2212yes—
22C22×#626C2212yes—
23C22×#624C2212yes—
24C2×#3804—216no—
25C2×#3804C22116yescomplemented
26C22×D3×Dic3C2212yes—
27#64139C2218yescomplemented
28C2×#3752C2212yes—
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×#930C2218yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2218yescomplemented
36#63978C22116yescomplemented
37C2×Dic3⋊Dic3C2212yes—
38C2×#3722C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40#63910C22116yescomplemented
41#63895C22116yescomplemented
42#63893C22116yescomplemented
43#63886C22116yescomplemented
44C22×#237—32no—
45C22×#235—32no—
46C2×C3×#121—31no—
47C22×C3×C4⋊C4—31no—
48C2×#939—32no—
49C2×#939—32no—
50C2×#930—31no—
51C2×#930—31no—
52C2×#930—32no—
53C2×#930—61no—
54C2×#930D311yescharacteristic, complemented
55C22×Dic3⋊C4D311yescharacteristic, complemented
56#5597—316no—
57#5510—316no—
58C2×#897—32no—
59C2×#897—32no—
60C2×#896—32no—
61C2×#895—32no—
62C2×#895—32no—
63C2×#884—32no—
64C2×#878—32no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2312yes—
67C23×C3×D3C2312yes—
68C22×C32×C4—42no—
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2314yes—
72C2×#638—28no—
73C2×#638C2318yes—
74C22×C3⋊Dic3C2312yes—
75C2×C4⋊(C3⋊D3)—42no—
76C2×C4⋊(C3⋊D3)C2314yes—
77C2×C3×#67—28no—
78C2×C3×#67C2318yes—
79C22×C3×Dic3—42no—
80C22×C3×Dic3D418yescomplemented
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2314yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2314yes—
86C2×C3×D12—42no—
87C2×C3×D12C2314yes—
88C2×#627—28no—
89C2×#627C2318yes—
90C2×#626—28no—
91C2×#626—44no—
92C2×#626C2318yes—
93C2×#626C2318yes—
94C2×#624—28no—
95C2×#624C2318yes—
96#3804—264no—
97C2×D3×Dic3—28no—
98C2×D3×Dic3C2318yes—
99#3752C2318yes—
100C4⋊(C3⋊Dic3)C2314yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×Dic3⋊C4C2318yes—
104C3×Dic3⋊C4C2318yes—
105Dic3⋊Dic3C2318yes—
106#3722C2318yes—
107(C2×D3)⋊Dic3C2318yes—
108C2×#537—91noSylow
109C22×C3×D4—32no—
110C22×C3×D4—31no—
111C23×C3×C4—21no—
112C23×C3×C4—31no—
113C23×C3×C4—31no—
114C23×C3×C4C2×D311yescharacteristic
115C23×C3×C4C2×D311yescharacteristic
116C22×#67—32no—
117C22×#67—32no—
118C22×#67—32no—
119C22×#67—32no—
120C22×#67—62no—
121C22×#67C2×D312yes—
122C23×Dic3—32no—
123C23×Dic3C2×D311yescharacteristic
124C23×Dic3C2×D311yescharacteristic
125C2×#237—316no—
126C2×#237—616no—
127C2×#235—316no—
128C2×#235—616no—
129C22×D12—32no—
130C22×D12—32no—
131C22×D12—31no—
132C22×D12—31no—
133C22×D12—61no—
134C22×D12C2×D311yescharacteristic
135C22×C4×D3—32no—
136C22×C4×D3—32no—
137C22×C4×D3—32no—
138C22×Dic6—32no—
139C22×Dic6—32no—
140C3×#121—38no—
141C2×C3×C4⋊C4—32no—
142C2×C3×C4⋊C4—32no—
143C2×C3×C4⋊C4—38no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C22⋊C4—32no—
146C2×#217—32no—
147#939—316no—
148#939—316no—
149#930—38no—
150#930—38no—
151#930—316no—
152#930—68no—
153#930C2×D318yescomplemented
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—62no—
160C2×(C2×D3)⋊C4C2×D312yes—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—32no—
164C2×C4⋊Dic3—61no—
165C2×C4⋊Dic3C2×D311yescharacteristic
166C2×Dic3⋊C4—32no—
167C2×Dic3⋊C4C2×D312yes—
168C2×Dic3⋊C4C2×D312yes—
169C2×Dic3⋊C4C2×D318yescomplemented
170#897—316no—
171#897—316no—
172#896—316no—
173#895—316no—
174#895—316no—
175#884—316no—
176#878—316no—
177C23×C32—22no—
178C23×C32—22no—
179C23×C32C2×D414yes—
180C23×C32C2412yes—
181C23×C32C2411yescharacteristic
182C22×C3⋊D3—24no—
183C22×C3⋊D3—24no—
184C22×C3⋊D3—24no—
185C22×C3⋊D3C2414yes—
186C22×C3×D3—24no—
187C22×C3×D3—24no—
188C22×C3×D3—24no—
189C22×C3×D3C2414yes—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4—44no—
193C2×C32×C4C2412yes—
194C2×C32×C4C2412yes—
195#638—216no—
196C2×C3⋊Dic3—24no—
197C2×C3⋊Dic3C2414yes—
198C4⋊(C3⋊D3)—44no—
199C3×#67—216no—
200C2×C3×Dic3—24no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—44no—
203C2×C3×Dic3C2×D418yes—
204C2×C3×Dic3C2×D4116yescomplemented
205C2×C3×Dic3C2414yes—
206C2×C3×Dic3C2414yes—
207C2×C3×Dic3C2414yes—
208C3×D12—44no—
209#627—216no—
210#626—216no—
211#626—48no—
212#624—216no—
213D3×Dic3—216no—
214C22×#41—92no—
215#537—916no—
216C2×C22⋊Q8—92no—
217C2×C22⋊Q8—92no—
218C2×#121—31no—
219C2×#121—92no—
220C2×#121—92no—
221C2×#121—92no—
222C2×#121—91no—
223C22×C4⋊C4—31no—
224C24×C3—21no—
225C24×C3—32no—
226C24×C3C22×D311yescharacteristic
227C24×C3C22×D311yescharacteristic
228C23×D3—32no—
229C23×D3—32no—
230C23×D3—62no—
231C23×D3C22×D312yes—
232C2×C3×D4—38no—
233C2×C3×D4—34no—
234C2×C3×D4—68no—
235C2×C3×D4—122no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—24no—
239C22×C3×C4—38no—
240C22×C3×C4—32no—
241C22×C3×C4—34no—
242C22×C3×C4—32no—
243C22×C3×C4—32no—
244C22×C3×C4—34no—
245C22×C3×C4—42no—
246C22×C3×C4—42no—
247C22×C3×C4—44no—
248C22×C3×C4—122no—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D314yes—
254C22×C3×C4C22×D314yes—
255C2×#67—28no—
256C2×#67—38no—
257C2×#67—38no—
258C2×#67—38no—
259C2×#67—38no—
260C2×#67—68no—
261C2×#67—68no—
262C2×#67—68no—
263C2×#67—68no—
264C2×#67—128no—
265C2×#67—124no—
266C2×#67C22×D318yes—
267C22×Dic3—32no—
268C22×Dic3—32no—
269C22×Dic3—38no—
270C22×Dic3—42no—
271C22×Dic3—62no—
272C22×Dic3—68no—
273C22×Dic3D1218yescomplemented
274C22×Dic3C22×D312yes—
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D314yes—
277C22×Dic3C22×D312yes—
278C22×Dic3C22×D314yes—
279#237—664no—
280#235—664no—
281C2×D12—38no—
282C2×D12—38no—
283C2×D12—34no—
284C2×D12—34no—
285C2×D12—42no—
286C2×D12—64no—
287C2×D12—68no—
288C2×D12—122no—
289C2×D12—122no—
290C2×D12—124no—
291C2×D12—124no—
292C2×D12C22×D314yes—
293C2×C4×D3—38no—
294C2×C4×D3—38no—
295C2×C4×D3—38no—
296C2×C4×D3—68no—
297C2×C4×D3—68no—
298C2×C4×D3—68no—
299C2×Dic6—38no—
300C2×Dic6—38no—
301C2×Dic6—68no—
302C2×Dic6—68no—
303C3×C4⋊C4—38no—
304C3×C4⋊C4—38no—
305C3×C4⋊C4—34no—
306C3×C22⋊C4—38no—
307#217—38no—
308(C2×D3)⋊C4—38no—
309(C2×D3)⋊C4—38no—
310(C2×D3)⋊C4—38no—
311(C2×D3)⋊C4—38no—
312(C2×D3)⋊C4—38no—
313(C2×D3)⋊C4—68no—
314(C2×D3)⋊C4C22×D318yes—
315C4⋊Dic3—34no—
316C4⋊Dic3—34no—
317C4⋊Dic3—38no—
318C4⋊Dic3—64no—
319C4⋊Dic3C22×D314yes—
320Dic3⋊C4—38no—
321Dic3⋊C4C22×D318yes—
322Dic3⋊C4C22×D318yes—
323C22×C32—28no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32C22×D414yes—
327C22×C32C22×D412yes—
328C22×C32H(5,𝔽2)12yes—
329C22×C322−1+412yes—
330C22×C32C2511yescharacteristic
331C2×C3⋊D3—24no—
332C2×C3⋊D3—24no—
333C2×C3⋊D3—24no—
334C2×C3⋊D3—48no—
335C2×C3×D3—24no—
336C2×C3×D3—24no—
337C2×C3×D3—24no—
338C2×C3×D3—48no—
339C32×C4—22no—
340C32×C4—22no—
341C3⋊Dic3—24no—
342C3×Dic3—24no—
343C3×Dic3—24no—
344C3×Dic3C22×D418yes—
345C2×#41—916no—
346C2×#41—1816no—
347C22×Q8—92no—
348C22×D4—32no—
349C22×D4—31no—
350C22×D4—92no—
351C22×D4—92no—
352C22×D4—92no—
353C22×D4—91no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—92no—
357C23×C4—92no—
358C23×C4D3211yescharacteristic
359C22⋊Q8—916no—
360C22⋊Q8—916no—
361#121—38no—
362#121—916no—
363#121—916no—
364#121—916no—
365#121—98no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—38no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4—91no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—21no—
382C23×C3—24no—
383C23×C3—34no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—64no—
387C23×C3—64no—
388C23×C3—64no—
389C23×C3C2×D1214yes—
390C23×C3D3×D414yes—
391C23×C3C23×D312yes—
392C23×C3C23×D312yes—
393C23×C3C23×D311yescharacteristic
394C23×C3C23×D311yescharacteristic
395C22×D3—24no—
396C22×D3—24no—
397C22×D3—24no—
398C22×D3—34no—
399C22×D3—34no—
400C22×D3—64no—
401C22×D3—64no—
402C22×D3—64no—
403C22×D3—64no—
404C22×D3—64no—
405C22×D3—64no—
406C22×D3—64no—
407C22×D3—124no—
408C22×D3—124no—
409C22×D3—124no—
410C22×D3C23×D314yes—
411C3×D4—616no—
412C3×D4—124no—
413C2×C3×C4—24no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—38no—
421C2×C3×C4—316no—
422C2×C3×C4—34no—
423C2×C3×C4—34no—
424C2×C3×C4—34no—
425C2×C3×C4—42no—
426C2×C3×C4—44no—
427C2×C3×C4—44no—
428C2×C3×C4—48no—
429C2×C3×C4—64no—
430C2×C3×C4—64no—
431C2×C3×C4—124no—
432C2×C3×C4C23×D312yes—
433C2×C3×C4C23×D312yes—
434C2×C3×C4C23×D312yes—
435C2×C3×C4C23×D312yes—
436#67—216no—
437#67—616no—
438#67—616no—
439#67—616no—
440#67—1216no—
441#67—128no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—34no—
445C2×Dic3—34no—
446C2×Dic3—44no—
447C2×Dic3—64no—
448C2×Dic3—64no—
449C2×Dic3—64no—
450C2×Dic3—616no—
451C2×Dic3—124no—
452C2×Dic3C2×D1218yes—
453C2×Dic3C2×D12116yescomplemented
454C2×Dic3C23×D314yes—
455C2×Dic3C23×D314yes—
456C2×Dic3C23×D314yes—
457D12—44no—
458D12—616no—
459D12—124no—
460D12—124no—
461D12—128no—
462D12—128no—
463C4×D3—616no—
464C4×D3—616no—
465C4×D3—616no—
466Dic6—616no—
467Dic6—616no—
468C2×C32—24no—
469C2×C32#53714yescomplemented
470C2×C32C23×D411yescharacteristic
471C2×C32C2×H(5,𝔽2)11yescharacteristic
472C2×C32C2×2−1+411yescharacteristic
473C3⋊D3—44no—
474C3×D3—44no—
475C24—32no—
476C24—92no—
477C24C2×D3211yescharacteristic
478#41—1864no—
479C2×Q8—98no—
480C2×Q8—188no—
481C2×D4—38no—
482C2×D4—34no—
483C2×D4—68no—
484C2×D4—98no—
485C2×D4—98no—
486C2×D4—98no—
487C2×D4—94no—
488C2×D4—122no—
489C2×D4—188no—
490C2×D4—188no—
491C2×D4—362no—
492C2×D4—364no—
493C22×C4—34no—
494C22×C4—32no—
495C22×C4—38no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—34no—
499C22×C4—42no—
500C22×C4—98no—
501C22×C4—98no—
502C22×C4—92no—
503C22×C4—122no—
504C22×C4—188no—
505C22×C4—188no—
506C22×C4C2×D3211yescharacteristic
507C22×C4C2×D3211yescharacteristic
508C22×C4C2×D3214yes—
509C4⋊C4—38no—
510C4⋊C4—38no—
511C4⋊C4—34no—
512C4⋊C4—98no—
513C4⋊C4—94no—
514C22⋊C4—38no—
515C22⋊C4—98no—
516C22⋊C4—98no—
517C22⋊C4—98no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—28no—
523C22×C3—28no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—24no—
527C22×C3—22no—
528C22×C3—21no—
529C22×C3—42no—
530C22×C3—42no—
531C22×C3—48no—
532C22×C3—64no—
533C22×C3—64no—
534C22×C3—64no—
535C22×C3—128no—
536C22×C3C22×D1214yes—
537C22×C3C22×D1212yes—
538C22×C3C2×D3×D414yes—
539C22×C3C2×D3×D412yes—
540C22×C3#100412yes—
541C22×C3#100412yes—
542C22×C3#100712yes—
543C22×C3#101012yes—
544C22×C3C24×D311yescharacteristic
545C22×C3C24×D311yescharacteristic
546C2×D3—24no—
547C2×D3—24no—
548C2×D3—24no—
549C2×D3—48no—
550C2×D3—64no—
551C2×D3—64no—
552C2×D3—64no—
553C2×D3—64no—
554C2×D3—64no—
555C2×D3—64no—
556C2×D3—124no—
557C2×D3—124no—
558C2×D3—124no—
559C2×D3—128no—
560C2×D3—128no—
561C2×D3—248no—
562C3×C4—24no—
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—22no—
566C3×C4—22no—
567C3×C4—38no—
568C3×C4—42no—
569C3×C4—64no—
570C3×C4—64no—
571Dic3—24no—
572Dic3—24no—
573Dic3—64no—
574Dic3—64no—
575Dic3—124no—
576Dic3C22×D1218yes—
577C32C2×#53711yescharacteristic, complemented, Sylow
578C23—22no—
579C23—22no—
580C23—34no—
581C23—64no—
582C23—64no—
583C23—64no—
584C23—94no—
585C23—184no—
586C23—184no—
587C23—184no—
588C23D3×D1214yes—
589C23C22×D3212yes—
590C23C22×D3211yescharacteristic
591Q8—1816no—
592D4—616no—
593D4—124no—
594D4—1816no—
595D4—1816no—
596D4—364no—
597D4—368no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—38no—
601C2×C4—316no—
602C2×C4—34no—
603C2×C4—34no—
604C2×C4—34no—
605C2×C4—44no—
606C2×C4—64no—
607C2×C4—64no—
608C2×C4—94no—
609C2×C4—124no—
610C2×C4—1816no—
611C2×C4—1816no—
612C2×C4—184no—
613C2×C4C22×D3212yes—
614C2×C4C22×D3212yes—
615C2×C3—24no—
616C2×C3—24no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—24no—
620C2×C3—21no—
621C2×C3—44no—
622C2×C3—124no—
623C2×C3#551014yescomplemented
624C2×C3#559714yescomplemented
625C2×C3C23×D1211yescharacteristic
626C2×C3C22×D3×D411yescharacteristic
627C2×C3C2×#100411yescharacteristic
628C2×C3C2×#100411yescharacteristic
629C2×C3C2×#100711yescharacteristic
630C2×C3C2×#101011yescharacteristic
631D3—44no—
632D3—124no—
633D3—124no—
634D3—244no—
635C22—22no—
636C22—28no—
637C22—22no—
638C22—64no—
639C22—64no—
640C22—64no—
641C22—128no—
642C22—184no—
643C22—184no—
644C22—184no—
645C22—368no—
646C22#6429712yes—
647C22C2×D3×D1214yes—
648C22C2×D3×D1212yes—
649C22#6433012yes—
650C22C23×D3211yescharacteristic
651C4—22no—
652C4—22no—
653C4—38no—
654C4—64no—
655C4—64no—
656C4—184no—
657C3—21no—
658C3C2×#551011yescharacteristic, complemented
659C3C2×#559711yescharacteristic, complemented
660C2—24no—
661C2—124no—
662C2—364no—
663C2#1059491114yesdirect product factor
664C2C2×#6429711yescharacteristic
665C2C22×D3×D1211yescharacteristic
666C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3804C2semidirect
2. C2×#64139C2semidirect
3. C2×C3×#930C2semidirect
4. C22×C3×Dic3⋊C4C2semidirect
5. C2×#63978C2semidirect
6. C2×#63910C2semidirect
7. C2×#63895C2semidirect
8. #10594911C2direct (N × H)
9. C2×#63893C2semidirect
10. C2×#63886C2semidirect
25. C2×#3804C22semidirect
27. #64139C22semidirect
30. C3×#930C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. #63978C22semidirect
40. #63910C22semidirect
41. #63895C22semidirect
42. #63893C22semidirect
43. #63886C22semidirect
54. C2×#930D3semidirect
55. C22×Dic3⋊C4D3semidirect
80. C22×C3×Dic3D4semidirect
153. #930C2×D3semidirect
169. C2×Dic3⋊C4C2×D3semidirect
204. C2×C3×Dic3C2×D4semidirect
273. C22×Dic3D12semidirect
453. C2×Dic3C2×D12semidirect
469. C2×C32#537semidirect
577. C32C2×#537semidirect
623. C2×C3#5510semidirect
624. C2×C3#5597semidirect
658. C3C2×#5510semidirect
659. C3C2×#5597semidirect
663. C2#10594911direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C2×#641392
C2×C3×#9302
C22×C3×Dic3⋊C42
C2×#639782
C2×#639102
C2×#638952
#105949112
C2×#638932
C2×#638862
C2×#55973
C2×#55103