Finite Group Databasebeta

← C2×#10594345 #11901588

Subgroups — C2×#10594345 #11901588

Order 1152.

2121 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64099C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×#63873C211yesmaximal, characteristic, complemented
5C2×#63869C212yesmaximal, complemented
6C2×#63861C212yesmaximal
7C2×#63859C212yesmaximal
8C2×#63856C211yesmaximal, characteristic
9C2×#63855C211yesmaximal, characteristic
10C2×#63847C212yesmaximal, complemented
11C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
12#10594345C2116yesmaximal, direct product factor
13C2×#5625—31nomaximal
14C2×#5583—31nomaximal
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2212yes—
21C2×#3750C2212yes—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64099C2218yescomplemented
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29C3×#897C2218yes—
30C3×#887C2218yescomplemented
31C2×#3724C2212yes—
32C2×#3724C2212yes—
33C2×#3724C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×Dic32C2212yes—
41#63873C2218yescomplemented
42#63869C22116yescomplemented
43#63861C22116yes—
44#63859C22116yes—
45#63856C2218yes—
46#63855C2218yes—
47#63847C22116yescomplemented
48Dic3×Dic6C2218yescomplemented
49C2×C3×C22⋊Q8—31no—
50C2×C3×C4×Q8—31no—
51C2×#946—31no—
52C2×Q8×Dic3—31no—
53C2×#944—31no—
54C2×#944—31no—
55C2×#926—31no—
56C2×#924—31no—
57#5625—316no—
58#5583—316no—
59C2×#898—32no—
60C2×#897D311yescharacteristic
61C2×#890—31no—
62C2×#890—31no—
63C2×#890—32no—
64C2×#890—61no—
65C2×#889—32no—
66C2×#889—32no—
67C2×#887D311yescharacteristic, complemented
68C2×#879—32no—
69C2×#879—32no—
70C2×#876—32no—
71C2×#872—31no—
72C2×#870—32no—
73C2×C4×Dic6—31no—
74C23×C3×D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C2×C3×C4×D3—24no—
86C2×C3×C4×D3C2314yes—
87C2×C3×Dic6—24no—
88C2×C3×Dic6—24no—
89C2×C3×Dic6C2314yes—
90C2×C3×Dic6C2314yes—
91C32×C4⋊C4C2314yes—
92C4⋊(C3⋊Dic3)C2314yes—
93C4⋊(C3⋊Dic3)C2318yes—
94#3750C2318yes—
95C4×C3⋊Dic3C2314yes—
96C3×(C2×D3)⋊C4C2318yes—
97C3×C4⋊Dic3C2318yes—
98C3×Dic3⋊C4C2318yes—
99C3×C4×Dic3C2314yes—
100C3×C4×Dic3C2318yes—
101#3724C2318yes—
102#3724C2318yes—
103#3724C2318yes—
104Dic3⋊Dic3C2318yes—
105Dic3⋊Dic3C2314yes—
106Dic3⋊Dic3C2314yes—
107(C2×D3)⋊Dic3C2314yes—
108(C2×D3)⋊Dic3C2314yes—
109(C2×D3)⋊Dic3C2318yes—
110Dic32C2318yes—
111C2×#541—91noSylow
112C22×C3×Q8—31no—
113C22×C3×Q8—31no—
114C23×C3×C4—31no—
115C22×C4×D3C2×D311yescharacteristic
116C22×Dic6C2×D311yescharacteristic
117C22×Dic6C2×D311yescharacteristic
118C3×C22⋊Q8—38no—
119C3×C4×Q8—38no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4C2×D311yescharacteristic
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C22⋊C4—32no—
126C2×C3×C42—31no—
127C2×C3×C42—32no—
128C2×#217—32no—
129C2×#217—31no—
130C2×#217—31no—
131#946—38no—
132Q8×Dic3—38no—
133#944—38no—
134#944—38no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4C2×D312yes—
139#926—38no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—32no—
142C2×C4⋊Dic3—32no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—32no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—61no—
148C2×C4⋊Dic3—62no—
149C2×C4⋊Dic3C2×D312yes—
150#924—38no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—62no—
163C2×Dic3⋊C4C2×D312yes—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—61no—
169C2×C4×Dic3C2×D312yes—
170C2×C4×Dic3C2×D311yescharacteristic
171#898—316no—
172#897C2×D318yes—
173#890—38no—
174#890—38no—
175#890—316no—
176#890—68no—
177#889—316no—
178#889—316no—
179#887C2×D318yescomplemented
180#879—316no—
181#879—316no—
182#876—316no—
183#872—38no—
184#870—316no—
185C4×Dic6—38no—
186C23×C32C2411yescharacteristic
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3—22no—
190C22×C3×D3C2412yes—
191C2×C32×C4—24no—
192C2×C32×C4#4114yes—
193C2×C32×C4C2414yes—
194C2×C32×C4C2412yes—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—24no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3C2414yes—
199C2×C3⋊Dic3C2412yes—
200C2×C3⋊Dic3C2412yes—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3C2412yes—
207C2×C3×Dic3C2414yes—
208C2×C3×Dic3C2412yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2412yes—
211C3×C4×D3—28no—
212C3×Dic6—28no—
213C3×Dic6—28no—
214#541—916no—
215C2×C4⋊Q8—91no—
216C2×#126—92no—
217C2×#126—92no—
218C2×#125—92no—
219C2×#125—92no—
220C2×#125—91no—
221C2×C22⋊Q8—31no—
222C2×C22⋊Q8—91no—
223C2×C4×Q8—31no—
224C2×C4×Q8—91no—
225C2×#117—91no—
226C24×C3—31no—
227C23×D3C22×D311yescharacteristic
228C2×C3×Q8—34no—
229C2×C3×Q8—34no—
230C2×C3×Q8—64no—
231C2×C3×Q8—64no—
232C22×C3×C4—21no—
233C22×C3×C4—22no—
234C22×C3×C4—31no—
235C22×C3×C4—32no—
236C22×C3×C4—31no—
237C22×C3×C4—32no—
238C22×C3×C4—31no—
239C22×C3×C4—34no—
240C22×C3×C4—64no—
241C22×C3×C4C22×D312yes—
242C22×C3×C4C22×D312yes—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—32no—
249C22×Dic3—31no—
250C22×Dic3—32no—
251C22×Dic3—61no—
252C22×Dic3—61no—
253C22×Dic3—62no—
254C22×Dic3C22×D311yescharacteristic
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D311yescharacteristic
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D311yescharacteristic
259C2×C4×D3—24no—
260C2×C4×D3C22×D314yes—
261C2×Dic6—24no—
262C2×Dic6—24no—
263C2×Dic6C22×D314yes—
264C2×Dic6C22×D314yes—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—38no—
267C3×C4⋊C4—38no—
268C3×C4⋊C4C22×D314yes—
269C3×C4⋊C4C22×D314yes—
270C3×C22⋊C4—38no—
271C3×C42—34no—
272C3×C42—38no—
273#217—38no—
274#217—34no—
275#217—34no—
276(C2×D3)⋊C4—34no—
277(C2×D3)⋊C4—34no—
278(C2×D3)⋊C4—38no—
279(C2×D3)⋊C4C22×D318yes—
280C4⋊Dic3—34no—
281C4⋊Dic3—38no—
282C4⋊Dic3—38no—
283C4⋊Dic3—34no—
284C4⋊Dic3—38no—
285C4⋊Dic3—34no—
286C4⋊Dic3—34no—
287C4⋊Dic3—64no—
288C4⋊Dic3—68no—
289C4⋊Dic3C22×D318yes—
290Dic3⋊C4—38no—
291Dic3⋊C4—38no—
292Dic3⋊C4—38no—
293Dic3⋊C4—34no—
294Dic3⋊C4—38no—
295Dic3⋊C4—38no—
296Dic3⋊C4—34no—
297Dic3⋊C4—38no—
298Dic3⋊C4—38no—
299Dic3⋊C4—38no—
300Dic3⋊C4—38no—
301Dic3⋊C4—68no—
302Dic3⋊C4C22×D318yes—
303C4×Dic3—34no—
304C4×Dic3—34no—
305C4×Dic3—38no—
306C4×Dic3—38no—
307C4×Dic3—64no—
308C4×Dic3C22×D318yes—
309C4×Dic3C22×D314yes—
310C22×C32C2×#4112yes—
311C22×C322−1+412yes—
312C22×C322−1+412yes—
313C22×C32C2511yescharacteristic
314C2×C3×D3—22no—
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—44no—
318C32×C4—24no—
319C32×C4C2×#4114yes—
320C3⋊Dic3—24no—
321C3⋊Dic3—22no—
322C3⋊Dic3—22no—
323C3×Dic3—24no—
324C3×Dic3—24no—
325C3×Dic3—22no—
326C3×Dic3—22no—
327C3×Dic3—22no—
328C22×Q8—31no—
329C22×Q8—31no—
330C23×C4—31no—
331C4⋊Q8—98no—
332#126—916no—
333#126—916no—
334#125—916no—
335#125—916no—
336#125—98no—
337C22⋊Q8—38no—
338C22⋊Q8—98no—
339C4×Q8—38no—
340C4×Q8—98no—
341#117—98no—
342C2×C4⋊C4—32no—
343C2×C4⋊C4—32no—
344C2×C4⋊C4—91no—
345C2×C4⋊C4—91no—
346C2×C4⋊C4—92no—
347C2×C4⋊C4—92no—
348C2×C4⋊C4—92no—
349C2×C4⋊C4—92no—
350C2×C4⋊C4—91no—
351C2×C4⋊C4—92no—
352C2×C4⋊C4—92no—
353C2×C4⋊C4D3211yescharacteristic
354C2×C22⋊C4—32no—
355C2×C22⋊C4—91no—
356C2×C22⋊C4—91no—
357C2×C22⋊C4—92no—
358C2×C42—31no—
359C2×C42—32no—
360C2×C42—92no—
361C2×C42—91no—
362C23×C3—21no—
363C23×C3—32no—
364C23×C3—62no—
365C23×C3—62no—
366C23×C3—62no—
367C23×C3C23×D311yescharacteristic
368C23×C3C23×D311yescharacteristic
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3C23×D312yes—
373C3×Q8—68no—
374C3×Q8—68no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—32no—
381C2×C3×C4—34no—
382C2×C3×C4—32no—
383C2×C3×C4—34no—
384C2×C3×C4—32no—
385C2×C3×C4—44no—
386C2×C3×C4—62no—
387C2×C3×C4—64no—
388C2×C3×C4—64no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—68no—
392C2×C3×C4#23514yes—
393C2×C3×C4#23714yes—
394C2×C3×C4C23×D314yes—
395C2×C3×C4C23×D314yes—
396C2×C3×C4C23×D312yes—
397C2×C3×C4C23×D312yes—
398C2×Dic3—24no—
399C2×Dic3—24no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—34no—
406C2×Dic3—32no—
407C2×Dic3—34no—
408C2×Dic3—32no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—64no—
412C2×Dic3—62no—
413C2×Dic3—64no—
414C2×Dic3—62no—
415C2×Dic3—64no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3—124no—
421C2×Dic3C23×D312yes—
422C2×Dic3C23×D314yes—
423C2×Dic3C23×D312yes—
424C2×Dic3C23×D314yes—
425C2×Dic3C23×D312yes—
426C4×D3—28no—
427Dic6—28no—
428Dic6—28no—
429C2×C32#54114yescomplemented
430C2×C32C22×#4111yescharacteristic
431C2×C32C2×2−1+411yescharacteristic
432C2×C32C2×2−1+411yescharacteristic
433C3×D3—42no—
434C24—31no—
435C2×Q8—34no—
436C2×Q8—34no—
437C2×Q8—64no—
438C2×Q8—64no—
439C22×C4—31no—
440C22×C4—31no—
441C22×C4—32no—
442C22×C4—32no—
443C22×C4—31no—
444C22×C4—34no—
445C22×C4—64no—
446C22×C4—91no—
447C22×C4—92no—
448C22×C4—91no—
449C22×C4C2×D3212yes—
450C22×C4C2×D3211yescharacteristic
451C4⋊C4—38no—
452C4⋊C4—38no—
453C4⋊C4—94no—
454C4⋊C4—94no—
455C4⋊C4—98no—
456C4⋊C4—98no—
457C4⋊C4—98no—
458C4⋊C4—98no—
459C4⋊C4—94no—
460C4⋊C4—98no—
461C4⋊C4—98no—
462C4⋊C4C2×D3214yes—
463C22⋊C4—38no—
464C22⋊C4—94no—
465C22⋊C4—94no—
466C22⋊C4—98no—
467C42—34no—
468C42—38no—
469C42—98no—
470C42—94no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—21no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3—62no—
478C22×C3—124no—
479C22×C3C2×#23512yes—
480C22×C3C2×#23712yes—
481C22×C3#100712yes—
482C22×C3#100712yes—
483C22×C3#101012yes—
484C22×C3#101012yes—
485C22×C3C24×D311yescharacteristic
486C22×C3C24×D311yescharacteristic
487C2×D3—22no—
488C2×D3—22no—
489C2×D3—22no—
490C2×D3—44no—
491C3×C4—24no—
492C3×C4—24no—
493C3×C4—24no—
494C3×C4—44no—
495C3×C4—62no—
496C3×C4—64no—
497C3×C4—64no—
498C3×C4—62no—
499C3×C4—62no—
500C3×C4C2×#23514yes—
501C3×C4C2×#23714yes—
502Dic3—24no—
503Dic3—24no—
504Dic3—22no—
505Dic3—22no—
506Dic3—22no—
507Dic3—64no—
508Dic3—62no—
509Dic3—64no—
510Dic3—62no—
511Dic3—62no—
512Dic3—62no—
513Dic3—122no—
514Dic3—122no—
515Dic3—124no—
516C32C2×#54111yescharacteristic, complemented, Sylow
517C23—32no—
518C23—62no—
519C23—62no—
520C23—62no—
521C23C22×D3211yescharacteristic
522Q8—68no—
523Q8—68no—
524C2×C4—24no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—34no—
528C2×C4—34no—
529C2×C4—32no—
530C2×C4—62no—
531C2×C4—64no—
532C2×C4—64no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—68no—
536C2×C4—92no—
537C2×C4—94no—
538C2×C4—92no—
539C2×C4—182no—
540C2×C4—184no—
541C2×C4—182no—
542C2×C4#379514yes—
543C2×C4C22×D3214yes—
544C2×C4C22×D3212yes—
545C2×C3—24no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—122no—
550C2×C3#558314yescomplemented
551C2×C3#562514yescomplemented
552C2×C3C22×#23511yescharacteristic
553C2×C3C22×#23711yescharacteristic
554C2×C3C2×#100711yescharacteristic
555C2×C3C2×#100711yescharacteristic
556C2×C3C2×#101011yescharacteristic
557C2×C3C2×#101011yescharacteristic
558D3—42no—
559C22—62no—
560C22—62no—
561C22—62no—
562C22—124no—
563C22C2×#379512yes—
564C22#6430912yes—
565C22#6431612yes—
566C22C23×D3211yescharacteristic
567C4—24no—
568C4—62no—
569C4—64no—
570C4—64no—
571C4—62no—
572C4—62no—
573C4—182no—
574C4—184no—
575C4—182no—
576C4C2×#379514yes—
577C3—21no—
578C3C2×#558311yescharacteristic, complemented
579C3C2×#562511yescharacteristic, complemented
580C2—122no—
581C2#1059434514yesdirect product factor
582C2C22×#379511yescharacteristic
583C2C2×#6430911yescharacteristic
584C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64099C2semidirect
3. C2×C3×#887C2semidirect
4. C2×#63873C2semidirect
5. C2×#63869C2semidirect
10. C2×#63847C2semidirect
11. C2×Dic3×Dic6C2semidirect
12. #10594345C2direct (N × H)
23. #64099C22semidirect
30. C3×#887C22semidirect
41. #63873C22semidirect
42. #63869C22semidirect
47. #63847C22semidirect
48. Dic3×Dic6C22semidirect
67. C2×#887D3semidirect
179. #887C2×D3semidirect
429. C2×C32#541semidirect
516. C32C2×#541semidirect
550. C2×C3#5583semidirect
551. C2×C3#5625semidirect
578. C3C2×#5583semidirect
579. C3C2×#5625semidirect
581. C2#10594345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×C3×#8972
C2×C3×#8872
C2×#638732
C2×#638692
C2×#638612
C2×#638592
C2×#638562
C2×#638552
C2×#638472
C2×Dic3×Dic62
#105943452
C2×#56253
C2×#55833