Finite Group Databasebeta

← C2×#10594452 #11903291

Subgroups — C2×#10594452 #11903291

Order 1152.

2513 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64099C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic
3C2×C3×#890C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×C4×#627C211yesmaximal, characteristic, complemented
6C2×#63899C212yesmaximal, complemented
7C2×#63898C211yesmaximal, characteristic
8C2×#63893C212yesmaximal, complemented
9C2×Dic3×D12C211yesmaximal, characteristic
10C2×D3×C4⋊Dic3C212yesmaximal, complemented
11C2×#63851C212yesmaximal, complemented
12#10594452C2116yesmaximal, direct product factor
13C2×#5690—31nomaximal
14C2×#5543—31nomaximal
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×#627C2211yescharacteristic
18C22×#627C2212yes—
19C22×D3×Dic3C2212yes—
20C22×D3×Dic3C2212yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2212yes—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64099C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×#893C2218yes—
34C3×#890C2218yescomplemented
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63918C2218yescomplemented
42C4×#627C2218yescomplemented
43#63899C22116yescomplemented
44#63898C2218yes—
45#63893C22116yescomplemented
46Dic3×D12C2218yes—
47D3×C4⋊Dic3C22116yescomplemented
48#63851C22116yescomplemented
49C2×C3×#125—31no—
50C2×C3×C4×D4—31no—
51C2×D4×Dic3—31no—
52C2×D4×Dic3—31no—
53C22×C4⋊Dic3—32no—
54C2×#924—32no—
55#5690—316no—
56#5543—316no—
57C2×#897—32no—
58C2×#896—32no—
59C2×#896—32no—
60C2×#893—31no—
61C2×#893D311yescharacteristic
62C2×D3×C4⋊C4—32no—
63C2×#890—31no—
64C2×#890—31no—
65C2×#890—61no—
66C2×#890D311yescharacteristic, complemented
67C2×#888—31no—
68C2×#878—32no—
69C2×#878—32no—
70C2×C4×D12—31no—
71C2×#869—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C23×C3×D3C2312yes—
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C2×C3×D12Q818yescomplemented
86C2×C3×D12C2314yes—
87C2×C3×C4×D3—28no—
88C2×C3×C4×D3C2318yes—
89C2×#627—24no—
90C2×#627—44no—
91C2×#627C2314yes—
92C2×#627C2318yes—
93C2×D3×Dic3—44no—
94C2×D3×Dic3—44no—
95C2×D3×Dic3C2318yes—
96C2×D3×Dic3C2318yes—
97C32×C4⋊C4C2314yes—
98C4⋊(C3⋊Dic3)C2318yes—
99C4⋊(C3⋊Dic3)C2314yes—
100#3750C2318yes—
101C4×C3⋊Dic3C2314yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×C4⋊Dic3C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2318yes—
106C3×C4×Dic3C2314yes—
107C3×C4×Dic3C2314yes—
108#3724C2314yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2314yes—
111Dic3⋊Dic3C2314yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#554—91noSylow
115C22×C3×D4—31no—
116C23×C3×C4—32no—
117C23×Dic3—32no—
118C23×Dic3—32no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—32no—
121C22×C4×D3—32no—
122C22×C4×D3C2×D312yes—
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—32no—
126C22×Dic6—32no—
127C3×#125—38no—
128C3×C4×D4—38no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—32no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C4⋊C4C2×D311yescharacteristic
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C22⋊C4—32no—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×#217—32no—
139C2×#217—32no—
140D4×Dic3—38no—
141D4×Dic3—38no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4C2×D312yes—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—32no—
148C2×C4⋊Dic3—32no—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—32no—
152C2×C4⋊Dic3—316no—
153C2×C4⋊Dic3—62no—
154C2×C4⋊Dic3—61no—
155C2×C4⋊Dic3C2×D311yescharacteristic
156C2×C4⋊Dic3C2×D312yes—
157#924—316no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—62no—
166C2×Dic3⋊C4C2×D312yes—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—61no—
170C2×C4×Dic3C2×D311yescharacteristic
171C2×C4×Dic3C2×D311yescharacteristic
172#897—316no—
173#896—316no—
174#896—316no—
175#893—38no—
176#893C2×D318yes—
177D3×C4⋊C4—316no—
178#890—38no—
179#890—38no—
180#890—68no—
181#890C2×D318yescomplemented
182#888—38no—
183#878—316no—
184#878—316no—
185C4×D12—38no—
186#869—38no—
187C4×Dic6—38no—
188C4×Dic6—38no—
189C23×C32C2411yescharacteristic
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2×Q818yes—
193C22×C3×D3C2414yes—
194C2×C32×C4—24no—
195C2×C32×C4C2×Q814yes—
196C2×C32×C4C2414yes—
197C2×C32×C4C2412yes—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3—24no—
201C2×C3⋊Dic3C2412yes—
202C2×C3⋊Dic3C2414yes—
203C2×C3⋊Dic3C2412yes—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—24no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3#4114yes—
209C2×C3×Dic3C2412yes—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C3×D12C2×Q8116yescomplemented
215C3×C4×D3—216no—
216#627—28no—
217#627—48no—
218D3×Dic3—48no—
219D3×Dic3—48no—
220#554—916no—
221C2×C4⋊Q8—91no—
222C2×#125—31no—
223C2×#125—91no—
224C2×C22⋊Q8—92no—
225C2×C22⋊Q8—92no—
226C2×C22⋊Q8—92no—
227C2×C4×Q8—91no—
228C2×C4×D4—31no—
229C2×C4×D4—91no—
230C2×C4×D4—91no—
231C22×C4⋊C4—92no—
232C24×C3—32no—
233C23×D3C22×D312yes—
234C2×C3×D4—38no—
235C2×C3×D4—34no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—32no—
242C22×C3×C4—31no—
243C22×C3×C4—38no—
244C22×C3×C4—68no—
245C22×C3×C4C22×D312yes—
246C22×C3×C4C22×D312yes—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—32no—
254C22×Dic3—32no—
255C22×Dic3—38no—
256C22×Dic3—38no—
257C22×Dic3—61no—
258C22×Dic3—61no—
259C22×Dic3—62no—
260C22×Dic3—124no—
261C22×Dic3—124no—
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D311yescharacteristic
265C22×Dic3C22×D312yes—
266C22×Dic3C22×D311yescharacteristic
267C2×D12Dic618yescomplemented
268C2×D12C22×D314yes—
269C2×C4×D3—28no—
270C2×C4×D3—38no—
271C2×C4×D3—38no—
272C2×C4×D3—124no—
273C2×C4×D3—124no—
274C2×C4×D3C22×D318yes—
275C2×Dic6—34no—
276C2×Dic6—34no—
277C2×Dic6—38no—
278C2×Dic6—38no—
279C2×Dic6—64no—
280C2×Dic6—64no—
281C2×Dic6—124no—
282C2×Dic6—124no—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—38no—
286C3×C4⋊C4—38no—
287C3×C4⋊C4C22×D314yes—
288C3×C4⋊C4C22×D314yes—
289C3×C22⋊C4—38no—
290C3×C42—34no—
291C3×C42—34no—
292#217—38no—
293#217—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4C22×D318yes—
297C4⋊Dic3—34no—
298C4⋊Dic3—34no—
299C4⋊Dic3—38no—
300C4⋊Dic3—38no—
301C4⋊Dic3—34no—
302C4⋊Dic3—34no—
303C4⋊Dic3—38no—
304C4⋊Dic3—68no—
305C4⋊Dic3—64no—
306C4⋊Dic3C22×D314yes—
307C4⋊Dic3C22×D318yes—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—34no—
311Dic3⋊C4—34no—
312Dic3⋊C4—34no—
313Dic3⋊C4—34no—
314Dic3⋊C4—38no—
315Dic3⋊C4—68no—
316Dic3⋊C4C22×D318yes—
317C4×Dic3—34no—
318C4×Dic3—34no—
319C4×Dic3—64no—
320C4×Dic3C22×D314yes—
321C4×Dic3C22×D314yes—
322C22×C32C22×Q812yes—
323C22×C32C2×#4112yes—
324C22×C32H(5,𝔽2)12yes—
325C22×C32C2511yescharacteristic
326C2×C3×D3—216no—
327C2×C3×D3—24no—
328C2×C3×D3—24no—
329C2×C3×D3C22×Q818yes—
330C32×C4—24no—
331C32×C4C22×Q814yes—
332C3⋊Dic3—22no—
333C3⋊Dic3—22no—
334C3⋊Dic3—24no—
335C3×Dic3—22no—
336C3×Dic3—22no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3C2×#4114yes—
340C22×Q8—91no—
341C22×Q8—92no—
342C22×D4—31no—
343C23×C4—32no—
344C23×C4—92no—
345C23×C4—92no—
346C4⋊Q8—98no—
347#125—38no—
348#125—98no—
349C22⋊Q8—916no—
350C22⋊Q8—916no—
351C22⋊Q8—916no—
352C4×Q8—98no—
353C4×D4—38no—
354C4×D4—98no—
355C4×D4—98no—
356C2×C4⋊C4—32no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—916no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4—91no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—92no—
367C2×C4⋊C4D3211yescharacteristic
368C2×C22⋊C4—32no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—92no—
371C2×C42—31no—
372C2×C42—31no—
373C2×C42—91no—
374C23×C3—21no—
375C23×C3—38no—
376C23×C3—34no—
377C23×C3—64no—
378C23×C3—64no—
379C23×C3C23×D311yescharacteristic
380C23×C3C23×D311yescharacteristic
381C22×D3—24no—
382C22×D3—24no—
383C22×D3C2×Dic618yes—
384C22×D3C23×D314yes—
385C3×D4—316no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—22no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—34no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—34no—
396C2×C3×C4—32no—
397C2×C3×C4—44no—
398C2×C3×C4—616no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—64no—
402C2×C3×C4—62no—
403C2×C3×C4C2×Dic614yes—
404C2×C3×C4D3×Q814yes—
405C2×C3×C4C23×D314yes—
406C2×C3×C4C23×D314yes—
407C2×C3×C4C23×D312yes—
408C2×C3×C4C23×D312yes—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—24no—
412C2×Dic3—22no—
413C2×Dic3—32no—
414C2×Dic3—32no—
415C2×Dic3—32no—
416C2×Dic3—32no—
417C2×Dic3—34no—
418C2×Dic3—34no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—64no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—64no—
425C2×Dic3—64no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—122no—
429C2×Dic3—122no—
430C2×Dic3—124no—
431C2×Dic3—128no—
432C2×Dic3—128no—
433C2×Dic3#23714yes—
434C2×Dic3C23×D312yes—
435C2×Dic3C23×D312yes—
436C2×Dic3C23×D312yes—
437C2×Dic3C23×D314yes—
438C2×Dic3C23×D312yes—
439D12C2×Dic6116yescomplemented
440C4×D3—216no—
441C4×D3—128no—
442C4×D3—128no—
443Dic6—68no—
444Dic6—68no—
445Dic6—128no—
446Dic6—128no—
447C2×C32#55414yescomplemented
448C2×C32C23×Q811yescharacteristic
449C2×C32C22×#4111yescharacteristic
450C2×C32C2×H(5,𝔽2)11yescharacteristic
451C3×D3—28no—
452C24—32no—
453C2×Q8—94no—
454C2×Q8—98no—
455C2×Q8—184no—
456C2×Q8—364no—
457C2×D4—34no—
458C2×D4—38no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—32no—
464C22×C4—38no—
465C22×C4—68no—
466C22×C4—98no—
467C22×C4—98no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—92no—
471C22×C4—364no—
472C22×C4—364no—
473C22×C4C2×D3212yes—
474C22×C4C2×D3211yescharacteristic
475C4⋊C4—38no—
476C4⋊C4—34no—
477C4⋊C4—38no—
478C4⋊C4—94no—
479C4⋊C4—98no—
480C4⋊C4—94no—
481C4⋊C4—94no—
482C4⋊C4—98no—
483C4⋊C4—94no—
484C4⋊C4—98no—
485C4⋊C4C2×D3214yes—
486C22⋊C4—38no—
487C22⋊C4—98no—
488C22⋊C4—98no—
489C42—34no—
490C42—34no—
491C42—94no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—21no—
496C22×C3—38no—
497C22×C3—616no—
498C22×C3—64no—
499C22×C3—64no—
500C22×C3C22×Dic612yes—
501C22×C3C2×#23712yes—
502C22×C3C2×D3×Q812yes—
503C22×C3D3×#4112yes—
504C22×C3#100912yes—
505C22×C3#100912yes—
506C22×C3C24×D311yescharacteristic
507C22×C3C24×D311yescharacteristic
508C2×D3—24no—
509C2×D3—24no—
510C2×D3—216no—
511C2×D3C22×Dic618yes—
512C3×C4—24no—
513C3×C4—24no—
514C3×C4—24no—
515C3×C4—34no—
516C3×C4—44no—
517C3×C4—62no—
518C3×C4—62no—
519C3×C4—64no—
520C3×C4—62no—
521C3×C4C22×Dic614yes—
522C3×C4C2×D3×Q814yes—
523Dic3—22no—
524Dic3—22no—
525Dic3—24no—
526Dic3—22no—
527Dic3—62no—
528Dic3—62no—
529Dic3—64no—
530Dic3—64no—
531Dic3—62no—
532Dic3—62no—
533Dic3—122no—
534Dic3—122no—
535Dic3—124no—
536Dic3C2×#23714yes—
537C32C2×#55411yescharacteristic, complemented, Sylow
538C23—38no—
539C23—34no—
540C23—64no—
541C23—64no—
542C23C22×D3211yescharacteristic
543Q8—188no—
544Q8—368no—
545D4—316no—
546C2×C4—24no—
547C2×C4—34no—
548C2×C4—32no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—34no—
553C2×C4—616no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—64no—
557C2×C4—62no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—94no—
561C2×C4—182no—
562C2×C4—182no—
563C2×C4—184no—
564C2×C4—368no—
565C2×C4—368no—
566C2×C4D3×Dic614yes—
567C2×C4C22×D3214yes—
568C2×C4C22×D3212yes—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—24no—
573C2×C3—68no—
574C2×C3#554314yescomplemented
575C2×C3#569014yescomplemented
576C2×C3C23×Dic611yescharacteristic
577C2×C3C22×#23711yescharacteristic
578C2×C3C22×D3×Q811yescharacteristic
579C2×C3C2×D3×#4111yescharacteristic
580C2×C3C2×#100911yescharacteristic
581C2×C3C2×#100911yescharacteristic
582D3—28no—
583C22—38no—
584C22—64no—
585C22—64no—
586C22—616no—
587C22C2×D3×Dic612yes—
588C22D3×#23712yes—
589C22#6432012yes—
590C22C23×D3211yescharacteristic
591C4—24no—
592C4—34no—
593C4—62no—
594C4—62no—
595C4—64no—
596C4—62no—
597C4—182no—
598C4—182no—
599C4—184no—
600C4C2×D3×Dic614yes—
601C3—21no—
602C3C2×#554311yescharacteristic, complemented
603C3C2×#569011yescharacteristic, complemented
604C2—68no—
605C2#1059445214yesdirect product factor
606C2C22×D3×Dic611yescharacteristic
607C2C2×D3×#23711yescharacteristic
608C2C2×#6432011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#554
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×#890C2semidirect
4. C2×#63918C2semidirect
5. C2×C4×#627C2semidirect
6. C2×#63899C2semidirect
8. C2×#63893C2semidirect
10. C2×D3×C4⋊Dic3C2semidirect
11. C2×#63851C2semidirect
12. #10594452C2direct (N × H)
26. #64099C22semidirect
34. C3×#890C22semidirect
41. #63918C22semidirect
42. C4×#627C22semidirect
43. #63899C22semidirect
45. #63893C22semidirect
47. D3×C4⋊Dic3C22semidirect
48. #63851C22semidirect
66. C2×#890D3semidirect
85. C2×C3×D12Q8semidirect
181. #890C2×D3semidirect
214. C3×D12C2×Q8semidirect
267. C2×D12Dic6semidirect
439. D12C2×Dic6semidirect
447. C2×C32#554semidirect
537. C32C2×#554semidirect
574. C2×C3#5543semidirect
575. C2×C3#5690semidirect
602. C3C2×#5543semidirect
603. C3C2×#5690semidirect
605. C2#10594452direct (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×#8932
C2×C3×#8902
C2×#639182
C2×C4×#6272
C2×#638992
C2×#638982
C2×#638932
C2×Dic3×D122
C2×D3×C4⋊Dic32
C2×#638512
#105944522
C2×#56903
C2×#55433