Finite Group Databasebeta

← C2×#10593929 #11903262

Subgroups — C2×#10593929 #11903262

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×#64079C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×#63899C212yesmaximal, complemented
6C2×Dic3×D12C211yesmaximal, characteristic
7C2×Dic3×D12C211yesmaximal, characteristic
8C2×#63887C212yesmaximal, complemented
9C2×D3×Dic3⋊C4C212yesmaximal, complemented
10C2×#63869C211yesmaximal, characteristic, complemented
11C2×#63851C212yesmaximal, complemented
12#10593929C2116yesmaximal, direct product factor
13C2×#5579—31nomaximal
14C2×#5539—31nomaximal
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×Dic6C2211yescharacteristic
18C22×#627C2212yes—
19C22×D3×Dic3C2212yes—
20C22×D3×Dic3C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2212yes—
25C2×#3750C2212yes—
26#64079C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×C4×D12C2218yes—
35C3×C4×Dic6C2218yescomplemented
36C2×#3724C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63918C2218yescomplemented
42#63899C22116yescomplemented
43Dic3×D12C2218yes—
44Dic3×D12C2218yes—
45#63887C22116yescomplemented
46D3×Dic3⋊C4C22116yescomplemented
47#63869C2218yescomplemented
48#63851C22116yescomplemented
49C2×C3×C4×Q8—31no—
50C2×C3×C4×D4—31no—
51C2×#946—32no—
52C2×D4×Dic3—31no—
53C2×D4×Dic3—31no—
54C2×#924—32no—
55C22×Dic3⋊C4—32no—
56#5579—316no—
57#5539—316no—
58C2×#896—32no—
59C2×#896—32no—
60C2×D3×C4⋊C4—32no—
61C2×#890—31no—
62C2×#888—31no—
63C2×#878—32no—
64C2×#878—32no—
65C2×C4×D12—31no—
66C2×C4×D12—31no—
67C2×C4×D12D311yescharacteristic
68C2×#870—31no—
69C2×#870—31no—
70C2×#870—31no—
71C2×#870—61no—
72C2×#869—31no—
73C2×C4×Dic6D311yescharacteristic, complemented
74C23×C3×D3C2312yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2312yes—
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—44no—
88C2×C3×C4×D3C2318yes—
89C2×C3×Dic6—24no—
90C2×C3×Dic6C2314yes—
91C2×#627—44no—
92C2×#627C2318yes—
93C2×D3×Dic3—28no—
94C2×D3×Dic3—44no—
95C2×D3×Dic3C2318yes—
96C2×D3×Dic3C2318yes—
97C32×C42C2314yes—
98C4⋊(C3⋊Dic3)C2314yes—
99C4⋊(C3⋊Dic3)C2314yes—
100#3750C2318yes—
101#3750C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×C4⋊Dic3C2314yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2314yes—
106C3×Dic3⋊C4C2314yes—
107C3×C4×Dic3C2314yes—
108C3×C4×Dic3C2314yes—
109#3724C2318yes—
110Dic3⋊Dic3C2318yes—
111Dic3⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#554—91noSylow
115C22×C3×Q8—31no—
116C22×C3×D4—31no—
117C23×C3×C4—32no—
118C23×Dic3—32no—
119C23×Dic3—32no—
120C22×D12C2×D311yescharacteristic
121C22×C4×D3—32no—
122C22×C4×D3—32no—
123C22×C4×D3C2×D312yes—
124C22×Dic6—32no—
125C22×Dic6—32no—
126C22×Dic6C2×D311yescharacteristic
127C3×C4×Q8—38no—
128C3×C4×D4—38no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C42—21no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×C3×C42C2×D311yescharacteristic
138C2×C3×C42C2×D311yescharacteristic
139C2×#217—32no—
140C2×#217—32no—
141#946—316no—
142D4×Dic3—38no—
143D4×Dic3—38no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4C2×D312yes—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—32no—
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—61no—
154C2×C4⋊Dic3—61no—
155C2×C4⋊Dic3C2×D311yescharacteristic
156C2×C4⋊Dic3C2×D311yescharacteristic
157#924—316no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—316no—
167C2×Dic3⋊C4—62no—
168C2×Dic3⋊C4—62no—
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×C4×Dic3C2×D311yescharacteristic
172C2×C4×Dic3C2×D311yescharacteristic
173#896—316no—
174#896—316no—
175D3×C4⋊C4—316no—
176#890—38no—
177#888—38no—
178#878—316no—
179#878—316no—
180C4×D12—38no—
181C4×D12—38no—
182C4×D12C2×D318yes—
183#870—38no—
184#870—38no—
185#870—38no—
186#870—68no—
187#869—38no—
188C4×Dic6C2×D318yescomplemented
189C23×C32C2411yescharacteristic
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2×Q818yes—
193C22×C3×D3C2414yes—
194C2×C32×C4—22no—
195C2×C32×C4—22no—
196C2×C32×C4C2×Q814yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2412yes—
199C2×C32×C4C2412yes—
200C2×C3⋊Dic3—24no—
201C2×C3⋊Dic3—24no—
202C2×C3⋊Dic3C2414yes—
203C2×C3⋊Dic3C2414yes—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3#4114yes—
209C2×C3×Dic3C2412yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C3×D12C2×Q8116yescomplemented
215C3×C4×D3—48no—
216C3×Dic6—28no—
217#627—48no—
218D3×Dic3—216no—
219D3×Dic3—48no—
220#554—916no—
221C2×C4⋊Q8—91no—
222C2×#125—91no—
223C2×#125—91no—
224C2×C22⋊Q8—92no—
225C2×C22⋊Q8—92no—
226C2×C22⋊Q8—92no—
227C2×C4×Q8—31no—
228C2×C4×D4—31no—
229C2×C4×D4—91no—
230C2×C4×D4—91no—
231C22×C4⋊C4—92no—
232C24×C3—32no—
233C23×D3C22×D312yes—
234C2×C3×Q8—34no—
235C2×C3×Q8—64no—
236C2×C3×D4—38no—
237C2×C3×D4—34no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—32no—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—38no—
247C22×C3×C4—124no—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×Dic3—32no—
255C22×Dic3—32no—
256C22×Dic3—32no—
257C22×Dic3—32no—
258C22×Dic3—38no—
259C22×Dic3—38no—
260C22×Dic3—62no—
261C22×Dic3—62no—
262C22×Dic3—68no—
263C22×Dic3—124no—
264C22×Dic3C22×D311yescharacteristic
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D311yescharacteristic
267C22×Dic3C22×D312yes—
268C22×Dic3C22×D311yescharacteristic
269C2×D12Dic618yescomplemented
270C2×D12C22×D314yes—
271C2×C4×D3—38no—
272C2×C4×D3—38no—
273C2×C4×D3—44no—
274C2×C4×D3—68no—
275C2×C4×D3—124no—
276C2×C4×D3C22×D318yes—
277C2×Dic6—24no—
278C2×Dic6—38no—
279C2×Dic6—38no—
280C2×Dic6—124no—
281C2×Dic6—124no—
282C2×Dic6C22×D314yes—
283C3×C4⋊C4—34no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—34no—
286C3×C4⋊C4—34no—
287C3×C22⋊C4—38no—
288C3×C42—24no—
289C3×C42—34no—
290C3×C42—34no—
291C3×C42C22×D314yes—
292C3×C42C22×D314yes—
293#217—38no—
294#217—38no—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4C22×D318yes—
298C4⋊Dic3—34no—
299C4⋊Dic3—34no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302C4⋊Dic3—38no—
303C4⋊Dic3—38no—
304C4⋊Dic3—64no—
305C4⋊Dic3—64no—
306C4⋊Dic3C22×D314yes—
307C4⋊Dic3C22×D314yes—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—38no—
313Dic3⋊C4—38no—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4—68no—
317Dic3⋊C4—68no—
318Dic3⋊C4C22×D314yes—
319Dic3⋊C4C22×D314yes—
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—22no—
331C32×C4—22no—
332C32×C4C22×Q814yes—
333C3⋊Dic3—24no—
334C3⋊Dic3—24no—
335C3×Dic3—22no—
336C3×Dic3—22no—
337C3×Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3C2×#4114yes—
340C22×Q8—31no—
341C22×Q8—92no—
342C22×D4—31no—
343C23×C4—32no—
344C23×C4—92no—
345C23×C4—92no—
346C4⋊Q8—98no—
347#125—98no—
348#125—98no—
349C22⋊Q8—916no—
350C22⋊Q8—916no—
351C22⋊Q8—916no—
352C4×Q8—38no—
353C4×D4—38no—
354C4×D4—98no—
355C4×D4—98no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—916no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—92no—
368C2×C22⋊C4—32no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—92no—
371C2×C42—31no—
372C2×C42—31no—
373C2×C42D3211yescharacteristic
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×Q8—68no—
386C3×D4—316no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—24no—
395C2×C3×C4—34no—
396C2×C3×C4—32no—
397C2×C3×C4—34no—
398C2×C3×C4—32no—
399C2×C3×C4—32no—
400C2×C3×C4—32no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—64no—
407C2×C3×C4—128no—
408C2×C3×C4C2×Dic614yes—
409C2×C3×C4D3×Q814yes—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D312yes—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415C2×C3×C4C23×D312yes—
416C2×Dic3—22no—
417C2×Dic3—24no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—34no—
421C2×Dic3—34no—
422C2×Dic3—34no—
423C2×Dic3—34no—
424C2×Dic3—64no—
425C2×Dic3—64no—
426C2×Dic3—64no—
427C2×Dic3—64no—
428C2×Dic3—64no—
429C2×Dic3—64no—
430C2×Dic3—616no—
431C2×Dic3—124no—
432C2×Dic3—124no—
433C2×Dic3—128no—
434C2×Dic3#23514yes—
435C2×Dic3C23×D312yes—
436C2×Dic3C23×D312yes—
437C2×Dic3C23×D312yes—
438C2×Dic3C23×D314yes—
439C2×Dic3C23×D312yes—
440D12C2×Dic6116yescomplemented
441C4×D3—48no—
442C4×D3—616no—
443C4×D3—128no—
444Dic6—28no—
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—34no—
454C2×Q8—64no—
455C2×Q8—98no—
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—98no—
466C22×C4—98no—
467C22×C4—92no—
468C22×C4—92no—
469C22×C4—124no—
470C22×C4—188no—
471C22×C4—364no—
472C22×C4C2×D3211yescharacteristic
473C22×C4C2×D3211yescharacteristic
474C22×C4C2×D3211yescharacteristic
475C4⋊C4—34no—
476C4⋊C4—34no—
477C4⋊C4—34no—
478C4⋊C4—34no—
479C4⋊C4—98no—
480C4⋊C4—98no—
481C4⋊C4—98no—
482C4⋊C4—98no—
483C4⋊C4—94no—
484C4⋊C4—94no—
485C4⋊C4—98no—
486C22⋊C4—38no—
487C22⋊C4—98no—
488C22⋊C4—98no—
489C42—34no—
490C42—34no—
491C42C2×D3214yes—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—21no—
496C22×C3—38no—
497C22×C3—64no—
498C22×C3—64no—
499C22×C3—616no—
500C22×C3C22×Dic612yes—
501C22×C3C2×#23512yes—
502C22×C3#100412yes—
503C22×C3C2×D3×Q812yes—
504C22×C3D3×#4112yes—
505C22×C3#100912yes—
506C22×C3C24×D311yescharacteristic
507C22×C3C24×D311yescharacteristic
508C2×D3—24no—
509C2×D3—24no—
510C2×D3—216no—
511C2×D3C22×Dic618yes—
512C3×C4—22no—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—22no—
516C3×C4—24no—
517C3×C4—34no—
518C3×C4—42no—
519C3×C4—42no—
520C3×C4—62no—
521C3×C4—62no—
522C3×C4—62no—
523C3×C4—64no—
524C3×C4C22×Dic614yes—
525C3×C4C2×D3×Q814yes—
526Dic3—22no—
527Dic3—24no—
528Dic3—22no—
529Dic3—22no—
530Dic3—64no—
531Dic3—64no—
532Dic3—64no—
533Dic3—64no—
534Dic3—124no—
535Dic3—124no—
536Dic3C2×#23514yes—
537C32C2×#55411yescharacteristic, complemented, Sylow
538C23—38no—
539C23—34no—
540C23—64no—
541C23—64no—
542C23C22×D3211yescharacteristic
543Q8—68no—
544Q8—368no—
545D4—316no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—34no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—34no—
554C2×C4—62no—
555C2×C4—64no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—94no—
559C2×C4—94no—
560C2×C4—128no—
561C2×C4—1816no—
562C2×C4—184no—
563C2×C4—184no—
564C2×C4—368no—
565C2×C4D3×Dic614yes—
566C2×C4C22×D3212yes—
567C2×C4C22×D3212yes—
568C2×C4C22×D3212yes—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—24no—
573C2×C3—68no—
574C2×C3#553914yescomplemented
575C2×C3#557914yescomplemented
576C2×C3C23×Dic611yescharacteristic
577C2×C3C22×#23511yescharacteristic
578C2×C3C2×#100411yescharacteristic
579C2×C3C22×D3×Q811yescharacteristic
580C2×C3C2×D3×#4111yescharacteristic
581C2×C3C2×#100911yescharacteristic
582D3—28no—
583C22—38no—
584C22—64no—
585C22—64no—
586C22—616no—
587C22C2×D3×Dic612yes—
588C22D3×#23512yes—
589C22#6430712yes—
590C22C23×D3211yescharacteristic
591C4—22no—
592C4—22no—
593C4—34no—
594C4—62no—
595C4—64no—
596C4—62no—
597C4—62no—
598C4—184no—
599C4—184no—
600C4C2×D3×Dic614yes—
601C3—21no—
602C3C2×#553911yescharacteristic, complemented
603C3C2×#557911yescharacteristic, complemented
604C2—68no—
605C2#1059392914yesdirect product factor
606C2C22×D3×Dic611yescharacteristic
607C2C2×D3×#23511yescharacteristic
608C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64079C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. C2×#63918C2semidirect
5. C2×#63899C2semidirect
8. C2×#63887C2semidirect
9. C2×D3×Dic3⋊C4C2semidirect
10. C2×#63869C2semidirect
11. C2×#63851C2semidirect
12. #10593929C2direct (N × H)
26. #64079C22semidirect
35. C3×C4×Dic6C22semidirect
41. #63918C22semidirect
42. #63899C22semidirect
45. #63887C22semidirect
46. D3×Dic3⋊C4C22semidirect
47. #63869C22semidirect
48. #63851C22semidirect
73. C2×C4×Dic6D3semidirect
85. C2×C3×D12Q8semidirect
188. C4×Dic6C2×D3semidirect
214. C3×D12C2×Q8semidirect
269. C2×D12Dic6semidirect
440. D12C2×Dic6semidirect
447. C2×C32#554semidirect
537. C32C2×#554semidirect
574. C2×C3#5539semidirect
575. C2×C3#5579semidirect
602. C3C2×#5539semidirect
603. C3C2×#5579semidirect
605. C2#10593929direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640792
C2×C3×C4×D122
C2×C3×C4×Dic62
C2×#639182
C2×#638992
C2×Dic3×D122
C2×#638872
C2×D3×Dic3⋊C42
C2×#638692
C2×#638512
#105939292
C2×#55793
C2×#55393