Finite Group Databasebeta

← C2×#83468 #11668113

Subgroups — C2×#83468 #11668113

Order 768.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#542C211yesmaximal, characteristic
2C2×#5518C211yesmaximal, characteristic, complemented
3#83468C2116yesmaximal, direct product factor
4C2×#5091C211yesmaximal, characteristic, complemented
5C2×#5094C211yesmaximal, characteristic, complemented
6C2×#5054C211yesmaximal, characteristic, complemented
7C2×#5054C211yesmaximal, characteristic, complemented
8C2×#5052C211yesmaximal, characteristic, complemented
9C2×#5051C211yesmaximal, characteristic, complemented
10C2×#5042C211yesmaximal, characteristic
11C2×#5041C211yesmaximal, characteristic
12C2×#5031C211yesmaximal, characteristic, complemented
13C2×#5022C211yesmaximal, characteristic, complemented
14C2×#5019C211yesmaximal, characteristic, complemented
15C2×#5009C211yesmaximal, characteristic, complemented
16C2×#4999C211yesmaximal, characteristic, complemented
17C2×#3258—31nomaximal, Sylow
18C3×#542—24no—
19C3×#542C2218yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#126—21no—
22C2×C3×#124—21no—
23C2×C3×#124C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×#117C2211yescharacteristic
31C22×#216C2211yescharacteristic
32C22×#216C2211yescharacteristic
33C22×#214C2211yescharacteristic
34C22×#214C2211yescharacteristic
35C2×#924C2211yescharacteristic
36C2×#924C2211yescharacteristic
37C22×#208C2211yescharacteristic
38C23×C3⋊C8C2211yescharacteristic
39#5518—24no—
40#5518C2218yescomplemented
41C2×#889—21no—
42C2×#889—21no—
43C2×#879—21no—
44C2×#879—21no—
45C2×#870C2211yescharacteristic
46C2×#869C2211yescharacteristic
47C2×C4×Dic6C2211yescharacteristic
48C2×C4×Dic6C2211yescharacteristic
49C2×#835C2211yescharacteristic
50C2×#835C2211yescharacteristic
51C2×#832C2211yescharacteristic
52C2×#832C2211yescharacteristic
53#5094C2218yescomplemented
54#5091C2218yescomplemented
55#5054C2218yescomplemented
56#5054C2218yescomplemented
57#5052C2218yescomplemented
58#5051C2218yescomplemented
59#5042C2218yes—
60#5041C2218yes—
61#5031C2218yescomplemented
62#5022C2218yescomplemented
63#5019C2218yescomplemented
64#5009C2218yescomplemented
65#4999C2218yescomplemented
66C2×#810C2211yescharacteristic
67C2×#810C2211yescharacteristic
68C2×#810C2211yescharacteristic
69C2×#810C2211yescharacteristic
70C2×#808C2211yescharacteristic
71C2×#808C2211yescharacteristic
72C2×#807C2211yescharacteristic
73C2×#807C2211yescharacteristic
74C2×C4⋊(C3⋊C8)C2211yescharacteristic
75C2×C4⋊(C3⋊C8)C2211yescharacteristic
76C2×C4⋊(C3⋊C8)C2211yescharacteristic
77C2×C4⋊(C3⋊C8)C2211yescharacteristic
78C2×#542D311yescharacteristic
79C2×#541—31no—
80#3258—316no—
81C2×#479—31no—
82C2×#477—31no—
83C2×#475—31no—
84C2×#478—31no—
85C2×#470—31no—
86C2×#468—31no—
87C2×#467—31no—
88C2×#465—31no—
89C2×#464—31no—
90C2×#464—31no—
91C2×#462—31no—
92C2×#461—31no—
93C2×#424—31no—
94C22×C3×Q8—21no—
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4C2311yescharacteristic
98C23×C3×C4—21no—
99C23×C3×C4C2311yescharacteristic
100C22×Dic6C2311yescharacteristic
101C22×Dic6C2311yescharacteristic
102C3×C4⋊Q8—22no—
103C3×C4⋊Q8C2314yes—
104C3×#126—28no—
105C3×#124—28no—
106C3×#124—22no—
107C3×#124C2314yes—
108C3×#123—28no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—28no—
111C3×C22⋊Q8C2314yes—
112C3×#121—22no—
113C3×#121C2314yes—
114C3×C4×Q8—22no—
115C3×C4×Q8C2314yes—
116C3×C4×D4—22no—
117C3×C4×D4C2314yes—
118C3×#117D414yes—
119C3×#117C2314yes—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4D411yescharacteristic
124C2×C3×C4⋊C4D411yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4D411yescharacteristic
133C2×C3×C22⋊C4D411yescharacteristic
134C2×C3×C42—21no—
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137C2×#217—21no—
138C2×#217—21no—
139C2×#216—42no—
140C2×#216—42no—
141C2×#216C2314yes—
142C2×#216C2314yes—
143C2×#214—42no—
144C2×#214—42no—
145C2×#214C2314yes—
146C2×#214C2314yes—
147C2×C4⋊Dic3—21no—
148C2×C4⋊Dic3—21no—
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151#924—22no—
152#924—22no—
153#924C2314yes—
154#924C2314yes—
155C2×Dic3⋊C4—21no—
156C2×Dic3⋊C4—21no—
157C2×Dic3⋊C4—21no—
158C2×Dic3⋊C4—21no—
159C2×Dic3⋊C4—21no—
160C2×Dic3⋊C4—21no—
161C2×C4×Dic3—21no—
162C2×C4×Dic3—21no—
163C2×#208—42no—
164C2×#208C2314yes—
165C22×C3⋊C8—42no—
166C22×C3⋊C8C2311yescharacteristic
167C22×C3⋊C8C2311yescharacteristic
168C22×C3⋊C8C2311yescharacteristic
169C22×C3⋊C8C2311yescharacteristic
170C22×C3⋊C8C2314yes—
171#889—28no—
172#889—28no—
173#879—28no—
174#879—28no—
175#870—22no—
176#870C2314yes—
177#869—22no—
178#869C2314yes—
179C4×Dic6—22no—
180C4×Dic6—22no—
181C4×Dic6C2314yes—
182C4×Dic6C2314yes—
183#835C2314yes—
184#835C2314yes—
185#832C2314yes—
186#832C2314yes—
187#810C2314yes—
188#810C2314yes—
189#810C2314yes—
190#810C2314yes—
191#808C2314yes—
192#808C2314yes—
193#807C2314yes—
194#807C2314yes—
195C4⋊(C3⋊C8)C2314yes—
196C4⋊(C3⋊C8)C2314yes—
197C4⋊(C3⋊C8)C2314yes—
198C4⋊(C3⋊C8)C2314yes—
199C22×Q16—31no—
200C22×Q16—31no—
201C22×SD16—31no—
202C22×SD16—31no—
203C22×M16—31no—
204C23×C8—31no—
205#542—24no—
206#542C2×D318yes—
207#541—38no—
208#541—64no—
209C2×C4⋊Q8—31no—
210C2×C4⋊Q8C2×D311yescharacteristic
211C2×#126—21no—
212C2×#126—61no—
213C2×#126—61no—
214C2×#125—31no—
215C2×#125—61no—
216C2×#125—61no—
217C2×#124—21no—
218C2×#124C2×D311yescharacteristic
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—31no—
222C2×C22⋊Q8—31no—
223C2×C22⋊Q8C2×D311yescharacteristic
224C2×#121C2×D311yescharacteristic
225C2×C4×Q8—31no—
226C2×C4×Q8—31no—
227C2×C4×Q8C2×D311yescharacteristic
228C2×C4×D4C2×D311yescharacteristic
229C2×#117C2×D311yescharacteristic
230#479—38no—
231#478—38no—
232#477—38no—
233#475—38no—
234#470—38no—
235#468—38no—
236#467—38no—
237#465—38no—
238#464—38no—
239#464—38no—
240#462—38no—
241#461—38no—
242C2×#107—31no—
243C2×#107—31no—
244C2×#106—31no—
245C2×#106—31no—
246#424—38no—
247C2×C4⋊C8—31no—
248C2×C4⋊C8—31no—
249C2×C4⋊C8—31no—
250C2×C4⋊C8—31no—
251C2×#103—31no—
252C2×#103—31no—
253C2×#103—31no—
254C2×#103—31no—
255C2×#103—31no—
256C2×#103—31no—
257C2×#102—31no—
258C2×#102—31no—
259C24×C3—21no—
260C24×C3C2×D411yescharacteristic
261C2×C3×Q8—21no—
262C2×C3×Q8—24no—
263C2×C3×Q8—22no—
264C2×C3×Q8—22no—
265C2×C3×Q8—82no—
266C2×C3×Q8C2412yes—
267C2×C3×D4—24no—
268C2×C3×D4—21no—
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4—82no—
272C2×C3×D4C2412yes—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—24no—
279C22×C3×C4—82no—
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2411yescharacteristic
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C2×Dic6—22no—
293C2×Dic6—22no—
294C2×Dic6—22no—
295C2×Dic6—22no—
296C2×Dic6—21no—
297C2×Dic6—21no—
298C2×Dic6C2412yes—
299C2×Dic6C2412yes—
300C3×C4⋊C4—24no—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—24no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4C2×D414yes—
306C3×C4⋊C4C2×D414yes—
307C3×C4⋊C4C2412yes—
308C3×C4⋊C4C2412yes—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—24no—
312C3×C22⋊C4—24no—
313C3×C22⋊C4—24no—
314C3×C22⋊C4C2×D414yes—
315C3×C22⋊C4C2×D414yes—
316C3×C42—24no—
317C3×C42C2×D412yes—
318C3×C42C2×D412yes—
319C3×C42C2412yes—
320C3×C42C2412yes—
321#217—24no—
322#217—24no—
323#216—44no—
324#216—44no—
325#214—44no—
326#214—44no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—24no—
330C4⋊Dic3—24no—
331C4⋊Dic3C2412yes—
332C4⋊Dic3C2412yes—
333Dic3⋊C4—24no—
334Dic3⋊C4—24no—
335Dic3⋊C4—24no—
336Dic3⋊C4—24no—
337Dic3⋊C4—24no—
338Dic3⋊C4—24no—
339C4×Dic3—24no—
340C4×Dic3—24no—
341#208—44no—
342C2×C3⋊C8—22no—
343C2×C3⋊C8—22no—
344C2×C3⋊C8—22no—
345C2×C3⋊C8—22no—
346C2×C3⋊C8—44no—
347C2×C3⋊C8C2412yes—
348C2×C3⋊C8C2412yes—
349C2×C3⋊C8C2412yes—
350C2×C3⋊C8C2412yes—
351C22×Q8—21no—
352C22×Q8—31no—
353C22×Q8—31no—
354C22×Q8C22×D311yescharacteristic
355C22×D4—21no—
356C22×D4C22×D311yescharacteristic
357C23×C4—21no—
358C23×C4C22×D311yescharacteristic
359C2×Q16—34no—
360C2×Q16—34no—
361C2×Q16—122no—
362C2×Q16—122no—
363C2×SD16—34no—
364C2×SD16—34no—
365C2×SD16—122no—
366C2×SD16—122no—
367C2×M16—34no—
368C2×M16—122no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8—31no—
372C22×C8—31no—
373C22×C8—34no—
374C22×C8—122no—
375C4⋊Q8—22no—
376C4⋊Q8—34no—
377C4⋊Q8—62no—
378C4⋊Q8C22×D314yes—
379#126—28no—
380#126—68no—
381#126—68no—
382#125—34no—
383#125—68no—
384#125—68no—
385#125—62no—
386#124—28no—
387#124—22no—
388#124C22×D314yes—
389#123—28no—
390C22⋊Q8—22no—
391C22⋊Q8—28no—
392C22⋊Q8—34no—
393C22⋊Q8—34no—
394C22⋊Q8—62no—
395C22⋊Q8—62no—
396C22⋊Q8C22×D314yes—
397#121—22no—
398#121C22×D314yes—
399C4×Q8—22no—
400C4×Q8—34no—
401C4×Q8—34no—
402C4×Q8—62no—
403C4×Q8—62no—
404C4×Q8C22×D314yes—
405C4×D4—22no—
406C4×D4C22×D314yes—
407#117#6714yes—
408#117C22×D314yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4#6711yescharacteristic
423C2×C4⋊C4#6711yescharacteristic
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4#6711yescharacteristic
434C2×C22⋊C4#6711yescharacteristic
435C2×C42—21no—
436C2×C42—61no—
437C2×C42—61no—
438C2×C42C22×D311yescharacteristic
439C2×C42C22×D311yescharacteristic
440#107—34no—
441#107—34no—
442#106—34no—
443#106—34no—
444C4⋊C8—34no—
445C4⋊C8—34no—
446C4⋊C8—34no—
447C4⋊C8—34no—
448#103—34no—
449#103—34no—
450#103—34no—
451#103—34no—
452#103—34no—
453#103—34no—
454#102—34no—
455#102—34no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—42no—
461C23×C3—42no—
462C23×C3—42no—
463C23×C3C22×D412yes—
464C23×C3C22×D411yescharacteristic
465C3×Q8—22no—
466C3×Q8—22no—
467C3×Q8—42no—
468C3×Q8—84no—
469C3×D4—22no—
470C3×D4—22no—
471C3×D4—42no—
472C3×D4—84no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—24no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4—42no—
487C2×C3×C4—84no—
488C2×C3×C4C22×D412yes—
489C2×C3×C4C22×D412yes—
490C2×C3×C4C22×D412yes—
491C2×C3×C4C22×D412yes—
492C2×C3×C4C22×D412yes—
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4H(5,𝔽2)12yes—
495C2×C3×C42−1+412yes—
496C2×C3×C4C2511yescharacteristic
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—42no—
502C2×Dic3—42no—
503C2×Dic3—42no—
504C2×Dic3—42no—
505Dic6—22no—
506Dic6—22no—
507Dic6—22no—
508Dic6—22no—
509Dic6—42no—
510Dic6—42no—
511C3⋊C8—22no—
512C3⋊C8—22no—
513C3⋊C8—22no—
514C3⋊C8—22no—
515C24—21no—
516C24C2×#6711yescharacteristic
517C2×Q8—21no—
518C2×Q8—24no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—32no—
522C2×Q8—32no—
523C2×Q8—61no—
524C2×Q8—61no—
525C2×Q8—62no—
526C2×Q8—62no—
527C2×Q8—62no—
528C2×Q8—62no—
529C2×Q8—82no—
530C2×Q8C23×D312yes—
531C2×D4—24no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—21no—
535C2×D4—82no—
536C2×D4C23×D312yes—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—24no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—82no—
548C22×C4C2×#6712yes—
549C22×C4C2×#6711yescharacteristic
550C22×C4C2×#6711yescharacteristic
551C22×C4C2×#6711yescharacteristic
552C22×C4C2×#6711yescharacteristic
553C22×C4C2×#6711yescharacteristic
554C22×C4C23×D312yes—
555C22×C4C23×D311yescharacteristic
556Q16—124no—
557Q16—124no—
558SD16—124no—
559SD16—124no—
560M16—124no—
561C2×C8—32no—
562C2×C8—32no—
563C2×C8—32no—
564C2×C8—32no—
565C2×C8—62no—
566C2×C8—62no—
567C2×C8—62no—
568C2×C8—62no—
569C2×C8—124no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—32no—
576C4⋊C4—32no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—64no—
580C4⋊C4—64no—
581C4⋊C4—64no—
582C4⋊C4—64no—
583C4⋊C4—64no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4C2×#6714yes—
588C4⋊C4C2×#6714yes—
589C4⋊C4C23×D312yes—
590C4⋊C4C23×D312yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4C2×#6714yes—
599C22⋊C4C2×#6714yes—
600C42—24no—
601C42—64no—
602C42—64no—
603C42C2×#6712yes—
604C42C2×#6712yes—
605C42C23×D312yes—
606C42C23×D312yes—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—44no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—84no—
615C22×C3#53712yes—
616C22×C3#57712yes—
617C22×C3#57812yes—
618C22×C3C23×D411yescharacteristic
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—42no—
625C3×C4—42no—
626C3×C4—42no—
627C3×C4#53712yes—
628C3×C4C2×H(5,𝔽2)11yescharacteristic
629C3×C4C2×2−1+411yescharacteristic
630Dic3—42no—
631Dic3—42no—
632Dic3—42no—
633Dic3—42no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23C22×#6712yes—
642C23C22×#6711yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—62no—
647Q8—62no—
648Q8—62no—
649Q8—62no—
650Q8—84no—
651Q8—122no—
652Q8—122no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—84no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—84no—
676C2×C4—122no—
677C2×C4—122no—
678C2×C4—122no—
679C2×C4—122no—
680C2×C4#100912yes—
681C2×C4#101012yes—
682C2×C4C22×#6712yes—
683C2×C4C22×#6712yes—
684C2×C4C22×#6712yes—
685C2×C4C22×#6712yes—
686C2×C4C22×#6712yes—
687C2×C4C22×#6711yescharacteristic
688C2×C4C24×D311yescharacteristic
689C8—62no—
690C8—62no—
691C8—62no—
692C8—62no—
693C2×C3—42no—
694C2×C3—82no—
695C2×C3#325814yescomplemented
696C2×C3C2×#53711yescharacteristic
697C2×C3C2×#57711yescharacteristic
698C2×C3C2×#57811yescharacteristic
699C22—22no—
700C22—22no—
701C22—22no—
702C22—44no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—84no—
707C22#583312yes—
708C22#583612yes—
709C22#583812yes—
710C22C23×#6711yescharacteristic
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—122no—
720C4—122no—
721C4—122no—
722C4—122no—
723C4#583312yes—
724C4C2×#100911yescharacteristic
725C4C2×#101011yescharacteristic
726C3C2×#325811yescharacteristic, complemented, Sylow
727C2—42no—
728C2—82no—
729C2#8346814yesdirect product factor
730C2C2×#583311yescharacteristic
731C2C2×#583611yescharacteristic
732C2C2×#583811yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#542C2
socleC23×C3C22×D4
prime radicalC2×C3×#121C22
hypercenterC2×#542D3
hypocenterC3C2×#3258
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
2. C2×#5518C2semidirect
3. #83468C2direct (N × H)
4. C2×#5091C2semidirect
5. C2×#5094C2semidirect
6. C2×#5054C2semidirect
7. C2×#5054C2semidirect
8. C2×#5052C2semidirect
9. C2×#5051C2semidirect
12. C2×#5031C2semidirect
13. C2×#5022C2semidirect
14. C2×#5019C2semidirect
15. C2×#5009C2semidirect
16. C2×#4999C2semidirect
40. #5518C22semidirect
53. #5094C22semidirect
54. #5091C22semidirect
55. #5054C22semidirect
56. #5054C22semidirect
57. #5052C22semidirect
58. #5051C22semidirect
61. #5031C22semidirect
62. #5022C22semidirect
63. #5019C22semidirect
64. #5009C22semidirect
65. #4999C22semidirect
695. C2×C3#3258semidirect
726. C3C2×#3258semidirect
729. C2#83468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×#55182
#834682
C2×#50912
C2×#50942
C2×#50542
C2×#50522
C2×#50512
C2×#50422
C2×#50412
C2×#50312
C2×#50222
C2×#50192
C2×#50092
C2×#49992
C2×#32583