Finite Group Databasebeta

← C2×#79855 #11675665

Subgroups — C2×#79855 #11675665

Order 768.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5539C211yesmaximal, characteristic, complemented
2C2×D4×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×#442C211yesmaximal, characteristic
4C2×#5152C211yesmaximal, characteristic
5C2×Dic3×D8C211yesmaximal, characteristic
6C2×#5009C211yesmaximal, characteristic, complemented
7C2×#5008C211yesmaximal, characteristic, complemented
8#79855C2116yesmaximal, direct product factor
9C2×#4856C211yesmaximal, characteristic, complemented
10C2×#4855C211yesmaximal, characteristic, complemented
11C2×#4766C211yesmaximal, characteristic, complemented
12C2×#4761C211yesmaximal, characteristic, complemented
13C2×#4761C211yesmaximal, characteristic, complemented
14C2×#4759C211yesmaximal, characteristic, complemented
15C2×#4702C211yesmaximal, characteristic, complemented
16C2×#4701C211yesmaximal, characteristic, complemented
17C2×#3384—31nomaximal, Sylow
18C23×Dic6—21no—
19C22×C3×D8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C2×D4×Dic3C2211yescharacteristic
24C2×D4×Dic3C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26C2×#924—21no—
27C2×#924—21no—
28C22×Dic3⋊C4—21no—
29#5539—24no—
30#5539C2218yescomplemented
31D4×Dic6—24no—
32D4×Dic6C2218yescomplemented
33C2×#890C2211yescharacteristic
34C2×#888C2211yescharacteristic
35C2×#888C2211yescharacteristic
36C2×#888C2211yescharacteristic
37C2×#878—21no—
38C2×#878—21no—
39C2×#878—21no—
40C2×#878—21no—
41C2×#870C2211yescharacteristic
42C2×#869C2211yescharacteristic
43C2×C4×Dic6C2211yescharacteristic
44C3×#442C2218yes—
45C2×C3×#106C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#97C2211yescharacteristic
49C2×#832C2211yescharacteristic
50C2×#832C2211yescharacteristic
51C2×#832C2211yescharacteristic
52C2×#832C2211yescharacteristic
53#5152C2218yes—
54Dic3×D8C2218yes—
55C2×#818C2211yescharacteristic
56C2×#818C2211yescharacteristic
57C2×#817C2211yescharacteristic
58C2×#817C2211yescharacteristic
59C2×#815C2211yescharacteristic
60C2×Dic3⋊C8C2211yescharacteristic
61C2×Dic3⋊C8C2211yescharacteristic
62C2×C8×Dic3C2211yescharacteristic
63#5009C2218yescomplemented
64#5008C2218yescomplemented
65C2×#808C2211yescharacteristic
66C2×#808C2211yescharacteristic
67C2×#808C2211yescharacteristic
68C2×#807C2211yescharacteristic
69C2×C4⋊(C3⋊C8)C2211yescharacteristic
70#4856C2218yescomplemented
71#4855C2218yescomplemented
72#4766C2218yescomplemented
73#4761C2218yescomplemented
74#4761C2218yescomplemented
75#4759C2218yescomplemented
76#4702C2218yescomplemented
77#4701C2218yescomplemented
78C2×#554—31no—
79C2×D4×Q8—31no—
80#3384—316no—
81C2×#501—31no—
82C2×#501—31no—
83C2×#498—31no—
84C2×#478—31no—
85C2×#478—31no—
86C2×#476—31no—
87C2×#476—31no—
88C2×#476—31no—
89C2×#474—31no—
90C2×#446—31no—
91C2×#442—31no—
92C2×#442D311yescharacteristic
93C2×C4×D8—31no—
94C22×C3×D4C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C23×C3×C4—21no—
97C23×C3×C4—21no—
98C23×Dic3—21no—
99C23×Dic3—21no—
100C23×Dic3—21no—
101C23×Dic3—21no—
102C22×Dic6—21no—
103C22×Dic6—21no—
104C22×Dic6—21no—
105C22×Dic6—21no—
106C22×Dic6—28no—
107C22×Dic6—48no—
108C22×Dic6D411yescharacteristic
109C2×C3×D8Q818yescomplemented
110C2×C3×D8C2314yes—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×C4×D4C2314yes—
116C3×C4×D4C2314yes—
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C42C2311yescharacteristic
122C2×#217—21no—
123C2×#217—21no—
124C2×#217—21no—
125C2×#217—21no—
126D4×Dic3—22no—
127D4×Dic3—22no—
128D4×Dic3—22no—
129D4×Dic3—22no—
130D4×Dic3C2314yes—
131D4×Dic3C2314yes—
132D4×Dic3C2314yes—
133D4×Dic3C2314yes—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3D411yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141#924—28no—
142#924—28no—
143C2×Dic3⋊C4—21no—
144C2×Dic3⋊C4—21no—
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4—28no—
150C2×Dic3⋊C4D411yescharacteristic
151C2×Dic3⋊C4D411yescharacteristic
152C2×C4×Dic3C2311yescharacteristic
153C2×C4×Dic3C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155C22×C3⋊C8C2311yescharacteristic
156#890—22no—
157#890C2314yes—
158#888—22no—
159#888—22no—
160#888—22no—
161#888C2314yes—
162#888C2314yes—
163#888C2314yes—
164#878—28no—
165#878—28no—
166#878—28no—
167#878—28no—
168#870—22no—
169#870C2314yes—
170#869—22no—
171#869C2314yes—
172C4×Dic6D414yes—
173C4×Dic6C2314yes—
174C3×#106C2314yes—
175C3×#102C2314yes—
176C3×#102C2314yes—
177C3×#97C2314yes—
178#832C2314yes—
179#832C2314yes—
180#832C2314yes—
181#832C2314yes—
182#818C2314yes—
183#818C2314yes—
184#817C2314yes—
185#817C2314yes—
186#815C2314yes—
187Dic3⋊C8C2314yes—
188Dic3⋊C8C2314yes—
189C8×Dic3C2314yes—
190#808C2314yes—
191#808C2314yes—
192#808C2314yes—
193#807C2314yes—
194C4⋊(C3⋊C8)C2314yes—
195C23×Q8—61no—
196C22×D8C2×D311yescharacteristic
197#554—38no—
198#554—64no—
199D4×Q8—38no—
200D4×Q8—64no—
201C2×C4⋊Q8—31no—
202C2×C4⋊Q8—31no—
203C2×C4⋊Q8—31no—
204C2×C4⋊Q8—31no—
205C2×#125—31no—
206C2×#125—31no—
207C2×C22⋊Q8—61no—
208C2×C22⋊Q8—61no—
209C2×C22⋊Q8—61no—
210C2×C22⋊Q8—61no—
211C2×C22⋊Q8—61no—
212C2×C22⋊Q8—61no—
213C2×C4×Q8—31no—
214C2×C4×D4—31no—
215C2×C4×D4—31no—
216C2×C4×D4—31no—
217C2×C4×D4—31no—
218C2×C4×D4C2×D311yescharacteristic
219C2×C4×D4C2×D311yescharacteristic
220C22×C4⋊C4—61no—
221#501—38no—
222#501—38no—
223#498—38no—
224#478—38no—
225#478—38no—
226#476—38no—
227#476—38no—
228#476—38no—
229#474—38no—
230#446—38no—
231#442—38no—
232#442C2×D318yes—
233C4×D8—38no—
234C2×#107—31no—
235C2×#107—31no—
236C2×#107—31no—
237C2×#106—31no—
238C2×#106—31no—
239C2×#106—31no—
240C2×#106—31no—
241C2×#106—31no—
242C2×#106C2×D311yescharacteristic
243C2×C4⋊C8—31no—
244C2×C4⋊C8—31no—
245C2×C4⋊C8—31no—
246C2×#102—31no—
247C2×#102—31no—
248C2×#102—31no—
249C2×#102—31no—
250C2×#102C2×D311yescharacteristic
251C2×#102C2×D311yescharacteristic
252C2×#97—31no—
253C2×#97C2×D311yescharacteristic
254C2×C4×C8—31no—
255C24×C3—21no—
256C24×C3—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4C2×Q814yes—
262C2×C3×D4C2×Q814yescomplemented
263C2×C3×D4C2412yes—
264C2×C3×D4C2412yes—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—44no—
270C22×C3×C4—82no—
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2411yescharacteristic
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—24no—
279C22×Dic3—24no—
280C22×Dic3—24no—
281C22×Dic3—24no—
282C22×Dic3—44no—
283C22×Dic3—44no—
284C22×Dic3—44no—
285C22×Dic3—82no—
286C22×Dic3C2×D411yescharacteristic
287C22×Dic3C2×D411yescharacteristic
288C22×Dic3C2×D411yescharacteristic
289C22×Dic3C2×D411yescharacteristic
290C2×Dic6—24no—
291C2×Dic6—24no—
292C2×Dic6—24no—
293C2×Dic6—24no—
294C2×Dic6—24no—
295C2×Dic6—432no—
296C2×Dic6—44no—
297C2×Dic6—44no—
298C2×Dic6—44no—
299C2×Dic6—82no—
300C2×Dic6C2×D414yes—
301C3×D8C2×Q8116yescomplemented
302C2×C3×C8—22no—
303C2×C3×C8C2×Q814yescomplemented
304C2×C3×C8C2412yes—
305C2×C3×C8C2412yes—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4C2412yes—
309C3×C4⋊C4C2412yes—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—24no—
312C3×C42C2×D412yes—
313C3×C42C2412yes—
314#217—24no—
315#217—24no—
316#217—24no—
317#217—24no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—24no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3—24no—
324C4⋊Dic3C2×D414yes—
325C4⋊Dic3C2412yes—
326C4⋊Dic3C2412yes—
327C4⋊Dic3C2412yes—
328C4⋊Dic3C2412yes—
329Dic3⋊C4—24no—
330Dic3⋊C4—24no—
331Dic3⋊C4—24no—
332Dic3⋊C4—24no—
333Dic3⋊C4—24no—
334Dic3⋊C4—24no—
335Dic3⋊C4C2×D414yes—
336Dic3⋊C4C2×D414yes—
337C4×Dic3C2×D412yes—
338C4×Dic3C2×D412yes—
339C4×Dic3C2412yes—
340C4×Dic3C2412yes—
341C2×C3⋊C8—22no—
342C2×C3⋊C8—22no—
343C2×C3⋊C8C2412yes—
344C2×C3⋊C8C2412yes—
345C22×Q8—31no—
346C22×Q8—61no—
347C22×Q8—61no—
348C22×Q8—61no—
349C22×Q8—68no—
350C22×Q8—61no—
351C22×Q8—128no—
352C22×D4C22×D311yescharacteristic
353C22×D4C22×D311yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—61no—
357C23×C4—61no—
358C23×C4—61no—
359C23×C4—61no—
360C2×D8Dic618yescomplemented
361C2×D8C22×D314yes—
362C22×C8—31no—
363C22×C8—31no—
364C22×C8C22×D311yescharacteristic
365C22×C8C22×D311yescharacteristic
366C4⋊Q8—34no—
367C4⋊Q8—34no—
368C4⋊Q8—34no—
369C4⋊Q8—34no—
370C4⋊Q8—62no—
371C4⋊Q8—62no—
372C4⋊Q8—62no—
373C4⋊Q8—62no—
374#125—34no—
375#125—34no—
376#125—62no—
377#125—62no—
378C22⋊Q8—68no—
379C22⋊Q8—68no—
380C22⋊Q8—68no—
381C22⋊Q8—68no—
382C22⋊Q8—68no—
383C22⋊Q8—68no—
384C4×Q8—34no—
385C4×Q8—34no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—34no—
389C4×D4—34no—
390C4×D4—34no—
391C4×D4—34no—
392C4×D4—62no—
393C4×D4—62no—
394C4×D4—62no—
395C4×D4—62no—
396C4×D4C22×D314yes—
397C4×D4C22×D314yes—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—68no—
406C2×C4⋊C4—61no—
407C2×C4⋊C4—61no—
408C2×C4⋊C4—61no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4—61no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C42—31no—
423C2×C42—31no—
424C2×C42C22×D311yescharacteristic
425#107—34no—
426#107—34no—
427#107—34no—
428#106—34no—
429#106—34no—
430#106—34no—
431#106—34no—
432#106—34no—
433#106C22×D314yes—
434C4⋊C8—34no—
435C4⋊C8—34no—
436C4⋊C8—34no—
437#102—34no—
438#102—34no—
439#102—34no—
440#102—34no—
441#102C22×D314yes—
442#102C22×D314yes—
443#97—34no—
444#97C22×D314yes—
445C4×C8—34no—
446C23×C3—24no—
447C23×C3—24no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—42no—
453C23×C3—42no—
454C23×C3C22×D411yescharacteristic
455C3×D4—24no—
456C3×D4—24no—
457C3×D4—22no—
458C3×D4—22no—
459C3×D4C22×Q814yes—
460C3×D4C22×Q814yescomplemented
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—48no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—84no—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×D412yes—
471C2×C3×C4C22×D411yescharacteristic
472C2×C3×C4C22×Q812yes—
473C2×C3×C42−1+412yes—
474C2×C3×C4C2511yescharacteristic
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—48no—
483C2×Dic3—42no—
484C2×Dic3—42no—
485C2×Dic3—42no—
486C2×Dic3—42no—
487C2×Dic3—48no—
488C2×Dic3—48no—
489C2×Dic3—84no—
490C2×Dic3AGL(1,ℤ/8)14yes—
491C2×Dic3C22×D412yes—
492C2×Dic3C22×D412yes—
493C2×Dic3C22×D412yes—
494C2×Dic3C22×D412yes—
495Dic6—28no—
496Dic6—48no—
497Dic6—48no—
498Dic6—48no—
499Dic6—84no—
500C3×C8—22no—
501C3×C8C22×Q814yescomplemented
502C3⋊C8—22no—
503C3⋊C8—22no—
504C24—21no—
505C24—21no—
506C2×Q8—34no—
507C2×Q8—64no—
508C2×Q8—64no—
509C2×Q8—64no—
510C2×Q8—64no—
511C2×Q8—64no—
512C2×Q8—124no—
513C2×Q8—124no—
514C2×Q8—124no—
515C2×Q8—1232no—
516C2×Q8—242no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4C2×Dic614yes—
522C2×D4C2×Dic614yescomplemented
523C2×D4C23×D312yes—
524C2×D4C23×D312yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—44no—
534C22×C4—64no—
535C22×C4—64no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—82no—
543C22×C4—124no—
544C22×C4—124no—
545C22×C4—124no—
546C22×C4—242no—
547C22×C4D3×D411yescharacteristic
548C22×C4D3×D411yescharacteristic
549C22×C4C23×D311yescharacteristic
550D8C2×Dic6116yescomplemented
551C2×C8—22no—
552C2×C8—32no—
553C2×C8—32no—
554C2×C8—62no—
555C2×C8—62no—
556C2×C8C2×Dic614yescomplemented
557C2×C8C23×D312yes—
558C2×C8C23×D312yes—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—34no—
562C4⋊C4—34no—
563C4⋊C4—34no—
564C4⋊C4—32no—
565C4⋊C4—32no—
566C4⋊C4—32no—
567C4⋊C4—32no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—64no—
578C4⋊C4—64no—
579C4⋊C4—64no—
580C4⋊C4C23×D312yes—
581C4⋊C4C23×D312yes—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—64no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—64no—
588C42—32no—
589C42—32no—
590C42—32no—
591C42—32no—
592C42D3×D412yes—
593C42C23×D312yes—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—48no—
597C22×C3—48no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3D4×Q812yes—
603C22×C3C2×AGL(1,ℤ/8)12yes—
604C22×C3#57712yes—
605C22×C3C23×D411yescharacteristic
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—42no—
609C3×C4—42no—
610C3×C4D4×Q812yes—
611C3×C4C23×Q811yescharacteristic
612C3×C4C2×2−1+411yescharacteristic
613Dic3—22no—
614Dic3—22no—
615Dic3—22no—
616Dic3—42no—
617Dic3—42no—
618Dic3—42no—
619Dic3—42no—
620Dic3C2×AGL(1,ℤ/8)14yes—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23C2×D3×D411yescharacteristic
630Q8—68no—
631Q8—128no—
632Q8—128no—
633Q8—128no—
634Q8—244no—
635D4—22no—
636D4—22no—
637D4—24no—
638D4—24no—
639D4C22×Dic614yes—
640D4C22×Dic614yescomplemented
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—32no—
646C2×C4—34no—
647C2×C4—32no—
648C2×C4—32no—
649C2×C4—32no—
650C2×C4—48no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—84no—
661C2×C4—128no—
662C2×C4—128no—
663C2×C4—128no—
664C2×C4—122no—
665C2×C4—122no—
666C2×C4—122no—
667C2×C4—122no—
668C2×C4—244no—
669C2×C4C22×Dic612yes—
670C2×C4C2×D3×D412yes—
671C2×C4C2×D3×D412yes—
672C2×C4C2×D3×D411yescharacteristic
673C2×C4#101012yes—
674C2×C4C24×D311yescharacteristic
675C8—22no—
676C8—62no—
677C8—62no—
678C8C22×Dic614yescomplemented
679C2×C3—44no—
680C2×C3—44no—
681C2×C3#338414yescomplemented
682C2×C3C2×D4×Q811yescharacteristic
683C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
684C2×C3C2×#57711yescharacteristic
685C22—24no—
686C22—24no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—48no—
692C22—48no—
693C22D4×Dic612yes—
694C22D3×AGL(1,ℤ/8)12yes—
695C22#577512yes—
696C22C22×D3×D411yescharacteristic
697C4—22no—
698C4—22no—
699C4—34no—
700C4—42no—
701C4—42no—
702C4—62no—
703C4—62no—
704C4—62no—
705C4—122no—
706C4—122no—
707C4—122no—
708C4—122no—
709C4D4×Dic612yes—
710C4C23×Dic611yescharacteristic
711C4C2×#101011yescharacteristic
712C3C2×#338411yescharacteristic, complemented, Sylow
713C2—44no—
714C2—44no—
715C2#7985514yesdirect product factor
716C2C2×D4×Dic611yescharacteristic
717C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
718C2C2×#577511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#442C2
socleC23×C3C22×D4
prime radicalC22×C3×D8C22
hypercenterC2×#442D3
hypocenterC3C2×#3384
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#5539C2semidirect
2. C2×D4×Dic6C2semidirect
6. C2×#5009C2semidirect
7. C2×#5008C2semidirect
8. #79855C2direct (N × H)
9. C2×#4856C2semidirect
10. C2×#4855C2semidirect
11. C2×#4766C2semidirect
12. C2×#4761C2semidirect
13. C2×#4761C2semidirect
14. C2×#4759C2semidirect
15. C2×#4702C2semidirect
16. C2×#4701C2semidirect
30. #5539C22semidirect
32. D4×Dic6C22semidirect
63. #5009C22semidirect
64. #5008C22semidirect
70. #4856C22semidirect
71. #4855C22semidirect
72. #4766C22semidirect
73. #4761C22semidirect
74. #4761C22semidirect
75. #4759C22semidirect
76. #4702C22semidirect
77. #4701C22semidirect
109. C2×C3×D8Q8semidirect
262. C2×C3×D4C2×Q8semidirect
301. C3×D8C2×Q8semidirect
303. C2×C3×C8C2×Q8semidirect
360. C2×D8Dic6semidirect
460. C3×D4C22×Q8semidirect
501. C3×C8C22×Q8semidirect
522. C2×D4C2×Dic6semidirect
550. D8C2×Dic6semidirect
556. C2×C8C2×Dic6semidirect
640. D4C22×Dic6semidirect
678. C8C22×Dic6semidirect
681. C2×C3#3384semidirect
712. C3C2×#3384semidirect
715. C2#79855direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#55392
C2×D4×Dic62
C2×C3×#4422
C2×#51522
C2×Dic3×D82
C2×#50092
C2×#50082
#798552
C2×#48562
C2×#48552
C2×#47662
C2×#47612
C2×#47592
C2×#47022
C2×#47012
C2×#33843