Finite Group Databasebeta

← #29706947

Subgroups — #29706947

Order 15616.

2198 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840326C211yesmaximal, characteristic, complemented
2C2×#16840326C211yesmaximal, characteristic, complemented
3C2×#16839779C211yesmaximal, characteristic, complemented
4#21454338C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic, complemented
6#21446845C214yesmaximal, complemented
7#21446831C214yesmaximal, complemented
8#21445530C211yesmaximal, characteristic, complemented
9C2×C61×#575C211yesmaximal, characteristic, complemented
10C23×D244C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16840326—22no—
13#16840326—24no—
14#16840326—22no—
15#16840326—24no—
16#16840326—22no—
17#16840326C2214yes—
18C2×#14519773—21no—
19C2×#14519773C2212yescomplemented
20C2×#14519766—21no—
21C2×#14519766C2212yescomplemented
22C2×#14519751—22no—
23C2×#14519751—22no—
24C2×#14519745—22no—
25C2×#14519745—22no—
26C2×#14519736C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28#16839779—24no—
29C2×#14519704C2214yescomplemented
30#16839771C2212yescomplemented
31#16839767C2212yescomplemented
32#16839763—22no—
33#16839758—22no—
34C2×#14519693—24no—
35C2×#14519693C2214yescomplemented
36#16839523C2214yescomplemented
37C22×#41×C61C2211yescharacteristic
38C22×#41×C61C2211yescharacteristic
39C61×#575—24no—
40C61×#575—24no—
41C2×#137×C61—21no—
42C2×#137×C61C2212yescomplemented
43C2×AGL(1,ℤ/8)×C61—21no—
44C2×AGL(1,ℤ/8)×C61C2212yescomplemented
45C2×#135×C61—22no—
46C22×M16×C61C2211yescharacteristic
47C24×D61D412yes—
48C22×D244—22no—
49C22×D244—21no—
50C22×D244—21no—
51C22×D244—22no—
52C22×D244—21no—
53C22×D244—21no—
54C22×D244—22no—
55C22×D244—22no—
56C22×D244D412yes—
57C22×D244C2312yes—
58C22×C22⋊D61—24no—
59C22×C22⋊D61—24no—
60C2×#11758194—21no—
61C2×#11758194—22no—
62C2×#11758194—22no—
63C2×#11758194C2312yes—
64C22×#92418—21no—
65#14519773—24no—
66#14519773—24no—
67#14519773—24no—
68#14519773—24no—
69#14519766—24no—
70#14519766—24no—
71#14519766—24no—
72#14519766—24no—
73#14519751—216no—
74#14519751—28no—
75#14519751—28no—
76#14519745—28no—
77#14519745—216no—
78#14519745—28no—
79#14519736—21no—
80#14519736—21no—
81#14519736—22no—
82#14519736D412yescomplemented
83#14519736D414yescomplemented
84#14519736C2312yes—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61D412yescomplemented
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×#11758198—24no—
90C2×#11758198—24no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61C2312yes—
93#14519704—28no—
94#14519701—24no—
95#14519698—24no—
96#14519693—28no—
97C2×#41×C61—21no—
98C2×#41×C61—22no—
99C2×#41×C61—21no—
100C2×#41×C61—21no—
101C2×#41×C61—21no—
102C2×#41×C61—22no—
103C2×#41×C61—22no—
104C2×#41×C61—22no—
105C2×#41×C61—21no—
106C2×#41×C61—21no—
107C2×#41×C61—22no—
108C2×#41×C61—22no—
109C2×#41×C61—22no—
110C2×#41×C61D412yescomplemented
111C2×#41×C61D414yescomplemented
112C2×#41×C61C2312yes—
113C22×Q8×C61D411yescharacteristic, complemented
114C22×Q8×C61C2311yescharacteristic
115C22×D4×C61—21no—
116C22×D4×C61—21no—
117C22×D4×C61D411yescharacteristic, complemented
118C22×D4×C61C2311yescharacteristic
119C23×C4×C61—21no—
120C23×C4×C61—21no—
121C23×C4×C61C2311yescharacteristic
122#137×C61—28no—
123#137×C61—24no—
124#137×C61—24no—
125AGL(1,ℤ/8)×C61—28no—
126AGL(1,ℤ/8)×C61—24no—
127AGL(1,ℤ/8)×C61—24no—
128#135×C61—216no—
129C2×Q16×C61—22no—
130C2×SD16×C61—22no—
131C2×SD16×C61—22no—
132C2×D8×C61—22no—
133C2×M16×C61—21no—
134C2×M16×C61—22no—
135C2×M16×C61D414yescomplemented
136C2×M16×C61C2312yes—
137C22×C8×C61—21no—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141C23×D61—22no—
142C23×D61—22no—
143C23×D61—24no—
144C23×D61—24no—
145C23×D61—84no—
146C23×D61C2×D414yes—
147#41×C61—24no—
148#41×C61—24no—
149#41×C61—24no—
150#41×C61—24no—
151#41×C61—24no—
152#41×C61—24no—
153#41×C61—22no—
154#41×C61—22no—
155#41×C61—22no—
156#41×C61—22no—
157#41×C61—42no—
158#41×C61—42no—
159#41×C61—42no—
160#41×C61—42no—
161#41×C61—42no—
162#41×C61—42no—
163#41×C61—42no—
164#41×C61—42no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—22no—
168C2×Q8×C61—22no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61C2×D412yes—
174C2×Q8×C61C2×D412yescomplemented
175C2×D4×C61—22no—
176C2×D4×C61—24no—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—21no—
180C2×D4×C61—22no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—41no—
187C2×D4×C61—41no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—42no—
191C2×D4×C61C2×D412yes—
192C2×D4×C61C2×D412yescomplemented
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—22no—
196C22×C4×C61—24no—
197C22×C4×C61—22no—
198C22×C4×C61—41no—
199C22×C4×C61—41no—
200C22×C4×C61—42no—
201C22×C4×C61—42no—
202C22×C4×C61—42no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D412yes—
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D412yes—
211C22×C4×C61#4112yes—
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—216no—
214C2×C22⋊D61—216no—
215C2×C22⋊D61—88no—
216C2×C22⋊D61—88no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C2×D244—22no—
220C2×D244—24no—
221C2×D244—22no—
222C2×D244—24no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—22no—
227C2×D244—22no—
228C2×D244—22no—
229C2×D244—42no—
230C2×D244—42no—
231C2×D244—42no—
232C2×D244—42no—
233C2×D244—42no—
234C2×D244—42no—
235C2×D244—42no—
236C2×D244—42no—
237Q16×C61—28no—
238SD16×C61—28no—
239SD16×C61—28no—
240D8×C61—28no—
241M16×C61—24no—
242M16×C61—22no—
243M16×C61C2×D414yescomplemented
244C2×C8×C61—24no—
245C2×C8×C61—22no—
246C22⋊Dic61—22no—
247C22⋊Dic61—24no—
248C22⋊Dic61—22no—
249#11758198—216no—
250#11758198—216no—
251C4⋊Dic61—24no—
252C4⋊Dic61—22no—
253C4⋊Dic61C2×D414yes—
254C4×Dic61—22no—
255C4×Dic61—22no—
256C4×Dic61—22no—
257C4×Dic61C2×D414yescomplemented
258#11758194—22no—
259#11758194—22no—
260#11758194—42no—
261C2×#92418—22no—
262C2×#92418—42no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—42no—
266C23×C61—44no—
267C23×C61—44no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—42no—
271C23×C61#12011yescharacteristic
272C23×C61#12011yescharacteristic
273C23×C61#12012yes—
274C23×C61#12112yes—
275C23×C61C22×D411yescharacteristic
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—24no—
279C22×D61—48no—
280C22×D61—48no—
281C22×D61—44no—
282C22×D61—44no—
283C22×D61—84no—
284C22×D61—88no—
285C22×D61—88no—
286Q8×C61—22no—
287Q8×C61—22no—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—41no—
291Q8×C61—41no—
292Q8×C61—42no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—42no—
298D4×C61—42no—
299D4×C61—44no—
300D4×C61—44no—
301D4×C61—44no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—42no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—44no—
313C2×C4×C61—44no—
314C2×C4×C61—44no—
315C2×C4×C61#12012yes—
316C2×C4×C61#12012yes—
317C2×C4×C61#12011yescharacteristic
318C2×C4×C61#12011yescharacteristic
319C2×C4×C61#12012yes—
320C2×C4×C61#12112yes—
321C2×C4×C61#12112yes—
322C2×C4×C61#12112yes—
323C2×C4×C61#12112yes—
324C2×C4×C61#12112yes—
325C2×C4×C61#12712yes—
326C2×C4×C61#12712yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C22⋊D61—816no—
334C22⋊D61—816no—
335C2×Dic61—24no—
336C2×Dic61—24no—
337C2×Dic61—44no—
338C2×Dic61—44no—
339D244—42no—
340D244—42no—
341D244—42no—
342D244—42no—
343D244—44no—
344D244—44no—
345C8×C61—24no—
346#92418—42no—
347#23402—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—44no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—44no—
357C22×C61—82no—
358C22×C61—84no—
359C22×C61—82no—
360C22×C61#39212yes—
361C22×C61#39212yes—
362C22×C61C2×#12011yescharacteristic
363C22×C61C2×#12011yescharacteristic
364C22×C61C2×#12111yescharacteristic
365C2×D61—48no—
366C2×D61—44no—
367C2×D61—48no—
368C2×D61—88no—
369C2×D61—88no—
370C2×D61—84no—
371C4×C61—42no—
372C4×C61—42no—
373C4×C61#39212yes—
374C4×C61#39212yes—
375C4×C61C2×#12011yescharacteristic
376C4×C61C2×#12111yescharacteristic
377C4×C61C2×#12111yescharacteristic
378C4×C61C2×#12711yescharacteristic
379Dic61—44no—
380Dic61—44no—
381C2×#575D6111yescharacteristic, complemented
382C2×#535—611no—
383C2×#535—611no—
384C2×#421—611no—
385#2896—611no—
386C22×#100—611no—
387#2004—614no—
388#2002—614no—
389#1733—611no—
390C2×C61—21no—
391C2×C61—21no—
392C2×C61—22no—
393C2×C61—22no—
394C2×C61—82no—
395C2×C61—82no—
396C2×C61C2×#39211yescharacteristic
397C2×C61#301912yes—
398D61—84no—
399C22×#41C2×D6111yescharacteristic
400C22×#41C2×D6111yescharacteristic
401C23×D4—611no—
402#575—24no—
403#575—24no—
404C2×#137—21no—
405C2×#137C2×D6112yescomplemented
406C2×AGL(1,ℤ/8)—21no—
407C2×AGL(1,ℤ/8)C2×D6112yescomplemented
408C2×#135—22no—
409C22×M16—611no—
410C22×M16C2×D6111yescharacteristic
411#535—614no—
412#535—1224no—
413#535—1222no—
414#535—1222no—
415#535—1222no—
416#535—1224no—
417C2×#127—612no—
418C2×#127—1221no—
419C2×#124—612no—
420C2×#124—1221no—
421C2×#121—1222no—
422C2×#121—1222no—
423C2×#120—1222no—
424C2×#120—1222no—
425C2×#117—611no—
426C2×#117—611no—
427#421—1224no—
428C2×#104—614no—
429#419—612no—
430#418—612no—
431#417—1222no—
432#416—1222no—
433C2×#100—614no—
434C2×#100—1224no—
435#339—614no—
436C61#2340211yescharacteristic, complemented, Sylow
437C25—612no—
438C2×#41—21no—
439C2×#41—22no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41C22⋊D6112yescomplemented
452C2×#41C22⋊D6114yescomplemented
453C2×#41C22×D6112yes—
454C22×Q8C22⋊D6111yescharacteristic, complemented
455C22×Q8C22×D6111yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—612no—
459C22×D4—612no—
460C22×D4—1224no—
461C22×D4—1224no—
462C22×D4—1221no—
463C22×D4—1221no—
464C22×D4—1222no—
465C22×D4—1222no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1222no—
469C22×D4—1222no—
470C22×D4C22⋊D6111yescharacteristic, complemented
471C22×D4C22×D6111yescharacteristic
472C23×C4—21no—
473C23×C4—21no—
474C23×C4C22×D6111yescharacteristic
475#137—28no—
476#137—24no—
477#137—24no—
478AGL(1,ℤ/8)—28no—
479AGL(1,ℤ/8)—24no—
480AGL(1,ℤ/8)—24no—
481#135—216no—
482C2×Q16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×D8—22no—
486C2×M16—21no—
487C2×M16—22no—
488C2×M16—612no—
489C2×M16—1221no—
490C2×M16—1222no—
491C2×M16—1222no—
492C2×M16C22⋊D6114yescomplemented
493C2×M16C22×D6112yes—
494C22×C8—21no—
495C22×C8—1221no—
496#127—1224no—
497#127—1224no—
498#127—1224no—
499#127—1224no—
500#124—1224no—
501#124—1224no—
502#124—1224no—
503#124—1224no—
504#121—1228no—
505#121—1228no—
506#121—12216no—
507#120—1228no—
508#120—12216no—
509#120—1228no—
510#117—614no—
511#117—612no—
512#117—612no—
513#117—1221no—
514#117—1222no—
515#117—1221no—
516C2×C4⋊C4—612no—
517C2×C4⋊C4—1221no—
518C2×C22⋊C4—1224no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C42—612no—
523C2×C42—1221no—
524#104—1228no—
525#103—1224no—
526#102—1224no—
527#100—1228no—
528C24—21no—
529C24—21no—
530C24—614no—
531C24—1224no—
532C24—1222no—
533C24—1224no—
534C24—1222no—
535C24—4884no—
536C24D4×D6111yescharacteristic
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—24no—
542#41—24no—
543#41—24no—
544#41—24no—
545#41—24no—
546#41—24no—
547#41—42no—
548#41—42no—
549#41—42no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—42no—
554#41—42no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8C2×C22⋊D6112yes—
564C2×Q8C2×C22⋊D6112yescomplemented
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—12216no—
582C2×D4—12216no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1224no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1224no—
593C2×D4—4888no—
594C2×D4—4888no—
595C2×D4—2442no—
596C2×D4—2442no—
597C2×D4—2442no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4—2442no—
601C2×D4—2442no—
602C2×D4—2442no—
603C2×D4C2×C22⋊D6112yes—
604C2×D4C2×C22⋊D6112yescomplemented
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4D4×D6112yes—
620C22×C4D4×D6111yescharacteristic
621C22×C4#1175822412yes—
622C22×C4C2×C22⋊D6111yescharacteristic
623C22×C4C2×C22⋊D6111yescharacteristic
624C22×C4C2×C22⋊D6112yes—
625C22×C4C2×C22⋊D6112yes—
626C22×C4C23×D6111yescharacteristic
627Q16—28no—
628SD16—28no—
629SD16—28no—
630D8—28no—
631M16—22no—
632M16—24no—
633M16—1222no—
634M16—1222no—
635M16—2442no—
636M16C2×C22⋊D6114yescomplemented
637C2×C8—22no—
638C2×C8—24no—
639C2×C8—1222no—
640C2×C8—2442no—
641C4⋊C4—614no—
642C4⋊C4—1222no—
643C4⋊C4—1224no—
644C22⋊C4—12216no—
645C22⋊C4—12216no—
646C22⋊C4—1222no—
647C22⋊C4—1224no—
648C22⋊C4—1222no—
649C42—614no—
650C42—1222no—
651C42—1222no—
652C42—1222no—
653C23—22no—
654C23—22no—
655C23—42no—
656C23—44no—
657C23—44no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—1224no—
662C23—1224no—
663C23—1224no—
664C23—4884no—
665C23—4888no—
666C23—4888no—
667C23—2448no—
668C23—2448no—
669C23—2444no—
670C23—2444no—
671C23#1451974511yescharacteristic
672C23#1451974511yescharacteristic
673C23#1451974512yes—
674C23#1451974812yes—
675C23C2×D4×D6111yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682Q8—42no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—41no—
693D4—41no—
694D4—42no—
695D4—48816no—
696D4—48816no—
697D4—2442no—
698D4—2442no—
699D4—2442no—
700D4—2442no—
701D4—2444no—
702D4—2444no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—1224no—
714C2×C4—1224no—
715C2×C4—2444no—
716C2×C4—2444no—
717C2×C4#1451974512yes—
718C2×C4#1451974511yescharacteristic
719C2×C4#1451974511yescharacteristic
720C2×C4#1451974612yes—
721C2×C4#1451974612yes—
722C2×C4#1451974812yes—
723C2×C4#1451974912yes—
724C2×C4#1451974912yes—
725C2×C4#1451974912yes—
726C2×C4#1451974912yes—
727C2×C4#1451977312yes—
728C2×C4#1451977312yes—
729C2×C4C2×D4×D6111yescharacteristic
730C2×C4C2×D4×D6111yescharacteristic
731C2×C4C22×C22⋊D6111yescharacteristic
732C2×C4C22×C22⋊D6111yescharacteristic
733C2×C4C22×C22⋊D6111yescharacteristic
734C2×C4C2×#1175822411yescharacteristic
735C8—24no—
736C8—2442no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—42no—
744C22—42no—
745C22—44no—
746C22—82no—
747C22—84no—
748C22—82no—
749C22—4884no—
750C22—4888no—
751C22—4888no—
752C22—2448no—
753C22—2444no—
754C22—2448no—
755C22#1683967012yes—
756C22#1683967012yes—
757C22C2×#1451974511yescharacteristic
758C22C2×#1451974511yescharacteristic
759C22C2×#1451974811yescharacteristic
760C4—42no—
761C4—42no—
762C4—2444no—
763C4—2444no—
764C4#1683967012yes—
765C4#1683967012yes—
766C4C2×#1451974611yescharacteristic
767C4C2×#1451974911yescharacteristic
768C4C2×#1451974911yescharacteristic
769C4C2×#1451977311yescharacteristic
770C2—21no—
771C2—21no—
772C2—22no—
773C2—22no—
774C2—82no—
775C2—82no—
776C2—4884no—
777C2C2×#1683967011yescharacteristic
778C2#2145517412yes—
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#575C2
socleC22×C61C2×#120
hypercenterC2×#575D61
hypocenterC61#23402
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#16840326C2semidirect
2. C2×#16840326C2semidirect
3. C2×#16839779C2semidirect
4. #21454338C2semidirect
5. C22×#14519693C2semidirect
6. #21446845C2semidirect
7. #21446831C2semidirect
8. #21445530C2semidirect
9. C2×C61×#575C2semidirect
19. C2×#14519773C22semidirect
21. C2×#14519766C22semidirect
29. C2×#14519704C22semidirect
30. #16839771C22semidirect
31. #16839767C22semidirect
35. C2×#14519693C22semidirect
36. #16839523C22semidirect
42. C2×#137×C61C22semidirect
44. C2×AGL(1,ℤ/8)×C61C22semidirect
82. #14519736D4semidirect
83. #14519736D4semidirect
86. C2×C4⋊Dic61D4semidirect
110. C2×#41×C61D4semidirect
111. C2×#41×C61D4semidirect
113. C22×Q8×C61D4semidirect
117. C22×D4×C61D4semidirect
135. C2×M16×C61D4semidirect
174. C2×Q8×C61C2×D4semidirect
192. C2×D4×C61C2×D4semidirect
243. M16×C61C2×D4semidirect
257. C4×Dic61C2×D4semidirect
381. C2×#575D61semidirect
405. C2×#137C2×D61semidirect
407. C2×AGL(1,ℤ/8)C2×D61semidirect
436. C61#23402semidirect
451. C2×#41C22⋊D61semidirect
452. C2×#41C22⋊D61semidirect
454. C22×Q8C22⋊D61semidirect
470. C22×D4C22⋊D61semidirect
492. C2×M16C22⋊D61semidirect
564. C2×Q8C2×C22⋊D61semidirect
604. C2×D4C2×C22⋊D61semidirect
636. M16C2×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403262
C2×#168397792
#214543382
C22×#145196932
#214468452
#214468312
#214455302
C2×C61×#5752
#2340261