Finite Group Databasebeta

← #29586770

Subgroups — #29586770

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519704C211yesmaximal, characteristic, complemented
2C2×#16839767C211yesmaximal, characteristic, complemented
3#21448411C211yesmaximal, characteristic, complemented
4C2×#16839665C211yesmaximal, characteristic, complemented
5C2×#16839530C211yesmaximal, characteristic, complemented
6C2×#16839523C211yesmaximal, characteristic, complemented
7C22×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic
8C22×#11758194C2211yescharacteristic
9C2×#14519736C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×C22⋊Dic61—22no—
12C22×C4×Dic61C2211yescharacteristic
13C2×#14519704—22no—
14C2×#14519704—22no—
15C2×#14519704—22no—
16#16839767—22no—
17#16839767—22no—
18C2×#14519698—22no—
19#16839669—21no—
20#16839665—22no—
21#16839665—22no—
22#16839665—21no—
23#16839642—22no—
24#16839622—22no—
25#16839530—22no—
26#16839523—22no—
27C22×#41×C61C2211yescharacteristic
28C23×D4×C61C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C61—22no—
30C2×AGL(1,ℤ/8)×C61—22no—
31C2×AGL(1,ℤ/8)×C61—22no—
32C2×AGL(1,ℤ/8)×C61—22no—
33C2×AGL(1,ℤ/8)×C61—22no—
34C2×AGL(1,ℤ/8)×C61C414yescomplemented
35C22×SD16×C61—21no—
36C22×D8×C61—21no—
37C22×M16×C61C2211yescharacteristic
38C23×Dic61—21no—
39C23×Dic61D412yes—
40C2×#11758194—21no—
41C2×#11758194—21no—
42C2×#11758194—21no—
43C2×#11758194—21no—
44C2×#11758194—21no—
45C2×#11758194D412yes—
46C22×#92418—21no—
47#14519736—21no—
48#14519736—21no—
49#14519736—21no—
50#14519736—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61D412yes—
58C2×C22⋊Dic61—28no—
59C2×C22⋊Dic61—21no—
60C2×C22⋊Dic61—24no—
61C2×C22⋊Dic61—48no—
62C2×C4×Dic61—21no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61D412yes—
69#14519704—28no—
70#14519698—28no—
71#14519684—24no—
72C25×C61—21no—
73C2×#41×C61—21no—
74C2×#41×C61—21no—
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—21no—
83C2×#41×C61C2×C412yes—
84C2×#41×C61D412yes—
85C22×Q8×C61D411yescharacteristic
86C22×D4×C61—21no—
87C22×D4×C61—21no—
88C22×D4×C61—21no—
89C22×D4×C61—21no—
90C22×D4×C61—21no—
91C22×D4×C61—21no—
92C22×D4×C61—21no—
93C22×D4×C61—21no—
94C22×D4×C61—21no—
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61—21no—
98C22×D4×C61C2×C412yes—
99C22×D4×C61D411yescharacteristic
100C22×D4×C61D412yes—
101C22×D4×C61D412yes—
102C23×C4×C61—21no—
103C23×C4×C61C2311yescharacteristic
104AGL(1,ℤ/8)×C61—28no—
105AGL(1,ℤ/8)×C61—28no—
106AGL(1,ℤ/8)×C61—28no—
107AGL(1,ℤ/8)×C61—28no—
108C2×SD16×C61—24no—
109C2×SD16×C61—24no—
110C2×SD16×C61—24no—
111C2×D8×C61—24no—
112C2×D8×C61—24no—
113C2×D8×C61—24no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61C2×C412yes—
118C2×M16×C61D412yes—
119C2×M16×C61D412yes—
120C22×C8×C61—21no—
121C24×C61—22no—
122C24×C61—21no—
123C24×C61—22no—
124C24×C61—22no—
125C24×C61—44no—
126C24×C61—44no—
127C24×C61—41no—
128C24×C61—41no—
129C24×C61—41no—
130C24×C61—41no—
131C24×C61C2×D411yescharacteristic
132#41×C61—22no—
133#41×C61—22no—
134#41×C61—22no—
135#41×C61—22no—
136#41×C61—22no—
137#41×C61—22no—
138#41×C61—22no—
139#41×C61—22no—
140#41×C61—41no—
141#41×C61—41no—
142#41×C61—41no—
143#41×C61—41no—
144#41×C61—41no—
145#41×C61—41no—
146#41×C61—41no—
147#41×C61—41no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61C22⋊C412yescomplemented
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—22no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—22no—
173C2×D4×C61—22no—
174C2×D4×C61—22no—
175C2×D4×C61—21no—
176C2×D4×C61—41no—
177C2×D4×C61—41no—
178C2×D4×C61—41no—
179C2×D4×C61—41no—
180C2×D4×C61—41no—
181C2×D4×C61—41no—
182C2×D4×C61—41no—
183C2×D4×C61—41no—
184C2×D4×C61—41no—
185C2×D4×C61—41no—
186C2×D4×C61—41no—
187C2×D4×C61—41no—
188C2×D4×C61—41no—
189C2×D4×C61—41no—
190C2×D4×C61—41no—
191C2×D4×C61—41no—
192C2×D4×C61C22⋊C412yescomplemented
193C2×D4×C61C22⋊C414yescomplemented
194C22×C4×C61—21no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—41no—
198C22×C4×C61—41no—
199C22×C4×C61—41no—
200C22×C4×C61—41no—
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61#4111yescharacteristic
212C22×C4×C61#4111yescharacteristic
213C22×C4×C61#4111yescharacteristic
214C22×C4×C61#4111yescharacteristic
215C22×Dic61—24no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—42no—
222C22×Dic61—41no—
223C22×Dic61—41no—
224C22×Dic61—44no—
225SD16×C61—216no—
226D8×C61—216no—
227M16×C61—22no—
228M16×C61—22no—
229M16×C61—22no—
230M16×C61C22⋊C414yescomplemented
231C2×C8×C61—22no—
232C2×C8×C61—22no—
233C2×C8×C61—22no—
234C22⋊Dic61—416no—
235C22⋊Dic61—41no—
236C22⋊Dic61—41no—
237C22⋊Dic61—84no—
238C4⋊Dic61—22no—
239C4⋊Dic61—22no—
240C4⋊Dic61—41no—
241C4⋊Dic61—41no—
242C4⋊Dic61—41no—
243C4⋊Dic61—41no—
244C4×Dic61—22no—
245C4×Dic61—22no—
246C4×Dic61—41no—
247C4×Dic61—41no—
248C4×Dic61—41no—
249C4×Dic61—41no—
250#11758194—22no—
251#11758194—22no—
252#11758194—41no—
253#11758194—41no—
254C2×#92418—22no—
255C2×#92418—41no—
256C2×#92418—41no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—24no—
261C23×C61—44no—
262C23×C61—48no—
263C23×C61—44no—
264C23×C61—48no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—42no—
270C23×C61—42no—
271C23×C61—42no—
272C23×C61—42no—
273C23×C61—42no—
274C23×C61—42no—
275C23×C61—84no—
276C23×C61—82no—
277C23×C61—82no—
278C23×C61—84no—
279C23×C61—82no—
280C23×C61—82no—
281C23×C61C4×D411yescharacteristic
282C23×C61#12011yescharacteristic
283C23×C61#12011yescharacteristic
284C23×C61#12111yescharacteristic
285C23×C61#12111yescharacteristic
286C23×C61#12111yescharacteristic
287C23×C61#12711yescharacteristic
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—41no—
291Q8×C61—41no—
292D4×C61—22no—
293D4×C61—24no—
294D4×C61—24no—
295D4×C61—22no—
296D4×C61—42no—
297D4×C61—42no—
298D4×C61—42no—
299D4×C61—42no—
300D4×C61—42no—
301D4×C61—42no—
302D4×C61—42no—
303D4×C61—42no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—41no—
307D4×C61—41no—
308C2×C4×C61—22no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C4×D411yescharacteristic
319C2×C4×C61C4×D411yescharacteristic
320C2×C4×C61C4×D411yescharacteristic
321C2×C4×C61#12011yescharacteristic
322C2×C4×C61#12011yescharacteristic
323C2×C4×C61#12011yescharacteristic
324C2×C4×C61#12011yescharacteristic
325C2×C4×C61#12011yescharacteristic
326C2×C4×C61#12011yescharacteristic
327C2×C4×C61#12111yescharacteristic
328C2×C4×C61#12111yescharacteristic
329C2×C4×C61#12111yescharacteristic
330C2×C4×C61#12111yescharacteristic
331C2×C4×C61#12111yescharacteristic
332C2×C4×C61#12111yescharacteristic
333C2×C4×C61#12111yescharacteristic
334C2×C4×C61#12111yescharacteristic
335C2×C4×C61#12111yescharacteristic
336C2×C4×C61#12311yescharacteristic
337C2×C4×C61#12311yescharacteristic
338C2×C4×C61#12311yescharacteristic
339C2×C4×C61#12311yescharacteristic
340C2×C4×C61#12411yescharacteristic
341C2×C4×C61#12411yescharacteristic
342C2×C4×C61#12711yescharacteristic
343C2×Dic61—24no—
344C2×Dic61—44no—
345C2×Dic61—42no—
346C2×Dic61—44no—
347C2×Dic61—42no—
348C2×Dic61—44no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61—44no—
353C2×Dic61—42no—
354C2×Dic61—82no—
355C8×C61—24no—
356#92418—42no—
357#11016—611nomaximal, Sylow
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—48no—
367C22×C61—44no—
368C22×C61—42no—
369C22×C61—44no—
370C22×C61—84no—
371C22×C61—84no—
372C22×C61—84no—
373C22×C61—84no—
374C22×C61—81no—
375C22×C61—82no—
376C22×C61—81no—
377C22×C61—82no—
378C22×C61—82no—
379C22×C61—84no—
380C22×C61#38611yescharacteristic
381C22×C61#38611yescharacteristic
382C22×C61#39011yescharacteristic
383C22×C61#39211yescharacteristic
384C22×C61#39211yescharacteristic
385C22×C61#39211yescharacteristic
386C22×C61#39411yescharacteristic
387C22×C61#45312yes—
388C22×C61#45412yes—
389C4×C61—42no—
390C4×C61#37911yescharacteristic
391C4×C61#38611yescharacteristic
392C4×C61#38611yescharacteristic
393C4×C61#39011yescharacteristic
394C4×C61#39211yescharacteristic
395C4×C61#39411yescharacteristic
396C4×C61#39411yescharacteristic
397C4×C61#39411yescharacteristic
398Dic61—44no—
399Dic61—82no—
400Dic61—82no—
401C22×AGL(1,ℤ/8)D6111yescharacteristic
402C22×#104—611no—
403C2×#418—611no—
404#2311—611no—
405C2×#390—611no—
406C2×#343—611no—
407C2×#339—611no—
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—82no—
413C2×C61—84no—
414C2×C61#143811yescharacteristic
415C2×C61#188312yes—
416C2×C61#200211yescharacteristic
417C2×C61#200311yescharacteristic
418C2×C61#200612yes—
419C22×#41C2×D6111yescharacteristic
420C23×D4C2×D6111yescharacteristic
421C2×AGL(1,ℤ/8)—22no—
422C2×AGL(1,ℤ/8)—22no—
423C2×AGL(1,ℤ/8)—22no—
424C2×AGL(1,ℤ/8)—22no—
425C2×AGL(1,ℤ/8)—22no—
426C2×AGL(1,ℤ/8)Dic6114yescomplemented
427C22×SD16—21no—
428C22×D8—21no—
429C22×M16—611no—
430C22×M16C2×D6111yescharacteristic
431C2×#117—611no—
432C22×C4⋊C4—611no—
433C22×C22⋊C4—1222no—
434C22×C42—611no—
435C2×#104—1222no—
436C2×#104—1222no—
437C2×#104—1222no—
438#418—1222no—
439#418—1222no—
440C2×#102—1222no—
441#391—1221no—
442#390—1222no—
443#390—1221no—
444#390—1222no—
445#386—1222no—
446#380—1222no—
447#343—1222no—
448#339—1222no—
449C61#1101611yescharacteristic, complemented, Sylow
450C25—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41C2×Dic6112yes—
462C2×#41C22⋊D6112yes—
463C22×Q8C22⋊D6111yescharacteristic
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4C2×Dic6112yes—
477C22×D4C22⋊D6111yescharacteristic
478C22×D4C22⋊D6112yes—
479C22×D4C22⋊D6112yes—
480C23×C4—21no—
481C23×C4—612no—
482C23×C4—1221no—
483C23×C4C22×D6111yescharacteristic
484AGL(1,ℤ/8)—28no—
485AGL(1,ℤ/8)—28no—
486AGL(1,ℤ/8)—28no—
487AGL(1,ℤ/8)—28no—
488C2×SD16—24no—
489C2×SD16—24no—
490C2×SD16—24no—
491C2×D8—24no—
492C2×D8—24no—
493C2×D8—24no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—612no—
498C2×M16—1221no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16C2×Dic6112yes—
504C2×M16C22⋊D6112yes—
505C2×M16C22⋊D6112yes—
506C22×C8—21no—
507C22×C8—1221no—
508#117—1221no—
509#117—1221no—
510#117—1221no—
511#117—1221no—
512C2×C4⋊C4—612no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1228no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—2448no—
523C2×C42—612no—
524C2×C42—1221no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530#104—1228no—
531#102—1228no—
532#95—1224no—
533C24—22no—
534C24—22no—
535C24—21no—
536C24—22no—
537C24—44no—
538C24—44no—
539C24—41no—
540C24—41no—
541C24—41no—
542C24—41no—
543C24D4×D6111yescharacteristic
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8C22⋊Dic6112yescomplemented
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4C22⋊Dic6112yescomplemented
605C2×D4C22⋊Dic6114yescomplemented
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—1224no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—2444no—
620C22×C4—2442no—
621C22×C4—2441no—
622C22×C4—2441no—
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4D4×D6111yescharacteristic
626C22×C4#1175822411yescharacteristic
627C22×C4#1175822411yescharacteristic
628C22×C4#1175822411yescharacteristic
629C22×C4#1175822411yescharacteristic
630C22×C4C22×Dic6111yescharacteristic
631C22×C4C2×C22⋊D6111yescharacteristic
632C22×C4C2×C22⋊D6111yescharacteristic
633C22×C4C2×C22⋊D6111yescharacteristic
634C22×C4C2×C22⋊D6111yescharacteristic
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C2×C22⋊D6111yescharacteristic
637SD16—216no—
638D8—216no—
639M16—22no—
640M16—22no—
641M16—22no—
642M16—1222no—
643M16—1222no—
644M16—2441no—
645M16—2441no—
646M16C22⋊Dic6114yescomplemented
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—1222no—
651C2×C8—2441no—
652C2×C8—2441no—
653C4⋊C4—1222no—
654C4⋊C4—1222no—
655C4⋊C4—2441no—
656C4⋊C4—2441no—
657C4⋊C4—2441no—
658C4⋊C4—2441no—
659C22⋊C4—4884no—
660C22⋊C4—24416no—
661C22⋊C4—2441no—
662C22⋊C4—2441no—
663C42—1222no—
664C42—1222no—
665C42—2441no—
666C42—2441no—
667C42—2441no—
668C42—2441no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—44no—
674C23—48no—
675C23—44no—
676C23—48no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—84no—
688C23—82no—
689C23—82no—
690C23—84no—
691C23—82no—
692C23—82no—
693C23D4×Dic6111yescharacteristic
694C23#1451974511yescharacteristic
695C23#1451974511yescharacteristic
696C23#1451974811yescharacteristic
697C23#1451974911yescharacteristic
698C23#1451974911yescharacteristic
699C23#1451977311yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—41no—
703Q8—41no—
704D4—22no—
705D4—24no—
706D4—24no—
707D4—22no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720C2×C4—22no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—1224no—
728C2×C4—4882no—
729C2×C4—2444no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2444no—
734C2×C4—2442no—
735C2×C4—2444no—
736C2×C4—2442no—
737C2×C4—2444no—
738C2×C4—2442no—
739C2×C4C2×C22⋊Dic6111yescharacteristic
740C2×C4C2×C22⋊Dic6111yescharacteristic
741C2×C4C2×C22⋊Dic6111yescharacteristic
742C2×C4D4×Dic6111yescharacteristic
743C2×C4D4×Dic6111yescharacteristic
744C2×C4D4×Dic6111yescharacteristic
745C2×C4#1451974511yescharacteristic
746C2×C4#1451974511yescharacteristic
747C2×C4#1451974611yescharacteristic
748C2×C4#1451974611yescharacteristic
749C2×C4#1451974611yescharacteristic
750C2×C4#1451974611yescharacteristic
751C2×C4#1451974811yescharacteristic
752C2×C4#1451974811yescharacteristic
753C2×C4#1451974811yescharacteristic
754C2×C4#1451974911yescharacteristic
755C2×C4#1451974911yescharacteristic
756C2×C4#1451974911yescharacteristic
757C2×C4#1451974911yescharacteristic
758C2×C4#1451974911yescharacteristic
759C2×C4#1451974911yescharacteristic
760C2×C4#1451975811yescharacteristic
761C2×C4#1451975811yescharacteristic
762C2×C4#1451975811yescharacteristic
763C2×C4#1451975811yescharacteristic
764C2×C4#1451976411yescharacteristic
765C2×C4#1451976411yescharacteristic
766C2×C4#1451977311yescharacteristic
767C8—24no—
768C8—2442no—
769C22—22no—
770C22—22no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—22no—
777C22—48no—
778C22—44no—
779C22—42no—
780C22—44no—
781C22—84no—
782C22—84no—
783C22—84no—
784C22—84no—
785C22—81no—
786C22—82no—
787C22—81no—
788C22—82no—
789C22—82no—
790C22—84no—
791C22#1683964211yescharacteristic
792C22#1683964211yescharacteristic
793C22#1683966511yescharacteristic
794C22#1683967011yescharacteristic
795C22#1683967011yescharacteristic
796C22#1683967011yescharacteristic
797C22#1683967611yescharacteristic
798C22#1683992812yes—
799C22#1683993312yes—
800C4—42no—
801C4—4882no—
802C4—4882no—
803C4—2444no—
804C4#1683961811yescharacteristic
805C4#1683964211yescharacteristic
806C4#1683964211yescharacteristic
807C4#1683966511yescharacteristic
808C4#1683967011yescharacteristic
809C4#1683967611yescharacteristic
810C4#1683967611yescharacteristic
811C4#1683967611yescharacteristic
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—84no—
817C2—82no—
818C2#2144406011yescharacteristic
819C2#2144619712yes—
820C2#2144683111yescharacteristic
821C2#2144683811yescharacteristic
822C2#2144685912yes—
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
Fitting, prime radicalC22×AGL(1,ℤ/8)×C61C2
socleC23×C61#120
cosocleC23×C4×C61C23
hypercenterC22×AGL(1,ℤ/8)D61
hypocenterC61#11016
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#14519704C2semidirect
2. C2×#16839767C2semidirect
3. #21448411C2semidirect
4. C2×#16839665C2semidirect
5. C2×#16839530C2semidirect
6. C2×#16839523C2semidirect
34. C2×AGL(1,ℤ/8)×C61C4semidirect
153. C2×Q8×C61C22⋊C4semidirect
192. C2×D4×C61C22⋊C4semidirect
193. C2×D4×C61C22⋊C4semidirect
230. M16×C61C22⋊C4semidirect
426. C2×AGL(1,ℤ/8)Dic61semidirect
449. C61#11016semidirect
565. C2×Q8C22⋊Dic61semidirect
604. C2×D4C22⋊Dic61semidirect
605. C2×D4C22⋊Dic61semidirect
646. M16C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197042
C2×#168397672
#214484112
C2×#168396652
C2×#168395302
C2×#168395232
C22×AGL(1,ℤ/8)×C612
#1101661