Finite Group Databasebeta

← #29586520

Subgroups — #29586520

Order 15616.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519752C211yesmaximal, characteristic
2C22×#14519699C211yesmaximal, characteristic, complemented
3C22×#14519697C211yesmaximal, characteristic, complemented
4C22×#14519689C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic, complemented
6C2×#16839524C211yesmaximal, characteristic, complemented
7C2×C61×#340C211yesmaximal, characteristic, complemented
8C23×D244—21no—
9C23×D244C2211yescharacteristic
10C23×C4×D61C2211yescharacteristic
11C23×#92418C2211yescharacteristic
12C2×#14519752—22no—
13C2×#14519752—22no—
14C2×#14519752—22no—
15C2×#14519752—22no—
16C2×#14519752—22no—
17C2×#14519752C414yescomplemented
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758198—21no—
20C22×#11758198—21no—
21C2×#14519699—22no—
22C2×#14519699—22no—
23C2×#14519699—22no—
24C2×#14519697—22no—
25C2×#14519697—22no—
26C2×#14519697—22no—
27C2×#14519689—22no—
28C2×#14519689—22no—
29C2×#14519689—22no—
30#16839619—22no—
31#16839619—22no—
32C2×#14519684—21no—
33#16839524—22no—
34C23×C8×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C61×#340—22no—
38C24×D61—21no—
39C24×D61D411yescharacteristic
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—21no—
48C22×D244—24no—
49C22×D244—24no—
50C22×D244—24no—
51C22×D244—21no—
52C22×D244—21no—
53C22×D244—21no—
54C22×D244—42no—
55C22×D244—42no—
56C22×D244—42no—
57C22×D244—42no—
58C22×D244C2×C412yes—
59C22×D244D412yes—
60C22×D244D412yes—
61C23×Dic61—21no—
62C23×Dic61D411yescharacteristic
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61C2×C412yes—
76C22×C4×D61D412yes—
77C22×#92418—21no—
78C22×#92418—21no—
79C22×#92418—21no—
80C22×#92418—21no—
81C22×#92418—21no—
82C22×#92418—21no—
83C22×#92418D412yescomplemented
84#14519752—28no—
85#14519752—28no—
86#14519752—28no—
87#14519752—28no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61D412yescomplemented
94C2×#11758198—24no—
95C2×#11758198—24no—
96C2×#11758198—24no—
97C2×#11758198—24no—
98C2×#11758198—42no—
99C2×#11758198—42no—
100#14519699—28no—
101#14519697—28no—
102#14519689—28no—
103#14519684—24no—
104C23×C4×C61—21no—
105C23×C4×C61—21no—
106C23×C4×C61C2311yescharacteristic
107C22×C8×C61—21no—
108C22×C8×C61—21no—
109C22×C8×C61—21no—
110C22×C8×C61—21no—
111C22×C8×C61—21no—
112C22×C8×C61—21no—
113C22×C8×C61D412yescomplemented
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61C2×C412yes—
123C2×C4⋊C4×C61D412yes—
124C2×C4⋊C4×C61D412yes—
125C2×C4⋊C4×C61D412yescomplemented
126C24×C61C2×D411yescharacteristic
127C23×D61—21no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—21no—
136C23×D61—21no—
137C23×D61—21no—
138C23×D61—21no—
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—22no—
142C23×D61—41no—
143C23×D61—41no—
144C23×D61—41no—
145C23×D61—41no—
146C23×D61—41no—
147C23×D61—41no—
148C23×D61—41no—
149C23×D61—41no—
150C23×D61—41no—
151C23×D61—41no—
152C23×D61—41no—
153C23×D61—41no—
154C23×D61C22⋊C412yes—
155C23×D61D812yes—
156C23×D61SD1612yes—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—41no—
162C22×C4×C61—41no—
163C22×C4×C61—41no—
164C22×C4×C61—41no—
165C22×C4×C61—41no—
166C22×C4×C61—41no—
167C22×C4×C61—41no—
168C22×C4×C61—41no—
169C22×C4×C61—41no—
170C22×C4×C61—41no—
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61#4111yescharacteristic
182C22×C4×C61#4111yescharacteristic
183C22×C4×C61#4111yescharacteristic
184C22×C4×C61#4111yescharacteristic
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—22no—
192C22×Dic61—41no—
193C22×Dic61—41no—
194C22×Dic61—41no—
195C22×Dic61—41no—
196C22×Dic61—41no—
197C22×Dic61—41no—
198C22×Dic61C22⋊C412yes—
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—22no—
202C2×D244—22no—
203C2×D244—22no—
204C2×D244—22no—
205C2×D244—22no—
206C2×D244—22no—
207C2×D244—22no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—22no—
211C2×D244—216no—
212C2×D244—22no—
213C2×D244—22no—
214C2×D244—22no—
215C2×D244—48no—
216C2×D244—48no—
217C2×D244—48no—
218C2×D244—48no—
219C2×D244—48no—
220C2×D244—48no—
221C2×D244—41no—
222C2×D244—41no—
223C2×D244—41no—
224C2×D244—41no—
225C2×D244—41no—
226C2×D244—41no—
227C2×D244—41no—
228C2×D244—41no—
229C2×D244—41no—
230C2×D244—41no—
231C2×D244—41no—
232C2×D244—41no—
233C2×D244C22⋊C414yescomplemented
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—22no—
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—41no—
247C2×C4×D61—41no—
248C2×C4×D61—41no—
249C2×C4×D61—41no—
250C2×C4×D61—41no—
251C2×C4×D61—41no—
252C2×C4×D61—41no—
253C2×C4×D61—41no—
254C2×C4×D61—41no—
255C2×C4×D61—41no—
256C2×C4×D61—41no—
257C2×C4×D61—41no—
258C2×C4×D61—41no—
259C2×C4×D61—41no—
260C2×C4×D61—41no—
261C2×C4×D61—41no—
262C2×C8×C61—22no—
263C2×C8×C61—22no—
264C2×C8×C61—22no—
265C2×C8×C61—41no—
266C2×C8×C61—41no—
267C2×C8×C61—41no—
268C2×C8×C61—41no—
269C4⋊C4×C61—22no—
270C4⋊C4×C61—22no—
271C4⋊C4×C61—22no—
272C4⋊C4×C61—22no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61—41no—
275C4⋊C4×C61—41no—
276C4⋊C4×C61C22⋊C414yescomplemented
277#11758198—216no—
278#11758198—48no—
279C4⋊Dic61—22no—
280C4⋊Dic61—22no—
281C4⋊Dic61—41no—
282C4⋊Dic61—41no—
283C2×#92418—22no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418—41no—
287C2×#92418—41no—
288C2×#92418—41no—
289C2×#92418—41no—
290C23×C61C2×C22⋊C411yescharacteristic
291C23×C61#12011yescharacteristic
292C23×C61#12011yescharacteristic
293C23×C61#12011yescharacteristic
294C23×C61#12111yescharacteristic
295C23×C61#12111yescharacteristic
296C23×C61#12311yescharacteristic
297C23×C61C2×D811yescharacteristic
298C23×C61C2×SD1611yescharacteristic
299C23×C61#13511yescharacteristic
300C23×C61#13511yescharacteristic
301C23×C61AGL(1,ℤ/8)11yescharacteristic
302C23×C61AGL(1,ℤ/8)11yescharacteristic
303C23×C61AGL(1,ℤ/8)11yescharacteristic
304C23×C61#13711yescharacteristic
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—24no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—42no—
346C22×D61—42no—
347C22×D61—42no—
348C22×D61—42no—
349C22×D61—42no—
350C22×D61—42no—
351C22×D61—42no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—81no—
359C22×D61—81no—
360C22×D61—81no—
361C22×D61—81no—
362C22×D61—81no—
363C22×D61—81no—
364C22×D61—81no—
365C22×D61—81no—
366C22×D61—81no—
367C22×D61—81no—
368C22×D61—81no—
369C22×D61—81no—
370C22×D61—81no—
371C22×D61—81no—
372C22×D61—81no—
373C22×D61—81no—
374C22×D61#10214yescomplemented
375C2×C4×C61—24no—
376C2×C4×C61—42no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—42no—
380C2×C4×C61—42no—
381C2×C4×C61—42no—
382C2×C4×C61—42no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—81no—
386C2×C4×C61—81no—
387C2×C4×C61—81no—
388C2×C4×C61—81no—
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C4×D411yescharacteristic
392C2×C4×C61C4×D411yescharacteristic
393C2×C4×C61C4×D411yescharacteristic
394C2×C4×C61C4×D411yescharacteristic
395C2×C4×C61#12011yescharacteristic
396C2×C4×C61#12011yescharacteristic
397C2×C4×C61#12011yescharacteristic
398C2×C4×C61#12011yescharacteristic
399C2×C4×C61#12011yescharacteristic
400C2×C4×C61#12111yescharacteristic
401C2×C4×C61#12111yescharacteristic
402C2×C4×C61#12111yescharacteristic
403C2×C4×C61#12111yescharacteristic
404C2×C4×C61#12111yescharacteristic
405C2×C4×C61#12111yescharacteristic
406C2×C4×C61#12111yescharacteristic
407C2×C4×C61#12111yescharacteristic
408C2×C4×C61#12111yescharacteristic
409C2×C4×C61#12111yescharacteristic
410C2×C4×C61#12311yescharacteristic
411C2×C4×C61#12311yescharacteristic
412C2×C4×C61#12311yescharacteristic
413C2×C4×C61#12411yescharacteristic
414C2×C4×C61#12411yescharacteristic
415C2×C4×C61#12711yescharacteristic
416C2×C4×C61#12711yescharacteristic
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—42no—
425C2×Dic61—42no—
426C2×Dic61—42no—
427C2×Dic61—81no—
428C2×Dic61—81no—
429C2×Dic61—81no—
430C2×Dic61—81no—
431D244—24no—
432D244—24no—
433D244—432no—
434D244—42no—
435D244—42no—
436D244—42no—
437D244—42no—
438D244—42no—
439D244—42no—
440C4×D61—42no—
441C4×D61—42no—
442C4×D61—42no—
443C4×D61—42no—
444C4×D61—42no—
445C4×D61—42no—
446C4×D61—42no—
447C4×D61—42no—
448C8×C61—42no—
449#92418—42no—
450#10969—611nomaximal, Sylow
451C22×C61#37911yescharacteristic
452C22×C61#38611yescharacteristic
453C22×C61#38611yescharacteristic
454C22×C61#39211yescharacteristic
455C22×C61#39211yescharacteristic
456C22×C61#39411yescharacteristic
457C22×C61#39411yescharacteristic
458C22×C61C2×#10211yescharacteristic
459C22×C61#41611yescharacteristic
460C22×C61#41711yescharacteristic
461C22×C61#41811yescharacteristic
462C22×C61#44711yescharacteristic
463C22×C61#44711yescharacteristic
464C22×C61#44711yescharacteristic
465C22×C61#44811yescharacteristic
466C22×C61#44911yescharacteristic
467C22×C61#44911yescharacteristic
468C22×C61#44911yescharacteristic
469C22×C61#44911yescharacteristic
470C22×C61#45011yescharacteristic
471C22×C61#45011yescharacteristic
472C22×C61#45211yescharacteristic
473C22×C61#45211yescharacteristic
474C22×C61#46511yescharacteristic
475C22×C61#46511yescharacteristic
476C22×C61#46611yescharacteristic
477C22×C61#46611yescharacteristic
478C22×C61#46811yescharacteristic
479C22×C61#46811yescharacteristic
480C22×C61#46911yescharacteristic
481C22×C61#46911yescharacteristic
482C22×C61#48011yescharacteristic
483C22×C61#48111yescharacteristic
484C22×C61#48211yescharacteristic
485C22×C61#48211yescharacteristic
486C2×D61—24no—
487C2×D61—24no—
488C2×D61—24no—
489C2×D61—42no—
490C2×D61—42no—
491C2×D61—42no—
492C2×D61—42no—
493C2×D61—42no—
494C2×D61—42no—
495C2×D61—42no—
496C2×D61—42no—
497C2×D61—42no—
498C2×D61—42no—
499C2×D61—42no—
500C2×D61—42no—
501C2×D61—44no—
502C2×D61—44no—
503C2×D61—44no—
504C2×D61—82no—
505C2×D61—82no—
506C2×D61—82no—
507C2×D61—82no—
508C2×D61—82no—
509C2×D61—82no—
510C2×D61—82no—
511C2×D61—82no—
512C2×D61—82no—
513C2×D61—82no—
514C2×D61—82no—
515C2×D61—82no—
516C4×C61—44no—
517C4×C61—82no—
518C4×C61#38611yescharacteristic
519C4×C61#38611yescharacteristic
520C4×C61#39011yescharacteristic
521C4×C61#39011yescharacteristic
522C4×C61#39211yescharacteristic
523C4×C61#39211yescharacteristic
524C4×C61#39411yescharacteristic
525C4×C61#39411yescharacteristic
526Dic61—42no—
527Dic61—82no—
528C22×#121—611no—
529C22×#102—611no—
530C22×#102—611no—
531C22×C22⋊C8—611no—
532C2×#380—611no—
533C2×#340—611no—
534C2×#340D6111yescharacteristic, complemented
535C2×C61#143811yescharacteristic
536C2×C61#178611yescharacteristic
537C2×C61#178811yescharacteristic
538C2×C61#187411yescharacteristic
539C2×C61#187511yescharacteristic
540C2×C61#189311yescharacteristic
541C2×C61#189511yescharacteristic
542C2×C61#199911yescharacteristic
543C2×C61#199911yescharacteristic
544C2×C61#200011yescharacteristic
545C2×C61#200011yescharacteristic
546C2×C61#203311yescharacteristic
547C2×C61#203311yescharacteristic
548C2×C61#203411yescharacteristic
549C2×C61#203411yescharacteristic
550D61—44no—
551D61—84no—
552C23×D4—611no—
553C23×D4—1221no—
554C24×C4—611no—
555C23×C8—611no—
556C23×C8C2×D6111yescharacteristic
557C2×#121—614no—
558C2×#121—1222no—
559C2×#121—1222no—
560C2×#121—1222no—
561C2×#121—1222no—
562C2×#121—1222no—
563C22×C4⋊C4—611no—
564C22×C4⋊C4C2×D6111yescharacteristic
565C22×C4⋊C4C2×D6111yescharacteristic
566C22×C22⋊C4—1221no—
567C22×C22⋊C4—1221no—
568C2×#102—1222no—
569C2×#102—1222no—
570C2×#102—1222no—
571C2×#102—1222no—
572C2×#102—1222no—
573C2×#102—1222no—
574C2×C22⋊C8—1222no—
575C2×C22⋊C8—1222no—
576C2×C22⋊C8—1222no—
577#380—1222no—
578#380—1222no—
579C2×#95—1221no—
580#340—22no—
581#340—1222no—
582C61#1096911yescharacteristic, complemented, Sylow
583C25—611no—
584C25—1221no—
585C22×D4—612no—
586C22×D4—612no—
587C22×D4—612no—
588C22×D4—1224no—
589C22×D4—1224no—
590C22×D4—1224no—
591C22×D4—1221no—
592C22×D4—1221no—
593C22×D4—1221no—
594C22×D4—1221no—
595C22×D4—1221no—
596C22×D4—1221no—
597C22×D4—1221no—
598C22×D4—1221no—
599C22×D4—1221no—
600C22×D4—1221no—
601C22×D4—1221no—
602C22×D4—2442no—
603C22×D4—2442no—
604C22×D4—2442no—
605C22×D4—2442no—
606C23×C4—21no—
607C23×C4—21no—
608C23×C4—611no—
609C23×C4—612no—
610C23×C4—612no—
611C23×C4—1221no—
612C23×C4—1221no—
613C23×C4—1221no—
614C23×C4—1221no—
615C23×C4—1221no—
616C23×C4—1221no—
617C23×C4—1221no—
618C23×C4—1221no—
619C23×C4—1221no—
620C23×C4—1221no—
621C23×C4—1221no—
622C23×C4—1221no—
623C23×C4—1221no—
624C23×C4C22×D6111yescharacteristic
625C22×C8—21no—
626C22×C8—21no—
627C22×C8—21no—
628C22×C8—21no—
629C22×C8—21no—
630C22×C8—21no—
631C22×C8—612no—
632C22×C8—1221no—
633C22×C8—1221no—
634C22×C8—1221no—
635C22×C8—1221no—
636C22×C8—1221no—
637C22×C8—1221no—
638C22×C8D24412yescomplemented
639#121—1228no—
640#121—1228no—
641#121—1228no—
642#121—1228no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—612no—
652C2×C4⋊C4—1221no—
653C2×C4⋊C4—1221no—
654C2×C4⋊C4—1221no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C4⋊C4C4×D6112yes—
658C2×C4⋊C4D24412yes—
659C2×C4⋊C4D24412yescomplemented
660C2×C4⋊C4C22⋊D6112yes—
661C2×C22⋊C4—1224no—
662C2×C22⋊C4—1224no—
663C2×C22⋊C4—1224no—
664C2×C22⋊C4—1224no—
665C2×C22⋊C4—2442no—
666C2×C22⋊C4—2442no—
667#102—1228no—
668#102—1228no—
669C22⋊C8—1228no—
670#95—1224no—
671C24—612no—
672C24—612no—
673C24—612no—
674C24—1221no—
675C24—1221no—
676C24—1221no—
677C24—1221no—
678C24—1221no—
679C24—1221no—
680C24—1221no—
681C24—1221no—
682C24—1221no—
683C24—1221no—
684C24—1221no—
685C24—1221no—
686C24—1222no—
687C24—1222no—
688C24—1222no—
689C24—2441no—
690C24—2441no—
691C24—2441no—
692C24—2441no—
693C24—2441no—
694C24—2441no—
695C24—2441no—
696C24—2441no—
697C24—2441no—
698C24—2441no—
699C24—2441no—
700C24—2441no—
701C24D4×D6111yescharacteristic
702C2×D4—614no—
703C2×D4—12216no—
704C2×D4—1222no—
705C2×D4—1222no—
706C2×D4—1222no—
707C2×D4—1222no—
708C2×D4—1222no—
709C2×D4—1222no—
710C2×D4—1222no—
711C2×D4—1222no—
712C2×D4—1222no—
713C2×D4—1222no—
714C2×D4—1222no—
715C2×D4—1222no—
716C2×D4—1222no—
717C2×D4—1222no—
718C2×D4—1222no—
719C2×D4—2448no—
720C2×D4—2448no—
721C2×D4—2448no—
722C2×D4—2448no—
723C2×D4—2448no—
724C2×D4—2448no—
725C2×D4—2441no—
726C2×D4—2441no—
727C2×D4—2441no—
728C2×D4—2441no—
729C2×D4—2441no—
730C2×D4—2441no—
731C2×D4—2441no—
732C2×D4—2441no—
733C2×D4—2441no—
734C2×D4—2441no—
735C2×D4—2441no—
736C2×D4—2441no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—612no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1222no—
759C22×C4—1222no—
760C22×C4—1222no—
761C22×C4—1222no—
762C22×C4—1222no—
763C22×C4—1222no—
764C22×C4—1222no—
765C22×C4—1222no—
766C22×C4—1222no—
767C22×C4—1222no—
768C22×C4—1222no—
769C22×C4—1222no—
770C22×C4—1222no—
771C22×C4—2441no—
772C22×C4—2441no—
773C22×C4—2441no—
774C22×C4—2441no—
775C22×C4—2441no—
776C22×C4—2441no—
777C22×C4—2441no—
778C22×C4—2441no—
779C22×C4—2441no—
780C22×C4—2441no—
781C22×C4—2441no—
782C22×C4—2441no—
783C22×C4—2441no—
784C22×C4—2441no—
785C22×C4—2441no—
786C22×C4—2441no—
787C22×C4—2441no—
788C22×C4—2441no—
789C22×C4—2441no—
790C22×C4—2441no—
791C22×C4—2441no—
792C22×C4—2441no—
793C22×C4C2×C4×D6111yescharacteristic
794C22×C4C2×D24411yescharacteristic
795C22×C4C2×D24411yescharacteristic
796C22×C4C2×D24411yescharacteristic
797C22×C4#1175822211yescharacteristic
798C22×C4#1175822211yescharacteristic
799C22×C4D4×D6111yescharacteristic
800C22×C4D4×D6111yescharacteristic
801C22×C4D4×D6111yescharacteristic
802C22×C4D4×D6111yescharacteristic
803C22×C4D4×D6111yescharacteristic
804C22×C4#1175822611yescharacteristic
805C22×C4#1175822611yescharacteristic
806C22×C4C2×C22⋊D6111yescharacteristic
807C2×C8—22no—
808C2×C8—22no—
809C2×C8—22no—
810C2×C8—41no—
811C2×C8—41no—
812C2×C8—41no—
813C2×C8—41no—
814C2×C8—1222no—
815C2×C8—1222no—
816C2×C8—1222no—
817C2×C8—2441no—
818C2×C8—2441no—
819C2×C8—2441no—
820C2×C8—2441no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—41no—
827C4⋊C4—41no—
828C4⋊C4—1222no—
829C4⋊C4—1222no—
830C4⋊C4—2441no—
831C4⋊C4—2441no—
832C4⋊C4#1175819814yescomplemented
833C22⋊C4—12216no—
834C22⋊C4—2448no—
835C23—614no—
836C23—1222no—
837C23—1222no—
838C23—1222no—
839C23—1222no—
840C23—1222no—
841C23—1222no—
842C23—1222no—
843C23—1222no—
844C23—1222no—
845C23—1222no—
846C23—1222no—
847C23—1222no—
848C23—1222no—
849C23—1222no—
850C23—1222no—
851C23—1222no—
852C23—1222no—
853C23—1222no—
854C23—1224no—
855C23—4881no—
856C23—4881no—
857C23—4881no—
858C23—4881no—
859C23—4881no—
860C23—4881no—
861C23—4881no—
862C23—4881no—
863C23—4881no—
864C23—4881no—
865C23—4881no—
866C23—4881no—
867C23—4881no—
868C23—4881no—
869C23—4881no—
870C23—4881no—
871C23—2442no—
872C23—2442no—
873C23—2442no—
874C23—2442no—
875C23—2442no—
876C23—2442no—
877C23—2442no—
878C23—2442no—
879C23—2442no—
880C23—2442no—
881C23—2442no—
882C23—2442no—
883C23—2442no—
884C23—2442no—
885C23—2442no—
886C23—2442no—
887C23—2442no—
888C23—2442no—
889C23—2441no—
890C23—2441no—
891C23—2441no—
892C23—2441no—
893C23—2441no—
894C23—2441no—
895C23—2441no—
896C23—2441no—
897C23—2441no—
898C23—2441no—
899C23—2441no—
900C23—2441no—
901C23—2441no—
902C23—2441no—
903C23—2441no—
904C23—2441no—
905C23C22⋊C4×D6111yescharacteristic
906C23#1451974511yescharacteristic
907C23#1451974711yescharacteristic
908C23#1451974711yescharacteristic
909C23#1451975011yescharacteristic
910C23#1451975211yescharacteristic
911C23#1451976211yescharacteristic
912C23D8×D6111yescharacteristic
913C23SD16×D6111yescharacteristic
914C23#1451979811yescharacteristic
915C23#1451980011yescharacteristic
916C23#1451980111yescharacteristic
917C23#1451980411yescharacteristic
918C23#1451980411yescharacteristic
919C23#1451980911yescharacteristic
920D4—1224no—
921D4—1224no—
922D4—24432no—
923D4—2442no—
924D4—2442no—
925D4—2442no—
926D4—2442no—
927D4—2442no—
928D4—2442no—
929C2×C4—24no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—81no—
943C2×C4—1222no—
944C2×C4—1222no—
945C2×C4—1222no—
946C2×C4—4881no—
947C2×C4—4881no—
948C2×C4—4881no—
949C2×C4—4881no—
950C2×C4—2442no—
951C2×C4—2442no—
952C2×C4—2442no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4—2441no—
956C2×C4—2441no—
957C2×C4—2442no—
958C2×C4—2442no—
959C2×C4—2442no—
960C2×C4—2442no—
961C2×C4—2442no—
962C2×C4—2442no—
963C2×C4—2442no—
964C2×C4—2442no—
965C2×C4C22⋊C4×D6111yescharacteristic
966C2×C4C2×#1175819811yescharacteristic
967C2×C4#1451973911yescharacteristic
968C2×C4#1451973911yescharacteristic
969C2×C4C4×D24411yescharacteristic
970C2×C4C4×D24411yescharacteristic
971C2×C4#1451974511yescharacteristic
972C2×C4#1451974711yescharacteristic
973C2×C4#1451974711yescharacteristic
974C2×C4#1451974711yescharacteristic
975C2×C4#1451974711yescharacteristic
976C2×C4#1451975011yescharacteristic
977C2×C4#1451975011yescharacteristic
978C2×C4#1451975011yescharacteristic
979C2×C4#1451975111yescharacteristic
980C2×C4#1451975111yescharacteristic
981C2×C4#1451975211yescharacteristic
982C2×C4#1451975211yescharacteristic
983C2×C4#1451975211yescharacteristic
984C2×C4#1451975211yescharacteristic
985C2×C4#1451975211yescharacteristic
986C2×C4#1451976211yescharacteristic
987C2×C4#1451976211yescharacteristic
988C2×C4#1451976211yescharacteristic
989C2×C4#1451976511yescharacteristic
990C2×C4#1451976611yescharacteristic
991C2×C4#1451977311yescharacteristic
992C2×C4#1451977411yescharacteristic
993C8—42no—
994C8—2442no—
995C22—1224no—
996C22—1224no—
997C22—1224no—
998C22—4882no—
999C22—4882no—
1000C22—4882no—
1001C22—4882no—
1002C22—4882no—
1003C22—4882no—
1004C22—4882no—
1005C22—4882no—
1006C22—4882no—
1007C22—4882no—
1008C22—4882no—
1009C22—4882no—
1010C22—2444no—
1011C22—2444no—
1012C22—2444no—
1013C22—2442no—
1014C22—2442no—
1015C22—2442no—
1016C22—2442no—
1017C22—2442no—
1018C22—2442no—
1019C22—2442no—
1020C22—2442no—
1021C22—2442no—
1022C22—2442no—
1023C22—2442no—
1024C22—2442no—
1025C22#1683961711yescharacteristic
1026C22#1683964011yescharacteristic
1027C22#1683964011yescharacteristic
1028C22#1683967111yescharacteristic
1029C22#1683967211yescharacteristic
1030C22#1683967911yescharacteristic
1031C22#1683968011yescharacteristic
1032C22#102×D6111yescharacteristic
1033C22#1683975711yescharacteristic
1034C22#1683976211yescharacteristic
1035C22#1683976511yescharacteristic
1036C22#1683989411yescharacteristic
1037C22#1683989711yescharacteristic
1038C22#1683989711yescharacteristic
1039C22#1683990211yescharacteristic
1040C22#1683990611yescharacteristic
1041C22#1683990811yescharacteristic
1042C22#1683991011yescharacteristic
1043C22#1683991011yescharacteristic
1044C22#1683991111yescharacteristic
1045C22#1683991411yescharacteristic
1046C22#1683992311yescharacteristic
1047C22#1683992711yescharacteristic
1048C22#1683999211yescharacteristic
1049C22#1683999411yescharacteristic
1050C22#1683999711yescharacteristic
1051C22#1683999911yescharacteristic
1052C22#1684000911yescharacteristic
1053C22#1684001111yescharacteristic
1054C22#1684001411yescharacteristic
1055C22#1684001611yescharacteristic
1056C22#1684007711yescharacteristic
1057C22#1684008211yescharacteristic
1058C22#1684008811yescharacteristic
1059C22#1684008911yescharacteristic
1060C4—44no—
1061C4—82no—
1062C4—4882no—
1063C4—2442no—
1064C4#1683964011yescharacteristic
1065C4#1683964011yescharacteristic
1066C4#1683966311yescharacteristic
1067C4#1683966411yescharacteristic
1068C4#1683967111yescharacteristic
1069C4#1683967211yescharacteristic
1070C4#1683967911yescharacteristic
1071C4#1683968011yescharacteristic
1072C2—4884no—
1073C2—2444no—
1074C2#2144405911yescharacteristic
1075C2#2144574811yescharacteristic
1076C2#2144575811yescharacteristic
1077C2#2144613511yescharacteristic
1078C2#2144614011yescharacteristic
1079C2#2144624611yescharacteristic
1080C2#2144625611yescharacteristic
1081C2#2144681611yescharacteristic
1082C2#2144681811yescharacteristic
1083C2#2144682111yescharacteristic
1084C2#2144682511yescharacteristic
1085C2#2144700311yescharacteristic
1086C2#2144700411yescharacteristic
1087C2#2144701011yescharacteristic
1088C2#2144701111yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC22×#14519752C2
cosocleC23×C4×C61C23
hypercenterC2×#340D61
hypocenterC61#10969
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#14519699C2semidirect
3. C22×#14519697C2semidirect
4. C22×#14519689C2semidirect
5. C2×#16839619C2semidirect
6. C2×#16839524C2semidirect
7. C2×C61×#340C2semidirect
17. C2×#14519752C4semidirect
83. C22×#92418D4semidirect
93. C2×C4⋊Dic61D4semidirect
113. C22×C8×C61D4semidirect
125. C2×C4⋊C4×C61D4semidirect
233. C2×D244C22⋊C4semidirect
276. C4⋊C4×C61C22⋊C4semidirect
374. C22×D61#102semidirect
534. C2×#340D61semidirect
582. C61#10969semidirect
638. C22×C8D244semidirect
659. C2×C4⋊C4D244semidirect
832. C4⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197522
C22×#145196992
C22×#145196972
C22×#145196892
C2×#168396192
C2×#168395242
C2×C61×#3402
#1096961