Finite Group Databasebeta

← #29695555

Subgroups — #29695555

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D244C211yesmaximal, characteristic
2C2×#16839768C211yesmaximal, characteristic, complemented
3C22×#14519699C211yesmaximal, characteristic, complemented
4#21448748C211yesmaximal, characteristic, complemented
5#21446745C211yesmaximal, characteristic, complemented
6#21446643C211yesmaximal, characteristic, complemented
7#21446257C211yesmaximal, characteristic, complemented
8#21446247C211yesmaximal, characteristic, complemented
9#21446139C211yesmaximal, characteristic, complemented
10#21446134C211yesmaximal, characteristic, complemented
11#21445830C211yesmaximal, characteristic, complemented
12#21445751C211yesmaximal, characteristic, complemented
13#21445751C211yesmaximal, characteristic, complemented
14#21445645C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×D4×D61—21no—
19D4×D244—24no—
20D4×D244C418yescomplemented
21C2×#14519774C2211yescharacteristic
22C2×#14519752—21no—
23C2×#14519751C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×#14519747—21no—
26C2×#14519747—21no—
27C2×C4×D244C2211yescharacteristic
28C2×#14519736C2211yescharacteristic, complemented
29C22×C4⋊Dic61C2211yescharacteristic, complemented
30#16839768—24no—
31C2×#14519699—24no—
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic, complemented
37C2×#14519699C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic, complemented
39C2×#14519699C2211yescharacteristic, complemented
40C2×#14519699C2211yescharacteristic, complemented
41C2×#14519699C2211yescharacteristic, complemented
42C2×#14519699C2211yescharacteristic, complemented
43C2×#14519699C2211yescharacteristic, complemented
44#16839655—21no—
45#16839648—21no—
46#16839642—21no—
47#16839628C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic, complemented
49#16839622C2211yescharacteristic, complemented
50C4×C4⋊Dic61C2211yescharacteristic, complemented
51C22⋊C4×Dic61—21no—
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839525C2211yescharacteristic, complemented
56C22×M16×C61C2211yescharacteristic, complemented
57C23×C8×C61C2211yescharacteristic, complemented
58C2×C4×D4×C61C2211yescharacteristic
59C61×#435—24no—
60C2×C4⋊C8×C61C2211yescharacteristic, complemented
61C2×C22⋊C8×C61C2211yescharacteristic, complemented
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C2×#97×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C24×D61—21no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—22no—
69C22×D244—22no—
70C22×D244—21no—
71C22×D244—21no—
72C22×D244—21no—
73C22×D244—22no—
74C22×D244—22no—
75C22×D244—21no—
76C22×D244—41no—
77C22×D244—41no—
78C22×D244—41no—
79C22×D244—41no—
80C22×D244C2×C414yes—
81C22×D244C2×C414yescomplemented
82C22×D244C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C2×D4×D61—28no—
88C2×D4×D61—44no—
89C2×D4×D61—44no—
90C23×Dic61—21no—
91C22×C4×D61—21no—
92#14519774—22no—
93#14519774C2×C414yescomplemented
94#14519752—28no—
95#14519751—22no—
96#14519751—22no—
97#14519751C2×C414yes—
98#14519751C2×C414yescomplemented
99#14519747—28no—
100#14519747—28no—
101C4×D244—22no—
102C4×D244C2×C414yescomplemented
103#14519736—22no—
104#14519736—41no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121#14519699—22no—
122#14519699—22no—
123#14519699—22no—
124#14519699—22no—
125#14519699—22no—
126#14519699—22no—
127#14519699—22no—
128#14519699—41no—
129#14519699—41no—
130#14519699—41no—
131#14519699—41no—
132#14519699D414yescomplemented
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138C22×D4×C61D411yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C2×M16×C61—22no—
142C2×M16×C61—22no—
143C2×M16×C61—41no—
144C22×C8×C61—22no—
145C22×C8×C61—22no—
146C22×C8×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151C4×D4×C61C2×C414yes—
152C4×D4×C61D414yes—
153C2×C4⋊C4×C61D411yescharacteristic
154C2×C22⋊C4×C61D411yescharacteristic
155C2×C22⋊C4×C61D411yescharacteristic
156C2×C42×C61C2311yescharacteristic
157C4⋊C8×C61—22no—
158C22⋊C8×C61—22no—
159C22⋊C8×C61—22no—
160#97×C61—22no—
161C24×C61C2×D411yescharacteristic
162C24×C61C2×D411yescharacteristic
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—24no—
167C23×D61—24no—
168C23×D61—42no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—81no—
177C23×D61—81no—
178C23×D61—81no—
179C23×D61—81no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61C22⋊C414yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61C22×C412yes—
192C22×C4×C61C22×C412yes—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—24no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—42no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—42no—
212C22×Dic61—42no—
213C22×Dic61—81no—
214D4×D61—432no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—28no—
227C2×D244—28no—
228C2×D244—24no—
229C2×D244—24no—
230C2×D244—24no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—24no—
234C2×D244—44no—
235C2×D244—44no—
236C2×D244—44no—
237C2×D244—44no—
238C2×D244—44no—
239C2×D244—44no—
240C2×D244—42no—
241C2×D244—42no—
242C2×D244—42no—
243C2×D244—42no—
244C2×D244—42no—
245C2×D244—42no—
246C2×D244—81no—
247C2×D244—81no—
248C2×D244C22×C412yes—
249C2×D244C22×C412yes—
250C2×D244C22×C412yes—
251C2×D244C2×D412yes—
252C2×D244#4112yes—
253C2×C4×D61—24no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256M16×C61—44no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—44no—
269C2×C8×C61C2×D412yescomplemented
270C4⋊C4×C61C22⋊C414yes—
271C22⋊C4×C61C22⋊C414yes—
272C22⋊C4×C61C22⋊C414yes—
273C42×C61C22×C412yes—
274C42×C61C2×D412yes—
275C22⋊Dic61—42no—
276C22⋊Dic61—42no—
277C22⋊Dic61—81no—
278#11758198—24no—
279#11758198—24no—
280#11758198—24no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—42no—
290C4⋊Dic61C22×C412yes—
291C4⋊Dic61C2×D412yescomplemented
292C4×Dic61—42no—
293C4×Dic61—81no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61C2×C22⋊C412yes—
305C23×C61C2×C22⋊C412yes—
306C23×C61AGL(1,ℤ/8)12yes—
307C23×C61AGL(1,ℤ/8)12yes—
308C23×C61C22×D411yescharacteristic
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—48no—
315C22×D61—48no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—48no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
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—48no—
334C22×D61—84no—
335C22×D61—84no—
336C22×D61—84no—
337C22×D61—84no—
338C22×D61—84no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61—84no—
344D4×C61—28no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61C2×C22⋊C412yes—
362C2×C4×C61C2×C22⋊C412yes—
363C2×C4×C61C2×C22⋊C412yes—
364C2×C4×C61C2×C22⋊C412yes—
365C2×C4×C61C23×C411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C2×#4111yescharacteristic
369C2×C4×C61H(5,𝔽2)11yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C22⋊D61—48no—
372C22⋊D61—48no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—84no—
389D244—22no—
390D244—22no—
391D244—22no—
392D244—22no—
393D244—22no—
394D244—22no—
395D244—22no—
396D244—48no—
397D244—48no—
398D244—48no—
399D244—41no—
400D244—41no—
401D244—41no—
402D244—41no—
403D244—84no—
404D244C4×D414yes—
405C4×D61—48no—
406C8×C61—22no—
407C8×C61—41no—
408C8×C61—41no—
409C8×C61—41no—
410#22423—611nomaximal, Sylow
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61#41814yescomplemented
425C22×C61C22×C22⋊C411yescharacteristic
426C22×C61D4211yescharacteristic
427C22×C61#54611yescharacteristic
428C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C61#57611yescharacteristic
431C22×C61#57711yescharacteristic
432C2×D61—24no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61—42no—
439C2×D61—42no—
440C2×D61—42no—
441C2×D61—42no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—816no—
446C2×D61—816no—
447C2×D61—81no—
448C2×D61—81no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C4×C61—22no—
456C4×C61—22no—
457C4×C61—22no—
458C4×C61—22no—
459C4×C61C2×C4×D411yescharacteristic
460C4×C61#51811yescharacteristic
461C4×C61D4211yescharacteristic
462C4×C61#54611yescharacteristic
463Dic61—42no—
464Dic61—42no—
465Dic61—81no—
466Dic61—81no—
467Dic61—81no—
468C2×D42—611no—
469C2×#435D6111yescharacteristic, complemented
470C2×#418—611no—
471C22×#102—611no—
472#2352—611no—
473#1982—611no—
474#1961—611no—
475#1895—611no—
476#1893—611no—
477#1875—611no—
478#1874—611no—
479#1804—611no—
480#1786—611no—
481#1786—611no—
482#1762—611no—
483C2×C61—24no—
484C2×C61—42no—
485C2×C61D4×C22⋊C411yescharacteristic
486C2×C61C2×#41811yescharacteristic
487C2×C61#289711yescharacteristic
488C2×C61#326411yescharacteristic
489C2×C61#326511yescharacteristic
490C2×C61#331011yescharacteristic
491C2×C61#331811yescharacteristic
492D61—44no—
493D61—82no—
494D61—82no—
495C23×D4—611no—
496C23×D4—611no—
497C23×D4—1221no—
498C22×M16C2×D6111yescharacteristic, complemented
499C23×C8C2×D6111yescharacteristic, complemented
500D42—618no—
501D42—1224no—
502C2×#127—611no—
503C2×#121—611no—
504C2×#121—611no—
505C2×#121—1221no—
506C2×#120—1221no—
507C2×#120—1221no—
508C2×C4×D4—611no—
509C2×C4×D4C2×D6111yescharacteristic
510C2×#117—611no—
511C22×C4⋊C4—611no—
512#435—24no—
513C2×C4⋊C8C2×D6111yescharacteristic, complemented
514#418—1224no—
515C2×#102—611no—
516C2×#102—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102—1224no—
528C2×C22⋊C8C2×D6111yescharacteristic, complemented
529C2×C22⋊C8C2×D6111yescharacteristic, complemented
530C2×#97C2×D6111yescharacteristic, complemented
531#388—1221no—
532#387—1221no—
533#386—1221no—
534#382—611no—
535#380—611no—
536#380—611no—
537C4×C4⋊C4—611no—
538C4×C22⋊C4—1221no—
539#340—611no—
540#340—611no—
541#340—611no—
542#340—611no—
543C61#2242311yescharacteristic, complemented, Sylow
544C25—1221no—
545C25—1221no—
546C22×D4—614no—
547C22×D4—614no—
548C22×D4—611no—
549C22×D4—611no—
550C22×D4—611no—
551C22×D4—1222no—
552C22×D4—1222no—
553C22×D4—1222no—
554C22×D4—1222no—
555C22×D4—1221no—
556C22×D4—1221no—
557C22×D4—1228no—
558C22×D4—1221no—
559C22×D4—1221no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—1222no—
563C22×D4—1222no—
564C22×D4—2441no—
565C22×D4—2441no—
566C22×D4—2441no—
567C22×D4—2441no—
568C22×D4—2444no—
569C22×D4—2444no—
570C22×D4D24411yescharacteristic
571C23×C4—1221no—
572C23×C4—1221no—
573C23×C4C22×D6111yescharacteristic
574C23×C4C22×D6111yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C22×D6111yescharacteristic
582C22×C8C22×D6111yescharacteristic
583C22×C8C22×D6111yescharacteristic
584C22×C8C22×D6111yescharacteristic
585#127—614no—
586#127—1222no—
587#121—614no—
588#121—614no—
589#121—1222no—
590#121—1222no—
591#121—1228no—
592#120—1228no—
593#120—1228no—
594C4×D4—614no—
595C4×D4—1222no—
596C4×D4C4×D6114yes—
597C4×D4C22⋊D6114yes—
598#117—1222no—
599#117—2441no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—2441no—
608C2×C4⋊C4D24411yescharacteristic
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4D24411yescharacteristic
616C2×C22⋊C4D24411yescharacteristic
617C2×C42—1221no—
618C2×C42—1221no—
619C2×C42C22×D6111yescharacteristic
620C4⋊C8—22no—
621#102—614no—
622#102—1222no—
623#102—1222no—
624#102—1222no—
625#102—1222no—
626#102—1222no—
627#102—1222no—
628#102—1222no—
629#102—2441no—
630#102—2441no—
631#102—2441no—
632#102—2441no—
633C22⋊C8—22no—
634C22⋊C8—22no—
635#97—22no—
636#95—1221no—
637#95—1221no—
638#95—1221no—
639#95—1221no—
640#95—1221no—
641C24—1221no—
642C24—1224no—
643C24—1224no—
644C24—1221no—
645C24—1221no—
646C24—4881no—
647C24—4881no—
648C24—4881no—
649C24—4881no—
650C24—2442no—
651C24—2442no—
652C24—2442no—
653C24—2442no—
654C24—2442no—
655C24—2442no—
656C24—2442no—
657C24—2442no—
658C24C2×D24411yescharacteristic
659C24C2×D24411yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—612no—
663C2×D4—612no—
664C2×D4—612no—
665C2×D4—612no—
666C2×D4—612no—
667C2×D4—1228no—
668C2×D4—1228no—
669C2×D4—1224no—
670C2×D4—1224no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1224no—
685C2×D4—1224no—
686C2×D4—1224no—
687C2×D4—1224no—
688C2×D4—4881no—
689C2×D4—4881no—
690C2×D4—2444no—
691C2×D4—2444no—
692C2×D4—2444no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4—2444no—
696C2×D4—2442no—
697C2×D4—2442no—
698C2×D4—2442no—
699C2×D4—2442no—
700C2×D4—2442no—
701C2×D4—2442no—
702C2×D4—24432no—
703C2×D4—2442no—
704C2×D4—2442no—
705C2×D4—2442no—
706C2×D4—2442no—
707C2×D4#1175819814yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1224no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—4881no—
723C22×C4—2442no—
724C22×C4—2442no—
725C22×C4—2442no—
726C22×C4—2442no—
727C22×C4C2×C4×D6112yes—
728C22×C4C2×C4×D6112yes—
729C22×C4C2×D24411yescharacteristic
730C22×C4C2×D24411yescharacteristic
731C22×C4C2×D24411yescharacteristic
732C22×C4C2×D24411yescharacteristic
733C22×C4C2×C22⋊D6112yes—
734C22×C4C2×C22⋊D6112yes—
735C22×C4C23×D6111yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8D4×D6112yescomplemented
750C4⋊C4—612no—
751C4⋊C4—612no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—2442no—
761C4⋊C4#1175819814yes—
762C22⋊C4—1224no—
763C22⋊C4—1224no—
764C22⋊C4—1224no—
765C22⋊C4—4881no—
766C22⋊C4—2442no—
767C22⋊C4—2442no—
768C22⋊C4#1175819814yes—
769C22⋊C4#1175819814yes—
770C42—4881no—
771C42—2442no—
772C42C2×C4×D6112yes—
773C42C2×C22⋊D6112yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—1222no—
785C23—1222no—
786C23—1222no—
787C23—1222no—
788C23—1222no—
789C23—4884no—
790C23—4884no—
791C23—4884no—
792C23—4884no—
793C23—4884no—
794C23—4884no—
795C23—4884no—
796C23—4884no—
797C23—4884no—
798C23—4884no—
799C23—2448no—
800C23—2448no—
801C23—2448no—
802C23—2448no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23—2441no—
807C23—2441no—
808C23—2441no—
809C23—2441no—
810C23—2441no—
811C23—2441no—
812C23—2441no—
813C23—2441no—
814C23—2441no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23C2×#1175819812yes—
820C23C2×#1175819812yes—
821C23#1451980512yes—
822C23#1451980512yes—
823C23C22×D24411yescharacteristic
824D4—28no—
825D4—614no—
826D4—1222no—
827D4—1222no—
828D4—1222no—
829D4—1222no—
830D4—1222no—
831D4—1222no—
832D4—1222no—
833D4—4884no—
834D4—2448no—
835D4—2448no—
836D4—2448no—
837D4—2448no—
838D4—2448no—
839D4—2441no—
840D4—2441no—
841D4—2441no—
842D4—2441no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—4884no—
862C2×C4—2448no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4C2×#1175819812yes—
877C2×C4C2×#1175819812yes—
878C2×C4C2×#1175819812yes—
879C2×C4C2×#1175819812yes—
880C2×C4C22×C4×D6111yescharacteristic
881C2×C4C2×D4×D6111yescharacteristic
882C2×C4C22×C22⋊D6111yescharacteristic
883C2×C4#41×D6111yescharacteristic
884C2×C4#1451982211yescharacteristic
885C2×C4#1451982311yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—1224no—
904C22—48816no—
905C22—48816no—
906C22—4881no—
907C22—4881no—
908C22—4881no—
909C22—4881no—
910C22—4881no—
911C22—4881no—
912C22—4881no—
913C22—4881no—
914C22—2442no—
915C22—2442no—
916C22—2442no—
917C22—2442no—
918C22—2442no—
919C22—2442no—
920C22—2442no—
921C22—2442no—
922C22—2442no—
923C22—2442no—
924C22—2442no—
925C22—2442no—
926C22#1683976814yescomplemented
927C22C22×#1175819811yescharacteristic
928C22D4×D24411yescharacteristic
929C22#1684040711yescharacteristic
930C22C2×#1451980511yescharacteristic
931C22C2×#1451980511yescharacteristic
932C22#1684056711yescharacteristic
933C22#1684057411yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—4881no—
939C4—4881no—
940C4—4881no—
941C4—2442no—
942C4—2442no—
943C4C4×D4×D6111yescharacteristic
944C4#1684023411yescharacteristic
945C4D4×C22⋊D6111yescharacteristic
946C4#1684040011yescharacteristic
947C2—24no—
948C2—42no—
949C2—4882no—
950C2—4882no—
951C2—2444no—
952C2D4×#1175819811yescharacteristic
953C2C2×#1683976811yescharacteristic
954C2#2145434611yescharacteristic
955C2#2145730411yescharacteristic
956C2#2145731911yescharacteristic
957C2#2145784211yescharacteristic
958C2#2145796211yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC2×D4×D244C2
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22423
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#16839768C2semidirect
3. C22×#14519699C2semidirect
4. #21448748C2semidirect
5. #21446745C2semidirect
6. #21446643C2semidirect
7. #21446257C2semidirect
8. #21446247C2semidirect
9. #21446139C2semidirect
10. #21446134C2semidirect
11. #21445830C2semidirect
12. #21445751C2semidirect
13. #21445751C2semidirect
14. #21445645C2semidirect
15. C2×C61×#435C2semidirect
20. D4×D244C4semidirect
28. C2×#14519736C22semidirect
29. C22×C4⋊Dic61C22semidirect
36. C2×#14519699C22semidirect
37. C2×#14519699C22semidirect
38. C2×#14519699C22semidirect
39. C2×#14519699C22semidirect
40. C2×#14519699C22semidirect
41. C2×#14519699C22semidirect
42. C2×#14519699C22semidirect
43. C2×#14519699C22semidirect
47. #16839628C22semidirect
48. #16839622C22semidirect
49. #16839622C22semidirect
50. C4×C4⋊Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839525C22semidirect
56. C22×M16×C61C22semidirect
57. C23×C8×C61C22semidirect
60. C2×C4⋊C8×C61C22semidirect
61. C2×C22⋊C8×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C2×#97×C61C22semidirect
81. C22×D244C2×C4semidirect
93. #14519774C2×C4semidirect
98. #14519751C2×C4semidirect
102. C4×D244C2×C4semidirect
132. #14519699D4semidirect
269. C2×C8×C61C2×D4semidirect
291. C4⋊Dic61C2×D4semidirect
424. C22×C61#418semidirect
469. C2×#435D61semidirect
498. C22×M16C2×D61semidirect
499. C23×C8C2×D61semidirect
513. C2×C4⋊C8C2×D61semidirect
528. C2×C22⋊C8C2×D61semidirect
529. C2×C22⋊C8C2×D61semidirect
530. C2×#97C2×D61semidirect
543. C61#22423semidirect
749. C2×C8D4×D61semidirect
926. C22#16839768semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D2442
C2×#168397682
C22×#145196992
#214487482
#214467452
#214466432
#214462572
#214462472
#214461392
#214461342
#214458302
#214457512
#214456452
C2×C61×#4352
#2242361