Finite Group Databasebeta

← #29695495

Subgroups — #29695495

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic
2C2×#16839764C211yesmaximal, characteristic, complemented
3C22×#14519699C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic61C211yesmaximal, characteristic, complemented
5#21446749C211yesmaximal, characteristic, complemented
6#21446635C211yesmaximal, characteristic, complemented
7#21446257C211yesmaximal, characteristic, complemented
8#21446242C211yesmaximal, characteristic, complemented
9#21446134C211yesmaximal, characteristic, complemented
10#21446124C211yesmaximal, characteristic, complemented
11#21445820C211yesmaximal, characteristic, complemented
12#21445760C211yesmaximal, characteristic, complemented
13#21445751C211yesmaximal, characteristic, complemented
14#21445645C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18#16840408—24no—
19#16840408C418yescomplemented
20C2×#14519765C2211yescharacteristic
21C2×#14519762—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519745—21no—
26C2×C4×D244C2211yescharacteristic
27C2×D4×Dic61—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic, complemented
30C2×C22⋊C4×D61—21no—
31#16839764—24no—
32C2×#14519702C2211yescharacteristic, complemented
33C2×#14519702C2211yescharacteristic, complemented
34C2×#14519702C2211yescharacteristic, complemented
35C2×#14519702C2211yescharacteristic, complemented
36C2×#14519699—24no—
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44C2×#14519699C2211yescharacteristic
45#16839661—21no—
46#16839637—21no—
47#16839637—21no—
48#16839632C2211yescharacteristic, complemented
49#16839622C2211yescharacteristic
50#16839622C2211yescharacteristic, complemented
51C4×C4⋊Dic61C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839525C2211yescharacteristic, complemented
56C22×M16×C61C2211yescharacteristic, complemented
57C23×C8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C61×#435—24no—
60C2×C4⋊C8×C61C2211yescharacteristic, complemented
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C2×#97×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222C2×C414yescomplemented
71C22×Dic122C2311yescharacteristic
72C22×D244—22no—
73C22×D244—22no—
74C22×D244—21no—
75C22×D244—22no—
76C22×D244—41no—
77C22×D244—41no—
78C22×D244C2×C414yescomplemented
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87#14519765—22no—
88#14519765C2×C414yescomplemented
89#14519762—28no—
90#14519756—22no—
91#14519756C2×C414yescomplemented
92#14519751—22no—
93#14519751C2×C414yescomplemented
94#14519750—28no—
95#14519745—28no—
96C4×D244—22no—
97C4×D244C2×C414yescomplemented
98D4×Dic61—44no—
99C2×C4⋊Dic61—22no—
100C2×C4⋊Dic61—22no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—41no—
106C2×C4⋊Dic61—41no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×#11758196—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C22⋊C4×D61—28no—
121C2×C4×Dic61—21no—
122#14519702—22no—
123#14519702—22no—
124#14519702—41no—
125#14519702—41no—
126#14519699—22no—
127#14519699—22no—
128#14519699—22no—
129#14519699—22no—
130#14519699—22no—
131#14519699—41no—
132#14519699—41no—
133#14519699D414yescomplemented
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C22×D4×C61D411yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×M16×C61—22no—
141C2×M16×C61—22no—
142C2×M16×C61—41no—
143C22×C8×C61—22no—
144C22×C8×C61—22no—
145C22×C8×C61—41no—
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C4×D4×C61C2×C414yes—
151C4×D4×C61D414yes—
152C2×C4⋊C4×C61D411yescharacteristic
153C2×C22⋊C4×C61D411yescharacteristic
154C2×C22⋊C4×C61D411yescharacteristic
155C2×C42×C61C2311yescharacteristic
156C4⋊C8×C61—22no—
157C22⋊C8×C61—22no—
158C22⋊C8×C61—22no—
159#97×C61—22no—
160C24×C61C2×D411yescharacteristic
161C24×C61C2×D411yescharacteristic
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—24no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—42no—
169C23×D61—81no—
170C23×D61—81no—
171C2×D4×C61—22no—
172C2×D4×C61—22no—
173C2×D4×C61C22⋊C414yes—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61C22×C412yes—
183C22×C4×C61C22×C412yes—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2411yescharacteristic
191C2×C22⋊D61—24no—
192C2×C22⋊D61—24no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—81no—
196C2×C22⋊D61—81no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—42no—
204C22×Dic61—42no—
205C22×Dic61—42no—
206C22×Dic61—42no—
207C22×Dic61—81no—
208C22×Dic61—81no—
209#11758222—28no—
210#11758222—44no—
211#11758222—44no—
212#11758222—44no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—28no—
221C2×D244—24no—
222C2×D244—21no—
223C2×D244—44no—
224C2×D244—44no—
225C2×D244—44no—
226C2×D244—42no—
227C2×D244—42no—
228C2×D244C22×C412yes—
229C2×D244C22×C412yes—
230C2×D244C2×D412yes—
231C2×D244#4112yes—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—81no—
237C2×C4×D61—81no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122C22×C412yes—
244M16×C61—44no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—44no—
257C2×C8×C61C2×D412yes—
258C4⋊C4×C61C22⋊C414yes—
259C22⋊C4×C61C22⋊C414yes—
260C22⋊C4×C61C22⋊C414yes—
261C42×C61C22×C412yes—
262C42×C61C2×D412yes—
263C22⋊Dic61—24no—
264C22⋊Dic61—42no—
265C22⋊Dic61—42no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—42no—
279C4⋊Dic61—42no—
280C4⋊Dic61—42no—
281C4⋊Dic61—81no—
282C4⋊Dic61C22×C412yes—
283C4⋊Dic61C2×D412yes—
284#11758196—24no—
285C4×Dic61—42no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61C2×C22⋊C412yes—
297C23×C61C2×C22⋊C412yes—
298C23×C61AGL(1,ℤ/8)12yes—
299C23×C61#13712yes—
300C23×C61C22×D411yescharacteristic
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—48no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—48no—
317C22×D61—84no—
318C22×D61—84no—
319C22×D61—84no—
320C22×D61—84no—
321C22×D61—84no—
322D4×C61—28no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61C2×C22⋊C412yes—
340C2×C4×C61C2×C22⋊C412yes—
341C2×C4×C61C2×C22⋊C412yes—
342C2×C4×C61C2×C22⋊C412yes—
343C2×C4×C61C23×C411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C22⋊D61—48no—
350C22⋊D61—84no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—84no—
370C2×Dic61—84no—
371D244—22no—
372D244—22no—
373D244—22no—
374D244—22no—
375D244—22no—
376D244—48no—
377D244—41no—
378D244—41no—
379D244C4×D414yescomplemented
380C4×D61—48no—
381C4×D61—84no—
382Dic122—22no—
383Dic122—22no—
384Dic122—41no—
385Dic122—41no—
386C8×C61—22no—
387C8×C61—41no—
388C8×C61—41no—
389C8×C61—41no—
390#22419—611nomaximal, Sylow
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—22no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61#41714yescomplemented
405C22×C61C22×C22⋊C411yescharacteristic
406C22×C61D4211yescharacteristic
407C22×C61#54611yescharacteristic
408C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C61C2×#13711yescharacteristic
410C22×C61#57611yescharacteristic
411C22×C61#57711yescharacteristic
412C2×D61—24no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—816no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C4×C61—22no—
428C4×C61—22no—
429C4×C61—22no—
430C4×C61—22no—
431C4×C61C2×C4×D411yescharacteristic
432C4×C61#51811yescharacteristic
433C4×C61D4211yescharacteristic
434C4×C61#54611yescharacteristic
435Dic61—42no—
436Dic61—42no—
437Dic61—42no—
438Dic61—81no—
439Dic61—81no—
440Dic61—81no—
441C2×#546—611no—
442C2×#435D6111yescharacteristic, complemented
443C2×#417—611no—
444C22×#102—611no—
445D4×C4⋊C4—611no—
446#1983—611no—
447#1959—611no—
448#1895—611no—
449#1892—611no—
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788—611no—
454#1786—611no—
455#1762—611no—
456C2×C61—24no—
457C2×C61—42no—
458C2×C61D4×C22⋊C411yescharacteristic
459C2×C61C2×#41711yescharacteristic
460C2×C61#289711yescharacteristic
461C2×C61#326411yescharacteristic
462C2×C61#326611yescharacteristic
463C2×C61#330611yescharacteristic
464C2×C61#331411yescharacteristic
465D61—44no—
466D61—82no—
467C22×#41—611no—
468C23×D4—611no—
469C22×M16C2×D6111yescharacteristic, complemented
470C23×C8C2×D6111yescharacteristic
471#546—618no—
472#546—1224no—
473C2×#124—611no—
474C2×#123—1221no—
475C2×C22⋊Q8—611no—
476C2×#121—611no—
477C2×#121—1221no—
478C2×#120—1221no—
479C2×C4×D4—611no—
480C2×C4×D4—1221no—
481C2×C4×D4C2×D6111yescharacteristic
482C22×C4⋊C4—611no—
483C22×C4⋊C4—611no—
484C22×C22⋊C4—1221no—
485#435—24no—
486C2×C4⋊C8C2×D6111yescharacteristic, complemented
487#417—1224no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—611no—
499C2×#102—611no—
500C2×#102—1224no—
501C2×C22⋊C8C2×D6111yescharacteristic
502C2×C22⋊C8C2×D6111yescharacteristic, complemented
503C2×#97C2×D6111yescharacteristic, complemented
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384—611no—
508#380—611no—
509#380—611no—
510C4×C4⋊C4—611no—
511#340—611no—
512#340—611no—
513#340—611no—
514#340—611no—
515C61#2241911yescharacteristic, complemented, Sylow
516C25—1221no—
517C2×#41—614no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—2441no—
522C2×#41—2441no—
523C22×Q8—611no—
524C22×D4—614no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—1222no—
528C22×D4—1222no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4—1222no—
533C22×D4—2441no—
534C22×D4—2441no—
535C22×D4D24411yescharacteristic
536C23×C4—1221no—
537C23×C4—1221no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4C22×D6111yescharacteristic
541C23×C4C22×D6111yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C22×D6111yescharacteristic
549C22×C8C22×D6111yescharacteristic
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#124—614no—
553#124—1222no—
554#123—1228no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557#121—614no—
558#121—1222no—
559#121—1228no—
560#120—1228no—
561C4×D4—614no—
562C4×D4—1222no—
563C4×D4—2444no—
564C4×D4C4×D6114yes—
565C4×D4C22⋊D6114yes—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—1222no—
572C2×C4⋊C4—1222no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—2441no—
579C2×C4⋊C4—2441no—
580C2×C4⋊C4D24411yescharacteristic
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1228no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4D24411yescharacteristic
590C2×C22⋊C4D24411yescharacteristic
591C2×C42—1221no—
592C2×C42C22×D6111yescharacteristic
593C4⋊C8—22no—
594#103—1222no—
595#103—1222no—
596#103—2441no—
597#103—2441no—
598#102—614no—
599#102—1222no—
600#102—1222no—
601#102—1222no—
602#102—1222no—
603#102—1222no—
604#102—2441no—
605#102—2441no—
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—1221no—
610#95—1221no—
611#95—1221no—
612C24—1221no—
613C24—1224no—
614C24—1221no—
615C24—4881no—
616C24—4881no—
617C24—2442no—
618C24—2442no—
619C24—2442no—
620C24—2442no—
621C24C2×D24411yescharacteristic
622C24C2×D24411yescharacteristic
623#41—1228no—
624#41—2444no—
625#41—2444no—
626#41—2444no—
627C2×Q8—612no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—612no—
636C2×D4—612no—
637C2×D4—612no—
638C2×D4—612no—
639C2×D4—1228no—
640C2×D4—1224no—
641C2×D4—1224no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1224no—
651C2×D4—4881no—
652C2×D4—4881no—
653C2×D4—2444no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4—2442no—
657C2×D4—2442no—
658C2×D4—2442no—
659C2×D4—2442no—
660C2×D4#1175819814yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1224no—
673C22×C4—1224no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—4881no—
678C22×C4—4881no—
679C22×C4—4881no—
680C22×C4—4881no—
681C22×C4—2442no—
682C22×C4—2442no—
683C22×C4—2442no—
684C22×C4—2442no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4C2×C4×D6112yes—
688C22×C4C2×C4×D6112yes—
689C22×C4C2×D24411yescharacteristic
690C22×C4C2×D24411yescharacteristic
691C22×C4C2×D24411yescharacteristic
692C22×C4C2×D24411yescharacteristic
693C22×C4C2×C22⋊D6112yes—
694C22×C4C2×C22⋊D6112yes—
695C22×C4C23×D6111yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8D4×D6112yes—
710C4⋊C4—612no—
711C4⋊C4—612no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1224no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—4881no—
722C4⋊C4—2442no—
723C4⋊C4—2442no—
724C4⋊C4—2442no—
725C4⋊C4#1175819814yes—
726C22⋊C4—1224no—
727C22⋊C4—1224no—
728C22⋊C4—1224no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—2442no—
732C22⋊C4—2442no—
733C22⋊C4#1175819814yes—
734C22⋊C4#1175819814yes—
735C42—2442no—
736C42C2×C4×D6112yes—
737C42C2×C22⋊D6112yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—1222no—
749C23—1222no—
750C23—1222no—
751C23—1222no—
752C23—4884no—
753C23—4884no—
754C23—4884no—
755C23—4884no—
756C23—4884no—
757C23—2448no—
758C23—2448no—
759C23—2441no—
760C23—2441no—
761C23—2441no—
762C23—2441no—
763C23—2441no—
764C23—2441no—
765C23—2441no—
766C23—2441no—
767C23—2441no—
768C23—2441no—
769C23C2×#1175819812yes—
770C23C2×#1175819812yes—
771C23#1451980512yes—
772C23#1451981012yes—
773C23C22×D24411yescharacteristic
774Q8—1222no—
775Q8—1222no—
776Q8—2441no—
777Q8—2441no—
778D4—28no—
779D4—614no—
780D4—1222no—
781D4—1222no—
782D4—1222no—
783D4—1222no—
784D4—1222no—
785D4—4884no—
786D4—2448no—
787D4—2448no—
788D4—2441no—
789D4—2441no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—4884no—
810C2×C4—4884no—
811C2×C4—4884no—
812C2×C4—2448no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4C2×#1175819812yes—
829C2×C4C2×#1175819812yes—
830C2×C4C2×#1175819812yes—
831C2×C4C2×#1175819812yes—
832C2×C4C22×C4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C22×C22⋊D6111yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982311yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—1224no—
856C22—48816no—
857C22—4881no—
858C22—4881no—
859C22—4881no—
860C22—4881no—
861C22—2442no—
862C22—2442no—
863C22—2442no—
864C22—2442no—
865C22—2442no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2442no—
870C22#1683976414yescomplemented
871C22C22×#1175819811yescharacteristic
872C22D4×D24411yescharacteristic
873C22#1684040711yescharacteristic
874C22C2×#1451980511yescharacteristic
875C22C2×#1451981011yescharacteristic
876C22#1684056711yescharacteristic
877C22#1684057411yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—4881no—
883C4—4881no—
884C4—4881no—
885C4—2442no—
886C4—2442no—
887C4—2442no—
888C4C4×D4×D6111yescharacteristic
889C4#1684023411yescharacteristic
890C4D4×C22⋊D6111yescharacteristic
891C4#1684040011yescharacteristic
892C2—24no—
893C2—42no—
894C2—4882no—
895C2—2444no—
896C2D4×#1175819811yescharacteristic
897C2C2×#1683976411yescharacteristic
898C2#2145434611yescharacteristic
899C2#2145730411yescharacteristic
900C2#2145733411yescharacteristic
901C2#2145778211yescharacteristic
902C2#2145790211yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22419
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×#16839764C2semidirect
3. C22×#14519699C2semidirect
4. D4×C4⋊Dic61C2semidirect
5. #21446749C2semidirect
6. #21446635C2semidirect
7. #21446257C2semidirect
8. #21446242C2semidirect
9. #21446134C2semidirect
10. #21446124C2semidirect
11. #21445820C2semidirect
12. #21445760C2semidirect
13. #21445751C2semidirect
14. #21445645C2semidirect
15. C2×C61×#435C2semidirect
19. #16840408C4semidirect
29. C22×C4⋊Dic61C22semidirect
32. C2×#14519702C22semidirect
33. C2×#14519702C22semidirect
34. C2×#14519702C22semidirect
35. C2×#14519702C22semidirect
48. #16839632C22semidirect
50. #16839622C22semidirect
51. C4×C4⋊Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839525C22semidirect
56. C22×M16×C61C22semidirect
60. C2×C4⋊C8×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C2×#97×C61C22semidirect
70. C2×#11758222C2×C4semidirect
78. C22×D244C2×C4semidirect
88. #14519765C2×C4semidirect
91. #14519756C2×C4semidirect
93. #14519751C2×C4semidirect
97. C4×D244C2×C4semidirect
133. #14519699D4semidirect
379. D244C4×D4semidirect
404. C22×C61#417semidirect
442. C2×#435D61semidirect
469. C22×M16C2×D61semidirect
486. C2×C4⋊C8C2×D61semidirect
502. C2×C22⋊C8C2×D61semidirect
503. C2×#97C2×D61semidirect
515. C61#22419semidirect
870. C22#16839764semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168397642
C22×#145196992
D4×C4⋊Dic612
#214467492
#214466352
#214462572
#214462422
#214461342
#214461242
#214458202
#214457602
#214457512
#214456452
C2×C61×#4352
#2241961