Finite Group Databasebeta

← #29586308

Subgroups — #29586308

Order 15616.

1354 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519699C211yesmaximal, characteristic
2C22×#14519697C211yesmaximal, characteristic
3C2×#16839663C211yesmaximal, characteristic
4C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
5C2×#16839524C211yesmaximal, characteristic, complemented
6C2×#16839516C211yesmaximal, characteristic, complemented
7C2×C61×#340C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C23×#92418C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×#11758198—21no—
12C22×#11758198—21no—
13C22×C4×Dic61—21no—
14C22×C4×Dic61C2211yescharacteristic
15C2×#14519699—22no—
16C2×#14519699—22no—
17C2×#14519699C414yescomplemented
18C2×#14519697—22no—
19C2×#14519697—22no—
20C2×#14519697C414yescomplemented
21#16839663—22no—
22#16839663C414yescomplemented
23C4⋊C4×Dic61—22no—
24C4⋊C4×Dic61—22no—
25C2×#14519684—21no—
26#16839524—22no—
27#16839516—22no—
28C23×C8×C61C2211yescharacteristic
29C22×C4⋊C4×C61C2211yescharacteristic
30C22×C4⋊C4×C61C2211yescharacteristic
31C61×#340—22no—
32C24×D61—21no—
33C22×D244—21no—
34C22×D244—21no—
35C22×D244—21no—
36C22×D244—21no—
37C22×D244—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244C2×C412yes—
45C22×D244C2×C412yes—
46C22×D244C2×C412yes—
47C23×Dic61—21no—
48C23×Dic61D411yescharacteristic
49C23×Dic61D411yescharacteristic
50C22×#92418—21no—
51C22×#92418—21no—
52C22×#92418—21no—
53C22×#92418—21no—
54C22×#92418—21no—
55C22×#92418—21no—
56C22×#92418C2×C412yes—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61C2×C412yes—
61C2×C4⋊Dic61D412yes—
62C2×C4⋊Dic61D412yes—
63C2×#11758198—24no—
64C2×#11758198—24no—
65C2×#11758198—42no—
66C2×#11758198—42no—
67C2×#11758198—42no—
68C2×#11758198—42no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61—21no—
71C2×C4×Dic61—21no—
72C2×C4×Dic61—21no—
73C2×C4×Dic61—24no—
74C2×C4×Dic61—42no—
75C2×C4×Dic61—42no—
76C2×C4×Dic61C2×C412yes—
77C2×C4×Dic61D412yes—
78#14519699—28no—
79#14519697—28no—
80#14519684—24no—
81C23×C4×C61—21no—
82C23×C4×C61—21no—
83C23×C4×C61C2311yescharacteristic
84C22×C8×C61—21no—
85C22×C8×C61—21no—
86C22×C8×C61—21no—
87C22×C8×C61—21no—
88C22×C8×C61—21no—
89C22×C8×C61—21no—
90C22×C8×C61C2×C412yes—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61C2×C412yes—
100C2×C4⋊C4×C61C2×C412yes—
101C2×C4⋊C4×C61D412yes—
102C2×C4⋊C4×C61D412yes—
103C24×C61C2×D411yescharacteristic
104C23×D61—22no—
105C23×D61—22no—
106C23×D61—22no—
107C23×D61—41no—
108C23×D61—41no—
109C23×D61—41no—
110C23×D61—41no—
111C23×D61—41no—
112C23×D61—41no—
113C23×D61—41no—
114C23×D61—41no—
115C23×D61—41no—
116C23×D61—41no—
117C23×D61—41no—
118C23×D61—41no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61—41no—
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61#4111yescharacteristic
142C22×C4×C61#4111yescharacteristic
143C22×C4×C61#4111yescharacteristic
144C22×C4×C61#4111yescharacteristic
145C22×C4×C61#4111yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—21no—
154C22×Dic61—22no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—41no—
161C22×Dic61—41no—
162C22×Dic61—41no—
163C22×Dic61—41no—
164C22×Dic61C22⋊C412yes—
165C22×Dic61C22⋊C412yes—
166C22×Dic61D812yes—
167C22×Dic61SD1612yes—
168C2×D244—22no—
169C2×D244—22no—
170C2×D244—22no—
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—41no—
184C2×D244—41no—
185C2×D244—41no—
186C2×D244—41no—
187C2×D244—41no—
188C2×D244—41no—
189C2×D244—41no—
190C2×D244—41no—
191C2×D244—41no—
192C2×D244—41no—
193C2×D244—41no—
194C2×D244—41no—
195C2×D244C4214yescomplemented
196C2×C8×C61—22no—
197C2×C8×C61—22no—
198C2×C8×C61—22no—
199C2×C8×C61—41no—
200C2×C8×C61—41no—
201C2×C8×C61—41no—
202C2×C8×C61—41no—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—22no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—41no—
209C4⋊C4×C61—41no—
210C4⋊C4×C61C22⋊C414yescomplemented
211#11758198—48no—
212#11758198—48no—
213C4⋊Dic61—22no—
214C4⋊Dic61—22no—
215C4⋊Dic61—22no—
216C4⋊Dic61C22⋊C414yescomplemented
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—22no—
220C4×Dic61—22no—
221C4×Dic61—48no—
222C2×#92418—22no—
223C2×#92418—22no—
224C2×#92418—22no—
225C2×#92418—41no—
226C2×#92418—41no—
227C2×#92418—41no—
228C2×#92418—41no—
229C23×C61C2×C22⋊C411yescharacteristic
230C23×C61C4×D411yescharacteristic
231C23×C61C4×D411yescharacteristic
232C23×C61#12011yescharacteristic
233C23×C61#12111yescharacteristic
234C23×C61#12111yescharacteristic
235C23×C61#12311yescharacteristic
236C23×C61C2×D811yescharacteristic
237C23×C61C2×SD1611yescharacteristic
238C23×C61#13511yescharacteristic
239C23×C61#13511yescharacteristic
240C23×C61AGL(1,ℤ/8)11yescharacteristic
241C23×C61AGL(1,ℤ/8)11yescharacteristic
242C23×C61AGL(1,ℤ/8)11yescharacteristic
243C23×C61#13711yescharacteristic
244C22×D61—24no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—42no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61—42no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—81no—
264C22×D61—81no—
265C22×D61—81no—
266C22×D61—81no—
267C22×D61—81no—
268C22×D61—81no—
269C22×D61—81no—
270C22×D61—81no—
271C22×D61—81no—
272C22×D61—81no—
273C22×D61—81no—
274C22×D61—81no—
275C22×D61—81no—
276C22×D61—81no—
277C22×D61—81no—
278C22×D61—81no—
279C2×C4×C61—24no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—81no—
290C2×C4×C61—81no—
291C2×C4×C61—81no—
292C2×C4×C61—81no—
293C2×C4×C61C2×C4211yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61#11711yescharacteristic
297C2×C4×C61#11711yescharacteristic
298C2×C4×C61#11711yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61C4×D411yescharacteristic
303C2×C4×C61C4×D411yescharacteristic
304C2×C4×C61C4×D411yescharacteristic
305C2×C4×C61C4×D411yescharacteristic
306C2×C4×C61C4×D411yescharacteristic
307C2×C4×C61C4×D411yescharacteristic
308C2×C4×C61C4×D411yescharacteristic
309C2×C4×C61#12111yescharacteristic
310C2×C4×C61#12111yescharacteristic
311C2×C4×C61#12111yescharacteristic
312C2×C4×C61#12111yescharacteristic
313C2×C4×C61#12311yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61#12411yescharacteristic
316C2×C4×C61#12411yescharacteristic
317C2×C4×C61#12411yescharacteristic
318C2×C4×C61#12611yescharacteristic
319C2×C4×C61#12611yescharacteristic
320C2×C4×C61#12711yescharacteristic
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—24no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61#10214yescomplemented
342D244—24no—
343D244—24no—
344D244—42no—
345D244—42no—
346D244—42no—
347D244—42no—
348D244—42no—
349D244—42no—
350C8×C61—42no—
351#92418—42no—
352#10931—611nomaximal, Sylow
353C22×C61C4×C22⋊C411yescharacteristic
354C22×C61#38611yescharacteristic
355C22×C61#38611yescharacteristic
356C22×C61#38611yescharacteristic
357C22×C61#38811yescharacteristic
358C22×C61#38811yescharacteristic
359C22×C61#39011yescharacteristic
360C22×C61C2×#10211yescharacteristic
361C22×C61#41611yescharacteristic
362C22×C61#41711yescharacteristic
363C22×C61#41811yescharacteristic
364C22×C61C4×D811yescharacteristic
365C22×C61C4×D811yescharacteristic
366C22×C61C4×SD1611yescharacteristic
367C22×C61C4×SD1611yescharacteristic
368C22×C61#44011yescharacteristic
369C22×C61#44011yescharacteristic
370C22×C61#44211yescharacteristic
371C22×C61#44211yescharacteristic
372C22×C61#44711yescharacteristic
373C22×C61#44811yescharacteristic
374C22×C61#44911yescharacteristic
375C22×C61#44911yescharacteristic
376C22×C61#45911yescharacteristic
377C22×C61#45911yescharacteristic
378C22×C61#46011yescharacteristic
379C22×C61#46011yescharacteristic
380C22×C61#46311yescharacteristic
381C22×C61#46311yescharacteristic
382C22×C61#46411yescharacteristic
383C22×C61#46411yescharacteristic
384C22×C61#48011yescharacteristic
385C22×C61#48111yescharacteristic
386C22×C61#48211yescharacteristic
387C22×C61#48211yescharacteristic
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—82no—
392C2×D61—82no—
393C2×D61—82no—
394C2×D61—82no—
395C2×D61—82no—
396C2×D61—82no—
397C2×D61—82no—
398C2×D61—82no—
399C2×D61—82no—
400C2×D61—82no—
401C2×D61—82no—
402C2×D61—82no—
403C4×C61—44no—
404C4×C61—82no—
405C4×C61C4×C22⋊C411yescharacteristic
406C4×C61C4×C22⋊C411yescharacteristic
407C4×C61#38811yescharacteristic
408C4×C61#38811yescharacteristic
409C4×C61#38811yescharacteristic
410C4×C61#38811yescharacteristic
411C4×C61#39011yescharacteristic
412C4×C61#39011yescharacteristic
413Dic61—24no—
414Dic61—42no—
415Dic61—44no—
416C22×#102—611no—
417C22×#102—611no—
418C2×#390—611no—
419C2×C4×C4⋊C4—611no—
420C2×#340—611no—
421C2×#340D6111yescharacteristic, complemented
422C2×#336—611no—
423C2×C61#143711yescharacteristic
424C2×C61C4×#10211yescharacteristic
425C2×C61#176211yescharacteristic
426C2×C61#187411yescharacteristic
427C2×C61#187511yescharacteristic
428C2×C61#187911yescharacteristic
429C2×C61#187911yescharacteristic
430C2×C61#188011yescharacteristic
431C2×C61#188011yescharacteristic
432C2×C61#192511yescharacteristic
433C2×C61#192511yescharacteristic
434C2×C61#192611yescharacteristic
435C2×C61#192611yescharacteristic
436C2×C61#198211yescharacteristic
437C2×C61#198311yescharacteristic
438D61—84no—
439C23×D4—611no—
440C23×C8—611no—
441C23×C8C2×D6111yescharacteristic
442C22×C4⋊C4—611no—
443C22×C4⋊C4C2×D6111yescharacteristic
444C22×C4⋊C4C2×D6111yescharacteristic
445C22×C22⋊C4—1221no—
446C22×C22⋊C4—1221no—
447C22×C42—611no—
448C22×C42—1221no—
449C2×#102—614no—
450C2×#102—614no—
451C2×#102—1222no—
452C2×#102—1222no—
453C2×#102—1222no—
454C2×#102—1222no—
455#390—614no—
456#390—1222no—
457C4×C4⋊C4—1222no—
458C4×C4⋊C4—1222no—
459C2×#95—1221no—
460#340—22no—
461#340—1222no—
462#336—1222no—
463C61#1093111yescharacteristic, complemented, Sylow
464C25—1221no—
465C22×D4—612no—
466C22×D4—612no—
467C22×D4—612no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4—1221no—
477C22×D4—1221no—
478C22×D4—1221no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—1221no—
484C23×C4C22×D6111yescharacteristic
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8—21no—
491C22×C8—612no—
492C22×C8—1221no—
493C22×C8—1221no—
494C22×C8—1221no—
495C22×C8—1221no—
496C22×C8—1221no—
497C22×C8—1221no—
498C22×C8C4×D6112yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—612no—
508C2×C4⋊C4—612no—
509C2×C4⋊C4—612no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4C4×D6112yes—
514C2×C4⋊C4C4×D6112yes—
515C2×C4⋊C4D24412yes—
516C2×C4⋊C4C22⋊D6112yes—
517C2×C22⋊C4—1224no—
518C2×C22⋊C4—1224no—
519C2×C22⋊C4—2442no—
520C2×C22⋊C4—2442no—
521C2×C22⋊C4—2442no—
522C2×C22⋊C4—2442no—
523C2×C42—612no—
524C2×C42—612no—
525C2×C42—1221no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1224no—
530C2×C42—2442no—
531C2×C42—2442no—
532#102—1228no—
533#102—1228no—
534#95—1224no—
535C24—1222no—
536C24—1222no—
537C24—1222no—
538C24—2441no—
539C24—2441no—
540C24—2441no—
541C24—2441no—
542C24—2441no—
543C24—2441no—
544C24—2441no—
545C24—2441no—
546C24—2441no—
547C24—2441no—
548C24—2441no—
549C24—2441no—
550C24D4×D6111yescharacteristic
551C2×D4—614no—
552C2×D4—1222no—
553C2×D4—1222no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—2441no—
568C2×D4—2441no—
569C2×D4—2441no—
570C2×D4—2441no—
571C2×D4—2441no—
572C2×D4—2441no—
573C2×D4—2441no—
574C2×D4—2441no—
575C2×D4—2441no—
576C2×D4—2441no—
577C2×D4—2441no—
578C2×D4—2441no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1222no—
602C22×C4—1221no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—2441no—
611C22×C4—2441no—
612C22×C4—2441no—
613C22×C4—2441no—
614C22×C4C2×C4×D6111yescharacteristic
615C22×C4C2×C4×D6111yescharacteristic
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C2×D24411yescharacteristic
618C22×C4#1175822211yescharacteristic
619C22×C4#1175822211yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4D4×D6111yescharacteristic
622C22×C4D4×D6111yescharacteristic
623C22×C4#1175822411yescharacteristic
624C22×C4#1175822411yescharacteristic
625C22×C4#1175822611yescharacteristic
626C22×C4#1175822611yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—1222no—
636C2×C8—1222no—
637C2×C8—1222no—
638C2×C8—2441no—
639C2×C8—2441no—
640C2×C8—2441no—
641C2×C8—2441no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—614no—
650C4⋊C4—1222no—
651C4⋊C4—1222no—
652C4⋊C4—1222no—
653C4⋊C4#1175819814yescomplemented
654C22⋊C4—2448no—
655C22⋊C4—2448no—
656C42—1222no—
657C42—1222no—
658C42—1222no—
659C42—1222no—
660C42—2448no—
661C23—1224no—
662C23—4881no—
663C23—4881no—
664C23—4881no—
665C23—4881no—
666C23—4881no—
667C23—4881no—
668C23—4881no—
669C23—4881no—
670C23—4881no—
671C23—4881no—
672C23—4881no—
673C23—4881no—
674C23—4881no—
675C23—4881no—
676C23—4881no—
677C23—4881no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23—2442no—
688C23—2442no—
689C23—2442no—
690C23—2442no—
691C23—2442no—
692C23—2442no—
693C23—2442no—
694C23—2442no—
695C23—2442no—
696C23C22⋊C4×D6111yescharacteristic
697C23#1451973711yescharacteristic
698C23#1451973911yescharacteristic
699C23#1451974711yescharacteristic
700C23#1451974911yescharacteristic
701C23#1451975011yescharacteristic
702C23#1451976211yescharacteristic
703C23D8×D6111yescharacteristic
704C23SD16×D6111yescharacteristic
705C23#1451979811yescharacteristic
706C23#1451980011yescharacteristic
707C23#1451980111yescharacteristic
708C23#1451980411yescharacteristic
709C23#1451980411yescharacteristic
710C23#1451980911yescharacteristic
711D4—1224no—
712D4—1224no—
713D4—2442no—
714D4—2442no—
715D4—2442no—
716D4—2442no—
717D4—2442no—
718D4—2442no—
719C2×C4—24no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—614no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1224no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2442no—
754C2×C4C42×D6111yescharacteristic
755C2×C4C22⋊C4×D6111yescharacteristic
756C2×C4C2×#1175819811yescharacteristic
757C2×C4#1451973411yescharacteristic
758C2×C4#1451973511yescharacteristic
759C2×C4#1451973511yescharacteristic
760C2×C4#1451973711yescharacteristic
761C2×C4#1451973711yescharacteristic
762C2×C4#1451973711yescharacteristic
763C2×C4C4×C22⋊D6111yescharacteristic
764C2×C4C4×C22⋊D6111yescharacteristic
765C2×C4#1451973911yescharacteristic
766C2×C4#1451973911yescharacteristic
767C2×C4#1451973911yescharacteristic
768C2×C4C4×D24411yescharacteristic
769C2×C4C4×D24411yescharacteristic
770C2×C4#1451974911yescharacteristic
771C2×C4#1451975011yescharacteristic
772C2×C4#1451975211yescharacteristic
773C2×C4#1451975211yescharacteristic
774C2×C4#1451976111yescharacteristic
775C2×C4#1451976211yescharacteristic
776C2×C4#1451976311yescharacteristic
777C2×C4#1451976311yescharacteristic
778C2×C4#1451976611yescharacteristic
779C2×C4#1451977211yescharacteristic
780C2×C4#1451977211yescharacteristic
781C2×C4#1451977311yescharacteristic
782C8—42no—
783C8—2442no—
784C22—4882no—
785C22—4882no—
786C22—4882no—
787C22—4882no—
788C22—4882no—
789C22—4882no—
790C22—4882no—
791C22—4882no—
792C22—4882no—
793C22—4882no—
794C22—4882no—
795C22—4882no—
796C22—2444no—
797C22—2444no—
798C22—2444no—
799C22#1683960911yescharacteristic
800C22#1683963911yescharacteristic
801C22#1683964011yescharacteristic
802C22#1683964011yescharacteristic
803C22#1683965111yescharacteristic
804C22#1683965211yescharacteristic
805C22#1683966211yescharacteristic
806C22#102×D6111yescharacteristic
807C22#1683975711yescharacteristic
808C22#1683976211yescharacteristic
809C22#1683976511yescharacteristic
810C22#1683984211yescharacteristic
811C22#1683984411yescharacteristic
812C22#1683984711yescharacteristic
813C22#1683984911yescharacteristic
814C22#1683986111yescharacteristic
815C22#1683986511yescharacteristic
816C22#1683987111yescharacteristic
817C22#1683987311yescharacteristic
818C22#1683989711yescharacteristic
819C22#1683990211yescharacteristic
820C22#1683990811yescharacteristic
821C22#1683991011yescharacteristic
822C22#1683995511yescharacteristic
823C22#1683995611yescharacteristic
824C22#1683996011yescharacteristic
825C22#1683996111yescharacteristic
826C22#1683997911yescharacteristic
827C22#1683998011yescharacteristic
828C22#1683998611yescharacteristic
829C22#1683998711yescharacteristic
830C22#1684007711yescharacteristic
831C22#1684008211yescharacteristic
832C22#1684008811yescharacteristic
833C22#1684008911yescharacteristic
834C4—44no—
835C4—82no—
836C4—1224no—
837C4—2444no—
838C4—2442no—
839C4#1683960911yescharacteristic
840C4C4×#1175819811yescharacteristic
841C4#1683965111yescharacteristic
842C4#1683965211yescharacteristic
843C4#1683965411yescharacteristic
844C4#1683965411yescharacteristic
845C4#1683966211yescharacteristic
846C4#1683966311yescharacteristic
847C2—4884no—
848C2#2144405511yescharacteristic
849C2#2144563311yescharacteristic
850C2#2144564311yescharacteristic
851C2#2144613511yescharacteristic
852C2#2144614011yescharacteristic
853C2#2144616511yescharacteristic
854C2#2144616811yescharacteristic
855C2#2144617211yescharacteristic
856C2#2144617511yescharacteristic
857C2#2144643711yescharacteristic
858C2#2144643811yescharacteristic
859C2#2144644411yescharacteristic
860C2#2144644511yescharacteristic
861C2#2144674411yescharacteristic
862C2#2144674811yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenterC2×#340D61
hypocenterC61#10931
LCSG ▷ C2×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
4. C2×C4⋊C4×Dic61C2semidirect
5. C2×#16839524C2semidirect
6. C2×#16839516C2semidirect
7. C2×C61×#340C2semidirect
17. C2×#14519699C4semidirect
20. C2×#14519697C4semidirect
22. #16839663C4semidirect
195. C2×D244C42semidirect
210. C4⋊C4×C61C22⋊C4semidirect
216. C4⋊Dic61C22⋊C4semidirect
341. C2×Dic61#102semidirect
421. C2×#340D61semidirect
463. C61#10931semidirect
653. C4⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145196992
C22×#145196972
C2×#168396632
C2×C4⋊C4×Dic612
C2×#168395242
C2×#168395162
C2×C61×#3402
#1093161