Finite Group Databasebeta

← #29727566

Subgroups — #29727566

Order 15616.

1316 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839977C211yesmaximal, characteristic, complemented
2C2×#16839913C211yesmaximal, characteristic, complemented
3C2×#16839896C211yesmaximal, characteristic
4C2×C4×#11758199C211yesmaximal, characteristic, complemented
5#21449396C211yesmaximal, characteristic, complemented
6#21447207C211yesmaximal, characteristic, complemented
7#21447022C211yesmaximal, characteristic, complemented
8#21447008C211yesmaximal, characteristic, complemented
9#21446895C211yesmaximal, characteristic, complemented
10#21446672C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446170C211yesmaximal, characteristic, complemented
13#21446153C211yesmaximal, characteristic, complemented
14#21446080C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C2×#14519765C2211yescharacteristic, complemented
21C2×#14519756C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic, complemented
24#16839977—24no—
25#16839913—24no—
26#16839896—24no—
27C4×#11758199—24no—
28C2×#14519710C2211yescharacteristic, complemented
29C2×#14519708C2211yescharacteristic, complemented
30C2×C4⋊#92418C2211yescharacteristic, complemented
31C2×#14519700C2211yescharacteristic, complemented
32C2×#14519700C2211yescharacteristic, complemented
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic, complemented
38C2×#14519697C2211yescharacteristic, complemented
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic, complemented
42#16839691—21no—
43#16839677—21no—
44#16839668C2211yescharacteristic, complemented
45#16839660C2211yescharacteristic, complemented
46#16839638—21no—
47#16839621—21no—
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C23×D4×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C22×C22⋊C4×C61—21no—
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#386—21no—
59C61×#386—21no—
60C61×#380C2211yescharacteristic
61C61×#379—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—41no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C2×#11758199—41no—
78C2×#11758199D414yes—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519765—22no—
84#14519765—41no—
85#14519756—22no—
86#14519756—41no—
87#14519751—22no—
88#14519751—41no—
89C4×D244—22no—
90C4×D244—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100#14519710—22no—
101#14519708—41no—
102C4⋊#92418—22no—
103#14519700—22no—
104#14519700—41no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698D414yescomplemented
109#14519697—22no—
110#14519697—22no—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C4×#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C25×C61—21no—
118C22×D4×C61—22no—
119C22×D4×C61—22no—
120C22×D4×C61—22no—
121C22×D4×C61—22no—
122C22×D4×C61—21no—
123C22×D4×C61—41no—
124C22×D4×C61—41no—
125C22×D4×C61C2311yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61—21no—
129C23×C4×C61C2311yescharacteristic
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C4×D4×C61—41no—
133C4×D4×C61—41no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—44no—
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61—21no—
152C24×C61—24no—
153C24×C61—21no—
154C24×C61—42no—
155C24×C61—42no—
156C24×C61—42no—
157C24×C61—42no—
158C24×C61—81no—
159C24×C61—81no—
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C2×D4×C61—24no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—44no—
174C2×D4×C61—44no—
175C2×D4×C61—44no—
176C2×D4×C61—44no—
177C2×D4×C61C2×D412yes—
178C2×D4×C61C2×D412yes—
179C2×D4×C61#4112yes—
180C2×D4×C61#4112yes—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
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—42no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61—42no—
193C22×C4×C61—81no—
194C22×C4×C61—81no—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—42no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—81no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244C2×D412yes—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—81no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C22⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—42no—
229C22⋊C4×C61—42no—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—42no—
232C22⋊C4×C61—42no—
233C22⋊C4×C61—81no—
234C22⋊C4×C61—81no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61—21no—
238C42×C61—21no—
239C22⋊Dic61—42no—
240#11758200—44no—
241#11758200—44no—
242#11758199—28no—
243#11758199—44no—
244#11758198—42no—
245#11758198—42no—
246#11758198—42no—
247#11758198—42no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61C2×D412yes—
252#11758196—42no—
253#11758196—81no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418C2×D412yes—
265C2×#92418C2×D412yes—
266C23×C61—21no—
267C23×C61—22no—
268C23×C61—21no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—22no—
276C23×C61—48no—
277C23×C61—48no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—84no—
289C23×C61—84no—
290C23×C61—84no—
291C23×C61—84no—
292C23×C61—84no—
293C23×C61#13512yes—
294C23×C61C22×D411yescharacteristic
295C22×D61—22no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—48no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61#12114yes—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—84no—
336C2×C4×C61—84no—
337C2×C4×C61AGL(1,ℤ/8)12yes—
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C22⋊D61—84no—
345C2×Dic61—22no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354D244—22no—
355D244—22no—
356D244—41no—
357D244—41no—
358C4×D61—84no—
359Dic122—41no—
360Dic122—41no—
361Dic122—41no—
362Dic122—41no—
363#92418—22no—
364#92418—22no—
365#92418—41no—
366#92418—41no—
367#25160—611nomaximal, Sylow
368C22×C61—22no—
369C22×C61—24no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—42no—
373C22×C61—41no—
374C22×C61—42no—
375C22×C61—41no—
376C22×C61—42no—
377C22×C61—41no—
378C22×C61—42no—
379C22×C61—41no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—816no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61#52511yescharacteristic
391C22×C61D4211yescharacteristic
392C22×C61D4211yescharacteristic
393C22×C61C2×#13511yescharacteristic
394C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C61#57611yescharacteristic
396C22×C61#57711yescharacteristic
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61—81no—
404C4×C61—22no—
405C4×C61—41no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61—81no—
410C4×C61—81no—
411C4×C61C2×#12111yescharacteristic
412C4×C61#53811yescharacteristic
413C4×C61#54611yescharacteristic
414C4×C61#54611yescharacteristic
415Dic61—42no—
416Dic61—81no—
417Dic61—81no—
418C2×#463—611no—
419C2×#450—611no—
420C2×#447—611no—
421C2×C4×D8—611no—
422#2427—611no—
423D4×C22⋊C4D6111yescharacteristic, complemented
424#2067—611no—
425#2036—611no—
426#2034—611no—
427#2012—611no—
428#1968—611no—
429#1923—611no—
430#1879—611no—
431#1877—611no—
432#1864—611no—
433C2×C61—42no—
434C2×C61—44no—
435C2×C61—82no—
436C2×C61#242411yescharacteristic
437C2×C61#310511yescharacteristic
438C2×C61#311811yescharacteristic
439C2×C61#326411yescharacteristic
440C2×C61#327211yescharacteristic
441C2×C61#328011yescharacteristic
442C2×C61#328211yescharacteristic
443D61—82no—
444C23×D4C2×D6111yescharacteristic
445C22×SD16—611no—
446C22×SD16—611no—
447C22×D8—611no—
448C22×D8—611no—
449C2×#124—611no—
450C2×C22⋊Q8—611no—
451C2×#121—611no—
452C2×C4×D4—611no—
453C2×C4×D4C2×D6111yescharacteristic
454C2×C4×D4C2×D6111yescharacteristic
455C22×C22⋊C4—21no—
456#463—1224no—
457#450—1224no—
458#447—1224no—
459C4×D8—1224no—
460C2×#107—611no—
461C2×#106—611no—
462C2×C4⋊C8—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×C4×C8—611no—
474#397—1221no—
475#394—1221no—
476#391—611no—
477#390C2×D6111yescharacteristic
478#390C2×D6111yescharacteristic
479#389—611no—
480#386—21no—
481#386—21no—
482#386—1221no—
483#380—1221no—
484#380C2×D6111yescharacteristic
485#379—21no—
486C4×C22⋊C4C2×D6111yescharacteristic
487#340—611no—
488#340—611no—
489#336—611no—
490#336—611no—
491C61#2516011yescharacteristic, complemented, Sylow
492C25—21no—
493C22×Q8—611no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—611no—
502C22×D4—1221no—
503C22×D4C22×D6111yescharacteristic
504C22×D4C22×D6111yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—1221no—
508C23×C4C22×D6111yescharacteristic
509C2×SD16—1222no—
510C2×SD16—1222no—
511C2×SD16—1222no—
512C2×SD16—1222no—
513C2×SD16—1222no—
514C2×SD16—2441no—
515C2×D8—614no—
516C2×D8—1222no—
517C2×D8—1222no—
518C2×D8—1222no—
519C2×D8—1222no—
520C2×D8—2441no—
521C22×C8—611no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8—611no—
525#124—1222no—
526#124—2441no—
527C22⋊Q8—1222no—
528C22⋊Q8—2441no—
529#121—1222no—
530#121—2441no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C4×D4—1222no—
536C4×D4—2441no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4C22×D6111yescharacteristic
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—44no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4C22⋊D6111yescharacteristic
557C2×C22⋊C4C22⋊D6111yescharacteristic
558C2×C42C22×D6111yescharacteristic
559C2×C42C22×D6111yescharacteristic
560#107—1222no—
561#106—2441no—
562C4⋊C8—1222no—
563#103—1222no—
564#103—2441no—
565#102—614no—
566#102—1222no—
567#102—1222no—
568#102—1222no—
569#102—1222no—
570#102—1222no—
571C22⋊C8—1222no—
572C22⋊C8—1222no—
573C4×C8—1222no—
574#95—21no—
575#95—1221no—
576#95—1221no—
577#95—1221no—
578#95C22⋊D6111yescharacteristic
579#95C22⋊D6111yescharacteristic
580C24—21no—
581C24—24no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24—1221no—
590C24C2×C22⋊D6111yescharacteristic
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—612no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—4881no—
619C2×D4—2442no—
620C2×D4—2442no—
621C2×D4#1175822212yes—
622C2×D4#1175822212yes—
623C2×D4D4×D6112yes—
624C2×D4D4×D6112yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—4881no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4C2×C22⋊D6111yescharacteristic
646C22×C4C2×C22⋊D6111yescharacteristic
647C22×C4C2×C22⋊D6111yescharacteristic
648C22×C4C2×C22⋊D6111yescharacteristic
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C23×D6111yescharacteristic
651SD16—2444no—
652SD16—2444no—
653D8—1228no—
654D8—2444no—
655C2×C8—612no—
656C2×C8—612no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—612no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—4881no—
676C4⋊C4—2442no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—81no—
685C22⋊C4—81no—
686C22⋊C4—2442no—
687C22⋊C4—2442no—
688C22⋊C4—2442no—
689C22⋊C4—2442no—
690C22⋊C4—2442no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—48no—
706C23—48no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23—84no—
722C23—1222no—
723C23—2441no—
724C23—2441no—
725C23—2441no—
726C23—2441no—
727C23—2441no—
728C23—2441no—
729C23#1451979712yes—
730C23C22×C22⋊D6111yescharacteristic
731Q8—2441no—
732Q8—2441no—
733Q8—2441no—
734Q8—2441no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—41no—
742D4—41no—
743D4—1222no—
744D4—1222no—
745D4—4884no—
746D4—2441no—
747D4—2441no—
748D4#1451975014yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—1222no—
776C2×C4—4884no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4#1451980312yes—
786C2×C4C2×D4×D6111yescharacteristic
787C2×C4C2×D4×D6111yescharacteristic
788C2×C4C2×#1175822211yescharacteristic
789C2×C4C2×#1175822211yescharacteristic
790C2×C4#1451982211yescharacteristic
791C2×C4#1451982211yescharacteristic
792C8—1222no—
793C8—1222no—
794C8—2441no—
795C8—2441no—
796C22—22no—
797C22—22no—
798C22—24no—
799C22—22no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—816no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—4881no—
819C22—4881no—
820C22—4881no—
821C22—4881no—
822C22—2442no—
823C22—2442no—
824C22—2442no—
825C22#1684027311yescharacteristic
826C22D4×C22⋊D6111yescharacteristic
827C22D4×C22⋊D6111yescharacteristic
828C22C2×#1451979711yescharacteristic
829C22C2×#1451980311yescharacteristic
830C22#1684056511yescharacteristic
831C22#1684057311yescharacteristic
832C4—22no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—4881no—
840C4—4881no—
841C4—2442no—
842C4C2×#1451975011yescharacteristic
843C4#1684035011yescharacteristic
844C4#1684040211yescharacteristic
845C4#1684040211yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—4882no—
850C2#2144935511yescharacteristic
851C2#2145586611yescharacteristic
852C2#2145600311yescharacteristic
853C2#2145729511yescharacteristic
854C2#2145741511yescharacteristic
855C2#2145750011yescharacteristic
856C2#2145752211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
hypercenterD4×C22⋊C4D61
hypocenterC61#25160
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839977C2semidirect
2. C2×#16839913C2semidirect
4. C2×C4×#11758199C2semidirect
5. #21449396C2semidirect
6. #21447207C2semidirect
7. #21447022C2semidirect
8. #21447008C2semidirect
9. #21446895C2semidirect
10. #21446672C2semidirect
11. #21446427C2semidirect
12. #21446170C2semidirect
13. #21446153C2semidirect
14. #21446080C2semidirect
15. D4×C22⋊C4×C61C2semidirect
20. C2×#14519765C22semidirect
23. C2×C4×D244C22semidirect
28. C2×#14519710C22semidirect
29. C2×#14519708C22semidirect
30. C2×C4⋊#92418C22semidirect
31. C2×#14519700C22semidirect
32. C2×#14519700C22semidirect
37. C2×#14519697C22semidirect
38. C2×#14519697C22semidirect
41. C2×C4×#92418C22semidirect
44. #16839668C22semidirect
45. #16839660C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
108. #14519698D4semidirect
423. D4×C22⋊C4D61semidirect
491. C61#25160semidirect

Maximal subgroups

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

subgroupindex
C2×#168399772
C2×#168399132
C2×#168398962
C2×C4×#117581992
#214493962
#214472072
#214470222
#214470082
#214468952
#214466722
#214464272
#214461702
#214461532
#214460802
D4×C22⋊C4×C612
#2516061