Finite Group Databasebeta

← #29727443

Subgroups — #29727443

Order 15616.

1302 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839974C211yesmaximal, characteristic, complemented
2C2×#16839912C211yesmaximal, characteristic, complemented
3C2×#16839895C211yesmaximal, characteristic
4C2×C4×#11758201C211yesmaximal, characteristic, complemented
5C22⋊C4×D244C211yesmaximal, characteristic, complemented
6#21447190C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21447005C211yesmaximal, characteristic, complemented
9#21446896C211yesmaximal, characteristic, complemented
10#21446684C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446174C211yesmaximal, characteristic, complemented
13#21446170C211yesmaximal, characteristic, complemented
14#21446065C211yesmaximal, characteristic, complemented
15C61×#2426C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C22⋊C4×D61—21no—
24#16839974—24no—
25#16839912—24no—
26#16839895—24no—
27C4×#11758201—24no—
28C2×#14519710C2211yescharacteristic, complemented
29C2×#14519708C2211yescharacteristic, complemented
30C2×C4⋊#92418C2211yescharacteristic, complemented
31C2×#14519701C2211yescharacteristic, complemented
32C2×#14519701C2211yescharacteristic, complemented
33C2×#14519698C2211yescharacteristic, complemented
34C2×#14519698C2211yescharacteristic, complemented
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic, complemented
42#16839664C2211yescharacteristic
43#16839664C2211yescharacteristic
44#16839640—21no—
45#16839640—21no—
46#16839622C2211yescharacteristic
47#16839617—21no—
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C2×#124×C61C2211yescharacteristic, complemented
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic, complemented
56C61×#396—21no—
57C61×#394—21no—
58C61×#390—21no—
59C61×#390C2211yescharacteristic, complemented
60C61×#389C2211yescharacteristic, complemented
61C61×#388—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C24×D61—21no—
64C22×D244—21no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—22no—
69C22×D244—41no—
70C22×D244—41no—
71C22×D244C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758201—22no—
76C2×#11758201—22no—
77C2×#11758201—22no—
78C2×#11758201—22no—
79C2×#11758201—41no—
80C2×#11758201D414yescomplemented
81C2×#11758199—22no—
82C2×#11758199—22no—
83C2×#11758199—22no—
84C2×#11758199—22no—
85C2×#11758199—22no—
86C2×#11758199—41no—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—41no—
94C4×D244—41no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C22⋊C4×D61—44no—
105#14519710—41no—
106#14519708—22no—
107C4⋊#92418—22no—
108#14519701—22no—
109#14519701—22no—
110#14519698—22no—
111#14519698—41no—
112#14519697—22no—
113#14519697—22no—
114#14519697—22no—
115#14519697D414yes—
116C22⋊#92418—22no—
117C22⋊#92418—22no—
118C4×#92418—22no—
119#14519684—21no—
120C22×Q8×C61C2311yescharacteristic
121C22×D4×C61—21no—
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124#124×C61—22no—
125#124×C61—41no—
126C22⋊Q8×C61—22no—
127C22⋊Q8×C61—41no—
128#121×C61—22no—
129#121×C61—41no—
130C4×Q8×C61—22no—
131C4×Q8×C61—41no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
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×C61D411yescharacteristic
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61—21no—
152C24×C61C2×D411yescharacteristic
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—24no—
156C23×D61—42no—
157C23×D61—42no—
158C23×D61—42no—
159C23×D61—42no—
160C23×D61—81no—
161C23×D61—81no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C2×D412yes—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—42no—
175C2×D4×C61—42no—
176C2×D4×C61—81no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2411yescharacteristic
192C22×Dic61—21no—
193C22×Dic61—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—24no—
202C2×D244—21no—
203C2×D244—44no—
204C2×D244—44no—
205C2×D244—44no—
206C2×D244—42no—
207C2×D244—42no—
208C2×D244—44no—
209C2×D244C2×D412yes—
210C2×D244C2×D412yes—
211C2×D244#4112yes—
212C2×D244#4112yes—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61—81no—
218C2×C4×D61—81no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—42no—
223C4⋊C4×C61—42no—
224C4⋊C4×C61—81no—
225C4⋊C4×C61C2×D412yes—
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—
234C42×C61—21no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61—21no—
238C42×C61—42no—
239C22⋊Dic61—42no—
240#11758201—28no—
241#11758201—44no—
242#11758199—44no—
243#11758199—44no—
244#11758198—42no—
245#11758198—42no—
246#11758198—42no—
247#11758198—42no—
248#11758198—81no—
249#11758198—81no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
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—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61#13512yes—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—48no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—48no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—84no—
298C22×D61—84no—
299C22×D61—84no—
300C22×D61—84no—
301C22×D61—84no—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—41no—
305Q8×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—84no—
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—22no—
318C2×C4×C61—22no—
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—21no—
326C2×C4×C61—21no—
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—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61AGL(1,ℤ/8)12yes—
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351D244—22no—
352D244—22no—
353D244—22no—
354D244—22no—
355D244—22no—
356D244—48no—
357D244—41no—
358D244—41no—
359D244#12114yes—
360C4×D61—84no—
361C4×D61—84no—
362#92418—22no—
363#92418—22no—
364#92418—41no—
365#92418—41no—
366#25152—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61#52511yescharacteristic
382C22×C61D4211yescharacteristic
383C22×C61D4211yescharacteristic
384C22×C61C2×#13511yescharacteristic
385C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
386C22×C61#57611yescharacteristic
387C22×C61#57711yescharacteristic
388C2×D61—24no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—816no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C4×C61—22no—
404C4×C61—41no—
405C4×C61—42no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—42no—
409C4×C61—41no—
410C4×C61—81no—
411C4×C61C2×#12111yescharacteristic
412C4×C61#53811yescharacteristic
413C4×C61#54611yescharacteristic
414C4×C61#54611yescharacteristic
415Dic61—81no—
416Dic61—81no—
417C2×#463—611no—
418C2×#450—611no—
419C2×#447—611no—
420C2×C4×SD16—611no—
421#2426D6111yescharacteristic, complemented
422D4×C22⋊C4—611no—
423#2065—611no—
424#2036—611no—
425#2034—611no—
426#2012—611no—
427#1970—611no—
428#1923—611no—
429#1880—611no—
430#1879—611no—
431#1862—611no—
432C2×C61—42no—
433C2×C61—161no—
434C2×C61#242411yescharacteristic
435C2×C61#310511yescharacteristic
436C2×C61#311811yescharacteristic
437C2×C61#326511yescharacteristic
438C2×C61#327411yescharacteristic
439C2×C61#328011yescharacteristic
440C2×C61#328211yescharacteristic
441D61—44no—
442D61—82no—
443C23×D4—611no—
444C22×SD16—611no—
445C22×SD16—611no—
446C22×D8—611no—
447C22×D8—611no—
448C2×#124C2×D6111yescharacteristic, complemented
449C2×C22⋊Q8C2×D6111yescharacteristic
450C2×#121C2×D6111yescharacteristic
451C2×C4×Q8C2×D6111yescharacteristic, complemented
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C22×C22⋊C4—1221no—
455#463—1224no—
456#450—1224no—
457#447—1224no—
458C4×SD16—1224no—
459C2×#107—611no—
460C2×#106—611no—
461C2×C4⋊C8—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×C4×C8—611no—
473#396—21no—
474#394—21no—
475#390—21no—
476#390—611no—
477#390—611no—
478#390C2×D6111yescharacteristic, complemented
479#389C2×D6111yescharacteristic, complemented
480#388—21no—
481#386—1221no—
482#386—1221no—
483#380—611no—
484#379—1221no—
485C4×C22⋊C4C2×D6111yescharacteristic
486#340—611no—
487#340—611no—
488#336—611no—
489#336—611no—
490C61#2515211yescharacteristic, complemented, Sylow
491C25—1221no—
492C22×Q8C22×D6111yescharacteristic
493C22×D4—21no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—1222no—
497C22×D4—1222no—
498C22×D4—1222no—
499C22×D4—1222no—
500C22×D4—1221no—
501C22×D4—2441no—
502C22×D4—2441no—
503C22×D4C22×D6111yescharacteristic
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4C22×D6111yescharacteristic
507C2×SD16—614no—
508C2×SD16—1222no—
509C2×SD16—1222no—
510C2×SD16—1222no—
511C2×SD16—1222no—
512C2×SD16—2441no—
513C2×D8—1222no—
514C2×D8—1222no—
515C2×D8—1222no—
516C2×D8—1222no—
517C2×D8—1222no—
518C2×D8—2441no—
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—611no—
522C22×C8—611no—
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—1222no—
532C4×D4—1222no—
533C4×D4—2441no—
534C4×D4—2441no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4C22×D6111yescharacteristic
541C2×C4⋊C4C22×D6111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—2444no—
556C2×C22⋊C4C22⋊D6111yescharacteristic
557C2×C22⋊C4C22⋊D6111yescharacteristic
558C2×C42—21no—
559C2×C42C22×D6111yescharacteristic
560C2×C42C22×D6111yescharacteristic
561#107—2441no—
562#106—1222no—
563C4⋊C8—1222no—
564#103—1222no—
565#103—1222no—
566#102—614no—
567#102—1222no—
568#102—1222no—
569#102—1222no—
570#102—1222no—
571#102—2441no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C4×C8—1222no—
575#95—21no—
576#95—1221no—
577#95C22⋊D6111yescharacteristic
578#95C22⋊D6111yescharacteristic
579C24—21no—
580C24—1224no—
581C24—1221no—
582C24—1221no—
583C24—4881no—
584C24—4881no—
585C24—2442no—
586C24—2442no—
587C24—2442no—
588C24—2442no—
589C24C2×C22⋊D6111yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8D4×D6112yes—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—612no—
606C2×D4—612no—
607C2×D4—612no—
608C2×D4—612no—
609C2×D4—1224no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—2442no—
619C2×D4—2442no—
620C2×D4—2444no—
621C2×D4—2444no—
622C2×D4—2444no—
623C2×D4—2444no—
624C22×C4—21no—
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—1221no—
634C22×C4—1221no—
635C22×C4—4881no—
636C22×C4—4881no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4C2×C22⋊D6111yescharacteristic
642C22×C4C2×C22⋊D6111yescharacteristic
643C22×C4C2×C22⋊D6111yescharacteristic
644C22×C4C2×C22⋊D6111yescharacteristic
645C22×C4C2×C22⋊D6111yescharacteristic
646C22×C4C23×D6111yescharacteristic
647SD16—1228no—
648SD16—2444no—
649D8—2444no—
650D8—2444no—
651C2×C8—612no—
652C2×C8—612no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—81no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4D4×D6112yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C22⋊C4—4881no—
683C22⋊C4—4881no—
684C22⋊C4—2442no—
685C22⋊C4—2442no—
686C22⋊C4—2442no—
687C22⋊C4—2442no—
688C22⋊C4—2442no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—1222no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—4884no—
712C23—4884no—
713C23—4884no—
714C23—4884no—
715C23—4884no—
716C23—2448no—
717C23—2448no—
718C23—2441no—
719C23—2441no—
720C23—2441no—
721C23—2441no—
722C23—2441no—
723C23—2441no—
724C23—2441no—
725C23—2441no—
726C23—2441no—
727C23—2441no—
728C23#1451979712yes—
729C23C22×C22⋊D6111yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—84no—
739D4—614no—
740D4—1222no—
741D4—1222no—
742D4—1222no—
743D4—1222no—
744D4—1222no—
745D4—2448no—
746D4—2441no—
747D4—2441no—
748C2×C4—21no—
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—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
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—41no—
774C2×C4—41no—
775C2×C4—4884no—
776C2×C4—4884no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4#1451980212yes—
784C2×C4C2×D4×D6111yescharacteristic
785C2×C4C2×D4×D6111yescharacteristic
786C2×C4#41×D6111yescharacteristic
787C2×C4#41×D6111yescharacteristic
788C2×C4#1451982211yescharacteristic
789C2×C4#1451982211yescharacteristic
790C8—1222no—
791C8—1222no—
792C8—2441no—
793C8—2441no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—1224no—
809C22—48816no—
810C22—4881no—
811C22—4881no—
812C22—4881no—
813C22—4881no—
814C22—2442no—
815C22—2442no—
816C22—2442no—
817C22—2442no—
818C22—2442no—
819C22—2442no—
820C22—2442no—
821C22—2442no—
822C22—2442no—
823C22#1684026911yescharacteristic
824C22D4×C22⋊D6111yescharacteristic
825C22D4×C22⋊D6111yescharacteristic
826C22C2×#1451979711yescharacteristic
827C22C2×#1451980211yescharacteristic
828C22#1684056511yescharacteristic
829C22#1684057011yescharacteristic
830C4—22no—
831C4—41no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—42no—
837C4—81no—
838C4—4881no—
839C4—4881no—
840C4#121×D6111yescharacteristic
841C4#1684034411yescharacteristic
842C4#1684040111yescharacteristic
843C4#1684040911yescharacteristic
844C2—42no—
845C2—161no—
846C2—4882no—
847C2—2444no—
848C2#2144935211yescharacteristic
849C2#2145586211yescharacteristic
850C2#2145599711yescharacteristic
851C2#2145731511yescharacteristic
852C2#2145743911yescharacteristic
853C2#2145750011yescharacteristic
854C2#2145752711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2426C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
hypercenter#2426D61
hypocenterC61#25152
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2426

Complements

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

NH ≅ G/Ntype
1. C2×#16839974C2semidirect
2. C2×#16839912C2semidirect
4. C2×C4×#11758201C2semidirect
5. C22⋊C4×D244C2semidirect
6. #21447190C2semidirect
7. #21447019C2semidirect
8. #21447005C2semidirect
9. #21446896C2semidirect
10. #21446684C2semidirect
11. #21446427C2semidirect
12. #21446174C2semidirect
13. #21446170C2semidirect
14. #21446065C2semidirect
15. C61×#2426C2semidirect
28. C2×#14519710C22semidirect
29. C2×#14519708C22semidirect
30. C2×C4⋊#92418C22semidirect
31. C2×#14519701C22semidirect
32. C2×#14519701C22semidirect
33. C2×#14519698C22semidirect
34. C2×#14519698C22semidirect
41. C2×C4×#92418C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
52. C2×#124×C61C22semidirect
55. C2×C4×Q8×C61C22semidirect
59. C61×#390C22semidirect
60. C61×#389C22semidirect
80. C2×#11758201D4semidirect
421. #2426D61semidirect
448. C2×#124C2×D61semidirect
451. C2×C4×Q8C2×D61semidirect
478. #390C2×D61semidirect
479. #389C2×D61semidirect
490. C61#25152semidirect

Maximal subgroups

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

subgroupindex
C2×#168399742
C2×#168399122
C2×#168398952
C2×C4×#117582012
C22⋊C4×D2442
#214471902
#214470192
#214470052
#214468962
#214466842
#214464272
#214461742
#214461702
#214460652
C61×#24262
#2515261