Finite Group Databasebeta

← #29723810

Subgroups — #29723810

Order 15616.

1204 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839895C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3C22⋊C4×D244C211yesmaximal, characteristic, complemented
4#21447343C211yesmaximal, characteristic, complemented
5#21447250C211yesmaximal, characteristic, complemented
6#21447129C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446501C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446079C211yesmaximal, characteristic, complemented
13#21445826C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic, complemented
15C61×#2420C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C22⋊C4×D61—21no—
22#16839895—24no—
23C4×#11758199—24no—
24C2×#14519710C2211yescharacteristic, complemented
25C2×#14519708C2211yescharacteristic, complemented
26C2×C4⋊#92418C2211yescharacteristic, complemented
27C2×#14519698C2211yescharacteristic, complemented
28C2×#14519698C2211yescharacteristic, complemented
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic, complemented
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839640—21no—
41#16839640—21no—
42#16839622C2211yescharacteristic
43#16839617—21no—
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C2×#121×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic, complemented
52C61×#397—21no—
53C61×#394—21no—
54C61×#390C2211yescharacteristic, complemented
55C61×#389C2211yescharacteristic, complemented
56C61×#386—21no—
57C61×#382C2211yescharacteristic, complemented
58C61×#381—21no—
59C61×#380C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C24×D61—21no—
62C22×D244—21no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—41no—
68C22×D244—41no—
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C4×D61—21no—
72C22×C4×D61—21no—
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
83C4×D244—22no—
84C4×D244—22no—
85C4×D244—41no—
86C4×D244—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C22⋊C4×D61—44no—
97#14519710—22no—
98#14519708—41no—
99C4⋊#92418—41no—
100#14519698—22no—
101#14519698—41no—
102#14519697—22no—
103#14519697—22no—
104#14519697—22no—
105#14519697—22no—
106#14519697—22no—
107#14519697—41no—
108C22⋊#92418—22no—
109C22⋊#92418—41no—
110C4×#92418—22no—
111#14519684—21no—
112C22×D4×C61—21no—
113C22×D4×C61C2311yescharacteristic
114C23×C4×C61—21no—
115C23×C4×C61C2311yescharacteristic
116#121×C61—22no—
117#121×C61—41no—
118C4×D4×C61—22no—
119C4×D4×C61—41no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141C23×D61—21no—
142C23×D61—21no—
143C23×D61—24no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61—81no—
149C23×D61—81no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—42no—
156C2×D4×C61—42no—
157C2×D4×C61—81no—
158C2×D4×C61C2×D412yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—42no—
169C22×C4×C61—42no—
170C22×C4×C61—81no—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2411yescharacteristic
177C22×Dic61—21no—
178C22×Dic61—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—24no—
187C2×D244—21no—
188C2×D244—44no—
189C2×D244—44no—
190C2×D244—44no—
191C2×D244—42no—
192C2×D244—42no—
193C2×D244—44no—
194C2×D244C2×D412yes—
195C2×D244#4112yes—
196C2×D244#4112yes—
197C2×D244#4112yes—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—81no—
203C2×C4×D61—81no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—81no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—81no—
216C22⋊C4×C61—81no—
217C22⋊C4×C61—81no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C22⋊Dic61—42no—
223#11758199—28no—
224#11758199—44no—
225#11758198—42no—
226#11758198—42no—
227#11758198—42no—
228#11758198—42no—
229#11758198—81no—
230#11758198—81no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418C2×D412yes—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—22no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61#13512yes—
261C23×C61C22×D411yescharacteristic
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—48no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—48no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—84no—
279C22×D61—84no—
280C22×D61—84no—
281C22×D61—84no—
282C22×D61—84no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—84no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—84no—
316C2×C4×C61AGL(1,ℤ/8)12yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329D244—22no—
330D244—22no—
331D244—22no—
332D244—22no—
333D244—22no—
334D244—48no—
335D244—41no—
336D244—41no—
337D244#12314yes—
338C4×D61—84no—
339C4×D61—84no—
340#92418—22no—
341#92418—41no—
342#92418—41no—
343#92418—41no—
344#24897—611nomaximal, Sylow
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61#52511yescharacteristic
360C22×C61D4211yescharacteristic
361C22×C61#54611yescharacteristic
362C22×C61C2×#13511yescharacteristic
363C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C61#57611yescharacteristic
365C22×C61#57611yescharacteristic
366C2×D61—24no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—816no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—81no—
380C2×D61—81no—
381C4×C61—22no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61—41no—
386C4×C61—81no—
387C4×C61—81no—
388C4×C61—81no—
389C4×C61C2×#12311yescharacteristic
390C4×C61#53811yescharacteristic
391C4×C61#54611yescharacteristic
392C4×C61#55111yescharacteristic
393Dic61—81no—
394Dic61—81no—
395C2×#447—611no—
396C2×C4×D8—611no—
397#2420D6111yescharacteristic, complemented
398D4×C22⋊C4—611no—
399#2092—611no—
400#2076—611no—
401#2054—611no—
402#2034—611no—
403#1934—611no—
404#1923—611no—
405#1879—611no—
406#1879—611no—
407#1864—611no—
408#1804—611no—
409#1786—611no—
410C2×C61—42no—
411C2×C61—82no—
412C2×C61#241811yescharacteristic
413C2×C61#310511yescharacteristic
414C2×C61#312211yescharacteristic
415C2×C61#326411yescharacteristic
416C2×C61#328011yescharacteristic
417C2×C61#329711yescharacteristic
418C2×C61#332511yescharacteristic
419D61—44no—
420D61—82no—
421C23×D4—611no—
422C22×D8—611no—
423C22×D8—611no—
424C2×#121C2×D6111yescharacteristic
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×C4×D4C2×D6111yescharacteristic, complemented
428C22×C22⋊C4—1221no—
429#447—1224no—
430C4×D8—1224no—
431C2×#107—611no—
432C2×#106—611no—
433C2×C4⋊C8—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C4×C8—611no—
445#397—21no—
446#394—21no—
447#390—611no—
448#390—611no—
449#390C2×D6111yescharacteristic, complemented
450#389C2×D6111yescharacteristic, complemented
451#386—21no—
452#386—1221no—
453#386—1221no—
454#382C2×D6111yescharacteristic, complemented
455#381—21no—
456#380—611no—
457#380C2×D6111yescharacteristic
458#379—1221no—
459C4×C22⋊C4C2×D6111yescharacteristic
460#340—611no—
461#340—611no—
462#340—611no—
463#340—611no—
464#336—611no—
465#336—611no—
466C61#2489711yescharacteristic, complemented, Sylow
467C25—1221no—
468C22×D4—21no—
469C22×D4—611no—
470C22×D4—611no—
471C22×D4—1222no—
472C22×D4—1222no—
473C22×D4—1222no—
474C22×D4—1222no—
475C22×D4—1221no—
476C22×D4—2441no—
477C22×D4—2441no—
478C22×D4C22×D6111yescharacteristic
479C23×C4—21no—
480C23×C4—1221no—
481C23×C4—1221no—
482C23×C4C22×D6111yescharacteristic
483C2×D8—614no—
484C2×D8—1222no—
485C2×D8—1222no—
486C2×D8—1222no—
487C2×D8—1222no—
488C2×D8—2441no—
489C22×C8—611no—
490C22×C8—611no—
491C22×C8—611no—
492C22×C8—611no—
493#121—22no—
494#121—41no—
495C4×D4—22no—
496C4×D4—41no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—2441no—
500C4×D4—2441no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—2444no—
520C2×C22⋊C4C22⋊D6111yescharacteristic
521C2×C22⋊C4C22⋊D6111yescharacteristic
522C2×C42C22×D6111yescharacteristic
523C2×C42C22×D6111yescharacteristic
524#107—1222no—
525#106—2441no—
526C4⋊C8—2441no—
527#102—1222no—
528#102—1222no—
529#102—1222no—
530#102—1222no—
531#102—1222no—
532#102—1222no—
533#102—2441no—
534#102—2441no—
535C22⋊C8—1222no—
536C22⋊C8—2441no—
537C4×C8—1222no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—1221no—
543#95C22⋊D6111yescharacteristic
544#95C22⋊D6111yescharacteristic
545C24—21no—
546C24—1224no—
547C24—1221no—
548C24—1221no—
549C24—4881no—
550C24—4881no—
551C24—2442no—
552C24—2442no—
553C24—2442no—
554C24—2442no—
555C24C2×C22⋊D6111yescharacteristic
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—81no—
564C2×D4—612no—
565C2×D4—612no—
566C2×D4—612no—
567C2×D4—612no—
568C2×D4—1224no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—2442no—
578C2×D4—2442no—
579C2×D4—2444no—
580C2×D4—2444no—
581C2×D4—2444no—
582C2×D4—2444no—
583C2×D4D4×D6112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—4881no—
599C22×C4—4881no—
600C22×C4—2442no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4—2442no—
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6111yescharacteristic
606C22×C4C2×C22⋊D6111yescharacteristic
607C22×C4C2×C22⋊D6111yescharacteristic
608C22×C4C2×C22⋊D6111yescharacteristic
609C22×C4C23×D6111yescharacteristic
610D8—1228no—
611D8—2444no—
612C2×C8—612no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—81no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—4881no—
643C22⋊C4—4881no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C22⋊C4—2442no—
648C22⋊C4—2442no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—4884no—
671C23—4884no—
672C23—4884no—
673C23—4884no—
674C23—4884no—
675C23—2448no—
676C23—2448no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23#1451979712yes—
688C23C22×C22⋊D6111yescharacteristic
689D4—22no—
690D4—22no—
691D4—41no—
692D4—41no—
693D4—84no—
694D4—614no—
695D4—1222no—
696D4—1222no—
697D4—1222no—
698D4—1222no—
699D4—1222no—
700D4—2448no—
701D4—2441no—
702D4—2441no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—4884no—
732C2×C4—4884no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4#1451980212yes—
740C2×C4C2×D4×D6111yescharacteristic
741C2×C4#41×D6111yescharacteristic
742C2×C4#41×D6111yescharacteristic
743C2×C4#41×D6111yescharacteristic
744C2×C4#1451982211yescharacteristic
745C2×C4#1451982311yescharacteristic
746C8—1222no—
747C8—2441no—
748C8—2441no—
749C8—2441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—1224no—
765C22—48816no—
766C22—4881no—
767C22—4881no—
768C22—4881no—
769C22—4881no—
770C22—2442no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22—2442no—
779C22#1684026911yescharacteristic
780C22D4×C22⋊D6111yescharacteristic
781C22#1684040011yescharacteristic
782C22C2×#1451979711yescharacteristic
783C22C2×#1451980211yescharacteristic
784C22#1684056511yescharacteristic
785C22#1684056511yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—4881no—
795C4—4881no—
796C4#123×D6111yescharacteristic
797C4#1684034811yescharacteristic
798C4#1684040411yescharacteristic
799C4#1684044011yescharacteristic
800C2—42no—
801C2—82no—
802C2—4882no—
803C2—2444no—
804C2#2144927811yescharacteristic
805C2#2145586211yescharacteristic
806C2#2145605711yescharacteristic
807C2#2145730011yescharacteristic
808C2#2145750011yescharacteristic
809C2#2145766311yescharacteristic
810C2#2145805511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2420C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
hypercenter#2420D61
hypocenterC61#24897
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2420

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758199C2semidirect
3. C22⋊C4×D244C2semidirect
4. #21447343C2semidirect
5. #21447250C2semidirect
6. #21447129C2semidirect
7. #21447005C2semidirect
8. #21446501C2semidirect
9. #21446427C2semidirect
10. #21446170C2semidirect
11. #21446167C2semidirect
12. #21446079C2semidirect
13. #21445826C2semidirect
14. #21445749C2semidirect
15. C61×#2420C2semidirect
24. C2×#14519710C22semidirect
25. C2×#14519708C22semidirect
26. C2×C4⋊#92418C22semidirect
27. C2×#14519698C22semidirect
28. C2×#14519698C22semidirect
37. C2×C4×#92418C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
51. C2×C4×D4×C61C22semidirect
54. C61×#390C22semidirect
55. C61×#389C22semidirect
57. C61×#382C22semidirect
397. #2420D61semidirect
427. C2×C4×D4C2×D61semidirect
449. #390C2×D61semidirect
450. #389C2×D61semidirect
454. #382C2×D61semidirect
466. C61#24897semidirect

Maximal subgroups

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

subgroupindex
C2×#168398952
C2×C4×#117581992
C22⋊C4×D2442
#214473432
#214472502
#214471292
#214470052
#214465012
#214464272
#214461702
#214461672
#214460792
#214458262
#214457492
C61×#24202
#2489761