Finite Group Databasebeta

← #29723753

Subgroups — #29723753

Order 15616.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839896C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3#21449333C211yesmaximal, characteristic, complemented
4#21447347C211yesmaximal, characteristic, complemented
5#21447245C211yesmaximal, characteristic, complemented
6#21447129C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic, complemented
8#21446505C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446066C211yesmaximal, characteristic, complemented
13#21445819C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519759—21no—
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic, complemented
21#16839896—24no—
22C4×#11758199—24no—
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519710C2211yescharacteristic, complemented
25C2×C4⋊#92418C2211yescharacteristic, complemented
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519697C2211yescharacteristic, complemented
33C2×#14519697C2211yescharacteristic, complemented
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic, complemented
37#16839689—21no—
38#16839678—21no—
39#16839664C2211yescharacteristic, complemented
40#16839660C2211yescharacteristic, complemented
41#16839636—21no—
42#16839632C2211yescharacteristic, complemented
43#16839622C2211yescharacteristic
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C23×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C22×C22⋊C4×C61—21no—
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#386—21no—
57C61×#386—21no—
58C61×#380C2211yescharacteristic
59C61×#379—21no—
60C4×C22⋊C4×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C2×#11758199—22no—
65C2×#11758199—22no—
66C2×#11758199—22no—
67C2×#11758199—22no—
68C2×#11758199—41no—
69C2×#11758199D414yes—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519759—44no—
75#14519751—22no—
76#14519751—41no—
77C4×D244—22no—
78C4×D244—41no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90#14519710—22no—
91#14519710—41no—
92C4⋊#92418—41no—
93#14519698—22no—
94#14519698—22no—
95#14519698—22no—
96#14519698—22no—
97#14519698—22no—
98#14519698—41no—
99#14519697—22no—
100#14519697—41no—
101C22⋊#92418—22no—
102C22⋊#92418—41no—
103C4×#92418—22no—
104#14519684—21no—
105#14519684—21no—
106C25×C61—21no—
107C22×D4×C61—22no—
108C22×D4×C61—22no—
109C22×D4×C61—22no—
110C22×D4×C61—22no—
111C22×D4×C61—21no—
112C22×D4×C61—41no—
113C22×D4×C61—41no—
114C22×D4×C61C2311yescharacteristic
115C22×D4×C61C2311yescharacteristic
116C23×C4×C61—21no—
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119C4×D4×C61—22no—
120C4×D4×C61—22no—
121C4×D4×C61—41no—
122C4×D4×C61—41no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—44no—
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137#95×C61—21no—
138#95×C61D411yescharacteristic
139#95×C61D411yescharacteristic
140C24×C61—21no—
141C24×C61—24no—
142C24×C61—21no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—42no—
146C24×C61—42no—
147C24×C61—81no—
148C24×C61—81no—
149C24×C61C2×D411yescharacteristic
150C23×D61—21no—
151C2×D4×C61—24no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—44no—
163C2×D4×C61—44no—
164C2×D4×C61—44no—
165C2×D4×C61—44no—
166C2×D4×C61C2×D412yes—
167C2×D4×C61#4112yes—
168C2×D4×C61#4112yes—
169C2×D4×C61#4112yes—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—42no—
179C22×C4×C61—42no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61—81no—
183C22×C4×C61—81no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—81no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244C2×D412yes—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—81no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C22⋊C4×C61—41no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—81no—
216C22⋊C4×C61—81no—
217C22⋊C4×C61D814yescomplemented
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—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—42no—
236C4⋊Dic61—81no—
237#11758196—42no—
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×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418C2×D412yes—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—21no—
254C23×C61—22no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—22no—
260C23×C61—48no—
261C23×C61—48no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—84no—
273C23×C61—84no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61—84no—
277C23×C61C2×D812yes—
278C23×C61C22×D411yescharacteristic
279C22×D61—22no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—48no—
292D4×C61—41no—
293D4×C61—41no—
294D4×C61#12314yescomplemented
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—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
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—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—84no—
319C2×C4×C61—84no—
320C2×C4×C61C2×D812yes—
321C2×C4×C61C2×D812yes—
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C2×C4×C61C2×#4111yescharacteristic
326C2×C4×C61H(5,𝔽2)11yescharacteristic
327C2×C4×C61H(5,𝔽2)11yescharacteristic
328C22⋊D61—84no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338D244—22no—
339D244—22no—
340D244—41no—
341D244—41no—
342C4×D61—84no—
343#92418—22no—
344#92418—41no—
345#92418—41no—
346#92418—41no—
347#24893—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—24no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—42no—
353C22×C61—41no—
354C22×C61—42no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—41no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—816no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61#52511yescharacteristic
371C22×C61D4211yescharacteristic
372C22×C61#54611yescharacteristic
373C22×C61C22×D811yescharacteristic
374C22×C61#57511yescharacteristic
375C22×C61#57611yescharacteristic
376C22×C61#57711yescharacteristic
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C2×D61—81no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—41no—
387C4×C61—41no—
388C4×C61—41no—
389C4×C61—81no—
390C4×C61—81no—
391C4×C61C2×#12311yescharacteristic
392C4×C61#53811yescharacteristic
393C4×C61#54611yescharacteristic
394C4×C61#55111yescharacteristic
395Dic61—81no—
396Dic61—81no—
397Dic61—81no—
398C2×#447—611no—
399C2×C4×D8—611no—
400#2422—611no—
401D4×C22⋊C4D6111yescharacteristic, complemented
402#2093—611no—
403#2075—611no—
404#2054—611no—
405#2033—611no—
406#1934—611no—
407#1923—611no—
408#1879—611no—
409#1879—611no—
410#1862—611no—
411#1802—611no—
412#1786—611no—
413C2×C61—42no—
414C2×C61—44no—
415C2×C61—82no—
416C2×C61#241811yescharacteristic
417C2×C61#310011yescharacteristic
418C2×C61#311811yescharacteristic
419C2×C61#326711yescharacteristic
420C2×C61D4×D811yescharacteristic
421C2×C61#329411yescharacteristic
422C2×C61#332211yescharacteristic
423D61—82no—
424C23×D4C2×D6111yescharacteristic
425C22×D8—611no—
426C22×D8—611no—
427C2×#123—1221no—
428C2×#121—611no—
429C2×C4×D4—611no—
430C2×C4×D4C2×D6111yescharacteristic
431C2×C4×D4C2×D6111yescharacteristic
432C22×C22⋊C4—21no—
433#447—1224no—
434C4×D8—1224no—
435C2×#107—611no—
436C2×#107—611no—
437C2×C4⋊C8—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—611no—
448C2×C4×C8—611no—
449#397—1221no—
450#394—1221no—
451#390—611no—
452#390C2×D6111yescharacteristic
453#390C2×D6111yescharacteristic
454#389—611no—
455#386—21no—
456#386—21no—
457#385—1221no—
458#384—611no—
459#380—611no—
460#380C2×D6111yescharacteristic
461#379—21no—
462C4×C22⋊C4C2×D6111yescharacteristic
463#340—611no—
464#340—611no—
465#340—611no—
466#340—611no—
467#336—611no—
468#336—611no—
469C61#2489311yescharacteristic, complemented, Sylow
470C25—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—41no—
477C22×D4—41no—
478C22×D4—611no—
479C22×D4—1221no—
480C22×D4C22×D6111yescharacteristic
481C22×D4C22×D6111yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—1221no—
485C23×C4C22×D6111yescharacteristic
486C2×D8—614no—
487C2×D8—1222no—
488C2×D8—1222no—
489C2×D8—1222no—
490C2×D8—1222no—
491C2×D8—2441no—
492C22×C8—611no—
493C22×C8—611no—
494C22×C8—611no—
495C22×C8—611no—
496#123—2444no—
497#121—1222no—
498#121—2441no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—41no—
502C4×D4—41no—
503C4×D4—1222no—
504C4×D4—2441no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—44no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4C22⋊D6111yescharacteristic
527C2×C22⋊C4C22⋊D6111yescharacteristic
528C2×C42C22×D6111yescharacteristic
529C2×C42C22×D6111yescharacteristic
530#107—1222no—
531#107—2441no—
532C4⋊C8—2441no—
533#102—1222no—
534#102—1222no—
535#102—1222no—
536#102—1222no—
537#102—1222no—
538#102—1222no—
539#102—2441no—
540#102—2441no—
541C22⋊C8—1222no—
542C22⋊C8—2441no—
543C4×C8—1222no—
544#95—21no—
545#95—1221no—
546#95—1221no—
547#95C22⋊D6111yescharacteristic
548#95C22⋊D6111yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—42no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—81no—
557C24—81no—
558C24—1221no—
559C24C2×C22⋊D6111yescharacteristic
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—612no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—4881no—
582C2×D4—2442no—
583C2×D4—2442no—
584C2×D4#1175822212yes—
585C2×D4#1175822212yes—
586C2×D4D4×D6112yes—
587C2×D4#1175822412yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—81no—
601C22×C4—81no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—4881no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4C2×C22⋊D6111yescharacteristic
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611C22×C4C2×C22⋊D6111yescharacteristic
612C22×C4C2×C22⋊D6111yescharacteristic
613C22×C4C23×D6111yescharacteristic
614D8—1228no—
615D8—2444no—
616C2×C8—612no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—4881no—
639C4⋊C4—2442no—
640C4⋊C4—2442no—
641C22⋊C4—41no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C22⋊C4—2442no—
650C22⋊C4—2442no—
651C22⋊C4—2442no—
652C22⋊C4—2442no—
653C22⋊C4—2442no—
654C22⋊C4#1175819914yescomplemented
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—22no—
667C23—21no—
668C23—22no—
669C23—48no—
670C23—48no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—1222no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693C23C2×#1175819912yes—
694C23C22×C22⋊D6111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—48no—
701D4—41no—
702D4—41no—
703D4—1222no—
704D4—1222no—
705D4—4884no—
706D4—2441no—
707D4—2441no—
708D4#1451975914yescomplemented
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—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
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—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4—4884no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4C2×#1175819912yes—
745C2×C4C2×#1175819912yes—
746C2×C4C2×D4×D6111yescharacteristic
747C2×C4C2×#1175822411yescharacteristic
748C2×C4C2×#1175822211yescharacteristic
749C2×C4C2×#1175822211yescharacteristic
750C2×C4#1451982211yescharacteristic
751C2×C4#1451982211yescharacteristic
752C8—1222no—
753C8—2441no—
754C8—2441no—
755C8—2441no—
756C22—24no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—816no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—4881no—
779C22—4881no—
780C22—4881no—
781C22—4881no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22#1684027311yescharacteristic
786C22D4×C22⋊D6111yescharacteristic
787C22#1684040611yescharacteristic
788C22C22×#1175819911yescharacteristic
789C22#1684056011yescharacteristic
790C22#1684056511yescharacteristic
791C22#1684057311yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—4881no—
800C4—4881no—
801C4—4881no—
802C4C2×#1451975911yescharacteristic
803C4#1684035011yescharacteristic
804C4#1684040211yescharacteristic
805C4#1684043811yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—4882no—
810C2#2144928111yescharacteristic
811C2#2145581911yescharacteristic
812C2#2145600311yescharacteristic
813C2#2145734011yescharacteristic
814C2D4×#1175819911yescharacteristic
815C2#2145763211yescharacteristic
816C2#2145802011yescharacteristic
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#24893
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
2. C2×C4×#11758199C2semidirect
3. #21449333C2semidirect
4. #21447347C2semidirect
5. #21447245C2semidirect
6. #21447129C2semidirect
7. #21447001C2semidirect
8. #21446505C2semidirect
9. #21446427C2semidirect
10. #21446170C2semidirect
11. #21446167C2semidirect
12. #21446066C2semidirect
13. #21445819C2semidirect
14. #21445750C2semidirect
15. D4×C22⋊C4×C61C2semidirect
20. C2×C4×D244C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519710C22semidirect
25. C2×C4⋊#92418C22semidirect
32. C2×#14519697C22semidirect
33. C2×#14519697C22semidirect
36. C2×C4×#92418C22semidirect
39. #16839664C22semidirect
40. #16839660C22semidirect
42. #16839632C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
217. C22⋊C4×C61D8semidirect
294. D4×C61#123semidirect
401. D4×C22⋊C4D61semidirect
469. C61#24893semidirect
654. C22⋊C4#11758199semidirect
708. D4#14519759semidirect

Maximal subgroups

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

subgroupindex
C2×#168398962
C2×C4×#117581992
#214493332
#214473472
#214472452
#214471292
#214470012
#214465052
#214464272
#214461702
#214461672
#214460662
#214458192
#214457502
D4×C22⋊C4×C612
#2489361