Finite Group Databasebeta

← #29700486

Subgroups — #29700486

Order 15616.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839894C211yesmaximal, characteristic
2C2×#16839874C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4#21448862C211yesmaximal, characteristic, complemented
5D4×#11758198C211yesmaximal, characteristic, complemented
6#21446684C211yesmaximal, characteristic, complemented
7#21446514C211yesmaximal, characteristic, complemented
8#21446447C211yesmaximal, characteristic, complemented
9#21446254C211yesmaximal, characteristic, complemented
10#21446165C211yesmaximal, characteristic, complemented
11#21446064C211yesmaximal, characteristic, complemented
12#21446019C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic, complemented
14#21445599C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic, complemented
22C2×#14519735C2211yescharacteristic
23C22×#11758198—21no—
24#16839894C418yescomplemented
25#16839874—24no—
26C2×#14519710C2211yescharacteristic, complemented
27C2×#14519709C2211yescharacteristic, complemented
28#16839765—24no—
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic, complemented
34C2×#14519697C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519687C2211yescharacteristic, complemented
37C2×C4×#92418C2211yescharacteristic, complemented
38#16839664C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839662—21no—
41#16839658C2211yescharacteristic, complemented
42#16839656—21no—
43#16839641—21no—
44#16839639—21no—
45#16839639—21no—
46#16839619C2211yescharacteristic
47#16839617—21no—
48C4×C4⋊Dic61C2211yescharacteristic, complemented
49C22⋊C4×Dic61—21no—
50C4×#11758198C2211yescharacteristic
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55C22×D8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic, complemented
59C61×#390C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—41no—
70C2×D4×D61—41no—
71C2×D4×D61C2×C414yescomplemented
72C23×Dic61—21no—
73C23×Dic61—21no—
74C22×C4×D61C2311yescharacteristic
75C2×#11758199—41no—
76C2×#11758199—41no—
77C2×#11758199C2×C414yescomplemented
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519748—22no—
84#14519748C2×C414yescomplemented
85D4×Dic61—22no—
86D4×Dic61—22no—
87D4×Dic61—41no—
88D4×Dic61—41no—
89#14519735—22no—
90#14519735—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—44no—
105C2×#11758198D411yescharacteristic
106C2×#11758198D411yescharacteristic
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61C2311yescharacteristic
110#14519710—41no—
111#14519709—22no—
112#14519699—22no—
113#14519699C2×C414yescomplemented
114#14519698—22no—
115#14519698C2×C414yescomplemented
116#14519698D414yescomplemented
117#14519697—22no—
118#14519689C2×C414yescomplemented
119#14519687—22no—
120C4×#92418—41no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684D411yescharacteristic
125#14519684D411yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C22×D4×C61C2311yescharacteristic
128C23×C4×C61—21no—
129C2×D8×C61—22no—
130C2×D8×C61—22no—
131C2×D8×C61C2×C414yes—
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C4×D4×C61—22no—
135C4×D4×C61—41no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C42×C61C2311yescharacteristic
142#102×C61—22no—
143#102×C61—41no—
144C24×C61—21no—
145C24×C61—21no—
146C23×D61—21no—
147C23×D61—24no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—81no—
153C23×D61—81no—
154C23×D61C2×D411yescharacteristic
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61C22×C412yes—
164C2×D4×C61C22×C412yes—
165C2×D4×C61C2×D412yes—
166C2×D4×C61#4112yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—42no—
170C22×C4×C61—42no—
171C22×C4×C61—81no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—24no—
176C2×C22⋊D61—24no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—81no—
180C2×C22⋊D61—81no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—42no—
185C22×Dic61—42no—
186C22×Dic61—42no—
187C22×Dic61—42no—
188C22×Dic61—81no—
189C22×Dic61—81no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193D4×D61—28no—
194D4×D61—44no—
195D4×D61—44no—
196D4×D61—44no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244C22×C412yes—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61#4112yes—
209D8×C61—28no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61C22×C412yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—81no—
223C42×C61—21no—
224C42×C61—21no—
225C22⋊Dic61—24no—
226C22⋊Dic61—42no—
227C22⋊Dic61—42no—
228#11758199—44no—
229#11758198—22no—
230#11758198—41no—
231#11758198—42no—
232#11758198—42no—
233#11758198—42no—
234#11758198—42no—
235#11758198—81no—
236#11758198—81no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61C22×C412yes—
242C4⋊Dic61C2×D412yes—
243#11758196—81no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—42no—
247C4×Dic61—81no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418C22×C412yes—
253C2×#92418C2×D412yes—
254#11758189—44no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61C22×D411yescharacteristic
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—22no—
277C22×D61—48no—
278C22×D61—48no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61C4×D412yes—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—41no—
297D4×C61—41no—
298D4×C61C4×D414yes—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
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—84no—
311C2×C4×C61AGL(1,ℤ/8)12yes—
312C2×C4×C61C23×C411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C22⋊D61—48no—
319C22⋊D61—84no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—22no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—84no—
338C2×Dic61—84no—
339C2×Dic61C4×D412yes—
340D244—22no—
341D244—22no—
342D244—41no—
343D244—41no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C8×C61—22no—
349C8×C61—41no—
350#92418—22no—
351#92418—22no—
352#22868—611nomaximal, Sylow
353C22×C61—24no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61C2×C4×D411yescharacteristic
368C22×C61D4211yescharacteristic
369C22×C61#54611yescharacteristic
370C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C61#57511yescharacteristic
372C22×C61#57611yescharacteristic
373C22×C61#57611yescharacteristic
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—816no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C4×C61—22no—
390C4×C61—41no—
391C4×C61—81no—
392C4×C61—81no—
393C4×C61C2×C4×D411yescharacteristic
394C4×C61#51811yescharacteristic
395C4×C61#54611yescharacteristic
396C4×C61#55111yescharacteristic
397Dic61—22no—
398Dic61—42no—
399Dic61—41no—
400Dic61—42no—
401Dic61—41no—
402Dic61—81no—
403C2×#447—611no—
404C2×#442—611no—
405C2×#418—611no—
406#2363—611no—
407D4×C22⋊C4—611no—
408#1970—611no—
409#1936—611no—
410#1926—611no—
411#1895—611no—
412#1879—611no—
413#1879D6111yescharacteristic, complemented
414#1862—611no—
415#1854—611no—
416C4×#102—611no—
417#1753—611no—
418C2×C61—44no—
419C2×C61—82no—
420C2×C61#235811yescharacteristic
421C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
422C2×C61#294811yescharacteristic
423C2×C61#327311yescharacteristic
424C2×C61#327411yescharacteristic
425C2×C61#331811yescharacteristic
426C2×C61#331911yescharacteristic
427D61—42no—
428D61—82no—
429C23×D4—611no—
430C22×D8—611no—
431C22×D8C2×D6111yescharacteristic
432C22×M16—611no—
433C2×#121—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4C2×D6111yescharacteristic
437C2×#117—611no—
438C22×C22⋊C4—1221no—
439#447—618no—
440#442—1224no—
441C2×#107—611no—
442C2×#106—611no—
443#418—1224no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102C2×D6111yescharacteristic
451C2×#102C2×D6111yescharacteristic, complemented
452C2×C22⋊C8—611no—
453C2×#97—611no—
454C2×C4×C8—611no—
455#390—611no—
456#390—611no—
457#390—1221no—
458#390C2×D6111yescharacteristic, complemented
459#389—611no—
460#388—1221no—
461#386—1221no—
462#386—1221no—
463#386—1221no—
464#380—611no—
465#379—1221no—
466C4×C4⋊C4—611no—
467C4×C22⋊C4—611no—
468C4×C22⋊C4—1221no—
469#340—611no—
470#340—611no—
471#340—611no—
472#340C2×D6111yescharacteristic, complemented
473#336—611no—
474#336C2×D6111yescharacteristic, complemented
475C61#2286811yescharacteristic, complemented, Sylow
476C25—1221no—
477C22×D4—614no—
478C22×D4—611no—
479C22×D4—1222no—
480C22×D4—1221no—
481C22×D4—1222no—
482C22×D4—1222no—
483C22×D4—1221no—
484C22×D4—2441no—
485C22×D4—2441no—
486C22×D4C22×D6111yescharacteristic
487C22×D4C22×D6111yescharacteristic
488C23×C4—21no—
489C23×C4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—614no—
495C2×D8—2441no—
496C2×D8—2441no—
497C2×D8C4×D6114yes—
498C2×M16—1222no—
499C2×M16—1222no—
500C2×M16—2441no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505#121—614no—
506#121—1222no—
507C4×D4—22no—
508C4×D4—41no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—2441no—
512C4×D4—2441no—
513#117—1222no—
514#117—2441no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—2444no—
536C2×C42—611no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
540#107—2441no—
541#106—1222no—
542#102—22no—
543#102—41no—
544#102—614no—
545#102—614no—
546#102—614no—
547#102—1222no—
548#102—1222no—
549#102—1222no—
550C22⋊C8—614no—
551#97—1222no—
552C4×C8—2441no—
553#95—611no—
554#95—611no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558C24—21no—
559C24—21no—
560C24—611no—
561C24—1224no—
562C24—1221no—
563C24—4881no—
564C24—4881no—
565C24—2442no—
566C24—2442no—
567C24—2442no—
568C24—2442no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—612no—
578C2×D4—1224no—
579C2×D4—1228no—
580C2×D4—1224no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—4881no—
587C2×D4—4881no—
588C2×D4—2444no—
589C2×D4—2444no—
590C2×D4—2444no—
591C2×D4—2442no—
592C2×D4—2442no—
593C2×D4C2×C4×D6112yes—
594C2×D4C2×C4×D6112yes—
595C2×D4D4×D6112yes—
596C2×D4#1175822412yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—611no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—4881no—
615C22×C4—4881no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4D4×D6111yescharacteristic
621C22×C4D4×D6111yescharacteristic
622C22×C4C23×D6111yescharacteristic
623D8—28no—
624D8—2444no—
625M16—2444no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—612no—
632C2×C8—612no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8C2×C4×D6112yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—612no—
643C4⋊C4—612no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—4881no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—81no—
652C22⋊C4—1224no—
653C22⋊C4—1222no—
654C22⋊C4—4881no—
655C22⋊C4—4881no—
656C22⋊C4—2441no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C22⋊C4—2442no—
662C22⋊C4—2442no—
663C42—21no—
664C42—21no—
665C42—1221no—
666C42—1221no—
667C42—4881no—
668C42—2442no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—612no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1222no—
691C23—4884no—
692C23—4884no—
693C23—4884no—
694C23—4884no—
695C23—4884no—
696C23—2448no—
697C23—2448no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23C2×D4×D6111yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—41no—
711D4—41no—
712D4—1222no—
713D4—1222no—
714D4—4884no—
715D4—2448no—
716D4—2441no—
717D4—2441no—
718D4#1451973714yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—612no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1222no—
746C2×C4—4884no—
747C2×C4—4884no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4#1451980112yes—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4C2×#1175822411yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982311yescharacteristic
762C8—22no—
763C8—41no—
764C8—1222no—
765C8—1222no—
766C22—24no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—1222no—
781C22—1222no—
782C22—1222no—
783C22—48816no—
784C22—4881no—
785C22—4881no—
786C22—4881no—
787C22—4881no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2441no—
792C22—2441no—
793C22—2441no—
794C22—2441no—
795C22C4×D4×D6111yescharacteristic
796C22#1684039611yescharacteristic
797C22#1684039911yescharacteristic
798C22C2×#1451980111yescharacteristic
799C22#1684055911yescharacteristic
800C22#1684056611yescharacteristic
801C22#1684056611yescharacteristic
802C4—22no—
803C4—41no—
804C4—81no—
805C4—81no—
806C4—1222no—
807C4—4881no—
808C4—2441no—
809C4—2442no—
810C4—2441no—
811C4—2442no—
812C4C2×#1451973711yescharacteristic
813C4#1684023411yescharacteristic
814C4#1684040111yescharacteristic
815C4#1684043511yescharacteristic
816C2—44no—
817C2—82no—
818C2—4882no—
819C2—2442no—
820C2#2144879911yescharacteristic
821C2C4×#1451980111yescharacteristic
822C2#2145466811yescharacteristic
823C2#2145742511yescharacteristic
824C2#2145744211yescharacteristic
825C2#2145796411yescharacteristic
826C2#2145797911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×#16839874C2semidirect
3. C2×#16839765C2semidirect
4. #21448862C2semidirect
5. D4×#11758198C2semidirect
6. #21446684C2semidirect
7. #21446514C2semidirect
8. #21446447C2semidirect
9. #21446254C2semidirect
10. #21446165C2semidirect
11. #21446064C2semidirect
12. #21446019C2semidirect
13. C4×#14519698C2semidirect
14. #21445599C2semidirect
15. C61×#1879C2semidirect
21. C2×D4×Dic61C22semidirect
24. #16839894C4semidirect
26. C2×#14519710C22semidirect
27. C2×#14519709C22semidirect
33. C2×#14519698C22semidirect
36. C2×#14519687C22semidirect
37. C2×C4×#92418C22semidirect
41. #16839658C22semidirect
48. C4×C4⋊Dic61C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839516C22semidirect
58. C2×#102×C61C22semidirect
59. C61×#390C22semidirect
60. C61×#340C22semidirect
61. C61×#336C22semidirect
71. C2×D4×D61C2×C4semidirect
77. C2×#11758199C2×C4semidirect
84. #14519748C2×C4semidirect
113. #14519699C2×C4semidirect
115. #14519698C2×C4semidirect
116. #14519698D4semidirect
118. #14519689C2×C4semidirect
413. #1879D61semidirect
451. C2×#102C2×D61semidirect
458. #390C2×D61semidirect
472. #340C2×D61semidirect
474. #336C2×D61semidirect
475. C61#22868semidirect

Maximal subgroups

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

subgroupindex
C2×#168398942
C2×#168398742
C2×#168397652
#214488622
D4×#117581982
#214466842
#214465142
#214464472
#214462542
#214461652
#214460642
#214460192
C4×#145196982
#214455992
C61×#18792
#2286861