Finite Group Databasebeta

← #29700474

Subgroups — #29700474

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×#16839765C211yesmaximal, characteristic, complemented
3#21448853C211yesmaximal, characteristic, complemented
4D4×#11758198C211yesmaximal, characteristic, complemented
5#21446682C211yesmaximal, characteristic, complemented
6#21446516C211yesmaximal, characteristic, complemented
7#21446445C211yesmaximal, characteristic, complemented
8#21446254C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446066C211yesmaximal, characteristic, complemented
12#21446017C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445604C211yesmaximal, characteristic, complemented
15C2×C61×#442C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C22×#11758198—21no—
23#16839894C418yescomplemented
24C2×#14519710C2211yescharacteristic, complemented
25#16839765—24no—
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic, complemented
31C2×#14519697C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic, complemented
34#16839665C2211yescharacteristic, complemented
35#16839664C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839662—21no—
38#16839660C2211yescharacteristic, complemented
39#16839650—21no—
40#16839641—21no—
41#16839641—21no—
42#16839639—21no—
43#16839619C2211yescharacteristic
44#16839617—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C4×#11758198C2211yescharacteristic
47C4×C22⋊Dic61—21no—
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C22×D8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic, complemented
57C61×#442—24no—
58C2×#106×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic, complemented
61C2×#97×C61C2211yescharacteristic, 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—
73C22×C4×D61C2311yescharacteristic
74C2×#11758199—41no—
75C2×#11758199—41no—
76C2×#11758199C2×C414yescomplemented
77C2×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519748—22no—
83#14519748C2×C414yescomplemented
84D4×Dic61—22no—
85D4×Dic61—41no—
86#14519735—22no—
87#14519735—41no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—44no—
103C2×#11758198D411yescharacteristic
104C2×#11758198D411yescharacteristic
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61C2311yescharacteristic
108#14519710—41no—
109#14519699—22no—
110#14519699C2×C414yescomplemented
111#14519698—22no—
112#14519698—41no—
113#14519698C2×C414yescomplemented
114#14519697—22no—
115#14519689C2×C414yescomplemented
116C8×Dic61—41no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684D411yescharacteristic
121#14519684D411yescharacteristic
122C22×D4×C61C2311yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C23×C4×C61—21no—
126C2×D8×C61—22no—
127C2×D8×C61—22no—
128C2×D8×C61C2×C414yes—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C4×D4×C61—22no—
132C4×D4×C61—22no—
133C4×D4×C61—41no—
134C4×D4×C61—41no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#106×C61—22no—
141#102×C61—22no—
142#102×C61D414yescomplemented
143#97×C61—22no—
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—42no—
172C22×C4×C61—42no—
173C22×C4×C61—81no—
174C22×C4×C61—81no—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2411yescharacteristic
178C2×C22⋊D61—24no—
179C2×C22⋊D61—24no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—81no—
183C2×C22⋊D61—81no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
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×C61C22×C412yes—
215C2×C8×C61C2×D412yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61C2×D412yes—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C42×C61—21no—
223C42×C61—21no—
224C22⋊Dic61—24no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227C22⋊Dic61—81no—
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⋊Dic61—21no—
242C4⋊Dic61C22×C412yes—
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×#92418—21no—
253C2×#92418C22×C412yes—
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—22no—
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—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—84no—
312C2×C4×C61—84no—
313C2×C4×C61C23×C411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C22⋊D61—48no—
320C22⋊D61—84no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
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—84no—
338C2×Dic61C4×D412yes—
339C2×Dic61AGL(1,ℤ/8)12yes—
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—22no—
350#92418—22no—
351#92418—41no—
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—41no—
390C4×C61—42no—
391C4×C61—41no—
392C4×C61—81no—
393C4×C61C2×C4×D411yescharacteristic
394C4×C61#51811yescharacteristic
395C4×C61#54611yescharacteristic
396C4×C61#55111yescharacteristic
397Dic61—22no—
398Dic61—22no—
399Dic61—42no—
400Dic61—41no—
401Dic61—81no—
402Dic61—81no—
403C2×#447—611no—
404C2×#442D6111yescharacteristic, complemented
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#1879—611no—
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×D4C2×D6111yescharacteristic
436C2×C4×D4C2×D6111yescharacteristic, complemented
437C2×#117—611no—
438C22×C22⋊C4—1221no—
439#447—618no—
440#442—24no—
441C2×#107—611no—
442C2×#106C2×D6111yescharacteristic, complemented
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×#97C2×D6111yescharacteristic, complemented
454C2×C4×C8—611no—
455#390—611no—
456#390—611no—
457#390—611no—
458#390—1221no—
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#340—611no—
473#336—611no—
474#336—611no—
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—21no—
490C23×C4—611no—
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—22no—
509C4×D4—41no—
510C4×D4—41no—
511C4×D4—1222no—
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—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—1221no—
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—22no—
542#102—22no—
543#102—614no—
544#102—614no—
545#102—1222no—
546#102—1222no—
547#102—1222no—
548#102—2441no—
549#102C22⋊D6114yescomplemented
550C22⋊C8—614no—
551#97—22no—
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×D4#1175822212yes—
596C2×D4C2×C22⋊D6112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—611no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—4881no—
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—612no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8C2×C4×D6112yes—
637C2×C8C2×C22⋊D6112yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—612no—
642C4⋊C4—1221no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—4881no—
648C4⋊C4C2×C22⋊D6112yes—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—1222no—
652C22⋊C4—1224no—
653C22⋊C4—4881no—
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—
718D4C4×C22⋊D6114yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—612no—
734C2×C4—612no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
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—2441no—
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C22×C22⋊D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4C2×#1175822211yescharacteristic
760C2×C4#1451982211yescharacteristic
761C2×C4#1451982311yescharacteristic
762C8—22no—
763C8—22no—
764C8—1222no—
765C8—2441no—
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
796C22D4×C22⋊D6111yescharacteristic
797C22#1684040811yescharacteristic
798C22AGL(1,ℤ/8)×D6111yescharacteristic
799C22#1684055811yescharacteristic
800C22#1684056611yescharacteristic
801C22#1684056611yescharacteristic
802C4—41no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—1222no—
807C4—1222no—
808C4—4881no—
809C4—4881no—
810C4—2441no—
811C4—2442no—
812C4C2×C4×C22⋊D6111yescharacteristic
813C4#1684023411yescharacteristic
814C4#1684040011yescharacteristic
815C4#1684044111yescharacteristic
816C2—44no—
817C2—82no—
818C2—4882no—
819C2—2442no—
820C2#2144879611yescharacteristic
821C2#2145463011yescharacteristic
822C2#2145466811yescharacteristic
823C2#2145742411yescharacteristic
824C2#2145743311yescharacteristic
825C2#2145796511yescharacteristic
826C2#2145798011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#442C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenterC2×#442D61
hypocenterC61#22868
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×#16839765C2semidirect
3. #21448853C2semidirect
4. D4×#11758198C2semidirect
5. #21446682C2semidirect
6. #21446516C2semidirect
7. #21446445C2semidirect
8. #21446254C2semidirect
9. #21446169C2semidirect
10. #21446167C2semidirect
11. #21446066C2semidirect
12. #21446017C2semidirect
13. #102×Dic61C2semidirect
14. #21445604C2semidirect
15. C2×C61×#442C2semidirect
23. #16839894C4semidirect
24. C2×#14519710C22semidirect
30. C2×#14519698C22semidirect
33. C2×C8×Dic61C22semidirect
34. #16839665C22semidirect
38. #16839660C22semidirect
45. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839516C22semidirect
56. C2×C4×D4×C61C22semidirect
58. C2×#106×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C2×#97×C61C22semidirect
71. C2×D4×D61C2×C4semidirect
76. C2×#11758199C2×C4semidirect
83. #14519748C2×C4semidirect
110. #14519699C2×C4semidirect
113. #14519698C2×C4semidirect
115. #14519689C2×C4semidirect
142. #102×C61D4semidirect
404. C2×#442D61semidirect
436. C2×C4×D4C2×D61semidirect
442. C2×#106C2×D61semidirect
451. C2×#102C2×D61semidirect
453. C2×#97C2×D61semidirect
475. C61#22868semidirect
549. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398942
C2×#168397652
#214488532
D4×#117581982
#214466822
#214465162
#214464452
#214462542
#214461692
#214461672
#214460662
#214460172
#102×Dic612
#214456042
C2×C61×#4422
#2286861