Finite Group Databasebeta

← #30621755

Subgroups — #30621755

Order 15616.

1330 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×#6923C211yesmaximal, characteristic, complemented
2C2×#16840754C211yesmaximal, characteristic, complemented
3#21462346C211yesmaximal, characteristic, complemented
4D4×C22⋊#6923C211yesmaximal, characteristic, complemented
5#21461968C211yesmaximal, characteristic, complemented
6#21461909C211yesmaximal, characteristic, complemented
7#21461896C211yesmaximal, characteristic, complemented
8#21461835C211yesmaximal, characteristic, complemented
9#21461814C211yesmaximal, characteristic, complemented
10#21461814C211yesmaximal, characteristic, complemented
11#21461784C211yesmaximal, characteristic, complemented
12#21461770C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#21461562C211yesmaximal, characteristic, complemented
15#447×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic, complemented
20C2×#14519856C2211yescharacteristic
21C22×C22⋊#6923—21no—
22D8×#6923—24no—
23C2×#14519846C2211yescharacteristic, complemented
24C2×#14519845C2211yescharacteristic, complemented
25#16840754—24no—
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic, complemented
31C2×#14519839C2211yescharacteristic, complemented
32C2×#14519831C2211yescharacteristic, complemented
33C2×C8×#6923C2211yescharacteristic, complemented
34#16840714—21no—
35#16840714C2211yescharacteristic
36#16840714C2211yescharacteristic
37#16840714C2211yescharacteristic, complemented
38#16840713C2211yescharacteristic, complemented
39#16840712—21no—
40#16840710—21no—
41#16840710—21no—
42#16840710—21no—
43#16840704C2211yescharacteristic
44#16840703—21no—
45C4⋊C4×#6923C2211yescharacteristic, complemented
46C22⋊C4×#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840636C2211yescharacteristic, complemented
49#16840636C2211yescharacteristic, complemented
50#16840635C2211yescharacteristic, complemented
51#16840635C2211yescharacteristic, complemented
52(C2×#6923)⋊C8C2211yescharacteristic, complemented
53(C2×#6923)⋊C8C2211yescharacteristic, complemented
54C22×D4×D61C2211yescharacteristic
55C2×D8×D61C2211yescharacteristic
56C2×D8×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16839898C411yescharacteristic, complemented
59#16839897C411yescharacteristic, complemented
60#16839897C411yescharacteristic, complemented
61#16839896C411yescharacteristic, complemented
62#16839895C411yescharacteristic, complemented
63#16839894C411yescharacteristic, complemented
64#16839894C411yescharacteristic, complemented
65#102×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#447C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C2×#11758213—21no—
73D61⋊M16—22no—
74D61⋊M16—41no—
75C2×#11758217—21no—
76C2×D61⋊C8C2311yescharacteristic
77C2×D61⋊C8C2311yescharacteristic
78D4×#6923—22no—
79D4×#6923—22no—
80D4×#6923—22no—
81D4×#6923—41no—
82D4×#6923—41no—
83D4×#6923—41no—
84#14519856—22no—
85#14519856—41no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C22⋊#6923—21no—
100C2×C22⋊#6923—21no—
101C2×C22⋊#6923—21no—
102C2×C22⋊#6923—44no—
103C2×C22⋊#6923D411yescharacteristic
104C2×C22⋊#6923D411yescharacteristic
105C2×C4×#6923—21no—
106C2×C4×#6923—21no—
107C2×C4×#6923C2311yescharacteristic
108C2×C4×#6923C2311yescharacteristic
109#14519846—22no—
110#14519845—41no—
111#14519839—22no—
112#14519839—22no—
113#14519839—22no—
114#14519839—22no—
115#14519839—41no—
116#14519839D414yescomplemented
117#14519831—41no—
118C8×#6923—22no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
122(C2×#6923)⋊C4D411yescharacteristic
123(C2×#6923)⋊C4D411yescharacteristic
124C24×D61—21no—
125C22×D244C2×C411yescharacteristic, complemented
126C22×C22⋊D61—21no—
127C2×D4×D61—22no—
128C2×D4×D61—22no—
129C2×D4×D61—21no—
130C2×D4×D61—21no—
131C2×D4×D61—21no—
132C2×D4×D61—41no—
133C2×D4×D61—41no—
134C2×D4×D61C2×C411yescharacteristic, complemented
135C2×D4×D61C2×C411yescharacteristic, complemented
136C2×D4×D61C2311yescharacteristic
137C2×D4×D61C2311yescharacteristic
138C2×D4×D61C2311yescharacteristic
139C22×C4×D61C2311yescharacteristic
140C2×D488C2×C411yescharacteristic
141C2×D488C2×C411yescharacteristic, complemented
142C2×#11758199C2×C411yescharacteristic
143C2×#11758199C2×C411yescharacteristic
144C2×#11758199C2×C411yescharacteristic, complemented
145C2×#11758199C2×C411yescharacteristic, complemented
146D8×D61—22no—
147D8×D61—22no—
148D8×D61—41no—
149D8×D61—41no—
150C2×C8×D61C2311yescharacteristic
151C2×C8×D61C2311yescharacteristic
152#14519752C2×C411yescharacteristic, complemented
153#14519751C2×C411yescharacteristic, complemented
154#14519750—21no—
155#14519749—21no—
156#14519748C2×C411yescharacteristic, complemented
157C4⋊C4×D61C2311yescharacteristic
158C22⋊C4×D61—21no—
159#14519699C2×C411yescharacteristic, complemented
160#14519699C2×C411yescharacteristic, complemented
161#14519698C2×C411yescharacteristic, complemented
162#14519698C2×C411yescharacteristic, complemented
163#14519697C2×C411yescharacteristic, complemented
164#14519697C2×C411yescharacteristic, complemented
165C22⋊#92418C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167#14519689C2×C411yescharacteristic, complemented
168C22×D4×C61C2×C411yescharacteristic, complemented
169C2×D8×C61C2×C411yescharacteristic
170C2×D8×C61C2×C411yescharacteristic, complemented
171#121×C61C2×C411yescharacteristic, complemented
172#102×C61C2×C411yescharacteristic, complemented
173#102×C61C2×C411yescharacteristic, complemented
174C22⋊C8×C61C2×C411yescharacteristic, complemented
175C24×C61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—42no—
183C23×D61—42no—
184C23×D61—42no—
185C23×D61—42no—
186C23×D61—81no—
187C23×D61—81no—
188C23×D61C2×D411yescharacteristic
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—42no—
194C22×#6923—42no—
195C22×#6923—42no—
196C22×#6923—42no—
197C22×#6923—42no—
198C22×#6923—42no—
199C22×#6923—81no—
200C22×#6923—81no—
201C22×#6923—81no—
202C22×#6923C2×D411yescharacteristic
203C22×#6923C2×D411yescharacteristic
204C22×#6923C2×D411yescharacteristic
205C22×#6923C2×D411yescharacteristic
206C2×D4×C61—22no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—41no—
210C2×D4×C61C22×C411yescharacteristic
211C2×D4×C61C22×C411yescharacteristic
212C2×D4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—42no—
223C22×Dic61#4111yescharacteristic
224D4×D61—22no—
225D4×D61—22no—
226D4×D61—21no—
227D4×D61—21no—
228D4×D61—21no—
229D4×D61—21no—
230D4×D61—21no—
231D4×D61—21no—
232D4×D61—21no—
233D4×D61—21no—
234D4×D61—21no—
235D4×D61—21no—
236D4×D61—41no—
237D4×D61—41no—
238D4×D61—42no—
239D4×D61—42no—
240D4×D61—42no—
241D4×D61—42no—
242D4×D61—81no—
243D4×D61—81no—
244D4×D61C2×D412yes—
245D4×D61#4112yes—
246C2×D244—22no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—41no—
250C2×D244C22×C411yescharacteristic
251C2×D244C22×C411yescharacteristic
252C2×D244C22×C411yescharacteristic
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61C22×C411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61#4111yescharacteristic
261C2×C4×D61C2411yescharacteristic
262C22⋊#6923—22no—
263C22⋊#6923—41no—
264C22⋊#6923—42no—
265C22⋊#6923—42no—
266C22⋊#6923—42no—
267C22⋊#6923—42no—
268C22⋊#6923—42no—
269C22⋊#6923—42no—
270C22⋊#6923—42no—
271C22⋊#6923—42no—
272C22⋊#6923—81no—
273C22⋊#6923—81no—
274C22⋊#6923—81no—
275#11758217—42no—
276C2×#92420—21no—
277C2×#92420—21no—
278C4⋊#6923—21no—
279C4⋊#6923—21no—
280C4⋊#6923—21no—
281C4⋊#6923—21no—
282C4⋊#6923—21no—
283C4⋊#6923—21no—
284C4⋊#6923—21no—
285C4⋊#6923—81no—
286C4⋊#6923C2×D412yes—
287C4×#6923—21no—
288C4×#6923—21no—
289C4×#6923—21no—
290C4×#6923—21no—
291C4×#6923—42no—
292C4×#6923—81no—
293#11758213—42no—
294D61⋊C8—21no—
295D61⋊C8—21no—
296D61⋊C8—21no—
297D61⋊C8C2×D412yes—
298D8×C61—22no—
299D8×C61—41no—
300C2×C8×C61C22×C411yescharacteristic
301C2×C8×C61C22×C411yescharacteristic
302C4⋊C4×C61C22×C411yescharacteristic
303C22⋊C4×C61—21no—
304C22⋊Dic61—21no—
305#11758199—22no—
306#11758199—22no—
307#11758199—41no—
308#11758199—41no—
309#11758198—21no—
310#11758198—21no—
311C4⋊Dic61C22×C411yescharacteristic
312#11758196—21no—
313C2×#92418C22×C411yescharacteristic
314C2×#92418C22×C411yescharacteristic
315D488—22no—
316D488—41no—
317C8×D61—21no—
318C8×D61—21no—
319C8×D61—21no—
320C8×D61—21no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—42no—
325C23×C61—42no—
326C23×C61—81no—
327C23×C61C4×D411yescharacteristic
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—42no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—81no—
362C22×D61—81no—
363C22×D61—81no—
364C22×D61—84no—
365C22×D61—84no—
366C22×D61—84no—
367C22×D61—84no—
368C22×D61C4×D411yescharacteristic
369C22×D61C22×D411yescharacteristic
370C2×#6923—21no—
371C2×#6923—21no—
372C2×#6923—21no—
373C2×#6923—22no—
374C2×#6923—21no—
375C2×#6923—21no—
376C2×#6923—21no—
377C2×#6923—21no—
378C2×#6923—21no—
379C2×#6923—21no—
380C2×#6923—21no—
381C2×#6923—21no—
382C2×#6923—41no—
383C2×#6923—41no—
384C2×#6923—41no—
385C2×#6923—41no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—84no—
394C2×#6923—84no—
395C2×#6923—84no—
396C2×#6923AGL(1,ℤ/8)12yes—
397D4×C61—21no—
398D4×C61—21no—
399D4×C61—21no—
400D4×C61—21no—
401D4×C61—21no—
402D4×C61—42no—
403D4×C61—81no—
404D4×C61C4×D412yes—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61C4×D411yescharacteristic
409C2×C4×C61C23×C411yescharacteristic
410C22⋊D61—22no—
411C22⋊D61—22no—
412C22⋊D61—42no—
413C22⋊D61—42no—
414C22⋊D61—41no—
415C22⋊D61—41no—
416C22⋊D61—41no—
417C22⋊D61—41no—
418C22⋊D61—81no—
419C22⋊D61—81no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61C4×D411yescharacteristic
424C2×Dic61C2×#4111yescharacteristic
425D244—21no—
426D244—21no—
427D244—21no—
428D244—21no—
429D244—21no—
430D244—42no—
431D244—81no—
432D244C4×D412yes—
433C4×D61—21no—
434C4×D61—21no—
435C4×D61—21no—
436C4×D61—21no—
437C4×D61—21no—
438C4×D61—21no—
439C4×D61—41no—
440C4×D61—41no—
441C4×D61C22×D411yescharacteristic
442C4×D61C2×#4111yescharacteristic
443C4×D61H(5,𝔽2)11yescharacteristic
444C4×D61H(5,𝔽2)11yescharacteristic
445#92420—22no—
446#92420—41no—
447C8×C61—21no—
448C8×C61—21no—
449#92418—21no—
450#92418—21no—
451#22880—611nomaximal, Sylow
452C22×C61—21no—
453C22×C61—22no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—41no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—84no—
465C22×C61C2×C4×D411yescharacteristic
466C2×D61—21no—
467C2×D61—22no—
468C2×D61—21no—
469C2×D61—21no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—42no—
473C2×D61—41no—
474C2×D61—41no—
475C2×D61—42no—
476C2×D61—41no—
477C2×D61—42no—
478C2×D61—42no—
479C2×D61—41no—
480C2×D61—41no—
481C2×D61—41no—
482C2×D61—41no—
483C2×D61—41no—
484C2×D61—41no—
485C2×D61—41no—
486C2×D61—84no—
487C2×D61—84no—
488C2×D61—84no—
489C2×D61—81no—
490C2×D61—81no—
491C2×D61—81no—
492C2×D61—81no—
493C2×D61—81no—
494C2×D61—81no—
495C2×D61—81no—
496C2×D61—81no—
497C2×D61D4211yescharacteristic
498C2×D61#54611yescharacteristic
499C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
500C2×D61#57511yescharacteristic
501C2×D61#57611yescharacteristic
502C2×D61#57611yescharacteristic
503#6923—22no—
504#6923—42no—
505#6923—41no—
506#6923—41no—
507#6923—41no—
508#6923—81no—
509#6923—81no—
510#6923—81no—
511C4×C61—21no—
512C4×C61—41no—
513C4×C61C2×C4×D411yescharacteristic
514C4×C61#51811yescharacteristic
515Dic61—21no—
516Dic61—41no—
517Dic61#54611yescharacteristic
518Dic61#55111yescharacteristic
519C2×#447—611no—
520C2×C4×D8—611no—
521C2×#418—611no—
522#2363—611no—
523D4×C22⋊C4—611no—
524#1972—611no—
525#1934—611no—
526#1925—611no—
527#1895—611no—
528#1879—611no—
529#1879—611no—
530#1864—611no—
531#1854—611no—
532#1762—611no—
533#1753—611no—
534C2×C61—41no—
535C2×C61—42no—
536C2×C61—81no—
537C2×C61—81no—
538C2×C61#235811yescharacteristic
539C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
540C2×C61#294811yescharacteristic
541D61—41no—
542D61—42no—
543D61—81no—
544D61—81no—
545D61#326411yescharacteristic
546D61#326811yescharacteristic
547D61#332211yescharacteristic
548D61#332511yescharacteristic
549C23×D4—611no—
550C22×D8—611no—
551C22×D8—611no—
552C22×M16—611no—
553C2×#121—611no—
554C2×C4×D4—611no—
555C2×C4×D4—611no—
556C2×C4×D4—611no—
557C2×#117—611no—
558C22×C22⋊C4—1221no—
559#447—611no—
560#447—611no—
561#447—611no—
562#447—611no—
563#447—611no—
564#447—611no—
565#447—611no—
566#447#692311yescharacteristic, complemented
567C4×D8—1224no—
568C2×#107—611no—
569C2×#106—611no—
570#418—1224no—
571C2×#102—611no—
572C2×#102—611no—
573C2×#102—611no—
574C2×#102—611no—
575C2×#102—611no—
576C2×#102—611no—
577C2×#102—611no—
578C2×#102—611no—
579C2×C22⋊C8—611no—
580C2×#97—611no—
581C2×C4×C8—611no—
582#390—611no—
583#390—611no—
584#390—611no—
585#390—1221no—
586#389—611no—
587#388—1221no—
588#386—1221no—
589#386—1221no—
590#386—1221no—
591#380—611no—
592#379—1221no—
593C4×C4⋊C4—611no—
594C4×C22⋊C4—611no—
595C4×C22⋊C4—1221no—
596#340—611no—
597#340—611no—
598#340—611no—
599#340—611no—
600#336—611no—
601#336—611no—
602C61#2288011yescharacteristic, complemented, Sylow
603C25—1221no—
604C22×D4—611no—
605C22×D4—611no—
606C22×D4—611no—
607C22×D4—611no—
608C22×D4—611no—
609C22×D4—611no—
610C22×D4—1221no—
611C22×D4—1221no—
612C22×D4—1221no—
613C22×D4—1222no—
614C22×D4—1222no—
615C22×D4—1221no—
616C22×D4—2441no—
617C22×D4—2441no—
618C22×D4C2×#692311yescharacteristic, complemented
619C23×C4—611no—
620C23×C4—1221no—
621C23×C4—1221no—
622C23×C4—1221no—
623C2×D8—611no—
624C2×D8—611no—
625C2×D8—611no—
626C2×D8—611no—
627C2×D8—611no—
628C2×D8—611no—
629C2×D8—1222no—
630C2×D8—1222no—
631C2×D8—2441no—
632C2×D8—2441no—
633C2×D8C2×#692311yescharacteristic
634C2×D8C2×#692311yescharacteristic, complemented
635C2×M16—1222no—
636C2×M16—1221no—
637C2×M16—1221no—
638C2×M16—2441no—
639C22×C8—611no—
640C22×C8—611no—
641C22×C8—611no—
642C22×C8—611no—
643#121—611no—
644#121—611no—
645#121—611no—
646#121—1221no—
647#121—1221no—
648#121C2×#692311yescharacteristic, complemented
649C4×D4—1222no—
650C4×D4—1222no—
651C4×D4—1222no—
652C4×D4—2441no—
653C4×D4—2441no—
654C4×D4—2441no—
655#117—1222no—
656#117—2441no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—611no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—611no—
662C2×C4⋊C4—1221no—
663C2×C22⋊C4—611no—
664C2×C22⋊C4—611no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C22⋊C4—1221no—
671C2×C22⋊C4—1221no—
672C2×C22⋊C4—1221no—
673C2×C22⋊C4—1221no—
674C2×C22⋊C4—1221no—
675C2×C22⋊C4—1221no—
676C2×C22⋊C4—1221no—
677C2×C22⋊C4—2444no—
678C2×C42—611no—
679C2×C42—611no—
680C2×C42—1221no—
681C2×C42—1221no—
682#107—1222no—
683#106—2441no—
684#102—614no—
685#102—611no—
686#102—611no—
687#102—611no—
688#102—611no—
689#102—611no—
690#102—611no—
691#102—1222no—
692#102—1222no—
693#102—1222no—
694#102—1222no—
695#102—2441no—
696#102C2×#692311yescharacteristic, complemented
697#102C2×#692311yescharacteristic, complemented
698C22⋊C8—611no—
699C22⋊C8—611no—
700C22⋊C8—611no—
701C22⋊C8C2×#692311yescharacteristic, complemented
702#97—2441no—
703C4×C8—1222no—
704#95—611no—
705#95—611no—
706#95—1221no—
707#95—1221no—
708#95—1221no—
709C24—21no—
710C24—611no—
711C24—1221no—
712C24—1221no—
713C24—1221no—
714C24—1221no—
715C24—1221no—
716C24—1221no—
717C24—4881no—
718C24—4881no—
719C24—2442no—
720C24—2442no—
721C24—2442no—
722C24—2442no—
723C2×D4—22no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—41no—
727C2×D4—612no—
728C2×D4—612no—
729C2×D4—611no—
730C2×D4—611no—
731C2×D4—611no—
732C2×D4—1222no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—1221no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1222no—
750C2×D4—1222no—
751C2×D4—1221no—
752C2×D4—1221no—
753C2×D4—1221no—
754C2×D4—4881no—
755C2×D4—4881no—
756C2×D4—2441no—
757C2×D4—2441no—
758C2×D4—2441no—
759C2×D4—2442no—
760C2×D4—2442no—
761C2×D4—2442no—
762C2×D4—2442no—
763C2×D4—2442no—
764C2×D4—2442no—
765C2×D4C22×#692311yescharacteristic
766C2×D4C22×#692311yescharacteristic
767C2×D4C22×#692311yescharacteristic
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—4881no—
787C22×C4—4881no—
788C22×C4—4881no—
789C22×C4—2442no—
790C22×C4—2442no—
791C22×C4—2442no—
792C22×C4—2442no—
793C22×C4—2442no—
794C22×C4—2442no—
795C22×C4C22×#692311yescharacteristic
796D8—22no—
797D8—41no—
798D8—1222no—
799D8—1222no—
800D8—1222no—
801D8—2441no—
802D8—2441no—
803D8—2441no—
804M16—2442no—
805M16—2442no—
806C2×C8—612no—
807C2×C8—611no—
808C2×C8—611no—
809C2×C8—1221no—
810C2×C8—1221no—
811C2×C8—1221no—
812C2×C8—1221no—
813C2×C8—1221no—
814C2×C8—1221no—
815C2×C8—1221no—
816C2×C8—1221no—
817C2×C8—1221no—
818C2×C8C22×#692311yescharacteristic
819C2×C8C22×#692311yescharacteristic
820C4⋊C4—612no—
821C4⋊C4—611no—
822C4⋊C4—1221no—
823C4⋊C4—1221no—
824C4⋊C4—1221no—
825C4⋊C4—1221no—
826C4⋊C4—1221no—
827C4⋊C4—1221no—
828C4⋊C4—1221no—
829C4⋊C4—1221no—
830C4⋊C4—4881no—
831C4⋊C4C22×#692311yescharacteristic
832C22⋊C4—21no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1222no—
836C22⋊C4—1221no—
837C22⋊C4—4881no—
838C22⋊C4—4881no—
839C22⋊C4—4881no—
840C22⋊C4—2442no—
841C22⋊C4—2441no—
842C22⋊C4—2442no—
843C22⋊C4—2442no—
844C22⋊C4—2442no—
845C22⋊C4—2442no—
846C22⋊C4—2442no—
847C22⋊C4—2442no—
848C22⋊C4—2442no—
849C42—1221no—
850C42—1221no—
851C42—1221no—
852C42—1221no—
853C42—4881no—
854C42—2442no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—611no—
862C23—611no—
863C23—1221no—
864C23—1221no—
865C23—1222no—
866C23—1222no—
867C23—1221no—
868C23—1221no—
869C23—1221no—
870C23—1221no—
871C23—1221no—
872C23—1221no—
873C23—1221no—
874C23—4881no—
875C23—4881no—
876C23—4881no—
877C23—4884no—
878C23—4884no—
879C23—4884no—
880C23—4884no—
881C23—2442no—
882C23—2442no—
883C23—2442no—
884C23—2441no—
885C23—2441no—
886C23—2441no—
887C23—2441no—
888C23—2441no—
889C23—2441no—
890C23—2441no—
891C23—2441no—
892C23—2441no—
893C23—2441no—
894C23—2441no—
895C23—2441no—
896C23—2441no—
897C23—2441no—
898C23—2441no—
899C23—2441no—
900C23—2442no—
901C23—2442no—
902C23—2442no—
903C23D4×#692311yescharacteristic
904D4—21no—
905D4—21no—
906D4—21no—
907D4—21no—
908D4—21no—
909D4—42no—
910D4—81no—
911D4—612no—
912D4—1222no—
913D4—1222no—
914D4—1221no—
915D4—1221no—
916D4—1221no—
917D4—1221no—
918D4—1221no—
919D4—4881no—
920D4—4881no—
921D4—4881no—
922D4—2442no—
923D4—2441no—
924D4—2441no—
925D4—2441no—
926D4—2441no—
927D4—2442no—
928D4—2442no—
929D4D4×#692312yes—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—611no—
934C2×C4—611no—
935C2×C4—611no—
936C2×C4—611no—
937C2×C4—611no—
938C2×C4—612no—
939C2×C4—611no—
940C2×C4—1221no—
941C2×C4—1221no—
942C2×C4—1221no—
943C2×C4—1221no—
944C2×C4—1221no—
945C2×C4—1221no—
946C2×C4—1221no—
947C2×C4—1221no—
948C2×C4—1221no—
949C2×C4—1221no—
950C2×C4—1221no—
951C2×C4—1221no—
952C2×C4—1221no—
953C2×C4—1221no—
954C2×C4—1222no—
955C2×C4—1221no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—4884no—
962C2×C4—4884no—
963C2×C4—4884no—
964C2×C4—2441no—
965C2×C4—2441no—
966C2×C4—2441no—
967C2×C4—2441no—
968C2×C4—2441no—
969C2×C4—2441no—
970C2×C4—2441no—
971C2×C4—2441no—
972C2×C4—2441no—
973C2×C4—2441no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4D4×#692311yescharacteristic
978C2×C4C23×#692311yescharacteristic
979C8—21no—
980C8—21no—
981C8—1222no—
982C8—1221no—
983C8—1221no—
984C8—2441no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—22no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—84no—
998C22—611no—
999C22—611no—
1000C22—611no—
1001C22—611no—
1002C22—611no—
1003C22—611no—
1004C22—1221no—
1005C22—1221no—
1006C22—1221no—
1007C22—1222no—
1008C22—4884no—
1009C22—4884no—
1010C22—4881no—
1011C22—4881no—
1012C22—4881no—
1013C22—4881no—
1014C22—4881no—
1015C22—4881no—
1016C22—4881no—
1017C22—4881no—
1018C22—4884no—
1019C22—2442no—
1020C22—2442no—
1021C22—2441no—
1022C22—2441no—
1023C22—2441no—
1024C22—2441no—
1025C22—2442no—
1026C22—2442no—
1027C22—2441no—
1028C22—2441no—
1029C22—2441no—
1030C22—2441no—
1031C22—2441no—
1032C22—2441no—
1033C22—2441no—
1034C22—2441no—
1035C22C2×D4×#692311yescharacteristic
1036C4—21no—
1037C4—41no—
1038C4—611no—
1039C4—611no—
1040C4—1222no—
1041C4—1221no—
1042C4—4881no—
1043C4—4881no—
1044C4—4881no—
1045C4—2441no—
1046C4—2441no—
1047C4—2441no—
1048C4—2442no—
1049C4—2441no—
1050C4C2×D4×#692311yescharacteristic
1051C4#1684082911yescharacteristic
1052C2—41no—
1053C2—42no—
1054C2—81no—
1055C2—81no—
1056C2—611no—
1057C2—611no—
1058C2—611no—
1059C2—611no—
1060C2—4881no—
1061C2—4881no—
1062C2—2441no—
1063C2—2442no—
1064C2#2146234111yescharacteristic
1065C2AGL(1,ℤ/8)×#692311yescharacteristic
1066C2#2146257811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#447C4
socleC22×C61C2×C4×D4
prime radical#447×D61C2
cosocleC2×C4×D61C24
hypercenter#447#6923
hypocenterC61#22880
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×D8×#6923C2semidirect
2. C2×#16840754C2semidirect
3. #21462346C2semidirect
4. D4×C22⋊#6923C2semidirect
5. #21461968C2semidirect
6. #21461909C2semidirect
7. #21461896C2semidirect
8. #21461835C2semidirect
9. #21461814C2semidirect
10. #21461814C2semidirect
11. #21461784C2semidirect
12. #21461770C2semidirect
13. #21461590C2semidirect
14. #21461562C2semidirect
19. C2×D4×#6923C22semidirect
23. C2×#14519846C22semidirect
24. C2×#14519845C22semidirect
30. C2×#14519839C22semidirect
31. C2×#14519839C22semidirect
32. C2×#14519831C22semidirect
33. C2×C8×#6923C22semidirect
37. #16840714C22semidirect
38. #16840713C22semidirect
45. C4⋊C4×#6923C22semidirect
48. #16840636C22semidirect
49. #16840636C22semidirect
50. #16840635C22semidirect
51. #16840635C22semidirect
52. (C2×#6923)⋊C8C22semidirect
53. (C2×#6923)⋊C8C22semidirect
58. #16839898C4semidirect
59. #16839897C4semidirect
60. #16839897C4semidirect
61. #16839896C4semidirect
62. #16839895C4semidirect
63. #16839894C4semidirect
64. #16839894C4semidirect
68. C61×#447C4semidirect
116. #14519839D4semidirect
125. C22×D244C2×C4semidirect
134. C2×D4×D61C2×C4semidirect
135. C2×D4×D61C2×C4semidirect
141. C2×D488C2×C4semidirect
144. C2×#11758199C2×C4semidirect
145. C2×#11758199C2×C4semidirect
152. #14519752C2×C4semidirect
153. #14519751C2×C4semidirect
156. #14519748C2×C4semidirect
159. #14519699C2×C4semidirect
160. #14519699C2×C4semidirect
161. #14519698C2×C4semidirect
162. #14519698C2×C4semidirect
163. #14519697C2×C4semidirect
164. #14519697C2×C4semidirect
165. C22⋊#92418C2×C4semidirect
166. #14519689C2×C4semidirect
167. #14519689C2×C4semidirect
168. C22×D4×C61C2×C4semidirect
170. C2×D8×C61C2×C4semidirect
171. #121×C61C2×C4semidirect
172. #102×C61C2×C4semidirect
173. #102×C61C2×C4semidirect
174. C22⋊C8×C61C2×C4semidirect
566. #447#6923semidirect
602. C61#22880semidirect
618. C22×D4C2×#6923semidirect
634. C2×D8C2×#6923semidirect
648. #121C2×#6923semidirect
696. #102C2×#6923semidirect
697. #102C2×#6923semidirect
701. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×D8×#69232
C2×#168407542
#214623462
D4×C22⋊#69232
#214619682
#214619092
#214618962
#214618352
#214618142
#214617842
#214617702
#214615902
#214615622
#447×D612
#2288061