Finite Group Databasebeta

← C2×#21458527 #30559665

Subgroups — C2×#21458527 #30559665

Order 15616.

2198 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840471C211yesmaximal, characteristic, complemented
2C2×#16840433C211yesmaximal, characteristic, complemented
3#21458527C2116yesmaximal, direct product factor
4C2×#16840127C211yesmaximal, characteristic, complemented
5C2×#16840125C211yesmaximal, characteristic, complemented
6C2×#16840107C211yesmaximal, characteristic, complemented
7C2×#16840062C211yesmaximal, characteristic, complemented
8C2×#16840061C211yesmaximal, characteristic, complemented
9C2×#16840051C211yesmaximal, characteristic, complemented
10C2×#16839957C211yesmaximal, characteristic, complemented
11C2×#16839955C211yesmaximal, characteristic, complemented
12C2×#16839955C211yesmaximal, characteristic, complemented
13C2×#16839890C211yesmaximal, characteristic, complemented
14C2×#16839871C211yesmaximal, characteristic, complemented
15C2×#16839842C211yesmaximal, characteristic, complemented
16C2×C61×#442C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758199C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20#16840471—24no—
21#16840471C2218yescomplemented
22#16840433—24no—
23#16840433C2218yescomplemented
24C2×#14519776C2211yescharacteristic
25C2×#14519774C2211yescharacteristic
26C2×#14519773C2211yescharacteristic
27C2×#14519773C2211yescharacteristic
28C2×#14519769C2211yescharacteristic
29C2×#14519768C2211yescharacteristic
30C2×#14519756—21no—
31C2×#14519754—21no—
32C2×#14519754—21no—
33C2×#14519751—21no—
34C2×#14519750—21no—
35C2×#14519750—21no—
36C2×C4×Dic122C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×D4×Dic61C2211yescharacteristic
39C2×#14519739C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C22×#11758196—21no—
42#16840127C2218yescomplemented
43#16840125C2218yescomplemented
44#16840107C2218yescomplemented
45#16840062C2218yescomplemented
46#16840061C2218yescomplemented
47#16840051C2218yescomplemented
48#16839957C2218yescomplemented
49#16839955C2218yescomplemented
50#16839955C2218yescomplemented
51#16839890C2218yescomplemented
52#16839871C2218yescomplemented
53#16839842C2218yescomplemented
54C2×#14519710C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×C4⋊#92418C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519699C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#442C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×Dic122D411yescharacteristic
81C22×D244—21no—
82C22×D244—21no—
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C23×Dic61—21no—
90C23×Dic61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C2×#11758199—24no—
94C2×#11758199—24no—
95C2×#11758199C2314yes—
96C2×#11758199C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519776—22no—
100#14519776C2314yes—
101#14519774—22no—
102#14519774C2314yes—
103#14519773—22no—
104#14519773—22no—
105#14519773C2314yes—
106#14519773C2314yes—
107#14519769—22no—
108#14519769C2314yes—
109#14519768—22no—
110#14519768C2314yes—
111#14519756—28no—
112#14519754—28no—
113#14519754—28no—
114#14519751—28no—
115#14519750—28no—
116#14519750—28no—
117C4×Dic122D414yes—
118C4×Dic122C2314yes—
119D4×Dic61—22no—
120D4×Dic61—22no—
121D4×Dic61C2314yes—
122D4×Dic61C2314yes—
123#14519739—22no—
124#14519739—22no—
125#14519739C2314yes—
126#14519739C2314yes—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61D411yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—28no—
136C2×#11758196D411yescharacteristic
137C2×#11758196D411yescharacteristic
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×C4×Dic61C2311yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144#14519710C2314yes—
145#14519708C2314yes—
146C4⋊#92418C2314yes—
147#14519706C2314yes—
148#14519706C2314yes—
149#14519699C2314yes—
150#14519699C2314yes—
151#14519699C2314yes—
152#14519699C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155#14519697C2314yes—
156#14519697C2314yes—
157#14519687C2314yes—
158C8×Dic61C2314yes—
159C22×D4×C61C2311yescharacteristic
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61—21no—
162C23×C4×C61—21no—
163C2×D8×C61—24no—
164C2×D8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C4×D4×C61—22no—
168C4×D4×C61—22no—
169C4×D4×C61C2314yes—
170C4×D4×C61C2314yes—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61C2311yescharacteristic
176#106×C61C2314yes—
177#102×C61C2314yes—
178#102×C61C2314yes—
179#97×C61C2314yes—
180C24×C61—21no—
181C24×C61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61#4114yescomplemented
190C2×D4×C61C2412yes—
191C2×D4×C61C2412yes—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—24no—
195C22×C4×C61—24no—
196C22×C4×C61—44no—
197C22×C4×C61—82no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—44no—
206C2×C22⋊D61—44no—
207C2×C22⋊D61—82no—
208C2×C22⋊D61—82no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—24no—
212C22×Dic61—24no—
213C22×Dic61—44no—
214C22×Dic61—82no—
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219#11758222—432no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—24no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—24no—
228C2×D244—44no—
229C2×D244—82no—
230C2×D244C2412yes—
231C2×D244C2412yes—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—44no—
235C2×C4×D61—44no—
236C2×Dic122—24no—
237C2×Dic122—24no—
238C2×Dic122—82no—
239C2×Dic122C2×D414yes—
240D8×C61—28no—
241C2×C8×C61—22no—
242C2×C8×C61—22no—
243C2×C8×C61C2412yes—
244C2×C8×C61C2412yes—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2412yes—
248C4⋊C4×C61C2412yes—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C42×C61C2×D412yes—
252C42×C61C2412yes—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255#11758199—28no—
256#11758199—28no—
257#11758198—24no—
258#11758198—24no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—24no—
262C4⋊Dic61C2×D414yes—
263C4⋊Dic61C2412yes—
264C4⋊Dic61C2412yes—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269#11758196C2×D414yes—
270#11758196C2×D414yes—
271C4×Dic61C2×D412yes—
272C4×Dic61C2×D412yes—
273C4×Dic61C2412yes—
274C4×Dic61C2412yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279C23×C61—24no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61C22×D411yescharacteristic
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296D4×C61—24no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—42no—
301D4×C61C2×#4114yescomplemented
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—48no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—84no—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4112yes—
314C2×C4×C612−1+412yes—
315C2×C4×C61C2511yescharacteristic
316C22⋊D61—48no—
317C22⋊D61—48no—
318C22⋊D61—84no—
319C22⋊D61—84no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—48no—
328C2×Dic61—84no—
329C2×Dic61AGL(1,ℤ/8)14yes—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334D244—22no—
335D244—22no—
336D244—22no—
337D244—22no—
338D244—48no—
339D244—42no—
340D244—42no—
341D244—84no—
342C4×D61—48no—
343C4×D61—48no—
344Dic122—28no—
345Dic122—84no—
346C8×C61—22no—
347C8×C61—22no—
348#92418—22no—
349#92418—22no—
350C2×#3366—611nomaximal, Sylow
351C22×C61—24no—
352C22×C61—48no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—84no—
359C22×C61#54812yes—
360C22×C61C2×AGL(1,ℤ/8)12yes—
361C22×C61#57612yes—
362C22×C61C23×D411yescharacteristic
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—84no—
370C2×D61—84no—
371C4×C61—22no—
372C4×C61—22no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61#54812yes—
376C4×C61C22×#4111yescharacteristic
377C4×C61C2×2−1+411yescharacteristic
378Dic61—22no—
379Dic61—22no—
380Dic61—22no—
381Dic61—42no—
382Dic61—42no—
383Dic61C2×AGL(1,ℤ/8)14yes—
384C2×#554—611no—
385C2×#550—611no—
386#3366—6116no—
387C2×#490—611no—
388C2×#490—611no—
389C2×#486—611no—
390C2×#478—611no—
391C2×#478—611no—
392C2×#476—611no—
393C2×#459—611no—
394C2×#459—611no—
395C2×#459—611no—
396C2×#446—611no—
397C2×#442—611no—
398C2×#442D6111yescharacteristic, complemented
399C2×C4×D8—611no—
400C2×C61—44no—
401C2×C61—82no—
402C2×C61#336614yescomplemented
403C2×C61C2×#54811yescharacteristic
404C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
405C2×C61C2×#57611yescharacteristic
406D61—82no—
407D61—82no—
408C22×#41—1221no—
409C22×D8—611no—
410C22×D8—611no—
411C22×D8C2×D6111yescharacteristic
412#554—618no—
413#554—1224no—
414#550—618no—
415#550—1224no—
416C2×C4⋊Q8—611no—
417C2×#127—611no—
418C2×#127—611no—
419C2×#127—611no—
420C2×#125—611no—
421C2×#125—611no—
422C2×C22⋊Q8—1221no—
423C2×C22⋊Q8—1221no—
424C2×C22⋊Q8—1221no—
425C2×#121—1221no—
426C2×#121—1221no—
427C2×#121—1221no—
428C2×C4×Q8—611no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×C4×D4—611no—
432C2×C4×D4—611no—
433C2×C4×D4C2×D6111yescharacteristic
434C2×C4×D4C2×D6111yescharacteristic
435C22×C4⋊C4—1221no—
436#490—618no—
437#490—618no—
438#486—618no—
439#478—618no—
440#478—618no—
441#476—618no—
442#459—618no—
443#459—618no—
444#459—618no—
445#446—618no—
446#442—618no—
447#442C2×D6118yescomplemented
448C4×D8—618no—
449C2×#107—611no—
450C2×#106—611no—
451C2×#106C2×D6111yescharacteristic
452C2×C4⋊C8—611no—
453C2×C4⋊C8—611no—
454C2×C4⋊C8—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×#102—611no—
460C2×#102—611no—
461C2×#102—611no—
462C2×#102—611no—
463C2×#102C2×D6111yescharacteristic
464C2×#102C2×D6111yescharacteristic
465C2×#97—611no—
466C2×#97C2×D6111yescharacteristic
467C2×C4×C8—611no—
468C61C2×#336611yescharacteristic, complemented, Sylow
469C2×#41—1228no—
470C2×#41—2448no—
471C22×Q8—611no—
472C22×Q8—1221no—
473C22×D4—611no—
474C22×D4—611no—
475C22×D4—1221no—
476C22×D4—1221no—
477C22×D4—1221no—
478C22×D4—1221no—
479C22×D4—1221no—
480C22×D4—1221no—
481C22×D4C22×D6111yescharacteristic
482C22×D4C22×D6111yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—1221no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4—1221no—
489C2×D8—24no—
490C2×D8—614no—
491C2×D8—614no—
492C2×D8—1224no—
493C2×D8—1224no—
494C2×D8C22×D6114yes—
495C22×C8—611no—
496C22×C8—611no—
497C22×C8C22×D6111yescharacteristic
498C22×C8C22×D6111yescharacteristic
499C4⋊Q8—614no—
500C4⋊Q8—1222no—
501#127—614no—
502#127—614no—
503#127—614no—
504#127—1222no—
505#127—1222no—
506#127—1222no—
507#125—614no—
508#125—614no—
509#125—1222no—
510#125—1222no—
511C22⋊Q8—1228no—
512C22⋊Q8—1228no—
513C22⋊Q8—1228no—
514#121—1228no—
515#121—1228no—
516#121—1228no—
517C4×Q8—614no—
518C4×Q8—614no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—614no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4C22×D6114yes—
530C4×D4C22×D6114yes—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—1228no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C42—611no—
551C2×C42—611no—
552C2×C42C22×D6111yescharacteristic
553#107—614no—
554#106—614no—
555#106C22×D6114yes—
556C4⋊C8—614no—
557C4⋊C8—614no—
558C4⋊C8—614no—
559#102—614no—
560#102—614no—
561#102—614no—
562#102—614no—
563#102—614no—
564#102—614no—
565#102—614no—
566#102—614no—
567#102C22×D6114yes—
568#102C22×D6114yes—
569#97—614no—
570#97C22×D6114yes—
571C4×C8—614no—
572C24—21no—
573C24—21no—
574C24—1221no—
575C24—1221no—
576#41—24432no—
577C2×Q8—614no—
578C2×Q8—1224no—
579C2×Q8—1224no—
580C2×Q8—4882no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—612no—
587C2×D4—612no—
588C2×D4—1224no—
589C2×D4—1224no—
590C2×D4—1224no—
591C2×D4—1224no—
592C2×D4—1224no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1224no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—4882no—
601C2×D4—4882no—
602C2×D4—4882no—
603C2×D4—2444no—
604C2×D4—2444no—
605C2×D4—2444no—
606C2×D4#1175822214yescomplemented
607C2×D4C23×D6112yes—
608C2×D4C23×D6112yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—44no—
614C22×C4—82no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—1224no—
620C22×C4—1224no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—4882no—
626C22×C4—2444no—
627C22×C4—2444no—
628C22×C4—2444no—
629C22×C4D4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4C23×D6111yescharacteristic
632D8—28no—
633D8—1228no—
634D8—1228no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—612no—
638C2×C8—612no—
639C2×C8—1222no—
640C2×C8—1222no—
641C2×C8C23×D6112yes—
642C2×C8C23×D6112yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—614no—
646C4⋊C4—614no—
647C4⋊C4—614no—
648C4⋊C4—612no—
649C4⋊C4—612no—
650C4⋊C4—1224no—
651C4⋊C4—1224no—
652C4⋊C4—1224no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1224no—
656C4⋊C4—1224no—
657C4⋊C4C23×D6112yes—
658C4⋊C4C23×D6112yes—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C42—612no—
666C42—612no—
667C42—612no—
668C42—612no—
669C42D4×D6112yes—
670C42C23×D6112yes—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—1222no—
680C23—1222no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23C2×D4×D6111yescharacteristic
688Q8—1228no—
689Q8—4884no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—24no—
694D4—42no—
695D4—1222no—
696D4—1222no—
697D4—1222no—
698D4—1222no—
699D4—4884no—
700D4—4884no—
701D4—4884no—
702D4—2448no—
703D4—2448no—
704D4—2448no—
705D4—2442no—
706D4—2442no—
707D4C2×#1175822214yescomplemented
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—84no—
716C2×C4—614no—
717C2×C4—612no—
718C2×C4—612no—
719C2×C4—612no—
720C2×C4—612no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—4884no—
727C2×C4—2448no—
728C2×C4—2448no—
729C2×C4—2448no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4C2×D4×D6112yes—
733C2×C4C2×D4×D6112yes—
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4C2×#1175822212yes—
736C2×C4#1451982412yes—
737C2×C4C24×D6111yescharacteristic
738C8—22no—
739C8—22no—
740C8—1222no—
741C8—1222no—
742C22—24no—
743C22—42no—
744C22—42no—
745C22—48no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22—4884no—
751C22—4884no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22—2442no—
757C22—2442no—
758C22#1684042112yes—
759C22AGL(1,ℤ/8)×D6112yes—
760C22#1684056612yes—
761C22C22×D4×D6111yescharacteristic
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—614no—
767C4—1222no—
768C4—1222no—
769C4—1222no—
770C4—2442no—
771C4—2442no—
772C4#1684042112yes—
773C4C22×#1175822211yescharacteristic
774C4C2×#1451982411yescharacteristic
775C2—44no—
776C2—82no—
777C2—4882no—
778C2—4882no—
779C2#2145852714yesdirect product factor
780C2C2×#1684042111yescharacteristic
781C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
782C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#442C2
socleC23×C61C22×D4
hypercenterC2×#442D61
hypocenterC61C2×#3366
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
1. C2×#16840471C2semidirect
2. C2×#16840433C2semidirect
3. #21458527C2direct (N × H)
4. C2×#16840127C2semidirect
5. C2×#16840125C2semidirect
6. C2×#16840107C2semidirect
7. C2×#16840062C2semidirect
8. C2×#16840061C2semidirect
9. C2×#16840051C2semidirect
10. C2×#16839957C2semidirect
11. C2×#16839955C2semidirect
12. C2×#16839955C2semidirect
13. C2×#16839890C2semidirect
14. C2×#16839871C2semidirect
15. C2×#16839842C2semidirect
16. C2×C61×#442C2semidirect
21. #16840471C22semidirect
23. #16840433C22semidirect
42. #16840127C22semidirect
43. #16840125C22semidirect
44. #16840107C22semidirect
45. #16840062C22semidirect
46. #16840061C22semidirect
47. #16840051C22semidirect
48. #16839957C22semidirect
49. #16839955C22semidirect
50. #16839955C22semidirect
51. #16839890C22semidirect
52. #16839871C22semidirect
53. #16839842C22semidirect
72. C61×#442C22semidirect
189. C2×D4×C61#41semidirect
301. D4×C61C2×#41semidirect
398. C2×#442D61semidirect
402. C2×C61#3366semidirect
447. #442C2×D61semidirect
468. C61C2×#3366semidirect
606. C2×D4#11758222semidirect
707. D4C2×#11758222semidirect
779. C2#21458527direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404712
C2×#168404332
#214585272
C2×#168401272
C2×#168401252
C2×#168401072
C2×#168400622
C2×#168400612
C2×#168400512
C2×#168399572
C2×#168399552
C2×#168398902
C2×#168398712
C2×#168398422
C2×C61×#4422
C2×#336661