Finite Group Databasebeta

← C2×#21457938 #30556724

Subgroups — C2×#21457938 #30556724

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840454C211yesmaximal, characteristic, complemented
2C2×#16840431C211yesmaximal, characteristic
3#21457938C2116yesmaximal, direct product factor
4C2×#16840125C211yesmaximal, characteristic, complemented
5C2×#16840081C211yesmaximal, characteristic, complemented
6C2×#16840085C211yesmaximal, characteristic, complemented
7C2×#16840067C211yesmaximal, characteristic, complemented
8C2×#16840010C211yesmaximal, characteristic, complemented
9C2×#16839988C211yesmaximal, characteristic, complemented
10C2×#16839960C211yesmaximal, characteristic, complemented
11C2×#16839923C211yesmaximal, characteristic, complemented
12C2×#16839869C211yesmaximal, characteristic, complemented
13C2×#16839836C211yesmaximal, characteristic, complemented
14C2×#16839763C211yesmaximal, characteristic, complemented
15C2×#16839757C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840454—24no—
22#16840454C2218yescomplemented
23#16840431—24no—
24#16840431C2218yes—
25C2×#14519773—21no—
26C2×#14519773C2211yescharacteristic
27C2×#14519772—21no—
28C2×#14519768—21no—
29C2×#14519768C2211yescharacteristic
30C2×#14519761—21no—
31C2×#14519753C2211yescharacteristic
32C2×#14519751—21no—
33C2×#14519751C2211yescharacteristic
34C2×#14519748—21no—
35C2×#14519748C2211yescharacteristic
36C2×Q8×Dic61C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519735C2211yescharacteristic
41C2×#14519733—21no—
42C22×C4⋊Dic61C2211yescharacteristic
43#16840125C2218yescomplemented
44#16840085C2218yescomplemented
45#16840081C2218yescomplemented
46#16840067C2218yescomplemented
47#16840010C2218yescomplemented
48#16839988C2218yescomplemented
49#16839960C2218yescomplemented
50#16839923C2218yescomplemented
51#16839869C2218yescomplemented
52#16839836C2218yescomplemented
53C2×#14519710C2211yescharacteristic
54C2×#14519709C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57#16839763C2218yescomplemented
58#16839757C2218yescomplemented
59C2×#14519701C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#452C2218yescomplemented
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×D244—21no—
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61D411yescharacteristic
88C23×Dic61—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758201—42no—
92C2×#11758201C2314yes—
93C2×#11758194—42no—
94C2×#11758194C2314yes—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C2×C8×D61—42no—
98C2×C8×D61C2314yes—
99#14519773—28no—
100#14519773—22no—
101#14519773C2314yes—
102#14519772—28no—
103#14519768—28no—
104#14519768—22no—
105#14519768C2314yes—
106#14519761—28no—
107#14519753—22no—
108#14519753C2314yes—
109#14519751—22no—
110#14519751—28no—
111#14519751C2314yes—
112#14519748—22no—
113#14519748—28no—
114#14519748C2314yes—
115Q8×Dic61—22no—
116Q8×Dic61—22no—
117Q8×Dic61C2314yes—
118Q8×Dic61C2314yes—
119C4×C22⋊D61—28no—
120C4×C22⋊D61D414yes—
121C4×C22⋊D61C2314yes—
122#14519735—22no—
123#14519735C2314yes—
124#14519733—28no—
125C2×C4⋊Dic61—22no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61C2314yes—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61D411yescharacteristic
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198D411yescharacteristic
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519710C2314yes—
148#14519709C2314yes—
149#14519709C2314yes—
150#14519706C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154#14519699C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519698C2314yes—
158#14519697C2314yes—
159#14519689C2314yes—
160#14519687C2314yes—
161C2×#41×C61—22no—
162C2×#41×C61—24no—
163C2×#41×C61—42no—
164C2×#41×C61C2314yes—
165C22×Q8×C61C2311yescharacteristic
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61C2311yescharacteristic
171C2×Q16×C61—24no—
172C2×Q16×C61C2314yes—
173C2×SD16×C61—42no—
174C2×SD16×C61C2314yes—
175C22×C8×C61C2311yescharacteristic
176C22×C8×C61C2311yescharacteristic
177C22⋊Q8×C61—22no—
178C22⋊Q8×C61C2314yes—
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182#103×C61C2314yes—
183#102×C61C2314yes—
184C22⋊C8×C61C2314yes—
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61C2×D411yescharacteristic
189#41×C61—28no—
190#41×C61—44no—
191#41×C61—48no—
192C2×Q8×C61—21no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61#4114yes—
198C2×Q8×C61C2412yes—
199C2×Q8×C61C2412yes—
200C2×D4×C61—24no—
201C2×D4×C61—21no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—44no—
205C2×D4×C61C2412yes—
206C22×C4×C61—21no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—24no—
212C22×C4×C61—44no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2412yes—
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—82no—
224C2×C22⋊D61—82no—
225C2×C22⋊D61—82no—
226C2×C22⋊D61C2×D414yes—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—24no—
230C22×Dic61—21no—
231C22×Dic61—44no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235#11758226—28no—
236#11758226—44no—
237#11758226—48no—
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—24no—
241C2×D244—21no—
242C2×D244—44no—
243C2×D244C2412yes—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—24no—
247C2×C4×D61—44no—
248C2×C4×D61C2×D412yes—
249C2×C4×D61C2412yes—
250Q16×C61—28no—
251SD16×C61—44no—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61C2412yes—
255C2×C8×C61C2412yes—
256C4⋊C4×C61—24no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C2412yes—
259C22⋊C4×C61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61C2×D414yes—
262#11758201—44no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266#11758198C2×D414yes—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—24no—
270C4⋊Dic61—21no—
271C4⋊Dic61—24no—
272C4⋊Dic61—24no—
273C4⋊Dic61—24no—
274C4⋊Dic61C2412yes—
275C4⋊Dic61C2412yes—
276C4⋊Dic61C2412yes—
277#11758196—24no—
278#11758196—24no—
279#11758196C2×D414yes—
280C4×Dic61—24no—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61C2×D412yes—
284C4×Dic61C2412yes—
285#11758194—44no—
286C2×#92418—22no—
287C2×#92418—22no—
288C2×#92418C2412yes—
289C2×#92418C2412yes—
290C8×D61—44no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61C22×D412yes—
299C23×C61C22×D411yescharacteristic
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61C22×D412yes—
308Q8×C61—24no—
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—42no—
313Q8×C61C2×#4114yes—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—48no—
317D4×C61—42no—
318C2×C4×C61—24no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—24no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—48no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61C22×D412yes—
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C2×#4112yes—
332C2×C4×C61H(5,𝔽2)12yes—
333C2×C4×C61C2511yescharacteristic
334C22⋊D61—44no—
335C22⋊D61—48no—
336C22⋊D61—84no—
337C22⋊D61—84no—
338C22⋊D61—84no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—48no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61C22×D412yes—
350C2×Dic61C22×D412yes—
351C2×Dic61C22×D412yes—
352D244—22no—
353D244—22no—
354D244—48no—
355D244—42no—
356C4×D61—24no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—48no—
360C8×C61—22no—
361C8×C61—22no—
362#92418—22no—
363#92418—22no—
364C2×#3317—611nomaximal, Sylow
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—44no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—84no—
373C22×C61#54612yes—
374C22×C61#57512yes—
375C22×C61#57712yes—
376C22×C61C23×D411yescharacteristic
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—44no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—84no—
385C4×C61—24no—
386C4×C61—22no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61#54612yes—
390C4×C61C22×#4111yescharacteristic
391C4×C61C2×H(5,𝔽2)11yescharacteristic
392Dic61—22no—
393Dic61—22no—
394Dic61—22no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#552—611no—
399C2×#550—611no—
400#3317—6116no—
401C2×#490—611no—
402C2×#481—611no—
403C2×#482—611no—
404C2×#479—611no—
405C2×#468—611no—
406C2×#465—611no—
407C2×#460—611no—
408C2×#452—611no—
409C2×#452D6111yescharacteristic, complemented
410C2×#441—611no—
411C2×#435—611no—
412C2×#417—611no—
413C2×#416—611no—
414C2×C61—42no—
415C2×C61—82no—
416C2×C61#331714yescomplemented
417C2×C61C2×#54611yescharacteristic
418C2×C61C2×#57511yescharacteristic
419C2×C61C2×#57711yescharacteristic
420D61—42no—
421D61—82no—
422C22×#41—611no—
423C22×#41C2×D6111yescharacteristic
424C22×Q16C2×D6111yescharacteristic
425C22×SD16—611no—
426C22×SD16C2×D6111yescharacteristic
427C22×M16—611no—
428C23×C8—611no—
429#552—618no—
430#552—1224no—
431#550—618no—
432#550—1224no—
433C2×#127—611no—
434C2×#127—1221no—
435C2×#126—1221no—
436C2×#125—611no—
437C2×#125—1221no—
438C2×#123—1221no—
439C2×C22⋊Q8—611no—
440C2×C22⋊Q8C2×D6111yescharacteristic
441C2×#121—611no—
442C2×#121—611no—
443C2×#121—1221no—
444C2×#121—1221no—
445C2×C4×Q8—611no—
446C2×C4×Q8—611no—
447C2×C4×D4—611no—
448C2×C4×D4—1221no—
449C2×#117—611no—
450C2×#117—1221no—
451C22×C4⋊C4—611no—
452#490—618no—
453#482—618no—
454#481—618no—
455#479—618no—
456#468—618no—
457#465—618no—
458#460—618no—
459#452—618no—
460#452C2×D6118yescomplemented
461#441—618no—
462#435—618no—
463C2×#107—611no—
464C2×#106—611no—
465C2×#106—611no—
466C2×C4⋊C8—611no—
467#417—618no—
468#416—618no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103C2×D6111yescharacteristic
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102C2×D6111yescharacteristic
479C2×C22⋊C8—611no—
480C2×C22⋊C8C2×D6111yescharacteristic
481C2×#97—611no—
482C61C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41—614no—
487C2×#41—1222no—
488C2×#41—1224no—
489C2×#41—2442no—
490C2×#41C22×D6114yes—
491C22×Q8C22×D6111yescharacteristic
492C22×Q8C22×D6111yescharacteristic
493C22×D4—21no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4—1221no—
501C22×D4C22×D6111yescharacteristic
502C23×C4—21no—
503C23×C4—611no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4C22×D6111yescharacteristic
507C2×Q16—24no—
508C2×Q16C22×D6114yes—
509C2×SD16—42no—
510C2×SD16—614no—
511C2×SD16—2442no—
512C2×SD16C22×D6114yes—
513C2×M16—614no—
514C2×M16—2442no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—614no—
518C22×C8—2442no—
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6111yescharacteristic
521#127—614no—
522#127—1222no—
523#127—1228no—
524#126—1228no—
525#125—614no—
526#125—1222no—
527#125—1228no—
528#123—1228no—
529C22⋊Q8—22no—
530C22⋊Q8—614no—
531C22⋊Q8—1222no—
532C22⋊Q8C22×D6114yes—
533#121—614no—
534#121—614no—
535#121—1228no—
536#121—1228no—
537#121—1222no—
538#121—1222no—
539C4×Q8—614no—
540C4×Q8—614no—
541C4×Q8—1222no—
542C4×Q8—1222no—
543C4×D4—614no—
544C4×D4—614no—
545C4×D4—1228no—
546#117—614no—
547#117—1228no—
548#117—1222no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—614no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1222no—
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—611no—
565C2×C22⋊C4—611no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C42—611no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42—1221no—
574#107—614no—
575#106—614no—
576#106—614no—
577C4⋊C8—614no—
578#103—614no—
579#103—614no—
580#103—614no—
581#103C22×D6114yes—
582#102—614no—
583#102—614no—
584#102—614no—
585#102—614no—
586#102—614no—
587#102C22×D6114yes—
588C22⋊C8—614no—
589C22⋊C8C22×D6114yes—
590#97—614no—
591C24—21no—
592C24—611no—
593C24—1221no—
594C24D4×D6111yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598#41—1228no—
599#41—2444no—
600#41—2448no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8#1175822414yes—
607C2×Q8C23×D6112yes—
608C2×Q8C23×D6112yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—44no—
614C2×D4—614no—
615C2×D4—612no—
616C2×D4—1224no—
617C2×D4—1224no—
618C2×D4—1224no—
619C2×D4—1224no—
620C2×D4—1224no—
621C2×D4—1221no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—4882no—
625C2×D4—4882no—
626C2×D4—4882no—
627C2×D4—2444no—
628C2×D4—2442no—
629C2×D4—2444no—
630C2×D4C23×D6112yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—44no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—612no—
642C22×C4—612no—
643C22×C4—1224no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1224no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4D4×D6112yes—
653C22×C4D4×D6111yescharacteristic
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656Q16—28no—
657SD16—44no—
658SD16—2444no—
659M16—2444no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—1222no—
665C2×C8—1222no—
666C2×C8—2444no—
667C2×C8C23×D6112yes—
668C2×C8C23×D6112yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—614no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—612no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1224no—
683C4⋊C4—1221no—
684C4⋊C4C23×D6112yes—
685C22⋊C4—24no—
686C22⋊C4—614no—
687C22⋊C4—614no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C42—612no—
693C42—612no—
694C42—1224no—
695C42—1224no—
696C42—1224no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—612no—
705C23—1222no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23C2×D4×D6112yes—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—22no—
717Q8—22no—
718Q8—42no—
719Q8C2×#1175822414yes—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—42no—
724D4—1222no—
725D4—1222no—
726D4—4884no—
727D4—4884no—
728D4—4884no—
729D4—2448no—
730D4—2444no—
731D4—2448no—
732D4—2442no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—612no—
745C2×C4—612no—
746C2×C4—612no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1224no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—2448no—
757C2×C4—2448no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4C2×D4×D6112yes—
762C2×C4C2×D4×D6111yescharacteristic
763C2×C4C2×#1175822412yes—
764C2×C4#1451982212yes—
765C2×C4C24×D6111yescharacteristic
766C8—22no—
767C8—22no—
768C8—1222no—
769C8—1222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—1222no—
779C22—1222no—
780C22—1222no—
781C22—4884no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2444no—
786C22#1684039912yes—
787C22#1684056112yes—
788C22#1684056912yes—
789C22C22×D4×D6111yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—1222no—
795C4—1222no—
796C4—1222no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4#1684039912yes—
801C4C22×#1175822411yescharacteristic
802C4C2×#1451982211yescharacteristic
803C2—42no—
804C2—82no—
805C2—4882no—
806C2—2442no—
807C2#2145793814yesdirect product factor
808C2C2×#1684039911yescharacteristic
809C2C2×#1684056111yescharacteristic
810C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC2×#16840431C2
hypercenterC2×#452D61
hypocenterC61C2×#3317
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16840454C2semidirect
3. #21457938C2direct (N × H)
4. C2×#16840125C2semidirect
5. C2×#16840081C2semidirect
6. C2×#16840085C2semidirect
7. C2×#16840067C2semidirect
8. C2×#16840010C2semidirect
9. C2×#16839988C2semidirect
10. C2×#16839960C2semidirect
11. C2×#16839923C2semidirect
12. C2×#16839869C2semidirect
13. C2×#16839836C2semidirect
14. C2×#16839763C2semidirect
15. C2×#16839757C2semidirect
16. C2×C61×#452C2semidirect
22. #16840454C22semidirect
43. #16840125C22semidirect
44. #16840085C22semidirect
45. #16840081C22semidirect
46. #16840067C22semidirect
47. #16840010C22semidirect
48. #16839988C22semidirect
49. #16839960C22semidirect
50. #16839923C22semidirect
51. #16839869C22semidirect
52. #16839836C22semidirect
57. #16839763C22semidirect
58. #16839757C22semidirect
73. C61×#452C22semidirect
409. C2×#452D61semidirect
416. C2×C61#3317semidirect
460. #452C2×D61semidirect
482. C61C2×#3317semidirect
807. C2#21457938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404542
C2×#168404312
#214579382
C2×#168401252
C2×#168400812
C2×#168400852
C2×#168400672
C2×#168400102
C2×#168399882
C2×#168399602
C2×#168399232
C2×#168398692
C2×#168398362
C2×#168397632
C2×#168397572
C2×C61×#4522
C2×#331761