Finite Group Databasebeta

← C2×#21458070 #30556864

Subgroups — C2×#21458070 #30556864

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×#16840456C211yesmaximal, characteristic, complemented
2C2×#16840418C211yesmaximal, characteristic, complemented
3#21458070C2116yesmaximal, direct product factor
4C2×#16840115C211yesmaximal, characteristic, complemented
5C2×#16840094C211yesmaximal, characteristic, complemented
6C2×#16840068C211yesmaximal, characteristic, complemented
7C2×#16840013C211yesmaximal, characteristic, complemented
8C2×#16840009C211yesmaximal, characteristic, complemented
9C2×#16839976C211yesmaximal, characteristic, complemented
10C2×#16839908C211yesmaximal, characteristic, complemented
11C2×#16839903C211yesmaximal, characteristic, complemented
12C2×#16839849C211yesmaximal, characteristic, complemented
13C2×#16839837C211yesmaximal, characteristic, complemented
14C2×#16839760C211yesmaximal, characteristic, complemented
15C2×#16839770C211yesmaximal, characteristic, complemented
16C2×C61×#482C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×#11758194C2211yescharacteristic
23C22×#11758189C2211yescharacteristic
24#16840456—24no—
25#16840456C2218yescomplemented
26#16840418—24no—
27#16840418C2218yescomplemented
28C2×#14519771—21no—
29C2×#14519768C2211yescharacteristic
30C2×#14519764C2211yescharacteristic
31C2×#14519763—21no—
32C2×#14519759—21no—
33C2×#14519757C2211yescharacteristic
34C2×#14519754—21no—
35C2×#14519752C2211yescharacteristic
36C2×#14519751C2211yescharacteristic
37C2×#14519750—21no—
38C2×#14519749—21no—
39C2×#14519742C2211yescharacteristic
40C2×C4×D244—21no—
41C2×D4×Dic61—21no—
42C2×#14519739C2211yescharacteristic
43C2×C4×C22⋊D61C2211yescharacteristic
44C2×C4⋊C4×D61C2211yescharacteristic
45#16840115C2218yescomplemented
46#16840094C2218yescomplemented
47#16840068C2218yescomplemented
48#16840013C2218yescomplemented
49#16840009C2218yescomplemented
50#16839976C2218yescomplemented
51#16839908C2218yescomplemented
52#16839903C2218yescomplemented
53#16839849C2218yescomplemented
54#16839837C2218yescomplemented
55C2×#14519708C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57#16839770C2218yescomplemented
58#16839760C2218yescomplemented
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#482C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758224—22no—
78C2×#11758224—24no—
79C2×#11758224—42no—
80C2×#11758224C2314yes—
81C22×Dic122—24no—
82C22×Dic122—21no—
83C22×Dic122—22no—
84C22×Dic122—42no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2314yes—
87C22×Dic122C2311yescharacteristic
88C22×D244—21no—
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61D411yescharacteristic
93C23×Dic61—21no—
94C23×Dic61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98C2×#11758190—24no—
99C2×#11758190—42no—
100C2×#11758190C2314yes—
101C2×#11758190C2314yes—
102C2×#11758199—42no—
103C2×#11758199C2314yes—
104C2×#11758194—42no—
105C2×#11758194C2314yes—
106C2×#11758189—42no—
107C2×#11758189C2314yes—
108C22×#92418C2311yescharacteristic
109C22×#92418C2311yescharacteristic
110#14519771—28no—
111#14519768—22no—
112#14519768C2314yes—
113#14519764—22no—
114#14519764C2314yes—
115#14519763—28no—
116#14519759—28no—
117#14519757—22no—
118#14519757C2314yes—
119#14519754—28no—
120#14519752—22no—
121#14519752C2314yes—
122#14519751—22no—
123#14519751C2314yes—
124#14519750—28no—
125#14519749—28no—
126#14519742—22no—
127#14519742C2314yes—
128C4×D244—28no—
129D4×Dic61—28no—
130#14519739—22no—
131#14519739C2314yes—
132C4×C22⋊D61D414yes—
133C4×C22⋊D61C2314yes—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61—21no—
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196D411yescharacteristic
141C4⋊C4×D61—22no—
142C4⋊C4×D61C2314yes—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61D411yescharacteristic
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198D411yescharacteristic
151C2×C4×Dic61—21no—
152C2×C4×Dic61C2311yescharacteristic
153#14519708C2314yes—
154#14519706C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519700C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519700C2314yes—
161#14519698C2314yes—
162#14519697C2314yes—
163#14519689C2314yes—
164C8×Dic61C2314yes—
165C22×D4×C61—21no—
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170#121×C61—22no—
171#121×C61C2314yes—
172#117×C61—22no—
173#117×C61C2314yes—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C42×C61—21no—
180#107×C61C2314yes—
181#106×C61C2314yes—
182#102×C61C2314yes—
183#102×C61C2314yes—
184C22⋊C8×C61C2314yes—
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61C2×D411yescharacteristic
189C2×D4×C61—24no—
190C2×D4×C61—21no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—44no—
194C2×D4×C61C2412yes—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D412yes—
202C22×C4×C61C2412yes—
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—44no—
208C2×C22⋊D61—82no—
209C2×C22⋊D61C2×D414yes—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—24no—
214C22×Dic61—24no—
215C22×Dic61—44no—
216C22×Dic61—44no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220#11758224—28no—
221#11758224—44no—
222#11758224—48no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—24no—
226C2×D244—21no—
227C2×D244—44no—
228C2×D244C2412yes—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—24no—
232C2×C4×D61—24no—
233C2×C4×D61—82no—
234C2×C4×D61—82no—
235C2×C4×D61C2×D412yes—
236C2×C4×D61C2412yes—
237C2×Dic122—21no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—28no—
242C2×Dic122—24no—
243C2×Dic122—21no—
244C2×Dic122—44no—
245C2×Dic122—48no—
246C2×Dic122—44no—
247C2×Dic122#4114yes—
248C2×Dic122C2412yes—
249C2×Dic122C2412yes—
250C2×C8×C61—22no—
251C2×C8×C61—22no—
252C2×C8×C61C2412yes—
253C2×C8×C61C2412yes—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2412yes—
258C4⋊C4×C61C2412yes—
259C4⋊C4×C61C2412yes—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C42×C61—24no—
263C22⋊Dic61—24no—
264C22⋊Dic61—24no—
265C22⋊Dic61C2×D414yes—
266#11758199—44no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271#11758198C2×D414yes—
272C4⋊Dic61—21no—
273C4⋊Dic61—24no—
274C4⋊Dic61—24no—
275C4⋊Dic61C2412yes—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196C2×D414yes—
280C4×Dic61—24no—
281C4×Dic61C2×D412yes—
282C4×Dic61C2412yes—
283#11758194—44no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288#11758190—28no—
289#11758190—44no—
290#11758189—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—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—48no—
311D4×C61—42no—
312C2×C4×C61—22no—
313C2×C4×C61—24no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C61H(5,𝔽2)12yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—44no—
328C22⋊D61—48no—
329C22⋊D61—84no—
330C2×Dic61—24no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—48no—
338C2×Dic61—48no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344D244—22no—
345D244—22no—
346D244—48no—
347D244—42no—
348C4×D61—24no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—84no—
352C4×D61—84no—
353Dic122—24no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—48no—
358Dic122—42no—
359Dic122C2×#4114yes—
360C8×C61—22no—
361C8×C61—22no—
362#92418—22no—
363#92418—22no—
364C2×#3326—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—22no—
386C4×C61—42no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61#54612yes—
390C4×C61C22×#4111yescharacteristic
391C4×C61C2×H(5,𝔽2)11yescharacteristic
392Dic61—24no—
393Dic61—22no—
394Dic61—22no—
395Dic61—22no—
396Dic61—42no—
397Dic61—42no—
398C2×#553—611no—
399C2×#548—611no—
400#3326—6116no—
401C2×#488—611no—
402C2×#482D6111yescharacteristic, complemented
403C2×#483—611no—
404C2×#479—611no—
405C2×#469—611no—
406C2×#468—611no—
407C2×#463—611no—
408C2×#449—611no—
409C2×#448—611no—
410C2×C4×SD16—611no—
411C2×#436—611no—
412C2×#417—611no—
413C2×#419—611no—
414C2×C61—42no—
415C2×C61—82no—
416C2×C61#332614yescomplemented
417C2×C61C2×#54611yescharacteristic
418C2×C61C2×#57511yescharacteristic
419C2×C61C2×#57711yescharacteristic
420D61—42no—
421D61—82no—
422C22×#41—611no—
423C23×Q8—611no—
424C22×SD16—611no—
425C22×SD16—611no—
426C22×D8—611no—
427C22×M16—611no—
428C22×M16—611no—
429#553—618no—
430#553—1224no—
431#548—618no—
432#548—1224no—
433C2×#126—1221no—
434C2×#125—611no—
435C2×#124—611no—
436C2×#124—1221no—
437C2×#123—1221no—
438C2×C22⋊Q8—611no—
439C2×C22⋊Q8—1221no—
440C2×#121—611no—
441C2×#121—611no—
442C2×#121—1221no—
443C2×#121—1221no—
444C2×#121C2×D6111yescharacteristic
445C2×C4×Q8—611no—
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4—1221no—
449C2×C4×D4—1221no—
450C2×#117C2×D6111yescharacteristic
451C22×C4⋊C4—611no—
452#488—618no—
453#483—618no—
454#482C2×D6118yescomplemented
455#479—618no—
456#469—618no—
457#468—618no—
458#463—618no—
459#449—618no—
460#448—618no—
461C4×SD16—618no—
462#436—618no—
463C2×#107C2×D6111yescharacteristic
464C2×#106—611no—
465C2×#106C2×D6111yescharacteristic
466C2×C4⋊C8—611no—
467#419—618no—
468#417—618no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102C2×D6111yescharacteristic
478C2×#102C2×D6111yescharacteristic
479C2×C22⋊C8—611no—
480C2×C22⋊C8C2×D6111yescharacteristic
481C2×C4×C8—611no—
482C61C2×#332611yescharacteristic, complemented, Sylow
483C2×#41—614no—
484C2×#41—1222no—
485C2×#41—1224no—
486C2×#41—2442no—
487C22×Q8—611no—
488C22×Q8—611no—
489C22×Q8—614no—
490C22×Q8—1224no—
491C22×Q8—1221no—
492C22×Q8—1222no—
493C22×Q8—2442no—
494C22×D4—21no—
495C22×D4—611no—
496C22×D4—611no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4C22×D6111yescharacteristic
501C23×C4—611no—
502C23×C4—1221no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4C22×D6111yescharacteristic
507C2×SD16—614no—
508C2×SD16—614no—
509C2×SD16—1224no—
510C2×SD16—2442no—
511C2×D8—614no—
512C2×D8—2442no—
513C2×M16—614no—
514C2×M16—614no—
515C2×M16—2442no—
516C2×M16—2442no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6111yescharacteristic
521#126—1228no—
522#125—614no—
523#125—1222no—
524#124—614no—
525#124—1222no—
526#124—1228no—
527#123—1228no—
528C22⋊Q8—614no—
529C22⋊Q8—1228no—
530C22⋊Q8—1222no—
531#121—22no—
532#121—614no—
533#121—614no—
534#121—1228no—
535#121—1222no—
536#121—1228no—
537#121—1222no—
538#121C22×D6114yes—
539C4×Q8—614no—
540C4×Q8—1222no—
541C4×D4—614no—
542C4×D4—614no—
543C4×D4—614no—
544C4×D4—1228no—
545C4×D4—1222no—
546C4×D4—1228no—
547#117—22no—
548#117C22×D6114yes—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—614no—
552C2×C4⋊C4—1222no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—611no—
564C2×C22⋊C4—611no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C42—21no—
572C2×C42—611no—
573C2×C42—1221no—
574#107C22×D6114yes—
575#106—614no—
576#106C22×D6114yes—
577C4⋊C8—614no—
578#103—614no—
579#103—614no—
580#103—614no—
581#103—614no—
582#103—614no—
583#103—614no—
584#102—614no—
585#102—614no—
586#102C22×D6114yes—
587#102C22×D6114yes—
588C22⋊C8—614no—
589C22⋊C8C22×D6114yes—
590C4×C8—614no—
591C24—21no—
592C24—611no—
593C24—1221no—
594C24D4×D6111yescharacteristic
595#41—1228no—
596#41—2444no—
597#41—2448no—
598C2×Q8—614no—
599C2×Q8—612no—
600C2×Q8—612no—
601C2×Q8—1228no—
602C2×Q8—1221no—
603C2×Q8—1224no—
604C2×Q8—1221no—
605C2×Q8—1222no—
606C2×Q8—1222no—
607C2×Q8—1222no—
608C2×Q8—2444no—
609C2×Q8—2444no—
610C2×Q8—2448no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—44no—
616C2×D4—614no—
617C2×D4—612no—
618C2×D4—1224no—
619C2×D4—1224no—
620C2×D4—1224no—
621C2×D4—1221no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—4882no—
625C2×D4—2444no—
626C2×D4—2442no—
627C2×D4—2444no—
628C2×D4C23×D6112yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—612no—
638C22×C4—612no—
639C22×C4—1224no—
640C22×C4—1224no—
641C22×C4—1224no—
642C22×C4—1221no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1224no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—4882no—
649C22×C4—4882no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4D4×D6112yes—
653C22×C4D4×D6111yescharacteristic
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656SD16—1228no—
657SD16—2444no—
658D8—2444no—
659M16—2444no—
660M16—2444no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—612no—
664C2×C8—612no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8C23×D6112yes—
668C2×C8C23×D6112yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—614no—
673C4⋊C4—612no—
674C4⋊C4—1224no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1221no—
680C4⋊C4C23×D6112yes—
681C4⋊C4C23×D6112yes—
682C4⋊C4C23×D6112yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—614no—
686C22⋊C4—614no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C42—24no—
694C42—612no—
695C42—612no—
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—614no—
715Q8—1222no—
716Q8—1224no—
717Q8—1222no—
718Q8—1222no—
719Q8—2448no—
720Q8—2442no—
721D4—22no—
722D4—22no—
723D4—48no—
724D4—42no—
725D4—1222no—
726D4—1222no—
727D4—4884no—
728D4—2448no—
729D4—2444no—
730D4—2448no—
731D4—2442no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—612no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1224no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1224no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—4884no—
756C2×C4—4884no—
757C2×C4—2448no—
758C2×C4—2448no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4C2×D4×D6112yes—
762C2×C4C2×D4×D6111yescharacteristic
763C2×C4#41×D6112yes—
764C2×C4#1451982312yes—
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#1684040412yes—
787C22#1684055812yes—
788C22#1684056912yes—
789C22C22×D4×D6111yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—1222no—
795C4—1224no—
796C4—1222no—
797C4—1222no—
798C4—2442no—
799C4—2442no—
800C4#1684040412yes—
801C4C2×#41×D6111yescharacteristic
802C4C2×#1451982311yescharacteristic
803C2—42no—
804C2—82no—
805C2—4882no—
806C2—2442no—
807C2#2145807014yesdirect product factor
808C2C2×#1684040411yescharacteristic
809C2C2×#1684055811yescharacteristic
810C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#482C2
socleC23×C61C22×D4
hypercenterC2×#482D61
hypocenterC61C2×#3326
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16840456C2semidirect
2. C2×#16840418C2semidirect
3. #21458070C2direct (N × H)
4. C2×#16840115C2semidirect
5. C2×#16840094C2semidirect
6. C2×#16840068C2semidirect
7. C2×#16840013C2semidirect
8. C2×#16840009C2semidirect
9. C2×#16839976C2semidirect
10. C2×#16839908C2semidirect
11. C2×#16839903C2semidirect
12. C2×#16839849C2semidirect
13. C2×#16839837C2semidirect
14. C2×#16839760C2semidirect
15. C2×#16839770C2semidirect
16. C2×C61×#482C2semidirect
25. #16840456C22semidirect
27. #16840418C22semidirect
45. #16840115C22semidirect
46. #16840094C22semidirect
47. #16840068C22semidirect
48. #16840013C22semidirect
49. #16840009C22semidirect
50. #16839976C22semidirect
51. #16839908C22semidirect
52. #16839903C22semidirect
53. #16839849C22semidirect
54. #16839837C22semidirect
57. #16839770C22semidirect
58. #16839760C22semidirect
71. C61×#482C22semidirect
402. C2×#482D61semidirect
416. C2×C61#3326semidirect
454. #482C2×D61semidirect
482. C61C2×#3326semidirect
807. C2#21458070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404562
C2×#168404182
#214580702
C2×#168401152
C2×#168400942
C2×#168400682
C2×#168400132
C2×#168400092
C2×#168399762
C2×#168399082
C2×#168399032
C2×#168398492
C2×#168398372
C2×#168397602
C2×#168397702
C2×C61×#4822
C2×#332661