Finite Group Databasebeta

← C2×#21458069 #30556863

Subgroups — C2×#21458069 #30556863

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×#16840465C211yesmaximal, characteristic, complemented
2C2×#16840424C211yesmaximal, characteristic, complemented
3#21458069C2116yesmaximal, direct product factor
4C2×#16840119C211yesmaximal, characteristic, complemented
5C2×#16840089C211yesmaximal, characteristic, complemented
6C2×#16840094C211yesmaximal, characteristic, complemented
7C2×#16840016C211yesmaximal, characteristic, complemented
8C2×#16840009C211yesmaximal, characteristic, complemented
9C2×#16839978C211yesmaximal, characteristic, complemented
10C2×#16839910C211yesmaximal, characteristic, complemented
11C2×#16839902C211yesmaximal, characteristic, complemented
12C2×C4×#11758201C211yesmaximal, characteristic, complemented
13C2×#16839839C211yesmaximal, characteristic, complemented
14C2×#16839762C211yesmaximal, characteristic, complemented
15C2×#16839769C211yesmaximal, characteristic, complemented
16C2×C61×#479C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×D488C2211yescharacteristic
22C22×#11758189C2211yescharacteristic
23C22×#11758189C2211yescharacteristic
24#16840465—24no—
25#16840465C2218yescomplemented
26#16840424—24no—
27#16840424C2218yescomplemented
28C2×#14519772—21no—
29C2×#14519765—21no—
30C2×#14519765C2211yescharacteristic
31C2×#14519762—21no—
32C2×#14519757—21no—
33C2×#14519757C2211yescharacteristic
34C2×#14519752—21no—
35C2×#14519752—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519752C2211yescharacteristic
38C2×#14519752C2211yescharacteristic
39C2×C4×D244—21no—
40C2×C4×D244C2211yescharacteristic
41C2×C4×D244C2211yescharacteristic
42C2×#14519739—21no—
43C2×#14519735C2211yescharacteristic
44C2×C4⋊C4×D61C2211yescharacteristic
45#16840119C2218yescomplemented
46#16840094C2218yescomplemented
47#16840089C2218yescomplemented
48#16840016C2218yescomplemented
49#16840009C2218yescomplemented
50#16839978C2218yescomplemented
51#16839910C2218yescomplemented
52#16839902C2218yescomplemented
53C4×#11758201C2218yescomplemented
54#16839839C2218yescomplemented
55C2×#14519708C2211yescharacteristic
56#16839769C2218yescomplemented
57#16839762C2218yescomplemented
58C2×#14519702C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519700C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic
69C2×#125×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C61×#479C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C2×Q8×D61—22no—
84C2×Q8×D61—24no—
85C2×Q8×D61—42no—
86C2×Q8×D61C2314yes—
87C22×D244—21no—
88C22×D244—21no—
89C22×D244—21no—
90C22×D244—21no—
91C22×D244D411yescharacteristic
92C22×D244C2311yescharacteristic
93C22×D244C2311yescharacteristic
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C22×C4×D61C2311yescharacteristic
99C22×C4×D61C2311yescharacteristic
100C2×#11758190—42no—
101C2×#11758190C2314yes—
102C2×#11758201—24no—
103C2×#11758201C2314yes—
104C2×D488—42no—
105C2×D488C2314yes—
106C2×#11758189—42no—
107C2×#11758189—42no—
108C2×#11758189C2314yes—
109C2×#11758189C2314yes—
110C22×#92418C2311yescharacteristic
111C22×#92418C2311yescharacteristic
112#14519772—28no—
113#14519765—22no—
114#14519765—28no—
115#14519765C2314yes—
116#14519762—28no—
117#14519757—22no—
118#14519757—28no—
119#14519757C2314yes—
120#14519752—28no—
121#14519752—28no—
122#14519752—22no—
123#14519752—22no—
124#14519752—22no—
125#14519752C2314yes—
126#14519752C2314yes—
127#14519752C2314yes—
128C4×D244—22no—
129C4×D244—28no—
130C4×D244D414yes—
131C4×D244C2314yes—
132C4×D244C2314yes—
133#14519739—28no—
134#14519735—22no—
135#14519735C2314yes—
136C2×C4⋊Dic61—21no—
137C2×C4⋊Dic61D411yescharacteristic
138C2×C4⋊Dic61C2311yescharacteristic
139C2×#11758196—21no—
140C4⋊C4×D61—22no—
141C4⋊C4×D61C2314yes—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198D411yescharacteristic
151C2×#11758198D411yescharacteristic
152C2×C4×Dic61—21no—
153#14519708C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519700C2314yes—
157#14519700C2314yes—
158#14519699C2314yes—
159#14519697C2314yes—
160#14519697C2314yes—
161#14519697C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164C4×#92418C2314yes—
165C22×Q8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#125×C61—22no—
169#125×C61C2314yes—
170C4×Q8×C61—22no—
171C4×Q8×C61C2314yes—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C42×C61—21no—
179C2×C42×C61C2311yescharacteristic
180#107×C61C2314yes—
181#106×C61C2314yes—
182C4⋊C8×C61C2314yes—
183#103×C61C2314yes—
184#103×C61C2314yes—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61C2×D411yescharacteristic
188C23×D61C2×D411yescharacteristic
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61#4114yes—
192C2×Q8×C61C2412yes—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204#11758226—28no—
205#11758226—44no—
206#11758226—48no—
207Q8×D61—28no—
208Q8×D61—44no—
209Q8×D61—48no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—22no—
213C2×D244—22no—
214C2×D244—24no—
215C2×D244—24no—
216C2×D244—24no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—24no—
220C2×D244—42no—
221C2×D244—44no—
222C2×D244—44no—
223C2×D244—44no—
224C2×D244—82no—
225C2×D244C2×D414yes—
226C2×D244C2412yes—
227C2×D244C2412yes—
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—44no—
237C2×C4×D61—44no—
238C2×C4×D61—82no—
239C2×C4×D61—82no—
240C2×C4×D61C2×D412yes—
241C2×C4×D61C2×D412yes—
242C2×C4×D61C2412yes—
243C2×C4×D61C2412yes—
244C2×Dic122—22no—
245C2×Dic122—22no—
246C2×Dic122—21no—
247C2×Dic122—24no—
248C2×Dic122—44no—
249C2×Dic122C2412yes—
250C2×C8×C61—22no—
251C2×C8×C61—22no—
252C2×C8×C61C2412yes—
253C2×C8×C61C2412yes—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—24no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61C2412yes—
261C4⋊C4×C61C2412yes—
262C4⋊C4×C61C2412yes—
263C42×C61—24no—
264C42×C61C2×D412yes—
265C42×C61C2412yes—
266#11758201—28no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198C2×D414yes—
276#11758198C2×D414yes—
277C4⋊Dic61—21no—
278C4⋊Dic61—24no—
279C4⋊Dic61C2×D414yes—
280C4⋊Dic61C2412yes—
281#11758196—24no—
282C4×Dic61—24no—
283C2×#92418—22no—
284C2×#92418—22no—
285C2×#92418C2412yes—
286C2×#92418C2412yes—
287D488—44no—
288#11758190—44no—
289#11758189—44no—
290#11758189—44no—
291C23×C61C22×D411yescharacteristic
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61C22×D412yes—
307C22×D61C22×D412yes—
308Q8×C61—24no—
309Q8×C61—22no—
310Q8×C61C2×#4114yes—
311C2×C4×C61—24no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C61H(5,𝔽2)12yes—
326C2×C4×C61C2511yescharacteristic
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335D244—22no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—44no—
340D244—48no—
341D244—48no—
342D244—48no—
343D244—42no—
344D244—42no—
345D244—84no—
346C4×D61—24no—
347C4×D61—24no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—48no—
353C4×D61—48no—
354C4×D61—84no—
355C4×D61—84no—
356Dic122—22no—
357Dic122—22no—
358Dic122—48no—
359Dic122—42no—
360C8×C61—22no—
361C8×C61—22no—
362#92418—22no—
363#92418—22no—
364C2×#3326—611nomaximal, Sylow
365C22×C61#54612yes—
366C22×C61#57512yes—
367C22×C61#57712yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—44no—
376C2×D61—44no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—84no—
384C2×D61—84no—
385C4×C61—24no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61#54612yes—
392C4×C61C22×#4111yescharacteristic
393C4×C61C2×H(5,𝔽2)11yescharacteristic
394Dic61—22no—
395Dic61—22no—
396Dic61—42no—
397Dic61—42no—
398C2×#553—611no—
399C2×#548—611no—
400#3326—6116no—
401C2×#488—611no—
402C2×#482—611no—
403C2×#483—611no—
404C2×#479D6111yescharacteristic, complemented
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#332614yescomplemented
415C2×C61C2×#54611yescharacteristic
416C2×C61C2×#57511yescharacteristic
417C2×C61C2×#57711yescharacteristic
418D61—42no—
419D61—42no—
420D61—82no—
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×#125C2×D6111yescharacteristic
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—611no—
443C2×#121—1221no—
444C2×#121—1221no—
445C2×C4×Q8C2×D6111yescharacteristic
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4—1221no—
449C2×C4×D4—1221no—
450C2×#117—611no—
451C22×C4⋊C4—611no—
452#488—618no—
453#483—618no—
454#482—618no—
455#479C2×D6118yescomplemented
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⋊C8C2×D6111yescharacteristic
467#419—618no—
468#417—618no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103C2×D6111yescharacteristic
474C2×#103C2×D6111yescharacteristic
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×C4×C8—611no—
482C61C2×#332611yescharacteristic, complemented, Sylow
483C2×#41—614no—
484C2×#41—1222no—
485C2×#41—1224no—
486C2×#41—2442no—
487C22×Q8—614no—
488C22×Q8—611no—
489C22×Q8—1221no—
490C22×Q8—1222no—
491C22×Q8—1224no—
492C22×Q8—2442no—
493C22×Q8C22×D6111yescharacteristic
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—611no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4—1221no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4—1221no—
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—22no—
523#125C22×D6114yes—
524#124—614no—
525#124—1228no—
526#124—1222no—
527#123—1228no—
528C22⋊Q8—614no—
529C22⋊Q8—1228no—
530C22⋊Q8—1222no—
531#121—614no—
532#121—614no—
533#121—614no—
534#121—1222no—
535#121—1222no—
536#121—1222no—
537#121—1228no—
538#121—1228no—
539C4×Q8—22no—
540C4×Q8C22×D6114yes—
541C4×D4—614no—
542C4×D4—614no—
543C4×D4—614no—
544C4×D4—1228no—
545C4×D4—1228no—
546C4×D4—1222no—
547#117—614no—
548#117—1222no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—614no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C22⋊C4—611no—
562C2×C22⋊C4—611no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
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—1221no—
573C2×C42C22×D6111yescharacteristic
574#107C22×D6114yes—
575#106—614no—
576#106C22×D6114yes—
577C4⋊C8C22×D6114yes—
578#103—614no—
579#103—614no—
580#103—614no—
581#103—614no—
582#103C22×D6114yes—
583#103C22×D6114yes—
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588C22⋊C8—614no—
589C22⋊C8—614no—
590C4×C8—614no—
591C24—611no—
592C24—611no—
593C24—1221no—
594C24—1221no—
595#41—1228no—
596#41—2444no—
597#41—2448no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—612no—
601C2×Q8—1224no—
602C2×Q8—1221no—
603C2×Q8—1228no—
604C2×Q8—1222no—
605C2×Q8—1222no—
606C2×Q8—2444no—
607C2×Q8—2444no—
608C2×Q8—2448no—
609C2×Q8#1175822614yes—
610C2×Q8C23×D6112yes—
611C2×D4—614no—
612C2×D4—612no—
613C2×D4—612no—
614C2×D4—1224no—
615C2×D4—1224no—
616C2×D4—1224no—
617C2×D4—1224no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1222no—
621C2×D4—1222no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—4882no—
625C2×D4—2442no—
626C2×D4—2444no—
627C2×D4—2444no—
628C2×D4—2444no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—612no—
639C22×C4—1224no—
640C22×C4—1224no—
641C22×C4—1224no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1224no—
649C22×C4—4882no—
650C22×C4—4882no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
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—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—614no—
676C4⋊C4—612no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1221no—
680C4⋊C4C23×D6112yes—
681C4⋊C4C23×D6112yes—
682C4⋊C4C23×D6112yes—
683C22⋊C4—614no—
684C22⋊C4—614no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C42—24no—
694C42—1224no—
695C42D4×D6112yes—
696C42C23×D6112yes—
697C23—612no—
698C23—612no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1222no—
707C23—2442no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23—2442no—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—1222no—
717Q8—1222no—
718Q8—2448no—
719Q8—2442no—
720Q8C2×#1175822614yes—
721D4—1222no—
722D4—1222no—
723D4—1222no—
724D4—1222no—
725D4—4884no—
726D4—2444no—
727D4—2448no—
728D4—2448no—
729D4—2448no—
730D4—2442no—
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—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1224no—
751C2×C4—1224no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—4884no—
755C2×C4—4884no—
756C2×C4—2448no—
757C2×C4—2448no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4C2×D4×D6112yes—
761C2×C4C2×D4×D6112yes—
762C2×C4C2×D4×D6111yescharacteristic
763C2×C4C2×#1175822612yes—
764C2×C4#1451982312yes—
765C2×C4C24×D6111yescharacteristic
766C8—22no—
767C8—22no—
768C8—1222no—
769C8—1222no—
770C22—1222no—
771C22—1222no—
772C22—1222no—
773C22—1222no—
774C22—1222no—
775C22—1222no—
776C22—4884no—
777C22—4884no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2444no—
785C22—2444no—
786C22#1684040312yes—
787C22#1684055912yes—
788C22#1684057112yes—
789C22C22×D4×D6111yescharacteristic
790C4—24no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—1222no—
797C4—1222no—
798C4—2442no—
799C4—2442no—
800C4#1684040312yes—
801C4C22×#1175822611yescharacteristic
802C4C2×#1451982311yescharacteristic
803C2—4882no—
804C2—4882no—
805C2—2442no—
806C2—2442no—
807C2#2145806914yesdirect product factor
808C2C2×#1684040311yescharacteristic
809C2C2×#1684055911yescharacteristic
810C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#479C2
socleC23×C61C22×D4
hypercenterC2×#479D61
hypocenterC61C2×#3326
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#16840465C2semidirect
2. C2×#16840424C2semidirect
3. #21458069C2direct (N × H)
4. C2×#16840119C2semidirect
5. C2×#16840089C2semidirect
6. C2×#16840094C2semidirect
7. C2×#16840016C2semidirect
8. C2×#16840009C2semidirect
9. C2×#16839978C2semidirect
10. C2×#16839910C2semidirect
11. C2×#16839902C2semidirect
12. C2×C4×#11758201C2semidirect
13. C2×#16839839C2semidirect
14. C2×#16839762C2semidirect
15. C2×#16839769C2semidirect
16. C2×C61×#479C2semidirect
25. #16840465C22semidirect
27. #16840424C22semidirect
45. #16840119C22semidirect
46. #16840094C22semidirect
47. #16840089C22semidirect
48. #16840016C22semidirect
49. #16840009C22semidirect
50. #16839978C22semidirect
51. #16839910C22semidirect
52. #16839902C22semidirect
53. C4×#11758201C22semidirect
54. #16839839C22semidirect
56. #16839769C22semidirect
57. #16839762C22semidirect
71. C61×#479C22semidirect
404. C2×#479D61semidirect
414. C2×C61#3326semidirect
455. #479C2×D61semidirect
482. C61C2×#3326semidirect
807. C2#21458069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404652
C2×#168404242
#214580692
C2×#168401192
C2×#168400892
C2×#168400942
C2×#168400162
C2×#168400092
C2×#168399782
C2×#168399102
C2×#168399022
C2×C4×#117582012
C2×#168398392
C2×#168397622
C2×#168397692
C2×C61×#4792
C2×#332661