Finite Group Databasebeta

← C2×#21456174 #30549250

Subgroups — C2×#21456174 #30549250

Order 15616.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840392C211yesmaximal, characteristic, complemented
2C2×#16840325C211yesmaximal, characteristic
3#21456174C2116yesmaximal, direct product factor
4C2×#16840125C211yesmaximal, characteristic, complemented
5C2×#16840122C211yesmaximal, characteristic, complemented
6C2×#16840120C211yesmaximal, characteristic, complemented
7C2×#16840119C211yesmaximal, characteristic, complemented
8C2×#16840115C211yesmaximal, characteristic, complemented
9C2×#16840108C211yesmaximal, characteristic, complemented
10C2×#16840107C211yesmaximal, characteristic, complemented
11C2×#16839760C211yesmaximal, characteristic, complemented
12C2×#16839765C211yesmaximal, characteristic, complemented
13C2×#16839755C211yesmaximal, characteristic, complemented
14C2×#102×D61C211yesmaximal, characteristic, complemented
15C2×#16839719C211yesmaximal, characteristic, complemented
16C2×C61×#490C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840392—24no—
22#16840392C2218yescomplemented
23#16840325—24no—
24#16840325C2218yes—
25C2×#14519777C2211yescharacteristic, complemented
26C2×#14519776—21no—
27C2×#14519776C2211yescharacteristic, complemented
28C2×#14519773C2211yescharacteristic
29C2×#14519768C2211yescharacteristic, complemented
30C2×#14519767—21no—
31C2×#14519765C2211yescharacteristic
32C2×#14519764C2211yescharacteristic
33C2×#14519757—21no—
34C2×#14519755—21no—
35C2×#14519749—21no—
36C2×#14519749—21no—
37C2×#14519745—21no—
38C2×#14519745—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519734C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840125C2218yescomplemented
43#16840122C2218yescomplemented
44#16840120C2218yescomplemented
45#16840119C2218yescomplemented
46#16840115C2218yescomplemented
47#16840108C2218yescomplemented
48#16840107C2218yescomplemented
49#16839765C2218yescomplemented
50#16839760C2218yescomplemented
51#16839755C2218yescomplemented
52C2×#14519702C2211yescharacteristic, complemented
53C2×#14519702C2211yescharacteristic, complemented
54C2×#14519700C2211yescharacteristic, complemented
55C2×#14519700C2211yescharacteristic, complemented
56C2×#14519699C2211yescharacteristic
57C2×#14519699C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×#14519698C2211yescharacteristic, complemented
61C2×#14519698C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64#102×D61C2218yescomplemented
65#16839719C2218yescomplemented
66C2×#14519687C2211yescharacteristic, complemented
67C2×C4×#92418C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C2×#127×C61C2211yescharacteristic
70C2×#125×C61C2211yescharacteristic, complemented
71C61×#490C2218yescomplemented
72C2×#102×C61C2211yescharacteristic
73C2×#102×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic, complemented
76C2×#97×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758224—22no—
79C2×#11758224—24no—
80C2×#11758224—24no—
81C2×#11758224C2314yes—
82C22×Dic122—21no—
83C22×Dic122—21no—
84C22×Dic122C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C2×D4×D61—22no—
91C2×D4×D61—24no—
92C2×D4×D61—24no—
93C2×D4×D61C2314yes—
94C23×Dic61—21no—
95C22×C4×D61—21no—
96C22×C4×D61C2311yescharacteristic
97C2×#11758189—24no—
98C2×#11758189C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C2×C8×D61—24no—
102C2×C8×D61C2314yes—
103#14519777—22no—
104#14519777C2314yescomplemented
105#14519776—28no—
106#14519776—22no—
107#14519776C2314yescomplemented
108#14519773—22no—
109#14519773C2314yes—
110#14519768—22no—
111#14519768C2314yescomplemented
112#14519767—28no—
113#14519765—22no—
114#14519765C2314yes—
115#14519764—22no—
116#14519764C2314yes—
117#14519757—28no—
118#14519755—28no—
119#14519749—28no—
120#14519749—28no—
121#14519745—28no—
122#14519745—28no—
123#14519735—22no—
124#14519735C2314yes—
125#14519734D414yes—
126#14519734C2314yes—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196D411yescharacteristic
135C2×#11758196D411yescharacteristic
136C4⋊C4×D61—22no—
137C4⋊C4×D61C2314yes—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198D411yescharacteristic
144C2×#11758198D411yescharacteristic
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519702C2314yescomplemented
148#14519702C2314yescomplemented
149#14519700C2314yescomplemented
150#14519700C2314yescomplemented
151#14519699C2314yes—
152#14519699C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155#14519698C2314yescomplemented
156#14519698C2314yescomplemented
157#14519697C2314yes—
158#14519697C2314yes—
159#14519687C2314yescomplemented
160C4×#92418C2314yescomplemented
161C8×Dic61C2314yescomplemented
162C22×D4×C61—21no—
163C22×D4×C61—21no—
164C22×D4×C61C2311yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#127×C61—22no—
169#127×C61C2314yes—
170#125×C61—22no—
171#125×C61C2314yescomplemented
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C42×C61C2311yescharacteristic
177#102×C61C2314yes—
178#102×C61C2314yes—
179#102×C61C2314yescomplemented
180#102×C61C2314yescomplemented
181#97×C61C2314yescomplemented
182C24×C61—21no—
183C24×C61—21no—
184C23×D61—21no—
185C23×D61—24no—
186C23×D61—44no—
187C23×D61—82no—
188C23×D61—82no—
189C23×D61C2×D411yescharacteristic
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—24no—
193C2×D4×C61—24no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—82no—
199C2×D4×C61—82no—
200C2×D4×C61C2412yes—
201C2×D4×C61C2412yes—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—44no—
212C2×C22⋊D61—44no—
213C2×C22⋊D61—82no—
214C2×C22⋊D61—82no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—44no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223#11758224—28no—
224#11758224—28no—
225#11758224—48no—
226D4×D61—28no—
227D4×D61—28no—
228D4×D61—48no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—21no—
232C2×D244C2412yes—
233C2×C4×D61—24no—
234C2×C4×D61—82no—
235C2×C4×D61C2×D412yes—
236C2×C4×D61#4114yes—
237C2×C4×D61#4114yes—
238C2×C4×D61C2412yes—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—21no—
242C2×Dic122—24no—
243C2×Dic122—24no—
244C2×Dic122—82no—
245C2×Dic122—82no—
246C2×Dic122C2412yes—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61C2412yes—
250C2×C8×C61C2412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C2412yes—
256C4⋊C4×C61C2412yes—
257C42×C61C2×D412yes—
258C42×C61C2412yes—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198C2×D414yes—
265#11758198C2×D414yes—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61—21no—
269C4⋊Dic61—24no—
270C4⋊Dic61C2412yes—
271C4⋊Dic61C2412yes—
272#11758196—24no—
273#11758196—24no—
274#11758196—24no—
275#11758196C2×D414yes—
276#11758196C2×D414yes—
277C4×Dic61—24no—
278C4×Dic61C2×D412yes—
279C4×Dic61C2412yes—
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418C2412yes—
283C2×#92418C2412yes—
284#11758189—28no—
285C8×D61—28no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61C22×D411yescharacteristic
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—48no—
302C22×D61—84no—
303C22×D61—84no—
304C22×D61—816no—
305C22×D61#12414yes—
306C22×D61C22×D412yes—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—42no—
312D4×C61—42no—
313D4×C61—84no—
314D4×C61—84no—
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×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C61C2×#4112yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—48no—
328C22⋊D61—48no—
329C22⋊D61—84no—
330C22⋊D61—84no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—48no—
340C2×Dic61#12414yes—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344D244—22no—
345D244—22no—
346D244—42no—
347C4×D61—84no—
348C4×D61#12418yes—
349C4×D61C2×#4114yes—
350C4×D61C2×#4114yes—
351Dic122—22no—
352Dic122—22no—
353Dic122—42no—
354Dic122—84no—
355Dic122—84no—
356C8×C61—22no—
357C8×C61—22no—
358#92418—22no—
359#92418—22no—
360C2×#3136—611nomaximal, Sylow
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—84no—
368C22×C61—84no—
369C22×C61C2×#12412yes—
370C22×C61#57612yes—
371C22×C61#57712yes—
372C22×C61C23×D411yescharacteristic
373C2×D61—28no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—816no—
380C2×D61—84no—
381C2×D61C2×#12414yes—
382C4×C61—22no—
383C4×C61—22no—
384C4×C61—42no—
385C4×C61—42no—
386C4×C61C2×#12412yes—
387C4×C61C22×#4111yescharacteristic
388C4×C61C22×#4111yescharacteristic
389Dic61—22no—
390Dic61—22no—
391Dic61—42no—
392Dic61—42no—
393Dic61—42no—
394Dic61C2×#12414yes—
395C2×#544—611no—
396C2×#535—611no—
397#3136—6116no—
398C2×#490—611no—
399C2×#490D6111yescharacteristic, complemented
400C2×#489—611no—
401C2×#489—611no—
402C2×#488—611no—
403C2×#488—611no—
404C2×#486—611no—
405C2×#486—611no—
406C2×#417—611no—
407C2×#418—611no—
408C2×#416—611no—
409C22×#102—611no—
410C2×#405—611no—
411C2×C61—82no—
412C2×C61—82no—
413C2×C61#313614yescomplemented
414C2×C61C22×#12411yescharacteristic
415C2×C61C2×#57611yescharacteristic
416C2×C61C2×#57711yescharacteristic
417D61—24no—
418D61—82no—
419C22×#41—611no—
420C23×D4—611no—
421C22×M16—611no—
422C23×C8—611no—
423#544—618no—
424#544—1224no—
425#535—618no—
426#535—1224no—
427C2×C4⋊Q8—611no—
428C2×C4⋊Q8—611no—
429C2×C4⋊Q8—1221no—
430C2×#127—611no—
431C2×#127C2×D6111yescharacteristic
432C2×#125—611no—
433C2×#125—1221no—
434C2×#125C2×D6111yescharacteristic, complemented
435C2×#124—611no—
436C2×#124—611no—
437C2×C22⋊Q8—1221no—
438C2×C22⋊Q8—1221no—
439C2×#121—1221no—
440C2×#121—1221no—
441C2×#120—1221no—
442C2×#120—1221no—
443C2×#117—611no—
444C2×#117—611no—
445C22×C4⋊C4—611no—
446#490—618no—
447#490C2×D6118yescomplemented
448#489—618no—
449#489—618no—
450#488—618no—
451#488—618no—
452#486—618no—
453#486—618no—
454#418—618no—
455#417—618no—
456#416—618no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#102—611no—
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—618no—
470C2×#102C2×D6111yescharacteristic
471C2×#102C2×D6111yescharacteristic
472C2×#102C2×D6111yescharacteristic, complemented
473C2×#102C2×D6111yescharacteristic, complemented
474#405—618no—
475C2×#97—611no—
476C2×#97C2×D6111yescharacteristic, complemented
477C2×C4×C8—611no—
478C2×C4×C8—611no—
479C61C2×#313611yescharacteristic, complemented, Sylow
480C25—1221no—
481C2×#41—614no—
482C2×#41—1222no—
483C2×#41—1224no—
484C2×#41—1224no—
485C22×Q8—611no—
486C22×Q8—1221no—
487C22×Q8—1221no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—614no—
491C22×D4—611no—
492C22×D4—1224no—
493C22×D4—1224no—
494C22×D4—1222no—
495C22×D4—1221no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4C22×D6111yescharacteristic
500C22×D4C22×D6111yescharacteristic
501C23×C4—611no—
502C23×C4—1221no—
503C23×C4—1221no—
504C2×M16—614no—
505C2×M16—1224no—
506C22×C8—611no—
507C22×C8—611no—
508C22×C8—614no—
509C22×C8—1224no—
510C22×C8C22×D6111yescharacteristic
511C22×C8C22×D6111yescharacteristic
512C4⋊Q8—614no—
513C4⋊Q8—614no—
514C4⋊Q8—1222no—
515C4⋊Q8—1228no—
516C4⋊Q8—1222no—
517#127—22no—
518#127—614no—
519#127—1222no—
520#127C22×D6114yes—
521#125—22no—
522#125—614no—
523#125—1222no—
524#125—1228no—
525#125C22×D6114yescomplemented
526#124—614no—
527#124—614no—
528#124—1222no—
529#124—1222no—
530C22⋊Q8—1228no—
531C22⋊Q8—1228no—
532#121—1228no—
533#121—1228no—
534#120—1228no—
535#120—1228no—
536#117—614no—
537#117—614no—
538#117—614no—
539#117—1222no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—614no—
547C2×C4⋊C4—1222no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C22⋊C4—611no—
556C2×C22⋊C4—611no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C42—611no—
563C2×C42—1221no—
564C2×C42C22×D6111yescharacteristic
565#103—614no—
566#103—614no—
567#103—614no—
568#103—614no—
569#102—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574#102—614no—
575#102—614no—
576#102—614no—
577#102C22×D6114yes—
578#102C22×D6114yes—
579#102C22×D6114yescomplemented
580#102C22×D6114yescomplemented
581#97—614no—
582#97C22×D6114yescomplemented
583C4×C8—614no—
584C4×C8—614no—
585C24—21no—
586C24—21no—
587C24—611no—
588C24—1224no—
589C24—1221no—
590C24—4882no—
591C24—4882no—
592C24—2444no—
593#41—1228no—
594#41—1228no—
595#41—2448no—
596C2×Q8—612no—
597C2×Q8—1224no—
598C2×Q8—1224no—
599C2×Q8—1221no—
600C2×Q8—1222no—
601C2×Q8—1222no—
602C2×Q8—4882no—
603C2×Q8—4882no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—82no—
613C2×D4—82no—
614C2×D4—612no—
615C2×D4—1228no—
616C2×D4—1228no—
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—2448no—
627C2×D4—2444no—
628C2×D4—2444no—
629C2×D4C23×D6112yes—
630C2×D4C23×D6112yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—611no—
634C22×C4—612no—
635C22×C4—614no—
636C22×C4—614no—
637C22×C4—612no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—1224no—
641C22×C4—1224no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—4882no—
646C22×C4—2444no—
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650M16—1228no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—612no—
654C2×C8—612no—
655C2×C8—1228no—
656C2×C8—1222no—
657C2×C8—1222no—
658C2×C8C23×D6112yes—
659C2×C8C23×D6112yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—614no—
665C4⋊C4—614no—
666C4⋊C4—612no—
667C4⋊C4—612no—
668C4⋊C4—1224no—
669C4⋊C4—1224no—
670C4⋊C4—1224no—
671C4⋊C4—1224no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1224no—
675C4⋊C4C23×D6112yes—
676C4⋊C4C23×D6112yes—
677C22⋊C4—614no—
678C22⋊C4—614no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C42—612no—
685C42—612no—
686C42—1224no—
687C42D4×D6112yes—
688C42C23×D6112yes—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—614no—
698C23—612no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—4884no—
703C23—4884no—
704C23—48816no—
705C23—2448no—
706C23—2442no—
707C23—2442no—
708C23—2442no—
709C23C2×D4×D6111yescharacteristic
710Q8—1222no—
711Q8—1222no—
712Q8—4884no—
713Q8—4884no—
714Q8—2442no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—84no—
723D4—1222no—
724D4—1222no—
725D4—4884no—
726D4—4884no—
727D4—2448no—
728D4—2448no—
729D4—2442no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—614no—
737C2×C4—612no—
738C2×C4—618no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—4884no—
749C2×C4—2448no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4C2×D4×D6112yes—
754C2×C4C2×D4×D6112yes—
755C2×C4C2×D4×D6111yescharacteristic
756C2×C4#41×D6112yes—
757C2×C4#41×D6112yes—
758C2×C4C24×D6111yescharacteristic
759C8—22no—
760C8—22no—
761C8—1222no—
762C8—1222no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—614no—
772C22—1228no—
773C22—1222no—
774C22—1222no—
775C22—48816no—
776C22—4884no—
777C22—2442no—
778C22—2442no—
779C22—2442no—
780C22#124×D6112yes—
781C22#1684056612yes—
782C22#1684057212yes—
783C22C22×D4×D6111yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—614no—
789C4—1222no—
790C4—1222no—
791C4—2442no—
792C4—2442no—
793C4—2442no—
794C4#124×D6112yes—
795C4C2×#41×D6111yescharacteristic
796C4C2×#41×D6111yescharacteristic
797C2—82no—
798C2—82no—
799C2—1224no—
800C2—4882no—
801C2#2145617414yesdirect product factor
802C2C2×#124×D6111yescharacteristic
803C2C2×#1684056611yescharacteristic
804C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#490C2
socleC23×C61C22×D4
prime radicalC2×#16840325C2
hypercenterC2×#490D61
hypocenterC61C2×#3136
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#16840392C2semidirect
3. #21456174C2direct (N × H)
4. C2×#16840125C2semidirect
5. C2×#16840122C2semidirect
6. C2×#16840120C2semidirect
7. C2×#16840119C2semidirect
8. C2×#16840115C2semidirect
9. C2×#16840108C2semidirect
10. C2×#16840107C2semidirect
11. C2×#16839760C2semidirect
12. C2×#16839765C2semidirect
13. C2×#16839755C2semidirect
14. C2×#102×D61C2semidirect
15. C2×#16839719C2semidirect
16. C2×C61×#490C2semidirect
22. #16840392C22semidirect
25. C2×#14519777C22semidirect
27. C2×#14519776C22semidirect
29. C2×#14519768C22semidirect
42. #16840125C22semidirect
43. #16840122C22semidirect
44. #16840120C22semidirect
45. #16840119C22semidirect
46. #16840115C22semidirect
47. #16840108C22semidirect
48. #16840107C22semidirect
49. #16839765C22semidirect
50. #16839760C22semidirect
51. #16839755C22semidirect
52. C2×#14519702C22semidirect
53. C2×#14519702C22semidirect
54. C2×#14519700C22semidirect
55. C2×#14519700C22semidirect
60. C2×#14519698C22semidirect
61. C2×#14519698C22semidirect
64. #102×D61C22semidirect
65. #16839719C22semidirect
66. C2×#14519687C22semidirect
67. C2×C4×#92418C22semidirect
68. C2×C8×Dic61C22semidirect
70. C2×#125×C61C22semidirect
71. C61×#490C22semidirect
74. C2×#102×C61C22semidirect
75. C2×#102×C61C22semidirect
76. C2×#97×C61C22semidirect
104. #14519777C23semidirect
107. #14519776C23semidirect
111. #14519768C23semidirect
147. #14519702C23semidirect
148. #14519702C23semidirect
149. #14519700C23semidirect
150. #14519700C23semidirect
155. #14519698C23semidirect
156. #14519698C23semidirect
159. #14519687C23semidirect
160. C4×#92418C23semidirect
161. C8×Dic61C23semidirect
171. #125×C61C23semidirect
179. #102×C61C23semidirect
180. #102×C61C23semidirect
181. #97×C61C23semidirect
399. C2×#490D61semidirect
413. C2×C61#3136semidirect
434. C2×#125C2×D61semidirect
447. #490C2×D61semidirect
472. C2×#102C2×D61semidirect
473. C2×#102C2×D61semidirect
476. C2×#97C2×D61semidirect
479. C61C2×#3136semidirect
525. #125C22×D61semidirect
579. #102C22×D61semidirect
580. #102C22×D61semidirect
582. #97C22×D61semidirect
801. C2#21456174direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403922
C2×#168403252
#214561742
C2×#168401252
C2×#168401222
C2×#168401202
C2×#168401192
C2×#168401152
C2×#168401082
C2×#168401072
C2×#168397602
C2×#168397652
C2×#168397552
C2×#102×D612
C2×#168397192
C2×C61×#4902
C2×#313661