Finite Group Databasebeta

← C2×#21460357 #30587375

Subgroups — C2×#21460357 #30587375

Order 15616.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460357C2132yesmaximal, direct product factor
2C2×#16840512C212yesmaximal, complemented
3C2×#16840506C212yesmaximal, complemented
4C2×#16840471C212yesmaximal, complemented
5C2×#16840464C212yesmaximal, complemented
6C2×#16840462C212yesmaximal, complemented
7C2×#16840412C212yesmaximal, complemented
8C2×#16840411C214yesmaximal, complemented
9C2×#16840389C212yesmaximal, complemented
10C2×#16840366C212yesmaximal, complemented
11C2×#16840357C212yesmaximal, complemented
12C2×#16840354C214yesmaximal, complemented
13C2×#16840339C212yesmaximal, complemented
14C2×#16840296C211yesmaximal, characteristic, complemented
15C22×#14519769C211yesmaximal, characteristic, complemented
16C2×C61×#532C211yesmaximal, characteristic, complemented
17C22×#11758224C2214yes—
18#16840512C22132yescomplemented
19#16840506C22132yescomplemented
20#16840471C22132yescomplemented
21#16840464C22132yescomplemented
22#16840462C22132yescomplemented
23#16840412C22132yescomplemented
24#16840411C22164yescomplemented
25#16840389C22132yescomplemented
26#16840366C22132yescomplemented
27#16840357C22132yescomplemented
28#16840354C22164yescomplemented
29#16840339C22132yescomplemented
30C2×#14519776C2212yes—
31C2×#14519775C2214yes—
32#16840296C22116yescomplemented
33C2×#14519771C2212yes—
34C2×#14519770C2214yes—
35C2×#14519770C2214yes—
36C2×#14519769C2212yes—
37C2×#14519769C2212yes—
38C2×#14519769C2212yes—
39C2×#14519769C2212yes—
40C2×#14519769C2211yescharacteristic
41C2×#14519769C22116yescomplemented
42C2×#14519768C2212yes—
43C2×#14519767C2214yes—
44C2×#14519765C2211yescharacteristic
45C2×#14519761C2214yes—
46C2×#14519760C2212yes—
47C2×#14519760C2214yes—
48C2×#14519759C2214yes—
49C2×#14519758C2214yes—
50C2×#14519758C2214yes—
51C2×#14519758C2214yes—
52C2×#14519756C2214yes—
53C2×#14519756C2211yescharacteristic
54C2×#14519755C2214yes—
55C2×#14519754C2214yes—
56C2×#14519754C2214yes—
57C2×#14519754C2214yes—
58C2×#14519753C2214yes—
59C2×#14519751C2211yescharacteristic
60C2×#14519750C2214yes—
61C2×#14519749C2214yes—
62C2×#14519749C2214yes—
63C2×#14519749C2214yes—
64C2×#14519748C2212yes—
65C2×#14519748C2212yes—
66C2×C4×Dic122C2211yescharacteristic
67C2×C4×D244C2211yescharacteristic
68C2×D4×Dic61C2214yes—
69C2×D4×Dic61C2212yes—
70C2×D4×Dic61C2212yes—
71C2×C4×C22⋊D61C2214yes—
72C2×C4×C22⋊D61C2212yes—
73C2×#14519735C2212yes—
74C2×#14519734C2212yes—
75C22×C4⋊Dic61C2211yescharacteristic
76C22×C4⋊Dic61C2211yescharacteristic
77C22×#11758196C2212yes—
78C22×#11758196C2214yes—
79C22×#11758196C2212yes—
80C2×C4⋊C4×D61C2212yes—
81C22×#41×C61C2212yes—
82C61×#532C22116yescomplemented
83C2×C4⋊Q8×C61C2211yescharacteristic
84C2×#127×C61C2211yescharacteristic
85C2×#124×C61C2212yes—
86C2×#121×C61C2212yes—
87C2×#121×C61C2212yes—
88C2×C4×D4×C61C2212yes—
89C2×C4×D4×C61C2212yes—
90C22×C42×C61C2211yescharacteristic
91C2×#11758224—416no—
92C2×#11758224C23132yes—
93C22×Dic122C2311yescharacteristic
94C22×Dic122C2314yes—
95C22×D244C2311yescharacteristic
96C22×C22⋊D61C2312yes—
97C22×C22⋊D61C2314yes—
98C22×C22⋊D61C2314yes—
99C23×Dic61C2312yes—
100C23×Dic61C2312yes—
101C23×Dic61C2314yes—
102C23×Dic61C2314yes—
103C22×C4×D61C2312yes—
104C22×C4×D61C2314yes—
105#14519776C23116yes—
106#14519775C23132yes—
107#14519771C23116yes—
108#14519770C23132yes—
109#14519770C23132yes—
110#14519769C23116yes—
111#14519769C23116yes—
112#14519769C2318yes—
113#14519769C23116yes—
114#14519769C23116yes—
115#14519768C23116yes—
116#14519767C23132yes—
117#14519765C2318yes—
118#14519761C23132yes—
119#14519760C23132yes—
120#14519760C23116yes—
121#14519759C23132yes—
122#14519758C23132yes—
123#14519758C23132yes—
124#14519758C23132yes—
125#14519756C23132yes—
126#14519756C2318yes—
127#14519755C23132yes—
128#14519754C23132yes—
129#14519754C23132yes—
130#14519754C23132yes—
131#14519753C23132yes—
132#14519751C2318yes—
133#14519750C23132yes—
134#14519749C23132yes—
135#14519749C23132yes—
136#14519749C23132yes—
137#14519748C23116yes—
138#14519748C23116yes—
139C4×Dic122C2318yes—
140C4×D244C2318yes—
141D4×Dic61C23116yes—
142D4×Dic61C23132yes—
143D4×Dic61C23116yes—
144C4×C22⋊D61C23132yes—
145C4×C22⋊D61C23116yes—
146#14519735C23116yes—
147#14519734C23116yes—
148C2×C4⋊Dic61C2318yes—
149C2×C4⋊Dic61C2312yes—
150C2×C4⋊Dic61C2312yes—
151C2×C4⋊Dic61C2312yes—
152C2×C4⋊Dic61C2312yes—
153C2×C4⋊Dic61C2318yes—
154C2×C4⋊Dic61C2314yes—
155C2×C4⋊Dic61C2311yescharacteristic
156C2×C4⋊Dic61C2311yescharacteristic
157C2×#11758196C2314yes—
158C2×#11758196C2314yes—
159C2×#11758196C2312yes—
160C2×#11758196C23132yes—
161C2×#11758196C2314yes—
162C2×#11758196C2314yes—
163C2×#11758196C2314yes—
164C2×#11758196C2314yes—
165C2×#11758196C2314yes—
166C2×#11758196C23116yes—
167C2×#11758196C23116yes—
168C2×#11758196C2312yes—
169C2×#11758196C2312yes—
170C2×#11758196C2312yes—
171C4⋊C4×D61C23116yes—
172C2×C22⋊Dic61C2312yes—
173C2×C22⋊Dic61C2314yes—
174C2×C22⋊Dic61C2314yes—
175C2×C22⋊Dic61C2314yes—
176C2×C22⋊Dic61C2314yes—
177C2×#11758198C2312yes—
178C2×#11758198C2312yes—
179C2×#11758198C2314yes—
180C2×#11758198C2312yes—
181C2×#11758198C2312yes—
182C2×C4×Dic61C2312yes—
183C2×C4×Dic61C2314yes—
184C2×#41×C61—48no—
185C2×#41×C61C23116yes—
186C22×Q8×C61C2312yes—
187C22×D4×C61C2312yes—
188C22×D4×C61C2314yes—
189C22×D4×C61C2312yes—
190C22×D4×C61C2312yes—
191C23×C4×C61C2311yescharacteristic
192C23×C4×C61C2311yescharacteristic
193C23×C4×C61C2311yescharacteristic
194C23×C4×C61C2314yes—
195C4⋊Q8×C61C2318yes—
196#127×C61C2318yes—
197#124×C61C23116yes—
198#121×C61C23116yes—
199#121×C61C23116yes—
200C4×D4×C61C23116yes—
201C4×D4×C61C23116yes—
202C2×C4⋊C4×C61C2312yes—
203C2×C4⋊C4×C61C2312yes—
204C2×C22⋊C4×C61C2314yes—
205C2×C22⋊C4×C61C2314yes—
206C2×C42×C61C2311yescharacteristic
207C2×C42×C61C2318yes—
208C2×C42×C61C2311yescharacteristic
209C2×C42×C61C2311yescharacteristic
210C2×C42×C61C2311yescharacteristic
211C24×C61C2414yes—
212C24×C61C2411yescharacteristic
213C23×D61C2412yes—
214#41×C61—432no—
215C2×Q8×C61—44no—
216C2×Q8×C61C2418yes—
217C2×D4×C61—216no—
218C2×D4×C61—28no—
219C2×D4×C61—44no—
220C2×D4×C61—44no—
221C2×D4×C61C24116yes—
222C2×D4×C61C2418yes—
223C2×D4×C61C2418yes—
224C2×D4×C61C2418yes—
225C22×C4×C61—24no—
226C22×C4×C61—24no—
227C22×C4×C61—42no—
228C22×C4×C61—48no—
229C22×C4×C61C2414yes—
230C22×C4×C61C2411yescharacteristic
231C22×C4×C61C2411yescharacteristic
232C22×C4×C61C2411yescharacteristic
233C22×C4×C61C2414yes—
234C22×C4×C61C2411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C22×C4×C61C2414yes—
237C22×C4×C61C2414yes—
238C22×C4×C61C24116yes—
239C22×C4×C61C2411yescharacteristic
240C2×C22⋊D61—28no—
241C2×C22⋊D61—48no—
242C2×C22⋊D61—48no—
243C2×C22⋊D61C2418yes—
244C2×C22⋊D61C24116yes—
245C2×C22⋊D61C24116yes—
246C22×Dic61—28no—
247C22×Dic61—48no—
248C22×Dic61—44no—
249C22×Dic61—48no—
250C22×Dic61C2414yes—
251C22×Dic61C2412yes—
252C22×Dic61C2412yes—
253C22×Dic61C2414yes—
254C22×Dic61C2412yes—
255C22×Dic61C2418yes—
256C22×Dic61C24116yes—
257C22×Dic61C2418yes—
258C22×Dic61C24116yes—
259#11758224—464no—
260C2×D244—42no—
261C2×D244C2414yes—
262C2×C4×D61—28no—
263C2×C4×D61—48no—
264C2×C4×D61C2418yes—
265C2×C4×D61C24116yes—
266C2×Dic122—42no—
267C2×Dic122—48no—
268C2×Dic122C24116yes—
269C2×Dic122C2414yes—
270C4⋊C4×C61C2418yes—
271C4⋊C4×C61C2418yes—
272C22⋊C4×C61C24116yes—
273C22⋊C4×C61C24116yes—
274C42×C61C2414yes—
275C42×C61C2414yes—
276C42×C61C2414yes—
277C42×C61C2414yes—
278C22⋊Dic61C2418yes—
279C22⋊Dic61C24116yes—
280C22⋊Dic61C24116yes—
281C22⋊Dic61C24116yes—
282C22⋊Dic61C24116yes—
283#11758198C2418yes—
284#11758198C2418yes—
285#11758198C24116yes—
286#11758198C2418yes—
287#11758198C2418yes—
288C4⋊Dic61C2418yes—
289C4⋊Dic61C2418yes—
290C4⋊Dic61C2418yes—
291C4⋊Dic61C2418yes—
292C4⋊Dic61C24116yes—
293C4⋊Dic61C2414yes—
294C4⋊Dic61C2414yes—
295#11758196C24116yes—
296#11758196C24116yes—
297#11758196C2418yes—
298#11758196C24116yes—
299#11758196C24116yes—
300#11758196C24116yes—
301#11758196C24116yes—
302#11758196C24116yes—
303#11758196C2418yes—
304#11758196C2418yes—
305#11758196C2418yes—
306C4×Dic61C2418yes—
307C4×Dic61C24116yes—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—28no—
311C23×C61—28no—
312C23×C61—28no—
313C23×C61H(5,𝔽2)14yes—
314C23×C61C2518yes—
315C23×C61C2512yes—
316C23×C61C2511yescharacteristic
317C22×D61—24no—
318C22×D61—24no—
319C22×D61—24no—
320C22×D61C2514yes—
321Q8×C61—48no—
322D4×C61—232no—
323D4×C61—216no—
324D4×C61—48no—
325D4×C61—48no—
326C2×C4×C61—28no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—28no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—28no—
334C2×C4×C61—44no—
335C2×C4×C61—416no—
336C2×C4×C612−1+414yes—
337C2×C4×C61C2518yes—
338C2×C4×C61C2512yes—
339C2×C4×C61C2512yes—
340C2×C4×C61C2512yes—
341C2×C4×C61C2512yes—
342C2×C4×C61C2512yes—
343C2×C4×C61C2512yes—
344C22⋊D61—216no—
345C22⋊D61—416no—
346C22⋊D61—416no—
347C2×Dic61—24no—
348C2×Dic61—28no—
349C2×Dic61—216no—
350C2×Dic61—24no—
351C2×Dic61—24no—
352C2×Dic61—28no—
353C2×Dic61—416no—
354C2×Dic61—416no—
355C2×Dic61—48no—
356C2×Dic61C2514yes—
357C2×Dic61C2518yes—
358C2×Dic61C2514yes—
359C2×Dic61C2514yes—
360C2×Dic61C2518yes—
361D244—44no—
362C4×D61—216no—
363C4×D61—416no—
364Dic122—44no—
365Dic122—416no—
366C2×#3559—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—28no—
370C22×C61—28no—
371C22×C61—28no—
372C22×C61—28no—
373C22×C61—416no—
374C22×C61C2×H(5,𝔽2)14yes—
375C22×C61C2×H(5,𝔽2)12yes—
376C22×C61C2×2−1+412yes—
377C22×C61#58512yes—
378C22×C61C2611yescharacteristic
379C2×D61—24no—
380C2×D61—24no—
381C2×D61—24no—
382C2×D61—48no—
383C4×C61—28no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61C2×2−1+414yes—
390Dic61—24no—
391Dic61—28no—
392Dic61—24no—
393Dic61—24no—
394Dic61—28no—
395#3559—6132no—
396C2×#563—612no—
397C2×#562—612no—
398C2×#554—612no—
399C2×#553—612no—
400C2×#553—612no—
401C2×#547—614no—
402C2×#547—612no—
403C2×#544—612no—
404C2×#540—612no—
405C2×#539—612no—
406C2×#539—614no—
407C2×#537—612no—
408C2×#532D6111yescharacteristic, complemented
409C2×#529—611no—
410C22×#125—611no—
411C2×C61—24no—
412C2×C61—48no—
413C2×C61#355914yescomplemented
414C2×C61C22×H(5,𝔽2)11yescharacteristic
415C2×C61C22×2−1+411yescharacteristic
416C2×C61C2×#58511yescharacteristic
417D61—44no—
418C22×#41—614no—
419C22×#41C2×D6112yes—
420#563—6132no—
421#562—6132no—
422#554—6132no—
423#553—6132no—
424#553—6132no—
425#547—6164no—
426#547—6132no—
427#544—6132no—
428#540—6132no—
429#539—6132no—
430#539—6164no—
431#537—6132no—
432#532C2×D61116yescomplemented
433C2×C4⋊Q8—614no—
434C2×C4⋊Q8—612no—
435C2×C4⋊Q8C2×D6111yescharacteristic
436C2×#127C2×D6111yescharacteristic
437#529—6116no—
438C2×#126—614no—
439C2×#126—614no—
440C2×#126—612no—
441C2×#125—614no—
442C2×#125—612no—
443C2×#125—612no—
444C2×#125—612no—
445C2×#125—612no—
446C2×#125—612no—
447C2×#125—611no—
448C2×#125—6116no—
449C2×#124—611no—
450C2×#124C2×D6112yes—
451C2×#123—614no—
452C2×#123—614no—
453C2×#123—614no—
454C2×#123—612no—
455C2×#123—614no—
456C2×#123—614no—
457C2×#123—614no—
458C2×C22⋊Q8—614no—
459C2×C22⋊Q8—611no—
460C2×C22⋊Q8—614no—
461C2×C22⋊Q8—614no—
462C2×C22⋊Q8—614no—
463C2×C22⋊Q8—614no—
464C2×C22⋊Q8—614no—
465C2×#121—612no—
466C2×#121—612no—
467C2×#121—614no—
468C2×#121—614no—
469C2×#121—614no—
470C2×#121—611no—
471C2×#121—614no—
472C2×#121C2×D6112yes—
473C2×#121C2×D6112yes—
474C2×C4×Q8—611no—
475C2×C4×D4—614no—
476C2×C4×D4—612no—
477C2×C4×D4—612no—
478C2×C4×D4—612no—
479C2×C4×D4—614no—
480C2×C4×D4—611no—
481C2×C4×D4C2×D6112yes—
482C2×C4×D4C2×D6112yes—
483C2×#117—612no—
484C2×#117—612no—
485C22×C4⋊C4—612no—
486C22×C4⋊C4—612no—
487C22×C4⋊C4—614no—
488C22×C4⋊C4—611no—
489C22×C4⋊C4—611no—
490C22×C4⋊C4—612no—
491C22×C42C2×D6111yescharacteristic
492C61C2×#355911yescharacteristic, complemented, Sylow
493C2×#41—48no—
494C2×#41—6132no—
495C2×#41—24416no—
496C2×#41C22×D61116yes—
497C22×Q8—611no—
498C22×Q8—614no—
499C22×Q8C22×D6112yes—
500C22×D4—612no—
501C22×D4—614no—
502C22×D4—614no—
503C22×D4—611no—
504C22×D4C22×D6112yes—
505C22×D4C22×D6114yes—
506C22×D4C22×D6112yes—
507C22×D4C22×D6112yes—
508C23×C4—612no—
509C23×C4—612no—
510C23×C4—614no—
511C23×C4—614no—
512C23×C4—612no—
513C23×C4—614no—
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C23×C4C22×D6111yescharacteristic
517C23×C4C22×D6114yes—
518C4⋊Q8—6132no—
519C4⋊Q8—6116no—
520C4⋊Q8C22×D6118yes—
521#127C22×D6118yes—
522#126—6132no—
523#126—6132no—
524#126—6116no—
525#125—6132no—
526#125—6116no—
527#125—6116no—
528#125—6116no—
529#125—6116no—
530#125—6116no—
531#125—618no—
532#124—618no—
533#124C22×D61116yes—
534#123—6132no—
535#123—6132no—
536#123—6132no—
537#123—6116no—
538#123—6132no—
539#123—6132no—
540#123—6132no—
541C22⋊Q8—6132no—
542C22⋊Q8—618no—
543C22⋊Q8—6132no—
544C22⋊Q8—6132no—
545C22⋊Q8—6132no—
546C22⋊Q8—6132no—
547C22⋊Q8—6132no—
548#121—6132no—
549#121—6132no—
550#121—6116no—
551#121—6132no—
552#121—6116no—
553#121—618no—
554#121—6132no—
555#121C22×D61116yes—
556#121C22×D61116yes—
557C4×Q8—618no—
558C4×D4—6132no—
559C4×D4—6116no—
560C4×D4—6116no—
561C4×D4—6116no—
562C4×D4—6132no—
563C4×D4—618no—
564C4×D4C22×D61116yes—
565C4×D4C22×D61116yes—
566#117—6116no—
567#117—6116no—
568C2×C4⋊C4—612no—
569C2×C4⋊C4—614no—
570C2×C4⋊C4—612no—
571C2×C4⋊C4—612no—
572C2×C4⋊C4—614no—
573C2×C4⋊C4—614no—
574C2×C4⋊C4—614no—
575C2×C4⋊C4—614no—
576C2×C4⋊C4—612no—
577C2×C4⋊C4—614no—
578C2×C4⋊C4—614no—
579C2×C4⋊C4—612no—
580C2×C4⋊C4—6116no—
581C2×C4⋊C4—6116no—
582C2×C4⋊C4—618no—
583C2×C4⋊C4—618no—
584C2×C4⋊C4—6132no—
585C2×C4⋊C4—612no—
586C2×C4⋊C4—612no—
587C2×C4⋊C4—614no—
588C2×C4⋊C4—612no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—6116no—
592C2×C4⋊C4C22×D6112yes—
593C2×C4⋊C4C22×D6112yes—
594C2×C22⋊C4—612no—
595C2×C22⋊C4—614no—
596C2×C22⋊C4—614no—
597C2×C22⋊C4—614no—
598C2×C22⋊C4—614no—
599C2×C22⋊C4—612no—
600C2×C22⋊C4—614no—
601C2×C22⋊C4—612no—
602C2×C22⋊C4—612no—
603C2×C22⋊C4—612no—
604C2×C22⋊C4C22×D6114yes—
605C2×C22⋊C4C22×D6114yes—
606C2×C42—612no—
607C2×C42—614no—
608C2×C42C22×D6111yescharacteristic
609C2×C42C22×D6111yescharacteristic
610C2×C42C22×D6111yescharacteristic
611C2×C42C22×D6111yescharacteristic
612C2×C42C22×D6118yes—
613C24—612no—
614C24C23×D6114yes—
615C24C23×D6111yescharacteristic
616#41—432no—
617#41—24464no—
618C2×Q8—44no—
619C2×Q8—614no—
620C2×Q8—6116no—
621C2×Q8—2442no—
622C2×Q8—2448no—
623C2×Q8C23×D6118yes—
624C2×D4—216no—
625C2×D4—28no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—618no—
629C2×D4—6116no—
630C2×D4—6116no—
631C2×D4—614no—
632C2×D4—1228no—
633C2×D4—2442no—
634C2×D4—2448no—
635C2×D4—2448no—
636C2×D4C23×D6118yes—
637C2×D4C23×D61116yes—
638C2×D4C23×D6118yes—
639C2×D4C23×D6118yes—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—48no—
643C22×C4—42no—
644C22×C4—618no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—614no—
648C22×C4—612no—
649C22×C4—614no—
650C22×C4—618no—
651C22×C4—6116no—
652C22×C4—6116no—
653C22×C4—618no—
654C22×C4—6116no—
655C22×C4—1228no—
656C22×C4—1228no—
657C22×C4—2448no—
658C22×C4—2448no—
659C22×C4—2444no—
660C22×C4—2448no—
661C22×C4C23×D6114yes—
662C22×C4C23×D6114yes—
663C22×C4C23×D6114yes—
664C22×C4C23×D6111yescharacteristic
665C22×C4C23×D6111yescharacteristic
666C22×C4C23×D6111yescharacteristic
667C22×C4C23×D6111yescharacteristic
668C22×C4C23×D6111yescharacteristic
669C22×C4C23×D6114yes—
670C22×C4C23×D61116yes—
671C22×C4C23×D6111yescharacteristic
672C4⋊C4—6116no—
673C4⋊C4—618no—
674C4⋊C4—618no—
675C4⋊C4—6116no—
676C4⋊C4—6116no—
677C4⋊C4—6116no—
678C4⋊C4—6116no—
679C4⋊C4—6116no—
680C4⋊C4—6116no—
681C4⋊C4—618no—
682C4⋊C4—618no—
683C4⋊C4—618no—
684C4⋊C4—618no—
685C4⋊C4—618no—
686C4⋊C4—618no—
687C4⋊C4—6116no—
688C4⋊C4—614no—
689C4⋊C4—614no—
690C4⋊C4C23×D6118yes—
691C4⋊C4C23×D6118yes—
692C22⋊C4—618no—
693C22⋊C4—6116no—
694C22⋊C4—6116no—
695C22⋊C4—6116no—
696C22⋊C4—6116no—
697C22⋊C4—618no—
698C22⋊C4—6116no—
699C22⋊C4—618no—
700C22⋊C4—618no—
701C22⋊C4—618no—
702C22⋊C4C23×D61116yes—
703C22⋊C4C23×D61116yes—
704C42—618no—
705C42—6116no—
706C42C23×D6114yes—
707C42C23×D6114yes—
708C42C23×D6114yes—
709C42C23×D6114yes—
710C23—22no—
711C23—22no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—614no—
716C23—1224no—
717C23—1224no—
718C23—1224no—
719C23#1451982214yes—
720C23C24×D6118yes—
721C23C24×D6112yes—
722C23C24×D6111yescharacteristic
723Q8—48no—
724Q8—2444no—
725Q8—24416no—
726D4—232no—
727D4—216no—
728D4—48no—
729D4—48no—
730D4—12216no—
731D4—2444no—
732D4—24416no—
733D4—24416no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—28no—
742C2×C4—44no—
743C2×C4—416no—
744C2×C4—614no—
745C2×C4—614no—
746C2×C4—618no—
747C2×C4—614no—
748C2×C4—618no—
749C2×C4—1228no—
750C2×C4—12216no—
751C2×C4—1224no—
752C2×C4—1224no—
753C2×C4—1228no—
754C2×C4—1224no—
755C2×C4—12216no—
756C2×C4—24416no—
757C2×C4—2448no—
758C2×C4—24416no—
759C2×C4—24416no—
760C2×C4#1451982414yes—
761C2×C4C24×D6118yes—
762C2×C4C24×D6112yes—
763C2×C4C24×D6112yes—
764C2×C4C24×D6112yes—
765C2×C4C24×D6112yes—
766C2×C4C24×D6112yes—
767C2×C4C24×D6112yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—28no—
772C22—28no—
773C22—28no—
774C22—416no—
775C22—1224no—
776C22—1224no—
777C22—1224no—
778C22—2448no—
779C22C2×#1451982214yes—
780C22C2×#1451982212yes—
781C22C2×#1451982412yes—
782C22#1684059812yes—
783C22C25×D6111yescharacteristic
784C4—22no—
785C4—22no—
786C4—28no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—1228no—
791C4—1224no—
792C4—1224no—
793C4—1228no—
794C4—1224no—
795C4C2×#1451982414yes—
796C2—24no—
797C2—48no—
798C2—2444no—
799C2#2146035714yesdirect product factor
800C2C22×#1451982211yescharacteristic
801C2C22×#1451982411yescharacteristic
802C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#532C2
socleC23×C61C25
hypercenterC2×#532D61
hypocenterC61C2×#3559
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #21460357C2direct (N × H)
2. C2×#16840512C2semidirect
3. C2×#16840506C2semidirect
4. C2×#16840471C2semidirect
5. C2×#16840464C2semidirect
6. C2×#16840462C2semidirect
7. C2×#16840412C2semidirect
8. C2×#16840411C2semidirect
9. C2×#16840389C2semidirect
10. C2×#16840366C2semidirect
11. C2×#16840357C2semidirect
12. C2×#16840354C2semidirect
13. C2×#16840339C2semidirect
14. C2×#16840296C2semidirect
15. C22×#14519769C2semidirect
16. C2×C61×#532C2semidirect
18. #16840512C22semidirect
19. #16840506C22semidirect
20. #16840471C22semidirect
21. #16840464C22semidirect
22. #16840462C22semidirect
23. #16840412C22semidirect
24. #16840411C22semidirect
25. #16840389C22semidirect
26. #16840366C22semidirect
27. #16840357C22semidirect
28. #16840354C22semidirect
29. #16840339C22semidirect
32. #16840296C22semidirect
41. C2×#14519769C22semidirect
82. C61×#532C22semidirect
408. C2×#532D61semidirect
413. C2×C61#3559semidirect
432. #532C2×D61semidirect
492. C61C2×#3559semidirect
799. C2#21460357direct (N × H)

Maximal subgroups

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

subgroupindex
#214603572
C2×#168405122
C2×#168405062
C2×#168404712
C2×#168404642
C2×#168404622
C2×#168404122
C2×#168404112
C2×#168403892
C2×#168403662
C2×#168403572
C2×#168403542
C2×#168403392
C2×#168402962
C22×#145197692
C2×C61×#5322
C2×#355961