Finite Group Databasebeta

← C2×#21459701 #30588454

Subgroups — C2×#21459701 #30588454

Order 15616.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459701C2132yesmaximal, direct product factor
2C2×#16840489C214yesmaximal, complemented
3C2×#16840479C214yesmaximal, complemented
4C2×#16840448C214yesmaximal, complemented
5C2×#16840444C214yesmaximal, complemented
6C2×#16840375C211yesmaximal, characteristic, complemented
7C2×#16840374C211yesmaximal, characteristic, complemented
8C2×#16840373C211yesmaximal, characteristic, complemented
9C2×#16840335C212yesmaximal
10C2×#16840318C211yesmaximal, characteristic, complemented
11C2×#16840316C212yesmaximal, complemented
12C2×#16840314C212yesmaximal, complemented
13C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
14C2×#16840238C212yesmaximal, complemented
15C2×#16840230C211yesmaximal, characteristic
16C2×C61×#541C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Q8×D61C2212yes—
19#16840489C22164yescomplemented
20#16840479C22164yescomplemented
21#16840448C22164yescomplemented
22#16840444C22164yescomplemented
23#16840375C22116yescomplemented
24#16840374C22116yescomplemented
25#16840373C22116yescomplemented
26#16840335C22132yes—
27#16840318C22116yescomplemented
28#16840316C22132yescomplemented
29#16840314C22132yescomplemented
30C2×#14519777C2211yescharacteristic
31C2×#14519776C2214yes—
32C2×#14519776C2212yes—
33C2×#14519776C2214yes—
34C2×#14519775C2212yes—
35C4⋊Q8×D61C22116yescomplemented
36C2×#14519772C2214yes—
37C2×#14519772C2214yes—
38C2×#14519770C2214yes—
39C2×#14519769C2211yescharacteristic
40C2×#14519768C2214yes—
41C2×#14519767C2214yes—
42C2×#14519767C2214yes—
43C2×#14519767C2214yes—
44C2×#14519767C2214yes—
45C2×#14519763C2214yes—
46C2×#14519762C2214yes—
47C2×#14519759C2214yes—
48C2×#14519757C2212yes—
49C2×#14519756C2212yes—
50C2×#14519755C2214yes—
51C2×#14519755C2214yes—
52C2×#14519754C2214yes—
53C2×#14519753C2212yes—
54#16840238C22132yescomplemented
55#16840230C22116yes—
56C2×Q8×Dic61C2212yes—
57C2×C4×Dic122C2214yes—
58C2×C4×Dic122C2212yes—
59C2×C4×Dic122C2214yes—
60C2×#14519742C2212yes—
61C2×#14519742C2212yes—
62C2×#14519742C2214yes—
63C2×#14519742C2214yes—
64C2×#14519742C2214yes—
65C2×#14519739C2212yes—
66C2×#14519737C2212yes—
67C2×#14519737C2212yes—
68C2×#14519735C2214yes—
69C2×#14519735C2212yes—
70C2×#14519734C2211yescharacteristic
71C2×#14519734C2211yescharacteristic
72C2×#14519734C2214yes—
73C2×#14519734C2214yes—
74C2×#14519733C2214yes—
75C2×C4⋊C4×D61C2214yes—
76C22×C4×Dic61C2211yescharacteristic
77C2×C42×D61C2211yescharacteristic
78C2×C42×D61C2211yescharacteristic
79C61×#541C22116yescomplemented
80C2×C4⋊Q8×C61C2211yescharacteristic
81C2×#126×C61C2214yes—
82C2×#125×C61C2214yes—
83C2×#125×C61C2211yescharacteristic
84C2×C22⋊Q8×C61C2212yes—
85C2×C4×Q8×C61C2212yes—
86C2×#117×C61C2211yescharacteristic
87C2×#11758222—28no—
88C2×#11758222C2318yes—
89C22×Dic122C2314yes—
90C22×Dic122C2311yescharacteristic
91C22×Dic122C2312yes—
92C22×Dic122C2314yes—
93C2×Q8×D61—216no—
94C2×Q8×D61C23116yes—
95C22×D244C2311yescharacteristic
96C22×C22⋊D61C2311yescharacteristic
97C22×C22⋊D61C2311yescharacteristic
98C23×Dic61C2312yes—
99C22×C4×D61C2312yes—
100C22×C4×D61C2312yes—
101C22×C4×D61C2311yescharacteristic
102C22×C4×D61C2314yes—
103C22×C4×D61C2311yescharacteristic
104#14519777C2318yes—
105#14519776C23132yes—
106#14519776C23132yes—
107#14519776C23116yes—
108#14519775C23116yes—
109#14519772C23132yes—
110#14519772C23132yes—
111#14519770C23132yes—
112#14519769C2318yes—
113#14519768C23132yes—
114#14519767C23132yes—
115#14519767C23132yes—
116#14519767C23132yes—
117#14519767C23132yes—
118#14519763C23132yes—
119#14519762C23132yes—
120#14519759C23132yes—
121#14519757C23116yes—
122#14519756C23116yes—
123#14519755C23132yes—
124#14519755C23132yes—
125#14519754C23132yes—
126#14519753C23116yes—
127Q8×Dic61C23116yes—
128C4×Dic122C23132yes—
129C4×Dic122C23132yes—
130C4×Dic122C23116yes—
131#14519742C23132yes—
132#14519742C23132yes—
133#14519742C23116yes—
134#14519742C23132yes—
135#14519742C23116yes—
136#14519739C23116yes—
137#14519737C23116yes—
138#14519737C23116yes—
139#14519735C23132yes—
140#14519735C23116yes—
141#14519734C23132yes—
142#14519734C23132yes—
143#14519734C2318yes—
144#14519734C2318yes—
145#14519733C23132yes—
146C2×C4⋊Dic61C2314yes—
147C2×C4⋊Dic61C2312yes—
148C2×C4⋊Dic61C2314yes—
149C2×C4⋊Dic61C2314yes—
150C2×#11758196C2314yes—
151C2×#11758196C2314yes—
152C2×#11758196C2314yes—
153C2×#11758196C2312yes—
154C2×#11758196C2312yes—
155C2×#11758196C2314yes—
156C2×#11758196C2314yes—
157C2×#11758196C2314yes—
158C2×#11758196C2314yes—
159C2×#11758196C2314yes—
160C4⋊C4×D61C23132yes—
161C2×C22⋊Dic61C2314yes—
162C2×#11758198C2312yes—
163C2×#11758198C2314yes—
164C2×#11758198C2312yes—
165C2×#11758198C2314yes—
166C2×#11758198C2314yes—
167C2×C4×Dic61C2311yescharacteristic
168C2×C4×Dic61C2312yes—
169C2×C4×Dic61C2312yes—
170C2×C4×Dic61C2311yescharacteristic
171C2×C4×Dic61C2312yes—
172C2×C4×Dic61C2318yes—
173C2×C4×Dic61C2314yes—
174C2×C4×Dic61C2314yes—
175C2×C4×Dic61C2314yes—
176C2×C4×Dic61C2314yes—
177C42×D61C2318yes—
178C42×D61C2318yes—
179C22×Q8×C61C2312yes—
180C23×C4×C61C2311yescharacteristic
181C4⋊Q8×C61C2318yes—
182#126×C61C23132yes—
183#125×C61C23132yes—
184#125×C61C2318yes—
185C22⋊Q8×C61C23116yes—
186C4×Q8×C61C23116yes—
187#117×C61C2318yes—
188C2×C4⋊C4×C61C2314yes—
189C2×C4⋊C4×C61C2314yes—
190C2×C4⋊C4×C61C2312yes—
191C2×C4⋊C4×C61C2312yes—
192C2×C4⋊C4×C61C2314yes—
193C2×C4⋊C4×C61C2314yes—
194C2×C22⋊C4×C61C2314yes—
195C2×C22⋊C4×C61C2312yes—
196C2×C42×C61C2311yescharacteristic
197C2×C42×C61C2311yescharacteristic
198C2×C42×C61C2314yes—
199C24×C61C2411yescharacteristic
200C23×D61C2411yescharacteristic
201C23×D61C2411yescharacteristic
202C2×Q8×C61—28no—
203C2×Q8×C61C2418yes—
204C22×C4×C61—24no—
205C22×C4×C61C2414yes—
206C22×C4×C61C2412yes—
207C22×C4×C61C2412yes—
208C22×C4×C61C2411yescharacteristic
209C22×C4×C61C2414yes—
210C22×C4×C61C2414yes—
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61C2414yes—
215C2×C22⋊D61C2414yes—
216C22×Dic61—28no—
217C22×Dic61C2411yescharacteristic
218C22×Dic61C2414yes—
219C22×Dic61C2412yes—
220C22×Dic61C2418yes—
221C22×Dic61C2414yes—
222C22×Dic61C2411yescharacteristic
223C22×Dic61C2412yes—
224Q8×D61—264no—
225#11758222—232no—
226C2×D244—24no—
227C2×D244C2414yes—
228C2×C4×D61—216no—
229C2×C4×D61—24no—
230C2×C4×D61—28no—
231C2×C4×D61—28no—
232C2×C4×D61#4118yes—
233C2×C4×D61C24116yes—
234C2×C4×D61C2414yes—
235C2×C4×D61C2418yes—
236C2×C4×D61C2418yes—
237C2×C4×D61C2414yes—
238C2×Dic122—28no—
239C2×Dic122—216no—
240C2×Dic122—24no—
241C2×Dic122—216no—
242C2×Dic122C2418yes—
243C2×Dic122C24116yes—
244C2×Dic122C2414yes—
245C2×Dic122C24116yes—
246C4⋊C4×C61C2418yes—
247C4⋊C4×C61C2418yes—
248C4⋊C4×C61C24116yes—
249C4⋊C4×C61C24116yes—
250C4⋊C4×C61C24116yes—
251C4⋊C4×C61C24116yes—
252C22⋊C4×C61C2418yes—
253C22⋊C4×C61C24116yes—
254C42×C61C2414yes—
255C42×C61C2414yes—
256C42×C61C24116yes—
257C22⋊Dic61C24116yes—
258#11758198C2418yes—
259#11758198C24116yes—
260#11758198C2418yes—
261#11758198C24116yes—
262#11758198C24116yes—
263C4⋊Dic61C24116yes—
264C4⋊Dic61C2418yes—
265C4⋊Dic61C24116yes—
266C4⋊Dic61C24116yes—
267#11758196C24116yes—
268#11758196C24116yes—
269#11758196C24116yes—
270#11758196C2418yes—
271#11758196C2418yes—
272#11758196C24116yes—
273#11758196C24116yes—
274#11758196C24116yes—
275#11758196C24116yes—
276#11758196C24116yes—
277C4×Dic61C2414yes—
278C4×Dic61C2418yes—
279C4×Dic61C2418yes—
280C4×Dic61C2414yes—
281C4×Dic61C2418yes—
282C4×Dic61C24116yes—
283C4×Dic61C24116yes—
284C4×Dic61C24116yes—
285C4×Dic61C24116yes—
286C23×C61—22no—
287C23×C61—24no—
288C23×C61C2512yes—
289C23×C61C2511yescharacteristic
290C22×D61—24no—
291C22×D61—22no—
292C22×D61—24no—
293C22×D61C2×#4114yes—
294C22×D61C2512yes—
295C22×D61C2512yes—
296Q8×C61—216no—
297C2×C4×C61—28no—
298C2×C4×C61—22no—
299C2×C4×C61—28no—
300C2×C4×C61—24no—
301C2×C4×C61—24no—
302C2×C4×C61—28no—
303C2×C4×C61C2×#4114yes—
304C2×C4×C61C2514yes—
305C2×C4×C61C2512yes—
306C2×C4×C61C2518yes—
307C2×C4×C61C2514yes—
308C2×C4×C61C2518yes—
309C2×C4×C61C2512yes—
310C22⋊D61—28no—
311C22⋊D61—28no—
312C2×Dic61—28no—
313C2×Dic61—22no—
314C2×Dic61—28no—
315C2×Dic61—24no—
316C2×Dic61—216no—
317C2×Dic61C2×#4114yes—
318C2×Dic612−1+418yes—
319C2×Dic61C2514yes—
320C2×Dic61C2518yes—
321C2×Dic61C2512yes—
322C2×Dic61C2518yes—
323C2×Dic61C2512yes—
324C2×Dic61C2514yes—
325D244—28no—
326C4×D61—232no—
327C4×D61—28no—
328C4×D61—216no—
329C4×D61—216no—
330C4×D61C2×#41116yes—
331Dic122—216no—
332Dic122—28no—
333Dic122—232no—
334Dic122—232no—
335C2×#3509—611nomaximal, Sylow
336C22×C61—22no—
337C22×C61—24no—
338C22×C61—44no—
339C22×C61C22×#4112yes—
340C22×C61C2×2−1+414yes—
341C22×C61C2611yescharacteristic
342C2×D61—24no—
343C2×D61—28no—
344C2×D61—22no—
345C2×D61—24no—
346C2×D61—44no—
347C2×D61C22×#4114yes—
348C4×C61—28no—
349C4×C61—22no—
350C4×C61—28no—
351C4×C61—24no—
352C4×C61—24no—
353C4×C61C22×#4114yes—
354Dic61—28no—
355Dic61—22no—
356Dic61—28no—
357Dic61—24no—
358Dic61C22×#4114yes—
359Dic61C2×2−1+418yes—
360#3509—6132no—
361C2×#557—614no—
362C2×#556—614no—
363C2×#552—614no—
364C2×#552—614no—
365C2×#541—611no—
366C2×#541—611no—
367C2×#541—611no—
368C2×#541D6111yescharacteristic, complemented
369C2×#536—612no—
370C2×#533—611no—
371C2×#533—612no—
372C2×#533—612no—
373C22×C4⋊Q8—611no—
374C2×#519—612no—
375C2×C4×#41—611no—
376C2×C61—42no—
377C2×C61#350914yescomplemented
378C2×C61C23×#4111yescharacteristic
379C2×C61C22×2−1+412yes—
380D61—24no—
381D61—42no—
382C22×#41—611no—
383C23×Q8—612no—
384#557—6164no—
385#556—6164no—
386#552—6164no—
387#552—6164no—
388#541—6116no—
389#541—6116no—
390#541—6116no—
391#541C2×D61116yescomplemented
392#536—6132no—
393#533—6116no—
394#533—6132no—
395#533—6132no—
396C2×C4⋊Q8—612no—
397C2×C4⋊Q8—6116no—
398C2×C4⋊Q8—614no—
399C2×C4⋊Q8—612no—
400C2×C4⋊Q8—614no—
401C2×C4⋊Q8—611no—
402C2×C4⋊Q8C2×D6111yescharacteristic
403C2×#126—614no—
404C2×#126—614no—
405C2×#126—614no—
406C2×#126C2×D6114yes—
407C2×#125—614no—
408C2×#125—614no—
409C2×#125—614no—
410C2×#125—614no—
411C2×#125—614no—
412C2×#125—611no—
413C2×#125C2×D6111yescharacteristic
414C2×#125C2×D6114yes—
415C2×#124—614no—
416C2×#123—614no—
417C2×#123—614no—
418C2×C22⋊Q8—612no—
419C2×C22⋊Q8—612no—
420C2×C22⋊Q8—614no—
421C2×C22⋊Q8—614no—
422C2×C22⋊Q8—612no—
423C2×C22⋊Q8—614no—
424C2×C22⋊Q8C2×D6112yes—
425#519—6132no—
426C4×#41—6116no—
427C2×C4×Q8—612no—
428C2×C4×Q8—612no—
429C2×C4×Q8—612no—
430C2×C4×Q8—614no—
431C2×C4×Q8—614no—
432C2×C4×Q8—614no—
433C2×C4×Q8—612no—
434C2×C4×Q8—614no—
435C2×C4×Q8—614no—
436C2×C4×Q8C2×D6112yes—
437C2×C4×D4—612no—
438C2×C4×D4—612no—
439C2×C4×D4—612no—
440C2×#117—612no—
441C2×#117—614no—
442C2×#117—614no—
443C2×#117—611no—
444C2×#117—611no—
445C2×#117—614no—
446C2×#117—614no—
447C2×#117C2×D6111yescharacteristic
448C22×C4⋊C4—614no—
449C22×C42—611no—
450C22×C42—611no—
451C22×C42—611no—
452C61C2×#350911yescharacteristic, complemented, Sylow
453C2×#41—618no—
454C2×#41—1228no—
455C22×Q8—6116no—
456C22×Q8—614no—
457C22×Q8—612no—
458C22×Q8—614no—
459C22×Q8—611no—
460C22×Q8—12216no—
461C22×Q8C22×D6112yes—
462C22×D4—611no—
463C22×D4—611no—
464C22×D4—611no—
465C23×C4—611no—
466C23×C4—612no—
467C23×C4—614no—
468C23×C4—612no—
469C23×C4—612no—
470C23×C4—611no—
471C23×C4C22×D6111yescharacteristic
472C4⋊Q8—6116no—
473C4⋊Q8—6132no—
474C4⋊Q8—6116no—
475C4⋊Q8—6132no—
476C4⋊Q8—618no—
477C4⋊Q8C22×D6118yes—
478#126—6132no—
479#126—6132no—
480#126—6132no—
481#126C22×D61132yes—
482#125—6132no—
483#125—6132no—
484#125—6132no—
485#125—6132no—
486#125—6132no—
487#125—618no—
488#125C22×D6118yes—
489#125C22×D61132yes—
490#124—6132no—
491#123—6132no—
492#123—6132no—
493C22⋊Q8—6116no—
494C22⋊Q8—6116no—
495C22⋊Q8—6116no—
496C22⋊Q8—6132no—
497C22⋊Q8—6132no—
498C22⋊Q8—6132no—
499C22⋊Q8C22×D61116yes—
500C4×Q8—6116no—
501C4×Q8—6116no—
502C4×Q8—6116no—
503C4×Q8—6132no—
504C4×Q8—6132no—
505C4×Q8—6132no—
506C4×Q8—6116no—
507C4×Q8—6132no—
508C4×Q8—6132no—
509C4×Q8C22×D61116yes—
510C4×D4—6116no—
511C4×D4—6116no—
512C4×D4—6116no—
513#117—6116no—
514#117—6132no—
515#117—6132no—
516#117—618no—
517#117—618no—
518#117—6132no—
519#117—6132no—
520#117C22×D6118yes—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—612no—
526C2×C4⋊C4—612no—
527C2×C4⋊C4—612no—
528C2×C4⋊C4—614no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—614no—
531C2×C4⋊C4—614no—
532C2×C4⋊C4—614no—
533C2×C4⋊C4—614no—
534C2×C4⋊C4—614no—
535C2×C4⋊C4—6132no—
536C2×C4⋊C4C22×D6114yes—
537C2×C4⋊C4C22×D6112yes—
538C2×C4⋊C4C22×D6114yes—
539C2×C4⋊C4C22×D6112yes—
540C2×C4⋊C4C22×D6114yes—
541C2×C4⋊C4C22×D6114yes—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—612no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—612no—
546C2×C22⋊C4—614no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4C22×D6114yes—
549C2×C22⋊C4C22×D6112yes—
550C2×C42—611no—
551C2×C42—614no—
552C2×C42—614no—
553C2×C42—614no—
554C2×C42—614no—
555C2×C42—612no—
556C2×C42—612no—
557C2×C42—612no—
558C2×C42—618no—
559C2×C42—611no—
560C2×C42—618no—
561C2×C42—618no—
562C2×C42C22×D6114yes—
563C2×C42C22×D6111yescharacteristic
564C2×C42C22×D6111yescharacteristic
565C24—611no—
566C24—611no—
567C24C23×D6111yescharacteristic
568#41—12232no—
569C2×Q8—28no—
570C2×Q8—6116no—
571C2×Q8—618no—
572C2×Q8—6116no—
573C2×Q8—614no—
574C2×Q8—12216no—
575C2×Q8—12216no—
576C2×Q8—1224no—
577C2×Q8—12264no—
578C2×Q8—1228no—
579C2×Q8C23×D6118yes—
580C2×D4—614no—
581C2×D4—614no—
582C2×D4—614no—
583C2×D4—1224no—
584C2×D4—1224no—
585C2×D4—1224no—
586C22×C4—24no—
587C22×C4—611no—
588C22×C4—612no—
589C22×C4—618no—
590C22×C4—614no—
591C22×C4—618no—
592C22×C4—612no—
593C22×C4—614no—
594C22×C4—614no—
595C22×C4—611no—
596C22×C4—618no—
597C22×C4—618no—
598C22×C4—614no—
599C22×C4—6116no—
600C22×C4—1228no—
601C22×C4—1228no—
602C22×C4—12216no—
603C22×C4—1228no—
604C22×C4—1224no—
605C22×C4C23×D6114yes—
606C22×C4C23×D6112yes—
607C22×C4C23×D6114yes—
608C22×C4C23×D6111yescharacteristic
609C22×C4C23×D6112yes—
610C22×C4C23×D6114yes—
611C22×C4C23×D6111yescharacteristic
612C4⋊C4—6116no—
613C4⋊C4—6116no—
614C4⋊C4—6116no—
615C4⋊C4—6116no—
616C4⋊C4—618no—
617C4⋊C4—618no—
618C4⋊C4—6116no—
619C4⋊C4—6116no—
620C4⋊C4—6116no—
621C4⋊C4—6116no—
622C4⋊C4—6116no—
623C4⋊C4—618no—
624C4⋊C4—6116no—
625C4⋊C4—6116no—
626C4⋊C4C23×D61116yes—
627C4⋊C4C23×D6118yes—
628C4⋊C4C23×D61116yes—
629C4⋊C4C23×D6118yes—
630C4⋊C4C23×D61116yes—
631C4⋊C4C23×D61116yes—
632C22⋊C4—6116no—
633C22⋊C4—618no—
634C22⋊C4—6116no—
635C22⋊C4—618no—
636C22⋊C4—6116no—
637C22⋊C4—6116no—
638C22⋊C4C23×D61116yes—
639C22⋊C4C23×D6118yes—
640C42—614no—
641C42—614no—
642C42—618no—
643C42—618no—
644C42—618no—
645C42—6116no—
646C42—6116no—
647C42—6116no—
648C42—6116no—
649C42C23×D6114yes—
650C42C23×D6114yes—
651C42C23×D61116yes—
652C23—22no—
653C23—24no—
654C23—614no—
655C23—612no—
656C23—612no—
657C23—1224no—
658C23—1222no—
659C23—1224no—
660C23C24×D6112yes—
661C23C24×D6111yescharacteristic
662Q8—216no—
663Q8—12232no—
664Q8—12232no—
665Q8—1228no—
666Q8—12216no—
667D4—1228no—
668D4—1228no—
669D4—1228no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—614no—
677C2×C4—618no—
678C2×C4—612no—
679C2×C4—614no—
680C2×C4—6116no—
681C2×C4—614no—
682C2×C4—618no—
683C2×C4—618no—
684C2×C4—612no—
685C2×C4—12216no—
686C2×C4—12216no—
687C2×C4—12232no—
688C2×C4—12216no—
689C2×C4—1222no—
690C2×C4—1228no—
691C2×C4—1224no—
692C2×C4—1228no—
693C2×C4—1228no—
694C2×C4#41×D6114yes—
695C2×C4C24×D6114yes—
696C2×C4C24×D6118yes—
697C2×C4C24×D6112yes—
698C2×C4C24×D6114yes—
699C2×C4C24×D6118yes—
700C2×C4C24×D6112yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—614no—
705C22—1224no—
706C22—1228no—
707C22—1222no—
708C22—1224no—
709C22—2444no—
710C22C2×#41×D6112yes—
711C222−1+4×D6114yes—
712C22C25×D6111yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—614no—
719C4—618no—
720C4—1222no—
721C4—1228no—
722C4—1224no—
723C4—1228no—
724C4C2×#41×D6114yes—
725C2—42no—
726C2—1224no—
727C2—2442no—
728C2#2145970114yesdirect product factor
729C2C22×#41×D6111yescharacteristic
730C2C2×2−1+4×D6112yes—
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#541C2
socleC23×C61C25
prime radicalC22×#11758222C22
hypercenterC2×#541D61
hypocenterC61C2×#3509
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #21459701C2direct (N × H)
2. C2×#16840489C2semidirect
3. C2×#16840479C2semidirect
4. C2×#16840448C2semidirect
5. C2×#16840444C2semidirect
6. C2×#16840375C2semidirect
7. C2×#16840374C2semidirect
8. C2×#16840373C2semidirect
10. C2×#16840318C2semidirect
11. C2×#16840316C2semidirect
12. C2×#16840314C2semidirect
13. C2×C4⋊Q8×D61C2semidirect
14. C2×#16840238C2semidirect
16. C2×C61×#541C2semidirect
19. #16840489C22semidirect
20. #16840479C22semidirect
21. #16840448C22semidirect
22. #16840444C22semidirect
23. #16840375C22semidirect
24. #16840374C22semidirect
25. #16840373C22semidirect
27. #16840318C22semidirect
28. #16840316C22semidirect
29. #16840314C22semidirect
35. C4⋊Q8×D61C22semidirect
54. #16840238C22semidirect
79. C61×#541C22semidirect
368. C2×#541D61semidirect
377. C2×C61#3509semidirect
391. #541C2×D61semidirect
452. C61C2×#3509semidirect
728. C2#21459701direct (N × H)

Maximal subgroups

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

subgroupindex
#214597012
C2×#168404892
C2×#168404792
C2×#168404482
C2×#168404442
C2×#168403752
C2×#168403742
C2×#168403732
C2×#168403352
C2×#168403182
C2×#168403162
C2×#168403142
C2×C4⋊Q8×D612
C2×#168402382
C2×#168402302
C2×C61×#5412
C2×#350961