Finite Group Databasebeta

← C2×#21459565 #30588433

Subgroups — C2×#21459565 #30588433

Order 15616.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459565C2132yesmaximal, direct product factor
2C2×#16840483C212yesmaximal, complemented
3C2×#16840470C212yesmaximal, complemented
4C2×#16840454C212yesmaximal, complemented
5C2×#16840447C214yesmaximal, complemented
6C2×#16840446C212yesmaximal, complemented
7C2×#16840438C214yesmaximal, complemented
8C2×#16840393C211yesmaximal, characteristic, complemented
9C2×#16840385C212yesmaximal, complemented
10C2×#16840372C212yesmaximal, complemented
11C2×#16840336C211yesmaximal, characteristic, complemented
12C2×#16840314C212yesmaximal, complemented
13C2×#16840298C212yesmaximal, complemented
14C2×#16840273C211yesmaximal, characteristic
15C2×#16840243C211yesmaximal, characteristic, complemented
16C2×#16840240C211yesmaximal, characteristic, complemented
17C22×#14519736C211yesmaximal, characteristic, complemented
18C22×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
19C22×#11758222C2211yescharacteristic
20#16840483C22132yescomplemented
21#16840470C22132yescomplemented
22#16840454C22132yescomplemented
23#16840447C22164yescomplemented
24#16840446C22132yescomplemented
25#16840438C22164yescomplemented
26#16840393C22116yescomplemented
27#16840385C22132yescomplemented
28#16840372C22132yescomplemented
29#16840336C22116yescomplemented
30#16840314C22132yescomplemented
31C2×#14519776C2212yescomplemented
32C2×#14519776C2212yescomplemented
33C2×#14519775C2212yescomplemented
34#16840298C22132yescomplemented
35C2×#14519772C2214yescomplemented
36C2×#14519772C2214yescomplemented
37C2×#14519770C2214yes—
38C2×#14519770C2214yes—
39C2×#14519768C2212yescomplemented
40C2×#14519768C2212yescomplemented
41C2×#14519768C2214yescomplemented
42C2×#14519767C2214yescomplemented
43C2×#14519767C2214yescomplemented
44C2×#14519766C2212yescomplemented
45C2×#14519763C2214yes—
46#16840273C22116yes—
47C2×#14519761C2214yes—
48C2×#14519760C2214yes—
49C2×#14519760C2212yes—
50C2×#14519759C2214yes—
51C2×#14519757C2214yescomplemented
52C2×#14519756C2214yes—
53C2×#14519756C2211yescharacteristic
54C2×#14519756C2211yescharacteristic
55C2×#14519754C2214yes—
56C2×#14519753C2212yescomplemented
57C2×#14519753C2212yescomplemented
58C2×#14519751C2211yescharacteristic
59C2×#14519751C2211yescharacteristic
60C2×#14519746C2212yes—
61#16840243C22116yescomplemented
62#16840240C22116yescomplemented
63C2×Q8×Dic61C2212yescomplemented
64C2×Q8×Dic61C2212yescomplemented
65C2×Q8×Dic61C2212yescomplemented
66C2×Q8×Dic61C2212yescomplemented
67C2×#14519742C2212yescomplemented
68C2×#14519742C2214yescomplemented
69C2×#14519739C2212yescomplemented
70C2×C4×C22⋊D61C2214yes—
71C2×C4×C22⋊D61C2212yes—
72C2×C4×C22⋊D61C2212yes—
73C2×#14519737C2214yes—
74C2×#14519736C2211yescharacteristic
75C2×#14519736C2211yescharacteristic
76C2×#14519736C2211yescharacteristic
77C2×#14519736C2211yescharacteristic
78C2×#14519736C2212yes—
79C2×#14519736C2211yescharacteristic
80C2×#14519736C2212yes—
81C2×#14519736C2214yes—
82C2×#14519736C22116yescomplemented
83C2×#14519735C2212yescomplemented
84C2×#14519735C2214yescomplemented
85C2×#14519733C2214yes—
86C22×C4⋊Dic61C2211yescharacteristic
87C22×C4⋊Dic61C2211yescharacteristic
88C2×C4⋊C4×D61C2212yescomplemented
89C22×C22⋊Dic61C2212yes—
90C22×C4×Dic61C2212yes—
91C23×Q8×C61C2211yescharacteristic
92C24×C4×C61C2211yescharacteristic
93C2×C22⋊Q8×C61C2212yes—
94C2×C22⋊Q8×C61C2212yes—
95C2×C22⋊Q8×C61C2212yes—
96C2×C22⋊Q8×C61C2212yes—
97C2×C22⋊Q8×C61C22116yescomplemented
98C22×C4⋊C4×C61C2211yescharacteristic
99C22×C4⋊C4×C61C2212yes—
100C22×C22⋊C4×C61C2212yes—
101C2×#11758222—28no—
102C2×#11758222C2318yes—
103C22×Dic122C2311yescharacteristic
104C22×Dic122C2314yes—
105C22×D244C2311yescharacteristic
106C22×C22⋊D61C2312yes—
107C22×C22⋊D61C2312yes—
108C22×C22⋊D61C2312yes—
109C23×Dic61C2312yes—
110C23×Dic61C2312yes—
111C22×C4×D61C2312yes—
112C22×C4×D61C2314yes—
113#14519776C23116yescomplemented
114#14519776C23116yescomplemented
115#14519775C23116yescomplemented
116#14519772C23132yescomplemented
117#14519772C23132yescomplemented
118#14519770C23132yes—
119#14519770C23132yes—
120#14519768C23132yescomplemented
121#14519768C23116yescomplemented
122#14519768C23116yescomplemented
123#14519767C23132yescomplemented
124#14519767C23132yescomplemented
125#14519766C23116yescomplemented
126#14519763C23132yes—
127#14519761C23132yes—
128#14519760C23116yes—
129#14519760C23132yes—
130#14519759C23132yes—
131#14519757C23132yescomplemented
132#14519756C2318yes—
133#14519756C2318yes—
134#14519756C23132yes—
135#14519754C23132yes—
136#14519753C23116yescomplemented
137#14519753C23116yescomplemented
138#14519751C2318yes—
139#14519751C2318yes—
140#14519746C23116yes—
141Q8×Dic61C23116yescomplemented
142Q8×Dic61C23116yescomplemented
143Q8×Dic61C23116yescomplemented
144Q8×Dic61C23116yescomplemented
145#14519742C23132yescomplemented
146#14519742C23116yescomplemented
147#14519739C23116yescomplemented
148C4×C22⋊D61C23116yes—
149C4×C22⋊D61C23116yes—
150C4×C22⋊D61C23132yes—
151#14519737C23132yes—
152#14519736C2318yes—
153#14519736C2318yes—
154#14519736C2318yes—
155#14519736C23116yes—
156#14519736C2318yes—
157#14519736C23116yes—
158#14519736C2318yes—
159#14519736C23132yes—
160#14519735C23116yescomplemented
161#14519735C23132yescomplemented
162#14519733C23132yes—
163C2×C4⋊Dic61C2318yes—
164C2×C4⋊Dic61C2311yescharacteristic
165C2×C4⋊Dic61C2318yes—
166C2×C4⋊Dic61C2311yescharacteristic
167C2×C4⋊Dic61C2311yescharacteristic
168C2×C4⋊Dic61C2311yescharacteristic
169C2×C4⋊Dic61C2312yes—
170C2×C4⋊Dic61C2312yes—
171C2×C4⋊Dic61C2314yes—
172C2×C4⋊Dic61C2311yescharacteristic
173C2×C4⋊Dic61C2311yescharacteristic
174C2×C4⋊Dic61C2314yes—
175C2×C4⋊Dic61C2314yes—
176C2×#11758196C2314yes—
177C2×#11758196C2314yes—
178C2×#11758196C2314yes—
179C2×#11758196C2314yes—
180C2×#11758196C2312yes—
181C2×#11758196C2312yes—
182C2×#11758196C2314yes—
183C4⋊C4×D61C23116yescomplemented
184C2×C22⋊Dic61C2312yes—
185C2×C22⋊Dic61C2312yes—
186C2×C22⋊Dic61C2312yes—
187C2×C22⋊Dic61C2312yes—
188C2×C22⋊Dic61C23116yes—
189C2×C22⋊Dic61C2312yes—
190C2×C22⋊Dic61C2312yes—
191C2×C22⋊Dic61C2312yes—
192C2×#11758198C2312yes—
193C2×#11758198C2314yes—
194C2×#11758198C2314yes—
195C2×#11758198C2314yes—
196C2×#11758198C2312yes—
197C2×C4×Dic61C2312yes—
198C2×C4×Dic61C2312yes—
199C2×C4×Dic61C2312yes—
200C2×C4×Dic61C2312yes—
201C2×C4×Dic61C23116yes—
202C2×C4×Dic61C2314yes—
203C2×C4×Dic61C2314yes—
204C2×C4×Dic61C2314yes—
205C2×C4×Dic61C2312yes—
206C25×C61C2311yescharacteristic
207C22×Q8×C61—28no—
208C22×Q8×C61C2312yes—
209C22×Q8×C61C2312yes—
210C22×Q8×C61C2318yes—
211C23×C4×C61—28no—
212C23×C4×C61C2311yescharacteristic
213C23×C4×C61C2311yescharacteristic
214C23×C4×C61C2311yescharacteristic
215C23×C4×C61C2311yescharacteristic
216C23×C4×C61C2311yescharacteristic
217C23×C4×C61C2312yes—
218C23×C4×C61C2318yes—
219C23×C4×C61C2312yes—
220C23×C4×C61C2311yescharacteristic
221C22⋊Q8×C61C23116yes—
222C22⋊Q8×C61C23116yes—
223C22⋊Q8×C61C23116yes—
224C22⋊Q8×C61C23116yes—
225C2×C4⋊C4×C61C2312yes—
226C2×C4⋊C4×C61C2314yes—
227C2×C4⋊C4×C61C2312yes—
228C2×C4⋊C4×C61C2318yes—
229C2×C4⋊C4×C61C2314yes—
230C2×C4⋊C4×C61C23116yes—
231C2×C22⋊C4×C61C2314yes—
232C2×C22⋊C4×C61C2314yes—
233C2×C22⋊C4×C61C23116yes—
234C24×C61—24no—
235C24×C61—24no—
236C24×C61—42no—
237C24×C61C2411yescharacteristic
238C24×C61C2414yes—
239C24×C61C2411yescharacteristic
240C24×C61C2411yescharacteristic
241C23×D61C2412yes—
242C2×Q8×C61—28no—
243C2×Q8×C61—28no—
244C2×Q8×C61—232no—
245C2×Q8×C61C2418yes—
246C2×Q8×C61C2418yes—
247C22×C4×C61—24no—
248C22×C4×C61—28no—
249C22×C4×C61—24no—
250C22×C4×C61—24no—
251C22×C4×C61—24no—
252C22×C4×C61—24no—
253C22×C4×C61—232no—
254C22×C4×C61—44no—
255C22×C4×C61#4118yes—
256C22×C4×C61C2414yes—
257C22×C4×C61C2414yes—
258C22×C4×C61C2418yes—
259C22×C4×C61C2411yescharacteristic
260C22×C4×C61C2411yescharacteristic
261C22×C4×C61C2414yes—
262C22×C4×C61C2414yes—
263C22×C4×C61C2414yes—
264C22×C4×C61C2414yes—
265C22×C4×C61C2414yes—
266C22×C4×C61C2418yes—
267C22×C4×C61C2411yescharacteristic
268C22×C4×C61C2411yescharacteristic
269C22×C4×C61C2414yes—
270C2×C22⋊D61—28no—
271C2×C22⋊D61—28no—
272C2×C22⋊D61—44no—
273C2×C22⋊D61C2418yes—
274C2×C22⋊D61C2418yes—
275C2×C22⋊D61C2418yes—
276C22×Dic61—28no—
277C22×Dic61—44no—
278C22×Dic61C2412yes—
279C22×Dic61C2412yes—
280C22×Dic61C2412yes—
281C22×Dic61C2412yes—
282C22×Dic61C2412yes—
283C22×Dic61C2418yes—
284C22×Dic61C2412yes—
285C22×Dic61C2412yes—
286C22×Dic61C2418yes—
287#11758222—232no—
288C2×D244—24no—
289C2×D244C2414yes—
290C2×C4×D61—28no—
291C2×C4×D61—48no—
292C2×C4×D61C2418yes—
293C2×C4×D61C24116yes—
294C2×Dic122—24no—
295C2×Dic122—48no—
296C2×Dic122C2414yes—
297C2×Dic122C24116yes—
298C4⋊C4×C61C2418yes—
299C4⋊C4×C61C24116yes—
300C4⋊C4×C61C2418yes—
301C4⋊C4×C61C24116yes—
302C22⋊C4×C61C24116yes—
303C22⋊C4×C61C24116yes—
304C22⋊Dic61C2418yes—
305C22⋊Dic61C2418yes—
306C22⋊Dic61C2418yes—
307C22⋊Dic61C2418yes—
308C22⋊Dic61C2418yes—
309C22⋊Dic61C2418yes—
310C22⋊Dic61C2418yes—
311#11758198C2418yes—
312#11758198C24116yes—
313#11758198C24116yes—
314#11758198C24116yes—
315#11758198C2418yes—
316C4⋊Dic61C2414yes—
317C4⋊Dic61C2414yes—
318C4⋊Dic61C2414yes—
319C4⋊Dic61C2414yes—
320C4⋊Dic61C2418yes—
321C4⋊Dic61C2418yes—
322C4⋊Dic61C24116yes—
323C4⋊Dic61C2414yes—
324C4⋊Dic61C2414yes—
325C4⋊Dic61C24116yes—
326C4⋊Dic61C24116yes—
327#11758196C24116yes—
328#11758196C24116yes—
329#11758196C24116yes—
330#11758196C24116yes—
331#11758196C2418yes—
332#11758196C2418yes—
333#11758196C24116yes—
334C4×Dic61C2418yes—
335C4×Dic61C2418yes—
336C4×Dic61C2418yes—
337C4×Dic61C2418yes—
338C4×Dic61C24116yes—
339C4×Dic61C24116yes—
340C4×Dic61C24116yes—
341C4×Dic61C2418yes—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—28no—
347C23×C61—22no—
348C23×C61—28no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—44no—
352C23×C61—416no—
353C23×C61C2×#4114yes—
354C23×C612−1+414yes—
355C23×C61C2512yes—
356C23×C61C2512yes—
357C23×C61C2512yes—
358C23×C61C2511yescharacteristic
359C22×D61—24no—
360C22×D61—24no—
361C22×D61—24no—
362C22×D61C2514yes—
363Q8×C61—216no—
364Q8×C61—216no—
365C2×C4×C61—28no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—216no—
369C2×C4×C61—28no—
370C2×C4×C61—28no—
371C2×C4×C61—28no—
372C2×C4×C61—28no—
373C2×C4×C61—28no—
374C2×C4×C61—28no—
375C2×C4×C61—48no—
376C2×C4×C61C2×#4114yes—
377C2×C4×C61C2×#4114yes—
378C2×C4×C61C2×#41116yes—
379C2×C4×C61C2512yes—
380C2×C4×C61C2518yes—
381C2×C4×C61C2518yes—
382C2×C4×C61C2512yes—
383C2×C4×C61C2512yes—
384C2×C4×C61C2512yes—
385C22⋊D61—216no—
386C22⋊D61—216no—
387C22⋊D61—48no—
388C2×Dic61—24no—
389C2×Dic61—216no—
390C2×Dic61—24no—
391C2×Dic61—24no—
392C2×Dic61—24no—
393C2×Dic61—24no—
394C2×Dic61—24no—
395C2×Dic61—24no—
396C2×Dic61—48no—
397C2×Dic61C2514yes—
398C2×Dic61C2514yes—
399C2×Dic61C2514yes—
400C2×Dic61C2514yes—
401C2×Dic61C2514yes—
402C2×Dic61C2514yes—
403C2×Dic61C2514yes—
404D244—28no—
405C4×D61—216no—
406C4×D61—416no—
407Dic122—28no—
408Dic122—416no—
409C2×#3495—611nomaximal, Sylow
410C22×C61—22no—
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—28no—
415C22×C61—28no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—416no—
420C22×C61—44no—
421C22×C61C22×#4114yes—
422C22×C61C22×#4112yes—
423C22×C61C2×2−1+414yes—
424C22×C61C2×2−1+412yes—
425C22×C61#58512yes—
426C22×C61C2611yescharacteristic
427C2×D61—24no—
428C2×D61—24no—
429C2×D61—24no—
430C2×D61—48no—
431C4×C61—22no—
432C4×C61—22no—
433C4×C61—28no—
434C4×C61—28no—
435C4×C61C22×#4114yes—
436C4×C61C22×#4114yes—
437Dic61—24no—
438Dic61—24no—
439Dic61—24no—
440Dic61—24no—
441Dic61—24no—
442Dic61—24no—
443Dic61—24no—
444#3495—6132no—
445C2×#556—612no—
446C2×#554—612no—
447C2×#552—612no—
448C2×#552—612no—
449C2×#552—614no—
450C2×#551—614no—
451C2×#544—611no—
452C2×#542—612no—
453C2×#541—612no—
454C2×#536—611no—
455C2×#533—612no—
456C2×#529—612no—
457C2×#525—611no—
458C22×C22⋊Q8D6111yescharacteristic, complemented
459C2×#520—611no—
460C2×#519—611no—
461C22×#117—611no—
462C2×C61—24no—
463C2×C61—24no—
464C2×C61—42no—
465C2×C61#349514yescomplemented
466C2×C61C23×#4111yescharacteristic
467C2×C61C22×2−1+411yescharacteristic
468C2×C61C2×#58511yescharacteristic
469D61—44no—
470C22×#41—611no—
471C23×Q8C2×D6111yescharacteristic
472C24×C4C2×D6111yescharacteristic
473#556—6132no—
474#554—6132no—
475#552—6132no—
476#552—6132no—
477#552—6164no—
478#551—6164no—
479#544—6116no—
480#542—6132no—
481#541—6132no—
482#536—6116no—
483#533—6132no—
484C2×C4⋊Q8—612no—
485C2×C4⋊Q8—612no—
486C2×C4⋊Q8—612no—
487#529—6132no—
488C2×#126—614no—
489C2×#126—614no—
490C2×#126—614no—
491C2×#126—614no—
492C2×#125—614no—
493C2×#125—614no—
494C2×#125—612no—
495C2×#125—614no—
496C2×#125—612no—
497C2×#124—612no—
498C2×#124—614no—
499#525—6116no—
500C2×#123—612no—
501C2×#123—614no—
502C2×#123—614no—
503C2×#123—614no—
504C2×C22⋊Q8—612no—
505C2×C22⋊Q8—612no—
506C2×C22⋊Q8—611no—
507C2×C22⋊Q8—611no—
508C2×C22⋊Q8—614no—
509C2×C22⋊Q8—614no—
510C2×C22⋊Q8—614no—
511C2×C22⋊Q8C2×D6112yes—
512C2×C22⋊Q8C2×D6112yes—
513C2×C22⋊Q8C2×D6112yes—
514C2×C22⋊Q8C2×D6112yes—
515C2×C22⋊Q8C2×D61116yescomplemented
516C2×#121—611no—
517C2×#121—611no—
518C2×#120—612no—
519#520—6116no—
520#519—6116no—
521C2×C4×Q8—612no—
522C2×C4×Q8—612no—
523C2×C4×Q8—612no—
524C2×C4×Q8—612no—
525C2×C4×Q8—612no—
526C2×C4×Q8—614no—
527C2×C4×D4—614no—
528C2×C4×D4—612no—
529C2×C4×D4—612no—
530C2×C4×D4—612no—
531C2×C4×D4—614no—
532C2×#117—611no—
533C2×#117—611no—
534C2×#117—612no—
535C2×#117—611no—
536C2×#117—612no—
537C2×#117—611no—
538C2×#117—611no—
539C2×#117—614no—
540C2×#117—6116no—
541C2×#117—612no—
542C2×#117—614no—
543C2×#117—614no—
544C22×C4⋊C4—611no—
545C22×C4⋊C4—611no—
546C22×C4⋊C4—612no—
547C22×C4⋊C4C2×D6111yescharacteristic
548C22×C4⋊C4C2×D6112yes—
549C22×C22⋊C4—612no—
550C22×C22⋊C4C2×D6112yes—
551C22×C42—612no—
552C61C2×#349511yescharacteristic, complemented, Sylow
553C25C22×D6111yescharacteristic
554C2×#41—618no—
555C2×#41—1228no—
556C22×Q8—28no—
557C22×Q8—611no—
558C22×Q8—614no—
559C22×Q8C22×D6112yes—
560C22×Q8C22×D6112yes—
561C22×Q8C22×D6118yes—
562C22×D4—612no—
563C22×D4—612no—
564C22×D4—612no—
565C22×D4—611no—
566C23×C4—28no—
567C23×C4—612no—
568C23×C4—612no—
569C23×C4—612no—
570C23×C4—614no—
571C23×C4C22×D6112yes—
572C23×C4C22×D6111yescharacteristic
573C23×C4C22×D6111yescharacteristic
574C23×C4C22×D6111yescharacteristic
575C23×C4C22×D6111yescharacteristic
576C23×C4C22×D6118yes—
577C23×C4C22×D6111yescharacteristic
578C23×C4C22×D6112yes—
579C23×C4C22×D6111yescharacteristic
580C4⋊Q8—6116no—
581C4⋊Q8—6116no—
582C4⋊Q8—6116no—
583#126—6132no—
584#126—6132no—
585#126—6132no—
586#126—6132no—
587#125—6116no—
588#125—6132no—
589#125—6132no—
590#125—6132no—
591#125—6116no—
592#124—6116no—
593#124—6132no—
594#123—6116no—
595#123—6132no—
596#123—6132no—
597#123—6132no—
598C22⋊Q8—6116no—
599C22⋊Q8—6116no—
600C22⋊Q8—618no—
601C22⋊Q8—618no—
602C22⋊Q8—6132no—
603C22⋊Q8—6132no—
604C22⋊Q8—6132no—
605C22⋊Q8C22×D61116yes—
606C22⋊Q8C22×D61116yes—
607C22⋊Q8C22×D61116yes—
608C22⋊Q8C22×D61116yes—
609#121—618no—
610#121—618no—
611#120—6116no—
612C4×Q8—6116no—
613C4×Q8—6116no—
614C4×Q8—6116no—
615C4×Q8—6116no—
616C4×Q8—6116no—
617C4×Q8—6132no—
618C4×D4—6132no—
619C4×D4—6116no—
620C4×D4—6116no—
621C4×D4—6116no—
622C4×D4—6132no—
623#117—618no—
624#117—618no—
625#117—6116no—
626#117—618no—
627#117—6116no—
628#117—618no—
629#117—618no—
630#117—6132no—
631#117—6116no—
632#117—6132no—
633#117—6132no—
634C2×C4⋊C4—611no—
635C2×C4⋊C4—611no—
636C2×C4⋊C4—612no—
637C2×C4⋊C4—611no—
638C2×C4⋊C4—611no—
639C2×C4⋊C4—612no—
640C2×C4⋊C4—618no—
641C2×C4⋊C4—618no—
642C2×C4⋊C4—614no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—614no—
646C2×C4⋊C4—614no—
647C2×C4⋊C4—614no—
648C2×C4⋊C4—614no—
649C2×C4⋊C4—614no—
650C2×C4⋊C4—612no—
651C2×C4⋊C4—612no—
652C2×C4⋊C4—614no—
653C2×C4⋊C4—614no—
654C2×C4⋊C4—6116no—
655C2×C4⋊C4C22×D6112yes—
656C2×C4⋊C4C22×D6114yes—
657C2×C4⋊C4C22×D6112yes—
658C2×C4⋊C4C22×D6118yes—
659C2×C4⋊C4C22×D6114yes—
660C2×C4⋊C4C22×D61116yes—
661C2×C22⋊C4—612no—
662C2×C22⋊C4—612no—
663C2×C22⋊C4—612no—
664C2×C22⋊C4—612no—
665C2×C22⋊C4—6116no—
666C2×C22⋊C4—612no—
667C2×C22⋊C4—612no—
668C2×C22⋊C4—612no—
669C2×C22⋊C4—612no—
670C2×C22⋊C4—614no—
671C2×C22⋊C4—614no—
672C2×C22⋊C4—612no—
673C2×C22⋊C4—614no—
674C2×C22⋊C4C22×D6114yes—
675C2×C22⋊C4C22×D6114yes—
676C2×C22⋊C4C22×D61116yes—
677C2×C42—612no—
678C2×C42—612no—
679C2×C42—614no—
680C2×C42—614no—
681C2×C42—614no—
682C2×C42—612no—
683C2×C42—612no—
684C2×C42—6116no—
685C2×C42—612no—
686C24—24no—
687C24—24no—
688C24—42no—
689C24—612no—
690C24C23×D6111yescharacteristic
691C24C23×D6114yes—
692C24C23×D6111yescharacteristic
693C24C23×D6111yescharacteristic
694#41—12232no—
695C2×Q8—28no—
696C2×Q8—28no—
697C2×Q8—232no—
698C2×Q8—614no—
699C2×Q8—6116no—
700C2×Q8—1224no—
701C2×Q8—2448no—
702C2×Q8C23×D6118yes—
703C2×Q8C23×D6118yes—
704C2×D4—618no—
705C2×D4—618no—
706C2×D4—618no—
707C2×D4—614no—
708C2×D4—1228no—
709C2×D4—1228no—
710C2×D4—1224no—
711C2×D4—2444no—
712C22×C4—24no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—232no—
719C22×C4—44no—
720C22×C4—618no—
721C22×C4—612no—
722C22×C4—612no—
723C22×C4—612no—
724C22×C4—612no—
725C22×C4—612no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—618no—
729C22×C4—618no—
730C22×C4—6116no—
731C22×C4—1228no—
732C22×C4—1228no—
733C22×C4—2448no—
734C22×C4—2444no—
735C22×C4#1175822418yes—
736C22×C4C23×D6114yes—
737C22×C4C23×D6118yes—
738C22×C4C23×D6114yes—
739C22×C4C23×D6114yes—
740C22×C4C23×D6114yes—
741C22×C4C23×D6114yes—
742C22×C4C23×D6111yescharacteristic
743C22×C4C23×D6114yes—
744C22×C4C23×D6114yes—
745C22×C4C23×D6111yescharacteristic
746C22×C4C23×D6118yes—
747C22×C4C23×D6114yes—
748C22×C4C23×D6111yescharacteristic
749C22×C4C23×D6111yescharacteristic
750C4⋊C4—614no—
751C4⋊C4—6116no—
752C4⋊C4—614no—
753C4⋊C4—618no—
754C4⋊C4—614no—
755C4⋊C4—614no—
756C4⋊C4—618no—
757C4⋊C4—6116no—
758C4⋊C4—6116no—
759C4⋊C4—618no—
760C4⋊C4—618no—
761C4⋊C4—6116no—
762C4⋊C4—6116no—
763C4⋊C4—614no—
764C4⋊C4—614no—
765C4⋊C4—6116no—
766C4⋊C4—6116no—
767C4⋊C4—6116no—
768C4⋊C4C23×D6118yes—
769C4⋊C4C23×D61116yes—
770C4⋊C4C23×D6118yes—
771C4⋊C4C23×D61116yes—
772C22⋊C4—618no—
773C22⋊C4—618no—
774C22⋊C4—618no—
775C22⋊C4—618no—
776C22⋊C4—618no—
777C22⋊C4—618no—
778C22⋊C4—618no—
779C22⋊C4—618no—
780C22⋊C4—6116no—
781C22⋊C4—6116no—
782C22⋊C4—618no—
783C22⋊C4—6116no—
784C22⋊C4C23×D61116yes—
785C22⋊C4C23×D61116yes—
786C42—618no—
787C42—618no—
788C42—618no—
789C42—618no—
790C42—6116no—
791C42—6116no—
792C42—6116no—
793C42—618no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—28no—
799C23—22no—
800C23—28no—
801C23—22no—
802C23—22no—
803C23—44no—
804C23—416no—
805C23—614no—
806C23—1224no—
807C23—1224no—
808C23—1224no—
809C23C2×#1175822414yes—
810C23#1451982514yes—
811C23C24×D6112yes—
812C23C24×D6112yes—
813C23C24×D6112yes—
814C23C24×D6111yescharacteristic
815Q8—216no—
816Q8—216no—
817Q8—1228no—
818Q8—24416no—
819D4—12216no—
820D4—12216no—
821D4—1228no—
822D4—2448no—
823C2×C4—28no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—216no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—48no—
834C2×C4—614no—
835C2×C4—614no—
836C2×C4—614no—
837C2×C4—614no—
838C2×C4—614no—
839C2×C4—614no—
840C2×C4—614no—
841C2×C4—1224no—
842C2×C4—12216no—
843C2×C4—1224no—
844C2×C4—1224no—
845C2×C4—1224no—
846C2×C4—1224no—
847C2×C4—1224no—
848C2×C4—1224no—
849C2×C4—12216no—
850C2×C4—24416no—
851C2×C4—2448no—
852C2×C4C2×#1175822414yes—
853C2×C4C2×#1175822414yes—
854C2×C4C2×#11758224116yes—
855C2×C4C24×D6112yes—
856C2×C4C24×D6118yes—
857C2×C4C24×D6118yes—
858C2×C4C24×D6112yes—
859C2×C4C24×D6112yes—
860C2×C4C24×D6112yes—
861C22—28no—
862C22—28no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—416no—
871C22—44no—
872C22—1224no—
873C22—1224no—
874C22—1224no—
875C22—2448no—
876C22C22×#1175822414yes—
877C22C22×#1175822412yes—
878C22C2×#1451982514yes—
879C22C2×#1451982512yes—
880C22#1684059812yes—
881C22C25×D6111yescharacteristic
882C4—22no—
883C4—22no—
884C4—28no—
885C4—28no—
886C4—1224no—
887C4—1224no—
888C4—1224no—
889C4—1224no—
890C4—1224no—
891C4—1224no—
892C4—1224no—
893C4C22×#1175822414yes—
894C4C22×#1175822414yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—2444no—
899C2#2145956514yesdirect product factor
900C2C23×#1175822411yescharacteristic
901C2C22×#1451982511yescharacteristic
902C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC22×C22⋊Q8×C61C2
socleC23×C61C25
prime radicalC2×#16840273C2
hypercenterC22×C22⋊Q8D61
hypocenterC61C2×#3495
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21459565C2direct (N × H)
2. C2×#16840483C2semidirect
3. C2×#16840470C2semidirect
4. C2×#16840454C2semidirect
5. C2×#16840447C2semidirect
6. C2×#16840446C2semidirect
7. C2×#16840438C2semidirect
8. C2×#16840393C2semidirect
9. C2×#16840385C2semidirect
10. C2×#16840372C2semidirect
11. C2×#16840336C2semidirect
12. C2×#16840314C2semidirect
13. C2×#16840298C2semidirect
15. C2×#16840243C2semidirect
16. C2×#16840240C2semidirect
17. C22×#14519736C2semidirect
18. C22×C22⋊Q8×C61C2semidirect
20. #16840483C22semidirect
21. #16840470C22semidirect
22. #16840454C22semidirect
23. #16840447C22semidirect
24. #16840446C22semidirect
25. #16840438C22semidirect
26. #16840393C22semidirect
27. #16840385C22semidirect
28. #16840372C22semidirect
29. #16840336C22semidirect
30. #16840314C22semidirect
31. C2×#14519776C22semidirect
32. C2×#14519776C22semidirect
33. C2×#14519775C22semidirect
34. #16840298C22semidirect
35. C2×#14519772C22semidirect
36. C2×#14519772C22semidirect
39. C2×#14519768C22semidirect
40. C2×#14519768C22semidirect
41. C2×#14519768C22semidirect
42. C2×#14519767C22semidirect
43. C2×#14519767C22semidirect
44. C2×#14519766C22semidirect
51. C2×#14519757C22semidirect
56. C2×#14519753C22semidirect
57. C2×#14519753C22semidirect
61. #16840243C22semidirect
62. #16840240C22semidirect
63. C2×Q8×Dic61C22semidirect
64. C2×Q8×Dic61C22semidirect
65. C2×Q8×Dic61C22semidirect
66. C2×Q8×Dic61C22semidirect
67. C2×#14519742C22semidirect
68. C2×#14519742C22semidirect
69. C2×#14519739C22semidirect
82. C2×#14519736C22semidirect
83. C2×#14519735C22semidirect
84. C2×#14519735C22semidirect
88. C2×C4⋊C4×D61C22semidirect
97. C2×C22⋊Q8×C61C22semidirect
113. #14519776C23semidirect
114. #14519776C23semidirect
115. #14519775C23semidirect
116. #14519772C23semidirect
117. #14519772C23semidirect
120. #14519768C23semidirect
121. #14519768C23semidirect
122. #14519768C23semidirect
123. #14519767C23semidirect
124. #14519767C23semidirect
125. #14519766C23semidirect
131. #14519757C23semidirect
136. #14519753C23semidirect
137. #14519753C23semidirect
141. Q8×Dic61C23semidirect
142. Q8×Dic61C23semidirect
143. Q8×Dic61C23semidirect
144. Q8×Dic61C23semidirect
145. #14519742C23semidirect
146. #14519742C23semidirect
147. #14519739C23semidirect
160. #14519735C23semidirect
161. #14519735C23semidirect
183. C4⋊C4×D61C23semidirect
458. C22×C22⋊Q8D61semidirect
465. C2×C61#3495semidirect
515. C2×C22⋊Q8C2×D61semidirect
552. C61C2×#3495semidirect
899. C2#21459565direct (N × H)

Maximal subgroups

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

subgroupindex
#214595652
C2×#168404832
C2×#168404702
C2×#168404542
C2×#168404472
C2×#168404462
C2×#168404382
C2×#168403932
C2×#168403852
C2×#168403722
C2×#168403362
C2×#168403142
C2×#168402982
C2×#168402732
C2×#168402432
C2×#168402402
C22×#145197362
C22×C22⋊Q8×C612
C2×#349561