Finite Group Databasebeta

← C2×#21460210 #30587707

Subgroups — C2×#21460210 #30587707

Order 15616.

7182 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#21460210C2132yesmaximal, direct product factor
2C2×#16840509C214yesmaximal, complemented
3C2×#16840477C211yesmaximal, characteristic, complemented
4C2×#16840477C212yesmaximal, complemented
5C2×#16840472C211yesmaximal, characteristic, complemented
6C2×#16840458C212yesmaximal, complemented
7C2×#16840450C212yesmaximal, complemented
8C2×Q8×D244C211yesmaximal, characteristic, complemented
9C2×#16840420C212yesmaximal, complemented
10C2×#16840416C211yesmaximal, characteristic, complemented
11C2×#16840390C212yesmaximal, complemented
12C2×#16840378C214yesmaximal, complemented
13C2×#16840367C212yesmaximal, complemented
14C2×#16840341C212yesmaximal, complemented
15C2×#16840335C212yesmaximal, complemented
16C2×#16840319C211yesmaximal, characteristic, complemented
17C2×#16840312C211yesmaximal, characteristic, complemented
18C2×C61×#529C211yesmaximal, characteristic, complemented
19C22×#11758222C2212yes—
20C22×#11758224C2212yes—
21C22×Q8×D61C2212yes—
22#16840509C22164yescomplemented
23#16840477C22132yescomplemented
24#16840477C22116yescomplemented
25#16840472C22116yescomplemented
26#16840458C22132yescomplemented
27#16840450C22132yescomplemented
28Q8×D244C22116yescomplemented
29#16840420C22132yescomplemented
30#16840416C22116yescomplemented
31#16840390C22132yescomplemented
32#16840378C22164yescomplemented
33#16840367C22132yescomplemented
34#16840341C22132yescomplemented
35#16840335C22132yescomplemented
36#16840319C22116yescomplemented
37#16840312C22116yescomplemented
38C2×#14519777C2211yescharacteristic
39C2×#14519777C2212yes—
40C2×#14519777C2211yescharacteristic
41C2×#14519777C2211yescharacteristic
42C2×#14519776C2214yes—
43C2×#14519774C2211yescharacteristic
44C2×#14519772C2214yes—
45C2×#14519769C2212yes—
46C2×#14519769C2212yes—
47C2×#14519768C2214yes—
48C2×#14519765C2212yes—
49C2×#14519763C2214yes—
50C2×#14519763C2214yes—
51C2×#14519763C2214yes—
52C2×#14519762C2214yes—
53C2×#14519762C2214yes—
54C2×#14519761C2214yes—
55C2×#14519759C2214yes—
56C2×#14519757C2212yes—
57C2×#14519757C2212yes—
58C2×#14519757C2214yes—
59C2×#14519756C2212yes—
60C2×#14519756C2212yes—
61C2×#14519755C2214yes—
62C2×#14519754C2214yes—
63C2×#14519754C2214yes—
64C2×#14519753C2212yes—
65C2×#14519751C2212yes—
66C2×#14519751C2211yescharacteristic
67C2×#14519751C2212yes—
68C2×#14519751C2211yescharacteristic
69C2×#14519751C2212yes—
70C2×#14519750C2214yes—
71C2×#14519750C2214yes—
72C2×#14519749C2214yes—
73C2×#14519748C2212yes—
74C2×#14519748C2214yes—
75C2×C4×Dic122C2212yes—
76C2×C4×Dic122C2212yes—
77C2×C4×D244C2211yescharacteristic
78C2×C4×D244C2212yes—
79C2×C4×D244C2212yes—
80C2×C4×D244C2211yescharacteristic
81C2×C4×D244C2212yes—
82C2×#14519737C2214yes—
83C2×#14519736C2212yes—
84C2×#14519736C2212yes—
85C2×#14519735C2212yes—
86C2×#14519735C2214yes—
87C22×C4⋊Dic61C2212yes—
88C2×C4⋊C4×D61C2212yes—
89C61×#529C22116yescomplemented
90C2×#126×C61C2212yes—
91C2×#125×C61C2211yescharacteristic
92C2×#124×C61C2211yescharacteristic
93C2×#123×C61C2212yes—
94C2×C22⋊Q8×C61C2211yescharacteristic
95C2×#121×C61C2211yescharacteristic
96C2×C4×Q8×C61C2211yescharacteristic
97C2×C4×D4×C61C2211yescharacteristic
98C2×C4×D4×C61C2212yes—
99C2×#117×C61C2212yes—
100C22×C42×C61C2211yescharacteristic
101C2×#11758222—48no—
102C2×#11758222C23116yes—
103C2×#11758224—48no—
104C2×#11758224C23116yes—
105C22×Dic122C2312yes—
106C22×Dic122C2312yes—
107C22×Dic122C2312yes—
108C22×Dic122C2314yes—
109C2×Q8×D61—48no—
110C2×Q8×D61C23116yes—
111C22×D244C2311yescharacteristic
112C22×D244C2311yescharacteristic
113C22×D244C2312yes—
114C22×D244C2312yes—
115C22×C22⋊D61C2314yes—
116C22×C22⋊D61C2312yes—
117C22×C22⋊D61C2314yes—
118C22×C22⋊D61C2312yes—
119C23×Dic61C2314yes—
120C22×C4×D61C2312yes—
121C22×C4×D61C2312yes—
122C22×C4×D61C2314yes—
123C22×C4×D61C2314yes—
124#14519777C2318yes—
125#14519777C23116yes—
126#14519777C2318yes—
127#14519777C2318yes—
128#14519776C23132yes—
129#14519774C2318yes—
130#14519772C23132yes—
131#14519769C23116yes—
132#14519769C23116yes—
133#14519768C23132yes—
134#14519765C23116yes—
135#14519763C23132yes—
136#14519763C23132yes—
137#14519763C23132yes—
138#14519762C23132yes—
139#14519762C23132yes—
140#14519761C23132yes—
141#14519759C23132yes—
142#14519757C23116yes—
143#14519757C23116yes—
144#14519757C23132yes—
145#14519756C23116yes—
146#14519756C23116yes—
147#14519755C23132yes—
148#14519754C23132yes—
149#14519754C23132yes—
150#14519753C23116yes—
151#14519751C2318yes—
152#14519751C23116yes—
153#14519751C2318yes—
154#14519751C23116yes—
155#14519751C23116yes—
156#14519750C23132yes—
157#14519750C23132yes—
158#14519749C23132yes—
159#14519748C23132yes—
160#14519748C23116yes—
161C4×Dic122C23116yes—
162C4×Dic122C23116yes—
163C4×D244C23116yes—
164C4×D244C23116yes—
165C4×D244C23116yes—
166C4×D244C2318yes—
167C4×D244C2318yes—
168#14519737C23132yes—
169#14519736C23116yes—
170#14519736C23116yes—
171#14519735C23116yes—
172#14519735C23132yes—
173C2×C4⋊Dic61C23116yes—
174C2×C4⋊Dic61C2312yes—
175C2×C4⋊Dic61C2311yescharacteristic
176C2×C4⋊Dic61C2312yes—
177C2×C4⋊Dic61C2314yes—
178C2×C4⋊Dic61C2314yes—
179C2×C4⋊Dic61C2312yes—
180C2×C4⋊Dic61C2311yescharacteristic
181C2×C4⋊Dic61C2312yes—
182C2×C4⋊Dic61C2312yes—
183C2×#11758196C2314yes—
184C2×#11758196C2314yes—
185C2×#11758196C2314yes—
186C2×#11758196C2314yes—
187C4⋊C4×D61C23116yes—
188C2×C22⋊Dic61C2314yes—
189C2×C22⋊Dic61C2314yes—
190C2×#11758198C2312yes—
191C2×#11758198C2314yes—
192C2×#11758198C2314yes—
193C2×#11758198C2312yes—
194C2×#11758198C2314yes—
195C2×#11758198C2314yes—
196C2×#11758198C2312yes—
197C2×#11758198C2312yes—
198C2×C4×Dic61C2314yes—
199C2×C4×Dic61C2314yes—
200C22×Q8×C61C2311yescharacteristic
201C22×D4×C61C2311yescharacteristic
202C22×D4×C61C2312yes—
203C23×C4×C61C2312yes—
204C23×C4×C61C2311yescharacteristic
205C23×C4×C61C2311yescharacteristic
206C23×C4×C61C2311yescharacteristic
207#126×C61C23116yes—
208#125×C61C2318yes—
209#124×C61C2318yes—
210#123×C61C23116yes—
211C22⋊Q8×C61C2318yes—
212#121×C61C2318yes—
213C4×Q8×C61C2318yes—
214C4×D4×C61C23116yes—
215C4×D4×C61C2318yes—
216#117×C61C23116yes—
217C2×C4⋊C4×C61C2311yescharacteristic
218C2×C4⋊C4×C61C2311yescharacteristic
219C2×C4⋊C4×C61C2312yes—
220C2×C4⋊C4×C61C2312yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C22⋊C4×C61C2312yes—
224C2×C22⋊C4×C61C2312yes—
225C2×C22⋊C4×C61C2312yes—
226C2×C22⋊C4×C61C2312yes—
227C2×C22⋊C4×C61C2312yes—
228C2×C42×C61C2311yescharacteristic
229C2×C42×C61C2312yes—
230C2×C42×C61C2311yescharacteristic
231C2×C42×C61C2311yescharacteristic
232C2×C42×C61C2311yescharacteristic
233C2×C42×C61C2318yes—
234C24×C61C2412yes—
235C24×C61C2411yescharacteristic
236C23×D61C2412yes—
237C23×D61C2412yes—
238C2×Q8×C61—24no—
239C2×Q8×C61C2414yes—
240C2×D4×C61—24no—
241C2×D4×C61—44no—
242C2×D4×C61C2414yes—
243C2×D4×C61C2418yes—
244C22×C4×C61—24no—
245C22×C4×C61—28no—
246C22×C4×C61—24no—
247C22×C4×C61—42no—
248C22×C4×C61C2412yes—
249C22×C4×C61C2412yes—
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2411yescharacteristic
252C22×C4×C61C2411yescharacteristic
253C22×C4×C61C2414yes—
254C22×C4×C61C2411yescharacteristic
255C22×C4×C61C2414yes—
256C22×C4×C61C2412yes—
257C22×C4×C61C2418yes—
258C22×C4×C61C2414yes—
259C22×C4×C61C2411yescharacteristic
260C22×C4×C61C2411yescharacteristic
261C2×C22⋊D61—48no—
262C2×C22⋊D61—48no—
263C2×C22⋊D61—44no—
264C2×C22⋊D61—44no—
265C2×C22⋊D61C24116yes—
266C2×C22⋊D61C2418yes—
267C2×C22⋊D61C2418yes—
268C2×C22⋊D61C24116yes—
269C22×Dic61—48no—
270C22×Dic61C2412yes—
271C22×Dic61C2414yes—
272C22×Dic61C2412yes—
273C22×Dic61C2414yes—
274C22×Dic61C24116yes—
275Q8×D61—432no—
276#11758224—432no—
277#11758222—432no—
278C2×D244—24no—
279C2×D244—24no—
280C2×D244—44no—
281C2×D244—44no—
282C2×D244C2414yes—
283C2×D244C2414yes—
284C2×D244C2418yes—
285C2×D244C2418yes—
286C2×C4×D61—28no—
287C2×C4×D61—28no—
288C2×C4×D61—48no—
289C2×C4×D61—48no—
290C2×C4×D61C2418yes—
291C2×C4×D61C2418yes—
292C2×C4×D61C24116yes—
293C2×C4×D61C24116yes—
294C2×Dic122—28no—
295C2×Dic122—48no—
296C2×Dic122—44no—
297C2×Dic122—44no—
298C2×Dic122C2418yes—
299C2×Dic122C24116yes—
300C2×Dic122C2418yes—
301C2×Dic122C2418yes—
302C4⋊C4×C61C2418yes—
303C4⋊C4×C61C2418yes—
304C4⋊C4×C61C2414yes—
305C4⋊C4×C61C2418yes—
306C4⋊C4×C61C2414yes—
307C4⋊C4×C61C2418yes—
308C22⋊C4×C61C2418yes—
309C22⋊C4×C61C2418yes—
310C22⋊C4×C61C2418yes—
311C22⋊C4×C61C2418yes—
312C22⋊C4×C61C2418yes—
313C42×C61C2414yes—
314C42×C61C2414yes—
315C42×C61C2414yes—
316C42×C61C2414yes—
317C42×C61C2418yes—
318C22⋊Dic61C24116yes—
319C22⋊Dic61C24116yes—
320#11758198C2418yes—
321#11758198C24116yes—
322#11758198C24116yes—
323#11758198C2418yes—
324#11758198C24116yes—
325#11758198C24116yes—
326#11758198C2418yes—
327#11758198C2418yes—
328C4⋊Dic61C2418yes—
329C4⋊Dic61C2414yes—
330C4⋊Dic61C2418yes—
331C4⋊Dic61C24116yes—
332C4⋊Dic61C24116yes—
333C4⋊Dic61C2418yes—
334C4⋊Dic61C2414yes—
335C4⋊Dic61C2418yes—
336C4⋊Dic61C2418yes—
337#11758196C24116yes—
338#11758196C24116yes—
339#11758196C24116yes—
340#11758196C24116yes—
341C4×Dic61C24116yes—
342C4×Dic61C24116yes—
343C23×C61—24no—
344C23×C61—22no—
345C23×C61—24no—
346C23×C61—22no—
347C23×C61—24no—
348C23×C61—22no—
349C23×C61C2512yes—
350C23×C61C2514yes—
351C23×C61C2511yescharacteristic
352C22×D61—24no—
353C22×D61—24no—
354C22×D61—24no—
355C22×D61—24no—
356C22×D61—24no—
357C22×D61—24no—
358C22×D61C2514yes—
359C22×D61C2514yes—
360Q8×C61—28no—
361D4×C61—28no—
362D4×C61—48no—
363C2×C4×C61—24no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—24no—
367C2×C4×C61—22no—
368C2×C4×C61—24no—
369C2×C4×C61—22no—
370C2×C4×C61—28no—
371C2×C4×C61—28no—
372C2×C4×C61—216no—
373C2×C4×C61—44no—
374C2×C4×C61H(5,𝔽2)14yes—
375C2×C4×C612−1+414yes—
376C2×C4×C61C2512yes—
377C2×C4×C61C2514yes—
378C2×C4×C61C2512yes—
379C2×C4×C61C2512yes—
380C2×C4×C61C2514yes—
381C2×C4×C61C2514yes—
382C2×C4×C61C2512yes—
383C2×C4×C61C2512yes—
384C2×C4×C61C2512yes—
385C22⋊D61—48no—
386C22⋊D61—48no—
387C22⋊D61—416no—
388C22⋊D61—416no—
389C2×Dic61—28no—
390C2×Dic61—24no—
391C2×Dic61—24no—
392C2×Dic61—28no—
393C2×Dic61—416no—
394C2×Dic61C2518yes—
395C2×Dic61C2514yes—
396C2×Dic61C2518yes—
397C2×Dic61C2514yes—
398D244—28no—
399D244—28no—
400D244—48no—
401D244—48no—
402C4×D61—216no—
403C4×D61—216no—
404C4×D61—416no—
405C4×D61—416no—
406Dic122—216no—
407Dic122—48no—
408Dic122—48no—
409Dic122—416no—
410C2×#3547—611nomaximal, Sylow
411C22×C61—24no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—24no—
415C22×C61—24no—
416C22×C61—22no—
417C22×C61—48no—
418C22×C61—44no—
419C22×C61C2×H(5,𝔽2)12yes—
420C22×C61C2×2−1+412yes—
421C22×C61#58512yes—
422C22×C61C2611yescharacteristic
423C2×D61—24no—
424C2×D61—24no—
425C2×D61—24no—
426C2×D61—24no—
427C2×D61—24no—
428C2×D61—24no—
429C2×D61—48no—
430C2×D61—48no—
431C4×C61—24no—
432C4×C61—22no—
433C4×C61—22no—
434C4×C61—24no—
435C4×C61—22no—
436C4×C61—24no—
437C4×C61—22no—
438C4×C61C2×H(5,𝔽2)14yes—
439C4×C61C2×2−1+414yes—
440Dic61—28no—
441Dic61—24no—
442Dic61—24no—
443Dic61—28no—
444#3547—6132no—
445C2×#562—614no—
446C2×#555—612no—
447C2×#555—611no—
448C2×#554—611no—
449C2×#553—612no—
450C2×#552—612no—
451C2×D4×Q8—611no—
452C2×#548—612no—
453C2×#547—611no—
454C2×#544—612no—
455C2×#542—614no—
456C2×#540—612no—
457C2×#537—612no—
458C2×#536—612no—
459C2×#533—611no—
460C2×#532—611no—
461C2×#529D6111yescharacteristic, complemented
462C2×C61—44no—
463C2×C61—42no—
464C2×C61#354714yescomplemented
465C2×C61C22×H(5,𝔽2)11yescharacteristic
466C2×C61C22×2−1+411yescharacteristic
467C2×C61C2×#58511yescharacteristic
468D61—44no—
469D61—44no—
470C22×#41—612no—
471C22×#41—612no—
472C23×Q8—612no—
473#562—6164no—
474#555—6132no—
475#555—6116no—
476#554—6116no—
477#553—6132no—
478#552—6132no—
479D4×Q8—6116no—
480#548—6132no—
481#547—6116no—
482#544—6132no—
483#542—6164no—
484#540—6132no—
485#537—6132no—
486#536—6132no—
487#533—6116no—
488#532—6116no—
489C2×C4⋊Q8—614no—
490C2×C4⋊Q8—611no—
491C2×C4⋊Q8—611no—
492C2×C4⋊Q8—611no—
493C2×C4⋊Q8—612no—
494C2×#127—611no—
495#529C2×D61116yescomplemented
496C2×#126—614no—
497C2×#126C2×D6112yes—
498C2×#125—614no—
499C2×#125—612no—
500C2×#125—612no—
501C2×#125C2×D6111yescharacteristic
502C2×#124—614no—
503C2×#124—614no—
504C2×#124—614no—
505C2×#124—612no—
506C2×#124C2×D6111yescharacteristic
507C2×#123—614no—
508C2×#123—614no—
509C2×#123—614no—
510C2×#123—614no—
511C2×#123C2×D6112yes—
512C2×C22⋊Q8—612no—
513C2×C22⋊Q8—612no—
514C2×C22⋊Q8—612no—
515C2×C22⋊Q8—614no—
516C2×C22⋊Q8—612no—
517C2×C22⋊Q8—612no—
518C2×C22⋊Q8—614no—
519C2×C22⋊Q8—614no—
520C2×C22⋊Q8—614no—
521C2×C22⋊Q8C2×D6111yescharacteristic
522C2×#121—612no—
523C2×#121—614no—
524C2×#121—614no—
525C2×#121—611no—
526C2×#121—611no—
527C2×#121—612no—
528C2×#121—612no—
529C2×#121—612no—
530C2×#121—614no—
531C2×#121—614no—
532C2×#121C2×D6111yescharacteristic
533C2×C4×Q8—612no—
534C2×C4×Q8—612no—
535C2×C4×Q8C2×D6111yescharacteristic
536C2×C4×D4—614no—
537C2×C4×D4—611no—
538C2×C4×D4—612no—
539C2×C4×D4—611no—
540C2×C4×D4—612no—
541C2×C4×D4—612no—
542C2×C4×D4C2×D6111yescharacteristic
543C2×C4×D4C2×D6112yes—
544C2×#117—612no—
545C2×#117—612no—
546C2×#117—612no—
547C2×#117—614no—
548C2×#117C2×D6112yes—
549C22×C4⋊C4—612no—
550C22×C4⋊C4—612no—
551C22×C42C2×D6111yescharacteristic
552C61C2×#354711yescharacteristic, complemented, Sylow
553C2×#41—6116no—
554C2×#41—6116no—
555C2×#41—2448no—
556C2×#41—2448no—
557C22×Q8—6116no—
558C22×Q8—612no—
559C22×Q8—612no—
560C22×Q8—614no—
561C22×Q8—612no—
562C22×Q8—2448no—
563C22×Q8C22×D6111yescharacteristic
564C22×D4—614no—
565C22×D4—612no—
566C22×D4—614no—
567C22×D4—612no—
568C22×D4—611no—
569C22×D4—611no—
570C22×D4—612no—
571C22×D4—612no—
572C22×D4C22×D6111yescharacteristic
573C22×D4C22×D6112yes—
574C23×C4—614no—
575C23×C4—612no—
576C23×C4—612no—
577C23×C4—614no—
578C23×C4—614no—
579C23×C4C22×D6112yes—
580C23×C4C22×D6111yescharacteristic
581C23×C4C22×D6111yescharacteristic
582C23×C4C22×D6111yescharacteristic
583C4⋊Q8—6132no—
584C4⋊Q8—618no—
585C4⋊Q8—618no—
586C4⋊Q8—618no—
587C4⋊Q8—6116no—
588#127—618no—
589#126—6132no—
590#126C22×D61116yes—
591#125—6132no—
592#125—6116no—
593#125—6116no—
594#125C22×D6118yes—
595#124—6132no—
596#124—6132no—
597#124—6132no—
598#124—6116no—
599#124C22×D6118yes—
600#123—6132no—
601#123—6132no—
602#123—6132no—
603#123—6132no—
604#123C22×D61116yes—
605C22⋊Q8—6116no—
606C22⋊Q8—6116no—
607C22⋊Q8—6116no—
608C22⋊Q8—6116no—
609C22⋊Q8—6116no—
610C22⋊Q8—6132no—
611C22⋊Q8—6132no—
612C22⋊Q8—6132no—
613C22⋊Q8—6132no—
614C22⋊Q8C22×D6118yes—
615#121—6116no—
616#121—6132no—
617#121—6132no—
618#121—618no—
619#121—618no—
620#121—6116no—
621#121—6116no—
622#121—6116no—
623#121—6132no—
624#121—6132no—
625#121C22×D6118yes—
626C4×Q8—6116no—
627C4×Q8—6116no—
628C4×Q8C22×D6118yes—
629C4×D4—6132no—
630C4×D4—618no—
631C4×D4—6116no—
632C4×D4—618no—
633C4×D4—6116no—
634C4×D4—6116no—
635C4×D4C22×D6118yes—
636C4×D4C22×D61116yes—
637#117—6116no—
638#117—6116no—
639#117—6116no—
640#117—6132no—
641#117C22×D61116yes—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—612no—
644C2×C4⋊C4—612no—
645C2×C4⋊C4—614no—
646C2×C4⋊C4—614no—
647C2×C4⋊C4—6116no—
648C2×C4⋊C4—612no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—614no—
651C2×C4⋊C4—612no—
652C2×C4⋊C4—614no—
653C2×C4⋊C4—614no—
654C2×C4⋊C4—614no—
655C2×C4⋊C4—612no—
656C2×C4⋊C4—6116no—
657C2×C4⋊C4C22×D6111yescharacteristic
658C2×C4⋊C4C22×D6111yescharacteristic
659C2×C4⋊C4C22×D6112yes—
660C2×C4⋊C4C22×D6112yes—
661C2×C4⋊C4C22×D6112yes—
662C2×C4⋊C4C22×D6112yes—
663C2×C22⋊C4—614no—
664C2×C22⋊C4—614no—
665C2×C22⋊C4—612no—
666C2×C22⋊C4—614no—
667C2×C22⋊C4—614no—
668C2×C22⋊C4—612no—
669C2×C22⋊C4—614no—
670C2×C22⋊C4—612no—
671C2×C22⋊C4—614no—
672C2×C22⋊C4—612no—
673C2×C22⋊C4C22×D6112yes—
674C2×C22⋊C4C22×D6112yes—
675C2×C22⋊C4C22×D6112yes—
676C2×C22⋊C4C22×D6112yes—
677C2×C22⋊C4C22×D6112yes—
678C2×C42—614no—
679C2×C42—614no—
680C2×C42C22×D6111yescharacteristic
681C2×C42C22×D6112yes—
682C2×C42C22×D6111yescharacteristic
683C2×C42C22×D6111yescharacteristic
684C2×C42C22×D6111yescharacteristic
685C2×C42C22×D6118yes—
686C24—612no—
687C24—612no—
688C24C23×D6111yescharacteristic
689C24C23×D6112yes—
690#41—24432no—
691#41—24432no—
692C2×Q8—24no—
693C2×Q8—618no—
694C2×Q8—618no—
695C2×Q8—6116no—
696C2×Q8—618no—
697C2×Q8—1228no—
698C2×Q8—2444no—
699C2×Q8—2448no—
700C2×Q8—2444no—
701C2×Q8—24432no—
702C2×Q8C23×D6114yes—
703C2×D4—24no—
704C2×D4—44no—
705C2×D4—6116no—
706C2×D4—618no—
707C2×D4—6116no—
708C2×D4—618no—
709C2×D4—614no—
710C2×D4—614no—
711C2×D4—618no—
712C2×D4—618no—
713C2×D4—1224no—
714C2×D4—1224no—
715C2×D4—2444no—
716C2×D4—2444no—
717C2×D4—2444no—
718C2×D4—2444no—
719C2×D4—2448no—
720C2×D4—2448no—
721C2×D4C23×D6114yes—
722C2×D4C23×D6118yes—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—42no—
727C22×C4—614no—
728C22×C4—612no—
729C22×C4—614no—
730C22×C4—612no—
731C22×C4—6116no—
732C22×C4—618no—
733C22×C4—618no—
734C22×C4—6116no—
735C22×C4—6116no—
736C22×C4—1228no—
737C22×C4—1228no—
738C22×C4—2448no—
739C22×C4—2448no—
740C22×C4—2448no—
741C22×C4C23×D6114yes—
742C22×C4C23×D6114yes—
743C22×C4C23×D6118yes—
744C22×C4C23×D6111yescharacteristic
745C22×C4C23×D6112yes—
746C22×C4C23×D6111yescharacteristic
747C22×C4C23×D6111yescharacteristic
748C22×C4C23×D6111yescharacteristic
749C22×C4C23×D6112yes—
750C22×C4C23×D6112yes—
751C22×C4C23×D6114yes—
752C22×C4C23×D6111yescharacteristic
753C22×C4C23×D6111yescharacteristic
754C4⋊C4—614no—
755C4⋊C4—6116no—
756C4⋊C4—618no—
757C4⋊C4—618no—
758C4⋊C4—6116no—
759C4⋊C4—6116no—
760C4⋊C4—6116no—
761C4⋊C4—6116no—
762C4⋊C4—618no—
763C4⋊C4—614no—
764C4⋊C4—6116no—
765C4⋊C4—618no—
766C4⋊C4—618no—
767C4⋊C4C23×D6114yes—
768C4⋊C4C23×D6114yes—
769C4⋊C4C23×D6118yes—
770C4⋊C4C23×D6118yes—
771C4⋊C4C23×D6118yes—
772C4⋊C4C23×D6118yes—
773C22⋊C4—6116no—
774C22⋊C4—6116no—
775C22⋊C4—618no—
776C22⋊C4—6116no—
777C22⋊C4—6116no—
778C22⋊C4—618no—
779C22⋊C4—6116no—
780C22⋊C4—618no—
781C22⋊C4—6116no—
782C22⋊C4—618no—
783C22⋊C4C23×D6118yes—
784C22⋊C4C23×D6118yes—
785C22⋊C4C23×D6118yes—
786C22⋊C4C23×D6118yes—
787C22⋊C4C23×D6118yes—
788C42—6116no—
789C42—6116no—
790C42C23×D6114yes—
791C42C23×D6114yes—
792C42C23×D6114yes—
793C42C23×D6114yes—
794C42C23×D6118yes—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—614no—
802C23—614no—
803C23—1224no—
804C23—1224no—
805C23—1224no—
806C23—1224no—
807C23—1224no—
808C23—1224no—
809C23C24×D6112yes—
810C23C24×D6114yes—
811C23C24×D6111yescharacteristic
812Q8—28no—
813Q8—12216no—
814Q8—2448no—
815Q8—24416no—
816Q8—2448no—
817D4—28no—
818D4—48no—
819D4—1228no—
820D4—1228no—
821D4—2448no—
822D4—2448no—
823D4—24416no—
824D4—2448no—
825D4—2448no—
826D4—24416no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—216no—
837C2×C4—44no—
838C2×C4—618no—
839C2×C4—614no—
840C2×C4—618no—
841C2×C4—614no—
842C2×C4—1224no—
843C2×C4—1224no—
844C2×C4—1228no—
845C2×C4—1228no—
846C2×C4—12216no—
847C2×C4—12216no—
848C2×C4—24416no—
849C2×C4—24416no—
850C2×C4—24416no—
851C2×C4#1451982314yes—
852C2×C4#1451982414yes—
853C2×C4C24×D6112yes—
854C2×C4C24×D6114yes—
855C2×C4C24×D6112yes—
856C2×C4C24×D6112yes—
857C2×C4C24×D6112yes—
858C2×C4C24×D6114yes—
859C2×C4C24×D6114yes—
860C2×C4C24×D6112yes—
861C2×C4C24×D6112yes—
862C22—22no—
863C22—24no—
864C22—22no—
865C22—24no—
866C22—22no—
867C22—24no—
868C22—44no—
869C22—48no—
870C22—1224no—
871C22—1224no—
872C22—1224no—
873C22—1224no—
874C22—1224no—
875C22—1224no—
876C22—2448no—
877C22—2448no—
878C22C2×#1451982312yes—
879C22C2×#1451982412yes—
880C22#1684059812yes—
881C22C25×D6111yescharacteristic
882C4—22no—
883C4—24no—
884C4—22no—
885C4—24no—
886C4—22no—
887C4—22no—
888C4—24no—
889C4—1224no—
890C4—1224no—
891C4—1228no—
892C4—1228no—
893C4C2×#1451982314yes—
894C4C2×#1451982414yes—
895C2—42no—
896C2—44no—
897C2—2444no—
898C2—2444no—
899C2#2146021014yesdirect product factor
900C2C22×#1451982311yescharacteristic
901C2C22×#1451982411yescharacteristic
902C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#529C2
socleC23×C61C25
hypercenterC2×#529D61
hypocenterC61C2×#3547
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #21460210C2direct (N × H)
2. C2×#16840509C2semidirect
3. C2×#16840477C2semidirect
4. C2×#16840477C2semidirect
5. C2×#16840472C2semidirect
6. C2×#16840458C2semidirect
7. C2×#16840450C2semidirect
8. C2×Q8×D244C2semidirect
9. C2×#16840420C2semidirect
10. C2×#16840416C2semidirect
11. C2×#16840390C2semidirect
12. C2×#16840378C2semidirect
13. C2×#16840367C2semidirect
14. C2×#16840341C2semidirect
15. C2×#16840335C2semidirect
16. C2×#16840319C2semidirect
17. C2×#16840312C2semidirect
18. C2×C61×#529C2semidirect
22. #16840509C22semidirect
23. #16840477C22semidirect
24. #16840477C22semidirect
25. #16840472C22semidirect
26. #16840458C22semidirect
27. #16840450C22semidirect
28. Q8×D244C22semidirect
29. #16840420C22semidirect
30. #16840416C22semidirect
31. #16840390C22semidirect
32. #16840378C22semidirect
33. #16840367C22semidirect
34. #16840341C22semidirect
35. #16840335C22semidirect
36. #16840319C22semidirect
37. #16840312C22semidirect
89. C61×#529C22semidirect
461. C2×#529D61semidirect
464. C2×C61#3547semidirect
495. #529C2×D61semidirect
552. C61C2×#3547semidirect
899. C2#21460210direct (N × H)

Maximal subgroups

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

subgroupindex
#214602102
C2×#168405092
C2×#168404772
C2×#168404722
C2×#168404582
C2×#168404502
C2×Q8×D2442
C2×#168404202
C2×#168404162
C2×#168403902
C2×#168403782
C2×#168403672
C2×#168403412
C2×#168403352
C2×#168403192
C2×#168403122
C2×C61×#5292
C2×#354761