Finite Group Databasebeta

← C2×#21459487 #30588325

Subgroups — C2×#21459487 #30588325

Order 15616.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519823C211yesmaximal, characteristic, complemented
2C22×#41×D61C211yesmaximal, characteristic, complemented
3#21459487C2132yesmaximal, direct product factor
4C2×#16840431C211yesmaximal, characteristic, complemented
5C2×#16840424C211yesmaximal, characteristic, complemented
6C2×#16840419C211yesmaximal, characteristic, complemented
7C2×#16840409C213yesmaximal, complemented
8C2×#16840408C213yesmaximal, complemented
9C2×#16840397C213yesmaximal, complemented
10C2×#16840396C213yesmaximal, complemented
11C2×#16840341C213yesmaximal, complemented
12C2×#16840325C213yesmaximal, complemented
13C2×#16840271C213yesmaximal, complemented
14C2×#121×D61C213yesmaximal, complemented
15C2×#16840244C211yesmaximal, characteristic, complemented
16C2×C61×#550C211yesmaximal, characteristic, complemented
17C2×#14519823—216no—
18C2×#14519823C22116yescomplemented
19C22×#11758226C2211yescharacteristic
20C22×#11758226C2211yescharacteristic, complemented
21C22×#11758222C2213yescomplemented
22C22×#11758222C2213yescomplemented
23C22×#11758224C2213yescomplemented
24C2×#41×D61—216no—
25C2×#41×D61C22116yescomplemented
26C22×Q8×D61C2211yescharacteristic, complemented
27C23×D244C2213yescomplemented
28C22×D4×D61C2213yescomplemented
29C22×D4×D61C2213yescomplemented
30C22×D4×D61C2213yescomplemented
31C22×D4×D61C2216yescomplemented
32C23×C4×D61C2213yescomplemented
33#16840431C22116yescomplemented
34#16840424C22116yescomplemented
35#16840419C22116yescomplemented
36#16840409C22148yescomplemented
37#16840408C22148yescomplemented
38#16840397C22148yescomplemented
39#16840396C22148yescomplemented
40#16840341C22148yescomplemented
41#16840325C22148yescomplemented
42C2×#14519773C2213yescomplemented
43C2×#14519765C2213yescomplemented
44C2×#14519764C2213yescomplemented
45#16840271C22148yescomplemented
46C2×#14519762C2213yescomplemented
47C2×#14519759C2213yescomplemented
48C2×#14519757C2213yescomplemented
49C2×#14519756C2213yescomplemented
50C2×#14519755C2211yescharacteristic, complemented
51C2×#14519754C2213yescomplemented
52C2×#14519752C2213yescomplemented
53C2×#14519751C2213yescomplemented
54C2×#14519750C2216yescomplemented
55C2×#14519750C2213yescomplemented
56C2×#14519749C2216yescomplemented
57C2×#14519749C2213yescomplemented
58C2×#14519748C2216yescomplemented
59C2×#14519748C2213yescomplemented
60C2×#14519748C2213yescomplemented
61#121×D61C22148yescomplemented
62C2×#14519747C2213yescomplemented
63C2×#14519745C2216yescomplemented
64C2×#14519745C2213yescomplemented
65C2×#14519745C2216yescomplemented
66#16840244C22116yescomplemented
67C2×Q8×Dic61C2211yescharacteristic, complemented
68C2×C4×D244C2213yescomplemented
69C2×C4×D244C2213yescomplemented
70C2×#14519739C2213yescomplemented
71C2×C4×C22⋊D61C2213yescomplemented
72C2×C4×C22⋊D61C2213yescomplemented
73C2×#14519734C2213yescomplemented
74C2×C4⋊C4×D61C2213yescomplemented
75C2×C22⋊C4×D61C2216yescomplemented
76C22×#41×C61C2211yescharacteristic, complemented
77C22×#41×C61C2211yescharacteristic, complemented
78C61×#550C22116yescomplemented
79C2×#127×C61C2213yescomplemented
80C2×#121×C61C2213yescomplemented
81C2×#121×C61C2213yescomplemented
82C2×C4×Q8×C61C2211yescharacteristic, complemented
83C2×C4×D4×C61C2213yescomplemented
84C24×D61C2313yes—
85C24×D61C2316yes—
86#14519823—2128no—
87C2×#11758226—28no—
88C2×#11758226D4116yescomplemented
89C2×#11758226C2318yes—
90C2×#11758226C2318yescomplemented
91C2×#11758222—224no—
92C2×#11758222—224no—
93C2×#11758222C23124yescomplemented
94C2×#11758222C23124yescomplemented
95C2×#11758224—224no—
96C2×#11758224C23124yescomplemented
97#41×D61—2128no—
98C22×Dic122C2311yescharacteristic
99C22×Dic122C2313yes—
100C2×Q8×D61—28no—
101C2×Q8×D61C2318yescomplemented
102C22×D244—224no—
103C22×D244C2313yes—
104C22×D244C2313yes—
105C22×D244C2313yes—
106C22×D244C2313yes—
107C22×D244C23124yescomplemented
108C22×C22⋊D61C2313yes—
109C22×C22⋊D61C2316yes—
110C22×C22⋊D61C2313yes—
111C22×C22⋊D61C2313yes—
112C22×C22⋊D61C2313yes—
113C22×C22⋊D61C2316yes—
114C2×D4×D61—224no—
115C2×D4×D61—224no—
116C2×D4×D61—224no—
117C2×D4×D61—424no—
118C2×D4×D61C23124yescomplemented
119C2×D4×D61C23124yescomplemented
120C2×D4×D61C23124yescomplemented
121C2×D4×D61C23148yescomplemented
122C23×Dic61C2313yes—
123C22×C4×D61—224no—
124C22×C4×D61C2313yes—
125C22×C4×D61C2313yes—
126C22×C4×D61C2313yes—
127C22×C4×D61C2311yescharacteristic
128C22×C4×D61C2316yes—
129C22×C4×D61C2313yes—
130C22×C4×D61C23124yescomplemented
131#14519773C23124yescomplemented
132#14519765C23124yescomplemented
133#14519764C23124yescomplemented
134#14519762C23124yescomplemented
135#14519759C23124yescomplemented
136#14519757C23124yescomplemented
137#14519756C23124yescomplemented
138#14519755C2318yescomplemented
139#14519754C23124yescomplemented
140#14519752C23124yescomplemented
141#14519751C23124yescomplemented
142#14519750C23124yescomplemented
143#14519750C23148yescomplemented
144#14519749C23148yescomplemented
145#14519749C23124yescomplemented
146#14519748C23124yescomplemented
147#14519748C23148yescomplemented
148#14519748C23124yescomplemented
149#14519747C23124yescomplemented
150#14519745C23124yescomplemented
151#14519745C23148yescomplemented
152#14519745C23148yescomplemented
153Q8×Dic61C2318yescomplemented
154C4×D244C23124yescomplemented
155C4×D244C23124yescomplemented
156#14519739C23124yescomplemented
157C4×C22⋊D61C23124yescomplemented
158C4×C22⋊D61C23124yescomplemented
159#14519734C23124yescomplemented
160C2×C4⋊Dic61C2313yes—
161C2×C4⋊Dic61C2313yes—
162C2×#11758196C2313yes—
163C2×#11758196C2311yescharacteristic
164C2×#11758196C2311yescharacteristic
165C2×#11758196C2313yes—
166C4⋊C4×D61C23124yescomplemented
167C2×C22⋊Dic61C2316yes—
168C2×C22⋊Dic61C2313yes—
169C2×C22⋊Dic61C2313yes—
170C2×#11758198C2313yes—
171C2×#11758198C2316yes—
172C2×#11758198C2313yes—
173C2×#11758198C2313yes—
174C2×#11758198C2311yescharacteristic
175C2×#11758198C2311yescharacteristic
176C2×#11758198C2313yes—
177C22⋊C4×D61C23148yescomplemented
178C2×C4×Dic61C2313yes—
179C2×#41×C61—28no—
180C2×#41×C61—28no—
181C2×#41×C61C2318yescomplemented
182C2×#41×C61C2318yescomplemented
183C22×Q8×C61C2311yescharacteristic
184C22×D4×C61C2313yes—
185C22×D4×C61C2313yes—
186C22×D4×C61C2313yes—
187C22×D4×C61C2316yes—
188C23×C4×C61C2313yes—
189C23×C4×C61C2313yes—
190#127×C61C23124yescomplemented
191#121×C61C23124yescomplemented
192#121×C61C23124yescomplemented
193C4×Q8×C61C2318yescomplemented
194C4×D4×C61C23124yescomplemented
195C2×C4⋊C4×C61C2313yes—
196C2×C4⋊C4×C61C2311yescharacteristic
197C2×C22⋊C4×C61C2313yes—
198C2×C22⋊C4×C61C2313yes—
199C2×C42×C61C2313yes—
200C24×C61C2413yes—
201C24×C61C2413yes—
202C23×D61—212no—
203C23×D61—212no—
204C23×D61—224no—
205C23×D61—46no—
206C23×D61—412no—
207C23×D61—412no—
208C23×D61C2413yes—
209C23×D61C24112yes—
210C23×D61C2413yes—
211C23×D61C2411yescharacteristic
212C23×D61C24124yes—
213#41×C61—232no—
214#41×C61—232no—
215C2×Q8×C61C2×D418yescomplemented
216C2×Q8×C61C2414yes—
217C2×D4×C61—212no—
218C2×D4×C61—212no—
219C2×D4×C61—412no—
220C2×D4×C61—46no—
221C2×D4×C61C24112yes—
222C2×D4×C61C24112yes—
223C2×D4×C61C24124yes—
224C2×D4×C61C24112yes—
225C22×C4×C61—212no—
226C22×C4×C61—212no—
227C22×C4×C61C2411yescharacteristic
228C22×C4×C61C2413yes—
229C22×C4×C61C24112yes—
230C22×C4×C61C2411yescharacteristic
231C22×C4×C61C24112yes—
232C22×C4×C61C2411yescharacteristic
233C22×C4×C61C2413yes—
234C2×C22⋊D61—212no—
235C2×C22⋊D61—224no—
236C2×C22⋊D61—212no—
237C2×C22⋊D61—212no—
238C2×C22⋊D61—412no—
239C2×C22⋊D61—46no—
240C2×C22⋊D61C24112yes—
241C2×C22⋊D61C24112yes—
242C2×C22⋊D61C24112yes—
243C2×C22⋊D61C24124yes—
244C2×C22⋊D61C24124yes—
245C2×C22⋊D61C24112yes—
246C22×Dic61—212no—
247C22×Dic61C2411yescharacteristic
248C22×Dic61C2413yes—
249C22×Dic61C2413yes—
250C22×Dic61C24112yes—
251C22×Dic61C2411yescharacteristic
252C22×Dic61C2411yescharacteristic
253#11758226—232no—
254#11758226C2×D4164yescomplemented
255Q8×D61—232no—
256#11758224—296no—
257D4×D61—296no—
258D4×D61—296no—
259D4×D61—296no—
260D4×D61—496no—
261#11758222—296no—
262#11758222—296no—
263C2×D244—212no—
264C2×D244—212no—
265C2×D244—212no—
266C2×D244—296no—
267C2×D244C2×D4124yescomplemented
268C2×D244C24112yes—
269C2×D244C24112yes—
270C2×D244C24112yes—
271C2×D244C24112yes—
272C2×C4×D61—212no—
273C2×C4×D61—212no—
274C2×C4×D61—212no—
275C2×C4×D61—24no—
276C2×C4×D61—296no—
277C2×C4×D61—412no—
278C2×C4×D61C2×D4124yescomplemented
279C2×C4×D61C2414yes—
280C2×C4×D61C24112yes—
281C2×C4×D61C24112yes—
282C2×C4×D61C24112yes—
283C2×C4×D61C24124yes—
284C2×C4×D61C24112yes—
285C2×Dic122—212no—
286C2×Dic122—24no—
287C2×Dic122C24112yes—
288C2×Dic122C2414yes—
289C4⋊C4×C61C2414yes—
290C4⋊C4×C61C24112yes—
291C22⋊C4×C61C24112yes—
292C22⋊C4×C61C24112yes—
293C42×C61C24112yes—
294C22⋊Dic61C24124yes—
295C22⋊Dic61C24112yes—
296C22⋊Dic61C24112yes—
297#11758198C24112yes—
298#11758198C24124yes—
299#11758198C24112yes—
300#11758198C24112yes—
301#11758198C2414yes—
302#11758198C2414yes—
303#11758198C24112yes—
304C4⋊Dic61C24112yes—
305C4⋊Dic61C24112yes—
306#11758196C24112yes—
307#11758196C2414yes—
308#11758196C2414yes—
309#11758196C24112yes—
310C4×Dic61C24112yes—
311C23×C61—26no—
312C23×C61—26no—
313C23×C61—26no—
314C23×C61—26no—
315C23×C61—26no—
316C23×C61—26no—
317C23×C61C2516yes—
318C23×C61C2516yes—
319C23×C61C2511yescharacteristic
320C22×D61—22no—
321C22×D61—26no—
322C22×D61—22no—
323C22×D61—26no—
324C22×D61—26no—
325C22×D61—26no—
326C22×D61—26no—
327C22×D61—224no—
328C22×D61—224no—
329C22×D61—248no—
330C22×D61—412no—
331C22×D61—448no—
332C22×D61—424no—
333C22×D61—424no—
334C22×D61—848no—
335C22×D61C22×D4112yes—
336C22×D61H(5,𝔽2)14yescomplemented
337C22×D61C2516yes—
338C22×D61C2516yes—
339C22×D61C2512yes—
340Q8×C61C22×D4116yescomplemented
341D4×C61—224no—
342D4×C61—224no—
343D4×C61—424no—
344D4×C61—412no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—26no—
348C2×C4×C61—22no—
349C2×C4×C61—224no—
350C2×C4×C61—224no—
351C2×C4×C61C22×D4112yes—
352C2×C4×C61C2512yes—
353C2×C4×C61C2516yes—
354C2×C4×C61C2512yes—
355C2×C4×C61C2512yes—
356C2×C4×C61C2516yes—
357C22⋊D61—224no—
358C22⋊D61—248no—
359C22⋊D61—224no—
360C22⋊D61—224no—
361C22⋊D61—424no—
362C22⋊D61—412no—
363C2×Dic61—26no—
364C2×Dic61—22no—
365C2×Dic61—26no—
366C2×Dic61—22no—
367C2×Dic61—224no—
368C2×Dic61C22×D414yes—
369C2×Dic61C2512yes—
370C2×Dic61C2516yes—
371C2×Dic61C2512yes—
372C2×Dic61C2516yes—
373C2×Dic61C2512yes—
374D244—224no—
375D244—224no—
376D244—224no—
377D244C22×D4148yescomplemented
378C4×D61—224no—
379C4×D61—224no—
380C4×D61—224no—
381C4×D61—28no—
382C4×D61—424no—
383C4×D61C22×D4148yescomplemented
384Dic122—224no—
385Dic122—28no—
386C2×#3488—611nomaximal, Sylow
387C22×C61—26no—
388C22×C61—26no—
389C22×C61—26no—
390C22×C61—26no—
391C22×C61—26no—
392C22×C61—26no—
393C22×C61—412no—
394C22×C61—412no—
395C22×C61C23×D412yes—
396C22×C61C2×H(5,𝔽2)12yes—
397C22×C61#58512yes—
398C22×C61C2611yescharacteristic
399C2×D61—22no—
400C2×D61—26no—
401C2×D61—22no—
402C2×D61—26no—
403C2×D61—28no—
404C2×D61—224no—
405C2×D61—26no—
406C2×D61—26no—
407C2×D61—26no—
408C2×D61—448no—
409C2×D61—412no—
410C2×D61—848no—
411C2×D61C23×D4112yes—
412C2×D61C2×H(5,𝔽2)14yescomplemented
413C4×C61—22no—
414C4×C61—22no—
415C4×C61—26no—
416C4×C61—22no—
417C4×C61C23×D4112yes—
418Dic61—26no—
419Dic61—22no—
420Dic61—26no—
421Dic61—22no—
422Dic61C23×D414yes—
423C22×H(5,𝔽2)—611no—
424C23×#41—611no—
425#3488—6132no—
426C2×#550—611no—
427C2×#550D6111yescharacteristic, complemented
428C2×#548—611no—
429C2×#548—611no—
430C2×#546—613no—
431C2×#546—613no—
432C2×D42—613no—
433C2×D42—613no—
434C2×#537—613no—
435C2×#535—613no—
436C2×#525—613no—
437C22×#121—613no—
438C2×#520—611no—
439C2×C61—46no—
440C2×C61—46no—
441C2×C61#348814yescomplemented
442C2×C61C24×D411yescharacteristic
443C2×C61C22×H(5,𝔽2)11yescharacteristic
444C2×C61C2×#58511yescharacteristic
445D61—24no—
446D61—212no—
447D61—46no—
448C2×H(5,𝔽2)—6116no—
449C2×H(5,𝔽2)—12216no—
450C22×#41—6116no—
451C22×#41—611no—
452C22×#41—611no—
453C22×#41—613no—
454C22×#41—613no—
455C22×#41—613no—
456C22×#41—12216no—
457C22×#41C2×D6111yescharacteristic, complemented
458C22×#41C2×D6111yescharacteristic, complemented
459C23×Q8—611no—
460C23×D4—613no—
461C23×D4—613no—
462C23×D4—613no—
463C23×D4—616no—
464C23×D4—613no—
465C24×C4—613no—
466#550—6116no—
467#550C2×D61116yescomplemented
468#548—6116no—
469#548—6116no—
470#546—6148no—
471#546—6148no—
472D42—6148no—
473D42—6148no—
474#537—6148no—
475#535—6148no—
476C2×#127—613no—
477C2×#127C2×D6113yescomplemented
478C2×#124—613no—
479C2×#124—613no—
480#525—6148no—
481C2×#123—613no—
482C2×#123—613no—
483C2×C22⋊Q8—613no—
484C2×C22⋊Q8—611no—
485C2×C22⋊Q8—613no—
486C2×C22⋊Q8—613no—
487C2×#121—613no—
488C2×#121—616no—
489C2×#121—613no—
490C2×#121—616no—
491C2×#121—613no—
492C2×#121—613no—
493C2×#121—6148no—
494C2×#121—613no—
495C2×#121—613no—
496C2×#121—616no—
497C2×#121C2×D6113yescomplemented
498C2×#121C2×D6113yescomplemented
499C2×#120—613no—
500C2×#120—616no—
501C2×#120—616no—
502C2×#120—613no—
503#520—6116no—
504C2×C4×Q8—611no—
505C2×C4×Q8C2×D6111yescharacteristic, complemented
506C2×C4×D4—613no—
507C2×C4×D4—613no—
508C2×C4×D4—613no—
509C2×C4×D4—613no—
510C2×C4×D4—613no—
511C2×C4×D4C2×D6113yescomplemented
512C2×#117—613no—
513C22×C4⋊C4—613no—
514C22×C22⋊C4—616no—
515C61C2×#348811yescharacteristic, complemented, Sylow
516C25—613no—
517C25—616no—
518H(5,𝔽2)—122128no—
519C2×#41—28no—
520C2×#41—28no—
521C2×#41—6116no—
522C2×#41—618no—
523C2×#41—618no—
524C2×#41—6124no—
525C2×#41—6124no—
526C2×#41—6124no—
527C2×#41—12224no—
528C2×#41—12224no—
529C2×#41—12224no—
530C2×#41—122128no—
531C2×#41—1228no—
532C2×#41C22×D6118yescomplemented
533C2×#41C22×D6118yescomplemented
534C22×Q8—618no—
535C22×Q8—611no—
536C22×Q8—613no—
537C22×Q8—1228no—
538C22×Q8C22×D6111yescharacteristic
539C22×D4—613no—
540C22×D4—616no—
541C22×D4—613no—
542C22×D4—613no—
543C22×D4—613no—
544C22×D4—616no—
545C22×D4—6124no—
546C22×D4—6124no—
547C22×D4—6124no—
548C22×D4—6148no—
549C22×D4—613no—
550C22×D4—613no—
551C22×D4—613no—
552C22×D4—613no—
553C22×D4—6124no—
554C22×D4—12224no—
555C22×D4—12224no—
556C22×D4—12224no—
557C22×D4—12224no—
558C22×D4—24424no—
559C22×D4C22×D6113yes—
560C22×D4C22×D6113yes—
561C22×D4C22×D6113yes—
562C22×D4C22×D6116yes—
563C23×C4—613no—
564C23×C4—613no—
565C23×C4—613no—
566C23×C4—613no—
567C23×C4—613no—
568C23×C4—611no—
569C23×C4—6124no—
570C23×C4—616no—
571C23×C4—12224no—
572C23×C4C22×D6113yes—
573C23×C4C22×D6113yes—
574#127—6124no—
575#127C22×D61124yescomplemented
576#124—6124no—
577#124—6124no—
578#123—6124no—
579#123—6124no—
580C22⋊Q8—6124no—
581C22⋊Q8—618no—
582C22⋊Q8—6124no—
583C22⋊Q8—6124no—
584#121—6148no—
585#121—6124no—
586#121—6124no—
587#121—6148no—
588#121—6124no—
589#121—6124no—
590#121—6124no—
591#121—6124no—
592#121—6148no—
593#121C22×D61124yescomplemented
594#121C22×D61124yescomplemented
595#120—6124no—
596#120—6148no—
597#120—6148no—
598#120—6124no—
599C4×Q8—618no—
600C4×Q8C22×D6118yescomplemented
601C4×D4—6124no—
602C4×D4—6124no—
603C4×D4—6124no—
604C4×D4—6124no—
605C4×D4—6124no—
606C4×D4C22×D61124yescomplemented
607#117—6124no—
608C2×C4⋊C4—613no—
609C2×C4⋊C4—613no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—613no—
613C2×C4⋊C4—613no—
614C2×C4⋊C4—6124no—
615C2×C4⋊C4C22×D6113yes—
616C2×C4⋊C4C22×D6111yescharacteristic
617C2×C22⋊C4—616no—
618C2×C22⋊C4—613no—
619C2×C22⋊C4—613no—
620C2×C22⋊C4—613no—
621C2×C22⋊C4—616no—
622C2×C22⋊C4—613no—
623C2×C22⋊C4—613no—
624C2×C22⋊C4—611no—
625C2×C22⋊C4—611no—
626C2×C22⋊C4—613no—
627C2×C22⋊C4—6148no—
628C2×C22⋊C4C22×D6113yes—
629C2×C22⋊C4C22×D6113yes—
630C2×C42—613no—
631C2×C42C22×D6113yes—
632C24—613no—
633C24—611no—
634C24—613no—
635C24—6112no—
636C24—6124no—
637C24—12224no—
638C24—12212no—
639C24—12212no—
640C24—24412no—
641C24—24412no—
642C24—2446no—
643C24C23×D6113yes—
644C24C23×D6113yes—
645#41—232no—
646#41—232no—
647#41—6164no—
648#41—12296no—
649#41—12296no—
650#41—12296no—
651#41—12232no—
652C2×Q8—614no—
653C2×Q8—6112no—
654C2×Q8—1224no—
655C2×Q8—12232no—
656C2×Q8—12212no—
657C2×Q8D4×D6118yescomplemented
658C2×Q8C23×D6114yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—412no—
662C2×D4—46no—
663C2×D4—6112no—
664C2×D4—6124no—
665C2×D4—6112no—
666C2×D4—6112no—
667C2×D4—6112no—
668C2×D4—6124no—
669C2×D4—6124no—
670C2×D4—6112no—
671C2×D4—6112no—
672C2×D4—6112no—
673C2×D4—6112no—
674C2×D4—12296no—
675C2×D4—12212no—
676C2×D4—12212no—
677C2×D4—12296no—
678C2×D4—12212no—
679C2×D4—12296no—
680C2×D4—12296no—
681C2×D4—12212no—
682C2×D4—12224no—
683C2×D4—12212no—
684C2×D4—12212no—
685C2×D4—24412no—
686C2×D4—2446no—
687C2×D4—24496no—
688C2×D4C23×D61112yes—
689C2×D4C23×D61112yes—
690C2×D4C23×D61112yes—
691C2×D4C23×D61124yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—611no—
695C22×C4—6124no—
696C22×C4—6112no—
697C22×C4—6112no—
698C22×C4—611no—
699C22×C4—613no—
700C22×C4—613no—
701C22×C4—611no—
702C22×C4—6112no—
703C22×C4—6112no—
704C22×C4—6112no—
705C22×C4—614no—
706C22×C4—6124no—
707C22×C4—1224no—
708C22×C4—12296no—
709C22×C4—12212no—
710C22×C4—12212no—
711C22×C4—12212no—
712C22×C4—12212no—
713C22×C4—24412no—
714C22×C4C23×D61112yes—
715C22×C4C23×D61112yes—
716C22×C4C23×D6111yescharacteristic
717C22×C4C23×D6113yes—
718C22×C4C23×D6111yescharacteristic
719C22×C4C23×D6111yescharacteristic
720C22×C4C23×D6113yes—
721C4⋊C4—6112no—
722C4⋊C4—6112no—
723C4⋊C4—614no—
724C4⋊C4—614no—
725C4⋊C4—6112no—
726C4⋊C4—6112no—
727C4⋊C4C23×D61112yes—
728C4⋊C4C23×D6114yes—
729C22⋊C4—6124no—
730C22⋊C4—6112no—
731C22⋊C4—6112no—
732C22⋊C4—6112no—
733C22⋊C4—6124no—
734C22⋊C4—6112no—
735C22⋊C4—6112no—
736C22⋊C4—614no—
737C22⋊C4—614no—
738C22⋊C4—6112no—
739C22⋊C4C23×D61112yes—
740C22⋊C4C23×D61112yes—
741C42—6112no—
742C42C23×D61112yes—
743C23—26no—
744C23—26no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—26no—
749C23—6112no—
750C23—614no—
751C23—616no—
752C23—612no—
753C23—616no—
754C23—12248no—
755C23—12224no—
756C23—12224no—
757C23—1222no—
758C23—1226no—
759C23—1226no—
760C23—1222no—
761C23—1226no—
762C23—1226no—
763C23—1226no—
764C23—48848no—
765C23—24424no—
766C23—24424no—
767C23—24412no—
768C23—24448no—
769C23C24×D6116yes—
770C23C24×D6116yes—
771C23C24×D6111yescharacteristic
772Q8—1228no—
773Q8—12224no—
774Q8C2×D4×D61116yescomplemented
775D4—224no—
776D4—224no—
777D4—424no—
778D4—412no—
779D4—6148no—
780D4—12224no—
781D4—12224no—
782D4—12224no—
783D4—12224no—
784D4—12248no—
785D4—12224no—
786D4—12224no—
787D4—24412no—
788D4—24424no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—614no—
796C2×C4—612no—
797C2×C4—6148no—
798C2×C4—612no—
799C2×C4—616no—
800C2×C4—616no—
801C2×C4—612no—
802C2×C4—1228no—
803C2×C4—12224no—
804C2×C4—12224no—
805C2×C4—1222no—
806C2×C4—1226no—
807C2×C4—1226no—
808C2×C4—1222no—
809C2×C4—12224no—
810C2×C4—12224no—
811C2×C4—24424no—
812C2×C4C2×D4×D61112yes—
813C2×C4C24×D6112yes—
814C2×C4C24×D6116yes—
815C2×C4C24×D6112yes—
816C2×C4C24×D6112yes—
817C2×C4C24×D6116yes—
818C22—26no—
819C22—26no—
820C22—26no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—412no—
826C22—6112no—
827C22—614no—
828C22—12224no—
829C22—1228no—
830C22—1222no—
831C22—1226no—
832C22—1226no—
833C22—1222no—
834C22—1226no—
835C22—1226no—
836C22—1226no—
837C22—48848no—
838C22—24448no—
839C22—24412no—
840C22C22×D4×D6112yes—
841C22H(5,𝔽2)×D6112yes—
842C22#1684059812yes—
843C22C25×D6111yescharacteristic
844C4—22no—
845C4—22no—
846C4—26no—
847C4—22no—
848C4—614no—
849C4—1222no—
850C4—1226no—
851C4—1226no—
852C4—1222no—
853C4C22×D4×D61112yes—
854C2—46no—
855C2—46no—
856C2—12212no—
857C2—1224no—
858C2—2446no—
859C2#2145948714yesdirect product factor
860C2C23×D4×D6111yescharacteristic
861C2C2×H(5,𝔽2)×D6111yescharacteristic
862C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#550C2
socleC23×C61C25
hypercenterC2×#550D61
hypocenterC61C2×#3488
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#14519823C2semidirect
2. C22×#41×D61C2semidirect
3. #21459487C2direct (N × H)
4. C2×#16840431C2semidirect
5. C2×#16840424C2semidirect
6. C2×#16840419C2semidirect
7. C2×#16840409C2semidirect
8. C2×#16840408C2semidirect
9. C2×#16840397C2semidirect
10. C2×#16840396C2semidirect
11. C2×#16840341C2semidirect
12. C2×#16840325C2semidirect
13. C2×#16840271C2semidirect
14. C2×#121×D61C2semidirect
15. C2×#16840244C2semidirect
16. C2×C61×#550C2semidirect
18. C2×#14519823C22semidirect
20. C22×#11758226C22semidirect
21. C22×#11758222C22semidirect
22. C22×#11758222C22semidirect
23. C22×#11758224C22semidirect
25. C2×#41×D61C22semidirect
26. C22×Q8×D61C22semidirect
27. C23×D244C22semidirect
28. C22×D4×D61C22semidirect
29. C22×D4×D61C22semidirect
30. C22×D4×D61C22semidirect
31. C22×D4×D61C22semidirect
32. C23×C4×D61C22semidirect
33. #16840431C22semidirect
34. #16840424C22semidirect
35. #16840419C22semidirect
36. #16840409C22semidirect
37. #16840408C22semidirect
38. #16840397C22semidirect
39. #16840396C22semidirect
40. #16840341C22semidirect
41. #16840325C22semidirect
42. C2×#14519773C22semidirect
43. C2×#14519765C22semidirect
44. C2×#14519764C22semidirect
45. #16840271C22semidirect
46. C2×#14519762C22semidirect
47. C2×#14519759C22semidirect
48. C2×#14519757C22semidirect
49. C2×#14519756C22semidirect
50. C2×#14519755C22semidirect
51. C2×#14519754C22semidirect
52. C2×#14519752C22semidirect
53. C2×#14519751C22semidirect
54. C2×#14519750C22semidirect
55. C2×#14519750C22semidirect
56. C2×#14519749C22semidirect
57. C2×#14519749C22semidirect
58. C2×#14519748C22semidirect
59. C2×#14519748C22semidirect
60. C2×#14519748C22semidirect
61. #121×D61C22semidirect
62. C2×#14519747C22semidirect
63. C2×#14519745C22semidirect
64. C2×#14519745C22semidirect
65. C2×#14519745C22semidirect
66. #16840244C22semidirect
67. C2×Q8×Dic61C22semidirect
68. C2×C4×D244C22semidirect
69. C2×C4×D244C22semidirect
70. C2×#14519739C22semidirect
71. C2×C4×C22⋊D61C22semidirect
72. C2×C4×C22⋊D61C22semidirect
73. C2×#14519734C22semidirect
74. C2×C4⋊C4×D61C22semidirect
75. C2×C22⋊C4×D61C22semidirect
76. C22×#41×C61C22semidirect
77. C22×#41×C61C22semidirect
78. C61×#550C22semidirect
79. C2×#127×C61C22semidirect
80. C2×#121×C61C22semidirect
81. C2×#121×C61C22semidirect
82. C2×C4×Q8×C61C22semidirect
83. C2×C4×D4×C61C22semidirect
88. C2×#11758226D4semidirect
90. C2×#11758226C23semidirect
93. C2×#11758222C23semidirect
94. C2×#11758222C23semidirect
96. C2×#11758224C23semidirect
101. C2×Q8×D61C23semidirect
107. C22×D244C23semidirect
118. C2×D4×D61C23semidirect
119. C2×D4×D61C23semidirect
120. C2×D4×D61C23semidirect
121. C2×D4×D61C23semidirect
130. C22×C4×D61C23semidirect
131. #14519773C23semidirect
132. #14519765C23semidirect
133. #14519764C23semidirect
134. #14519762C23semidirect
135. #14519759C23semidirect
136. #14519757C23semidirect
137. #14519756C23semidirect
138. #14519755C23semidirect
139. #14519754C23semidirect
140. #14519752C23semidirect
141. #14519751C23semidirect
142. #14519750C23semidirect
143. #14519750C23semidirect
144. #14519749C23semidirect
145. #14519749C23semidirect
146. #14519748C23semidirect
147. #14519748C23semidirect
148. #14519748C23semidirect
149. #14519747C23semidirect
150. #14519745C23semidirect
151. #14519745C23semidirect
152. #14519745C23semidirect
153. Q8×Dic61C23semidirect
154. C4×D244C23semidirect
155. C4×D244C23semidirect
156. #14519739C23semidirect
157. C4×C22⋊D61C23semidirect
158. C4×C22⋊D61C23semidirect
159. #14519734C23semidirect
166. C4⋊C4×D61C23semidirect
177. C22⋊C4×D61C23semidirect
181. C2×#41×C61C23semidirect
182. C2×#41×C61C23semidirect
190. #127×C61C23semidirect
191. #121×C61C23semidirect
192. #121×C61C23semidirect
193. C4×Q8×C61C23semidirect
194. C4×D4×C61C23semidirect
215. C2×Q8×C61C2×D4semidirect
254. #11758226C2×D4semidirect
267. C2×D244C2×D4semidirect
278. C2×C4×D61C2×D4semidirect
336. C22×D61H(5,𝔽2)semidirect
340. Q8×C61C22×D4semidirect
377. D244C22×D4semidirect
383. C4×D61C22×D4semidirect
412. C2×D61C2×H(5,𝔽2)semidirect
427. C2×#550D61semidirect
441. C2×C61#3488semidirect
457. C22×#41C2×D61semidirect
458. C22×#41C2×D61semidirect
467. #550C2×D61semidirect
477. C2×#127C2×D61semidirect
497. C2×#121C2×D61semidirect
498. C2×#121C2×D61semidirect
505. C2×C4×Q8C2×D61semidirect
511. C2×C4×D4C2×D61semidirect
515. C61C2×#3488semidirect
532. C2×#41C22×D61semidirect
533. C2×#41C22×D61semidirect
575. #127C22×D61semidirect
593. #121C22×D61semidirect
594. #121C22×D61semidirect
600. C4×Q8C22×D61semidirect
606. C4×D4C22×D61semidirect
657. C2×Q8D4×D61semidirect
774. Q8C2×D4×D61semidirect
859. C2#21459487direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198232
C22×#41×D612
#214594872
C2×#168404312
C2×#168404242
C2×#168404192
C2×#168404092
C2×#168404082
C2×#168403972
C2×#168403962
C2×#168403412
C2×#168403252
C2×#168402712
C2×#121×D612
C2×#168402442
C2×C61×#5502
C2×#348861