Finite Group Databasebeta

← C2×#21459485 #30588320

Subgroups — C2×#21459485 #30588320

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
2C23×#11758226C211yesmaximal, characteristic, complemented
3#21459485C2132yesmaximal, direct product factor
4C2×#16840434C211yesmaximal, characteristic, complemented
5C2×#16840431C211yesmaximal, characteristic, complemented
6C2×#16840423C211yesmaximal, characteristic, complemented
7C2×#16840405C213yesmaximal, complemented
8C2×#16840403C213yesmaximal, complemented
9C2×D4×D244C213yesmaximal, complemented
10C2×#16840396C213yesmaximal, complemented
11C2×#16840342C213yesmaximal, complemented
12C2×#16840330C213yesmaximal, complemented
13C2×#16840271C213yesmaximal, complemented
14C2×#121×D61C213yesmaximal, complemented
15C2×#16840244C211yesmaximal, characteristic, complemented
16C2×C61×#548C211yesmaximal, characteristic, complemented
17C2×#14519823—216no—
18C2×#14519823C22116yescomplemented
19C22×#11758226—216no—
20C22×#11758226C2211yescharacteristic
21C22×#11758226C2213yescomplemented
22C22×#11758226C2211yescharacteristic, complemented
23C22×#11758226C2211yescharacteristic, complemented
24C22×#11758226C2213yescomplemented
25C22×#11758226C22116yescomplemented
26C22×#11758222C2213yescomplemented
27C23×D244C2213yescomplemented
28C23×D244C2213yescomplemented
29C22×D4×D61C2213yescomplemented
30C22×D4×D61C2213yescomplemented
31C22×D4×D61C2216yescomplemented
32C23×C4×D61C2213yescomplemented
33#16840434C22116yescomplemented
34#16840431C22116yescomplemented
35#16840423C22116yescomplemented
36#16840405C22148yescomplemented
37#16840403C22148yescomplemented
38D4×D244C22148yescomplemented
39#16840396C22148yescomplemented
40#16840342C22148yescomplemented
41#16840330C22148yescomplemented
42C2×#14519774C2213yescomplemented
43C2×#14519773C2213yescomplemented
44C2×#14519766C2213yescomplemented
45#16840271C22148yescomplemented
46C2×#14519762C2213yescomplemented
47C2×#14519759C2213yescomplemented
48C2×#14519755C2213yescomplemented
49C2×#14519754C2211yescharacteristic, complemented
50C2×#14519753C2213yescomplemented
51C2×#14519752C2213yescomplemented
52C2×#14519752C2216yescomplemented
53C2×#14519752C2213yescomplemented
54C2×#14519751C2213yescomplemented
55C2×#14519751C2213yescomplemented
56C2×#14519750C2216yescomplemented
57C2×#14519750C2216yescomplemented
58C2×#14519750C2213yescomplemented
59C2×#14519749C2213yescomplemented
60C2×#14519748C2213yescomplemented
61#121×D61C22148yescomplemented
62C2×#14519747C2216yescomplemented
63C2×#14519747C2213yescomplemented
64C2×#14519747C2216yescomplemented
65C2×#14519745C2213yescomplemented
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
77C23×Q8×C61C2211yescharacteristic, complemented
78C61×#548C22116yescomplemented
79C2×#124×C61C2213yescomplemented
80C2×C22⋊Q8×C61C2213yescomplemented
81C2×#121×C61C2213yescomplemented
82C2×C4×Q8×C61C2211yescharacteristic, complemented
83C2×C4×D4×C61C2213yescomplemented
84C24×D61C2313yes—
85C24×D61C2316yes—
86#14519823—2128no—
87C2×#11758226—28no—
88C2×#11758226—28no—
89C2×#11758226—2128no—
90C2×#11758226—224no—
91C2×#11758226—224no—
92C2×#11758226D4116yescomplemented
93C2×#11758226C2318yes—
94C2×#11758226C23124yescomplemented
95C2×#11758226C23124yescomplemented
96C2×#11758226C2318yescomplemented
97C2×#11758226C2318yescomplemented
98C2×#11758222—224no—
99C2×#11758222C23124yescomplemented
100C22×Dic122C2311yescharacteristic
101C22×D244—224no—
102C22×D244—224no—
103C22×D244C2316yes—
104C22×D244C2313yes—
105C22×D244C2313yes—
106C22×D244C2313yes—
107C22×D244C2313yes—
108C22×D244C2316yes—
109C22×D244C2313yes—
110C22×D244C23124yescomplemented
111C22×D244C23124yescomplemented
112C22×C22⋊D61C2313yes—
113C22×C22⋊D61C2313yes—
114C22×C22⋊D61C2313yes—
115C22×C22⋊D61C2313yes—
116C22×C22⋊D61C2316yes—
117C2×D4×D61—224no—
118C2×D4×D61—224no—
119C2×D4×D61—424no—
120C2×D4×D61C23124yescomplemented
121C2×D4×D61C23124yescomplemented
122C2×D4×D61C23148yescomplemented
123C23×Dic61C2311yescharacteristic
124C22×C4×D61—224no—
125C22×C4×D61C2313yes—
126C22×C4×D61C2313yes—
127C22×C4×D61C2313yes—
128C22×C4×D61C2313yes—
129C22×C4×D61C2316yes—
130C22×C4×D61C2313yes—
131C22×C4×D61C23124yescomplemented
132#14519774C23124yescomplemented
133#14519773C23124yescomplemented
134#14519766C23124yescomplemented
135#14519762C23124yescomplemented
136#14519759C23124yescomplemented
137#14519755C23124yescomplemented
138#14519754C2318yescomplemented
139#14519753C23124yescomplemented
140#14519752C23124yescomplemented
141#14519752C23124yescomplemented
142#14519752C23148yescomplemented
143#14519751C23124yescomplemented
144#14519751C23124yescomplemented
145#14519750C23148yescomplemented
146#14519750C23124yescomplemented
147#14519750C23148yescomplemented
148#14519749C23124yescomplemented
149#14519748C23124yescomplemented
150#14519747C23124yescomplemented
151#14519747C23148yescomplemented
152#14519747C23148yescomplemented
153#14519745C23124yescomplemented
154Q8×Dic61C2318yescomplemented
155C4×D244C23124yescomplemented
156C4×D244C23124yescomplemented
157#14519739C23124yescomplemented
158C4×C22⋊D61C23124yescomplemented
159C4×C22⋊D61C23124yescomplemented
160#14519734C23124yescomplemented
161C2×C4⋊Dic61C2313yes—
162C2×C4⋊Dic61C2311yescharacteristic
163C2×#11758196C2313yes—
164C2×#11758196C2311yescharacteristic
165C2×#11758196C2311yescharacteristic
166C2×#11758196C2313yes—
167C4⋊C4×D61C23124yescomplemented
168C2×C22⋊Dic61C2313yes—
169C2×C22⋊Dic61C2311yescharacteristic
170C2×#11758198C2313yes—
171C2×#11758198C2316yes—
172C2×#11758198C2313yes—
173C2×#11758198C2313yes—
174C2×#11758198C2313yes—
175C2×#11758198C2313yes—
176C2×#11758198C2313yes—
177C22⋊C4×D61C23148yescomplemented
178C2×C4×Dic61C2313yes—
179C2×#41×C61—28no—
180C2×#41×C61C2318yescomplemented
181C22×Q8×C61—28no—
182C22×Q8×C61C2313yes—
183C22×Q8×C61C2311yescharacteristic
184C22×Q8×C61C2318yescomplemented
185C22×D4×C61C2313yes—
186C22×D4×C61C2313yes—
187C23×C4×C61C2313yes—
188C23×C4×C61C2313yes—
189#124×C61C23124yescomplemented
190C22⋊Q8×C61C23124yescomplemented
191#121×C61C23124yescomplemented
192C4×Q8×C61C2318yescomplemented
193C4×D4×C61C23124yescomplemented
194C2×C4⋊C4×C61C2313yes—
195C2×C4⋊C4×C61C2313yes—
196C2×C22⋊C4×C61C2316yes—
197C2×C22⋊C4×C61C2311yescharacteristic
198C2×C22⋊C4×C61C2313yes—
199C2×C42×C61C2313yes—
200C24×C61C2413yes—
201C24×C61C2411yescharacteristic
202C23×D61—212no—
203C23×D61—212no—
204C23×D61—224no—
205C23×D61—46no—
206C23×D61—412no—
207C23×D61—412no—
208C23×D61C2413yes—
209C23×D61C2413yes—
210C23×D61C24112yes—
211C23×D61C2413yes—
212C23×D61C24124yes—
213#41×C61—232no—
214C2×Q8×C61—232no—
215C2×Q8×C61—212no—
216C2×Q8×C61C2×D418yescomplemented
217C2×Q8×C61C24112yes—
218C2×Q8×C61C2414yes—
219C2×D4×C61—212no—
220C2×D4×C61—212no—
221C2×D4×C61C24112yes—
222C2×D4×C61C24112yes—
223C22×C4×C61—212no—
224C22×C4×C61—212no—
225C22×C4×C61C2413yes—
226C22×C4×C61C2413yes—
227C22×C4×C61C24112yes—
228C22×C4×C61C2411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C22×C4×C61C24112yes—
231C22×C4×C61C2413yes—
232C2×C22⋊D61—212no—
233C2×C22⋊D61—212no—
234C2×C22⋊D61—212no—
235C2×C22⋊D61—412no—
236C2×C22⋊D61—46no—
237C2×C22⋊D61C24112yes—
238C2×C22⋊D61C24112yes—
239C2×C22⋊D61C24112yes—
240C2×C22⋊D61C24124yes—
241C2×C22⋊D61C24112yes—
242C22×Dic61—24no—
243C22×Dic61C2411yescharacteristic
244C22×Dic61C2411yescharacteristic
245C22×Dic61C2413yes—
246C22×Dic61C2414yes—
247C22×Dic61C2411yescharacteristic
248C22×Dic61C2411yescharacteristic
249#11758226—232no—
250#11758226—232no—
251#11758226—296no—
252#11758226—296no—
253#11758226C2×D4164yescomplemented
254D4×D61—296no—
255D4×D61—296no—
256D4×D61—496no—
257#11758222—296no—
258C2×D244—212no—
259C2×D244—224no—
260C2×D244—212no—
261C2×D244—212no—
262C2×D244—296no—
263C2×D244—296no—
264C2×D244—412no—
265C2×D244—46no—
266C2×D244C2×D4124yescomplemented
267C2×D244C24112yes—
268C2×D244C24112yes—
269C2×D244C24124yes—
270C2×D244C24112yes—
271C2×D244C24124yes—
272C2×D244C24112yes—
273C2×D244C24112yes—
274C2×C4×D61—212no—
275C2×C4×D61—212no—
276C2×C4×D61—212no—
277C2×C4×D61—212no—
278C2×C4×D61—296no—
279C2×C4×D61—412no—
280C2×C4×D61C2×D4124yescomplemented
281C2×C4×D61C24112yes—
282C2×C4×D61C24112yes—
283C2×C4×D61C24112yes—
284C2×C4×D61C24112yes—
285C2×C4×D61C24124yes—
286C2×C4×D61C24112yes—
287C2×Dic122—24no—
288C2×Dic122C2414yes—
289C4⋊C4×C61C24112yes—
290C4⋊C4×C61C24112yes—
291C22⋊C4×C61C2414yes—
292C22⋊C4×C61C24112yes—
293C22⋊C4×C61C24124yes—
294C42×C61C24112yes—
295C22⋊Dic61C24112yes—
296C22⋊Dic61C2414yes—
297#11758198C24112yes—
298#11758198C24124yes—
299#11758198C24112yes—
300#11758198C24112yes—
301#11758198C24112yes—
302#11758198C24112yes—
303#11758198C24112yes—
304C4⋊Dic61C24112yes—
305C4⋊Dic61C2414yes—
306#11758196C24112yes—
307#11758196C2414yes—
308#11758196C2414yes—
309#11758196C24112yes—
310C4×Dic61C24112yes—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—26no—
314C23×C61—26no—
315C23×C61—26no—
316C23×C61H(5,𝔽2)14yescomplemented
317C23×C61C2516yes—
318C23×C61C2512yes—
319C23×C61C2511yescharacteristic
320C22×D61—26no—
321C22×D61—26no—
322C22×D61—26no—
323C22×D61—26no—
324C22×D61—26no—
325C22×D61—26no—
326C22×D61—224no—
327C22×D61—26no—
328C22×D61—26no—
329C22×D61—224no—
330C22×D61—248no—
331C22×D61—412no—
332C22×D61—424no—
333C22×D61—424no—
334C22×D61—448no—
335C22×D61—848no—
336C22×D61C22×D4112yes—
337C22×D61C2516yes—
338C22×D61C2516yes—
339C22×D61C2516yes—
340Q8×C61—224no—
341Q8×C61C22×D4116yescomplemented
342D4×C61—224no—
343D4×C61—224no—
344C2×C4×C61—22no—
345C2×C4×C61—26no—
346C2×C4×C61—26no—
347C2×C4×C61—22no—
348C2×C4×C61—224no—
349C2×C4×C61—224no—
350C2×C4×C61C22×D4112yes—
351C2×C4×C61C2512yes—
352C2×C4×C61C2516yes—
353C2×C4×C61C2516yes—
354C2×C4×C61C2512yes—
355C2×C4×C61C2516yes—
356C22⋊D61—224no—
357C22⋊D61—224no—
358C22⋊D61—224no—
359C22⋊D61—424no—
360C22⋊D61—412no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—26no—
364C2×Dic61—22no—
365C2×Dic61—28no—
366C2×Dic61C22×D414yes—
367C2×Dic61C2512yes—
368C2×Dic61C2516yes—
369C2×Dic61C2512yes—
370C2×Dic61C2512yes—
371C2×Dic61C2512yes—
372D244—224no—
373D244—248no—
374D244—224no—
375D244—224no—
376D244—412no—
377D244—424no—
378D244C22×D4148yescomplemented
379C4×D61—224no—
380C4×D61—224no—
381C4×D61—224no—
382C4×D61—224no—
383C4×D61—424no—
384C4×D61C22×D4148yescomplemented
385Dic122—28no—
386C2×#3488—611nomaximal, Sylow
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—28no—
390C22×C61—26no—
391C22×C61—26no—
392C22×C61—26no—
393C22×C61—412no—
394C22×C61C23×D412yes—
395C22×C61C2×H(5,𝔽2)12yes—
396C22×C61C2×H(5,𝔽2)14yescomplemented
397C22×C61#58512yes—
398C22×C61C2611yescharacteristic
399C2×D61—26no—
400C2×D61—26no—
401C2×D61—224no—
402C2×D61—26no—
403C2×D61—26no—
404C2×D61—26no—
405C2×D61—26no—
406C2×D61—26no—
407C2×D61—26no—
408C2×D61—448no—
409C2×D61—412no—
410C2×D61—412no—
411C2×D61—848no—
412C2×D61C23×D4112yes—
413C4×C61—22no—
414C4×C61—26no—
415C4×C61—26no—
416C4×C61—22no—
417C4×C61C23×D4112yes—
418Dic61—22no—
419Dic61—22no—
420Dic61—26no—
421Dic61—22no—
422Dic61C23×D414yes—
423C22×H(5,𝔽2)—611no—
424C23×#41—611no—
425#3488—6132no—
426C2×#550—611no—
427C2×#550—611no—
428C2×#548—611no—
429C2×#548D6111yescharacteristic, complemented
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—24no—
440C2×C61—46no—
441C2×C61#348814yescomplemented
442C2×C61C24×D411yescharacteristic
443C2×C61C22×H(5,𝔽2)11yescharacteristic
444C2×C61C2×#58511yescharacteristic
445D61—212no—
446D61—46no—
447D61—46no—
448C2×H(5,𝔽2)—6116no—
449C2×H(5,𝔽2)—12216no—
450C22×#41—611no—
451C22×#41—613no—
452C22×#41—613no—
453C22×#41—611no—
454C22×#41—611no—
455C22×#41—6116no—
456C22×#41—613no—
457C22×#41—12216no—
458C22×#41C2×D6111yescharacteristic, complemented
459C23×Q8C2×D6111yescharacteristic, complemented
460C23×D4—613no—
461C23×D4—613no—
462C23×D4—616no—
463C23×D4—613no—
464C23×D4—613no—
465C24×C4—613no—
466#550—6116no—
467#550—6116no—
468#548—6116no—
469#548C2×D61116yescomplemented
470#546—6148no—
471#546—6148no—
472D42—6148no—
473D42—6148no—
474#537—6148no—
475#535—6148no—
476C2×#127—613no—
477C2×#127—613no—
478C2×#124—613no—
479C2×#124C2×D6113yescomplemented
480#525—6148no—
481C2×#123—613no—
482C2×#123—613no—
483C2×C22⋊Q8—613no—
484C2×C22⋊Q8—613no—
485C2×C22⋊Q8—611no—
486C2×C22⋊Q8C2×D6113yescomplemented
487C2×#121—613no—
488C2×#121—613no—
489C2×#121—613no—
490C2×#121—613no—
491C2×#121—6148no—
492C2×#121—613no—
493C2×#121—616no—
494C2×#121—613no—
495C2×#121—616no—
496C2×#121—613no—
497C2×#121—616no—
498C2×#121C2×D6113yescomplemented
499C2×#120—613no—
500C2×#120—613no—
501C2×#120—616no—
502C2×#120—616no—
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—6116no—
521C2×#41—618no—
522C2×#41—6124no—
523C2×#41—6124no—
524C2×#41—618no—
525C2×#41—618no—
526C2×#41—6124no—
527C2×#41—12224no—
528C2×#41—12224no—
529C2×#41—12224no—
530C2×#41—122128no—
531C2×#41—1228no—
532C2×#41—1228no—
533C2×#41C22×D6118yescomplemented
534C22×Q8—28no—
535C22×Q8—611no—
536C22×Q8C22×D6113yes—
537C22×Q8C22×D6111yescharacteristic
538C22×Q8C22×D6118yescomplemented
539C22×D4—613no—
540C22×D4—613no—
541C22×D4—613no—
542C22×D4—613no—
543C22×D4—616no—
544C22×D4—6124no—
545C22×D4—6124no—
546C22×D4—6148no—
547C22×D4—613no—
548C22×D4—616no—
549C22×D4—613no—
550C22×D4—613no—
551C22×D4—613no—
552C22×D4—6124no—
553C22×D4—6124no—
554C22×D4—613no—
555C22×D4—616no—
556C22×D4—12224no—
557C22×D4—12224no—
558C22×D4—12224no—
559C22×D4—12224no—
560C22×D4—24424no—
561C22×D4C22×D6113yes—
562C22×D4C22×D6113yes—
563C23×C4—613no—
564C23×C4—611no—
565C23×C4—613no—
566C23×C4—613no—
567C23×C4—613no—
568C23×C4—613no—
569C23×C4—6124no—
570C23×C4—616no—
571C23×C4—12224no—
572C23×C4C22×D6113yes—
573C23×C4C22×D6113yes—
574#127—6124no—
575#127—6124no—
576#124—6124no—
577#124C22×D61124yescomplemented
578#123—6124no—
579#123—6124no—
580C22⋊Q8—6124no—
581C22⋊Q8—6124no—
582C22⋊Q8—618no—
583C22⋊Q8C22×D61124yescomplemented
584#121—6124no—
585#121—6124no—
586#121—6124no—
587#121—6124no—
588#121—6124no—
589#121—6148no—
590#121—6124no—
591#121—6148no—
592#121—6124no—
593#121—6148no—
594#121C22×D61124yescomplemented
595#120—6124no—
596#120—6124no—
597#120—6148no—
598#120—6148no—
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—611no—
613C2×C4⋊C4—613no—
614C2×C4⋊C4—6124no—
615C2×C4⋊C4C22×D6113yes—
616C2×C4⋊C4C22×D6113yes—
617C2×C22⋊C4—613no—
618C2×C22⋊C4—611no—
619C2×C22⋊C4—613no—
620C2×C22⋊C4—616no—
621C2×C22⋊C4—613no—
622C2×C22⋊C4—613no—
623C2×C22⋊C4—613no—
624C2×C22⋊C4—613no—
625C2×C22⋊C4—613no—
626C2×C22⋊C4—6148no—
627C2×C22⋊C4C22×D6116yes—
628C2×C22⋊C4C22×D6111yescharacteristic
629C2×C22⋊C4C22×D6113yes—
630C2×C42—613no—
631C2×C42C22×D6113yes—
632C24—613no—
633C24—613no—
634C24—613no—
635C24—6112no—
636C24—6124no—
637C24—12224no—
638C24—12212no—
639C24—12212no—
640C24—24412no—
641C24—24412no—
642C24—2446no—
643C24C23×D6113yes—
644C24C23×D6111yescharacteristic
645#41—232no—
646#41—6164no—
647#41—12296no—
648#41—12296no—
649#41—12296no—
650#41—12232no—
651#41—12232no—
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—614no—
655C2×Q8—1224no—
656C2×Q8D4×D6118yescomplemented
657C2×Q8C23×D61112yes—
658C2×Q8C23×D6114yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—6112no—
662C2×D4—6112no—
663C2×D4—6112no—
664C2×D4—6112no—
665C2×D4—6124no—
666C2×D4—6124no—
667C2×D4—6112no—
668C2×D4—6124no—
669C2×D4—6112no—
670C2×D4—6112no—
671C2×D4—6112no—
672C2×D4—6112no—
673C2×D4—6124no—
674C2×D4—12296no—
675C2×D4—12296no—
676C2×D4—12212no—
677C2×D4—12224no—
678C2×D4—12296no—
679C2×D4—12212no—
680C2×D4—12296no—
681C2×D4—12212no—
682C2×D4—12212no—
683C2×D4—12212no—
684C2×D4—12212no—
685C2×D4—24412no—
686C2×D4—2446no—
687C2×D4—24412no—
688C2×D4—2446no—
689C2×D4—24496no—
690C2×D4C23×D61112yes—
691C2×D4C23×D61112yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—611no—
695C22×C4—6124no—
696C22×C4—6112no—
697C22×C4—614no—
698C22×C4—611no—
699C22×C4—613no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—6112no—
703C22×C4—6112no—
704C22×C4—6112no—
705C22×C4—6112no—
706C22×C4—6124no—
707C22×C4—12212no—
708C22×C4—12296no—
709C22×C4—12212no—
710C22×C4—1224no—
711C22×C4—12212no—
712C22×C4—12212no—
713C22×C4—24412no—
714C22×C4C23×D61112yes—
715C22×C4C23×D61112yes—
716C22×C4C23×D6111yescharacteristic
717C22×C4C23×D6113yes—
718C22×C4C23×D6113yes—
719C22×C4C23×D6111yescharacteristic
720C22×C4C23×D6113yes—
721C4⋊C4—6112no—
722C4⋊C4—6112no—
723C4⋊C4—614no—
724C4⋊C4—614no—
725C4⋊C4—6112no—
726C4⋊C4—614no—
727C4⋊C4C23×D61112yes—
728C4⋊C4C23×D61112yes—
729C22⋊C4—6112no—
730C22⋊C4—614no—
731C22⋊C4—6112no—
732C22⋊C4—6124no—
733C22⋊C4—6112no—
734C22⋊C4—6112no—
735C22⋊C4—6112no—
736C22⋊C4—6112no—
737C22⋊C4—6112no—
738C22⋊C4C23×D61124yes—
739C22⋊C4C23×D6114yes—
740C22⋊C4C23×D61112yes—
741C42—6112no—
742C42C23×D61112yes—
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—6112no—
749C23—616no—
750C23—616no—
751C23—616no—
752C23—12248no—
753C23—12224no—
754C23—1226no—
755C23—1226no—
756C23—1226no—
757C23—1226no—
758C23—1226no—
759C23—1226no—
760C23—12224no—
761C23—1226no—
762C23—1226no—
763C23—48848no—
764C23—24424no—
765C23—24424no—
766C23—24412no—
767C23—24448no—
768C23#1451982314yescomplemented
769C23C24×D6116yes—
770C23C24×D6112yes—
771C23C24×D6111yescharacteristic
772Q8—224no—
773Q8—1228no—
774Q8C2×D4×D61116yescomplemented
775D4—224no—
776D4—224no—
777D4—6148no—
778D4—12224no—
779D4—12248no—
780D4—12224no—
781D4—12224no—
782D4—12224no—
783D4—12224no—
784D4—12224no—
785D4—24412no—
786D4—24424no—
787D4—24412no—
788D4—24424no—
789C2×C4—22no—
790C2×C4—26no—
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—612no—
801C2×C4—612no—
802C2×C4—12224no—
803C2×C4—12224no—
804C2×C4—1228no—
805C2×C4—1222no—
806C2×C4—1222no—
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×D6116yes—
816C2×C4C24×D6112yes—
817C2×C4C24×D6116yes—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—6112no—
826C22—12224no—
827C22—1226no—
828C22—1226no—
829C22—1226no—
830C22—1226no—
831C22—1226no—
832C22—1226no—
833C22—1226no—
834C22—1226no—
835C22—48848no—
836C22—24448no—
837C22—24412no—
838C22—24412no—
839C22C22×D4×D6112yes—
840C22C2×#1451982312yes—
841C22C2×#1451982314yescomplemented
842C22#1684059912yes—
843C22C25×D6111yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—614no—
849C4—1222no—
850C4—1222no—
851C4—1226no—
852C4—1222no—
853C4C22×D4×D61112yes—
854C2—24no—
855C2—46no—
856C2—12212no—
857C2—2446no—
858C2—2446no—
859C2#2145948514yesdirect product factor
860C2C23×D4×D6111yescharacteristic
861C2C22×#1451982311yescharacteristic
862C2C2×#1684059911yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#548C2
socleC23×C61C25
hypercenterC2×#548D61
hypocenterC61C2×#3488
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14519823C2semidirect
2. C23×#11758226C2semidirect
3. #21459485C2direct (N × H)
4. C2×#16840434C2semidirect
5. C2×#16840431C2semidirect
6. C2×#16840423C2semidirect
7. C2×#16840405C2semidirect
8. C2×#16840403C2semidirect
9. C2×D4×D244C2semidirect
10. C2×#16840396C2semidirect
11. C2×#16840342C2semidirect
12. C2×#16840330C2semidirect
13. C2×#16840271C2semidirect
14. C2×#121×D61C2semidirect
15. C2×#16840244C2semidirect
16. C2×C61×#548C2semidirect
18. C2×#14519823C22semidirect
21. C22×#11758226C22semidirect
22. C22×#11758226C22semidirect
23. C22×#11758226C22semidirect
24. C22×#11758226C22semidirect
25. C22×#11758226C22semidirect
26. C22×#11758222C22semidirect
27. C23×D244C22semidirect
28. C23×D244C22semidirect
29. C22×D4×D61C22semidirect
30. C22×D4×D61C22semidirect
31. C22×D4×D61C22semidirect
32. C23×C4×D61C22semidirect
33. #16840434C22semidirect
34. #16840431C22semidirect
35. #16840423C22semidirect
36. #16840405C22semidirect
37. #16840403C22semidirect
38. D4×D244C22semidirect
39. #16840396C22semidirect
40. #16840342C22semidirect
41. #16840330C22semidirect
42. C2×#14519774C22semidirect
43. C2×#14519773C22semidirect
44. C2×#14519766C22semidirect
45. #16840271C22semidirect
46. C2×#14519762C22semidirect
47. C2×#14519759C22semidirect
48. C2×#14519755C22semidirect
49. C2×#14519754C22semidirect
50. C2×#14519753C22semidirect
51. C2×#14519752C22semidirect
52. C2×#14519752C22semidirect
53. C2×#14519752C22semidirect
54. C2×#14519751C22semidirect
55. C2×#14519751C22semidirect
56. C2×#14519750C22semidirect
57. C2×#14519750C22semidirect
58. C2×#14519750C22semidirect
59. C2×#14519749C22semidirect
60. C2×#14519748C22semidirect
61. #121×D61C22semidirect
62. C2×#14519747C22semidirect
63. C2×#14519747C22semidirect
64. C2×#14519747C22semidirect
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. C23×Q8×C61C22semidirect
78. C61×#548C22semidirect
79. C2×#124×C61C22semidirect
80. C2×C22⋊Q8×C61C22semidirect
81. C2×#121×C61C22semidirect
82. C2×C4×Q8×C61C22semidirect
83. C2×C4×D4×C61C22semidirect
92. C2×#11758226D4semidirect
94. C2×#11758226C23semidirect
95. C2×#11758226C23semidirect
96. C2×#11758226C23semidirect
97. C2×#11758226C23semidirect
99. C2×#11758222C23semidirect
110. C22×D244C23semidirect
111. C22×D244C23semidirect
120. C2×D4×D61C23semidirect
121. C2×D4×D61C23semidirect
122. C2×D4×D61C23semidirect
131. C22×C4×D61C23semidirect
132. #14519774C23semidirect
133. #14519773C23semidirect
134. #14519766C23semidirect
135. #14519762C23semidirect
136. #14519759C23semidirect
137. #14519755C23semidirect
138. #14519754C23semidirect
139. #14519753C23semidirect
140. #14519752C23semidirect
141. #14519752C23semidirect
142. #14519752C23semidirect
143. #14519751C23semidirect
144. #14519751C23semidirect
145. #14519750C23semidirect
146. #14519750C23semidirect
147. #14519750C23semidirect
148. #14519749C23semidirect
149. #14519748C23semidirect
150. #14519747C23semidirect
151. #14519747C23semidirect
152. #14519747C23semidirect
153. #14519745C23semidirect
154. Q8×Dic61C23semidirect
155. C4×D244C23semidirect
156. C4×D244C23semidirect
157. #14519739C23semidirect
158. C4×C22⋊D61C23semidirect
159. C4×C22⋊D61C23semidirect
160. #14519734C23semidirect
167. C4⋊C4×D61C23semidirect
177. C22⋊C4×D61C23semidirect
180. C2×#41×C61C23semidirect
184. C22×Q8×C61C23semidirect
189. #124×C61C23semidirect
190. C22⋊Q8×C61C23semidirect
191. #121×C61C23semidirect
192. C4×Q8×C61C23semidirect
193. C4×D4×C61C23semidirect
216. C2×Q8×C61C2×D4semidirect
253. #11758226C2×D4semidirect
266. C2×D244C2×D4semidirect
280. C2×C4×D61C2×D4semidirect
316. C23×C61H(5,𝔽2)semidirect
341. Q8×C61C22×D4semidirect
378. D244C22×D4semidirect
384. C4×D61C22×D4semidirect
396. C22×C61C2×H(5,𝔽2)semidirect
429. C2×#548D61semidirect
441. C2×C61#3488semidirect
458. C22×#41C2×D61semidirect
459. C23×Q8C2×D61semidirect
469. #548C2×D61semidirect
479. C2×#124C2×D61semidirect
486. C2×C22⋊Q8C2×D61semidirect
498. C2×#121C2×D61semidirect
505. C2×C4×Q8C2×D61semidirect
511. C2×C4×D4C2×D61semidirect
515. C61C2×#3488semidirect
533. C2×#41C22×D61semidirect
538. C22×Q8C22×D61semidirect
577. #124C22×D61semidirect
583. C22⋊Q8C22×D61semidirect
594. #121C22×D61semidirect
600. C4×Q8C22×D61semidirect
606. C4×D4C22×D61semidirect
656. C2×Q8D4×D61semidirect
768. C23#14519823semidirect
774. Q8C2×D4×D61semidirect
841. C22C2×#14519823semidirect
859. C2#21459485direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198232
C23×#117582262
#214594852
C2×#168404342
C2×#168404312
C2×#168404232
C2×#168404052
C2×#168404032
C2×D4×D2442
C2×#168403962
C2×#168403422
C2×#168403302
C2×#168402712
C2×#121×D612
C2×#168402442
C2×C61×#5482
C2×#348861