Finite Group Databasebeta

← C2×#21459610 #30588481

Subgroups — C2×#21459610 #30588481

Order 15616.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519825C211yesmaximal, characteristic, complemented
2C22×#14519823C211yesmaximal, characteristic, complemented
3#21459610C2132yesmaximal, direct product factor
4C2×#16840424C211yesmaximal, characteristic, complemented
5C2×#16840423C211yesmaximal, characteristic, complemented
6C2×#16840419C211yesmaximal, characteristic, complemented
7C2×#16840409C213yesmaximal, complemented
8C2×#16840408C213yesmaximal, complemented
9C2×#16840405C213yesmaximal, complemented
10C2×#16840403C213yesmaximal, complemented
11C2×#16840335C213yesmaximal, complemented
12C2×#16840328C213yesmaximal, complemented
13C2×#16840309C213yesmaximal, complemented
14C2×#124×D61C213yesmaximal, complemented
15C2×C4×#11758226C211yesmaximal, characteristic, complemented
16C2×C61×#548C211yesmaximal, characteristic, complemented
17C2×#14519825—216no—
18C2×#14519825C22116yescomplemented
19C2×#14519823—216no—
20C2×#14519823C22116yescomplemented
21C22×#11758226C2211yescharacteristic
22C22×#11758226C2211yescharacteristic
23C22×#11758226C2213yescomplemented
24C22×#11758222C2213yes—
25C22×#11758222C2213yescomplemented
26C22×#11758222C2213yescomplemented
27C22×Q8×D61C2211yescharacteristic, complemented
28C22×Q8×D61C2213yescomplemented
29C23×D244C2213yes—
30C22×D4×D61C2213yes—
31C22×D4×D61C2213yes—
32#16840424C22116yescomplemented
33#16840423C22116yescomplemented
34#16840419C22116yescomplemented
35#16840409C22148yescomplemented
36#16840408C22148yescomplemented
37#16840405C22148yescomplemented
38#16840403C22148yescomplemented
39#16840335C22148yescomplemented
40#16840328C22148yescomplemented
41#16840309C22148yescomplemented
42C2×#14519776C2213yescomplemented
43C2×#14519773C2213yescomplemented
44C2×#14519766C2213yescomplemented
45C2×#14519765C2213yescomplemented
46C2×#14519764C2213yescomplemented
47C2×#14519763C2213yescomplemented
48C2×#14519763C2216yescomplemented
49C2×#14519763C2211yescharacteristic, complemented
50#124×D61C22148yescomplemented
51C2×#14519762C2216yescomplemented
52C2×#14519759C2216yescomplemented
53C2×#14519757C2213yescomplemented
54C2×#14519756C2213yescomplemented
55C2×#14519753C2213yescomplemented
56C2×#14519752C2213yescomplemented
57C2×#14519752C2213yescomplemented
58C2×#14519751C2213yescomplemented
59C2×#14519750C2213yescomplemented
60C2×#14519750C2213yescomplemented
61C2×#14519748C2213yescomplemented
62C2×#14519748C2213yescomplemented
63C2×#14519747C2216yescomplemented
64C2×#14519745C2216yescomplemented
65C4×#11758226C22116yescomplemented
66C2×Q8×Dic61C2211yescharacteristic, complemented
67C2×C4×D244C2213yescomplemented
68C2×C4×D244C2213yescomplemented
69C2×#14519739C2213yescomplemented
70C2×C4×C22⋊D61C2213yescomplemented
71C2×C4×C22⋊D61C2213yescomplemented
72C2×#14519735C2213yescomplemented
73C2×C22⋊C4×D61C2216yescomplemented
74C2×C22⋊C4×D61C2216yescomplemented
75C2×C42×D61C2213yescomplemented
76C22×#41×C61C2211yescharacteristic
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×D61C2316yes—
85#14519825—2128no—
86#14519823—2128no—
87C2×#11758226—28no—
88C2×#11758226—224no—
89C2×#11758226D4116yescomplemented
90C2×#11758226C2318yes—
91C2×#11758226C2318yes—
92C2×#11758226C23124yescomplemented
93C2×#11758222—224no—
94C2×#11758222—224no—
95C2×#11758222—224no—
96C2×#11758222C23124yes—
97C2×#11758222C23124yescomplemented
98C2×#11758222C23124yescomplemented
99C22×Dic122C2313yes—
100C22×Dic122C2313yes—
101C22×Dic122C2311yescharacteristic
102C2×Q8×D61—28no—
103C2×Q8×D61—224no—
104C2×Q8×D61C23124yescomplemented
105C2×Q8×D61C2318yescomplemented
106C22×D244—224no—
107C22×D244C2313yes—
108C22×D244C2313yes—
109C22×D244C2313yes—
110C22×D244C23124yes—
111C22×D244C2313yes—
112C22×D244C2313yes—
113C22×C22⋊D61C2313yes—
114C22×C22⋊D61C2313yes—
115C22×C22⋊D61C2313yes—
116C22×C22⋊D61C2311yescharacteristic
117C22×C22⋊D61C2313yes—
118C22×C22⋊D61C2313yes—
119C2×D4×D61—224no—
120C2×D4×D61—224no—
121C2×D4×D61C23124yes—
122C2×D4×D61C23124yes—
123C22×C4×D61C2316yes—
124C22×C4×D61C2313yes—
125C22×C4×D61C2313yes—
126C22×C4×D61C2313yes—
127C22×C4×D61C2313yes—
128C22×C4×D61C2313yes—
129#14519776C23124yescomplemented
130#14519773C23124yescomplemented
131#14519766C23124yescomplemented
132#14519765C23124yescomplemented
133#14519764C23124yescomplemented
134#14519763C23124yescomplemented
135#14519763C23148yescomplemented
136#14519763C2318yescomplemented
137#14519762C23148yescomplemented
138#14519759C23148yescomplemented
139#14519757C23124yescomplemented
140#14519756C23124yescomplemented
141#14519753C23124yescomplemented
142#14519752C23124yescomplemented
143#14519752C23124yescomplemented
144#14519751C23124yescomplemented
145#14519750C23124yescomplemented
146#14519750C23124yescomplemented
147#14519748C23124yescomplemented
148#14519748C23124yescomplemented
149#14519747C23148yescomplemented
150#14519745C23148yescomplemented
151Q8×Dic61C2318yescomplemented
152C4×D244C23124yescomplemented
153C4×D244C23124yescomplemented
154#14519739C23124yescomplemented
155C4×C22⋊D61C23124yescomplemented
156C4×C22⋊D61C23124yescomplemented
157#14519735C23124yescomplemented
158C2×C4⋊Dic61C2313yes—
159C2×C4⋊Dic61C2313yes—
160C2×#11758196C2313yes—
161C2×#11758196C2313yes—
162C2×C22⋊Dic61C2313yes—
163C2×C22⋊Dic61C2316yes—
164C2×C22⋊Dic61C2311yescharacteristic
165C2×#11758198C2313yes—
166C2×#11758198C2313yes—
167C2×#11758198C2316yes—
168C2×#11758198C2316yes—
169C2×#11758198C2316yes—
170C2×#11758198C2311yescharacteristic
171C2×#11758198C2311yescharacteristic
172C22⋊C4×D61C23148yescomplemented
173C22⋊C4×D61C23148yescomplemented
174C2×C4×Dic61C2311yescharacteristic
175C2×C4×Dic61C2313yes—
176C2×C4×Dic61C2313yes—
177C42×D61C23124yescomplemented
178C2×#41×C61—28no—
179C2×#41×C61C2318yes—
180C22×Q8×C61—28no—
181C22×Q8×C61C2313yes—
182C22×Q8×C61C2311yescharacteristic
183C22×Q8×C61C2318yescomplemented
184C22×D4×C61C2313yes—
185C22×D4×C61C2313yes—
186C23×C4×C61C2313yes—
187C23×C4×C61C2313yes—
188#124×C61C23124yescomplemented
189C22⋊Q8×C61C23124yescomplemented
190#121×C61C23124yescomplemented
191C4×Q8×C61C2318yescomplemented
192C4×D4×C61C23124yescomplemented
193C2×C4⋊C4×C61C2313yes—
194C2×C4⋊C4×C61C2313yes—
195C2×C22⋊C4×C61C2313yes—
196C2×C22⋊C4×C61C2316yes—
197C2×C22⋊C4×C61C2311yescharacteristic
198C2×C42×C61C2313yes—
199C24×C61C2411yescharacteristic
200C24×C61C2413yes—
201C23×D61—224no—
202C23×D61—412no—
203C23×D61—412no—
204C23×D61C2411yescharacteristic
205C23×D61C2413yes—
206C23×D61C2413yes—
207C23×D61C24124yes—
208#41×C61—232no—
209C2×Q8×C61—232no—
210C2×Q8×C61—212no—
211C2×Q8×C61C2×D418yes—
212C2×Q8×C61C24112yes—
213C2×Q8×C61C2414yes—
214C2×D4×C61—212no—
215C2×D4×C61—46no—
216C2×D4×C61C24112yes—
217C2×D4×C61C24112yes—
218C22×C4×C61—212no—
219C22×C4×C61—212no—
220C22×C4×C61C2411yescharacteristic
221C22×C4×C61C2413yes—
222C22×C4×C61C2413yes—
223C22×C4×C61C2411yescharacteristic
224C22×C4×C61C24112yes—
225C22×C4×C61C24112yes—
226C22×C4×C61C2413yes—
227C2×C22⋊D61—212no—
228C2×C22⋊D61—212no—
229C2×C22⋊D61—212no—
230C2×C22⋊D61—24no—
231C2×C22⋊D61—46no—
232C2×C22⋊D61—46no—
233C2×C22⋊D61C24112yes—
234C2×C22⋊D61C24112yes—
235C2×C22⋊D61C24112yes—
236C2×C22⋊D61C2414yes—
237C2×C22⋊D61C24112yes—
238C2×C22⋊D61C24112yes—
239C22×Dic61C2411yescharacteristic
240C22×Dic61C2413yes—
241C22×Dic61C2411yescharacteristic
242C22×Dic61C2413yes—
243C22×Dic61C2411yescharacteristic
244#11758226—232no—
245#11758226—296no—
246#11758226C2×D4164yescomplemented
247Q8×D61—232no—
248Q8×D61—296no—
249D4×D61—296no—
250D4×D61—296no—
251#11758222—296no—
252#11758222—296no—
253#11758222—296no—
254C2×D244—212no—
255C2×D244—212no—
256C2×D244—212no—
257C2×D244—296no—
258C2×D244—46no—
259C2×D244C2×D4124yes—
260C2×D244C24112yes—
261C2×D244C24112yes—
262C2×D244C24112yes—
263C2×D244C24112yes—
264C2×D244C24112yes—
265C2×C4×D61—224no—
266C2×C4×D61—212no—
267C2×C4×D61—212no—
268C2×C4×D61—46no—
269C2×C4×D61—46no—
270C2×C4×D61C2×D4124yes—
271C2×C4×D61C24112yes—
272C2×C4×D61C24124yes—
273C2×C4×D61C24112yes—
274C2×C4×D61C24112yes—
275C2×C4×D61C24112yes—
276C2×C4×D61C24112yes—
277C2×Dic122—212no—
278C2×Dic122—212no—
279C2×Dic122—24no—
280C2×Dic122C24112yes—
281C2×Dic122C24112yes—
282C2×Dic122C2414yes—
283C4⋊C4×C61C24112yes—
284C4⋊C4×C61C24112yes—
285C22⋊C4×C61C2414yes—
286C22⋊C4×C61C24112yes—
287C22⋊C4×C61C24124yes—
288C42×C61C24112yes—
289C22⋊Dic61C24112yes—
290C22⋊Dic61C24124yes—
291C22⋊Dic61C2414yes—
292#11758198C24112yes—
293#11758198C24112yes—
294#11758198C24124yes—
295#11758198C24124yes—
296#11758198C24124yes—
297#11758198C2414yes—
298#11758198C2414yes—
299C4⋊Dic61C24112yes—
300C4⋊Dic61C24112yes—
301#11758196C24112yes—
302#11758196C24112yes—
303C4×Dic61C2414yes—
304C4×Dic61C24112yes—
305C4×Dic61C24112yes—
306C23×C61—22no—
307C23×C61—26no—
308C23×C61—22no—
309C23×C61—26no—
310C23×C61—22no—
311C23×C61—26no—
312C23×C61C2516yes—
313C23×C61C2512yes—
314C23×C61C2511yescharacteristic
315C22×D61—26no—
316C22×D61—26no—
317C22×D61—22no—
318C22×D61—26no—
319C22×D61—22no—
320C22×D61—26no—
321C22×D61—22no—
322C22×D61—26no—
323C22×D61—248no—
324C22×D61—424no—
325C22×D61—424no—
326C22×D61—848no—
327C22×D61C22×D4112yes—
328C22×D61C2516yes—
329C22×D61C2512yes—
330C22×D61C2516yes—
331Q8×C61—224no—
332Q8×C61C22×D4116yes—
333D4×C61—224no—
334D4×C61—412no—
335C2×C4×C61—26no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—26no—
339C2×C4×C61—224no—
340C2×C4×C61—224no—
341C2×C4×C61C22×D4112yes—
342C2×C4×C61C2516yes—
343C2×C4×C61C2512yes—
344C2×C4×C61C2512yes—
345C2×C4×C61C2516yes—
346C2×C4×C61C2516yes—
347C22⋊D61—224no—
348C22⋊D61—224no—
349C22⋊D61—28no—
350C22⋊D61—224no—
351C22⋊D61—412no—
352C22⋊D61—412no—
353C2×Dic61—26no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—26no—
357C2×Dic61C22×D414yes—
358C2×Dic61C2512yes—
359C2×Dic61C2516yes—
360C2×Dic61C2512yes—
361C2×Dic61C2516yes—
362C2×Dic61C2512yes—
363D244—224no—
364D244—224no—
365D244—224no—
366D244—412no—
367D244C22×D4148yes—
368C4×D61—248no—
369C4×D61—224no—
370C4×D61—224no—
371C4×D61—412no—
372C4×D61—412no—
373C4×D61C22×D4148yes—
374Dic122—224no—
375Dic122—28no—
376Dic122—224no—
377C2×#3500—611nomaximal, Sylow
378C22×C61—22no—
379C22×C61—26no—
380C22×C61—22no—
381C22×C61—26no—
382C22×C61—22no—
383C22×C61—26no—
384C22×C61—412no—
385C22×C61—44no—
386C22×C61C23×D412yes—
387C22×C61#58512yes—
388C22×C61#58512yes—
389C22×C61C2611yescharacteristic
390C2×D61—26no—
391C2×D61—26no—
392C2×D61—224no—
393C2×D61—22no—
394C2×D61—26no—
395C2×D61—22no—
396C2×D61—26no—
397C2×D61—22no—
398C2×D61—26no—
399C2×D61—44no—
400C2×D61—412no—
401C2×D61—848no—
402C2×D61C23×D4112yes—
403C4×C61—26no—
404C4×C61—22no—
405C4×C61—22no—
406C4×C61—26no—
407C4×C61C23×D4112yes—
408Dic61—26no—
409Dic61—22no—
410Dic61—22no—
411Dic61—26no—
412Dic61C23×D414yes—
413C22×2−1+4—611no—
414C22×H(5,𝔽2)—611no—
415#3500—6132no—
416C2×#548—611no—
417C2×#548—611no—
418C2×#548—611no—
419C2×#548D6111yescharacteristic, complemented
420C2×#546—613no—
421C2×#546—613no—
422C2×#546—613no—
423C2×#546—613no—
424C2×#536—613no—
425C2×#535—613no—
426C2×#532—613no—
427C22×#124—613no—
428C2×C4×#41—611no—
429C2×C61—46no—
430C2×C61—42no—
431C2×C61#350014yescomplemented
432C2×C61C24×D411yescharacteristic
433C2×C61C2×#58511yescharacteristic
434C2×C61C2×#58511yescharacteristic
435D61—212no—
436D61—42no—
437D61—46no—
438C2×2−1+4—6116no—
439C2×2−1+4—12216no—
440C2×H(5,𝔽2)—6116no—
441C2×H(5,𝔽2)—12216no—
442C22×#41—611no—
443C22×#41—611no—
444C22×#41—613no—
445C22×#41—613no—
446C22×#41—613no—
447C22×#41—613no—
448C22×#41C2×D6111yescharacteristic
449C23×Q8—613no—
450C23×Q8—611no—
451C23×Q8C2×D6111yescharacteristic, complemented
452C23×D4—613no—
453C23×D4—613no—
454C23×D4—613no—
455#548—6116no—
456#548—6116no—
457#548—6116no—
458#548C2×D61116yescomplemented
459#546—6148no—
460#546—6148no—
461#546—6148no—
462#546—6148no—
463#536—6148no—
464#535—6148no—
465#532—6148no—
466C2×C4⋊Q8—613no—
467C2×#127—613no—
468C2×#124—613no—
469C2×#124—613no—
470C2×#124—6148no—
471C2×#124—613no—
472C2×#124—616no—
473C2×#124—611no—
474C2×#124—613no—
475C2×#124C2×D6113yescomplemented
476C2×#123—616no—
477C2×#123—616no—
478C2×C22⋊Q8—613no—
479C2×C22⋊Q8—613no—
480C2×C22⋊Q8—613no—
481C2×C22⋊Q8C2×D6113yescomplemented
482C2×#121—613no—
483C2×#121—613no—
484C2×#121—613no—
485C2×#121—613no—
486C2×#121—613no—
487C2×#121—613no—
488C2×#121—613no—
489C2×#121C2×D6113yescomplemented
490C2×#120—616no—
491C2×#120—616no—
492C4×#41—6116no—
493C2×C4×Q8—611no—
494C2×C4×Q8C2×D6111yescharacteristic, complemented
495C2×C4×D4—613no—
496C2×C4×D4—613no—
497C2×C4×D4—613no—
498C2×C4×D4—613no—
499C2×C4×D4—613no—
500C2×C4×D4C2×D6113yescomplemented
501C2×#117—613no—
502C22×C22⋊C4—616no—
503C22×C22⋊C4—616no—
504C22×C42—613no—
505C61C2×#350011yescharacteristic, complemented, Sylow
506C25—616no—
5072−1+4—122128no—
508H(5,𝔽2)—122128no—
509C2×#41—28no—
510C2×#41—6116no—
511C2×#41—618no—
512C2×#41—618no—
513C2×#41—6124no—
514C2×#41—6124no—
515C2×#41—6124no—
516C2×#41—6124no—
517C2×#41—12224no—
518C2×#41—12224no—
519C2×#41—12224no—
520C2×#41—12224no—
521C2×#41—1228no—
522C2×#41C22×D6118yes—
523C22×Q8—28no—
524C22×Q8—6124no—
525C22×Q8—618no—
526C22×Q8—613no—
527C22×Q8—613no—
528C22×Q8—611no—
529C22×Q8—12224no—
530C22×Q8—1228no—
531C22×Q8C22×D6113yes—
532C22×Q8C22×D6111yescharacteristic
533C22×Q8C22×D6118yescomplemented
534C22×D4—613no—
535C22×D4—613no—
536C22×D4—613no—
537C22×D4—611no—
538C22×D4—613no—
539C22×D4—613no—
540C22×D4—6124no—
541C22×D4—6124no—
542C22×D4—613no—
543C22×D4—613no—
544C22×D4—613no—
545C22×D4—613no—
546C22×D4—6124no—
547C22×D4—613no—
548C22×D4—12224no—
549C22×D4—12224no—
550C22×D4—12224no—
551C22×D4C22×D6113yes—
552C22×D4C22×D6113yes—
553C23×C4—613no—
554C23×C4—616no—
555C23×C4—613no—
556C23×C4—613no—
557C23×C4—613no—
558C23×C4—613no—
559C23×C4C22×D6113yes—
560C23×C4C22×D6113yes—
561C4⋊Q8—6124no—
562#127—6124no—
563#124—6124no—
564#124—6124no—
565#124—6124no—
566#124—6148no—
567#124—618no—
568#124—6124no—
569#124C22×D61124yescomplemented
570#123—6148no—
571#123—6148no—
572C22⋊Q8—6124no—
573C22⋊Q8—6124no—
574C22⋊Q8—6124no—
575C22⋊Q8C22×D61124yescomplemented
576#121—6124no—
577#121—6124no—
578#121—6124no—
579#121—6124no—
580#121—6124no—
581#121—6124no—
582#121—6124no—
583#121C22×D61124yescomplemented
584#120—6148no—
585#120—6148no—
586C4×Q8—618no—
587C4×Q8C22×D6118yescomplemented
588C4×D4—6124no—
589C4×D4—6124no—
590C4×D4—6124no—
591C4×D4—6124no—
592C4×D4—6124no—
593C4×D4C22×D61124yescomplemented
594#117—6124no—
595C2×C4⋊C4—613no—
596C2×C4⋊C4—613no—
597C2×C4⋊C4—613no—
598C2×C4⋊C4—613no—
599C2×C4⋊C4C22×D6113yes—
600C2×C4⋊C4C22×D6113yes—
601C2×C22⋊C4—613no—
602C2×C22⋊C4—616no—
603C2×C22⋊C4—611no—
604C2×C22⋊C4—613no—
605C2×C22⋊C4—613no—
606C2×C22⋊C4—616no—
607C2×C22⋊C4—616no—
608C2×C22⋊C4—616no—
609C2×C22⋊C4—611no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—6148no—
612C2×C22⋊C4—6148no—
613C2×C22⋊C4C22×D6113yes—
614C2×C22⋊C4C22×D6116yes—
615C2×C22⋊C4C22×D6111yescharacteristic
616C2×C42—613no—
617C2×C42—613no—
618C2×C42—611no—
619C2×C42—6124no—
620C2×C42C22×D6113yes—
621C24—613no—
622C24—613no—
623C24—611no—
624C24—6124no—
625C24—12224no—
626C24—24412no—
627C24—24412no—
628C24C23×D6113yes—
629C24C23×D6111yescharacteristic
630#41—232no—
631#41—6164no—
632#41—12296no—
633#41—12296no—
634#41—12296no—
635#41—12296no—
636#41—12232no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—6112no—
640C2×Q8—6112no—
641C2×Q8—614no—
642C2×Q8—12212no—
643C2×Q8—1224no—
644C2×Q8—12296no—
645C2×Q8—12232no—
646C2×Q8—12212no—
647C2×Q8D4×D6118yes—
648C2×Q8C23×D61112yes—
649C2×Q8C23×D6114yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—6112no—
653C2×D4—6112no—
654C2×D4—6112no—
655C2×D4—614no—
656C2×D4—6112no—
657C2×D4—6112no—
658C2×D4—6124no—
659C2×D4—6112no—
660C2×D4—6112no—
661C2×D4—6112no—
662C2×D4—6112no—
663C2×D4—6112no—
664C2×D4—12296no—
665C2×D4—12212no—
666C2×D4—12212no—
667C2×D4—12296no—
668C2×D4—12212no—
669C2×D4—1224no—
670C2×D4—12296no—
671C2×D4—12212no—
672C2×D4—12212no—
673C2×D4—12212no—
674C2×D4—2446no—
675C2×D4—2446no—
676C2×D4—2446no—
677C2×D4C23×D61112yes—
678C2×D4C23×D61112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—611no—
682C22×C4—6124no—
683C22×C4—6112no—
684C22×C4—611no—
685C22×C4—613no—
686C22×C4—613no—
687C22×C4—611no—
688C22×C4—6124no—
689C22×C4—6112no—
690C22×C4—6112no—
691C22×C4—6112no—
692C22×C4—6112no—
693C22×C4—12224no—
694C22×C4—12212no—
695C22×C4—12212no—
696C22×C4—2446no—
697C22×C4—2446no—
698C22×C4C23×D61112yes—
699C22×C4C23×D61112yes—
700C22×C4C23×D6111yescharacteristic
701C22×C4C23×D6113yes—
702C22×C4C23×D6113yes—
703C22×C4C23×D6111yescharacteristic
704C22×C4C23×D6113yes—
705C4⋊C4—6112no—
706C4⋊C4—6112no—
707C4⋊C4—6112no—
708C4⋊C4—6112no—
709C4⋊C4C23×D61112yes—
710C4⋊C4C23×D61112yes—
711C22⋊C4—6112no—
712C22⋊C4—6124no—
713C22⋊C4—614no—
714C22⋊C4—6112no—
715C22⋊C4—6112no—
716C22⋊C4—6124no—
717C22⋊C4—6124no—
718C22⋊C4—6124no—
719C22⋊C4—614no—
720C22⋊C4—614no—
721C22⋊C4C23×D61112yes—
722C22⋊C4C23×D61124yes—
723C22⋊C4C23×D6114yes—
724C42—614no—
725C42—6112no—
726C42—6112no—
727C42C23×D61112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—6112no—
735C23—616no—
736C23—616no—
737C23—612no—
738C23—12248no—
739C23—1226no—
740C23—1226no—
741C23—1222no—
742C23—1226no—
743C23—1222no—
744C23—1226no—
745C23—1222no—
746C23—1226no—
747C23—48848no—
748C23—24424no—
749C23—24424no—
750C23C24×D6116yes—
751C23C24×D6112yes—
752C23C24×D6111yescharacteristic
753Q8—224no—
754Q8—12224no—
755Q8—1228no—
756Q8—12224no—
757Q8C2×D4×D61116yes—
758D4—224no—
759D4—412no—
760D4—6148no—
761D4—12224no—
762D4—12224no—
763D4—12224no—
764D4—1228no—
765D4—12224no—
766D4—12224no—
767D4—12224no—
768D4—24412no—
769D4—24412no—
770D4—24412no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—614no—
778C2×C4—612no—
779C2×C4—6148no—
780C2×C4—612no—
781C2×C4—616no—
782C2×C4—616no—
783C2×C4—612no—
784C2×C4—12248no—
785C2×C4—1222no—
786C2×C4—1226no—
787C2×C4—1222no—
788C2×C4—1226no—
789C2×C4—12224no—
790C2×C4—12224no—
791C2×C4—24412no—
792C2×C4—24412no—
793C2×C4C2×D4×D61112yes—
794C2×C4C24×D6112yes—
795C2×C4C24×D6116yes—
796C2×C4C24×D6116yes—
797C2×C4C24×D6112yes—
798C2×C4C24×D6116yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—44no—
806C22—412no—
807C22—6112no—
808C22—1226no—
809C22—1226no—
810C22—12224no—
811C22—1222no—
812C22—1226no—
813C22—1222no—
814C22—1226no—
815C22—1222no—
816C22—1226no—
817C22—48848no—
818C22—2444no—
819C22—24412no—
820C22C22×D4×D6112yes—
821C22#1684059812yes—
822C22#1684059912yes—
823C22C25×D6111yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—614no—
829C4—1222no—
830C4—1226no—
831C4—1222no—
832C4—1226no—
833C4C22×D4×D61112yes—
834C2—46no—
835C2—42no—
836C2—12212no—
837C2—2446no—
838C2—2442no—
839C2#2145961014yesdirect product factor
840C2C23×D4×D6111yescharacteristic
841C2C2×#1684059811yescharacteristic
842C2C2×#1684059911yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#548C2
socleC23×C61C25
hypercenterC2×#548D61
hypocenterC61C2×#3500
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14519825C2semidirect
2. C22×#14519823C2semidirect
3. #21459610C2direct (N × H)
4. C2×#16840424C2semidirect
5. C2×#16840423C2semidirect
6. C2×#16840419C2semidirect
7. C2×#16840409C2semidirect
8. C2×#16840408C2semidirect
9. C2×#16840405C2semidirect
10. C2×#16840403C2semidirect
11. C2×#16840335C2semidirect
12. C2×#16840328C2semidirect
13. C2×#16840309C2semidirect
14. C2×#124×D61C2semidirect
15. C2×C4×#11758226C2semidirect
16. C2×C61×#548C2semidirect
18. C2×#14519825C22semidirect
20. C2×#14519823C22semidirect
23. C22×#11758226C22semidirect
25. C22×#11758222C22semidirect
26. C22×#11758222C22semidirect
27. C22×Q8×D61C22semidirect
28. C22×Q8×D61C22semidirect
32. #16840424C22semidirect
33. #16840423C22semidirect
34. #16840419C22semidirect
35. #16840409C22semidirect
36. #16840408C22semidirect
37. #16840405C22semidirect
38. #16840403C22semidirect
39. #16840335C22semidirect
40. #16840328C22semidirect
41. #16840309C22semidirect
42. C2×#14519776C22semidirect
43. C2×#14519773C22semidirect
44. C2×#14519766C22semidirect
45. C2×#14519765C22semidirect
46. C2×#14519764C22semidirect
47. C2×#14519763C22semidirect
48. C2×#14519763C22semidirect
49. C2×#14519763C22semidirect
50. #124×D61C22semidirect
51. C2×#14519762C22semidirect
52. C2×#14519759C22semidirect
53. C2×#14519757C22semidirect
54. C2×#14519756C22semidirect
55. C2×#14519753C22semidirect
56. C2×#14519752C22semidirect
57. C2×#14519752C22semidirect
58. C2×#14519751C22semidirect
59. C2×#14519750C22semidirect
60. C2×#14519750C22semidirect
61. C2×#14519748C22semidirect
62. C2×#14519748C22semidirect
63. C2×#14519747C22semidirect
64. C2×#14519745C22semidirect
65. C4×#11758226C22semidirect
66. C2×Q8×Dic61C22semidirect
67. C2×C4×D244C22semidirect
68. C2×C4×D244C22semidirect
69. C2×#14519739C22semidirect
70. C2×C4×C22⋊D61C22semidirect
71. C2×C4×C22⋊D61C22semidirect
72. C2×#14519735C22semidirect
73. C2×C22⋊C4×D61C22semidirect
74. C2×C22⋊C4×D61C22semidirect
75. C2×C42×D61C22semidirect
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
89. C2×#11758226D4semidirect
92. C2×#11758226C23semidirect
97. C2×#11758222C23semidirect
98. C2×#11758222C23semidirect
104. C2×Q8×D61C23semidirect
105. C2×Q8×D61C23semidirect
129. #14519776C23semidirect
130. #14519773C23semidirect
131. #14519766C23semidirect
132. #14519765C23semidirect
133. #14519764C23semidirect
134. #14519763C23semidirect
135. #14519763C23semidirect
136. #14519763C23semidirect
137. #14519762C23semidirect
138. #14519759C23semidirect
139. #14519757C23semidirect
140. #14519756C23semidirect
141. #14519753C23semidirect
142. #14519752C23semidirect
143. #14519752C23semidirect
144. #14519751C23semidirect
145. #14519750C23semidirect
146. #14519750C23semidirect
147. #14519748C23semidirect
148. #14519748C23semidirect
149. #14519747C23semidirect
150. #14519745C23semidirect
151. Q8×Dic61C23semidirect
152. C4×D244C23semidirect
153. C4×D244C23semidirect
154. #14519739C23semidirect
155. C4×C22⋊D61C23semidirect
156. C4×C22⋊D61C23semidirect
157. #14519735C23semidirect
172. C22⋊C4×D61C23semidirect
173. C22⋊C4×D61C23semidirect
177. C42×D61C23semidirect
183. C22×Q8×C61C23semidirect
188. #124×C61C23semidirect
189. C22⋊Q8×C61C23semidirect
190. #121×C61C23semidirect
191. C4×Q8×C61C23semidirect
192. C4×D4×C61C23semidirect
246. #11758226C2×D4semidirect
419. C2×#548D61semidirect
431. C2×C61#3500semidirect
451. C23×Q8C2×D61semidirect
458. #548C2×D61semidirect
475. C2×#124C2×D61semidirect
481. C2×C22⋊Q8C2×D61semidirect
489. C2×#121C2×D61semidirect
494. C2×C4×Q8C2×D61semidirect
500. C2×C4×D4C2×D61semidirect
505. C61C2×#3500semidirect
533. C22×Q8C22×D61semidirect
569. #124C22×D61semidirect
575. C22⋊Q8C22×D61semidirect
583. #121C22×D61semidirect
587. C4×Q8C22×D61semidirect
593. C4×D4C22×D61semidirect
839. C2#21459610direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198252
C22×#145198232
#214596102
C2×#168404242
C2×#168404232
C2×#168404192
C2×#168404092
C2×#168404082
C2×#168404052
C2×#168404032
C2×#168403352
C2×#168403282
C2×#168403092
C2×#124×D612
C2×C4×#117582262
C2×C61×#5482
C2×#350061