Finite Group Databasebeta

← C2×#21454365 #30543611

Subgroups — C2×#21454365 #30543611

Order 15616.

4946 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840598C211yesmaximal, characteristic
2C2×#16840528C211yesmaximal, characteristic, complemented
3C2×#16840230C211yesmaximal, characteristic, complemented
4#21454365C2116yesmaximal, direct product factor
5C2×#16839780C211yesmaximal, characteristic, complemented
6C2×#16839777C214yesmaximal, complemented
7C22×#14519704C211yesmaximal, characteristic, complemented
8C22×#14519703C211yesmaximal, characteristic, complemented
9C2×#104×D61C214yesmaximal, complemented
10C2×C61×#421C211yesmaximal, characteristic, complemented
11#16840598—24no—
12#16840598—24no—
13#16840598C418yescomplemented
14#16840598C2218yes—
15C2×#14519825C412yescomplemented
16C2×#14519824—21no—
17C2×#14519824C412yescomplemented
18C2×#14519823—21no—
19C2×#14519823C412yescomplemented
20C2×#14519822—22no—
21C2×#14519822C412yescomplemented
22C22×#11758222—22no—
23C22×#11758222C2211yescharacteristic
24C22×#11758222C2211yescharacteristic
25C2×#41×D61—22no—
26C2×#41×D61C2214yes—
27#16840528—24no—
28#16840528C2218yescomplemented
29C2×#14519785—22no—
30C2×#14519783—22no—
31C22×#11758194C2211yescharacteristic, complemented
32C2×M16×D61C2214yescomplemented
33#16840230—24no—
34#16840230C2218yescomplemented
35C2×#14519742—21no—
36C2×#14519739—21no—
37C2×#14519737—22no—
38C2×#14519734C2212yescomplemented
39C22×C4×Dic61C2211yescharacteristic, complemented
40C2×C42×D61C2212yescomplemented
41#16839780C2218yescomplemented
42#16839777C22132yescomplemented
43C2×#14519705C2214yescomplemented
44C2×#14519704C2212yescomplemented
45C2×#14519704C2212yescomplemented
46C2×#14519704C2218yescomplemented
47C2×#14519703C2212yescomplemented
48C2×#14519703C2212yescomplemented
49C2×#14519703C2218yescomplemented
50#104×D61C22132yescomplemented
51C22×#41×C61C2211yescharacteristic
52C22×M16×C61C2211yescharacteristic, complemented
53C2×#117×C61C2211yescharacteristic, complemented
54C61×#421C2218yescomplemented
55C2×#104×C61C2214yescomplemented
56#14519825—28no—
57#14519825C2×C4116yescomplemented
58#14519824—28no—
59#14519824—28no—
60#14519824—28no—
61#14519824C2×C4116yescomplemented
62#14519823—28no—
63#14519823—28no—
64#14519823—28no—
65#14519823C2×C4116yescomplemented
66#14519822—216no—
67#14519822—216no—
68#14519822—28no—
69#14519822C2×C4116yescomplemented
70C2×#11758226—22no—
71C2×#11758226C2×C414yescomplemented
72C2×#11758222—21no—
73C2×#11758222—21no—
74C2×#11758222—22no—
75C2×#11758222—22no—
76C2×#11758222—24no—
77C2×#11758222—216no—
78C2×#11758222—216no—
79C2×#11758222—22no—
80C2×#11758222—24no—
81C2×#11758222—22no—
82C2×#11758222C2×C412yes—
83C2×#11758222C2×C412yes—
84C2×#11758222C2×C414yes—
85C2×#11758222C2×C412yescomplemented
86C2×#11758222C2×C414yescomplemented
87C2×#11758222D412yes—
88C2×#11758222D412yes—
89C2×#11758222D414yes—
90C2×#11758222D414yes—
91C2×#11758222C2312yes—
92C2×#11758222C2314yes—
93C2×#11758222C2314yes—
94C2×#11758224—24no—
95C2×#11758224—24no—
96C2×#11758224—22no—
97C2×#11758224C2×C414yescomplemented
98#41×D61—216no—
99#41×D61—216no—
100#41×D61—28no—
101#41×D61—28no—
102#41×D61C2×C4116yescomplemented
103#41×D61C23116yes—
104C22×Dic122—22no—
105C22×Dic122C2×C411yescharacteristic, complemented
106C22×Dic122D411yescharacteristic
107C2×Q8×D61—22no—
108C2×Q8×D61C2×C414yescomplemented
109C22×D244—22no—
110C22×D244C2×C411yescharacteristic, complemented
111C22×D244D411yescharacteristic
112C22×C22⋊D61—21no—
113C22×C22⋊D61—24no—
114C22×C22⋊D61D412yes—
115C2×D4×D61—24no—
116C2×D4×D61—24no—
117C2×D4×D61—22no—
118C2×D4×D61C2×C414yescomplemented
119C23×Dic61—21no—
120C22×C4×D61—21no—
121C22×C4×D61—24no—
122C22×C4×D61—22no—
123C22×C4×D61C2312yes—
124#14519785—216no—
125#14519783—216no—
126C2×#11758194—21no—
127C2×#11758194—22no—
128C2×#11758194C2312yes—
129C2×#11758194C2314yescomplemented
130C2×#11758189—24no—
131M16×D61—28no—
132M16×D61C23116yescomplemented
133C22×#92418—21no—
134C2×C8×D61—24no—
135#14519742—28no—
136#14519739—28no—
137#14519737—216no—
138#14519734—24no—
139#14519734C2318yescomplemented
140C2×#11758196—22no—
141C2×#11758198—22no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—22no—
144C2×C4×Dic61—22no—
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147C2×C4×Dic61C2314yescomplemented
148C42×D61—24no—
149C42×D61C2318yescomplemented
150#14519705C23116yescomplemented
151#14519704C2318yescomplemented
152#14519704C2318yescomplemented
153#14519703C2318yescomplemented
154#14519703C2318yescomplemented
155C2×#41×C61—21no—
156C2×#41×C61—21no—
157C2×#41×C61—22no—
158C2×#41×C61—22no—
159C2×#41×C61C2×C412yescomplemented
160C2×#41×C61C2×C414yescomplemented
161C2×#41×C61C2312yes—
162C2×#41×C61C2314yes—
163C22×Q8×C61C2×C411yescharacteristic, complemented
164C22×D4×C61—21no—
165C22×D4×C61C2×C411yescharacteristic, complemented
166C23×C4×C61—21no—
167C23×C4×C61C2311yescharacteristic
168C2×M16×C61—21no—
169C2×M16×C61—22no—
170C2×M16×C61C2312yes—
171C2×M16×C61C2314yescomplemented
172C22×C8×C61—21no—
173#117×C61—22no—
174#117×C61C2314yescomplemented
175C2×C4⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C42×C61C2312yes—
178#104×C61C23116yescomplemented
179C24×C61—21no—
180C24×C61C2×D411yescharacteristic
181C23×D61—21no—
182C23×D61—24no—
183C23×D61C2×D412yes—
184#41×C61—24no—
185#41×C61—24no—
186#41×C61—24no—
187#41×C61—22no—
188#41×C61—24no—
189#41×C61—22no—
190#41×C61—24no—
191#41×C61C22×C414yes—
192#41×C61C22×C418yescomplemented
193#41×C61C2414yes—
194C2×Q8×C61—21no—
195C2×Q8×C61—22no—
196C2×Q8×C61C22×C412yes—
197C2×Q8×C61C22×C414yescomplemented
198C2×D4×C61—22no—
199C2×D4×C61—24no—
200C2×D4×C61—22no—
201C2×D4×C61—24no—
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61C22×C412yes—
205C2×D4×C61C22×C414yescomplemented
206C22×C4×C61—21no—
207C22×C4×C61—22no—
208C22×C4×C61—24no—
209C22×C4×C61—22no—
210C22×C4×C61—24no—
211C22×C4×C61—22no—
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C412yes—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D412yes—
220C22×C4×C61C2411yescharacteristic
221C22×C4×C61C2412yes—
222C2×C22⋊D61—22no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—22no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—232no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61C22⋊C414yes—
230C2×C22⋊D61C22⋊C414yes—
231C2×C22⋊D61C22⋊C418yes—
232C2×C22⋊D61C2×D418yes—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—24no—
236C22×Dic61—21no—
237C22×Dic61—24no—
238C22×Dic61—44no—
239C22×Dic61C2×D412yes—
240#11758226—216no—
241#11758226—28no—
242#11758226C22×C4116yescomplemented
243Q8×D61—28no—
244Q8×D61—216no—
245Q8×D61C22×C4116yescomplemented
246#11758224—232no—
247#11758224—216no—
248#11758224—216no—
249#11758224—28no—
250#11758224—216no—
251#11758224C22×C4116yescomplemented
252D4×D61—216no—
253D4×D61—216no—
254D4×D61—232no—
255D4×D61—216no—
256D4×D61—28no—
257D4×D61C22×C4116yescomplemented
258#11758222—24no—
259#11758222—24no—
260#11758222—24no—
261#11758222—22no—
262#11758222—22no—
263#11758222—24no—
264#11758222—24no—
265#11758222—232no—
266#11758222—216no—
267#11758222—216no—
268#11758222—216no—
269#11758222—216no—
270#11758222C22⋊C418yes—
271#11758222C22⋊C418yes—
272#11758222C22⋊C418yes—
273#11758222C22⋊C418yes—
274#11758222C22×C418yes—
275#11758222C22×C418yes—
276#11758222C22×C414yes—
277#11758222C22×C418yescomplemented
278#11758222C2×D418yes—
279#11758222C2×D418yes—
280#11758222C2414yes—
281C2×D244—24no—
282C2×D244—21no—
283C2×D244—22no—
284C2×D244—216no—
285C2×D244C22⋊C412yes—
286C2×D244C22⋊C412yes—
287C2×D244C22⋊C414yes—
288C2×D244C22×C412yes—
289C2×D244C22×C414yescomplemented
290C2×D244C2×D414yes—
291C2×C4×D61—24no—
292C2×C4×D61—22no—
293C2×C4×D61—24no—
294C2×C4×D61—22no—
295C2×C4×D61—24no—
296C2×C4×D61—24no—
297C2×C4×D61—216no—
298C2×C4×D61—216no—
299C2×C4×D61—28no—
300C2×C4×D61—48no—
301C2×C4×D61C22×C414yes—
302C2×C4×D61C22×C414yes—
303C2×C4×D61C2×D414yes—
304C2×C4×D61C2×D414yes—
305C2×C4×D61C2×D414yes—
306C2×C4×D61C2414yes—
307C2×Dic122—21no—
308C2×Dic122—22no—
309C2×Dic122—24no—
310C2×Dic122—216no—
311C2×Dic122C22⋊C412yes—
312C2×Dic122C22⋊C412yes—
313C2×Dic122C22⋊C414yes—
314C2×Dic122C22×C412yes—
315C2×Dic122C22×C414yescomplemented
316C2×Dic122C2×D414yes—
317M16×C61—22no—
318M16×C61—24no—
319M16×C61C2414yes—
320C2×C8×C61—22no—
321C2×C8×C61—24no—
322C4⋊C4×C61—24no—
323C22⋊C4×C61—24no—
324C42×C61—22no—
325C42×C61C2414yes—
326#11758198—28no—
327#11758196—28no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—24no—
331C4×Dic61—28no—
332C4×Dic61C2412yes—
333C4×Dic61C2412yes—
334#11758194—22no—
335#11758194—24no—
336#11758194C2414yes—
337C2×#92418—22no—
338C2×#92418—24no—
339#11758189—216no—
340C8×D61—216no—
341C23×C61—22no—
342C23×C61—24no—
343C23×C61—42no—
344C23×C61—82no—
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C2×C22⋊C412yes—
348C23×C61C22×D411yescharacteristic
349C23×C61C22×D412yes—
350C22×D61—22no—
351C22×D61—24no—
352C22×D61—216no—
353C22×D61—44no—
354C22×D61—88no—
355C22×D61—82no—
356C22×D61C2×C22⋊C414yes—
357C22×D61C2×C22⋊C414yes—
358C22×D61C22×D414yes—
359Q8×C61—22no—
360Q8×C61—24no—
361Q8×C61C23×C414yes—
362D4×C61—24no—
363D4×C61—28no—
364D4×C61—24no—
365D4×C61—22no—
366D4×C61—24no—
367D4×C61C23×C414yes—
368C2×C4×C61—22no—
369C2×C4×C61—24no—
370C2×C4×C61—28no—
371C2×C4×C61—24no—
372C2×C4×C61—24no—
373C2×C4×C61—24no—
374C2×C4×C61—44no—
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C412yes—
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C412yes—
379C2×C4×C61C2×C22⋊C412yes—
380C2×C4×C61C2×C22⋊C412yes—
381C2×C4×C61C2×C22⋊C412yes—
382C2×C4×C61C23×C411yescharacteristic
383C2×C4×C61C23×C412yes—
384C2×C4×C61C23×C411yescharacteristic
385C2×C4×C61C23×C412yes—
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61C22×D412yes—
388C2×C4×C61C22×D412yes—
389C2×C4×C61C22×D412yes—
390C2×C4×C61C22×D411yescharacteristic
391C2×C4×C61C22×D411yescharacteristic
392C2×C4×C61C2511yescharacteristic
393C22⋊D61—28no—
394C22⋊D61—24no—
395C22⋊D61—24no—
396C22⋊D61—216no—
397C22⋊D61—216no—
398C22⋊D61C2×C22⋊C4116yes—
399C22⋊D61C2×C22⋊C4116yes—
400C2×Dic61—24no—
401C2×Dic61—22no—
402C2×Dic61—24no—
403C2×Dic61—22no—
404C2×Dic61—216no—
405C2×Dic61—22no—
406C2×Dic61—48no—
407C2×Dic61—42no—
408C2×Dic61C2×C22⋊C414yes—
409C2×Dic61C2×C22⋊C414yes—
410C2×Dic61C22×D414yes—
411D244—216no—
412D244—24no—
413D244—22no—
414D244C2×C22⋊C418yes—
415D244C2×C22⋊C418yes—
416D244C23×C414yes—
417C4×D61—216no—
418C4×D61—24no—
419C4×D61—28no—
420C4×D61—24no—
421C4×D61—216no—
422C4×D61—416no—
423C4×D61C2×C22⋊C418yes—
424C4×D61C2×C22⋊C418yes—
425C4×D61C23×C418yes—
426C4×D61C22×D418yes—
427Dic122—24no—
428Dic122—22no—
429Dic122—216no—
430Dic122C2×C22⋊C418yes—
431Dic122C2×C22⋊C418yes—
432Dic122C23×C414yes—
433C8×C61—24no—
434#92418—24no—
435C2×#2901—611nomaximal, Sylow
436C22×C61—22no—
437C22×C61—22no—
438C22×C61—22no—
439C22×C61—24no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—44no—
443C22×C61—84no—
444C22×C61C22×C22⋊C412yes—
445C22×C61C22×C22⋊C411yescharacteristic
446C22×C61C22×C22⋊C412yes—
447C22×C61C22×C22⋊C411yescharacteristic
448C22×C61C23×D411yescharacteristic
449C2×D61—28no—
450C2×D61—24no—
451C2×D61—44no—
452C2×D61—44no—
453C2×D61—44no—
454C2×D61—816no—
455C2×D61—84no—
456C2×D61C22×C22⋊C418yes—
457C4×C61—24no—
458C4×C61—44no—
459C4×C61C22×C22⋊C412yes—
460C4×C61C22×C22⋊C411yescharacteristic
461C4×C61C22×C22⋊C412yes—
462C4×C61C22×C22⋊C411yescharacteristic
463C4×C61C24×C411yescharacteristic
464C4×C61C23×D411yescharacteristic
465Dic61—24no—
466Dic61—24no—
467Dic61—42no—
468Dic61C22×C22⋊C418yes—
469C2×#585—611no—
470C2×#568—611no—
471C2×C4×#41—611no—
472#2901—6116no—
473C2×#421—614no—
474C2×#421—611no—
475C2×#421D6111yescharacteristic, complemented
476C22×#104—614no—
477C22×#104—611no—
478C22×#104—611no—
479C2×C61—21no—
480C2×C61—21no—
481C2×C61—22no—
482C2×C61—22no—
483C2×C61—44no—
484C2×C61#290112yescomplemented
485C2×C61C23×C22⋊C411yescharacteristic
486D61—28no—
487D61—44no—
488#585—618no—
489#585—618no—
490#585—1224no—
491#585—1224no—
492C2×2−1+4—612no—
493C2×2−1+4—612no—
494C2×2−1+4—1221no—
495C2×H(5,𝔽2)—612no—
496C2×H(5,𝔽2)—612no—
497C2×H(5,𝔽2)—1222no—
498C2×H(5,𝔽2)—1221no—
499C22×#41—611no—
500C22×#41—614no—
501C22×#41—611no—
502C22×#41—1222no—
503C22×#41—1222no—
504C22×#41C2×D6111yescharacteristic
505#568—618no—
506#568—1224no—
507C2×#131—1222no—
508C2×#131—1222no—
509C22×M16—611no—
510C22×M16—614no—
511C22×M16C2×D6111yescharacteristic, complemented
512C4×#41—618no—
513C4×#41—1224no—
514C2×C4×Q8—1221no—
515C2×C4×D4—1222no—
516C2×C4×D4—1221no—
517C2×#117—612no—
518C2×#117C2×D6111yescharacteristic, complemented
519C22×C42—611no—
520C22×C42—612no—
521#421—618no—
522#421—6132no—
523#421C2×D6118yescomplemented
524C2×#104—612no—
525C2×#104—612no—
526C2×#104—618no—
527C2×#104—612no—
528C2×#104—612no—
529C2×#104—618no—
530C2×#104—614no—
531C2×#104—6132no—
532C2×#104C2×D6114yescomplemented
533C61C2×#290111yescharacteristic, complemented, Sylow
5342−1+4—6116no—
5352−1+4—6116no—
5362−1+4—1228no—
5372−1+4—1228no—
5382−1+4—1228no—
5392−1+4—1228no—
540H(5,𝔽2)—6116no—
541H(5,𝔽2)—6116no—
542H(5,𝔽2)—12216no—
543H(5,𝔽2)—12216no—
544H(5,𝔽2)—1228no—
545H(5,𝔽2)—1228no—
546H(5,𝔽2)—1228no—
547H(5,𝔽2)—1228no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—612no—
553C2×#41—612no—
554C2×#41—614no—
555C2×#41—614no—
556C2×#41—612no—
557C2×#41—612no—
558C2×#41—614no—
559C2×#41—614no—
560C2×#41—6116no—
561C2×#41—6116no—
562C2×#41—614no—
563C2×#41—614no—
564C2×#41—612no—
565C2×#41—614no—
566C2×#41—612no—
567C2×#41—614no—
568C2×#41—1224no—
569C2×#41—1224no—
570C2×#41—1222no—
571C2×#41—1222no—
572C2×#41—12216no—
573C2×#41—12216no—
574C2×#41—1224no—
575C2×#41—1228no—
576C2×#41—1228no—
577C2×#41—1224no—
578C2×#41—1222no—
579C2×#41—1222no—
580C2×#41—12216no—
581C2×#41—12216no—
582C2×#41—1221no—
583C2×#41—1221no—
584C2×#41—1222no—
585C2×#41—1222no—
586C2×#41C4×D6112yescomplemented
587C2×#41C4×D6114yescomplemented
588C2×#41C22×D6112yes—
589C2×#41C22×D6114yes—
590C22×Q8—611no—
591C22×Q8—614no—
592C22×Q8—611no—
593C22×Q8—1222no—
594C22×Q8—1222no—
595C22×Q8C4×D6111yescharacteristic, complemented
596C22×D4—21no—
597C22×D4—612no—
598C22×D4—614no—
599C22×D4—611no—
600C22×D4—611no—
601C22×D4—1222no—
602C22×D4—1224no—
603C22×D4—1222no—
604C22×D4—1224no—
605C22×D4—1224no—
606C22×D4—1221no—
607C22×D4C4×D6111yescharacteristic, complemented
608C23×C4—21no—
609C23×C4—612no—
610C23×C4—1224no—
611C23×C4—1222no—
612C23×C4—1221no—
613C23×C4—1221no—
614C23×C4C22×D6111yescharacteristic
615#131—12216no—
616#131—12216no—
617C2×M16—21no—
618C2×M16—22no—
619C2×M16—612no—
620C2×M16—614no—
621C2×M16—6116no—
622C2×M16—1224no—
623C2×M16—1228no—
624C2×M16—1221no—
625C2×M16—1222no—
626C2×M16C22×D6112yes—
627C2×M16C22×D6114yescomplemented
628C22×C8—21no—
629C22×C8—1224no—
630C22×C8—1221no—
631C4×Q8—1228no—
632C4×D4—12216no—
633C4×D4—1228no—
634#117—22no—
635#117—618no—
636#117—1224no—
637#117C22×D6114yescomplemented
638C2×C4⋊C4—21no—
639C2×C4⋊C4—1222no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—1222no—
642C2×C42—611no—
643C2×C42—614no—
644C2×C42—611no—
645C2×C42—618no—
646C2×C42—1224no—
647C2×C42—1222no—
648C2×C42—1221no—
649C2×C42—1222no—
650C2×C42C22×D6112yes—
651#104—618no—
652#104—618no—
653#104—618no—
654#104—618no—
655#104—6116no—
656#104C22×D61116yescomplemented
657C24—21no—
658C24—612no—
659C24—1224no—
660C24—1221no—
661C24D4×D6111yescharacteristic
662#41—22no—
663#41—24no—
664#41—22no—
665#41—24no—
666#41—24no—
667#41—24no—
668#41—24no—
669#41—618no—
670#41—618no—
671#41—618no—
672#41—618no—
673#41—618no—
674#41—618no—
675#41—618no—
676#41—618no—
677#41—6116no—
678#41—6116no—
679#41—614no—
680#41—618no—
681#41—614no—
682#41—12216no—
683#41—12216no—
684#41—12232no—
685#41—12216no—
686#41—12216no—
687#41—12216no—
688#41—12216no—
689#41—1228no—
690#41—1228no—
691#41—12232no—
692#41—12216no—
693#41—12216no—
694#41—1222no—
695#41—1224no—
696#41—1222no—
697#41—1224no—
698#41—1224no—
699#41—1224no—
700#41—1224no—
701#41C2×C4×D6114yes—
702#41C2×C4×D6118yescomplemented
703#41C23×D6114yes—
704C2×Q8—21no—
705C2×Q8—22no—
706C2×Q8—614no—
707C2×Q8—612no—
708C2×Q8—612no—
709C2×Q8—614no—
710C2×Q8—6116no—
711C2×Q8—612no—
712C2×Q8—614no—
713C2×Q8—1224no—
714C2×Q8—12216no—
715C2×Q8—1228no—
716C2×Q8—12216no—
717C2×Q8—1221no—
718C2×Q8—1222no—
719C2×Q8C2×C4×D6112yes—
720C2×Q8C2×C4×D6114yescomplemented
721C2×D4—22no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—21no—
726C2×D4—22no—
727C2×D4—618no—
728C2×D4—614no—
729C2×D4—614no—
730C2×D4—618no—
731C2×D4—6116no—
732C2×D4—612no—
733C2×D4—614no—
734C2×D4—614no—
735C2×D4—612no—
736C2×D4—612no—
737C2×D4—614no—
738C2×D4—12216no—
739C2×D4—1224no—
740C2×D4—1228no—
741C2×D4—1224no—
742C2×D4—12232no—
743C2×D4—12216no—
744C2×D4—12216no—
745C2×D4—12216no—
746C2×D4—12232no—
747C2×D4—1224no—
748C2×D4—1222no—
749C2×D4—1224no—
750C2×D4—1222no—
751C2×D4—1224no—
752C2×D4—1221no—
753C2×D4—1222no—
754C2×D4C2×C4×D6112yes—
755C2×D4C2×C4×D6114yescomplemented
756C22×C4—21no—
757C22×C4—24no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—24no—
761C22×C4—22no—
762C22×C4—612no—
763C22×C4—614no—
764C22×C4—614no—
765C22×C4—614no—
766C22×C4—614no—
767C22×C4—614no—
768C22×C4—614no—
769C22×C4—1224no—
770C22×C4—12216no—
771C22×C4—12216no—
772C22×C4—1224no—
773C22×C4—1228no—
774C22×C4—1224no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1224no—
778C22×C4—1222no—
779C22×C4—1222no—
780C22×C4—1224no—
781C22×C4—1221no—
782C22×C4—1224no—
783C22×C4—2448no—
784C22×C4—2444no—
785C22×C4C2×C4×D6111yescharacteristic
786C22×C4C2×C4×D6111yescharacteristic
787C22×C4C2×C4×D6112yes—
788C22×C4D4×D6112yes—
789C22×C4D4×D6111yescharacteristic
790C22×C4D4×D6111yescharacteristic
791C22×C4D4×D6111yescharacteristic
792C22×C4D4×D6112yes—
793C22×C4C23×D6112yes—
794C22×C4C23×D6111yescharacteristic
795M16—22no—
796M16—24no—
797M16—614no—
798M16—12216no—
799M16—1222no—
800M16—1224no—
801M16C23×D6114yes—
802C2×C8—24no—
803C2×C8—22no—
804C2×C8—12216no—
805C2×C8—1224no—
806C2×C8—1222no—
807C4⋊C4—24no—
808C4⋊C4—1228no—
809C22⋊C4—24no—
810C22⋊C4—1228no—
811C42—22no—
812C42—612no—
813C42—612no—
814C42—1228no—
815C42—1221no—
816C42—1221no—
817C42—1224no—
818C42C23×D6114yes—
819C23—22no—
820C23—24no—
821C23—42no—
822C23—82no—
823C23—614no—
824C23—614no—
825C23—614no—
826C23—12216no—
827C23—1224no—
828C23—1222no—
829C23—4882no—
830C23—4888no—
831C23—2444no—
832C23C22⋊C4×D6111yescharacteristic
833C23C22⋊C4×D6111yescharacteristic
834C23C22⋊C4×D6112yes—
835C23C2×D4×D6111yescharacteristic
836C23C2×D4×D6112yes—
837Q8—22no—
838Q8—24no—
839Q8—618no—
840Q8—618no—
841Q8—614no—
842Q8—12216no—
843Q8—1224no—
844Q8—1222no—
845Q8C22×C4×D6114yes—
846D4—24no—
847D4—28no—
848D4—24no—
849D4—22no—
850D4—24no—
851D4—6116no—
852D4—6116no—
853D4—618no—
854D4—618no—
855D4—614no—
856D4—12216no—
857D4—12216no—
858D4—12216no—
859D4—1228no—
860D4—1224no—
861D4—1224no—
862D4—1224no—
863D4—1222no—
864D4C22×C4×D6114yes—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—28no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—44no—
872C2×C4—614no—
873C2×C4—614no—
874C2×C4—614no—
875C2×C4—618no—
876C2×C4—618no—
877C2×C4—618no—
878C2×C4—618no—
879C2×C4—12216no—
880C2×C4—12216no—
881C2×C4—12216no—
882C2×C4—1224no—
883C2×C4—1222no—
884C2×C4—1224no—
885C2×C4—1222no—
886C2×C4—1224no—
887C2×C4—1228no—
888C2×C4—1224no—
889C2×C4—1222no—
890C2×C4—24416no—
891C2×C4—2448no—
892C2×C4—2442no—
893C2×C4C22⋊C4×D6111yescharacteristic
894C2×C4C22⋊C4×D6112yes—
895C2×C4C22⋊C4×D6111yescharacteristic
896C2×C4C22⋊C4×D6112yes—
897C2×C4C22⋊C4×D6112yes—
898C2×C4C22⋊C4×D6112yes—
899C2×C4C22⋊C4×D6112yes—
900C2×C4C22×C4×D6111yescharacteristic
901C2×C4C22×C4×D6111yescharacteristic
902C2×C4C22×C4×D6112yes—
903C2×C4C22×C4×D6112yes—
904C2×C4C2×D4×D6111yescharacteristic
905C2×C4C2×D4×D6112yes—
906C2×C4C2×D4×D6112yes—
907C2×C4C2×D4×D6112yes—
908C2×C4C2×D4×D6111yescharacteristic
909C2×C4C2×D4×D6111yescharacteristic
910C2×C4C24×D6111yescharacteristic
911C8—24no—
912C8—1224no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—44no—
920C22—84no—
921C22—618no—
922C22—1228no—
923C22—1224no—
924C22—4884no—
925C22—48816no—
926C22—2444no—
927C22—2444no—
928C22—2444no—
929C22C2×C22⋊C4×D6112yes—
930C22C2×C22⋊C4×D6111yescharacteristic
931C22C2×C22⋊C4×D6112yes—
932C22C2×C22⋊C4×D6111yescharacteristic
933C22C22×D4×D6111yescharacteristic
934C4—24no—
935C4—44no—
936C4—618no—
937C4—1224no—
938C4—1224no—
939C4—2442no—
940C4C2×C22⋊C4×D6111yescharacteristic
941C4C2×C22⋊C4×D6112yes—
942C4C2×C22⋊C4×D6111yescharacteristic
943C4C2×C22⋊C4×D6112yes—
944C4C23×C4×D6111yescharacteristic
945C4C22×D4×D6111yescharacteristic
946C2—21no—
947C2—22no—
948C2—22no—
949C2—21no—
950C2—44no—
951C2—1228no—
952C2—2444no—
953C2#2145436512yesdirect product factor
954C2C22×C22⋊C4×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#421C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840598C2
cosocleC2×C4×C61C25
hypercenterC2×#421D61
hypocenterC61C2×#2901
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16840528C2semidirect
3. C2×#16840230C2semidirect
4. #21454365C2direct (N × H)
5. C2×#16839780C2semidirect
6. C2×#16839777C2semidirect
7. C22×#14519704C2semidirect
8. C22×#14519703C2semidirect
9. C2×#104×D61C2semidirect
10. C2×C61×#421C2semidirect
13. #16840598C4semidirect
15. C2×#14519825C4semidirect
17. C2×#14519824C4semidirect
19. C2×#14519823C4semidirect
21. C2×#14519822C4semidirect
28. #16840528C22semidirect
31. C22×#11758194C22semidirect
32. C2×M16×D61C22semidirect
34. #16840230C22semidirect
38. C2×#14519734C22semidirect
39. C22×C4×Dic61C22semidirect
40. C2×C42×D61C22semidirect
41. #16839780C22semidirect
42. #16839777C22semidirect
43. C2×#14519705C22semidirect
44. C2×#14519704C22semidirect
45. C2×#14519704C22semidirect
46. C2×#14519704C22semidirect
47. C2×#14519703C22semidirect
48. C2×#14519703C22semidirect
49. C2×#14519703C22semidirect
50. #104×D61C22semidirect
52. C22×M16×C61C22semidirect
53. C2×#117×C61C22semidirect
54. C61×#421C22semidirect
55. C2×#104×C61C22semidirect
57. #14519825C2×C4semidirect
61. #14519824C2×C4semidirect
65. #14519823C2×C4semidirect
69. #14519822C2×C4semidirect
71. C2×#11758226C2×C4semidirect
85. C2×#11758222C2×C4semidirect
86. C2×#11758222C2×C4semidirect
97. C2×#11758224C2×C4semidirect
102. #41×D61C2×C4semidirect
105. C22×Dic122C2×C4semidirect
108. C2×Q8×D61C2×C4semidirect
110. C22×D244C2×C4semidirect
118. C2×D4×D61C2×C4semidirect
129. C2×#11758194C23semidirect
132. M16×D61C23semidirect
139. #14519734C23semidirect
147. C2×C4×Dic61C23semidirect
149. C42×D61C23semidirect
150. #14519705C23semidirect
151. #14519704C23semidirect
152. #14519704C23semidirect
153. #14519703C23semidirect
154. #14519703C23semidirect
159. C2×#41×C61C2×C4semidirect
160. C2×#41×C61C2×C4semidirect
163. C22×Q8×C61C2×C4semidirect
165. C22×D4×C61C2×C4semidirect
171. C2×M16×C61C23semidirect
174. #117×C61C23semidirect
178. #104×C61C23semidirect
192. #41×C61C22×C4semidirect
197. C2×Q8×C61C22×C4semidirect
205. C2×D4×C61C22×C4semidirect
242. #11758226C22×C4semidirect
245. Q8×D61C22×C4semidirect
251. #11758224C22×C4semidirect
257. D4×D61C22×C4semidirect
277. #11758222C22×C4semidirect
289. C2×D244C22×C4semidirect
315. C2×Dic122C22×C4semidirect
475. C2×#421D61semidirect
484. C2×C61#2901semidirect
511. C22×M16C2×D61semidirect
518. C2×#117C2×D61semidirect
523. #421C2×D61semidirect
532. C2×#104C2×D61semidirect
533. C61C2×#2901semidirect
586. C2×#41C4×D61semidirect
587. C2×#41C4×D61semidirect
595. C22×Q8C4×D61semidirect
607. C22×D4C4×D61semidirect
627. C2×M16C22×D61semidirect
637. #117C22×D61semidirect
656. #104C22×D61semidirect
702. #41C2×C4×D61semidirect
720. C2×Q8C2×C4×D61semidirect
755. C2×D4C2×C4×D61semidirect
953. C2#21454365direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405982
C2×#168405282
C2×#168402302
#214543652
C2×#168397802
C2×#168397772
C22×#145197042
C22×#145197032
C2×#104×D612
C2×C61×#4212
C2×#290161