Finite Group Databasebeta

← C22⋊C4×#11758199 #29695834

Subgroups — C22⋊C4×#11758199 #29695834

Order 15616.

1830 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758199C211yesmaximal, characteristic
2C2×C4×#11758199C212yesmaximal, complemented
3C22⋊C4×D244C211yesmaximal, characteristic, complemented
4#21446684C212yesmaximal, complemented
5#21446170C212yesmaximal, complemented
6#21446167C212yesmaximal, complemented
7#21445846C211yesmaximal, characteristic, complemented
8#21445750C211yesmaximal, characteristic, complemented
9#21445749C211yesmaximal, characteristic, complemented
10C22⋊C4×#92418C211yesmaximal, characteristic, complemented
11D4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C22×#11758199—28no—
14C22×#11758199C418yescomplemented
15C22×#11758199C2211yescharacteristic
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×C4×D244C2212yescomplemented
21C2×C22⋊C4×D61—21no—
22C4×#11758199—28no—
23C2×#14519710C2212yescomplemented
24C2×#14519698C2212yescomplemented
25C2×#14519698C2212yescomplemented
26C2×#14519697C2212yescomplemented
27C2×#14519697C2212yescomplemented
28C2×C22⋊#92418C2211yescharacteristic
29C2×C4×#92418C2212yescomplemented
30#16839664C2212yescomplemented
31#16839640—22no—
32#16839622C2211yescharacteristic
33#16839617—21no—
34#16839524C2212yescomplemented
35#16839517C2212yescomplemented
36C23×D4×C61C2211yescharacteristic
37C2×C4×D4×C61C2212yescomplemented
38C22×C22⋊C4×C61—21no—
39C61×#390C2212yescomplemented
40C61×#386—22no—
41C61×#380C2211yescharacteristic
42C61×#379—21no—
43C4×C22⋊C4×C61C2211yescharacteristic
44C24×D61—21no—
45C22×D244—24no—
46C22×D244—21no—
47C22×D244—22no—
48C22×D244—42no—
49C22×D244C2×C414yescomplemented
50C22×D244C2311yescharacteristic
51C22×D244C2311yescharacteristic
52C22×C4×D61—22no—
53C2×#11758199—24no—
54C2×#11758199—24no—
55C2×#11758199—232no—
56C2×#11758199—24no—
57C2×#11758199C2×C414yes—
58C2×#11758199C2×C414yescomplemented
59C2×#11758199C2×C414yescomplemented
60C2×#11758199C2×C414yescomplemented
61C2×#11758199D418yes—
62C22×#92418—24no—
63C22×#92418C2×C414yescomplemented
64C22×#92418C2312yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C4×D244—24no—
68C4×D244—42no—
69C2×C4⋊Dic61C2312yes—
70C2×C22⋊Dic61—21no—
71C2×#11758198—22no—
72C2×#11758198—22no—
73C2×#11758198—22no—
74C22⋊C4×D61—44no—
75#14519710—24no—
76#14519698—24no—
77#14519698—42no—
78#14519697—24no—
79#14519697—42no—
80C22⋊#92418—22no—
81C4×#92418—24no—
82#14519684—21no—
83C25×C61—21no—
84C22×D4×C61—24no—
85C22×D4×C61—21no—
86C22×D4×C61—22no—
87C22×D4×C61—42no—
88C22×D4×C61C2×C414yescomplemented
89C22×D4×C61C2311yescharacteristic
90C22×D4×C61C2311yescharacteristic
91C23×C4×C61—22no—
92C23×C4×C61C2311yescharacteristic
93C4×D4×C61—24no—
94C4×D4×C61—42no—
95C2×C4⋊C4×C61C2312yes—
96C2×C22⋊C4×C61—21no—
97C2×C22⋊C4×C61—22no—
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—44no—
101C2×C22⋊C4×C61D411yescharacteristic
102C2×C22⋊C4×C61D411yescharacteristic
103C2×C42×C61C2312yes—
104#95×C61—21no—
105#95×C61D412yes—
106C24×C61—21no—
107C24×C61—21no—
108C24×C61—24no—
109C24×C61—44no—
110C24×C61—42no—
111C24×C61—42no—
112C24×C61—82no—
113C24×C61C2×D411yescharacteristic
114C23×D61—21no—
115C23×D61—21no—
116C23×D61—24no—
117C23×D61—44no—
118C23×D61—42no—
119C23×D61—42no—
120C23×D61—82no—
121C2×D4×C61—28no—
122C2×D4×C61—24no—
123C2×D4×C61—22no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—22no—
127C2×D4×C61—22no—
128C2×D4×C61—44no—
129C2×D4×C61—48no—
130C2×D4×C61—44no—
131C2×D4×C61C22×C412yes—
132C2×D4×C61C22×C412yes—
133C2×D4×C61C2×D414yes—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—44no—
138C22×C4×C61—44no—
139C22×C4×C61—82no—
140C22×C4×C61C22×C412yes—
141C22×C4×C61C2×D412yes—
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D412yes—
144C22×C4×C61#4112yes—
145C22×C4×C61C2411yescharacteristic
146C22×Dic61—22no—
147C2×D244—21no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—22no—
151C2×D244—28no—
152C2×D244—24no—
153C2×D244—21no—
154C2×D244—44no—
155C2×D244—48no—
156C2×D244—44no—
157C2×D244C22×C412yes—
158C2×D244C22×C412yes—
159C2×D244C2×D414yes—
160C2×C4×D61—44no—
161C2×C4×D61—44no—
162C2×C4×D61—82no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—22no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—44no—
167C22⋊C4×C61—42no—
168C22⋊C4×C61—44no—
169C22⋊C4×C61—82no—
170C22⋊C4×C61D814yescomplemented
171C42×C61—22no—
172C42×C61—22no—
173C22⋊Dic61—42no—
174#11758199—28no—
175#11758199—28no—
176#11758199—28no—
177#11758199C22⋊C4116yesdirect product factor
178#11758198—44no—
179#11758198—44no—
180#11758198—82no—
181C4⋊Dic61—22no—
182C4⋊Dic61—22no—
183C2×#92418—22no—
184C2×#92418—28no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418C22×C412yes—
189C2×#92418C22×C412yes—
190C2×#92418C2×D414yes—
191C23×C61—22no—
192C23×C61—22no—
193C23×C61—22no—
194C23×C61—24no—
195C23×C61—22no—
196C23×C61—48no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61—42no—
200C23×C61—42no—
201C23×C61—41no—
202C23×C61—41no—
203C23×C61—42no—
204C23×C61—48no—
205C23×C61—84no—
206C23×C61—88no—
207C23×C61—88no—
208C23×C61C4×D412yes—
209C23×C61C2×D812yes—
210C23×C61#13512yes—
211C23×C61C22×D411yescharacteristic
212C22×D61—22no—
213C22×D61—24no—
214C22×D61—22no—
215C22×D61—48no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—42no—
223C22×D61—48no—
224C22×D61—84no—
225C22×D61—88no—
226C22×D61—88no—
227D4×C61—22no—
228D4×C61—22no—
229D4×C61—22no—
230D4×C61—24no—
231D4×C61—48no—
232D4×C61—42no—
233D4×C61C2×C22⋊C414yescomplemented
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—24no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—88no—
247C2×C4×C61C4×D412yes—
248C2×C4×C61C2×D814yescomplemented
249C2×C4×C61C23×C411yescharacteristic
250C2×C4×C61C22×D412yes—
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61H(5,𝔽2)12yes—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256D244—22no—
257D244—22no—
258D244—22no—
259D244—24no—
260D244—48no—
261D244—42no—
262D244C2×C22⋊C414yescomplemented
263C4×D61—88no—
264#92418—22no—
265#92418—42no—
266#92418C2×C22⋊C414yescomplemented
267C22⋊C4×D8—611nomaximal, Sylow
268C22×C61—22no—
269C22×C61—22no—
270C22×C61—24no—
271C22×C61—24no—
272C22×C61—24no—
273C22×C61—42no—
274C22×C61—42no—
275C22×C61—44no—
276C22×C61—44no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—816no—
281C22×C61—82no—
282C22×C61—82no—
283C22×C61C4×D814yescomplemented
284C22×C61C2×C4×D411yescharacteristic
285C22×C61D4212yes—
286C22×C61C22×D811yescharacteristic
287C22×C61C2×#13511yescharacteristic
288C22×C61#57612yes—
289C2×D61—24no—
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—44no—
293C2×D61—44no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—816no—
298C2×D61—82no—
299C2×D61—82no—
300C4×C61—22no—
301C4×C61—24no—
302C4×C61—42no—
303C4×C61—82no—
304C4×C61C22×C22⋊C411yescharacteristic
305C4×C61#51811yescharacteristic
306C4×C61#54612yes—
307Dic61—82no—
308C23×D8—611no—
309C2×C4×D8—612no—
310D4×C22⋊C4—611no—
311D4×C22⋊C4D6111yescharacteristic, complemented
312#1970—612no—
313#1879—612no—
314#1879—612no—
315#1808—611no—
316#1786—611no—
317#1786—611no—
318C8×C22⋊C4—611no—
319C2×C61—24no—
320C2×C61—44no—
321C2×C61—82no—
322C2×C61D4×C22⋊C411yescharacteristic
323C2×C61C2×C4×D811yescharacteristic
324C2×C61#294811yescharacteristic
325C2×C61D4×D812yes—
326C2×C61#328012yes—
327D61—44no—
328D61—82no—
329C23×D4—611no—
330C23×D4C2×D6111yescharacteristic
331C22×D8—611no—
332C22×D8—618no—
333C22×D8—611no—
334C22×D8—611no—
335C22×D8—611no—
336C22×D8—1228no—
337C23×C8—611no—
338C2×C4×D4—612no—
339C2×C4×D4C2×D6112yescomplemented
340C22×C22⋊C4—21no—
341C22×C22⋊C4—1221no—
342C4×D8—1228no—
343C2×#107—612no—
344C2×#102—612no—
345C2×#102—612no—
346C2×#102—612no—
347C2×#102—612no—
348C2×C22⋊C8—611no—
349C2×C4×C8—612no—
350#390—612no—
351#390C2×D6112yescomplemented
352#386—22no—
353#386—1222no—
354#380—611no—
355#380C2×D6111yescharacteristic
356#379—21no—
357#379—1221no—
358C4×C22⋊C4C2×D6111yescharacteristic
359#340—612no—
360#336—612no—
361C61C22⋊C4×D811yescharacteristic, complemented, Sylow
362C25—21no—
363C25—1221no—
364C22×D4—24no—
365C22×D4—22no—
366C22×D4—21no—
367C22×D4—42no—
368C22×D4—614no—
369C22×D4—611no—
370C22×D4—611no—
371C22×D4—1224no—
372C22×D4—1222no—
373C22×D4—1221no—
374C22×D4—2442no—
375C22×D4C4×D6114yescomplemented
376C22×D4C22×D6111yescharacteristic
377C22×D4C22×D6111yescharacteristic
378C23×C4—22no—
379C23×C4—1222no—
380C23×C4C22×D6111yescharacteristic
381C2×D8—614no—
382C2×D8—618no—
383C2×D8—614no—
384C2×D8—614no—
385C2×D8—614no—
386C2×D8—1224no—
387C2×D8—12232no—
388C2×D8—1224no—
389C2×D8—1224no—
390C22×C8—611no—
391C22×C8—614no—
392C22×C8—611no—
393C22×C8—612no—
394C22×C8—1224no—
395C4×D4—24no—
396C4×D4—42no—
397C4×D4—1224no—
398C4×D4—2442no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4C22×D6112yes—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—1222no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1222no—
409C2×C22⋊C4—1222no—
410C2×C22⋊C4—2444no—
411C2×C22⋊C4C22⋊D6111yescharacteristic
412C2×C22⋊C4C22⋊D6111yescharacteristic
413C2×C42C22×D6112yes—
414#107—1224no—
415#102—1224no—
416#102—1224no—
417#102—2442no—
418#102—2442no—
419C22⋊C8—1222no—
420C4×C8—1224no—
421#95—21no—
422#95—1221no—
423#95C22⋊D6112yes—
424C24—21no—
425C24—21no—
426C24—24no—
427C24—44no—
428C24—42no—
429C24—42no—
430C24—82no—
431C24—1221no—
432C24—1224no—
433C24—1221no—
434C24—4882no—
435C24—2444no—
436C24—2442no—
437C24—2442no—
438C24C2×C22⋊D6111yescharacteristic
439C2×D4—28no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—24no—
446C2×D4—44no—
447C2×D4—48no—
448C2×D4—44no—
449C2×D4—612no—
450C2×D4—612no—
451C2×D4—614no—
452C2×D4—1228no—
453C2×D4—1222no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—1224no—
459C2×D4—2444no—
460C2×D4—2448no—
461C2×D4—2444no—
462C2×D4C2×C4×D6112yes—
463C2×D4C2×C4×D6112yes—
464C2×D4D4×D6114yes—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—82no—
471C22×C4—1222no—
472C22×C4—4882no—
473C22×C4—2444no—
474C22×C4—2444no—
475C22×C4C2×C4×D6112yes—
476C22×C4#1175822212yes—
477C22×C4C2×C22⋊D6112yes—
478C22×C4C2×C22⋊D6111yescharacteristic
479C22×C4C2×C22⋊D6112yes—
480C22×C4C23×D6111yescharacteristic
481D8—6116no—
482D8—1228no—
483D8—1228no—
484D8—1228no—
485C2×C8—612no—
486C2×C8—614no—
487C2×C8—612no—
488C2×C8—1228no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8—1222no—
492C2×C8—1222no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C22⋊C4—22no—
498C22⋊C4—44no—
499C22⋊C4—42no—
500C22⋊C4—44no—
501C22⋊C4—82no—
502C22⋊C4—4882no—
503C22⋊C4—2444no—
504C22⋊C4—2442no—
505C22⋊C4—2444no—
506C22⋊C4#1175819914yesdirect product factor
507C42—22no—
508C42—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—22no—
514C23—48no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—48no—
522C23—42no—
523C23—84no—
524C23—88no—
525C23—88no—
526C23—1222no—
527C23—1224no—
528C23—1222no—
529C23—4888no—
530C23—4888no—
531C23—4884no—
532C23—2448no—
533C23—2441no—
534C23—2441no—
535C23—2442no—
536C23—2448no—
537C23—2442no—
538C23—2441no—
539C23—2441no—
540C23—2442no—
541C23C4×C22⋊D6112yes—
542C23C2×#1175819912yes—
543C23#1451979712yes—
544C23C22×C22⋊D6111yescharacteristic
545D4—22no—
546D4—22no—
547D4—22no—
548D4—24no—
549D4—48no—
550D4—42no—
551D4—614no—
552D4—1222no—
553D4—1222no—
554D4—1222no—
555D4—1224no—
556D4—2448no—
557D4—2442no—
558D4C22⋊C4×D6114yescomplemented
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—88no—
572C2×C4—4888no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4C4×C22⋊D6112yes—
577C2×C4C2×#1175819914yescomplemented
578C2×C4C22×C4×D6111yescharacteristic
579C2×C4C2×D4×D6112yes—
580C2×C4C2×#1175822211yescharacteristic
581C2×C4#1451982212yes—
582C8—614no—
583C8—1222no—
584C8—2442no—
585C22—22no—
586C22—24no—
587C22—24no—
588C22—22no—
589C22—24no—
590C22—42no—
591C22—44no—
592C22—44no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—816no—
598C22—82no—
599C22—82no—
600C22—1224no—
601C22—48816no—
602C22—4882no—
603C22—4882no—
604C22—2442no—
605C22—2442no—
606C22—2442no—
607C22—2442no—
608C22—2444no—
609C22—2444no—
610C22—2442no—
611C22C4×#1175819914yescomplemented
612C22C2×C4×C22⋊D6111yescharacteristic
613C22D4×C22⋊D6112yes—
614C22C22×#1175819911yescharacteristic
615C22C2×#1451979711yescharacteristic
616C22#1684056512yes—
617C4—24no—
618C4—22no—
619C4—42no—
620C4—82no—
621C4—4882no—
622C4C2×C22⋊C4×D6111yescharacteristic
623C4#1684023511yescharacteristic
624C4#1684040212yes—
625C2—24no—
626C2—44no—
627C2—82no—
628C2—4882no—
629C2—2444no—
630C2C22⋊C4×C22⋊D6111yescharacteristic
631C2C2×C4×#1175819911yescharacteristic
632C2#2145466911yescharacteristic
633C2D4×#1175819912yes—
634C2#2145750012yes—
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC23×#11758199C2
cosocleC22×C4×C61C24
hypercenterD4×C22⋊C4D61
hypocenterC61C22⋊C4×D8
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758199C2semidirect
3. C22⋊C4×D244C2semidirect
4. #21446684C2semidirect
5. #21446170C2semidirect
6. #21446167C2semidirect
7. #21445846C2semidirect
8. #21445750C2semidirect
9. #21445749C2semidirect
10. C22⋊C4×#92418C2semidirect
11. D4×C22⋊C4×C61C2semidirect
14. C22×#11758199C4semidirect
20. C2×C4×D244C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519698C22semidirect
25. C2×#14519698C22semidirect
26. C2×#14519697C22semidirect
27. C2×#14519697C22semidirect
29. C2×C4×#92418C22semidirect
30. #16839664C22semidirect
34. #16839524C22semidirect
35. #16839517C22semidirect
37. C2×C4×D4×C61C22semidirect
39. C61×#390C22semidirect
49. C22×D244C2×C4semidirect
58. C2×#11758199C2×C4semidirect
59. C2×#11758199C2×C4semidirect
60. C2×#11758199C2×C4semidirect
63. C22×#92418C2×C4semidirect
88. C22×D4×C61C2×C4semidirect
170. C22⋊C4×C61D8semidirect
177. #11758199C22⋊C4direct (N × H)
233. D4×C61C2×C22⋊C4semidirect
248. C2×C4×C61C2×D8semidirect
262. D244C2×C22⋊C4semidirect
266. #92418C2×C22⋊C4semidirect
283. C22×C61C4×D8semidirect
311. D4×C22⋊C4D61semidirect
339. C2×C4×D4C2×D61semidirect
351. #390C2×D61semidirect
361. C61C22⋊C4×D8semidirect
375. C22×D4C4×D61semidirect
506. C22⋊C4#11758199direct (N × H)
558. D4C22⋊C4×D61semidirect
577. C2×C4C2×#11758199semidirect
611. C22C4×#11758199semidirect

Maximal subgroups

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

subgroupindex
C23×#117581992
C2×C4×#117581992
C22⋊C4×D2442
#214466842
#214461702
#214461672
#214458462
#214457502
#214457492
C22⋊C4×#924182
D4×C22⋊C4×C612
C22⋊C4×D861