Finite Group Databasebeta

← C2×#21457610 #30556229

Subgroups — C2×#21457610 #30556229

Order 15616.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840573C211yesmaximal, characteristic, complemented
2C2×#16840570C211yesmaximal, characteristic, complemented
3C2×#16840569C211yesmaximal, characteristic, complemented
4#21457610C2116yesmaximal, direct product factor
5C2×#16840133C211yesmaximal, characteristic, complemented
6C2×#16840027C211yesmaximal, characteristic, complemented
7C2×#16840025C211yesmaximal, characteristic, complemented
8C2×#16840023C211yesmaximal, characteristic, complemented
9C2×#16840022C211yesmaximal, characteristic, complemented
10C2×#16839945C211yesmaximal, characteristic, complemented
11C2×#16839943C211yesmaximal, characteristic, complemented
12C2×#16839930C211yesmaximal, characteristic, complemented
13C2×#16839928C211yesmaximal, characteristic, complemented
14C2×#16839879C211yesmaximal, characteristic, complemented
15C2×#16839877C211yesmaximal, characteristic, complemented
16C2×C61×#577C211yesmaximal, characteristic, complemented
17C2×#14519824C2211yescharacteristic
18C2×#14519823C2211yescharacteristic, complemented
19#16840573—24no—
20#16840573C2218yescomplemented
21#16840570—24no—
22#16840570C2218yescomplemented
23#16840569—24no—
24#16840569C2218yescomplemented
25C2×#14519809—21no—
26C2×#14519808—21no—
27C2×#14519808C2211yescharacteristic, complemented
28C2×#14519807—21no—
29C2×#14519807C2211yescharacteristic, complemented
30C2×#14519807C2211yescharacteristic, complemented
31C2×#14519803—21no—
32C2×#14519803C2211yescharacteristic
33C2×#14519802—21no—
34C2×#14519802C2211yescharacteristic
35C2×#14519802C2211yescharacteristic
36C2×#14519801—21no—
37C2×#14519798—21no—
38C2×#14519797—21no—
39C2×#14519797—21no—
40C2×#14519797C2211yescharacteristic
41C22×#11758190C2211yescharacteristic, complemented
42C22×#11758200—21no—
43C22×#11758200C2211yescharacteristic, complemented
44C22×#11758201—21no—
45C22×#11758201C2211yescharacteristic, complemented
46C2×SD16×D61—21no—
47C2×#14519784C2211yescharacteristic, complemented
48C2×#14519784C2211yescharacteristic, complemented
49C2×#14519783C2211yescharacteristic, complemented
50C2×#14519775C2211yescharacteristic, complemented
51C2×#14519773C2211yescharacteristic
52#16840133C2218yescomplemented
53#16840027C2218yescomplemented
54#16840025C2218yescomplemented
55#16840023C2218yescomplemented
56#16840022C2218yescomplemented
57#16839945C2218yescomplemented
58#16839943C2218yescomplemented
59#16839930C2218yescomplemented
60#16839928C2218yescomplemented
61#16839879C2218yescomplemented
62#16839877C2218yescomplemented
63C2×#14519713C2211yescharacteristic, complemented
64C2×#14519712C2211yescharacteristic, complemented
65C2×#14519704C2211yescharacteristic, complemented
66C2×#14519704C2211yescharacteristic, complemented
67C2×#14519704C2211yescharacteristic, complemented
68C2×#14519703C2211yescharacteristic, complemented
69C2×#14519696C2211yescharacteristic, complemented
70C2×#14519695C2211yescharacteristic, complemented
71C2×#14519694C2211yescharacteristic, complemented
72C2×#14519693C2211yescharacteristic, complemented
73C2×C8×Dic61C2211yescharacteristic, complemented
74C2×2−1+4×C61C2211yescharacteristic
75C2×H(5,𝔽2)×C61C2211yescharacteristic, complemented
76C61×#577—24no—
77C61×#577C2218yescomplemented
78C2×#137×C61—21no—
79C2×#137×C61C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C61—21no—
81C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
82C2×#135×C61—21no—
83C2×#135×C61C2211yescharacteristic
84C22×SD16×C61—21no—
85C22×SD16×C61C2211yescharacteristic, complemented
86C2×#131×C61C2211yescharacteristic, complemented
87#14519824—22no—
88#14519824—22no—
89#14519824—41no—
90#14519824C2314yes—
91#14519823—22no—
92#14519823—22no—
93#14519823—41no—
94#14519823C2314yescomplemented
95C2×#11758226—21no—
96C2×#11758222—21no—
97C2×#11758222—21no—
98C2×#11758222C2311yescharacteristic
99C2×#11758224—21no—
100C2×#11758224—41no—
101C22×Dic122—21no—
102C22×Dic122C2311yescharacteristic
103C2×Q8×D61—21no—
104C22×D244—21no—
105C22×D244C2311yescharacteristic
106C22×C22⋊D61—41no—
107C2×D4×D61—21no—
108C2×D4×D61—41no—
109#14519809—28no—
110#14519808—22no—
111#14519808—28no—
112#14519808C2314yescomplemented
113#14519807—22no—
114#14519807—22no—
115#14519807—28no—
116#14519807C2314yescomplemented
117#14519807C2314yescomplemented
118#14519803—22no—
119#14519803—28no—
120#14519803C2314yes—
121#14519802—22no—
122#14519802—22no—
123#14519802—28no—
124#14519802C2314yes—
125#14519802C2314yes—
126#14519801—28no—
127#14519798—28no—
128#14519797—28no—
129#14519797—28no—
130#14519797D414yescomplemented
131#14519797C2314yes—
132C2×#11758202—21no—
133C2×#11758202—21no—
134C2×#11758202—21no—
135C2×#11758202D411yescharacteristic, complemented
136C2×#11758190—21no—
137C2×#11758190—21no—
138C2×#11758190—22no—
139C2×#11758190C2314yescomplemented
140C2×#11758200—21no—
141C2×#11758200—21no—
142C2×#11758200—21no—
143C2×#11758200—28no—
144C2×#11758200—21no—
145C2×#11758200—21no—
146C2×#11758200—22no—
147C2×#11758200D411yescharacteristic, complemented
148C2×#11758200C2314yescomplemented
149C2×#11758201—21no—
150C2×#11758201—21no—
151C2×#11758201—21no—
152C2×#11758201—28no—
153C2×#11758201—21no—
154C2×#11758201—21no—
155C2×#11758201—22no—
156C2×#11758201D411yescharacteristic, complemented
157C2×#11758201C2314yescomplemented
158SD16×D61—28no—
159C2×#11758199—21no—
160C2×#11758199—21no—
161C2×#11758199—21no—
162C2×#11758199D411yescharacteristic, complemented
163#14519784—22no—
164#14519784—22no—
165#14519784C2314yescomplemented
166#14519784C2314yescomplemented
167#14519783—22no—
168#14519783C2314yescomplemented
169C2×#11758194—21no—
170C2×#11758194—21no—
171C2×#11758194C2311yescharacteristic
172C2×#11758194C2311yescharacteristic
173C2×#11758194C2311yescharacteristic
174C2×#11758189—21no—
175C22×#92418—21no—
176C22×#92418—21no—
177C22×#92418C2311yescharacteristic
178C2×C8×D61—21no—
179#14519775—41no—
180#14519775C2314yescomplemented
181#14519773—41no—
182#14519773C2314yes—
183C2×#11758196—41no—
184C2×C4×Dic61C2311yescharacteristic
185#14519713C2314yescomplemented
186#14519712C2314yescomplemented
187#14519704C2314yescomplemented
188#14519704C2314yescomplemented
189#14519704C2314yescomplemented
190#14519703C2314yescomplemented
191#14519696C2314yescomplemented
192#14519695C2314yescomplemented
193#14519694C2314yescomplemented
194#14519693C2314yescomplemented
195C8×Dic61C2314yescomplemented
1962−1+4×C61—22no—
1972−1+4×C61—22no—
1982−1+4×C61—41no—
1992−1+4×C61C2314yes—
200H(5,𝔽2)×C61—22no—
201H(5,𝔽2)×C61—22no—
202H(5,𝔽2)×C61—41no—
203H(5,𝔽2)×C61C2314yescomplemented
204C2×#41×C61—21no—
205C2×#41×C61—21no—
206C2×#41×C61—21no—
207C2×#41×C61—21no—
208C2×#41×C61—41no—
209C2×#41×C61C2311yescharacteristic
210C2×#41×C61C2311yescharacteristic
211C2×#41×C61C2311yescharacteristic
212C22×Q8×C61—21no—
213C22×Q8×C61—21no—
214C22×Q8×C61C2311yescharacteristic
215C22×D4×C61—21no—
216C22×D4×C61—21no—
217C22×D4×C61—41no—
218C22×D4×C61C2311yescharacteristic
219#137×C61—22no—
220#137×C61—28no—
221#137×C61C2314yescomplemented
222AGL(1,ℤ/8)×C61—22no—
223AGL(1,ℤ/8)×C61—28no—
224AGL(1,ℤ/8)×C61C2314yes—
225#135×C61—28no—
226#135×C61D414yescomplemented
227#135×C61C2314yes—
228C2×Q16×C61—21no—
229C2×Q16×C61D411yescharacteristic, complemented
230C2×SD16×C61—21no—
231C2×SD16×C61—21no—
232C2×SD16×C61—28no—
233C2×SD16×C61—21no—
234C2×SD16×C61—21no—
235C2×SD16×C61—22no—
236C2×SD16×C61D411yescharacteristic, complemented
237C2×SD16×C61D411yescharacteristic, complemented
238C2×SD16×C61C2314yescomplemented
239C2×D8×C61—21no—
240C2×D8×C61D411yescharacteristic, complemented
241#131×C61—22no—
242#131×C61C2314yescomplemented
243C2×M16×C61—21no—
244C2×M16×C61C2311yescharacteristic
245C22×C8×C61—21no—
246C22×C8×C61C2311yescharacteristic
247C24×C61—21no—
248C24×C61—41no—
249C23×D61—21no—
250C23×D61—41no—
251#41×C61—21no—
252#41×C61—21no—
253#41×C61—21no—
254#41×C61—21no—
255#41×C61—21no—
256#41×C61—21no—
257#41×C61—24no—
258#41×C61—24no—
259#41×C61—24no—
260#41×C61—24no—
261#41×C61—44no—
262#41×C61—42no—
263#41×C61—42no—
264#41×C61—42no—
265#41×C61—42no—
266#41×C61—44no—
267#41×C61C2×D412yes—
268#41×C61C2×D412yes—
269#41×C61C2×D412yes—
270#41×C61C2412yes—
271#41×C61C2412yes—
272#41×C61C2412yes—
273C2×Q8×C61—21no—
274C2×Q8×C61—24no—
275C2×Q8×C61—24no—
276C2×Q8×C61—21no—
277C2×Q8×C61—21no—
278C2×Q8×C61—21no—
279C2×Q8×C61—21no—
280C2×Q8×C61—41no—
281C2×Q8×C61—42no—
282C2×Q8×C61—42no—
283C2×Q8×C61C2×D411yescharacteristic
284C2×Q8×C61C2×D411yescharacteristic
285C2×Q8×C61C2×D411yescharacteristic
286C2×Q8×C61C2412yes—
287C2×D4×C61—21no—
288C2×D4×C61—21no—
289C2×D4×C61—21no—
290C2×D4×C61—24no—
291C2×D4×C61—24no—
292C2×D4×C61—21no—
293C2×D4×C61—21no—
294C2×D4×C61—21no—
295C2×D4×C61—21no—
296C2×D4×C61—21no—
297C2×D4×C61—42no—
298C2×D4×C61—42no—
299C2×D4×C61—41no—
300C2×D4×C61—41no—
301C2×D4×C61—44no—
302C2×D4×C61—44no—
303C2×D4×C61—41no—
304C2×D4×C61C2×D411yescharacteristic
305C2×D4×C61C2×D411yescharacteristic
306C2×D4×C61C2×D411yescharacteristic
307C2×D4×C61C2412yes—
308C22×C4×C61—21no—
309C22×C4×C61—21no—
310C22×C4×C61—21no—
311C22×C4×C61—21no—
312C22×C4×C61—41no—
313C22×C4×C61—41no—
314C22×C4×C61—41no—
315C22×C4×C61C2411yescharacteristic
316C2×C22⋊D61—21no—
317C2×C22⋊D61—41no—
318C2×C22⋊D61—44no—
319C2×C22⋊D61—41no—
320C2×C22⋊D61—84no—
321C22×Dic61—21no—
322C22×Dic61—21no—
323C22×Dic61—41no—
324#11758226—24no—
325#11758226—42no—
326Q8×D61—24no—
327Q8×D61—42no—
328#11758224—24no—
329#11758224—42no—
330#11758224—44no—
331#11758224—44no—
332D4×D61—24no—
333D4×D61—42no—
334D4×D61—44no—
335D4×D61—44no—
336#11758222—21no—
337#11758222—21no—
338#11758222—24no—
339#11758222—24no—
340#11758222—42no—
341#11758222—42no—
342#11758222C2×D412yes—
343#11758222C2412yes—
344C2×D244—21no—
345C2×D244—21no—
346C2×D244—21no—
347C2×D244—21no—
348C2×D244—24no—
349C2×D244—21no—
350C2×D244—42no—
351C2×D244—41no—
352C2×D244C2×D411yescharacteristic
353C2×D244C2412yes—
354C2×C4×D61—21no—
355C2×C4×D61—41no—
356C2×C4×D61—41no—
357C2×Dic122—21no—
358C2×Dic122—21no—
359C2×Dic122—21no—
360C2×Dic122—21no—
361C2×Dic122—24no—
362C2×Dic122—21no—
363C2×Dic122—42no—
364C2×Dic122—41no—
365C2×Dic122C2×D411yescharacteristic
366C2×Dic122C2412yes—
367Q16×C61—24no—
368Q16×C61C2×D414yescomplemented
369SD16×C61—24no—
370SD16×C61—24no—
371SD16×C61—24no—
372SD16×C61—24no—
373SD16×C61C2×D414yescomplemented
374SD16×C61C2×D414yescomplemented
375D8×C61—24no—
376D8×C61C2×D414yescomplemented
377M16×C61—21no—
378M16×C61—24no—
379M16×C61C2412yes—
380C2×C8×C61—21no—
381C2×C8×C61—24no—
382C2×C8×C61C2×D411yescharacteristic
383C2×C8×C61C2×D411yescharacteristic
384C2×C8×C61C2×D412yes—
385C2×C8×C61C2412yes—
386#11758202—24no—
387#11758202—24no—
388#11758202—24no—
389#11758202C2×D414yescomplemented
390#11758201—24no—
391#11758201—24no—
392#11758201—24no—
393#11758201—24no—
394#11758201—24no—
395#11758201C2×D414yescomplemented
396#11758200—24no—
397#11758200—24no—
398#11758200—24no—
399#11758200—24no—
400#11758200—24no—
401#11758200C2×D414yescomplemented
402#11758199—24no—
403#11758199—24no—
404#11758199—24no—
405#11758199C2×D414yescomplemented
406#11758196—44no—
407C4×Dic61—21no—
408C4×Dic61C2412yes—
409#11758194—21no—
410#11758194—21no—
411#11758194—21no—
412#11758194—24no—
413#11758194—24no—
414#11758194C2412yes—
415#11758194C2412yes—
416#11758194C2412yes—
417C2×#92418—21no—
418C2×#92418—21no—
419C2×#92418—21no—
420C2×#92418—24no—
421C2×#92418—24no—
422C2×#92418C2×D411yescharacteristic
423C2×#92418C2×D411yescharacteristic
424C2×#92418C2×D412yes—
425C2×#92418C2412yes—
426#11758190—24no—
427#11758190—24no—
428#11758189—24no—
429C8×D61—24no—
430C23×C61—21no—
431C23×C61—21no—
432C23×C61—21no—
433C23×C61—22no—
434C23×C61—44no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—82no—
438C23×C61—162no—
439C23×C61H(5,𝔽2)11yescharacteristic
440C22×D61—21no—
441C22×D61—22no—
442C22×D61—44no—
443C22×D61—41no—
444C22×D61—41no—
445C22×D61—82no—
446C22×D61—162no—
447Q8×C61—21no—
448Q8×C61—21no—
449Q8×C61—21no—
450Q8×C61—22no—
451Q8×C61—22no—
452Q8×C61—44no—
453Q8×C61—41no—
454Q8×C61—41no—
455Q8×C61C22×D412yes—
456Q8×C61C22×D412yes—
457Q8×C61C22×D412yes—
458D4×C61—22no—
459D4×C61—22no—
460D4×C61—22no—
461D4×C61—22no—
462D4×C61—22no—
463D4×C61—22no—
464D4×C61—21no—
465D4×C61—21no—
466D4×C61—21no—
467D4×C61—22no—
468D4×C61—22no—
469D4×C61—44no—
470D4×C61—44no—
471D4×C61—44no—
472D4×C61—41no—
473D4×C61—41no—
474D4×C61C22×D412yes—
475D4×C61C22×D412yes—
476D4×C61C22×D412yes—
477C2×C4×C61—21no—
478C2×C4×C61—21no—
479C2×C4×C61—21no—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—44no—
488C2×C4×C61—44no—
489C2×C4×C61—44no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61C22×D411yescharacteristic
493C2×C4×C61C22×D411yescharacteristic
494C2×C4×C61C22×D411yescharacteristic
495C2×C4×C61C22×D411yescharacteristic
496C2×C4×C61H(5,𝔽2)11yescharacteristic
497C2×C4×C61C2511yescharacteristic
498C22⋊D61—22no—
499C22⋊D61—22no—
500C22⋊D61—44no—
501C22⋊D61—44no—
502C22⋊D61—88no—
503C2×Dic61—24no—
504C2×Dic61—21no—
505C2×Dic61—22no—
506C2×Dic61—22no—
507C2×Dic61—44no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510D244—21no—
511D244—22no—
512D244—22no—
513D244—44no—
514D244—41no—
515D244—41no—
516D244C22×D412yes—
517C4×D61—22no—
518C4×D61—22no—
519C4×D61—44no—
520C4×D61—44no—
521Dic122—21no—
522Dic122—22no—
523Dic122—22no—
524Dic122—44no—
525Dic122—41no—
526Dic122—41no—
527Dic122C22×D412yes—
528C8×C61—22no—
529C8×C61C22×D412yes—
530C8×C61C22×D412yes—
531#92418—22no—
532#92418—22no—
533#92418—22no—
534#92418C22×D412yes—
535#92418C22×D412yes—
536C2×#3291—611nomaximal, Sylow
537C22×C61—22no—
538C22×C61—22no—
539C22×C61—22no—
540C22×C61—22no—
541C22×C61—42no—
542C22×C61—42no—
543C22×C61—42no—
544C22×C61—42no—
545C22×C61—82no—
546C22×C61—82no—
547C22×C61—161no—
548C22×C61—164no—
549C22×C61D4211yescharacteristic
550C22×C61D4211yescharacteristic
551C22×C61C2×H(5,𝔽2)11yescharacteristic
552C2×D61—22no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—82no—
556C2×D61—82no—
557C2×D61—164no—
558C2×D61—161no—
559C4×C61—22no—
560C4×C61—22no—
561C4×C61—22no—
562C4×C61—42no—
563C4×C61D4211yescharacteristic
564C4×C61D4211yescharacteristic
565C4×C61C23×D411yescharacteristic
566C4×C61C23×D411yescharacteristic
567Dic61—24no—
568Dic61—22no—
569Dic61—42no—
570C2×#577—611no—
571C2×#577—611no—
572C2×#577—611no—
573C2×#577D6111yescharacteristic, complemented
574#3291—6116no—
575C2×#492—611no—
576C2×#471—611no—
577C2×#471—611no—
578C2×#471—611no—
579C2×#471—611no—
580C2×#456—611no—
581C2×#456—611no—
582C2×#453—611no—
583C2×#453—611no—
584C2×#443—611no—
585C2×#443—611no—
586C2×C61—21no—
587C2×C61—21no—
588C2×C61—42no—
589C2×C61—42no—
590C2×C61—42no—
591C2×C61—82no—
592C2×C61#329112yescomplemented
593C2×C61C2×D4211yescharacteristic
594D61—42no—
595D61—82no—
596C2×2−1+4—611no—
597C2×2−1+4C2×D6111yescharacteristic
598C2×H(5,𝔽2)—611no—
599C2×H(5,𝔽2)C2×D6111yescharacteristic, complemented
600#577—24no—
601#577—618no—
602#577—618no—
603#577—618no—
604#577—1224no—
605#577—1224no—
606#577—1224no—
607#577C2×D6118yescomplemented
608C2×#137—21no—
609C2×#137—611no—
610C2×#137—611no—
611C2×#137—611no—
612C2×#137—1221no—
613C2×#137—1221no—
614C2×#137—1221no—
615C2×#137C2×D6111yescharacteristic, complemented
616C2×AGL(1,ℤ/8)—21no—
617C2×AGL(1,ℤ/8)—611no—
618C2×AGL(1,ℤ/8)—611no—
619C2×AGL(1,ℤ/8)—611no—
620C2×AGL(1,ℤ/8)—1221no—
621C2×AGL(1,ℤ/8)—1221no—
622C2×AGL(1,ℤ/8)—1221no—
623C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
624C2×#135—21no—
625C2×#135—611no—
626C2×#135—1221no—
627C2×#135—1221no—
628C2×#135—1221no—
629C2×#135C2×D6111yescharacteristic
630C22×SD16—21no—
631C22×SD16—611no—
632C22×SD16—611no—
633C22×SD16—611no—
634C22×SD16—1221no—
635C22×SD16—1221no—
636C22×SD16—1221no—
637C22×SD16C2×D6111yescharacteristic, complemented
638C2×#131—611no—
639C2×#131—611no—
640C2×#131—611no—
641C2×#131C2×D6111yescharacteristic, complemented
642C2×C4⋊Q8—611no—
643C2×#127—611no—
644#492—618no—
645#471—618no—
646#471—618no—
647#471—618no—
648#471—618no—
649#456—618no—
650#456—618no—
651#453—618no—
652#453—618no—
653#443—618no—
654#443—618no—
655C2×#108—611no—
656C2×#108—611no—
657C2×#104—611no—
658C2×#104—611no—
659C2×#104—611no—
660C2×#104—611no—
661C2×#101—611no—
662C2×#101—611no—
663C2×#100—611no—
664C2×#100—611no—
665C2×C4×C8—611no—
666C61C2×#329111yescharacteristic, complemented, Sylow
6672−1+4—22no—
6682−1+4—22no—
6692−1+4—41no—
6702−1+4—614no—
6712−1+4—1222no—
6722−1+4—1222no—
6732−1+4—2441no—
6742−1+4C22×D6114yes—
675H(5,𝔽2)—22no—
676H(5,𝔽2)—22no—
677H(5,𝔽2)—41no—
678H(5,𝔽2)—614no—
679H(5,𝔽2)—1222no—
680H(5,𝔽2)—1222no—
681H(5,𝔽2)—2441no—
682H(5,𝔽2)C22×D6114yescomplemented
683C2×#41—21no—
684C2×#41—21no—
685C2×#41—21no—
686C2×#41—21no—
687C2×#41—41no—
688C2×#41—611no—
689C2×#41—1221no—
690C2×#41—1221no—
691C2×#41—1221no—
692C2×#41—1221no—
693C2×#41—2441no—
694C2×#41C22×D6111yescharacteristic
695C2×#41C22×D6111yescharacteristic
696C2×#41C22×D6111yescharacteristic
697C22×Q8—21no—
698C22×Q8—21no—
699C22×Q8—611no—
700C22×Q8—1221no—
701C22×Q8—1221no—
702C22×Q8C22×D6111yescharacteristic
703C22×D4—21no—
704C22×D4—21no—
705C22×D4—41no—
706C22×D4—611no—
707C22×D4—1221no—
708C22×D4—1221no—
709C22×D4—2441no—
710C22×D4—2441no—
711C22×D4C22×D6111yescharacteristic
712#137—22no—
713#137—28no—
714#137—614no—
715#137—614no—
716#137—614no—
717#137—1228no—
718#137—1228no—
719#137—1222no—
720#137—1222no—
721#137—1222no—
722#137—1228no—
723#137C22×D6114yescomplemented
724AGL(1,ℤ/8)—22no—
725AGL(1,ℤ/8)—28no—
726AGL(1,ℤ/8)—614no—
727AGL(1,ℤ/8)—614no—
728AGL(1,ℤ/8)—614no—
729AGL(1,ℤ/8)—1228no—
730AGL(1,ℤ/8)—1228no—
731AGL(1,ℤ/8)—1222no—
732AGL(1,ℤ/8)—1222no—
733AGL(1,ℤ/8)—1222no—
734AGL(1,ℤ/8)—1228no—
735AGL(1,ℤ/8)C22×D6114yes—
736#135—28no—
737#135—614no—
738#135—614no—
739#135—1228no—
740#135—1228no—
741#135—1228no—
742#135C22⋊D6114yescomplemented
743#135C22×D6114yes—
744C2×Q16—21no—
745C2×Q16—611no—
746C2×Q16—1221no—
747C2×Q16—1221no—
748C2×Q16—1221no—
749C2×Q16C22⋊D6111yescharacteristic, complemented
750C2×SD16—21no—
751C2×SD16—21no—
752C2×SD16—28no—
753C2×SD16—21no—
754C2×SD16—21no—
755C2×SD16—22no—
756C2×SD16—611no—
757C2×SD16—611no—
758C2×SD16—614no—
759C2×SD16—614no—
760C2×SD16—614no—
761C2×SD16—1221no—
762C2×SD16—1221no—
763C2×SD16—1222no—
764C2×SD16—1221no—
765C2×SD16—1221no—
766C2×SD16—1222no—
767C2×SD16—1228no—
768C2×SD16—1228no—
769C2×SD16—1221no—
770C2×SD16—1221no—
771C2×SD16—1221no—
772C2×SD16—1221no—
773C2×SD16—1221no—
774C2×SD16—1221no—
775C2×SD16—1228no—
776C2×SD16—1221no—
777C2×SD16—1221no—
778C2×SD16—1222no—
779C2×SD16C22⋊D6111yescharacteristic, complemented
780C2×SD16C22⋊D6111yescharacteristic, complemented
781C2×SD16C22×D6114yescomplemented
782C2×D8—21no—
783C2×D8—611no—
784C2×D8—1221no—
785C2×D8—1221no—
786C2×D8—1221no—
787C2×D8C22⋊D6111yescharacteristic, complemented
788#131—22no—
789#131—614no—
790#131—614no—
791#131—614no—
792#131—1222no—
793#131—1222no—
794#131—1222no—
795#131C22×D6114yescomplemented
796C2×M16—21no—
797C2×M16—611no—
798C2×M16—611no—
799C2×M16—611no—
800C2×M16—1221no—
801C2×M16—1221no—
802C2×M16—1221no—
803C2×M16C22×D6111yescharacteristic
804C22×C8—21no—
805C22×C8—611no—
806C22×C8—1221no—
807C22×C8—1221no—
808C22×C8—1221no—
809C22×C8C22×D6111yescharacteristic
810C4⋊Q8—614no—
811C4⋊Q8—2441no—
812#127—614no—
813#127—2441no—
814C2×C4⋊C4—2441no—
815C2×C42—611no—
816#108—614no—
817#108—614no—
818#104—614no—
819#104—614no—
820#104—614no—
821#104—614no—
822#101—614no—
823#101—614no—
824#100—614no—
825#100—614no—
826C4×C8—614no—
827C24—21no—
828C24—41no—
829C24—1221no—
830C24—2441no—
831#41—21no—
832#41—21no—
833#41—21no—
834#41—21no—
835#41—21no—
836#41—21no—
837#41—24no—
838#41—24no—
839#41—24no—
840#41—24no—
841#41—44no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41—42no—
846#41—44no—
847#41—612no—
848#41—612no—
849#41—1224no—
850#41—1224no—
851#41—1221no—
852#41—1221no—
853#41—1224no—
854#41—1224no—
855#41—2442no—
856#41—2442no—
857#41—2444no—
858#41—2442no—
859#41—2442no—
860#41—2444no—
861#41D4×D6112yes—
862#41C2×C22⋊D6112yes—
863#41C2×C22⋊D6112yes—
864#41C23×D6112yes—
865#41C23×D6112yes—
866#41C23×D6112yes—
867C2×Q8—21no—
868C2×Q8—24no—
869C2×Q8—24no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—41no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—611no—
878C2×Q8—612no—
879C2×Q8—1224no—
880C2×Q8—1221no—
881C2×Q8—1224no—
882C2×Q8—1221no—
883C2×Q8—1221no—
884C2×Q8—1221no—
885C2×Q8—1221no—
886C2×Q8—2441no—
887C2×Q8—2442no—
888C2×Q8—2442no—
889C2×Q8D4×D6111yescharacteristic
890C2×Q8C2×C22⋊D6111yescharacteristic
891C2×Q8C2×C22⋊D6111yescharacteristic
892C2×Q8C23×D6112yes—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—41no—
906C2×D4—41no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—41no—
910C2×D4—611no—
911C2×D4—612no—
912C2×D4—1224no—
913C2×D4—1221no—
914C2×D4—1224no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—4884no—
921C2×D4—2442no—
922C2×D4—2441no—
923C2×D4—2442no—
924C2×D4—2444no—
925C2×D4—2441no—
926C2×D4—2444no—
927C2×D4—2444no—
928C2×D4—2441no—
929C2×D4D4×D6111yescharacteristic
930C2×D4C2×C22⋊D6111yescharacteristic
931C2×D4C2×C22⋊D6111yescharacteristic
932C2×D4C23×D6112yes—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—1221no—
941C22×C4—1221no—
942C22×C4—1221no—
943C22×C4—2441no—
944C22×C4—2441no—
945C22×C4—2441no—
946C22×C4C23×D6111yescharacteristic
947Q16—24no—
948Q16—614no—
949Q16—1224no—
950Q16—1224no—
951Q16—1224no—
952Q16C2×C22⋊D6114yescomplemented
953SD16—24no—
954SD16—24no—
955SD16—24no—
956SD16—24no—
957SD16—614no—
958SD16—614no—
959SD16—1224no—
960SD16—1224no—
961SD16—1224no—
962SD16—1224no—
963SD16—1224no—
964SD16—1224no—
965SD16—1224no—
966SD16—1224no—
967SD16—1224no—
968SD16—1224no—
969SD16—1224no—
970SD16—1224no—
971SD16C2×C22⋊D6114yescomplemented
972SD16C2×C22⋊D6114yescomplemented
973D8—24no—
974D8—614no—
975D8—1224no—
976D8—1224no—
977D8—1224no—
978D8C2×C22⋊D6114yescomplemented
979M16—21no—
980M16—24no—
981M16—612no—
982M16—612no—
983M16—612no—
984M16—1224no—
985M16—1224no—
986M16—1221no—
987M16—1221no—
988M16—1221no—
989M16—1224no—
990M16C23×D6112yes—
991C2×C8—21no—
992C2×C8—24no—
993C2×C8—611no—
994C2×C8—611no—
995C2×C8—612no—
996C2×C8—612no—
997C2×C8—1224no—
998C2×C8—1224no—
999C2×C8—1221no—
1000C2×C8—1221no—
1001C2×C8—1221no—
1002C2×C8—1224no—
1003C2×C8C2×C22⋊D6111yescharacteristic
1004C2×C8C2×C22⋊D6111yescharacteristic
1005C2×C8C2×C22⋊D6112yes—
1006C2×C8C23×D6112yes—
1007C4⋊C4—2444no—
1008C42—612no—
1009C42—1221no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23—44no—
1015C23—41no—
1016C23—41no—
1017C23—82no—
1018C23—162no—
1019C23—1221no—
1020C23—1222no—
1021C23—9762no—
1022C23—4882no—
1023C23—2444no—
1024C23—2441no—
1025C23—2441no—
1026C23#1451982211yescharacteristic
1027Q8—21no—
1028Q8—21no—
1029Q8—21no—
1030Q8—22no—
1031Q8—22no—
1032Q8—44no—
1033Q8—41no—
1034Q8—41no—
1035Q8—612no—
1036Q8—1221no—
1037Q8—1222no—
1038Q8—1222no—
1039Q8—2444no—
1040Q8—2441no—
1041Q8—2441no—
1042Q8C2×D4×D6112yes—
1043Q8C22×C22⋊D6112yes—
1044Q8C22×C22⋊D6112yes—
1045D4—22no—
1046D4—22no—
1047D4—22no—
1048D4—22no—
1049D4—22no—
1050D4—22no—
1051D4—22no—
1052D4—22no—
1053D4—21no—
1054D4—21no—
1055D4—21no—
1056D4—44no—
1057D4—44no—
1058D4—44no—
1059D4—41no—
1060D4—41no—
1061D4—612no—
1062D4—1222no—
1063D4—1222no—
1064D4—1222no—
1065D4—1222no—
1066D4—1221no—
1067D4—4888no—
1068D4—2444no—
1069D4—2444no—
1070D4—2444no—
1071D4—2441no—
1072D4—2441no—
1073D4C2×D4×D6112yes—
1074D4C22×C22⋊D6112yes—
1075D4C22×C22⋊D6112yes—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—1224no—
1092C2×C4—1222no—
1093C2×C4—1221no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—2444no—
1098C2×C4—2444no—
1099C2×C4—2444no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4C2×D4×D6111yescharacteristic
1103C2×C4C2×D4×D6111yescharacteristic
1104C2×C4C22×C22⋊D6111yescharacteristic
1105C2×C4C22×C22⋊D6111yescharacteristic
1106C2×C4#1451982211yescharacteristic
1107C2×C4C24×D6111yescharacteristic
1108C8—22no—
1109C8—612no—
1110C8—612no—
1111C8—1222no—
1112C8—1222no—
1113C8—1222no—
1114C8C22×C22⋊D6112yes—
1115C8C22×C22⋊D6112yes—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—82no—
1125C22—82no—
1126C22—161no—
1127C22—164no—
1128C22—1222no—
1129C22—9761no—
1130C22—9764no—
1131C22—4882no—
1132C22—4882no—
1133C22—2442no—
1134C22—2442no—
1135C22D4×C22⋊D6111yescharacteristic
1136C22D4×C22⋊D6111yescharacteristic
1137C22C2×#1451982211yescharacteristic
1138C4—22no—
1139C4—22no—
1140C4—22no—
1141C4—42no—
1142C4—1224no—
1143C4—1222no—
1144C4—2442no—
1145C4D4×C22⋊D6111yescharacteristic
1146C4D4×C22⋊D6111yescharacteristic
1147C4C22×D4×D6111yescharacteristic
1148C4C23×C22⋊D6111yescharacteristic
1149C2—21no—
1150C2—21no—
1151C2—42no—
1152C2—42no—
1153C2—42no—
1154C2—82no—
1155C2—4882no—
1156C2—2442no—
1157C2#2145761012yesdirect product factor
1158C2C2×D4×C22⋊D6111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#577C2
socleC22×C61D42
hypercenterC2×#577D61
hypocenterC61C2×#3291
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#16840573C2semidirect
2. C2×#16840570C2semidirect
3. C2×#16840569C2semidirect
4. #21457610C2direct (N × H)
5. C2×#16840133C2semidirect
6. C2×#16840027C2semidirect
7. C2×#16840025C2semidirect
8. C2×#16840023C2semidirect
9. C2×#16840022C2semidirect
10. C2×#16839945C2semidirect
11. C2×#16839943C2semidirect
12. C2×#16839930C2semidirect
13. C2×#16839928C2semidirect
14. C2×#16839879C2semidirect
15. C2×#16839877C2semidirect
16. C2×C61×#577C2semidirect
18. C2×#14519823C22semidirect
20. #16840573C22semidirect
22. #16840570C22semidirect
24. #16840569C22semidirect
27. C2×#14519808C22semidirect
29. C2×#14519807C22semidirect
30. C2×#14519807C22semidirect
41. C22×#11758190C22semidirect
43. C22×#11758200C22semidirect
45. C22×#11758201C22semidirect
47. C2×#14519784C22semidirect
48. C2×#14519784C22semidirect
49. C2×#14519783C22semidirect
50. C2×#14519775C22semidirect
52. #16840133C22semidirect
53. #16840027C22semidirect
54. #16840025C22semidirect
55. #16840023C22semidirect
56. #16840022C22semidirect
57. #16839945C22semidirect
58. #16839943C22semidirect
59. #16839930C22semidirect
60. #16839928C22semidirect
61. #16839879C22semidirect
62. #16839877C22semidirect
63. C2×#14519713C22semidirect
64. C2×#14519712C22semidirect
65. C2×#14519704C22semidirect
66. C2×#14519704C22semidirect
67. C2×#14519704C22semidirect
68. C2×#14519703C22semidirect
69. C2×#14519696C22semidirect
70. C2×#14519695C22semidirect
71. C2×#14519694C22semidirect
72. C2×#14519693C22semidirect
73. C2×C8×Dic61C22semidirect
75. C2×H(5,𝔽2)×C61C22semidirect
77. C61×#577C22semidirect
79. C2×#137×C61C22semidirect
85. C22×SD16×C61C22semidirect
86. C2×#131×C61C22semidirect
94. #14519823C23semidirect
112. #14519808C23semidirect
116. #14519807C23semidirect
117. #14519807C23semidirect
130. #14519797D4semidirect
135. C2×#11758202D4semidirect
139. C2×#11758190C23semidirect
147. C2×#11758200D4semidirect
148. C2×#11758200C23semidirect
156. C2×#11758201D4semidirect
157. C2×#11758201C23semidirect
162. C2×#11758199D4semidirect
165. #14519784C23semidirect
166. #14519784C23semidirect
168. #14519783C23semidirect
180. #14519775C23semidirect
185. #14519713C23semidirect
186. #14519712C23semidirect
187. #14519704C23semidirect
188. #14519704C23semidirect
189. #14519704C23semidirect
190. #14519703C23semidirect
191. #14519696C23semidirect
192. #14519695C23semidirect
193. #14519694C23semidirect
194. #14519693C23semidirect
195. C8×Dic61C23semidirect
203. H(5,𝔽2)×C61C23semidirect
221. #137×C61C23semidirect
226. #135×C61D4semidirect
229. C2×Q16×C61D4semidirect
236. C2×SD16×C61D4semidirect
237. C2×SD16×C61D4semidirect
238. C2×SD16×C61C23semidirect
240. C2×D8×C61D4semidirect
242. #131×C61C23semidirect
368. Q16×C61C2×D4semidirect
373. SD16×C61C2×D4semidirect
374. SD16×C61C2×D4semidirect
376. D8×C61C2×D4semidirect
389. #11758202C2×D4semidirect
395. #11758201C2×D4semidirect
401. #11758200C2×D4semidirect
405. #11758199C2×D4semidirect
573. C2×#577D61semidirect
592. C2×C61#3291semidirect
599. C2×H(5,𝔽2)C2×D61semidirect
607. #577C2×D61semidirect
615. C2×#137C2×D61semidirect
637. C22×SD16C2×D61semidirect
641. C2×#131C2×D61semidirect
666. C61C2×#3291semidirect
682. H(5,𝔽2)C22×D61semidirect
723. #137C22×D61semidirect
742. #135C22⋊D61semidirect
749. C2×Q16C22⋊D61semidirect
779. C2×SD16C22⋊D61semidirect
780. C2×SD16C22⋊D61semidirect
781. C2×SD16C22×D61semidirect
787. C2×D8C22⋊D61semidirect
795. #131C22×D61semidirect
952. Q16C2×C22⋊D61semidirect
971. SD16C2×C22⋊D61semidirect
972. SD16C2×C22⋊D61semidirect
978. D8C2×C22⋊D61semidirect
1157. C2#21457610direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405732
C2×#168405702
C2×#168405692
#214576102
C2×#168401332
C2×#168400272
C2×#168400252
C2×#168400232
C2×#168400222
C2×#168399452
C2×#168399432
C2×#168399302
C2×#168399282
C2×#168398792
C2×#168398772
C2×C61×#5772
C2×#329161