Finite Group Databasebeta

← #29707035

Subgroups — #29707035

Order 15616.

1980 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic, complemented
2#21459148C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic, complemented
4C2×#16839779C211yesmaximal, characteristic, complemented
5#21454264C211yesmaximal, characteristic, complemented
6#21446884C218yesmaximal, complemented
7C2×#16839518C211yesmaximal, characteristic, complemented
8C61×#3449C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840560—22no—
11#16840560—22no—
12#16840560—22no—
13#16840560C2214yes—
14C2×#14519808—21no—
15C2×#14519807—21no—
16C2×#14519803—21no—
17C2×#14519802—21no—
18C2×#14519797—22no—
19C22×#11758194C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21#16840340—22no—
22#16840336—21no—
23#16840333—21no—
24#16840329—21no—
25#16840326—21no—
26#16840321—22no—
27#16840308—22no—
28#16840273C2214yescomplemented
29#16840269—22no—
30C2×#14519736C2211yescharacteristic
31#16839780—22no—
32#16839780C2214yescomplemented
33#16839779—22no—
34#16839779C2214yescomplemented
35C2×#14519705—22no—
36C2×#14519704—22no—
37#16839729—22no—
38#16839729—22no—
39#16839726C2214yescomplemented
40#16839518C2214yescomplemented
41C22×#41×C61C2211yescharacteristic
42C22×#41×C61C2211yescharacteristic
43C61×#537—22no—
44C61×#536—21no—
45C61×#536—21no—
46C61×#535—21no—
47C61×#535—21no—
48C61×#534—22no—
49C61×#532—22no—
50C61×#525—22no—
51C61×#525C2214yescomplemented
52C2×#117×C61C2211yescharacteristic
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222D412yescomplemented
64C2×#11758222C2312yes—
65C22×Dic122D411yescharacteristic, complemented
66C22×D244D411yescharacteristic, complemented
67C22×C22⋊D61—21no—
68C22×C4×D61—21no—
69#14519808—24no—
70#14519808—24no—
71#14519807—24no—
72#14519807—24no—
73#14519803—24no—
74#14519803—24no—
75#14519802—24no—
76#14519802—24no—
77#14519797—28no—
78#14519797—28no—
79C2×#11758202—22no—
80C2×#11758200—22no—
81C2×#11758201—22no—
82C2×#11758199—22no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194—21no—
87C2×#11758194—21no—
88C2×#11758194—21no—
89C2×#11758194—21no—
90C2×#11758194—21no—
91C2×#11758194—21no—
92C2×#11758194D412yescomplemented
93C2×#11758194C2312yes—
94C2×#11758194C2312yes—
95C22×#92418—21no—
96C22×#92418D412yescomplemented
97#14519775—22no—
98#14519773—22no—
99#14519766—22no—
100#14519764—22no—
101#14519760—24no—
102#14519758—24no—
103#14519756—24no—
104#14519753—24no—
105#14519751—24no—
106#14519749—28no—
107#14519748—24no—
108#14519746—24no—
109#14519745—24no—
110C4×C22⋊D61—28no—
111#14519736—21no—
112#14519736—21no—
113#14519736D412yescomplemented
114#14519736C2312yes—
115C2×C4⋊Dic61—21no—
116C2×C22⋊Dic61—21no—
117C2×C4×Dic61D412yescomplemented
118#14519705—28no—
119#14519704—28no—
120C22⋊#92418—28no—
121C2×#41×C61—21no—
122C2×#41×C61—21no—
123C2×#41×C61—21no—
124C2×#41×C61—21no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—21no—
128C2×#41×C61—21no—
129C2×#41×C61—21no—
130C2×#41×C61—21no—
131C2×#41×C61—21no—
132C2×#41×C61—21no—
133C2×#41×C61—21no—
134C2×#41×C61—21no—
135C2×#41×C61—21no—
136C2×#41×C61—21no—
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—21no—
140C2×#41×C61—21no—
141C2×#41×C61—21no—
142C2×#41×C61—21no—
143C2×#41×C61D412yescomplemented
144C2×#41×C61C2312yes—
145C22×Q8×C61D411yescharacteristic
146C22×Q8×C61D411yescharacteristic, complemented
147C22×D4×C61—21no—
148C22×D4×C61D412yes—
149C22×D4×C61D411yescharacteristic
150C22×D4×C61D411yescharacteristic, complemented
151C23×C4×C61—21no—
152C23×C4×C61C2312yes—
153C23×C4×C61C2311yescharacteristic
154C4⋊Q8×C61—22no—
155#127×C61—22no—
156#124×C61—22no—
157#124×C61—22no—
158#123×C61—24no—
159#123×C61—24no—
160C22⋊Q8×C61—24no—
161C22⋊Q8×C61—24no—
162#121×C61—28no—
163#121×C61—24no—
164#121×C61—24no—
165#120×C61—24no—
166#120×C61—24no—
167C4×D4×C61—28no—
168#117×C61—21no—
169#117×C61—21no—
170#117×C61D412yescomplemented
171#117×C61C2312yes—
172C2×C4⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C42×C61D412yescomplemented
175C24×C61—21no—
176C24×C61C2×D412yes—
177C24×C61C2×D411yescharacteristic
178C23×D61—21no—
179#41×C61—22no—
180#41×C61—22no—
181#41×C61—22no—
182#41×C61—22no—
183#41×C61—22no—
184#41×C61—22no—
185#41×C61—22no—
186#41×C61—22no—
187#41×C61—41no—
188#41×C61—41no—
189#41×C61—41no—
190#41×C61—41no—
191#41×C61—41no—
192#41×C61—41no—
193#41×C61—41no—
194#41×C61—41no—
195#41×C61—41no—
196#41×C61—41no—
197#41×C61—41no—
198#41×C61—41no—
199#41×C61—41no—
200#41×C61—41no—
201#41×C61—41no—
202#41×C61—41no—
203#41×C61—41no—
204#41×C61—41no—
205#41×C61—41no—
206#41×C61—41no—
207#41×C61—41no—
208#41×C61—41no—
209#41×C61—41no—
210#41×C61—41no—
211C2×Q8×C61—21no—
212C2×Q8×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—21no—
221C2×Q8×C61—21no—
222C2×Q8×C61C2×D412yes—
223C2×D4×C61—22no—
224C2×D4×C61—22no—
225C2×D4×C61—22no—
226C2×D4×C61—22no—
227C2×D4×C61—22no—
228C2×D4×C61—22no—
229C2×D4×C61—22no—
230C2×D4×C61—22no—
231C2×D4×C61—28no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—21no—
239C2×D4×C61—21no—
240C2×D4×C61—21no—
241C2×D4×C61—21no—
242C2×D4×C61—21no—
243C2×D4×C61—41no—
244C2×D4×C61—41no—
245C2×D4×C61—41no—
246C2×D4×C61—41no—
247C2×D4×C61C2×D412yes—
248C22×C4×C61—21no—
249C22×C4×C61—22no—
250C22×C4×C61—22no—
251C22×C4×C61—22no—
252C22×C4×C61—22no—
253C22×C4×C61—22no—
254C22×C4×C61—22no—
255C22×C4×C61—22no—
256C22×C4×C61—22no—
257C22×C4×C61—22no—
258C22×C4×C61—41no—
259C22×C4×C61—41no—
260C22×C4×C61—41no—
261C22×C4×C61—41no—
262C22×C4×C61C2×D412yes—
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61#4111yescharacteristic
275C22×C4×C61#4111yescharacteristic
276C22×C4×C61C2411yescharacteristic
277C2×C22⋊D61—22no—
278C2×C22⋊D61—22no—
279C2×C22⋊D61—28no—
280C2×C22⋊D61—41no—
281C2×C22⋊D61—41no—
282C2×C22⋊D61—41no—
283C2×C22⋊D61—41no—
284C22×Dic61—21no—
285C22×Dic61—22no—
286#11758222—22no—
287#11758222—22no—
288#11758222—22no—
289#11758222—22no—
290#11758222—22no—
291#11758222—22no—
292#11758222—22no—
293#11758222—22no—
294#11758222—41no—
295#11758222—41no—
296#11758222—41no—
297#11758222—41no—
298#11758222—41no—
299#11758222—41no—
300#11758222—41no—
301#11758222—41no—
302C2×D244—21no—
303C2×D244—21no—
304C2×D244—21no—
305C2×D244—21no—
306C2×D244—21no—
307C2×D244C2×D412yes—
308C2×C4×D61—22no—
309C2×C4×D61—22no—
310C2×C4×D61—41no—
311C2×C4×D61—41no—
312C2×C4×D61—41no—
313C2×C4×D61—41no—
314C2×Dic122—21no—
315C2×Dic122—21no—
316C2×Dic122—21no—
317C2×Dic122—21no—
318C2×Dic122—21no—
319C2×Dic122C2×D412yes—
320C4⋊C4×C61—28no—
321C4⋊C4×C61—22no—
322C4⋊C4×C61—22no—
323C22⋊C4×C61—28no—
324C22⋊C4×C61—28no—
325C22⋊C4×C61—22no—
326C22⋊C4×C61—22no—
327C42×C61—22no—
328C42×C61C2×D414yes—
329C22⋊Dic61—28no—
330C22⋊Dic61—22no—
331C22⋊Dic61—22no—
332#11758202—28no—
333#11758201—28no—
334#11758200—28no—
335#11758199—28no—
336#11758198—28no—
337C4⋊Dic61—22no—
338C4⋊Dic61—22no—
339#11758196—28no—
340C4×Dic61—22no—
341C4×Dic61C2×D414yes—
342#11758194—22no—
343#11758194—22no—
344#11758194—22no—
345#11758194—22no—
346#11758194—22no—
347#11758194—22no—
348#11758194—41no—
349#11758194—41no—
350C2×#92418—22no—
351C2×#92418—22no—
352C2×#92418—22no—
353C2×#92418—41no—
354C2×#92418—41no—
355C2×#92418C2×D414yes—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—81no—
363C23×C61—82no—
364C23×C61—82no—
365C23×C61#12011yescharacteristic
366C23×C61#12011yescharacteristic
367C23×C61#12011yescharacteristic
368C23×C61#12011yescharacteristic
369C23×C61#12111yescharacteristic
370C23×C61#12111yescharacteristic
371C23×C61C22×D411yescharacteristic
372C22×D61—22no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—82no—
376Q8×C61—22no—
377Q8×C61—22no—
378Q8×C61—41no—
379Q8×C61—41no—
380Q8×C61—41no—
381Q8×C61—41no—
382Q8×C61—41no—
383Q8×C61—41no—
384D4×C61—22no—
385D4×C61—22no—
386D4×C61—42no—
387D4×C61—42no—
388D4×C61—42no—
389D4×C61—42no—
390D4×C61—42no—
391D4×C61—42no—
392D4×C61—42no—
393D4×C61—42no—
394D4×C61—41no—
395D4×C61—41no—
396D4×C61—41no—
397D4×C61—41no—
398D4×C61—41no—
399D4×C61—41no—
400D4×C61—88no—
401C2×C4×C61—22no—
402C2×C4×C61—24no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—42no—
409C2×C4×C61—42no—
410C2×C4×C61—42no—
411C2×C4×C61—42no—
412C2×C4×C61—42no—
413C2×C4×C61—42no—
414C2×C4×C61—42no—
415C2×C4×C61—42no—
416C2×C4×C61—82no—
417C2×C4×C61#12011yescharacteristic
418C2×C4×C61#12011yescharacteristic
419C2×C4×C61#12011yescharacteristic
420C2×C4×C61#12011yescharacteristic
421C2×C4×C61#12011yescharacteristic
422C2×C4×C61#12011yescharacteristic
423C2×C4×C61#12011yescharacteristic
424C2×C4×C61#12011yescharacteristic
425C2×C4×C61#12111yescharacteristic
426C2×C4×C61#12111yescharacteristic
427C2×C4×C61#12111yescharacteristic
428C2×C4×C61#12111yescharacteristic
429C2×C4×C61#12111yescharacteristic
430C2×C4×C61#12111yescharacteristic
431C2×C4×C61#12111yescharacteristic
432C2×C4×C61#12111yescharacteristic
433C2×C4×C61#12111yescharacteristic
434C2×C4×C61#12111yescharacteristic
435C2×C4×C61#12711yescharacteristic
436C2×C4×C61#12711yescharacteristic
437C2×C4×C61#12711yescharacteristic
438C2×C4×C61#12711yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61C22×D411yescharacteristic
442C2×C4×C61C22×D411yescharacteristic
443C2×C4×C61C22×D411yescharacteristic
444C2×C4×C61C2×#4111yescharacteristic
445C22⋊D61—42no—
446C22⋊D61—42no—
447C22⋊D61—42no—
448C22⋊D61—42no—
449C22⋊D61—88no—
450C2×Dic61—24no—
451C2×Dic61—22no—
452C2×Dic61—41no—
453C2×Dic61—41no—
454C2×Dic61—82no—
455D244—22no—
456D244—22no—
457D244—41no—
458D244—41no—
459C4×D61—42no—
460C4×D61—42no—
461C4×D61—42no—
462C4×D61—42no—
463Dic122—22no—
464Dic122—22no—
465Dic122—41no—
466Dic122—41no—
467#92418—24no—
468#92418—42no—
469#23414—611nomaximal, Sylow
470C22×C61—41no—
471C22×C61—41no—
472C22×C61—41no—
473C22×C61—41no—
474C22×C61—41no—
475C22×C61—41no—
476C22×C61—41no—
477C22×C61—44no—
478C22×C61—44no—
479C22×C61—44no—
480C22×C61—44no—
481C22×C61—42no—
482C22×C61—42no—
483C22×C61—82no—
484C22×C61—82no—
485C22×C61#39211yescharacteristic
486C22×C61#39211yescharacteristic
487C22×C61#39211yescharacteristic
488C22×C61#39211yescharacteristic
489C22×C61C2×#12011yescharacteristic
490C22×C61C2×#12011yescharacteristic
491C22×C61C2×#12111yescharacteristic
492C2×D61—44no—
493C2×D61—42no—
494C2×D61—82no—
495C2×D61—82no—
496C4×C61—44no—
497C4×C61—42no—
498C4×C61—42no—
499C4×C61#39211yescharacteristic
500C4×C61#39211yescharacteristic
501C4×C61#39211yescharacteristic
502C4×C61#39211yescharacteristic
503C4×C61C2×#12011yescharacteristic
504C4×C61C2×#12111yescharacteristic
505C4×C61C2×#12111yescharacteristic
506C4×C61C2×#12711yescharacteristic
507Dic61—44no—
508Dic61—42no—
509C2×#575—611no—
510#3449—611no—
511#3449D6111yescharacteristic, complemented
512C2×#421—611no—
513C2×#421—611no—
514#2879—611no—
515#2010—618no—
516C2×H(3,ℤ/4)—611no—
517C2×C61—21no—
518C2×C61—21no—
519C2×C61—21no—
520C2×C61—21no—
521C2×C61—21no—
522C2×C61—21no—
523C2×C61—21no—
524C2×C61—82no—
525C2×C61—82no—
526C2×C61C2×#39211yescharacteristic
527D61—82no—
528C22×#41—611no—
529C22×#41C2×D6111yescharacteristic
530C22×#41C2×D6111yescharacteristic
531#575—614no—
532#575—1222no—
533#575—1222no—
534#575—1222no—
535C2×#137—1221no—
536C2×#137—1221no—
537C2×AGL(1,ℤ/8)—1221no—
538C2×AGL(1,ℤ/8)—1221no—
539C2×#135—1222no—
540C22×M16—611no—
541C22×M16—611no—
542#537—22no—
543#537—1222no—
544#536—21no—
545#536—21no—
546#536—1221no—
547#536—1221no—
548#535—21no—
549#535—21no—
550#535—1221no—
551#535—1221no—
552#534—22no—
553#534—1222no—
554#532—22no—
555#532—1222no—
556#525—22no—
557#525—614no—
558#525—1222no—
559#525C2×D6114yescomplemented
560C2×#117—611no—
561C2×#117C2×D6111yescharacteristic
562#421—614no—
563#421—614no—
564#421—1222no—
565#421—1222no—
566C2×#104—1222no—
567C2×#104—1222no—
568#408—1222no—
569#408—1222no—
570#407—614no—
571H(3,ℤ/4)—614no—
572C61#2341411yescharacteristic, complemented, Sylow
573C2×#41—21no—
574C2×#41—21no—
575C2×#41—21no—
576C2×#41—21no—
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—612no—
596C2×#41—612no—
597C2×#41—1221no—
598C2×#41—1221no—
599C2×#41—1221no—
600C2×#41—1221no—
601C2×#41—1221no—
602C2×#41—1221no—
603C2×#41—1221no—
604C2×#41—1221no—
605C2×#41—1221no—
606C2×#41—1221no—
607C2×#41C22⋊D6112yescomplemented
608C2×#41C22×D6112yes—
609C22×Q8—611no—
610C22×Q8C22⋊D6111yescharacteristic
611C22×Q8C22⋊D6111yescharacteristic, complemented
612C22×D4—21no—
613C22×D4—611no—
614C22×D4—1221no—
615C22×D4C22⋊D6112yes—
616C22×D4C22⋊D6111yescharacteristic
617C22×D4C22⋊D6111yescharacteristic, complemented
618C23×C4—21no—
619C23×C4—1221no—
620C23×C4C22×D6112yes—
621C23×C4C22×D6111yescharacteristic
622#137—1224no—
623#137—1224no—
624#137—1224no—
625#137—1224no—
626AGL(1,ℤ/8)—1224no—
627AGL(1,ℤ/8)—1224no—
628AGL(1,ℤ/8)—1224no—
629AGL(1,ℤ/8)—1224no—
630#135—1228no—
631#135—1228no—
632C2×Q16—1222no—
633C2×SD16—1222no—
634C2×SD16—1222no—
635C2×D8—1222no—
636C2×M16—612no—
637C2×M16—612no—
638C2×M16—612no—
639C2×M16—1221no—
640C2×M16—1221no—
641C2×M16—1221no—
642C2×M16—1221no—
643C2×M16—1221no—
644C2×M16—1221no—
645C2×M16—1221no—
646C2×M16—1221no—
647C2×M16—1221no—
648C22×C8—612no—
649C22×C8—1221no—
650C4⋊Q8—22no—
651C4⋊Q8—1222no—
652#127—22no—
653#127—1222no—
654#124—22no—
655#124—22no—
656#124—1222no—
657#124—1222no—
658#123—24no—
659#123—24no—
660#123—1224no—
661#123—1224no—
662C22⋊Q8—24no—
663C22⋊Q8—24no—
664C22⋊Q8—1224no—
665C22⋊Q8—1224no—
666#121—24no—
667#121—28no—
668#121—24no—
669#121—1224no—
670#121—1224no—
671#121—1228no—
672#120—24no—
673#120—24no—
674#120—1224no—
675#120—1224no—
676C4×D4—28no—
677C4×D4—1228no—
678#117—21no—
679#117—21no—
680#117—612no—
681#117—612no—
682#117—1221no—
683#117—1221no—
684#117C22⋊D6112yescomplemented
685#117C22×D6112yes—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—1221no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—1221no—
690C2×C42—612no—
691C2×C42C22⋊D6112yescomplemented
692#104—1228no—
693#104—1228no—
694C22⋊C8—1228no—
695C24—21no—
696C24—1221no—
697C24C2×C22⋊D6112yes—
698C24C2×C22⋊D6111yescharacteristic
699#41—22no—
700#41—22no—
701#41—22no—
702#41—22no—
703#41—22no—
704#41—22no—
705#41—22no—
706#41—22no—
707#41—41no—
708#41—41no—
709#41—41no—
710#41—41no—
711#41—41no—
712#41—41no—
713#41—41no—
714#41—41no—
715#41—41no—
716#41—41no—
717#41—41no—
718#41—41no—
719#41—41no—
720#41—41no—
721#41—41no—
722#41—41no—
723#41—41no—
724#41—41no—
725#41—41no—
726#41—41no—
727#41—41no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—1222no—
732#41—1222no—
733#41—1222no—
734#41—1222no—
735#41—1222no—
736#41—1222no—
737#41—1222no—
738#41—1222no—
739#41—2441no—
740#41—2441no—
741#41—2441no—
742#41—2441no—
743#41—2441no—
744#41—2441no—
745#41—2441no—
746#41—2441no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—612no—
759C2×Q8—1221no—
760C2×Q8—1221no—
761C2×Q8—1221no—
762C2×Q8—1221no—
763C2×Q8—1221no—
764C2×Q8C2×C22⋊D6112yes—
765C2×D4—22no—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—28no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—41no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—612no—
790C2×D4—1228no—
791C2×D4—1222no—
792C2×D4—1222no—
793C2×D4—1221no—
794C2×D4—1221no—
795C2×D4—1221no—
796C2×D4—1221no—
797C2×D4—1221no—
798C2×D4—2441no—
799C2×D4—2441no—
800C2×D4—2441no—
801C2×D4—2441no—
802C2×D4C2×C22⋊D6112yes—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—1222no—
818C22×C4—1221no—
819C22×C4—1222no—
820C22×C4—1222no—
821C22×C4—2441no—
822C22×C4—2441no—
823C22×C4—2441no—
824C22×C4—2441no—
825C22×C4D4×D6111yescharacteristic
826C22×C4D4×D6111yescharacteristic
827C22×C4D4×D6111yescharacteristic
828C22×C4D4×D6111yescharacteristic
829C22×C4D4×D6111yescharacteristic
830C22×C4D4×D6111yescharacteristic
831C22×C4#1175822411yescharacteristic
832C22×C4#1175822411yescharacteristic
833C22×C4C2×C22⋊D6112yes—
834C22×C4C2×C22⋊D6111yescharacteristic
835C22×C4C2×C22⋊D6111yescharacteristic
836C22×C4C2×C22⋊D6111yescharacteristic
837C22×C4C2×C22⋊D6111yescharacteristic
838C22×C4C2×C22⋊D6111yescharacteristic
839C22×C4C23×D6111yescharacteristic
840Q16—1228no—
841SD16—1228no—
842SD16—1228no—
843D8—1228no—
844M16—1222no—
845M16—1222no—
846M16—1222no—
847M16—1222no—
848M16—1222no—
849M16—1222no—
850M16—2441no—
851M16—2441no—
852C2×C8—614no—
853C2×C8—1222no—
854C2×C8—1222no—
855C2×C8—1222no—
856C2×C8—2441no—
857C2×C8—2441no—
858C4⋊C4—28no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—1228no—
862C4⋊C4—1222no—
863C4⋊C4—1222no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—1228no—
869C22⋊C4—1228no—
870C22⋊C4—1222no—
871C22⋊C4—1222no—
872C42—22no—
873C42—614no—
874C42—1222no—
875C42C2×C22⋊D6114yes—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—41no—
881C23—41no—
882C23—81no—
883C23—82no—
884C23—82no—
885C23—1222no—
886C23—4882no—
887C23—2441no—
888C23—2441no—
889C23#1451974511yescharacteristic
890C23#1451974511yescharacteristic
891C23#1451974611yescharacteristic
892C23#1451974611yescharacteristic
893C23#1451974911yescharacteristic
894C23#1451974911yescharacteristic
895C23C22×C22⋊D6111yescharacteristic
896Q8—22no—
897Q8—22no—
898Q8—41no—
899Q8—41no—
900Q8—41no—
901Q8—41no—
902Q8—41no—
903Q8—41no—
904Q8—1222no—
905Q8—1222no—
906Q8—2441no—
907Q8—2441no—
908D4—22no—
909D4—22no—
910D4—42no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922D4—41no—
923D4—41no—
924D4—88no—
925D4—1222no—
926D4—1222no—
927D4—4888no—
928D4—2442no—
929D4—2442no—
930D4—2442no—
931D4—2442no—
932D4—2441no—
933D4—2441no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—82no—
950C2×C4—1224no—
951C2×C4—1222no—
952C2×C4—4882no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4—2442no—
956C2×C4—2442no—
957C2×C4—2442no—
958C2×C4—2442no—
959C2×C4#1451974511yescharacteristic
960C2×C4#1451974511yescharacteristic
961C2×C4#1451974511yescharacteristic
962C2×C4#1451974511yescharacteristic
963C2×C4#1451974511yescharacteristic
964C2×C4#1451974511yescharacteristic
965C2×C4#1451974611yescharacteristic
966C2×C4#1451974611yescharacteristic
967C2×C4#1451974811yescharacteristic
968C2×C4#1451974811yescharacteristic
969C2×C4#1451974811yescharacteristic
970C2×C4#1451974811yescharacteristic
971C2×C4#1451974911yescharacteristic
972C2×C4#1451974911yescharacteristic
973C2×C4#1451974911yescharacteristic
974C2×C4#1451974911yescharacteristic
975C2×C4#1451974911yescharacteristic
976C2×C4#1451974911yescharacteristic
977C2×C4#1451977311yescharacteristic
978C2×C4#1451977311yescharacteristic
979C2×C4#1451977311yescharacteristic
980C2×C4#1451977311yescharacteristic
981C2×C4C2×D4×D6111yescharacteristic
982C2×C4C2×D4×D6111yescharacteristic
983C2×C4C2×D4×D6111yescharacteristic
984C2×C4C22×C22⋊D6111yescharacteristic
985C2×C4C22×C22⋊D6111yescharacteristic
986C2×C4C2×#1175822411yescharacteristic
987C8—1224no—
988C8—2442no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—42no—
1001C22—42no—
1002C22—82no—
1003C22—82no—
1004C22—4882no—
1005C22—4882no—
1006C22—2444no—
1007C22—2442no—
1008C22#1683967011yescharacteristic
1009C22#1683967011yescharacteristic
1010C22#1683967011yescharacteristic
1011C22#1683967011yescharacteristic
1012C22C2×#1451974511yescharacteristic
1013C22C2×#1451974611yescharacteristic
1014C22C2×#1451974911yescharacteristic
1015C4—44no—
1016C4—42no—
1017C4—42no—
1018C4—2444no—
1019C4—2442no—
1020C4#1683967011yescharacteristic
1021C4#1683967011yescharacteristic
1022C4#1683967011yescharacteristic
1023C4#1683967011yescharacteristic
1024C4C2×#1451974511yescharacteristic
1025C4C2×#1451974811yescharacteristic
1026C4C2×#1451974911yescharacteristic
1027C4C2×#1451977311yescharacteristic
1028C2—21no—
1029C2—21no—
1030C2—21no—
1031C2—21no—
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—82no—
1036C2—82no—
1037C2—4882no—
1038C2C2×#1683967011yescharacteristic
subgroupG/H
centerC4C2×#14519773
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3449C2
socleC2×C61C2×#392
hypercenter#3449D61
hypocenterC61#23414
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#16840560C2semidirect
2. #21459148C2semidirect
3. C2×#16839780C2semidirect
4. C2×#16839779C2semidirect
5. #21454264C2semidirect
6. #21446884C2semidirect
7. C2×#16839518C2semidirect
8. C61×#3449C2semidirect
28. #16840273C22semidirect
32. #16839780C22semidirect
34. #16839779C22semidirect
39. #16839726C22semidirect
40. #16839518C22semidirect
51. C61×#525C22semidirect
63. C2×#11758222D4semidirect
65. C22×Dic122D4semidirect
66. C22×D244D4semidirect
92. C2×#11758194D4semidirect
96. C22×#92418D4semidirect
113. #14519736D4semidirect
117. C2×C4×Dic61D4semidirect
143. C2×#41×C61D4semidirect
146. C22×Q8×C61D4semidirect
150. C22×D4×C61D4semidirect
170. #117×C61D4semidirect
174. C2×C42×C61D4semidirect
511. #3449D61semidirect
559. #525C2×D61semidirect
572. C61#23414semidirect
607. C2×#41C22⋊D61semidirect
611. C22×Q8C22⋊D61semidirect
617. C22×D4C22⋊D61semidirect
684. #117C22⋊D61semidirect
691. C2×C42C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405602
#214591482
C2×#168397802
C2×#168397792
#214542642
#214468842
C2×#168395182
C61×#34492
#2341461