Finite Group Databasebeta

← #29695859

Subgroups — #29695859

Order 15616.

1478 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519798C211yesmaximal, characteristic
2C2×SD16×Dic61C211yesmaximal, characteristic, complemented
3#21448657C211yesmaximal, characteristic, complemented
4#21448644C211yesmaximal, characteristic, complemented
5#21446673C211yesmaximal, characteristic, complemented
6#21446671C211yesmaximal, characteristic, complemented
7#21446167C211yesmaximal, characteristic, complemented
8#21446165C211yesmaximal, characteristic, complemented
9#21446160C211yesmaximal, characteristic, complemented
10#21446158C211yesmaximal, characteristic, complemented
11#21445841C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14C8×#11758198C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C2×#14519798—24no—
19C2×#14519798—24no—
20C2×#14519798C418yescomplemented
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×C8×D61C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27SD16×Dic61—24no—
28C2×#14519709C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839668C2211yescharacteristic
38#16839667C2211yescharacteristic
39#16839664—21no—
40#16839664C2211yescharacteristic
41#16839663—21no—
42#16839663C2211yescharacteristic
43#16839641—21no—
44#16839639—21no—
45#16839623—21no—
46#16839619—21no—
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49C4×#11758198—21no—
50C4×#11758198C2211yescharacteristic
51C2×#14519684—21no—
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839517C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×SD16×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C4×SD16×C61—24no—
60C2×#106×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×C4×C8×C61C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yescomplemented
70C2×#11758224—22no—
71C2×#11758224—22no—
72C2×#11758224—22no—
73C2×#11758224—41no—
74C2×#11758224—41no—
75C2×#11758224C2×C414yes—
76C22×Dic122C2311yescharacteristic
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C23×Dic61—21no—
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84#14519798—232no—
85C2×#11758202—22no—
86C2×#11758202—22no—
87C2×#11758202C2×C414yescomplemented
88C2×#11758190—22no—
89C2×#11758190—22no—
90C2×#11758190C2×C414yescomplemented
91C2×#11758199—22no—
92C2×#11758199—22no—
93C2×#11758199C2×C414yes—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C2×C8×D61—22no—
97C2×C8×D61—22no—
98C2×C8×D61C2×C414yescomplemented
99Q8×Dic61—22no—
100Q8×Dic61—41no—
101D4×Dic61—22no—
102D4×Dic61—41no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198D411yescharacteristic
114C2×#11758198D411yescharacteristic
115C2×C4×Dic61—21no—
116C2×C4×Dic61C2311yescharacteristic
117#14519709—22no—
118#14519702—41no—
119#14519701—22no—
120#14519700—41no—
121#14519699—41no—
122#14519698—22no—
123#14519697—41no—
124#14519689—22no—
125C8×Dic61—22no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132#14519684D411yescharacteristic
133#14519684D411yescharacteristic
134C22×Q8×C61C2311yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C2×SD16×C61C2×C414yes—
138C2×SD16×C61D414yes—
139C2×SD16×C61D414yes—
140C22×C8×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C4×Q8×C61—22no—
143C4×Q8×C61—41no—
144C4×D4×C61—22no—
145C4×D4×C61—41no—
146C2×C4⋊C4×C61—21no—
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150C2×C42×C61—21no—
151C2×C42×C61C2311yescharacteristic
152#106×C61—22no—
153#103×C61—22no—
154#102×C61—22no—
155C4×C8×C61—22no—
156C24×C61—21no—
157C23×D61—21no—
158C23×D61C2×D411yescharacteristic
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C22×C412yes—
163C2×Q8×C61C2×D412yes—
164C2×Q8×C61C2×D412yes—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61C22×C412yes—
169C2×D4×C61C2×D412yes—
170C2×D4×C61C2×D412yes—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—81no—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—24no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—42no—
183C22×Dic61—21no—
184C22×Dic61—24no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61—42no—
190C22×Dic61—42no—
191C22×Dic61—81no—
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195#11758226—28no—
196#11758226—44no—
197#11758226—44no—
198#11758226—44no—
199#11758224—28no—
200#11758224—44no—
201#11758224—44no—
202#11758224—44no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—24no—
208C2×D244—21no—
209C2×D244—42no—
210C2×D244—42no—
211C2×D244C22×C412yes—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—24no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61C22×C412yes—
220C2×C4×D61#4112yes—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122C22×C412yes—
227SD16×C61C22⋊C4116yescomplemented
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61C22×C412yes—
232C2×C8×C61C2×D412yes—
233C2×C8×C61C2×D412yes—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—42no—
239C22⋊C4×C61—42no—
240C42×C61—21no—
241C42×C61—21no—
242C42×C61—42no—
243C22⋊Dic61—42no—
244#11758202—28no—
245#11758199—28no—
246#11758198—22no—
247#11758198—22no—
248#11758198—42no—
249#11758198—42no—
250#11758198—81no—
251#11758198—81no—
252#11758198—81no—
253#11758198—81no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—42no—
259C4×Dic61—21no—
260C4×Dic61—21no—
261C4×Dic61—42no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418C22×C412yes—
268#11758190—28no—
269C8×D61—28no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61C22×D411yescharacteristic
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—22no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61C4×D412yes—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61C2×C22⋊C414yes—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61C2×C22⋊C414yes—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—21no—
303C2×C4×C61—22no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—84no—
315C2×C4×C61#13512yescomplemented
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C22⋊D61—48no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—22no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—48no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—84no—
341C2×Dic61C4×D412yes—
342C2×Dic61#13512yescomplemented
343D244—22no—
344D244—22no—
345D244—48no—
346D244—41no—
347D244—41no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—48no—
353Dic122—22no—
354Dic122—22no—
355Dic122—41no—
356Dic122—41no—
357C8×C61—41no—
358C8×C61C2×C22⋊C414yes—
359#92418—22no—
360#92418—41no—
361#22449—611nomaximal, Sylow
362C22×C61—24no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61C2×C4×D411yescharacteristic
370C22×C61D4211yescharacteristic
371C22×C61D4211yescharacteristic
372C22×C61C2×#13511yescharacteristic
373C22×C61C2×#13511yescharacteristic
374C22×C61#57711yescharacteristic
375C22×C61#57711yescharacteristic
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C4×C61—24no—
391C4×C61—22no—
392C4×C61—41no—
393C4×C61—81no—
394C4×C61—81no—
395C4×C61C22×C22⋊C411yescharacteristic
396C4×C61#51811yescharacteristic
397C4×C61#54611yescharacteristic
398C4×C61#54611yescharacteristic
399Dic61—22no—
400Dic61—22no—
401Dic61—42no—
402Dic61—41no—
403Dic61—81no—
404Dic61—81no—
405C22×#135—611no—
406C2×C4×SD16—611no—
407C2×C4×SD16D6111yescharacteristic, complemented
408#2341—611no—
409#2339—611no—
410#1968—611no—
411#1968—611no—
412#1879—611no—
413#1879—611no—
414#1878—611no—
415#1878—611no—
416#1807—611no—
417#1788—611no—
418#1788—611no—
419C8×C22⋊C4—611no—
420C2×C61—44no—
421C2×C61D4×C22⋊C411yescharacteristic
422C2×C61C4×#13511yescharacteristic
423C2×C61#295211yescharacteristic
424C2×C61#328211yescharacteristic
425C2×C61#328211yescharacteristic
426C2×C61#328411yescharacteristic
427C2×C61#328411yescharacteristic
428D61—42no—
429D61—82no—
430C22×#41—611no—
431C22×#41—611no—
432C2×#135—618no—
433C2×#135—1224no—
434C2×#135—1224no—
435C22×Q16—611no—
436C22×SD16—611no—
437C22×SD16C2×D6111yescharacteristic
438C22×D8—611no—
439C23×C8—611no—
440C2×C4×Q8—611no—
441C2×C4×Q8C2×D6111yescharacteristic
442C2×C4×D4—611no—
443C2×C4×D4C2×D6111yescharacteristic
444C4×SD16—24no—
445C4×SD16—1224no—
446C2×#106—611no—
447C2×#106C2×D6111yescharacteristic
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103C2×D6111yescharacteristic
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102C2×D6111yescharacteristic
456C2×C22⋊C8—611no—
457C2×C4×C8—611no—
458C2×C4×C8C2×D6111yescharacteristic
459#391—611no—
460#391—611no—
461#390—611no—
462#390—611no—
463#390—1221no—
464#390—1221no—
465#386—1221no—
466#386—1221no—
467#381—1221no—
468#380—611no—
469#380—611no—
470#380—1221no—
471C4×C22⋊C4—611no—
472C4×C22⋊C4—1221no—
473C2×#95—1221no—
474#340—611no—
475#340—611no—
476#336—611no—
477#336—611no—
478C61#2244911yescharacteristic, complemented, Sylow
479C2×#41—614no—
480C2×#41—614no—
481C2×#41—1222no—
482C2×#41—1222no—
483C2×#41—1222no—
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—2441no—
488C2×#41—2441no—
489C2×#41—2441no—
490C2×#41—2441no—
491C22×Q8—611no—
492C22×Q8C22×D6111yescharacteristic
493C22×D4—611no—
494C22×D4—1221no—
495C22×D4—1221no—
496C22×D4C22×D6111yescharacteristic
497C23×C4—21no—
498C23×C4—611no—
499C23×C4—1221no—
500C23×C4—1221no—
501C23×C4—1221no—
502#135—12232no—
503C2×Q16—614no—
504C2×Q16—1222no—
505C2×Q16—1222no—
506C2×SD16—614no—
507C2×SD16—1222no—
508C2×SD16—1222no—
509C2×SD16C4×D6114yes—
510C2×SD16D24414yes—
511C2×SD16C22⋊D6114yes—
512C2×D8—614no—
513C2×D8—1222no—
514C2×D8—1222no—
515C22×C8—611no—
516C22×C8—614no—
517C22×C8—611no—
518C22×C8—1222no—
519C22×C8—1222no—
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6111yescharacteristic
522C4×Q8—22no—
523C4×Q8—41no—
524C4×Q8—1222no—
525C4×Q8—2441no—
526C4×D4—22no—
527C4×D4—41no—
528C4×D4—1222no—
529C4×D4—2441no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4C22×D6111yescharacteristic
535C2×C4⋊C4C22×D6111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C42—21no—
547C2×C42—611no—
548C2×C42—1221no—
549C2×C42C22×D6111yescharacteristic
550#106—22no—
551#106—1222no—
552#103—22no—
553#103—1222no—
554#103—2441no—
555#103—2441no—
556#102—22no—
557#102—1222no—
558#102—2441no—
559#102—2441no—
560C22⋊C8—1222no—
561C4×C8—22no—
562C4×C8—1222no—
563#95—611no—
564#95—611no—
565#95—1221no—
566#95—1221no—
567#95—1221no—
568#95—1221no—
569#95—1221no—
570#95—1221no—
571C24—21no—
572C24—611no—
573C24—1221no—
574#41—1228no—
575#41—1228no—
576#41—2444no—
577#41—2444no—
578#41—2444no—
579#41—2444no—
580#41—2444no—
581#41—2444no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—612no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8C2×C4×D6112yes—
592C2×Q8C2×D24412yes—
593C2×Q8C2×C22⋊D6112yes—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—612no—
598C2×D4—1224no—
599C2×D4—1224no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—2442no—
606C2×D4—2442no—
607C2×D4—2442no—
608C2×D4—2442no—
609C2×D4C2×C4×D6112yes—
610C2×D4C2×D24412yes—
611C2×D4C2×C22⋊D6112yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—611no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—4881no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4—2442no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4D4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641C22×C4C23×D6111yescharacteristic
642Q16—1228no—
643SD16—1228no—
644SD16#11758198116yescomplemented
645D8—1228no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—612no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1228no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8C2×C4×D6112yes—
657C2×C8C2×D24412yes—
658C2×C8C2×C22⋊D6112yes—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—2442no—
669C22⋊C4—42no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—4881no—
673C22⋊C4—4881no—
674C22⋊C4—4881no—
675C22⋊C4—4881no—
676C22⋊C4—2442no—
677C22⋊C4—2442no—
678C22⋊C4—2442no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—1221no—
683C42—1221no—
684C42—2442no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—612no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23—1222no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23C2×D4×D6111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—1222no—
711Q8—1222no—
712Q8—2441no—
713Q8—2441no—
714Q8C2×#1175819814yes—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—1222no—
719D4—1222no—
720D4—2448no—
721D4—2448no—
722D4—2441no—
723D4—2441no—
724D4C2×#1175819814yes—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—84no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—4884no—
755C2×C4—2448no—
756C2×C4—2448no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4#1451979812yescomplemented
766C2×C4C22×C4×D6111yescharacteristic
767C2×C4C22×C22⋊D6111yescharacteristic
768C2×C4C22×D24411yescharacteristic
769C2×C4#41×D6111yescharacteristic
770C2×C4#1451982211yescharacteristic
771C2×C4#1451982311yescharacteristic
772C8—41no—
773C8—1222no—
774C8—2441no—
775C8C2×#1175819814yes—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—1222no—
784C22—1222no—
785C22—1222no—
786C22—4881no—
787C22—4881no—
788C22—4881no—
789C22—4881no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2441no—
794C22—2441no—
795C22—2441no—
796C22—2441no—
797C22C4×D4×D6111yescharacteristic
798C22D4×C22⋊D6111yescharacteristic
799C22D4×D24411yescharacteristic
800C22#135×D6111yescharacteristic
801C22C2×#1451979811yescharacteristic
802C22#1684056811yescharacteristic
803C22#1684056911yescharacteristic
804C4—22no—
805C4—24no—
806C4—41no—
807C4—81no—
808C4—81no—
809C4—1222no—
810C4—1222no—
811C4—4881no—
812C4—4881no—
813C4—2441no—
814C4—2442no—
815C4C22×#1175819811yescharacteristic
816C4#1684023411yescharacteristic
817C4#1684040011yescharacteristic
818C4#1684040711yescharacteristic
819C2—44no—
820C2—4882no—
821C2—2442no—
822C2D4×#1175819811yescharacteristic
823C2C4×#1451979811yescharacteristic
824C2#2145469711yescharacteristic
825C2#2145752611yescharacteristic
826C2#2145752811yescharacteristic
827C2#2145754311yescharacteristic
828C2#2145755011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC22×#14519798C2
cosocleC22×C4×C61C24
hypercenterC2×C4×SD16D61
hypocenterC61#22449
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic61C2semidirect
3. #21448657C2semidirect
4. #21448644C2semidirect
5. #21446673C2semidirect
6. #21446671C2semidirect
7. #21446167C2semidirect
8. #21446165C2semidirect
9. #21446160C2semidirect
10. #21446158C2semidirect
11. #21445841C2semidirect
12. #21445758C2semidirect
13. #21445756C2semidirect
14. C8×#11758198C2semidirect
15. C2×C4×SD16×C61C2semidirect
20. C2×#14519798C4semidirect
69. C2×#11758226C2×C4semidirect
87. C2×#11758202C2×C4semidirect
90. C2×#11758190C2×C4semidirect
98. C2×C8×D61C2×C4semidirect
227. SD16×C61C22⋊C4semidirect
315. C2×C4×C61#135semidirect
342. C2×Dic61#135semidirect
407. C2×C4×SD16D61semidirect
478. C61#22449semidirect
644. SD16#11758198semidirect
765. C2×C4#14519798semidirect

Maximal subgroups

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

subgroupindex
C22×#145197982
C2×SD16×Dic612
#214486572
#214486442
#214466732
#214466712
#214461672
#214461652
#214461602
#214461582
#214458412
#214457582
#214457562
C8×#117581982
C2×C4×SD16×C612
#2244961