Finite Group Databasebeta

← #29679552

Subgroups — #29679552

Order 15616.

1482 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D61C211yesmaximal, characteristic
2#423×D61C211yesmaximal, characteristic, complemented
3C2×#16839777C212yesmaximal
4#21448223C211yesmaximal, characteristic, complemented
5#21445840C211yesmaximal, characteristic, complemented
6#21445839C211yesmaximal, characteristic, complemented
7#21445838C212yesmaximal, complemented
8#21445837C212yesmaximal, complemented
9#21445836C211yesmaximal, characteristic, complemented
10#21445527C212yesmaximal, complemented
11C61×#1806C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13C2×M16×D61C2212yes—
14#41×Dic61C2211yescharacteristic
15C4×#11758226C411yescharacteristic, complemented
16C4×#11758226C411yescharacteristic, complemented
17C4×#11758222—21no—
18C4×#11758222C2211yescharacteristic
19#16840230—21no—
20#16840230C2211yescharacteristic
21C4×#11758224—21no—
22C4×#11758224—21no—
23C4×#11758224C411yescharacteristic, complemented
24C4×#11758224C411yescharacteristic, complemented
25C4×Q8×D61C411yescharacteristic, complemented
26C4×Q8×D61C411yescharacteristic, complemented
27C4×D4×D61—21no—
28C4×D4×D61—21no—
29C4×D4×D61C411yescharacteristic, complemented
30C4×D4×D61C411yescharacteristic, complemented
31C2×#14519734C2212yes—
32#117×D61—21no—
33#117×D61C2211yescharacteristic
34C2×C42×D61—21no—
35C2×C42×D61C2211yescharacteristic
36#16839786C2211yescharacteristic, complemented
37#16839785C2212yescomplemented
38#16839784—21no—
39#16839784—21no—
40C4⋊C8×D61—21no—
41C4⋊C8×D61—21no—
42#16839777—28no—
43C2×#14519705C2212yes—
44C2×#14519704C2212yes—
45C2×#14519703C2212yes—
46#16839631—21no—
47#16839626—21no—
48#16839621—21no—
49#16839619—21no—
50C4×#11758196C2212yescomplemented
51C4×C4⋊Dic61C2211yescharacteristic, complemented
52#16839523C2212yescomplemented
53#16839522C2212yescomplemented
54#16839521C2212yescomplemented
55C4×#41×C61C2211yescharacteristic
56C61×#423C2211yescharacteristic, complemented
57C2×#104×C61C2212yes—
58C4×C4⋊C4×C61C2211yescharacteristic, complemented
59C61×#339C2212yescomplemented
60C2×#11758226C2×C411yescharacteristic
61C2×#11758222—21no—
62C2×#11758222C2311yescharacteristic
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic
65#41×D61—22no—
66#41×D61—22no—
67#41×D61D414yes—
68#41×D61Q814yes—
69C2×Q8×D61C2×C411yescharacteristic
70C2×D4×D61—21no—
71C2×D4×D61C2×C411yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×#11758194C2312yes—
79C2×#11758189—22no—
80M16×D61—24no—
81M16×D61—24no—
82C2×C8×D61—22no—
83Q8×Dic61C2×C411yescharacteristic
84Q8×Dic61C2×C411yescharacteristic
85C4×Dic122—21no—
86C4×Dic122—21no—
87C4×Dic122C2×C411yescharacteristic
88C4×Dic122C2×C411yescharacteristic
89#14519742—21no—
90#14519742—21no—
91#14519742C2×C411yescharacteristic
92#14519742C2×C411yescharacteristic
93C4×D244—21no—
94C4×D244—21no—
95C4×D244C2×C411yescharacteristic
96C4×D244C2×C411yescharacteristic
97D4×Dic61—21no—
98D4×Dic61—21no—
99D4×Dic61C2×C411yescharacteristic
100D4×Dic61C2×C411yescharacteristic
101#14519739—21no—
102#14519739—21no—
103#14519739C2×C411yescharacteristic
104#14519739C2×C411yescharacteristic
105C4×C22⋊D61—21no—
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108C4×C22⋊D61—21no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111#14519737—21no—
112#14519737—21no—
113#14519737—21no—
114#14519737—21no—
115#14519737—21no—
116#14519737—21no—
117#14519736—21no—
118#14519736C2311yescharacteristic
119#14519735—21no—
120#14519735—21no—
121#14519735C2×C411yescharacteristic
122#14519735C2×C411yescharacteristic
123#14519734—21no—
124#14519734—21no—
125#14519734—24no—
126#14519734—24no—
127#14519734—21no—
128#14519733—21no—
129#14519733—21no—
130#14519733—21no—
131C2×C4⋊Dic61—21no—
132C2×#11758196—22no—
133C2×#11758196—22no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C4⋊C4×D61C2×C411yescharacteristic
137C4⋊C4×D61C2×C411yescharacteristic
138C2×#11758198—22no—
139C22⋊C4×D61—21no—
140C22⋊C4×D61—21no—
141C22⋊C4×D61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61C2312yes—
148C2×C4×Dic61C2311yescharacteristic
149C42×D61—21no—
150C42×D61—21no—
151C42×D61—21no—
152C42×D61—21no—
153C42×D61—21no—
154C42×D61—21no—
155C42×D61—21no—
156C42×D61C2×C411yescharacteristic
157C42×D61C2×C411yescharacteristic
158C42×D61C2×C411yescharacteristic
159C42×D61C2×C411yescharacteristic
160C42×D61D411yescharacteristic
161C42×D61D411yescharacteristic
162C42×D61D411yescharacteristic
163C42×D61D411yescharacteristic
164C4⋊#92418—21no—
165C4⋊#92418—21no—
166#14519706—22no—
167#14519706—22no—
168#14519705—24no—
169#14519704—24no—
170#14519703—24no—
171#14519684—21no—
172#14519684—22no—
173C2×#41×C61C2311yescharacteristic
174C2×M16×C61C2312yes—
175C4×Q8×C61C2×C411yescharacteristic
176C4×Q8×C61C2×C411yescharacteristic
177C4×D4×C61—21no—
178C4×D4×C61—21no—
179C4×D4×C61C2×C411yescharacteristic
180C4×D4×C61C2×C411yescharacteristic
181#117×C61—21no—
182#117×C61C2311yescharacteristic
183C2×C4⋊C4×C61—21no—
184C2×C42×C61—21no—
185C2×C42×C61C2312yes—
186C2×C42×C61C2311yescharacteristic
187C4⋊C8×C61—21no—
188C4⋊C8×C61—21no—
189#104×C61—24no—
190#95×C61—21no—
191C23×D61—21no—
192C23×D61C2×D411yescharacteristic
193#41×C61—21no—
194#41×C61—21no—
195#41×C61C2×D412yes—
196#41×C61C2×Q812yes—
197C2×Q8×C61C22×C411yescharacteristic
198C2×D4×C61—21no—
199C2×D4×C61C22×C411yescharacteristic
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—22no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—22no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217#11758226—22no—
218#11758226C4⋊C414yescomplemented
219Q8×D61—22no—
220Q8×D61C4⋊C414yescomplemented
221#11758224—24no—
222#11758224—24no—
223#11758224—22no—
224#11758224C4⋊C414yescomplemented
225D4×D61—24no—
226D4×D61—24no—
227D4×D61—22no—
228D4×D61C4⋊C414yescomplemented
229#11758222—21no—
230#11758222—21no—
231#11758222—24no—
232#11758222—24no—
233#11758222C2×D412yes—
234#11758222C2×Q812yes—
235C2×D244—21no—
236C2×D244C22×C411yescharacteristic
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—24no—
241C2×C4×D61—24no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—44no—
251C2×C4×D61—44no—
252C2×C4×D61C22⋊C411yescharacteristic
253C2×C4×D61C22⋊C411yescharacteristic
254C2×C4×D61C22⋊C411yescharacteristic
255C2×C4×D61C22⋊C411yescharacteristic
256C2×C4×D61C22⋊C411yescharacteristic
257C2×C4×D61C22⋊C411yescharacteristic
258C2×C4×D61C22⋊C411yescharacteristic
259C2×C4×D61C22⋊C411yescharacteristic
260C2×C4×D61C22×C411yescharacteristic
261C2×C4×D61C22×C411yescharacteristic
262C2×C4×D61C2×D412yes—
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×Q812yes—
266C2×C4×D61#4112yes—
267C2×C4×D61#4112yes—
268C2×Dic122—21no—
269C2×Dic122C22×C411yescharacteristic
270M16×C61—22no—
271M16×C61—22no—
272C2×C8×C61—22no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—42no—
276C4⋊C4×C61C22×C411yescharacteristic
277C4⋊C4×C61C22×C411yescharacteristic
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C42×C61—21no—
282C42×C61—21no—
283C42×C61—21no—
284C42×C61—22no—
285C42×C61—22no—
286C42×C61C22×C411yescharacteristic
287C42×C61C22×C411yescharacteristic
288C42×C61C2×D411yescharacteristic
289C42×C61C2×D411yescharacteristic
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—44no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—42no—
303C4⋊Dic61C22×C411yescharacteristic
304C4⋊Dic61C22×C411yescharacteristic
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—44no—
312#11758196—44no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—22no—
323C4×Dic61—22no—
324C4×Dic61C22⋊C411yescharacteristic
325C4×Dic61C22⋊C411yescharacteristic
326C4×Dic61C22⋊C411yescharacteristic
327C4×Dic61C22⋊C411yescharacteristic
328C4×Dic61C22⋊C411yescharacteristic
329C4×Dic61C22⋊C411yescharacteristic
330C4×Dic61C22⋊C411yescharacteristic
331C4×Dic61C22⋊C411yescharacteristic
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336#11758194—22no—
337#11758194—22no—
338C2×#92418—22no—
339#11758189—44no—
340C8×D61—44no—
341C23×C61—21no—
342C23×C61C22×D411yescharacteristic
343C22×D61—21no—
344C22×D61—24no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—42no—
348C22×D61—42no—
349C22×D61C2×C22⋊C411yescharacteristic
350C22×D61C2×C22⋊C411yescharacteristic
351C22×D61#12112yes—
352C22×D61C22⋊Q812yes—
353Q8×C61—21no—
354Q8×C61C2×C4⋊C412yes—
355D4×C61—22no—
356D4×C61—22no—
357D4×C61—21no—
358D4×C61C2×C4⋊C412yes—
359C2×C4×C61—21no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—41no—
366C2×C4×C61—42no—
367C2×C4×C61—42no—
368C2×C4×C61—42no—
369C2×C4×C61—42no—
370C2×C4×C61—42no—
371C2×C4×C61C2×C22⋊C411yescharacteristic
372C2×C4×C61C2×C22⋊C411yescharacteristic
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C23×C411yescharacteristic
376C2×C4×C61C22×D411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C2×C4×C61C22×Q811yescharacteristic
379C2×C4×C61C2×#4111yescharacteristic
380C2×C4×C61C2×#4111yescharacteristic
381C22⋊D61—22no—
382C22⋊D61—22no—
383C22⋊D61—24no—
384C22⋊D61—24no—
385C2×Dic61—21no—
386C2×Dic61—24no—
387C2×Dic61—22no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—41no—
391C2×Dic61—42no—
392C2×Dic61—42no—
393C2×Dic61—42no—
394C2×Dic61—42no—
395C2×Dic61—42no—
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61#12112yes—
403C2×Dic61C22⋊Q812yes—
404D244—24no—
405D244—21no—
406D244C2×C4⋊C412yes—
407C4×D61—24no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—24no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—42no—
420C4×D61—42no—
421C4×D61—42no—
422C4×D61—42no—
423C4×D61—42no—
424C4×D61—42no—
425C4×D61C2×C4⋊C412yes—
426C4×D61C2×C4⋊C412yes—
427C4×D61#11712yes—
428C4×D61#11712yes—
429C4×D61#12112yes—
430C4×D61#12112yes—
431C4×D61C22⋊Q812yes—
432C4×D61C22⋊Q812yes—
433Dic122—21no—
434Dic122—24no—
435Dic122C2×C4⋊C412yes—
436C8×C61—42no—
437#92418—42no—
438#20654—611nomaximal, Sylow
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—22no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61C22×C22⋊C411yescharacteristic
445C22×C61C2×#12111yescharacteristic
446C22×C61C2×C22⋊Q811yescharacteristic
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—22no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—48no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61#38012yes—
458C2×D61#38012yes—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—22no—
463C4×C61—41no—
464C4×C61—41no—
465C4×C61—82no—
466C4×C61#42112yescomplemented
467C4×C61C22×C4⋊C411yescharacteristic
468C4×C61C2×#11711yescharacteristic
469C4×C61C2×#12111yescharacteristic
470C4×C61C2×C22⋊Q811yescharacteristic
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
474Dic61—22no—
475Dic61—41no—
476Dic61—41no—
477Dic61—82no—
478Dic61#38012yes—
479Dic61#38012yes—
480Dic61#42112yescomplemented
481C2×C4×#41—611no—
482C2×#423—611no—
483C2×#421—612no—
484#2285—611no—
485#1806—611no—
486#1806—612no—
487#1806—611no—
488#1806—612no—
489#1806—611no—
490#1806D6111yescharacteristic, complemented
491#1733—612no—
492C2×C61—21no—
493C2×C61—21no—
494C2×C61—42no—
495C2×C61C2×#38011yescharacteristic
496C2×C61C2×#42111yescharacteristic
497C2×C61C2×#42111yescharacteristic
498D61—22no—
499D61—22no—
500D61—42no—
501C22×#41—611no—
502C22×M16—612no—
503C4×#41—611no—
504C4×#41—611no—
505C4×#41—611no—
506C4×#41—611no—
507C4×#41—611no—
508C4×#41—611no—
509C4×#41—611no—
510C4×#41—1221no—
511C4×#41—1221no—
512C4×#41—1221no—
513C4×#41—1221no—
514C4×#41C2×D6111yescharacteristic
515C2×C4×Q8—611no—
516C2×C4×Q8—611no—
517C2×C4×D4—611no—
518C2×C4×D4—611no—
519C2×C4×D4—1221no—
520C2×C4×D4—1221no—
521C2×#117—612no—
522C2×#117—611no—
523C2×#117—1221no—
524C22×C42—611no—
525C22×C42—1221no—
526#423—612no—
527#423—611no—
528#423—1221no—
529#423—1221no—
530#423C2×D6111yescharacteristic, complemented
531C2×C4⋊C8—1221no—
532C2×C4⋊C8—1221no—
533#421—1228no—
534C2×#104—612no—
535C2×#104—612no—
536C2×#104—612no—
537C2×#104C2×D6112yes—
538#384—1221no—
539#382—1221no—
540#380—1221no—
541#380—1221no—
542C4×C4⋊C4—612no—
543C4×C4⋊C4—611no—
544C4×C4⋊C4C2×D6111yescharacteristic, complemented
545#339—612no—
546#339—612no—
547#339—612no—
548#339C2×D6112yescomplemented
549C61#2065411yescharacteristic, complemented, Sylow
550C2×#41—614no—
551C2×#41—614no—
552C2×#41—611no—
553C2×#41—611no—
554C2×#41—611no—
555C2×#41—1221no—
556C2×#41—1221no—
557C2×#41—1222no—
558C2×#41—1222no—
559C2×#41C22×D6111yescharacteristic
560C22×Q8—611no—
561C22×D4—611no—
562C22×D4—1221no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—1221no—
567C23×C4—1221no—
568C23×C4—1221no—
569C2×M16—612no—
570C2×M16—1222no—
571C2×M16—1224no—
572C2×M16—1224no—
573C2×M16C22×D6112yes—
574C22×C8—1222no—
575C4×Q8—611no—
576C4×Q8—611no—
577C4×Q8—611no—
578C4×Q8—611no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—1221no—
582C4×Q8—1221no—
583C4×Q8—1221no—
584C4×Q8—1221no—
585C4×Q8C4×D6111yescharacteristic
586C4×Q8C4×D6111yescharacteristic
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—611no—
592C4×D4—611no—
593C4×D4—611no—
594C4×D4—611no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—1221no—
598C4×D4—1221no—
599C4×D4—1221no—
600C4×D4—1221no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4C4×D6111yescharacteristic
614C4×D4C4×D6111yescharacteristic
615#117—21no—
616#117—611no—
617#117—611no—
618#117—611no—
619#117—1221no—
620#117—1221no—
621#117—1224no—
622#117—1224no—
623#117—1221no—
624#117—1221no—
625#117—1221no—
626#117—1221no—
627#117—1221no—
628#117—1221no—
629#117—1221no—
630#117C22×D6111yescharacteristic
631C2×C4⋊C4—21no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4—1222no—
637C2×C4⋊C4—1222no—
638C2×C4⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C22⋊C4—1221no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1222no—
643C2×C42—21no—
644C2×C42—611no—
645C2×C42—611no—
646C2×C42—611no—
647C2×C42—611no—
648C2×C42—611no—
649C2×C42—611no—
650C2×C42—611no—
651C2×C42—611no—
652C2×C42—611no—
653C2×C42—611no—
654C2×C42—611no—
655C2×C42—612no—
656C2×C42—1221no—
657C2×C42—1221no—
658C2×C42—1221no—
659C2×C42—1221no—
660C2×C42—1221no—
661C2×C42—1221no—
662C2×C42—1221no—
663C2×C42—1221no—
664C2×C42—1221no—
665C2×C42—1221no—
666C2×C42C22×D6112yes—
667C2×C42C22×D6111yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670C4⋊C8—1222no—
671C4⋊C8—1222no—
672C4⋊C8—1221no—
673C4⋊C8—1221no—
674#104—24no—
675#104—1224no—
676#104—1224no—
677#104—1224no—
678#95—21no—
679#95—1222no—
680#95—1221no—
681C24—611no—
682C24—1221no—
683#41—21no—
684#41—21no—
685#41—614no—
686#41—614no—
687#41—612no—
688#41—612no—
689#41—1224no—
690#41—1224no—
691#41—1224no—
692#41—1224no—
693#41—1222no—
694#41—1222no—
695#41—1221no—
696#41—1221no—
697#41D4×D6112yes—
698#41Q8×D6112yes—
699C2×Q8—614no—
700C2×Q8—611no—
701C2×Q8—1221no—
702C2×Q8—1222no—
703C2×Q8C2×C4×D6111yescharacteristic
704C2×D4—21no—
705C2×D4—614no—
706C2×D4—611no—
707C2×D4—1221no—
708C2×D4—1222no—
709C2×D4—1221no—
710C2×D4—1224no—
711C2×D4—1224no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4C2×C4×D6111yescharacteristic
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—612no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—612no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—1221no—
739C22×C4—1224no—
740C22×C4—1224no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1222no—
753C22×C4—2442no—
754C22×C4—2442no—
755C22×C4—2444no—
756C22×C4—2444no—
757C22×C4D4×D6111yescharacteristic
758C22×C4D4×D6111yescharacteristic
759C22×C4C23×D6111yescharacteristic
760M16—22no—
761M16—22no—
762M16—1222no—
763M16—1222no—
764M16—2444no—
765C2×C8—22no—
766C2×C8—1222no—
767C2×C8—2444no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—611no—
772C4⋊C4—611no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—2442no—
782C4⋊C4—2444no—
783C4⋊C4—2444no—
784C4⋊C4C2×C4×D6111yescharacteristic
785C4⋊C4C2×C4×D6111yescharacteristic
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—2444no—
799C42—21no—
800C42—21no—
801C42—21no—
802C42—22no—
803C42—22no—
804C42—611no—
805C42—611no—
806C42—611no—
807C42—611no—
808C42—611no—
809C42—611no—
810C42—611no—
811C42—611no—
812C42—611no—
813C42—611no—
814C42—611no—
815C42—611no—
816C42—1221no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—1221no—
822C42—1221no—
823C42—1221no—
824C42—1221no—
825C42—1222no—
826C42—1222no—
827C42C2×C4×D6111yescharacteristic
828C42C2×C4×D6111yescharacteristic
829C42D4×D6111yescharacteristic
830C42D4×D6111yescharacteristic
831C23—21no—
832C23—611no—
833C23—611no—
834C23—612no—
835C23—612no—
836C23—1224no—
837C23—1221no—
838C23—2441no—
839C23—2441no—
840C23—2442no—
841C23—2442no—
842C23C2×D4×D6111yescharacteristic
843Q8—21no—
844Q8—612no—
845Q8—1224no—
846Q8—1221no—
847Q8C4⋊C4×D6112yes—
848D4—22no—
849D4—22no—
850D4—21no—
851D4—612no—
852D4—1224no—
853D4—1224no—
854D4—1224no—
855D4—1222no—
856D4—1222no—
857D4—1221no—
858D4C4⋊C4×D6112yes—
859C2×C4—21no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—612no—
875C2×C4—612no—
876C2×C4—612no—
877C2×C4—612no—
878C2×C4—612no—
879C2×C4—612no—
880C2×C4—612no—
881C2×C4—612no—
882C2×C4—612no—
883C2×C4—612no—
884C2×C4—611no—
885C2×C4—611no—
886C2×C4—611no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1224no—
890C2×C4—1224no—
891C2×C4—1222no—
892C2×C4—1224no—
893C2×C4—1221no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2442no—
905C2×C4—2442no—
906C2×C4—2442no—
907C2×C4—2442no—
908C2×C4—2442no—
909C2×C4—2442no—
910C2×C4—2441no—
911C2×C4—2442no—
912C2×C4—2442no—
913C2×C4—2442no—
914C2×C4—2442no—
915C2×C4—2442no—
916C2×C4C22⋊C4×D6111yescharacteristic
917C2×C4C22⋊C4×D6111yescharacteristic
918C2×C4C22⋊C4×D6111yescharacteristic
919C2×C4C22⋊C4×D6111yescharacteristic
920C2×C4C22×C4×D6111yescharacteristic
921C2×C4C2×D4×D6111yescharacteristic
922C2×C4C2×D4×D6111yescharacteristic
923C2×C4C2×Q8×D6111yescharacteristic
924C2×C4#41×D6111yescharacteristic
925C2×C4#41×D6111yescharacteristic
926C8—42no—
927C8—2442no—
928C22—21no—
929C22—21no—
930C22—22no—
931C22—41no—
932C22—41no—
933C22—612no—
934C22—612no—
935C22—1221no—
936C22—1221no—
937C22—1221no—
938C22—1221no—
939C22—1222no—
940C22—2442no—
941C22—2442no—
942C22—2448no—
943C22—2441no—
944C22—2441no—
945C22C2×C22⋊C4×D6111yescharacteristic
946C22#121×D6111yescharacteristic
947C22C22⋊Q8×D6111yescharacteristic
948C4—21no—
949C4—21no—
950C4—21no—
951C4—22no—
952C4—41no—
953C4—41no—
954C4—82no—
955C4—612no—
956C4—612no—
957C4—612no—
958C4—1221no—
959C4—1221no—
960C4—1221no—
961C4—1222no—
962C4—4882no—
963C4—2441no—
964C4—2441no—
965C4#1683977712yescomplemented
966C4C2×C4⋊C4×D6111yescharacteristic
967C4#117×D6111yescharacteristic
968C4#121×D6111yescharacteristic
969C4C22⋊Q8×D6111yescharacteristic
970C2—21no—
971C2—21no—
972C2—42no—
973C2—1222no—
974C2—1222no—
975C2—2442no—
976C2#380×D6111yescharacteristic
977C2#421×D6111yescharacteristic
978C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1806C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC22×C4×C61C24
hypercenter#1806D61
hypocenterC61#20654
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #423×D61C2semidirect
4. #21448223C2semidirect
5. #21445840C2semidirect
6. #21445839C2semidirect
7. #21445838C2semidirect
8. #21445837C2semidirect
9. #21445836C2semidirect
10. #21445527C2semidirect
11. C61×#1806C2semidirect
15. C4×#11758226C4semidirect
16. C4×#11758226C4semidirect
23. C4×#11758224C4semidirect
24. C4×#11758224C4semidirect
25. C4×Q8×D61C4semidirect
26. C4×Q8×D61C4semidirect
29. C4×D4×D61C4semidirect
30. C4×D4×D61C4semidirect
36. #16839786C22semidirect
37. #16839785C22semidirect
50. C4×#11758196C22semidirect
51. C4×C4⋊Dic61C22semidirect
52. #16839523C22semidirect
53. #16839522C22semidirect
54. #16839521C22semidirect
56. C61×#423C22semidirect
58. C4×C4⋊C4×C61C22semidirect
59. C61×#339C22semidirect
218. #11758226C4⋊C4semidirect
220. Q8×D61C4⋊C4semidirect
224. #11758224C4⋊C4semidirect
228. D4×D61C4⋊C4semidirect
466. C4×C61#421semidirect
480. Dic61#421semidirect
490. #1806D61semidirect
530. #423C2×D61semidirect
544. C4×C4⋊C4C2×D61semidirect
548. #339C2×D61semidirect
549. C61#20654semidirect
965. C4#16839777semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D612
#423×D612
C2×#168397772
#214482232
#214458402
#214458392
#214458382
#214458372
#214458362
#214455272
C61×#18062
#2065461