Finite Group Databasebeta

← D61×#1516 #29647343

Subgroups — D61×#1516 #29647343

Order 15616.

1498 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
3#381×D61C211yesmaximal, characteristic, complemented
4#21444376C211yesmaximal, characteristic, complemented
5#21444375C211yesmaximal, characteristic, complemented
6#21444374C212yesmaximal, complemented
7#21444373C211yesmaximal, characteristic, complemented
8#21444372C212yesmaximal, complemented
9#328×D61C212yesmaximal, complemented
10#327×D61C212yesmaximal, complemented
11C61×#1516C211yesmaximal, characteristic, complemented
12C2×#41×D61C411yescharacteristic, complemented
13C23×C4×D61C2211yescharacteristic
14C22×C8×D61—21no—
15#16840275C411yescharacteristic, complemented
16#16840275C2211yescharacteristic
17#16840274C411yescharacteristic, complemented
18#16840273C2211yescharacteristic
19#16840272C411yescharacteristic, complemented
20#16840272C2211yescharacteristic
21#16840271—21no—
22#16840271—21no—
23#16840270—21no—
24#16840269C411yescharacteristic, complemented
25#16840268—21no—
26#123×D61—21no—
27C22⋊Q8×D61C411yescharacteristic, complemented
28C22⋊Q8×D61C2211yescharacteristic
29#121×D61C411yescharacteristic, complemented
30#121×D61C2211yescharacteristic
31#120×D61—21no—
32C4×D4×D61—21no—
33C4×D4×D61—21no—
34#117×D61C411yescharacteristic, complemented
35C2×C22⋊C4×D61—21no—
36C2×C22⋊#92418C2211yescharacteristic, complemented
37C2×#14519689—21no—
38C22⋊C8×D61—21no—
39C22⋊C8×D61—21no—
40C22⋊C8×D61C2212yes—
41C22⋊C8×D61C2212yescomplemented
42#16839625C2211yescharacteristic, complemented
43#16839624—21no—
44#16839624C2212yescomplemented
45#16839623—21no—
46#95×D61—21no—
47#95×D61C2212yes—
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yescomplemented
52#16839496C2212yescomplemented
53#16839495C2212yescomplemented
54C61×#525C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic, complemented
56C61×#381C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yescomplemented
59C24×D61D411yescharacteristic
60C2×#11758226C2×C411yescharacteristic, complemented
61C2×#11758222—21no—
62C2×#11758222C2×C411yescharacteristic, complemented
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic, complemented
65#41×D61—44no—
66C2×Q8×D61C2×C411yescharacteristic
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61C2×C411yescharacteristic
71C23×Dic61D411yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—22no—
74C22×C4×D61—44no—
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×#92418—21no—
88C2×C8×D61—22no—
89C2×C8×D61—22no—
90C2×C8×D61—44no—
91#14519762—21no—
92#14519762—21no—
93#14519761—21no—
94#14519760—21no—
95#14519759—21no—
96#14519759—21no—
97#14519758—21no—
98#14519757C2×C411yescharacteristic
99#14519757C2×C411yescharacteristic, complemented
100#14519756C2×C411yescharacteristic, complemented
101#14519756C2311yescharacteristic
102#14519755—21no—
103#14519755—21no—
104#14519754—21no—
105#14519754—21no—
106#14519753C2×C411yescharacteristic
107#14519753C2×C411yescharacteristic, complemented
108#14519752C2×C411yescharacteristic
109#14519752C2×C411yescharacteristic, complemented
110#14519751C2×C411yescharacteristic, complemented
111#14519751C2311yescharacteristic
112#14519750—21no—
113#14519750—21no—
114#14519749—21no—
115#14519749—21no—
116#14519748C2×C411yescharacteristic
117#14519748C2×C411yescharacteristic, complemented
118#14519747—21no—
119#14519747—21no—
120#14519747—21no—
121#14519746—21no—
122#14519745—21no—
123#14519745—21no—
124#14519745—21no—
125C4×D244—21no—
126C4×D244—21no—
127D4×Dic61—21no—
128D4×Dic61—21no—
129#14519739—21no—
130#14519739—21no—
131C4×C22⋊D61—21no—
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134C4×C22⋊D61—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519736C2×C411yescharacteristic, complemented
140#14519735C2×C411yescharacteristic, complemented
141#14519735C2×C411yescharacteristic, complemented
142#14519734—21no—
143#14519733—21no—
144C4⋊C4×D61—21no—
145C4⋊C4×D61—21no—
146C4⋊C4×D61C2×C411yescharacteristic
147C4⋊C4×D61C2×C411yescharacteristic
148C2×C22⋊Dic61—21no—
149C2×#11758198—22no—
150C22⋊C4×D61—21no—
151C22⋊C4×D61—21no—
152C22⋊C4×D61—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—44no—
156C42×D61—21no—
157C22⋊#92418—21no—
158C22⋊#92418C2312yes—
159#14519689—22no—
160#14519689—22no—
161#14519684—21no—
162#14519684—22no—
163#14519684—22no—
164#14519684C2312yes—
165C2×#41×C61C2×C411yescharacteristic, complemented
166C23×C4×C61C2311yescharacteristic
167C22×C8×C61—21no—
168#123×C61—21no—
169C22⋊Q8×C61C2×C411yescharacteristic, complemented
170C22⋊Q8×C61C2311yescharacteristic
171#121×C61C2×C411yescharacteristic, complemented
172#121×C61C2311yescharacteristic
173#120×C61—21no—
174C4×D4×C61—21no—
175C4×D4×C61—21no—
176#117×C61C2×C411yescharacteristic, complemented
177C2×C22⋊C4×C61—21no—
178C22⋊C8×C61—21no—
179C22⋊C8×C61C2312yes—
180#95×C61—21no—
181#95×C61C2312yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—24no—
184C23×D61—24no—
185C23×D61—21no—
186C23×D61—42no—
187C23×D61C22⋊C411yescharacteristic
188C23×D61C22⋊C411yescharacteristic
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C2×D411yescharacteristic
192C23×D61C2×D411yescharacteristic
193#41×C61—42no—
194C2×Q8×C61C22×C411yescharacteristic
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61C22×C411yescharacteristic
199C22×C4×C61—21no—
200C22×C4×C61—22no—
201C22×C4×C61—42no—
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C22×Dic61—21no—
216C22×Dic61—22no—
217C22×Dic61—42no—
218C22×Dic61C22⋊C411yescharacteristic
219C22×Dic61C22⋊C411yescharacteristic
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C22⋊C411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224#11758226—42no—
225Q8×D61—42no—
226#11758224—42no—
227#11758224—44no—
228D4×D61—42no—
229D4×D61—44no—
230D4×D61—44no—
231D4×D61—44no—
232#11758222—44no—
233#11758222—42no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244C22×C411yescharacteristic
238C2×C4×D61—24no—
239C2×C4×D61—24no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—42no—
246C2×C4×D61—42no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—44no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61—44no—
257C2×C4×D61—44no—
258C2×C4×D61—44no—
259C2×C4×D61C22⋊C411yescharacteristic
260C2×C4×D61C22⋊C411yescharacteristic
261C2×C4×D61C22⋊C411yescharacteristic
262C2×C4×D61C22⋊C411yescharacteristic
263C2×C4×D61C22⋊C411yescharacteristic
264C2×C4×D61C22⋊C411yescharacteristic
265C2×C4×D61C22⋊C411yescharacteristic
266C2×C4×D61C22⋊C411yescharacteristic
267C2×C4×D61C22×C411yescharacteristic
268C2×C4×D61C22×C411yescharacteristic
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C22×C411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×Dic122—21no—
276C2×Dic122C22×C411yescharacteristic
277C2×C8×C61—22no—
278C2×C8×C61—42no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61C22×C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—42no—
289C42×C61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—42no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—44no—
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61C22×C411yescharacteristic
310C4⋊Dic61C22×C411yescharacteristic
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C2×#92418—22no—
321C2×#92418—42no—
322C8×D61—44no—
323C8×D61—44no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—21no—
327C23×C61—41no—
328C23×C61C2×C22⋊C411yescharacteristic
329C23×C61C2×C22⋊C411yescharacteristic
330C23×C61C22×D411yescharacteristic
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—21no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—416no—
349C22×D61—42no—
350C22×D61—42no—
351C22×D61—42no—
352C22×D61#9914yes—
353C22×D61C2×C22⋊C411yescharacteristic
354C22×D61C2×C22⋊C411yescharacteristic
355C22×D61C2×C22⋊C411yescharacteristic
356C22×D61C2×C22⋊C411yescharacteristic
357C22×D61#13514yes—
358Q8×C61—41no—
359D4×C61—41no—
360D4×C61—42no—
361D4×C61—42no—
362D4×C61—42no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C23×C411yescharacteristic
379C2×C4×C61C22×D411yescharacteristic
380C22⋊D61—42no—
381C22⋊D61—42no—
382C22⋊D61—42no—
383C22⋊D61—42no—
384C22⋊D61—42no—
385C22⋊D61—42no—
386C22⋊D61—42no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404D244—41no—
405D244—42no—
406D244—42no—
407D244—42no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—42no—
425C4×D61—42no—
426C4×D61—42no—
427C4×D61—42no—
428C4×D61—42no—
429C4×D61—88no—
430Dic122—42no—
431Dic122—41no—
432C8×C61—42no—
433#92418—42no—
434C2×#1516—611nomaximal, Sylow
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—44no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61C2×#9912yes—
447C22×C61C22×C22⋊C411yescharacteristic
448C22×C61C2×#13512yes—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—28no—
454C2×D61—28no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—21no—
458C2×D61—44no—
459C2×D61—44no—
460C2×D61—44no—
461C2×D61—44no—
462C2×D61—41no—
463C2×D61—41no—
464C2×D61—41no—
465C2×D61—84no—
466C2×D61C2×#9912yes—
467C2×D61C2×#9912yes—
468C2×D61#41612yes—
469C2×D61#41612yes—
470C2×D61#42112yes—
471C4×C61—21no—
472C4×C61—21no—
473C4×C61—21no—
474C4×C61—21no—
475C4×C61—41no—
476C4×C61—41no—
477C4×C61—41no—
478C4×C61—82no—
479Dic61—21no—
480Dic61—21no—
481Dic61—21no—
482Dic61—21no—
483Dic61—41no—
484Dic61—41no—
485Dic61—41no—
486Dic61—82no—
487C2×#525—611no—
488C22×C22⋊C8—611no—
489C2×#381—611no—
490#1516—611no—
491#1516—611no—
492#1516—612no—
493#1516—612no—
494#1516—611no—
495#1516D6111yescharacteristic, direct product factor
496C2×#328—612no—
497C2×#327—612no—
498C2×C61—22no—
499C2×C61—22no—
500C2×C61—41no—
501C2×C61—81no—
502C2×C61C22×#9911yescharacteristic
503C2×C61C2×#41611yescharacteristic
504C2×C61C2×#42111yescharacteristic
505D61—22no—
506D61—22no—
507D61—41no—
508D61—81no—
509D61#151614yesdirect product factor
510C22×#41—611no—
511C24×C4—611no—
512C23×C8—1221no—
513#525—611no—
514#525—611no—
515#525—611no—
516#525—611no—
517#525—611no—
518#525—611no—
519#525—611no—
520#525—1221no—
521#525—1221no—
522#525—1221no—
523#525—1221no—
524#525C2×D6111yescharacteristic
525C2×#123—1221no—
526C2×C22⋊Q8—611no—
527C2×C22⋊Q8—611no—
528C2×#121—611no—
529C2×#121—611no—
530C2×#120—1221no—
531C2×C4×D4—1221no—
532C2×C4×D4—1221no—
533C2×#117—611no—
534C22×C22⋊C4—1221no—
535C2×C22⋊C8—611no—
536C2×C22⋊C8—612no—
537C2×C22⋊C8—612no—
538C2×C22⋊C8—1221no—
539C2×C22⋊C8—1221no—
540C2×C22⋊C8—1221no—
541C2×C22⋊C8C2×D6111yescharacteristic, complemented
542#381—611no—
543#381—612no—
544#381—1221no—
545#381—1221no—
546#381C2×D6111yescharacteristic, complemented
547C2×#95—612no—
548C2×#95—1221no—
549#328—612no—
550#328—612no—
551#328—612no—
552#328C2×D6112yescomplemented
553#327—612no—
554#327—612no—
555#327—612no—
556#327C2×D6112yescomplemented
557C61C2×#151611yescharacteristic, complemented, Sylow
558C25—611no—
559C2×#41—611no—
560C2×#41—611no—
561C2×#41—611no—
562C2×#41—1221no—
563C2×#41—1221no—
564C2×#41—2444no—
565C2×#41C4×D6111yescharacteristic, complemented
566C22×Q8—611no—
567C22×D4—611no—
568C22×D4—1221no—
569C22×D4—1221no—
570C22×D4—1221no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—1221no—
585C23×C4—1222no—
586C23×C4—2444no—
587C23×C4C22×D6111yescharacteristic
588C22×C8—21no—
589C22×C8—1222no—
590C22×C8—1222no—
591C22×C8—1221no—
592C22×C8—2444no—
593#123—21no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601C22⋊Q8—611no—
602C22⋊Q8—611no—
603C22⋊Q8—611no—
604C22⋊Q8—611no—
605C22⋊Q8—611no—
606C22⋊Q8—611no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8C4×D6111yescharacteristic, complemented
612C22⋊Q8C22×D6111yescharacteristic
613#121—611no—
614#121—611no—
615#121—611no—
616#121—611no—
617#121—611no—
618#121—611no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121—1221no—
623#121C4×D6111yescharacteristic, complemented
624#121C22×D6111yescharacteristic
625#120—21no—
626#120—1221no—
627#120—1221no—
628#120—1221no—
629#120—1221no—
630#120—1221no—
631#120—1221no—
632#120—1221no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4—1221no—
640C4×D4—1221no—
641C4×D4—1221no—
642C4×D4—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4—1221no—
649#117—611no—
650#117—611no—
651#117—611no—
652#117—1221no—
653#117—1221no—
654#117C4×D6111yescharacteristic, complemented
655C2×C4⋊C4—611no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4—1221no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—1221no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1222no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—2444no—
668C2×C42—1221no—
669C22⋊C8—21no—
670C22⋊C8—612no—
671C22⋊C8—1222no—
672C22⋊C8—1222no—
673C22⋊C8—1221no—
674C22⋊C8C22×D6112yes—
675#95—21no—
676#95—612no—
677#95—1222no—
678#95—1222no—
679#95—1221no—
680#95C22×D6112yes—
681C24—611no—
682C24—611no—
683C24—611no—
684C24—611no—
685C24—611no—
686C24—611no—
687C24—1224no—
688C24—1224no—
689C24—1221no—
690C24—2442no—
691C24D4×D6111yescharacteristic
692#41—42no—
693#41—2442no—
694#41—2444no—
695#41—2444no—
696#41—2442no—
697#41—2442no—
698C2×Q8—611no—
699C2×Q8—1221no—
700C2×Q8—2442no—
701C2×Q8C2×C4×D6111yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—611no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—2442no—
717C2×D4—2444no—
718C2×D4—2444no—
719C2×D4—2444no—
720C2×D4C2×C4×D6111yescharacteristic
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—42no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
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—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—1221no—
747C22×C4—1224no—
748C22×C4—1224no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1222no—
755C22×C4—2442no—
756C22×C4—2442no—
757C22×C4—2442no—
758C22×C4—2442no—
759C22×C4—2442no—
760C22×C4—2442no—
761C22×C4—2442no—
762C22×C4—2442no—
763C22×C4—2442no—
764C22×C4—2442no—
765C22×C4—2444no—
766C22×C4—2444no—
767C22×C4—2444no—
768C22×C4—2444no—
769C22×C4—2442no—
770C22×C4C2×C4×D6111yescharacteristic
771C22×C4C2×C4×D6111yescharacteristic
772C22×C4D4×D6111yescharacteristic
773C22×C4D4×D6111yescharacteristic
774C22×C4D4×D6111yescharacteristic
775C22×C4C23×D6111yescharacteristic
776C2×C8—22no—
777C2×C8—42no—
778C2×C8—1222no—
779C2×C8—2444no—
780C2×C8—2444no—
781C2×C8—2442no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—611no—
785C4⋊C4—611no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4C2×C4×D6111yescharacteristic
795C4⋊C4C2×C4×D6111yescharacteristic
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—2444no—
818C22⋊C4—2442no—
819C42—21no—
820C42—1221no—
821C42—1221no—
822C42—1221no—
823C23—22no—
824C23—22no—
825C23—21no—
826C23—41no—
827C23—611no—
828C23—611no—
829C23—611no—
830C23—614no—
831C23—614no—
832C23—611no—
833C23—1222no—
834C23—1222no—
835C23—1222no—
836C23—1222no—
837C23—1222no—
838C23—1222no—
839C23—1222no—
840C23—1222no—
841C23—1222no—
842C23—1222no—
843C23—1222no—
844C23—1222no—
845C23—1222no—
846C23—1221no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2442no—
851C23—2442no—
852C23—2442no—
853C23—24416no—
854C23C22⋊C4×D6111yescharacteristic
855C23C22⋊C4×D6111yescharacteristic
856C23C2×D4×D6111yescharacteristic
857Q8—41no—
858Q8—2441no—
859Q8—2442no—
860D4—41no—
861D4—42no—
862D4—42no—
863D4—42no—
864D4—2441no—
865D4—2442no—
866D4—2442no—
867D4—2442no—
868D4—2442no—
869D4—2442no—
870D4—2442no—
871D4—2442no—
872D4—2442no—
873D4—2442no—
874D4—2442no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—611no—
889C2×C4—611no—
890C2×C4—611no—
891C2×C4—611no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1221no—
903C2×C4—1221no—
904C2×C4—1221no—
905C2×C4—4888no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2442no—
915C2×C4—2442no—
916C2×C4—2442no—
917C2×C4—2442no—
918C2×C4—2442no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2442no—
924C2×C4—2442no—
925C2×C4—2442no—
926C2×C4—2442no—
927C2×C4C22⋊C4×D6111yescharacteristic
928C2×C4C22⋊C4×D6111yescharacteristic
929C2×C4C22×C4×D6111yescharacteristic
930C2×C4C2×D4×D6111yescharacteristic
931C8—42no—
932C8—2442no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—21no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—44no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—612no—
945C22—612no—
946C22—612no—
947C22—612no—
948C22—612no—
949C22—1228no—
950C22—1228no—
951C22—1221no—
952C22—1221no—
953C22—1221no—
954C22—1221no—
955C22—1221no—
956C22—1221no—
957C22—1221no—
958C22—4884no—
959C22—2444no—
960C22—2444no—
961C22—2444no—
962C22—2444no—
963C22—2441no—
964C22—2441no—
965C22—2441no—
966C22#99×D6112yes—
967C22C2×C22⋊C4×D6111yescharacteristic
968C22#135×D6112yes—
969C4—21no—
970C4—21no—
971C4—21no—
972C4—21no—
973C4—41no—
974C4—41no—
975C4—41no—
976C4—82no—
977C4—1221no—
978C4—1221no—
979C4—1221no—
980C4—1221no—
981C4—4882no—
982C4—2441no—
983C4—2441no—
984C4—2441no—
985C2—22no—
986C2—22no—
987C2—41no—
988C2—81no—
989C2—614no—
990C2—1222no—
991C2—1222no—
992C2—4881no—
993C2—2441no—
994C2C2×#99×D6111yescharacteristic
995C2#416×D6111yescharacteristic
996C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1516C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1516D61
hypocenterC61C2×#1516
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C8×D61C2semidirect
3. #381×D61C2semidirect
4. #21444376C2semidirect
5. #21444375C2semidirect
6. #21444374C2semidirect
7. #21444373C2semidirect
8. #21444372C2semidirect
9. #328×D61C2semidirect
10. #327×D61C2semidirect
11. C61×#1516C2semidirect
12. C2×#41×D61C4semidirect
15. #16840275C4semidirect
17. #16840274C4semidirect
19. #16840272C4semidirect
24. #16840269C4semidirect
27. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
34. #117×D61C4semidirect
36. C2×C22⋊#92418C22semidirect
41. C22⋊C8×D61C22semidirect
42. #16839625C22semidirect
44. #16839624C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
51. #16839497C22semidirect
52. #16839496C22semidirect
53. #16839495C22semidirect
55. C2×C22⋊C8×C61C22semidirect
56. C61×#381C22semidirect
57. C61×#328C22semidirect
58. C61×#327C22semidirect
60. C2×#11758226C2×C4semidirect
62. C2×#11758222C2×C4semidirect
64. C2×#11758224C2×C4semidirect
99. #14519757C2×C4semidirect
100. #14519756C2×C4semidirect
107. #14519753C2×C4semidirect
109. #14519752C2×C4semidirect
110. #14519751C2×C4semidirect
117. #14519748C2×C4semidirect
139. #14519736C2×C4semidirect
140. #14519735C2×C4semidirect
141. #14519735C2×C4semidirect
165. C2×#41×C61C2×C4semidirect
169. C22⋊Q8×C61C2×C4semidirect
171. #121×C61C2×C4semidirect
176. #117×C61C2×C4semidirect
495. #1516D61direct (N × H)
509. D61#1516direct (N × H)
541. C2×C22⋊C8C2×D61semidirect
546. #381C2×D61semidirect
552. #328C2×D61semidirect
556. #327C2×D61semidirect
557. C61C2×#1516semidirect
565. C2×#41C4×D61semidirect
611. C22⋊Q8C4×D61semidirect
623. #121C4×D61semidirect
654. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#525×D612
C2×C22⋊C8×D612
#381×D612
#214443762
#214443752
#214443742
#214443732
#214443722
#328×D612
#327×D612
C61×#15162
C2×#151661