Finite Group Databasebeta

← D61×#1996 #29684650

Subgroups — D61×#1996 #29684650

Order 15616.

1698 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2#380×D61C211yesmaximal, characteristic
3C4×C22⋊C4×D61C211yesmaximal, characteristic
4#21446805C211yesmaximal, characteristic, complemented
5#21446804C211yesmaximal, characteristic, complemented
6#21446803C211yesmaximal, characteristic, complemented
7#21446802C214yesmaximal, complemented
8#342×D61C214yesmaximal
9C61×#1996C211yesmaximal, characteristic, complemented
10C22×Q8×D61C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C2×#14519757C411yescharacteristic, complemented
13C2×#14519756C2211yescharacteristic
14C2×#14519755C412yescomplemented
15C2×#14519754C2212yes—
16C2×#14519753C411yescharacteristic, complemented
17C22⋊Q8×D61—21no—
18C22⋊Q8×D61—21no—
19C22⋊Q8×D61—21no—
20C22⋊Q8×D61—21no—
21C22⋊Q8×D61—21no—
22C22⋊Q8×D61—21no—
23C22⋊Q8×D61—21no—
24C22⋊Q8×D61—21no—
25C2×C4⋊C4×D61—21no—
26C2×C4⋊C4×D61C411yescharacteristic, complemented
27C2×C4⋊C4×D61C412yescomplemented
28C2×C22⋊C4×D61C2212yes—
29C2×C22⋊C4×D61C2212yes—
30C2×C22⋊C4×D61C2212yes—
31C2×C42×D61—21no—
32#16839622C2211yescharacteristic
33#16839621—21no—
34#16839620C2212yes—
35#16839619—21no—
36C22⋊C4×Dic61C2212yes—
37C4×#11758198—21no—
38C4×C22⋊Dic61C2211yescharacteristic
39#16839609—21no—
40#95×D61—21no—
41#95×D61—21no—
42#16839529C2214yes—
43#16839528C2214yes—
44#16839528C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#380C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#342C2214yes—
49C24×D61C2311yescharacteristic
50C22×Dic122C2×C412yescomplemented
51C22×Dic122C2×C411yescharacteristic, complemented
52C2×Q8×D61—21no—
53C2×Q8×D61—21no—
54C2×Q8×D61—21no—
55C2×Q8×D61—21no—
56C2×Q8×D61—44no—
57C23×Dic61C2311yescharacteristic
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—44no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C412yes—
63C22×C4×D61C2×C412yes—
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75#14519757—21no—
76#14519757—21no—
77#14519757—21no—
78#14519757—21no—
79#14519756—21no—
80#14519756—21no—
81#14519756—21no—
82#14519756—21no—
83#14519755—22no—
84#14519755—22no—
85#14519755—22no—
86#14519755—22no—
87#14519754—22no—
88#14519754—22no—
89#14519754—22no—
90#14519754—22no—
91#14519753—21no—
92#14519753—21no—
93#14519753—21no—
94#14519753—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2×C411yescharacteristic, complemented
97C2×C4⋊Dic61C2×C412yescomplemented
98C2×#11758196—22no—
99C2×#11758196C2×C412yescomplemented
100C2×#11758196C2×C412yescomplemented
101C2×#11758196C2×C412yescomplemented
102C4⋊C4×D61—22no—
103C4⋊C4×D61—22no—
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—21no—
110C4⋊C4×D61—44no—
111C2×C22⋊Dic61C2312yes—
112C2×C22⋊Dic61C2312yes—
113C2×C22⋊Dic61C2312yes—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198C2×C412yes—
117C2×#11758198C2×C412yes—
118C22⋊C4×D61—22no—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C22⋊C4×D61—22no—
122C22⋊C4×D61—24no—
123C22⋊C4×D61—28no—
124C22⋊C4×D61Q818yescomplemented
125C2×C4×Dic61—21no—
126C2×C4×Dic61—22no—
127C42×D61—44no—
128#14519684—21no—
129#14519684—21no—
130#14519684—22no—
131#14519684—22no—
132C22×Q8×C61C2×C411yescharacteristic, complemented
133C23×C4×C61C2311yescharacteristic
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2×C412yescomplemented
140C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2312yes—
143C2×C22⋊C4×C61C2312yes—
144C2×C42×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147C24×C61C2411yescharacteristic
148C23×D61—42no—
149C23×D61—42no—
150C23×D61C22×C411yescharacteristic
151C23×D61C22×C411yescharacteristic
152C23×D61C2×D411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C23×D61C2×Q814yes—
157C23×D61#4114yes—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—42no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—42no—
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C412yes—
166C22×C4×C61C22×C412yes—
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—42no—
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C412yes—
177C22×Dic61C22×C412yes—
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183Q8×D61—44no—
184Q8×D61—44no—
185Q8×D61—44no—
186Q8×D61—44no—
187C2×C4×D61—24no—
188C2×C4×D61—24no—
189C2×C4×D61—24no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—28no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—44no—
205C2×C4×D61—44no—
206C2×C4×D61—44no—
207C2×C4×D61—44no—
208C2×C4×D61—44no—
209C2×C4×D61—44no—
210C2×C4×D61—44no—
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22⋊C411yescharacteristic
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—22no—
230C2×Dic122—22no—
231C2×Dic122—44no—
232C2×Dic122—42no—
233C4⋊C4×C61—22no—
234C4⋊C4×C61—22no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—42no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—24no—
242C22⋊C4×C61C2×Q814yescomplemented
243C42×C61—42no—
244C22⋊Dic61—22no—
245C22⋊Dic61—22no—
246C22⋊Dic61—22no—
247C22⋊Dic61—24no—
248C22⋊Dic61C2×Q814yescomplemented
249#11758198—22no—
250#11758198—22no—
251#11758198—22no—
252#11758198—22no—
253#11758198—28no—
254#11758198—44no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—22no—
258C4⋊Dic61—22no—
259C4⋊Dic61—42no—
260#11758196—22no—
261#11758196—22no—
262#11758196—22no—
263#11758196—22no—
264#11758196—22no—
265#11758196—22no—
266#11758196—44no—
267C4×Dic61—44no—
268C4×Dic61—42no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61C23×C411yescharacteristic
272C23×C61C22×D411yescharacteristic
273C23×C61C22×D411yescharacteristic
274C23×C61C22×Q812yes—
275C23×C61C2×#4112yes—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—48no—
283C22×D61—48no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61C2×C22⋊C411yescharacteristic
291C22×D61C2×C22⋊C411yescharacteristic
292C22×D61C2×C22⋊C411yescharacteristic
293C22×D61C2×C22⋊C411yescharacteristic
294C22×D61C4×Q814yes—
295C22×D61C4×Q814yes—
296C22×D61C22⋊Q814yes—
297C22×D61C22⋊Q814yes—
298C22×D61#12412yes—
299C22×D61#12412yes—
300C22×D61C4⋊Q812yes—
301C22×D61C4⋊Q812yes—
302Q8×C61—42no—
303Q8×C61—42no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—24no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—416no—
360C4×D61—44no—
361C4×D61—44no—
362C4×D61—44no—
363C4×D61—44no—
364C4×D61—88no—
365C4×D61#9914yes—
366Dic122—44no—
367Dic122—42no—
368Dic122—42no—
369Dic122—44no—
370C2×#1996—611nomaximal, Sylow
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61C22×C22⋊C411yescharacteristic
380C22×C61C2×C4×Q812yes—
381C22×C61C2×C22⋊Q812yes—
382C22×C61C2×#12411yescharacteristic
383C22×C61C2×C4⋊Q811yescharacteristic
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—28no—
391C2×D61—24no—
392C2×D61—28no—
393C2×D61—24no—
394C2×D61—44no—
395C2×D61—44no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61#39112yes—
399C2×D61#39112yes—
400C2×D61#39112yes—
401C2×D61#39112yes—
402C2×D61C2×#9912yes—
403C2×D61#41012yes—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—44no—
408C4×C61—42no—
409C4×C61—42no—
410C4×C61—82no—
411C4×C61C2×#9912yes—
412Dic61—21no—
413Dic61—21no—
414Dic61—21no—
415Dic61—44no—
416Dic61—42no—
417Dic61—42no—
418Dic61—82no—
419Dic61C2×#9912yes—
420C22×C22⋊Q8—611no—
421C2×#380—611no—
422C2×C4×C22⋊C4—611no—
423#1996—611no—
424#1996—611no—
425#1996—614no—
426#1996—611no—
427#1996D6111yescharacteristic, direct product factor
428C2×#342—614no—
429C2×C61—22no—
430C2×C61—21no—
431C2×C61—22no—
432C2×C61—21no—
433C2×C61C2×#39111yescharacteristic
434C2×C61C22×#9911yescharacteristic
435C2×C61C2×#41011yescharacteristic
436D61—22no—
437D61—22no—
438D61—22no—
439D61#199614yesdirect product factor
440C23×Q8—611no—
441C24×C4—611no—
442C2×C22⋊Q8—611no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8—612no—
445C2×C22⋊Q8—611no—
446C2×C22⋊Q8—612no—
447C2×C22⋊Q8—1221no—
448C2×C22⋊Q8—1221no—
449C2×C22⋊Q8—1221no—
450C2×C22⋊Q8—1221no—
451C2×C22⋊Q8—1221no—
452C2×C22⋊Q8—1221no—
453C2×C22⋊Q8—1221no—
454C2×C22⋊Q8—1221no—
455C2×C22⋊Q8C2×D6111yescharacteristic
456C22×C4⋊C4—611no—
457C22×C4⋊C4—612no—
458C22×C4⋊C4—1221no—
459C22×C22⋊C4—612no—
460C22×C22⋊C4—612no—
461C22×C22⋊C4—612no—
462C22×C42—1221no—
463#380—611no—
464#380—612no—
465#380—1221no—
466#380—1221no—
467#380C2×D6111yescharacteristic
468C4×C22⋊C4—611no—
469C4×C22⋊C4—612no—
470C4×C22⋊C4—1221no—
471C4×C22⋊C4—1221no—
472C4×C22⋊C4C2×D6111yescharacteristic
473C2×#95—1221no—
474C2×#95—1221no—
475#342—614no—
476#342—614no—
477#342—614no—
478#342C2×D6114yes—
479C61C2×#199611yescharacteristic, complemented, Sylow
480C25—611no—
481C22×Q8—612no—
482C22×Q8—611no—
483C22×Q8—1221no—
484C22×Q8—1221no—
485C22×Q8—1221no—
486C22×Q8—1221no—
487C22×Q8—2444no—
488C22×Q8C4×D6111yescharacteristic, complemented
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—612no—
503C23×C4—612no—
504C23×C4—1222no—
505C23×C4—1222no—
506C23×C4—2444no—
507C23×C4C22×D6111yescharacteristic
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514C22⋊Q8—1222no—
515C22⋊Q8—1222no—
516C22⋊Q8—1222no—
517C22⋊Q8—1222no—
518C22⋊Q8—1222no—
519C22⋊Q8—1222no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8—1221no—
523C22⋊Q8—1221no—
524C22⋊Q8—1221no—
525C22⋊Q8—1221no—
526C22⋊Q8—1221no—
527C22⋊Q8—1221no—
528C22⋊Q8—1221no—
529C22⋊Q8—1221no—
530C22⋊Q8—1221no—
531C22⋊Q8—1221no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—612no—
534C2×C4⋊C4—612no—
535C2×C4⋊C4—612no—
536C2×C4⋊C4—612no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1222no—
543C2×C4⋊C4—1222no—
544C2×C4⋊C4—1222no—
545C2×C4⋊C4—1222no—
546C2×C4⋊C4—1222no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—2444no—
549C2×C4⋊C4C4×D6111yescharacteristic, complemented
550C2×C4⋊C4C4×D6112yescomplemented
551C2×C22⋊C4—612no—
552C2×C22⋊C4—618no—
553C2×C22⋊C4—612no—
554C2×C22⋊C4—612no—
555C2×C22⋊C4—612no—
556C2×C22⋊C4—612no—
557C2×C22⋊C4—1222no—
558C2×C22⋊C4—1222no—
559C2×C22⋊C4—1222no—
560C2×C22⋊C4—1222no—
561C2×C22⋊C4—1224no—
562C2×C22⋊C4—1228no—
563C2×C22⋊C4—1222no—
564C2×C22⋊C4—1222no—
565C2×C22⋊C4C22×D6112yes—
566C2×C22⋊C4C22×D6112yes—
567C2×C22⋊C4C22×D6112yes—
568C2×C42—21no—
569C2×C42—1222no—
570C2×C42—1221no—
571C2×C42—2444no—
572#95—21no—
573#95—21no—
574#95—1222no—
575#95—1222no—
576#95—1221no—
577#95—1221no—
578C24—611no—
579C24—611no—
580C24—611no—
581C24—611no—
582C24—611no—
583C24—611no—
584C24—614no—
585C24—614no—
586C24—2442no—
587C24—2442no—
588C24C23×D6111yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—42no—
592C2×Q8—1222no—
593C2×Q8—1222no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—2442no—
597C2×Q8—2444no—
598C2×Q8—2444no—
599C2×Q8—2444no—
600C2×Q8—2444no—
601C2×Q8—2444no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—42no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—1224no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—1228no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2444no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4—2444no—
654C22×C4—2444no—
655C22×C4—2442no—
656C22×C4C2×C4×D6111yescharacteristic
657C22×C4C2×C4×D6112yes—
658C22×C4C2×C4×D6112yes—
659C22×C4C2×C4×D6111yescharacteristic
660C22×C4D4×D6111yescharacteristic
661C22×C4D4×D6111yescharacteristic
662C22×C4D4×D6111yescharacteristic
663C22×C4D4×D6111yescharacteristic
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—42no—
669C4⋊C4—1222no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—1222no—
675C4⋊C4—1222no—
676C4⋊C4—1222no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—2442no—
680C4⋊C4—2444no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—24no—
685C22⋊C4—614no—
686C22⋊C4—1228no—
687C22⋊C4—1222no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1224no—
695C22⋊C4—2444no—
696C22⋊C4Q8×D6114yescomplemented
697C42—42no—
698C42—2442no—
699C42—2444no—
700C23—41no—
701C23—41no—
702C23—611no—
703C23—611no—
704C23—611no—
705C23—611no—
706C23—614no—
707C23—614no—
708C23—612no—
709C23—612no—
710C23—614no—
711C23—614no—
712C23—612no—
713C23—612no—
714C23—1222no—
715C23—1222no—
716C23—1222no—
717C23—1222no—
718C23—1222no—
719C23—1222no—
720C23—2441no—
721C23—2441no—
722C23—2441no—
723C23—2441no—
724C23—2441no—
725C23—2441no—
726C23—2448no—
727C23—2448no—
728C23C22×C4×D6111yescharacteristic
729C23C2×D4×D6111yescharacteristic
730C23C2×D4×D6111yescharacteristic
731C23C2×Q8×D6112yes—
732C23#41×D6112yes—
733Q8—42no—
734Q8—42no—
735Q8—2442no—
736Q8—2444no—
737Q8—2444no—
738Q8—2442no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—611no—
756C2×C4—614no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—611no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1224no—
775C2×C4—4888no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2444no—
783C2×C4—2444no—
784C2×C4—24416no—
785C2×C4—2444no—
786C2×C4—2444no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4C22⋊C4×D6111yescharacteristic
798C2×C4C22⋊C4×D6111yescharacteristic
799C2×C4C22⋊C4×D6111yescharacteristic
800C2×C4C22⋊C4×D6111yescharacteristic
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—42no—
808C22—42no—
809C22—612no—
810C22—612no—
811C22—612no—
812C22—612no—
813C22—612no—
814C22—612no—
815C22—1224no—
816C22—1228no—
817C22—1228no—
818C22—1224no—
819C22—1221no—
820C22—1221no—
821C22—1221no—
822C22—1221no—
823C22—1221no—
824C22—1221no—
825C22—2444no—
826C22—2442no—
827C22—2444no—
828C22—2442no—
829C22C2×C22⋊C4×D6111yescharacteristic
830C22C4×Q8×D6112yes—
831C22C22⋊Q8×D6112yes—
832C22#124×D6111yescharacteristic
833C22C4⋊Q8×D6111yescharacteristic
834C4—21no—
835C4—21no—
836C4—21no—
837C4—44no—
838C4—42no—
839C4—42no—
840C4—82no—
841C4—612no—
842C4—1221no—
843C4—1221no—
844C4—1221no—
845C4—4882no—
846C4—2444no—
847C4—2442no—
848C4—2442no—
849C4#99×D6112yes—
850C2—22no—
851C2—21no—
852C2—22no—
853C2—21no—
854C2—614no—
855C2—1222no—
856C2—1222no—
857C2—1222no—
858C2#391×D6111yescharacteristic
859C2C2×#99×D6111yescharacteristic
860C2#410×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C23
cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61C2×#1996
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
4. #21446805C2semidirect
5. #21446804C2semidirect
6. #21446803C2semidirect
7. #21446802C2semidirect
9. C61×#1996C2semidirect
10. C22×Q8×D61C4semidirect
12. C2×#14519757C4semidirect
14. C2×#14519755C4semidirect
16. C2×#14519753C4semidirect
26. C2×C4⋊C4×D61C4semidirect
27. C2×C4⋊C4×D61C4semidirect
50. C22×Dic122C2×C4semidirect
51. C22×Dic122C2×C4semidirect
96. C2×C4⋊Dic61C2×C4semidirect
97. C2×C4⋊Dic61C2×C4semidirect
99. C2×#11758196C2×C4semidirect
100. C2×#11758196C2×C4semidirect
101. C2×#11758196C2×C4semidirect
124. C22⋊C4×D61Q8semidirect
132. C22×Q8×C61C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
140. C2×C4⋊C4×C61C2×C4semidirect
242. C22⋊C4×C61C2×Q8semidirect
248. C22⋊Dic61C2×Q8semidirect
427. #1996D61direct (N × H)
439. D61#1996direct (N × H)
479. C61C2×#1996semidirect
488. C22×Q8C4×D61semidirect
549. C2×C4⋊C4C4×D61semidirect
550. C2×C4⋊C4C4×D61semidirect
696. C22⋊C4Q8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
#380×D612
C4×C22⋊C4×D612
#214468052
#214468042
#214468032
#214468022
#342×D612
C61×#19962
C2×#199661