Finite Group Databasebeta

← D61⋊#1901 #30615732

Subgroups — D61⋊#1901 #30615732

Order 15616.

1854 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic
2C2×D61⋊#101C212yesmaximal, complemented
3D61⋊#407C211yesmaximal, characteristic
4#21461847C214yesmaximal, complemented
5#21461846C214yesmaximal, complemented
6#21461522C212yesmaximal, complemented
7C2×C22⋊Q8×D61C211yesmaximal, characteristic
8C22×#11758213—21no—
9C2×D61⋊M16—28no—
10C2×D61⋊M16—21no—
11C2×D61⋊M16—21no—
12C2×D61⋊M16C2212yes—
13C2×D61⋊M16C2212yes—
14C2×D61⋊M16C2212yes—
15C22×#11758217C2212yes—
16C22×D61⋊C8—21no—
17D61⋊#101—28no—
18C2×#14519838C2218yescomplemented
19#16840734C2212yes—
20#16840733—21no—
21#16840733—21no—
22#16840732C2212yes—
23D61⋊(C22⋊C8)—21no—
24D61⋊(C22⋊C8)—21no—
25#16840642C2218yescomplemented
26C22×Q8×D61C2211yescharacteristic
27C23×C4×D61C2211yescharacteristic
28C2×#14519757C411yescharacteristic
29C2×#14519756C411yescharacteristic
30C2×#14519755C2212yes—
31C2×#14519754C2212yes—
32C2×#14519753C411yescharacteristic
33C22⋊Q8×D61—21no—
34C22⋊Q8×D61—21no—
35C22⋊Q8×D61—21no—
36C22⋊Q8×D61—21no—
37C22⋊Q8×D61—21no—
38C22⋊Q8×D61—21no—
39C22⋊Q8×D61—21no—
40C22⋊Q8×D61—21no—
41C2×C4⋊C4×D61C412yes—
42C2×C4⋊C4×D61C2211yescharacteristic
43C2×C22⋊C4×D61C412yes—
44C2×C22⋊Q8×C61C411yescharacteristic
45C2×#11758213—28no—
46C2×#11758213—22no—
47C2×#11758213—22no—
48C2×#11758213—22no—
49D61⋊M16—28no—
50D61⋊M16—28no—
51D61⋊M16—24no—
52D61⋊M16—28no—
53D61⋊M16—24no—
54D61⋊M16—24no—
55D61⋊M16D418yes—
56C2×#11758217—22no—
57C2×#11758217—28no—
58C2×#11758217C2314yes—
59C2×#11758217C2314yes—
60C2×D61⋊C8—28no—
61C2×D61⋊C8—22no—
62C2×D61⋊C8—22no—
63C2×D61⋊C8—22no—
64C22×#92420—22no—
65#14519838—216no—
66#14519834—22no—
67#14519834—22no—
68C22⋊#92420—22no—
69C22⋊#92420—22no—
70C24×D61C2×C411yescharacteristic
71C22×Dic122C2×C411yescharacteristic
72C22×Dic122C2312yes—
73C2×Q8×D61—24no—
74C2×Q8×D61—21no—
75C2×Q8×D61—21no—
76C2×Q8×D61—21no—
77C2×Q8×D61—21no—
78C2×Q8×D61—24no—
79C23×Dic61C2311yescharacteristic
80C22×C4×D61—24no—
81C22×C4×D61—24no—
82C22×C4×D61C2×C412yes—
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C412yes—
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D411yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96#14519757—21no—
97#14519757—21no—
98#14519757—21no—
99#14519757—21no—
100#14519756—21no—
101#14519756—21no—
102#14519756—21no—
103#14519756—21no—
104#14519755—22no—
105#14519755—22no—
106#14519755—22no—
107#14519755—22no—
108#14519754—22no—
109#14519754—22no—
110#14519754—22no—
111#14519754—22no—
112#14519753—21no—
113#14519753—21no—
114#14519753—21no—
115#14519753—21no—
116C2×C4⋊Dic61C2×C412yes—
117C2×C4⋊Dic61C2×C411yescharacteristic
118C2×#11758196C2×C412yes—
119C2×#11758196C2×C412yes—
120C2×#11758196C2312yes—
121C4⋊C4×D61—22no—
122C4⋊C4×D61—22no—
123C4⋊C4×D61—22no—
124C4⋊C4×D61—22no—
125C4⋊C4×D61—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61—21no—
129C2×C22⋊Dic61C2×C412yes—
130C2×#11758198C2×C412yes—
131C2×#11758198C2×C412yes—
132C22⋊C4×D61—22no—
133C22⋊C4×D61—22no—
134C22⋊C4×D61—22no—
135C22⋊C4×D61—22no—
136C22×Q8×C61C2×C411yescharacteristic
137C23×C4×C61C2×C411yescharacteristic
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61—21no—
140C22⋊Q8×C61—21no—
141C22⋊Q8×C61—21no—
142C2×C4⋊C4×C61C2×C412yes—
143C2×C4⋊C4×C61C2×C411yescharacteristic
144C2×C22⋊C4×C61C2×C412yes—
145C24×C61C22×C411yescharacteristic
146C23×D61—24no—
147C23×D61—24no—
148C23×D61—42no—
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—24no—
158C22×C4×C61—24no—
159C22×C4×C61C22⋊C411yescharacteristic
160C22×C4×C61C22⋊C411yescharacteristic
161C22×C4×C61C22⋊C411yescharacteristic
162C22×C4×C61C22⋊C411yescharacteristic
163C22×C4×C61C22×C412yes—
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C412yes—
166C22×C4×C61C22×C411yescharacteristic
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61C22×C412yes—
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C412yes—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2411yescharacteristic
177Q8×D61—42no—
178Q8×D61—42no—
179Q8×D61—44no—
180Q8×D61—44no—
181Q8×D61—42no—
182Q8×D61—42no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—24no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—24no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—28no—
204C2×C4×D61—44no—
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2×D414yes—
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61#4114yes—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—24no—
226C2×Dic122—24no—
227C2×Dic122—22no—
228C2×Dic122—22no—
229C2×Dic122—24no—
230#11758217—28no—
231#11758217—24no—
232#11758217—24no—
233#11758217—24no—
234#11758217C2×D418yes—
235C2×#92420—28no—
236C2×#92420—24no—
237C2×#92420—24no—
238#11758213—28no—
239#11758213—28no—
240#11758213—44no—
241D61⋊C8—28no—
242D61⋊C8—28no—
243D61⋊C8—44no—
244C4⋊C4×C61—22no—
245C4⋊C4×C61—22no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—22no—
250C22⋊Dic61—22no—
251C22⋊Dic61—22no—
252#11758198—22no—
253#11758198—22no—
254#11758198—22no—
255#11758198—22no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—22no—
259C4⋊Dic61—22no—
260#11758196—22no—
261#11758196—22no—
262#11758196—22no—
263#11758196—22no—
264#11758196—22no—
265#11758196—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—41no—
269C23×C61C2×C22⋊C411yescharacteristic
270C23×C61C2×C22⋊C411yescharacteristic
271C23×C61C23×C411yescharacteristic
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—416no—
289C22×D61#10114yescomplemented
290C22×D61C2×C22⋊C411yescharacteristic
291C22×D61C2×C22⋊C411yescharacteristic
292C22×D61C2×C22⋊C411yescharacteristic
293C22×D61C2×C22⋊C411yescharacteristic
294C22×D61C4×D414yes—
295Q8×C61—42no—
296Q8×C61—42no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—24no—
305C2×C4×C61—42no—
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C4×D414yes—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—24no—
321C2×Dic61—42no—
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D411yescharacteristic
326C2×Dic61C22×D411yescharacteristic
327C2×Dic61C2×#4112yes—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—21no—
337C4×D61—21no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—21no—
341C4×D61—21no—
342C4×D61—44no—
343C4×D61—44no—
344C4×D61—44no—
345C4×D61—44no—
346C4×D61#12012yes—
347C4×D61#12012yes—
348C4×D61#12114yes—
349C4×D61#12114yes—
350C4×D61#12312yes—
351C4×D61#12312yes—
352Dic122—42no—
353Dic122—42no—
354Dic122—42no—
355Dic122—44no—
356Dic122—42no—
357#92420—28no—
358#92420—44no—
359C2×#1901—611nomaximal, Sylow
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—44no—
368C22×C61C2×#10112yescomplemented
369C22×C61C22×C22⋊C411yescharacteristic
370C22×C61C2×C4×D412yes—
371C2×D61—21no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—28no—
376C2×D61—28no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—44no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61#38612yes—
385C2×D61#38612yes—
386C2×D61C2×#10112yes—
387C2×D61C2×#10112yescomplemented
388C2×D61#41312yes—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61#38612yes—
394C4×C61#38612yes—
395Dic61—21no—
396Dic61—21no—
397Dic61—42no—
398Dic61—42no—
399Dic61C2×#12011yescharacteristic
400Dic61C2×#12112yes—
401Dic61C2×#12311yescharacteristic
402C23×M16—611no—
403C22×C22⋊Q8—611no—
404C22×#101—612no—
405C2×#407—611no—
406#1901—614no—
407#1901—614no—
408C2×#343—612no—
409C2×C61—22no—
410C2×C61—22no—
411C2×C61—41no—
412C2×C61C2×#38611yescharacteristic
413C2×C61C22×#10111yescharacteristic
414C2×C61C2×#41311yescharacteristic
415D61—22no—
416D61—22no—
417D61—41no—
418D61#190114yescomplemented
419C23×Q8—611no—
420C24×C4—611no—
421C22×M16—612no—
422C22×M16—612no—
423C22×M16—612no—
424C22×M16—612no—
425C22×M16—1228no—
426C22×M16—1221no—
427C22×M16—1221no—
428C22×M16—1221no—
429C23×C8—1221no—
430C2×C22⋊Q8—611no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—612no—
433C2×C22⋊Q8—611no—
434C2×C22⋊Q8—612no—
435C2×C22⋊Q8—1221no—
436C2×C22⋊Q8—1221no—
437C2×C22⋊Q8—1221no—
438C2×C22⋊Q8—1221no—
439C2×C22⋊Q8—1221no—
440C2×C22⋊Q8—1221no—
441C2×C22⋊Q8—1221no—
442C2×C22⋊Q8—1221no—
443C2×C22⋊Q8#692311yescharacteristic
444C22×C4⋊C4—612no—
445C22×C4⋊C4—611no—
446C22×C22⋊C4—612no—
447C2×#101—618no—
448C2×#101—1228no—
449#407—612no—
450#407—612no—
451#407—1221no—
452#407—1221no—
453C2×C22⋊C8—1221no—
454C2×C22⋊C8—1221no—
455#343—618no—
456C61C2×#190111yescharacteristic, complemented, Sylow
457C25—611no—
458C22×Q8—611no—
459C22×Q8—612no—
460C22×Q8—1221no—
461C22×Q8—1221no—
462C22×Q8—1221no—
463C22×Q8—1221no—
464C22×Q8—1224no—
465C22×Q8—1224no—
466C22×Q8C2×#692311yescharacteristic
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—612no—
481C23×C4—612no—
482C23×C4—1224no—
483C23×C4—1224no—
484C23×C4C2×#692311yescharacteristic
485C2×M16—614no—
486C2×M16—618no—
487C2×M16—614no—
488C2×M16—1228no—
489C2×M16—1228no—
490C2×M16—1222no—
491C2×M16—1224no—
492C2×M16—1222no—
493C2×M16—1222no—
494C2×M16—1228no—
495C2×M16—1228no—
496C2×M16—1228no—
497C2×M16—1222no—
498C2×M16—1224no—
499C2×M16—1224no—
500C22×C8—1222no—
501C22×C8—1222no—
502C22×C8—1222no—
503C22×C8—1228no—
504C22×C8—1222no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—1222no—
510C22⋊Q8—1222no—
511C22⋊Q8—1222no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514C22⋊Q8—1222no—
515C22⋊Q8—1222no—
516C22⋊Q8—1222no—
517C22⋊Q8—1221no—
518C22⋊Q8—1221no—
519C22⋊Q8—1221no—
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—
529C2×C4⋊C4—612no—
530C2×C4⋊C4—612no—
531C2×C4⋊C4—612no—
532C2×C4⋊C4—612no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1222no—
539C2×C4⋊C4—1222no—
540C2×C4⋊C4—1222no—
541C2×C4⋊C4—1222no—
542C2×C4⋊C4C2×#692312yes—
543C2×C4⋊C4C2×#692311yescharacteristic
544C2×C22⋊C4—612no—
545C2×C22⋊C4—612no—
546C2×C22⋊C4—612no—
547C2×C22⋊C4—1222no—
548C2×C22⋊C4—1222no—
549C2×C22⋊C4—1222no—
550C2×C22⋊C4—1222no—
551C2×C22⋊C4C2×#692312yes—
552#101—12216no—
553C22⋊C8—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1222no—
556C22⋊C8—1222no—
557C24—611no—
558C24—611no—
559C24—611no—
560C24—611no—
561C24—611no—
562C24—611no—
563C24—1224no—
564C24—1224no—
565C24—2442no—
566C24C22×#692311yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—24no—
570C2×Q8—1224no—
571C2×Q8—1222no—
572C2×Q8—1222no—
573C2×Q8—1224no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8—1224no—
577C2×Q8—2442no—
578C2×Q8—2442no—
579C2×Q8—2444no—
580C2×Q8—2444no—
581C2×Q8—2442no—
582C2×Q8—2442no—
583C22×C4—24no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—614no—
590C22×C4—614no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—612no—
609C22×C4—612no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1224no—
617C22×C4—1224no—
618C22×C4—1224no—
619C22×C4—1224no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1224no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1228no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1224no—
633C22×C4—2444no—
634C22×C4C22⋊#692311yescharacteristic
635C22×C4C22⋊#692311yescharacteristic
636C22×C4C22⋊#692311yescharacteristic
637C22×C4C22⋊#692311yescharacteristic
638C22×C4C22×#692312yes—
639C22×C4C22×#692311yescharacteristic
640C22×C4C22×#692312yes—
641C22×C4C22×#692311yescharacteristic
642M16—618no—
643M16—1228no—
644M16—1224no—
645M16—1228no—
646M16—1228no—
647M16—1224no—
648M16—1224no—
649M16—2444no—
650C2×C8—1228no—
651C2×C8—1224no—
652C2×C8—1228no—
653C2×C8—1228no—
654C2×C8—1224no—
655C2×C8—2444no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—1222no—
661C4⋊C4—1222no—
662C4⋊C4—1222no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—1222no—
677C22⋊C4—1222no—
678C23—22no—
679C23—22no—
680C23—41no—
681C23—611no—
682C23—614no—
683C23—611no—
684C23—611no—
685C23—614no—
686C23—611no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—24416no—
704C23C2×C22⋊#692311yescharacteristic
705C23C2×C22⋊#692311yescharacteristic
706C23C23×#692311yescharacteristic
707Q8—42no—
708Q8—42no—
709Q8—2442no—
710Q8—2444no—
711Q8—2442no—
712Q8—2442no—
713Q8—2442no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—42no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—614no—
730C2×C4—614no—
731C2×C4—612no—
732C2×C4—612no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1224no—
759C2×C4—2444no—
760C2×C4—2444no—
761C2×C4—2444no—
762C2×C4—2444no—
763C2×C4—2442no—
764C2×C4C2×C22⋊#692311yescharacteristic
765C2×C4C2×C22⋊#692311yescharacteristic
766C2×C4C2×C22⋊#692311yescharacteristic
767C2×C4C2×C22⋊#692311yescharacteristic
768C2×C4D4×#692314yes—
769C8—1228no—
770C8—2444no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—44no—
779C22—612no—
780C22—612no—
781C22—612no—
782C22—612no—
783C22—612no—
784C22—1228no—
785C22—1228no—
786C22—1221no—
787C22—1221no—
788C22—1221no—
789C22—1221no—
790C22—1221no—
791C22—1221no—
792C22—1221no—
793C22—2444no—
794C22—2444no—
795C22—2444no—
796C22—2444no—
797C22D61⋊#10112yescomplemented
798C22C22×C22⋊#692311yescharacteristic
799C22C2×D4×#692312yes—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—611no—
805C4—612no—
806C4—611no—
807C4—1221no—
808C4—1221no—
809C4—2442no—
810C4—2442no—
811C4#1684071012yes—
812C4#1684071012yes—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—614no—
817C2—1222no—
818C2—1222no—
819C2—2441no—
820C2C2×#1684071011yescharacteristic
821C2C2×D61⋊#10111yescharacteristic
822C2D61⋊#41311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61C2×#1901
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×D61⋊#101C2semidirect
4. #21461847C2semidirect
5. #21461846C2semidirect
6. #21461522C2semidirect
18. C2×#14519838C22semidirect
25. #16840642C22semidirect
289. C22×D61#101semidirect
368. C22×C61C2×#101semidirect
387. C2×D61C2×#101semidirect
418. D61#1901semidirect
456. C61C2×#1901semidirect
797. C22D61⋊#101semidirect

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
C2×D61⋊#1012
D61⋊#4072
#214618472
#214618462
#214615222
C2×C22⋊Q8×D612
C2×#190161