Finite Group Databasebeta

← #30610961

Subgroups — #30610961

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#21461219C212yesmaximal, complemented
4#21461215C212yesmaximal, complemented
5#21461205C214yesmaximal, complemented
6#21461194C214yesmaximal, complemented
7C2×#16840269C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9C22×C22⋊#6923—21no—
10C22×C4×#6923—21no—
11#16840734C2212yescomplemented
12#16840733—21no—
13#16840733C2212yes—
14#16840732—21no—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)C2212yescomplemented
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923C2212yes—
20C4×C22⋊#6923C2212yescomplemented
21C2×(C2×#6923)⋊C4C2212yescomplemented
22#16840616C2218yescomplemented
23#16840613C2218yescomplemented
24C23×C4×D61C2211yescharacteristic
25#16840269—21no—
26#16840269—21no—
27#16840269—21no—
28#16840269—21no—
29#16840269C412yescomplemented
30#16840269C412yescomplemented
31#16840269C2212yes—
32#16840269C2212yes—
33C2×#14519758—21no—
34C2×#14519753C411yescharacteristic, complemented
35C2×#14519753C2211yescharacteristic
36C2×#14519748C411yescharacteristic, complemented
37C2×#14519748C2211yescharacteristic
38C2×#14519745—21no—
39C2×C4×C22⋊D61—21no—
40C2×C4×C22⋊D61—21no—
41C2×#14519736C411yescharacteristic, complemented
42C22×#41×C61C411yescharacteristic, complemented
43C23×#6923—22no—
44C2×#11758213—22no—
45D61⋊M16—44no—
46C2×#11758217—22no—
47C2×D61⋊C8—22no—
48C2×C22⋊#6923—28no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923—22no—
51C2×C4×#6923—22no—
52C2×C4×#6923—22no—
53C2×C4×#6923—44no—
54#14519834—22no—
55#14519834C2314yes—
56C22⋊#92420—22no—
57C22⋊#92420—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4C2314yes—
60C24×D61D411yescharacteristic
61C22×C22⋊D61—21no—
62C22×C22⋊D61—21no—
63C23×Dic61D411yescharacteristic
64C22×C4×D61—44no—
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77#14519758—22no—
78#14519758—22no—
79#14519758—22no—
80#14519758—22no—
81#14519753—21no—
82#14519753—21no—
83#14519753—21no—
84#14519753—21no—
85#14519753C2×C412yes—
86#14519753C2×C412yescomplemented
87#14519753C2×C412yescomplemented
88#14519753C2312yes—
89#14519748—21no—
90#14519748—21no—
91#14519748—21no—
92#14519748—21no—
93#14519748C2×C412yes—
94#14519748C2×C412yescomplemented
95#14519748C2×C412yescomplemented
96#14519748C2312yes—
97#14519745—22no—
98#14519745—22no—
99#14519745—22no—
100#14519745—22no—
101C4×C22⋊D61—22no—
102C4×C22⋊D61—22no—
103C4×C22⋊D61—22no—
104C4×C22⋊D61—22no—
105C4×C22⋊D61—22no—
106C4×C22⋊D61—22no—
107C4×C22⋊D61—22no—
108C4×C22⋊D61—22no—
109#14519736—21no—
110#14519736—21no—
111#14519736C2×C412yes—
112#14519736C2×C412yescomplemented
113C2×C4⋊Dic61C2×C411yescharacteristic, complemented
114C2×C4⋊Dic61C2×C411yescharacteristic, complemented
115C2×#11758196—21no—
116C2×#11758196—21no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61—21no—
119C2×C22⋊Dic61—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×C4×Dic61—21no—
123C2×#41×C61—21no—
124C2×#41×C61—21no—
125C2×#41×C61—44no—
126C2×#41×C61C2×C412yes—
127C2×#41×C61C2×C412yescomplemented
128C22×Q8×C61C2×C411yescharacteristic, complemented
129C22×D4×C61—21no—
130C22×D4×C61C2×C411yescharacteristic, complemented
131C23×C4×C61—21no—
132C23×C4×C61C2×C411yescharacteristic
133C24×C61—21no—
134C24×C61C22⋊C411yescharacteristic
135C23×D61—24no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61C22⋊C411yescharacteristic
139C23×D61C22⋊C411yescharacteristic
140C23×D61C22⋊C411yescharacteristic
141C23×D61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C22×#6923—28no—
145C22×#6923—24no—
146C22×#6923—44no—
147C22×#6923—44no—
148#41×C61—44no—
149#41×C61—44no—
150#41×C61—44no—
151#41×C61—44no—
152C2×Q8×C61—21no—
153C2×Q8×C61—42no—
154C2×Q8×C61C22×C412yes—
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C2×D4×C61—44no—
160C2×D4×C61C22×C412yes—
161C22×C4×C61—24no—
162C22×C4×C61—21no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—44no—
166C22×C4×C61C22⋊C411yescharacteristic
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—44no—
177C2×C22⋊D61—44no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—42no—
181C22×Dic61C22⋊C411yescharacteristic
182C22×Dic61C22⋊C411yescharacteristic
183C22×Dic61C22⋊C411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C2×C4×D61—24no—
188C2×C4×D61—24no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61C22⋊C411yescharacteristic
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22×C411yescharacteristic
206C2×C4×D61C22×C411yescharacteristic
207C2×C4×D61C22×C411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2411yescharacteristic
215C22⋊#6923—28no—
216C22⋊#6923—28no—
217#11758217—44no—
218C2×#92420—24no—
219C4×#6923—44no—
220C4×#6923—44no—
221#11758213—44no—
222D61⋊C8—44no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61C22×C412yes—
236C4⋊Dic61C22×C412yes—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—41no—
247C23×C61—42no—
248C23×C61—42no—
249C23×C61—42no—
250C23×C61C2×C22⋊C411yescharacteristic
251C23×C61C2×C22⋊C411yescharacteristic
252C23×C61C2×C22⋊C411yescharacteristic
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—416no—
271C22×D61#10414yes—
272C22×D61C2×C22⋊C411yescharacteristic
273C22×D61C2×C22⋊C411yescharacteristic
274C22×D61C2×C22⋊C411yescharacteristic
275C22×D61C22×D411yescharacteristic
276C2×#6923—28no—
277C2×#6923—44no—
278C2×#6923—416no—
279C2×#6923—44no—
280Q8×C61—42no—
281Q8×C61—42no—
282D4×C61—42no—
283D4×C61—44no—
284D4×C61—44no—
285D4×C61—42no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—44no—
293C2×C4×C61—42no—
294C2×C4×C61—44no—
295C2×C4×C61#9914yes—
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C23×C411yescharacteristic
300C22⋊D61—44no—
301C22⋊D61—44no—
302C22⋊D61—44no—
303C22⋊D61—44no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61C2×C22⋊C411yescharacteristic
315C2×Dic61C2×C22⋊C411yescharacteristic
316C2×Dic61C2×C22⋊C411yescharacteristic
317C2×Dic61C22×D411yescharacteristic
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334#92420—44no—
335#17542—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—44no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—84no—
348C22×C61C2×#9912yes—
349C22×C61C2×#10412yes—
350C22×C61C22×C22⋊C411yescharacteristic
351C2×D61—28no—
352C2×D61—21no—
353C2×D61—21no—
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—44no—
362C2×D61—44no—
363C2×D61—44no—
364C2×D61—44no—
365C2×D61—44no—
366C2×D61C2×#10412yes—
367C2×D61C2×#10412yes—
368C2×D61#57512yes—
369#6923—48no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—42no—
373C4×C61C2×#9912yes—
374C4×C61C2×#9912yes—
375Dic61—21no—
376Dic61—21no—
377Dic61—21no—
378Dic61—21no—
379Dic61—42no—
380Dic61—42no—
381C2×#525—611no—
382C2×#407—611no—
383C2×C4×C22⋊C4—611no—
384#1508—612no—
385#1507—612no—
386#1504—614no—
387#1501—614no—
388C2×C61—22no—
389C2×C61—22no—
390C2×C61—41no—
391C2×C61—82no—
392C2×C61C22×#9911yescharacteristic
393C2×C61#289611yescharacteristic
394C2×C61C22×#10411yescharacteristic
395D61—22no—
396D61—22no—
397D61—22no—
398D61—41no—
399C22×#41#692311yescharacteristic, complemented
400C24×C4—611no—
401C22×M16—1221no—
402#525—612no—
403#525—612no—
404#525—612no—
405#525—612no—
406#525—1221no—
407#525—1221no—
408#525—1221no—
409#525—1221no—
410C2×#123—1221no—
411C2×C22⋊Q8—611no—
412C2×C22⋊Q8—611no—
413C2×#121—611no—
414C2×#121—611no—
415C2×#120—1221no—
416C2×C4×D4—1221no—
417C2×C4×D4—1221no—
418C2×#117—611no—
419C22×C22⋊C4—1221no—
420C22×C42—1221no—
421#407—612no—
422#407—612no—
423#407—1221no—
424#407—1221no—
425C2×C22⋊C8—612no—
426C2×C22⋊C8—1221no—
427C4×C22⋊C4—612no—
428C4×C22⋊C4—612no—
429C4×C22⋊C4—1221no—
430C4×C22⋊C4—1221no—
431C2×#95—612no—
432#328—618no—
433#327—618no—
434C61#1754211yescharacteristic, complemented, Sylow
435C25—611no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—44no—
439C2×#41C2×#692312yes—
440C2×#41C2×#692312yescomplemented
441C22×Q8C2×#692311yescharacteristic, complemented
442C22×D4—21no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4C2×#692311yescharacteristic, complemented
446C23×C4—21no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—1222no—
461C23×C4—2444no—
462C23×C4C2×#692311yescharacteristic
463C2×M16—1222no—
464C2×M16—1222no—
465C2×M16—2444no—
466C22×C8—1222no—
467#123—1222no—
468#123—1222no—
469#123—1222no—
470#123—1222no—
471C22⋊Q8—612no—
472C22⋊Q8—612no—
473C22⋊Q8—612no—
474C22⋊Q8—612no—
475C22⋊Q8—1221no—
476C22⋊Q8—1221no—
477C22⋊Q8—1221no—
478C22⋊Q8—1221no—
479#121—612no—
480#121—612no—
481#121—612no—
482#121—612no—
483#121—1221no—
484#121—1221no—
485#121—1221no—
486#121—1221no—
487#120—1222no—
488#120—1222no—
489#120—1222no—
490#120—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499#117—612no—
500#117—612no—
501#117—1221no—
502#117—1221no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1222no—
513C2×C22⋊C4—1228no—
514C2×C22⋊C4—1221no—
515C2×C42—1221no—
516C2×C42—1222no—
517C2×C42—1222no—
518C2×C42—2444no—
519C22⋊C8—614no—
520C22⋊C8—1222no—
521C22⋊C8—1222no—
522C22⋊C8—1222no—
523#95—614no—
524#95—1222no—
525C24—21no—
526C24—611no—
527C24—611no—
528C24—611no—
529C24—611no—
530C24—611no—
531C24—611no—
532C24—1224no—
533C24—2442no—
534C24—2442no—
535C24C22⋊#692311yescharacteristic
536#41—44no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—42no—
542C2×Q8C22×#692312yes—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—42no—
547C2×D4—44no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1222no—
551C2×D4—1222no—
552C2×D4—2444no—
553C2×D4—2444no—
554C2×D4C22×#692312yes—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—44no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—1224no—
583C22×C4—1224no—
584C22×C4—1224no—
585C22×C4—1228no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4—2442no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2444no—
600C22×C4—2444no—
601C22×C4C22⋊#692311yescharacteristic
602C22×C4C22⋊#692311yescharacteristic
603C22×C4C22⋊#692311yescharacteristic
604C22×C4C22×#692311yescharacteristic
605C22×C4C22×#692311yescharacteristic
606C22×C4C22×#692311yescharacteristic
607M16—2444no—
608M16—2444no—
609C2×C8—1224no—
610C2×C8—2444no—
611C4⋊C4—612no—
612C4⋊C4—612no—
613C4⋊C4—1222no—
614C4⋊C4—1222no—
615C4⋊C4—1222no—
616C4⋊C4—1222no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1228no—
628C22⋊C4—1228no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C42—1222no—
632C42—1222no—
633C42—2444no—
634C42—2444no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—611no—
643C23—611no—
644C23—611no—
645C23—614no—
646C23—611no—
647C23—1222no—
648C23—1222no—
649C23—1222no—
650C23—1222no—
651C23—1222no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—24416no—
665C23C2×C22⋊#692311yescharacteristic
666C23C2×C22⋊#692311yescharacteristic
667C23C2×C22⋊#692311yescharacteristic
668Q8—42no—
669Q8—42no—
670D4—42no—
671D4—44no—
672D4—44no—
673D4—42no—
674D4—2444no—
675D4—2444no—
676D4—2444no—
677D4—2444no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—611no—
688C2×C4—611no—
689C2×C4—611no—
690C2×C4—611no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1228no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2442no—
717C2×C4—2444no—
718C2×C4—2444no—
719C2×C4—24416no—
720C2×C4—2442no—
721C2×C4#1451983514yes—
722C2×C4C2×C22⋊#692311yescharacteristic
723C2×C4C2×C22⋊#692311yescharacteristic
724C2×C4C2×C22⋊#692311yescharacteristic
725C2×C4C23×#692311yescharacteristic
726C8—2444no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—44no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—84no—
739C22—612no—
740C22—612no—
741C22—612no—
742C22—1228no—
743C22—1221no—
744C22—1221no—
745C22—1221no—
746C22—1221no—
747C22—1221no—
748C22—1221no—
749C22—1221no—
750C22—1221no—
751C22—1221no—
752C22—2444no—
753C22—2444no—
754C22—2444no—
755C22—2444no—
756C22—2444no—
757C22C2×#1451983512yes—
758C22D61⋊#10412yes—
759C22C22×C22⋊#692311yescharacteristic
760C4—21no—
761C4—21no—
762C4—42no—
763C4—1221no—
764C4—1221no—
765C4—1221no—
766C4—1221no—
767C4—2448no—
768C4—2442no—
769C4—2442no—
770C4C2×#1451983512yes—
771C4C2×#1451983512yes—
772C2—22no—
773C2—22no—
774C2—41no—
775C2—82no—
776C2—1222no—
777C2—1222no—
778C2—1222no—
779C2—2441no—
780C2C22×#1451983511yescharacteristic
781C2#2146243911yescharacteristic
782C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC22×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840269C2
cosocleC2×C4×D61C24
hypercenterC22×#41#6923
hypocenterC61#17542
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. D61⋊#407C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21461219C2semidirect
4. #21461215C2semidirect
5. #21461205C2semidirect
6. #21461194C2semidirect
11. #16840734C22semidirect
16. D61⋊(C22⋊C8)C22semidirect
20. C4×C22⋊#6923C22semidirect
21. C2×(C2×#6923)⋊C4C22semidirect
22. #16840616C22semidirect
23. #16840613C22semidirect
29. #16840269C4semidirect
30. #16840269C4semidirect
34. C2×#14519753C4semidirect
36. C2×#14519748C4semidirect
41. C2×#14519736C4semidirect
42. C22×#41×C61C4semidirect
86. #14519753C2×C4semidirect
87. #14519753C2×C4semidirect
94. #14519748C2×C4semidirect
95. #14519748C2×C4semidirect
112. #14519736C2×C4semidirect
113. C2×C4⋊Dic61C2×C4semidirect
114. C2×C4⋊Dic61C2×C4semidirect
127. C2×#41×C61C2×C4semidirect
128. C22×Q8×C61C2×C4semidirect
130. C22×D4×C61C2×C4semidirect
399. C22×#41#6923semidirect
434. C61#17542semidirect
440. C2×#41C2×#6923semidirect
441. C22×Q8C2×#6923semidirect
445. C22×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×C4×C22⋊#69232
#214612192
#214612152
#214612052
#214611942
C2×#168402692
#1754261