Finite Group Databasebeta

← #30615209

Subgroups — #30615209

Order 15616.

1802 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#431C211yesmaximal, characteristic, complemented
2#21462268C211yesmaximal, characteristic, complemented
3#21461722C212yesmaximal, complemented
4#21461687C214yesmaximal, complemented
5#21461657C212yesmaximal
6C4×#14519839C214yesmaximal, complemented
7C2×C4×D4×D61C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840781—21no—
10#16840780—21no—
11#16840779—21no—
12#16840778—21no—
13D61⋊(C4⋊C8)C2212yescomplemented
14C2×#14519839C2218yes—
15D61⋊(C22⋊C8)C2212yes—
16C4×D61⋊C8C2212yescomplemented
17#16840708C2212yescomplemented
18#16840706—21no—
19#16840704—21no—
20#16840704C2212yes—
21C4×C4⋊#6923—21no—
22C4×C4⋊#6923C2212yescomplemented
23#16840635C2218yescomplemented
24C22×D4×D61C2211yescharacteristic
25C23×C4×D61—21no—
26C2×C4×D244C411yescharacteristic, complemented
27C2×D4×Dic61C411yescharacteristic, complemented
28C2×#14519739C411yescharacteristic, complemented
29C2×C4×C22⋊D61—21no—
30C2×#14519737—21no—
31C4×D4×D61—21no—
32C4×D4×D61—21no—
33C4×D4×D61—21no—
34C4×D4×D61—21no—
35C4×D4×D61C412yescomplemented
36C4×D4×D61C412yescomplemented
37C4×D4×D61C2212yes—
38C4×D4×D61C2212yes—
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C22⋊C4×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×D4×C61C411yescharacteristic, complemented
43C2×D61⋊C8C2314yes—
44#14519856—44no—
45C2×C4⋊#6923—22no—
46C2×C4⋊#6923—22no—
47C2×C4⋊#6923C2314yes—
48C2×C22⋊#6923—22no—
49C2×C4×#6923—22no—
50#14519844—22no—
51C4⋊#92420—22no—
52#14519839—216no—
53#14519834—22no—
54C22⋊#92420—22no—
55C4×#92420—22no—
56C4×#92420—22no—
57(C2×#6923)⋊C4—22no—
58(C2×#6923)⋊C4—22no—
59C24×D61—21no—
60C22×D244C2×C411yescharacteristic
61C22×C22⋊D61—21no—
62C2×D4×D61—28no—
63C2×D4×D61—21no—
64C2×D4×D61—21no—
65C2×D4×D61C2×C412yes—
66C2×D4×D61C2312yes—
67C23×Dic61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—44no—
76C22×C4×D61—44no—
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61C2311yescharacteristic
80C4×D244—21no—
81C4×D244—21no—
82C4×D244C2×C412yes—
83C4×D244C2×C412yes—
84D4×Dic61—21no—
85D4×Dic61—21no—
86D4×Dic61C2×C412yes—
87D4×Dic61C2×C412yes—
88#14519739—21no—
89#14519739—21no—
90#14519739C2×C412yes—
91#14519739C2×C412yes—
92C4×C22⋊D61—22no—
93C4×C22⋊D61—22no—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96#14519737—22no—
97#14519737—22no—
98#14519737—22no—
99#14519737—22no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×#11758196—21no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61C2×C412yes—
105C4⋊C4×D61C2312yes—
106C2×C22⋊Dic61—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C22⋊C4×D61—22no—
110C22⋊C4×D61—22no—
111C22⋊C4×D61—22no—
112C22⋊C4×D61—22no—
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C42×D61C2×C411yescharacteristic
117C42×D61C2×C411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C42×D61D411yescharacteristic
122C42×D61C2311yescharacteristic
123C42×D61C2311yescharacteristic
124C22×D4×C61C2×C411yescharacteristic
125C23×C4×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61C2×C412yes—
129C4×D4×C61C2×C412yes—
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2×C411yescharacteristic
133C24×C61—21no—
134C23×D61—28no—
135C23×D61—21no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—44no—
139C23×D61—42no—
140C23×D61—42no—
141C23×D61C2×D411yescharacteristic
142C22×#6923—24no—
143C2×D4×C61—24no—
144C2×D4×C61—21no—
145C2×D4×C61C22×C412yes—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—44no—
150C22×C4×C61C22⋊C411yescharacteristic
151C22×C4×C61C22⋊C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C2×C22⋊D61—28no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C22×Dic61—21no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—44no—
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163D4×D61—28no—
164D4×D61—28no—
165D4×D61—24no—
166D4×D61—24no—
167D4×D61—24no—
168D4×D61#4118yes—
169C2×D244—21no—
170C2×D244—24no—
171C2×D244C22×C412yes—
172C2×C4×D61—24no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—44no—
183C2×C4×D61—44no—
184C2×C4×D61—48no—
185C2×C4×D61—48no—
186C2×C4×D61—44no—
187C2×C4×D61—44no—
188C2×C4×D61—44no—
189C2×C4×D61—44no—
190C2×C4×D61C22⋊C411yescharacteristic
191C2×C4×D61C22⋊C411yescharacteristic
192C2×C4×D61C22⋊C411yescharacteristic
193C2×C4×D61C22⋊C411yescharacteristic
194C2×C4×D61D814yes—
195C2×C4×D61SD1614yes—
196C2×C4×D61C22×C411yescharacteristic
197C2×C4×D61C2×D411yescharacteristic
198C2×C4×D61C2×D411yescharacteristic
199C2×C4×D61C2×D411yescharacteristic
200C2×C4×D61C2×D411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2411yescharacteristic
204C22⋊#6923—44no—
205C2×#92420—24no—
206C4⋊#6923—28no—
207C4⋊#6923—44no—
208C4⋊#6923—44no—
209C4×#6923—44no—
210D61⋊C8—28no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61C22×C412yes—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C42×C61C22⋊C411yescharacteristic
216C42×C61C22⋊C411yescharacteristic
217C42×C61C22×C411yescharacteristic
218C42×C61C22×C411yescharacteristic
219C22⋊Dic61—22no—
220C22⋊Dic61—22no—
221#11758198—22no—
222#11758198—22no—
223#11758198—22no—
224#11758198—22no—
225C4⋊Dic61—21no—
226C4⋊Dic61C22×C412yes—
227#11758196—22no—
228#11758196—22no—
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22⋊C411yescharacteristic
234C4×Dic61C22⋊C411yescharacteristic
235C4×Dic61C22×C411yescharacteristic
236C4×Dic61C22×C411yescharacteristic
237C4×Dic61C2×D411yescharacteristic
238C4×Dic61C2×D411yescharacteristic
239C4×Dic61C2×D411yescharacteristic
240C4×Dic61C2×D411yescharacteristic
241C23×C61—24no—
242C23×C61—22no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61C2×C22⋊C411yescharacteristic
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—24no—
249C22×D61—28no—
250C22×D61—22no—
251C22×D61—28no—
252C22×D61—44no—
253C22×D61—416no—
254C22×D61—416no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—44no—
260C22×D61—44no—
261C22×D61C2×C22⋊C411yescharacteristic
262C22×D61C2×D812yes—
263C22×D61C2×SD1612yes—
264C22×D61C22×D411yescharacteristic
265C2×#6923—44no—
266C2×#6923—44no—
267C2×#6923—44no—
268D4×C61—24no—
269D4×C61—22no—
270D4×C61#11714yescomplemented
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—41no—
274C2×C4×C61—42no—
275C2×C4×C61—44no—
276C2×C4×C61—44no—
277C2×C4×C61#10214yescomplemented
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C2×C22⋊C411yescharacteristic
280C2×C4×C61C2×C22⋊C411yescharacteristic
281C2×C4×C61C2×C22⋊C411yescharacteristic
282C2×C4×C61C2×C22⋊C411yescharacteristic
283C2×C4×C61C23×C411yescharacteristic
284C22⋊D61—28no—
285C22⋊D61—28no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—41no—
289C2×Dic61—42no—
290C2×Dic61—44no—
291C2×Dic61—44no—
292C2×Dic61#10214yescomplemented
293C2×Dic61C2×C22⋊C411yescharacteristic
294C2×Dic61C2×C22⋊C411yescharacteristic
295C2×Dic61C2×C22⋊C411yescharacteristic
296C2×Dic61C2×C22⋊C411yescharacteristic
297C2×Dic61C2×C22⋊C411yescharacteristic
298C2×Dic61C22×D411yescharacteristic
299D244—24no—
300D244—22no—
301D244#11714yescomplemented
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—41no—
308C4×D61—41no—
309C4×D61—42no—
310C4×D61—42no—
311C4×D61—44no—
312C4×D61—44no—
313C4×D61—44no—
314C4×D61—44no—
315C4×D61—44no—
316C4×D61#10214yescomplemented
317C4×D61#10214yescomplemented
318C4×D61C2×D812yes—
319C4×D61C2×D812yes—
320C4×D61C2×SD1612yes—
321C4×D61C2×SD1612yes—
322C4×D61C2×#4114yes—
323#92420—44no—
324#20732—611nomaximal, Sylow
325C22×C61—21no—
326C22×C61—21no—
327C22×C61—24no—
328C22×C61—48no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61C2×#10212yes—
332C22×C61C22×C22⋊C411yescharacteristic
333C2×D61—21no—
334C2×D61—21no—
335C2×D61—24no—
336C2×D61—24no—
337C2×D61—24no—
338C2×D61—416no—
339C2×D61—48no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—48no—
343C2×D61—48no—
344C2×D61C2×#10212yes—
345C2×D61#52512yes—
346C2×D61C22×D811yescharacteristic
347C2×D61C22×SD1611yescharacteristic
348C2×D61#57512yes—
349#6923—84no—
350C4×C61—21no—
351C4×C61—21no—
352C4×C61—21no—
353C4×C61—42no—
354C4×C61C2×#10212yes—
355C4×C61C2×#10212yes—
356C4×C61C2×#11712yes—
357Dic61—21no—
358Dic61—21no—
359Dic61—21no—
360Dic61—42no—
361Dic61C2×#10212yes—
362Dic61C2×#10212yes—
363Dic61#52512yes—
364C22×C4×D4—611no—
365C2×#431—611no—
366#2285—611no—
367#1823—612no—
368#1802—614no—
369#1786—612no—
370C4×#102—614no—
371C2×C61—22no—
372C2×C61—44no—
373C2×C61#228011yescharacteristic
374C2×C61C22×#10211yescharacteristic
375C2×C61#289611yescharacteristic
376D61—22no—
377D61—44no—
378D61#310012yes—
379D61#310112yes—
380C23×D4—611no—
381C24×C4—1221no—
382C2×C4×D4—611no—
383C2×C4×D4—612no—
384C2×C4×D4—612no—
385C2×C4×D4—612no—
386C2×C4×D4—612no—
387C2×C4×D4—611no—
388C2×C4×D4—611no—
389C2×C4×D4—1221no—
390C2×C4×D4—1221no—
391C2×C4×D4—1221no—
392C2×C4×D4—1221no—
393C2×C4×D4—1221no—
394C2×C4×D4—1221no—
395C2×C4×D4#692311yescharacteristic, complemented
396C2×#117—1221no—
397C22×C4⋊C4—611no—
398C22×C22⋊C4—1221no—
399C22×C42—611no—
400#431—1221no—
401#431—1221no—
402#431—1221no—
403#431—1221no—
404C2×C4⋊C8—612no—
405C2×#102—618no—
406C2×C22⋊C8—612no—
407C2×C4×C8—612no—
408#384—612no—
409#382—1221no—
410#380—612no—
411#380—1221no—
412C4×C4⋊C4—612no—
413C4×C4⋊C4—1221no—
414#340—618no—
415C61#2073211yescharacteristic, complemented, Sylow
416C25—1221no—
417C22×D4—612no—
418C22×D4—612no—
419C22×D4—611no—
420C22×D4—1221no—
421C22×D4—1221no—
422C22×D4—1221no—
423C22×D4—1228no—
424C22×D4C2×#692311yescharacteristic
425C23×C4—21no—
426C23×C4—611no—
427C23×C4—611no—
428C23×C4—611no—
429C23×C4—1221no—
430C23×C4—1222no—
431C23×C4—1222no—
432C23×C4—1222no—
433C23×C4—1222no—
434C23×C4—1221no—
435C23×C4—1221no—
436C23×C4—1221no—
437C23×C4—2444no—
438C23×C4—2444no—
439C22×C8—614no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—612no—
443C4×D4—612no—
444C4×D4—612no—
445C4×D4—612no—
446C4×D4—612no—
447C4×D4—612no—
448C4×D4—1222no—
449C4×D4—1222no—
450C4×D4—1222no—
451C4×D4—1222no—
452C4×D4—1221no—
453C4×D4—1221no—
454C4×D4—1222no—
455C4×D4—1222no—
456C4×D4—1222no—
457C4×D4—1222no—
458C4×D4—1221no—
459C4×D4—1221no—
460C4×D4—1221no—
461C4×D4—1221no—
462C4×D4C2×#692312yes—
463C4×D4C2×#692312yes—
464#117—2444no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—612no—
467C2×C4⋊C4—612no—
468C2×C4⋊C4—614no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1222no—
473C2×C4⋊C4—1222no—
474C2×C4⋊C4C2×#692311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—1222no—
477C2×C22⋊C4—1222no—
478C2×C22⋊C4—1222no—
479C2×C22⋊C4—1222no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1222no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42—611no—
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—1222no—
496C2×C42C2×#692311yescharacteristic
497C4⋊C8—1222no—
498C4⋊C8—1222no—
499#102—12216no—
500C22⋊C8—1222no—
501C22⋊C8—1222no—
502C4×C8—1222no—
503C4×C8—1222no—
504#95—1222no—
505#95—1222no—
506C24—21no—
507C24—611no—
508C24—1222no—
509C24—1222no—
510C24—1228no—
511C24—1221no—
512C24—2442no—
513C24—2442no—
514C24—2444no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—618no—
518C2×D4—612no—
519C2×D4—1224no—
520C2×D4—1224no—
521C2×D4—1222no—
522C2×D4—1222no—
523C2×D4—1224no—
524C2×D4—1228no—
525C2×D4—1228no—
526C2×D4—1228no—
527C2×D4—1224no—
528C2×D4—1221no—
529C2×D4C22×#692312yes—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—44no—
534C22×C4—611no—
535C22×C4—614no—
536C22×C4—614no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—1224no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1221no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1224no—
562C22×C4—2444no—
563C22×C4—2448no—
564C22×C4—2448no—
565C22×C4—2444no—
566C22×C4—2444no—
567C22×C4—2444no—
568C22×C4—2444no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4—2444no—
573C22×C4—2444no—
574C22×C4C22⋊#692311yescharacteristic
575C22×C4C22⋊#692311yescharacteristic
576C22×C4C22×#692311yescharacteristic
577C2×C8—1224no—
578C2×C8—1228no—
579C4⋊C4—21no—
580C4⋊C4—612no—
581C4⋊C4—1222no—
582C4⋊C4—1222no—
583C4⋊C4—1228no—
584C4⋊C4—1221no—
585C4⋊C4—2444no—
586C4⋊C4—2444no—
587C4⋊C4C22×#692312yes—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—1222no—
591C22⋊C4—1222no—
592C22⋊C4—1222no—
593C22⋊C4—1222no—
594C22⋊C4—1222no—
595C22⋊C4—1222no—
596C22⋊C4—2444no—
597C42—611no—
598C42—611no—
599C42—611no—
600C42—611no—
601C42—611no—
602C42—611no—
603C42—611no—
604C42—611no—
605C42—611no—
606C42—611no—
607C42—611no—
608C42—611no—
609C42—2444no—
610C42C22⋊#692311yescharacteristic
611C42C22⋊#692311yescharacteristic
612C42C22×#692311yescharacteristic
613C42C22×#692311yescharacteristic
614C23—24no—
615C23—22no—
616C23—42no—
617C23—42no—
618C23—611no—
619C23—612no—
620C23—612no—
621C23—611no—
622C23—1222no—
623C23—1222no—
624C23—1228no—
625C23—1224no—
626C23—1228no—
627C23—1222no—
628C23—2442no—
629C23—2442no—
630C23—2442no—
631C23—2444no—
632C23—2444no—
633C23—24416no—
634C23—24416no—
635C23—2444no—
636C23—2442no—
637C23C2×C22⋊#692311yescharacteristic
638D4—24no—
639D4—22no—
640D4—614no—
641D4—1224no—
642D4—1228no—
643D4—1228no—
644D4—1222no—
645D4#1451985614yescomplemented
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—614no—
653C2×C4—611no—
654C2×C4—611no—
655C2×C4—611no—
656C2×C4—614no—
657C2×C4—614no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—614no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—611no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2444no—
676C2×C4—2444no—
677C2×C4—2442no—
678C2×C4—2442no—
679C2×C4—2444no—
680C2×C4—2444no—
681C2×C4—2444no—
682C2×C4—2441no—
683C2×C4—2444no—
684C2×C4—2444no—
685C2×C4—2444no—
686C2×C4—2442no—
687C2×C4—2444no—
688C2×C4—2444no—
689C2×C4#1451983914yescomplemented
690C2×C4C2×C22⋊#692311yescharacteristic
691C2×C4C2×C22⋊#692311yescharacteristic
692C2×C4C2×C22⋊#692311yescharacteristic
693C2×C4C2×C22⋊#692311yescharacteristic
694C2×C4C2×C22⋊#692311yescharacteristic
695C2×C4C23×#692311yescharacteristic
696C8—2444no—
697C22—21no—
698C22—21no—
699C22—24no—
700C22—48no—
701C22—42no—
702C22—42no—
703C22—611no—
704C22—611no—
705C22—612no—
706C22—612no—
707C22—612no—
708C22—1224no—
709C22—1224no—
710C22—1221no—
711C22—1221no—
712C22—1224no—
713C22—2448no—
714C22—2448no—
715C22—2448no—
716C22—24416no—
717C22—2442no—
718C22—2442no—
719C22C2×#1451983912yes—
720C22C22×C22⋊#692311yescharacteristic
721C4—21no—
722C4—21no—
723C4—21no—
724C4—42no—
725C4—612no—
726C4—612no—
727C4—612no—
728C4—1221no—
729C4—1221no—
730C4—1221no—
731C4—4884no—
732C4—2442no—
733C4C2×#1451983912yes—
734C4C2×#1451983912yes—
735C4C2×#1451985612yes—
736C2—22no—
737C2—44no—
738C2—612no—
739C2—612no—
740C2—1222no—
741C2—2444no—
742C2#2146226311yescharacteristic
743C2C22×#1451983911yescharacteristic
744C2#2146243911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61#20732
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. D61⋊#431C2semidirect
2. #21462268C2semidirect
3. #21461722C2semidirect
4. #21461687C2semidirect
6. C4×#14519839C2semidirect
13. D61⋊(C4⋊C8)C22semidirect
16. C4×D61⋊C8C22semidirect
17. #16840708C22semidirect
22. C4×C4⋊#6923C22semidirect
23. #16840635C22semidirect
26. C2×C4×D244C4semidirect
27. C2×D4×Dic61C4semidirect
28. C2×#14519739C4semidirect
35. C4×D4×D61C4semidirect
36. C4×D4×D61C4semidirect
42. C2×C4×D4×C61C4semidirect
270. D4×C61#117semidirect
277. C2×C4×C61#102semidirect
292. C2×Dic61#102semidirect
301. D244#117semidirect
316. C4×D61#102semidirect
317. C4×D61#102semidirect
395. C2×C4×D4#6923semidirect
415. C61#20732semidirect
645. D4#14519856semidirect
689. C2×C4#14519839semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4312
#214622682
#214617222
#214616872
#214616572
C4×#145198392
C2×C4×D4×D612
#2073261