Finite Group Databasebeta

← C4×D61⋊#99 #30614051

Subgroups — C4×D61⋊#99 #30614051

Order 15616.

2242 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
1C2×D61⋊#99C212yesmaximal
2C2×C4×C22⋊#6923C212yesmaximal, complemented
3#21461566C212yesmaximal, complemented
4C4×#14519836C212yesmaximal, complemented
5#21461564C212yesmaximal, complemented
6C4×#14519835C212yesmaximal, complemented
7#21461516C212yesmaximal, complemented
8C2×C4×D4×D61C211yesmaximal, characteristic
9C22×C22⋊#6923C2214yes—
10C22×C4×#6923—22no—
11C2×#14519836C2214yes—
12D61⋊#99C4116yesdirect product factor
13C2×#14519835C2214yes—
14C4×C22⋊#6923—22no—
15C4×C22⋊#6923—22no—
16C4×C22⋊#6923C2214yescomplemented
17C4×C22⋊#6923C2214yescomplemented
18C2×(C2×#6923)⋊C4—22no—
19#16840640C2214yescomplemented
20#16840640C2214yescomplemented
21C22×D4×D61C2211yescharacteristic
22C23×C4×D61C411yescharacteristic, complemented
23C23×C4×D61C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×D4×Dic61C411yescharacteristic, complemented
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61C411yescharacteristic, complemented
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737C411yescharacteristic, complemented
30C2×#14519737C2211yescharacteristic
31C4×D4×D61—22no—
32C4×D4×D61—22no—
33C4×D4×D61—22no—
34C4×D4×D61—22no—
35C2×C4⋊C4×D61C411yescharacteristic, complemented
36C2×C22⋊C4×D61C411yescharacteristic, complemented
37C2×C22⋊C4×D61C2211yescharacteristic
38C2×C42×D61C411yescharacteristic, complemented
39C2×C4×D4×C61C411yescharacteristic, complemented
40C23×#6923—24no—
41C2×C22⋊#6923—24no—
42C2×C22⋊#6923—28no—
43C2×C22⋊#6923C2×C4116yescomplemented
44C2×C22⋊#6923C2318yes—
45C2×C4×#6923—24no—
46C2×C4×#6923—24no—
47C2×C4×#6923—48no—
48#14519836C2×C4116yescomplemented
49#14519835C2×C4116yescomplemented
50(C2×#6923)⋊C4—24no—
51(C2×#6923)⋊C4—24no—
52C24×D61C2×C411yescharacteristic
53C24×D61C2311yescharacteristic
54C22×D244C2311yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2311yescharacteristic
57C2×D4×D61—22no—
58C2×D4×D61—22no—
59C2×D4×D61—24no—
60C2×D4×D61C2×C418yes—
61C23×Dic61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic, complemented
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61—44no—
68C22×C4×D61—44no—
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic, complemented
75C22×C4×D61C2×C411yescharacteristic, complemented
76C22×C4×D61D412yes—
77C22×C4×D61D412yes—
78C22×C4×D61D412yes—
79C22×C4×D61D412yes—
80C22×C4×D61C2311yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C4×D244—22no—
83C4×D244—22no—
84D4×Dic61—22no—
85D4×Dic61—22no—
86#14519739—22no—
87#14519739—22no—
88C4×C22⋊D61—22no—
89C4×C22⋊D61—22no—
90C4×C22⋊D61—22no—
91C4×C22⋊D61—22no—
92#14519737—22no—
93#14519737—22no—
94#14519737—22no—
95#14519737—22no—
96C2×C4⋊Dic61C2×C411yescharacteristic, complemented
97C2×#11758196C2×C411yescharacteristic, complemented
98C2×#11758196C2×C411yescharacteristic, complemented
99C4⋊C4×D61—22no—
100C4⋊C4×D61—22no—
101C2×C22⋊Dic61C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic, complemented
103C2×#11758198C2×C411yescharacteristic, complemented
104C2×#11758198C2×C411yescharacteristic, complemented
105C2×#11758198C2311yescharacteristic
106C2×#11758198C2311yescharacteristic
107C22⋊C4×D61—22no—
108C22⋊C4×D61—22no—
109C22⋊C4×D61—22no—
110C22⋊C4×D61—22no—
111C2×C4×Dic61C2×C411yescharacteristic, complemented
112C2×C4×Dic61C2×C411yescharacteristic, complemented
113C2×C4×Dic61C2×C411yescharacteristic, complemented
114C42×D61—21no—
115C42×D61—21no—
116C42×D61—21no—
117C42×D61—21no—
118C22×D4×C61C2×C411yescharacteristic
119C23×C4×C61C2×C411yescharacteristic
120C23×C4×C61C2×C411yescharacteristic, complemented
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
124C2×C22⋊C4×C61C2×C411yescharacteristic
125C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
126C2×C42×C61C2×C411yescharacteristic, complemented
127C24×C61C22×C411yescharacteristic
128C24×C61C22×C411yescharacteristic
129C23×D61—21no—
130C23×D61—21no—
131C23×D61—22no—
132C23×D61—42no—
133C23×D61—42no—
134C23×D61—42no—
135C23×D61—42no—
136C23×D61C4214yescomplemented
137C23×D61C22×C411yescharacteristic
138C23×D61C22×C411yescharacteristic
139C23×D61C22×C414yes—
140C23×D61C2×D412yes—
141C23×D61C2×D412yes—
142C23×D61#4114yes—
143C23×D61C2411yescharacteristic
144C22×#6923—216no—
145C22×#6923—28no—
146C22×#6923—48no—
147C22×#6923—48no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61C4214yescomplemented
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61C22⋊C412yes—
156C22×C4×C61C22⋊C412yes—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61C4214yescomplemented
167C2×C22⋊D61C22×C414yes—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—42no—
171C22×Dic61—42no—
172C22×Dic61C22⋊C412yes—
173C22×Dic61C22⋊C412yes—
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179D4×D61—216no—
180D4×D61—216no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244C22×C414yes—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—22no—
187C2×C4×D61—24no—
188C2×C4×D61—28no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—44no—
198C2×C4×D61—42no—
199C2×C4×D61—44no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—44no—
203C2×C4×D61—44no—
204C2×C4×D61—44no—
205C2×C4×D61—44no—
206C2×C4×D61—44no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61C4214yescomplemented
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C412yes—
216C2×C4×D61C22⋊C412yes—
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C2×D412yes—
219C2×C4×D61C2×D412yes—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2×D412yes—
222C22⋊#6923—216no—
223C22⋊#6923—28no—
224C22⋊#6923C22×C4116yescomplemented
225C4×#6923—48no—
226C4×#6923—48no—
227C4⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—22no—
230C42×C61—21no—
231C42×C61—21no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238C4⋊Dic61—22no—
239#11758196—22no—
240#11758196—22no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61C2×C4212yes—
254C23×C61C2×C4212yescomplemented
255C23×C61C2×C22⋊C412yes—
256C23×C61#11712yes—
257C23×C61C23×C411yescharacteristic
258C22×D61—22no—
259C22×D61—24no—
260C22×D61—22no—
261C22×D61—24no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—24no—
265C22×D61—24no—
266C22×D61—48no—
267C22×D61—48no—
268C22×D61—42no—
269C22×D61—41no—
270C22×D61—42no—
271C22×D61—41no—
272C22×D61—42no—
273C22×D61—42no—
274C22×D61—48no—
275C22×D61—48no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61C2×C4212yes—
281C22×D61C2×C4212yescomplemented
282C22×D61C2×C22⋊C411yescharacteristic
283C22×D61C2×C22⋊C411yescharacteristic
284C22×D61#11712yes—
285C22×D61C4×D418yes—
286C22×D61C4×D418yes—
287C22×D61C23×C412yes—
288C22×D61C22×D412yes—
289C22×D61C2×#4112yes—
290C2×#6923—216no—
291C2×#6923—48no—
292C2×#6923—48no—
293C2×#6923—432no—
294D4×C61—28no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—24no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—42no—
302C2×C4×C61—41no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61C2×C4212yescomplemented
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C412yes—
310C2×C4×C61C2×C22⋊C411yescharacteristic
311C22⋊D61—28no—
312C22⋊D61—28no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—22no—
316C2×Dic61—24no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—42no—
320C2×Dic61—41no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61C2×C4212yescomplemented
326C2×Dic61C2×C22⋊C411yescharacteristic
327C2×Dic61C2×C22⋊C412yes—
328C2×Dic61C2×C22⋊C411yescharacteristic
329D244—28no—
330C4×D61—24no—
331C4×D61—24no—
332C4×D61—22no—
333C4×D61—24no—
334C4×D61—24no—
335C4×D61—22no—
336C4×D61—24no—
337C4×D61—22no—
338C4×D61—42no—
339C4×D61—42no—
340C4×D61—42no—
341C4×D61—42no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61—42no—
347C4×D61—42no—
348C4×D61—42no—
349C4×D61#9914yescomplemented
350C2×C4×#99—611nomaximal, Sylow
351C22×C61—21no—
352C22×C61—22no—
353C22×C61—21no—
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61C4×C22⋊C414yes—
363C22×C61C22×C4211yescharacteristic
364C22×C61C22×C22⋊C411yescharacteristic
365C22×C61C2×#11711yescharacteristic
366C2×D61—21no—
367C2×D61—22no—
368C2×D61—21no—
369C2×D61—22no—
370C2×D61—216no—
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—22no—
374C2×D61—48no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—48no—
378C2×D61—42no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—48no—
382C2×D61—42no—
383C2×D61C4×C22⋊C412yes—
384C2×D61C4×C22⋊C412yes—
385C2×D61C2×#9912yes—
386C2×D61#41012yes—
387C2×D61C2×C4×D414yes—
388#6923—416no—
389C4×C61—21no—
390C4×C61—22no—
391C4×C61—22no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61C2×#9912yescomplemented
395Dic61—21no—
396Dic61—22no—
397Dic61—22no—
398Dic61—41no—
399Dic61—41no—
400Dic61C2×#9912yescomplemented
401C22×C4×D4—611no—
402C22×#99—612no—
403C2×C4×C22⋊C4—612no—
404C4×#99—612no—
405C4×#99—612no—
406C4×#99—612no—
407C4×#99—612no—
408C2×#342—612no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—24no—
412C2×C61—42no—
413C2×C61C2×C4×C22⋊C411yescharacteristic
414C2×C61C22×#9911yescharacteristic
415C2×C61C2×#41011yescharacteristic
416D61—24no—
417D61—22no—
418D61—42no—
419D61C4×#9914yescomplemented
420C23×D4—611no—
421C24×C4—611no—
422C24×C4—611no—
423C2×C4×D4—611no—
424C2×C4×D4—611no—
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×C4×D4—611no—
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4—1222no—
431C2×C4×D4—1222no—
432C2×C4×D4—1222no—
433C2×C4×D4—1222no—
434C2×C4×D4#692311yescharacteristic, complemented
435C22×C4⋊C4—611no—
436C22×C22⋊C4—614no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4—611no—
439C22×C42—611no—
440C22×C42—1222no—
441C2×#99—614no—
442C2×#99—6116no—
443C2×#99—614no—
444C4×C22⋊C4—614no—
445C4×C22⋊C4—614no—
446C4×C22⋊C4—1222no—
447C4×C22⋊C4—1222no—
448C2×#95—1222no—
449#342—614no—
450#342—614no—
451C61C2×C4×#9911yescharacteristic, complemented, Sylow
452C25—611no—
453C25—611no—
454C22×D4—611no—
455C22×D4—611no—
456C22×D4—618no—
457C22×D4—611no—
458C22×D4—1222no—
459C22×D4—1222no—
460C22×D4—1224no—
461C22×D4C2×#692311yescharacteristic
462C23×C4—611no—
463C23×C4—612no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—612no—
467C23×C4—612no—
468C23×C4—612no—
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—1221no—
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4—1224no—
482C23×C4—2444no—
483C23×C4—2444no—
484C23×C4C2×#692311yescharacteristic
485C23×C4C2×#692311yescharacteristic, complemented
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—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—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4C2×#692311yescharacteristic, complemented
508C2×C22⋊C4—6116no—
509C2×C22⋊C4—618no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—1222no—
517C2×C22⋊C4—1222no—
518C2×C22⋊C4—1222no—
519C2×C22⋊C4—1222no—
520C2×C22⋊C4—1228no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4C2×#692311yescharacteristic
523C2×C22⋊C4C2×#692311yescharacteristic, complemented
524C2×C42—611no—
525C2×C42—611no—
526C2×C42—611no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1224no—
532C2×C42—1224no—
533C2×C42—2448no—
534C2×C42C2×#692311yescharacteristic, complemented
535#99—6116no—
536#99—6116no—
537#95—1224no—
538#95—1224no—
539C24—612no—
540C24—611no—
541C24—614no—
542C24—612no—
543C24—614no—
544C24—611no—
545C24—614no—
546C24—611no—
547C24—1221no—
548C24—1221no—
549C24—1222no—
550C24—2442no—
551C24—2442no—
552C24—2442no—
553C24—2442no—
554C24C22×#692311yescharacteristic
555C24C22×#692311yescharacteristic
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—614no—
559C2×D4—614no—
560C2×D4—614no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—12216no—
564C2×D4—12216no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4C4×#692314yescomplemented
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—611no—
575C22×C4—612no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—612no—
579C22×C4—611no—
580C22×C4—614no—
581C22×C4—612no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—611no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—1228no—
593C22×C4—1224no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1222no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1228no—
606C22×C4—12216no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—2442no—
610C22×C4—2444no—
611C22×C4—2442no—
612C22×C4—2444no—
613C22×C4—2444no—
614C22×C4—2442no—
615C22×C4—2444no—
616C22×C4—2442no—
617C22×C4—2444no—
618C22×C4—2444no—
619C22×C4—2444no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2448no—
626C22×C4—2448no—
627C22×C4C22⋊#692312yes—
628C22×C4C22⋊#692312yes—
629C22×C4C22×#692311yescharacteristic
630C22×C4C22×#692311yescharacteristic
631C22×C4C22×#692311yescharacteristic
632C22×C4C22×#692311yescharacteristic
633C22×C4C22×#692311yescharacteristic
634C4⋊C4—22no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—6116no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1228no—
646C22⋊C4—12216no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C42—21no—
650C42—21no—
651C42—1221no—
652C42—1221no—
653C42—1221no—
654C42—1221no—
655C42—1221no—
656C42—1221no—
657C42—2448no—
658C42—2448no—
659C23—21no—
660C23—21no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—611no—
666C23—612no—
667C23—611no—
668C23—612no—
669C23—612no—
670C23—618no—
671C23—612no—
672C23—612no—
673C23—618no—
674C23—612no—
675C23—1224no—
676C23—1222no—
677C23—1224no—
678C23—1222no—
679C23—1224no—
680C23—1224no—
681C23—1221no—
682C23—1221no—
683C23—2441no—
684C23—2442no—
685C23—2441no—
686C23—2442no—
687C23—2441no—
688C23—2441no—
689C23—2442no—
690C23—2442no—
691C23—2448no—
692C23—2448no—
693C23—2448no—
694C23—2442no—
695C23—2448no—
696C23—2442no—
697C23C2×C4×#692312yes—
698C23C2×C4×#692312yescomplemented
699C23C2×C22⋊#692312yes—
700C23#1451985612yes—
701C23C23×#692311yescharacteristic
702D4—28no—
703D4—1228no—
704D4—1228no—
705D4—1228no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—611no—
719C2×C4—614no—
720C2×C4—612no—
721C2×C4—611no—
722C2×C4—612no—
723C2×C4—1224no—
724C2×C4—1222no—
725C2×C4—1224no—
726C2×C4—1222no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1222no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1224no—
734C2×C4—1222no—
735C2×C4—12216no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2441no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2448no—
753C2×C4—24432no—
754C2×C4—2448no—
755C2×C4—2442no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4C2×C4×#692312yescomplemented
759C2×C4C2×C22⋊#692311yescharacteristic
760C2×C4C2×C22⋊#692312yes—
761C2×C4C2×C22⋊#692311yescharacteristic
762C22—21no—
763C22—22no—
764C22—21no—
765C22—22no—
766C22—22no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—612no—
774C22—612no—
775C22—612no—
776C22—614no—
777C22—612no—
778C22—12216no—
779C22—1224no—
780C22—1224no—
781C22—1222no—
782C22—1221no—
783C22—1222no—
784C22—1221no—
785C22—1222no—
786C22—2442no—
787C22—2442no—
788C22—2448no—
789C22—2442no—
790C22—2442no—
791C22—2448no—
792C22—2448no—
793C22—2441no—
794C22—2441no—
795C22C4×C22⋊#692314yes—
796C22C22×C4×#692311yescharacteristic
797C22C22×C22⋊#692311yescharacteristic
798C22C2×#1451985611yescharacteristic
799C4—21no—
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—612no—
805C4—1222no—
806C4—1221no—
807C4—1222no—
808C4—24416no—
809C4—2441no—
810C4—2441no—
811C4D61⋊#9912yesdirect product factor
812C2—21no—
813C2—21no—
814C2—24no—
815C2—42no—
816C2—614no—
817C2—1224no—
818C2—1222no—
819C2—2442no—
820C2C2×C4×C22⋊#692311yescharacteristic
821C2C2×D61⋊#9911yescharacteristic
822C2D61⋊#41011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC22×C61C22×C42
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC23×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61C2×C4×#99
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊#6923C2semidirect
3. #21461566C2semidirect
4. C4×#14519836C2semidirect
5. #21461564C2semidirect
6. C4×#14519835C2semidirect
7. #21461516C2semidirect
12. D61⋊#99C4direct (N × H)
16. C4×C22⋊#6923C22semidirect
17. C4×C22⋊#6923C22semidirect
19. #16840640C22semidirect
20. #16840640C22semidirect
22. C23×C4×D61C4semidirect
25. C2×D4×Dic61C4semidirect
27. C2×C4×C22⋊D61C4semidirect
29. C2×#14519737C4semidirect
35. C2×C4⋊C4×D61C4semidirect
36. C2×C22⋊C4×D61C4semidirect
38. C2×C42×D61C4semidirect
39. C2×C4×D4×C61C4semidirect
43. C2×C22⋊#6923C2×C4semidirect
48. #14519836C2×C4semidirect
49. #14519835C2×C4semidirect
62. C23×Dic61C2×C4semidirect
74. C22×C4×D61C2×C4semidirect
75. C22×C4×D61C2×C4semidirect
96. C2×C4⋊Dic61C2×C4semidirect
97. C2×#11758196C2×C4semidirect
98. C2×#11758196C2×C4semidirect
102. C2×C22⋊Dic61C2×C4semidirect
103. C2×#11758198C2×C4semidirect
104. C2×#11758198C2×C4semidirect
111. C2×C4×Dic61C2×C4semidirect
112. C2×C4×Dic61C2×C4semidirect
113. C2×C4×Dic61C2×C4semidirect
120. C23×C4×C61C2×C4semidirect
123. C2×C4⋊C4×C61C2×C4semidirect
125. C2×C22⋊C4×C61C2×C4semidirect
126. C2×C42×C61C2×C4semidirect
136. C23×D61C42semidirect
150. C2×D4×C61C42semidirect
166. C2×C22⋊D61C42semidirect
211. C2×C4×D61C42semidirect
224. C22⋊#6923C22×C4semidirect
254. C23×C61C2×C42semidirect
281. C22×D61C2×C42semidirect
307. C2×C4×C61C2×C42semidirect
325. C2×Dic61C2×C42semidirect
349. C4×D61#99semidirect
394. C4×C61C2×#99semidirect
400. Dic61C2×#99semidirect
419. D61C4×#99semidirect
434. C2×C4×D4#6923semidirect
451. C61C2×C4×#99semidirect
485. C23×C4C2×#6923semidirect
507. C2×C4⋊C4C2×#6923semidirect
523. C2×C22⋊C4C2×#6923semidirect
534. C2×C42C2×#6923semidirect
569. C2×D4C4×#6923semidirect
698. C23C2×C4×#6923semidirect
758. C2×C4C2×C4×#6923semidirect
811. C4D61⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D61⋊#992
C2×C4×C22⋊#69232
#214615662
C4×#145198362
#214615642
C4×#145198352
#214615162
C2×C4×D4×D612
C2×C4×#9961