Finite Group Databasebeta

← #29645888

Subgroups — #29645888

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839726C211yesmaximal, characteristic, complemented
3#21444155C214yesmaximal, complemented
4#21444148C212yesmaximal, complemented
5#21444145C212yesmaximal, complemented
6#21444135C214yesmaximal, complemented
7C2×C61×#407C211yesmaximal, characteristic, complemented
8C23×C22⋊D61C411yescharacteristic
9C23×C4×D61C411yescharacteristic
10C22×#11758194—21no—
11C2×C4×C22⋊D61—21no—
12C2×C4×C22⋊D61—21no—
13C2×C4×C22⋊D61—21no—
14C2×C4×C22⋊D61—21no—
15C2×C4×C22⋊D61—21no—
16C2×C4×C22⋊D61—21no—
17C2×C4×C22⋊D61—21no—
18C2×C4×C22⋊D61—21no—
19C2×C4×C22⋊D61C412yes—
20C2×C4×C22⋊D61C412yes—
21C2×C4×C22⋊D61C2212yes—
22C2×C4×C22⋊D61C2212yes—
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C411yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×C4×Dic61C411yescharacteristic
27#16839726—21no—
28#16839726—21no—
29#16839726C2212yes—
30#16839726C2212yescomplemented
31C2×C22⋊#92418—21no—
32C2×C22⋊#92418C2212yescomplemented
33#16839487C2218yescomplemented
34#16839485C2218yescomplemented
35C24×C4×C61C2211yescharacteristic
36C22×M16×C61—21no—
37C61×#407—21no—
38C61×#407—21no—
39C61×#407C2212yes—
40C61×#407C2212yescomplemented
41C2×C22⋊C8×C61—21no—
42C2×C22⋊C8×C61C2212yescomplemented
43C24×D61C2×C411yescharacteristic
44C22×C22⋊D61—21no—
45C22×C22⋊D61—21no—
46C22×C22⋊D61—21no—
47C22×C22⋊D61—21no—
48C22×C22⋊D61—28no—
49C22×C22⋊D61C2×C412yes—
50C22×C22⋊D61C2×C412yes—
51C23×Dic61C2×C411yescharacteristic
52C23×Dic61C2×C411yescharacteristic
53C23×Dic61C2×C411yescharacteristic
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—44no—
59C22×C4×D61C2×C412yes—
60C22×C4×D61C2×C412yes—
61C2×#11758194—22no—
62C2×#11758194—22no—
63C2×#11758194—44no—
64C22×#92418—22no—
65C4×C22⋊D61—22no—
66C4×C22⋊D61—22no—
67C4×C22⋊D61—22no—
68C4×C22⋊D61—22no—
69C4×C22⋊D61—22no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—22no—
72C4×C22⋊D61—22no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—22no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77C4×C22⋊D61—22no—
78C4×C22⋊D61—22no—
79C4×C22⋊D61—22no—
80C4×C22⋊D61—22no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196C2×C412yes—
86C2×#11758196C2312yes—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61C2×C412yes—
92C2×C22⋊Dic61C2×C412yes—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198C2×C412yes—
98C2×#11758198C2312yes—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2×C412yes—
104C2×C4×Dic61C2×C412yes—
105C22⋊#92418—22no—
106C22⋊#92418—22no—
107C22⋊#92418—22no—
108C22⋊#92418C2314yes—
109C25×C61C2×C411yescharacteristic
110C23×C4×C61—44no—
111C23×C4×C61C2×C411yescharacteristic
112C23×C4×C61C2×C411yescharacteristic
113C23×C4×C61C2×C411yescharacteristic
114C23×C4×C61D411yescharacteristic
115C23×C4×C61D411yescharacteristic
116C23×C4×C61D411yescharacteristic
117C23×C4×C61D411yescharacteristic
118C23×C4×C61D411yescharacteristic
119C23×C4×C61D411yescharacteristic
120C23×C4×C61D411yescharacteristic
121C23×C4×C61D411yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C2×M16×C61—22no—
126C2×M16×C61—22no—
127C2×M16×C61—44no—
128C22×C8×C61—22no—
129C22⋊C8×C61—22no—
130C22⋊C8×C61—22no—
131C22⋊C8×C61—22no—
132C22⋊C8×C61C2314yes—
133C24×C61—24no—
134C24×C61—42no—
135C24×C61—42no—
136C24×C61C22⋊C411yescharacteristic
137C24×C61C22⋊C411yescharacteristic
138C24×C61C22⋊C411yescharacteristic
139C24×C61C22⋊C411yescharacteristic
140C24×C61C22×C411yescharacteristic
141C24×C61C22×C411yescharacteristic
142C24×C61C22×C411yescharacteristic
143C23×D61—21no—
144C23×D61—21no—
145C23×D61—24no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61C22×C412yes—
149C22×C4×C61—24no—
150C22×C4×C61—24no—
151C22×C4×C61—24no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61C22⋊C411yescharacteristic
164C22×C4×C61C22⋊C411yescharacteristic
165C22×C4×C61C22⋊C411yescharacteristic
166C22×C4×C61C22⋊C411yescharacteristic
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22⋊C411yescharacteristic
171C22×C4×C61C22⋊C411yescharacteristic
172C22×C4×C61C22⋊C411yescharacteristic
173C22×C4×C61C22⋊C411yescharacteristic
174C22×C4×C61C22⋊C411yescharacteristic
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2411yescharacteristic
191C2×C22⋊D61—28no—
192C2×C22⋊D61—28no—
193C2×C22⋊D61—28no—
194C2×C22⋊D61—28no—
195C2×C22⋊D61—22no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61M1618yescomplemented
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—42no—
211C22×Dic61—42no—
212C22×Dic61C22×C412yes—
213C22×Dic61C22×C412yes—
214C22×Dic61C22×C412yes—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—44no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C2×C4×D61—44no—
223C2×C4×D61—44no—
224C2×C4×D61—44no—
225M16×C61—44no—
226M16×C61—44no—
227C2×C8×C61—24no—
228C2×C8×C61—44no—
229C22⋊Dic61—22no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61—22no—
244C4×Dic61—22no—
245#11758194—44no—
246#11758194—44no—
247C2×#92418—24no—
248C2×#92418—44no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—416no—
270C23×C61C2×C22⋊C411yescharacteristic
271C23×C61C2×C22⋊C411yescharacteristic
272C23×C61C2×C22⋊C411yescharacteristic
273C23×C61C2×C22⋊C411yescharacteristic
274C23×C61C2×C22⋊C411yescharacteristic
275C23×C61C2×C22⋊C411yescharacteristic
276C23×C61C2×M1614yes—
277C23×C61C23×C411yescharacteristic
278C22×D61—24no—
279C22×D61—24no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—42no—
283C22×D61—416no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61C2×M1614yescomplemented
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
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—22no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61#9914yes—
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C22⋊D61—28no—
327C22⋊D61—28no—
328C22⋊D61—28no—
329C22⋊D61—28no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61C2×M1614yescomplemented
343C4×D61—44no—
344C4×D61—44no—
345C4×D61—44no—
346C4×D61—44no—
347C8×C61—44no—
348#92418—44no—
349#17362—611nomaximal, Sylow
350C22×C61—28no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
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×C61—44no—
369C22×C61—44no—
370C22×C61—44no—
371C22×C61—44no—
372C22×C61—44no—
373C22×C61#40712yes—
374C22×C61#40712yes—
375C22×C61C2×#9912yes—
376C22×C61#41312yes—
377C22×C61C22×C22⋊C411yescharacteristic
378C22×C61C22×M1612yes—
379C2×D61—24no—
380C2×D61—44no—
381C2×D61—48no—
382C2×D61—48no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—44no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61C2×#9912yes—
393C4×C61C2×#9912yes—
394Dic61—24no—
395Dic61—42no—
396Dic61—42no—
397C22×C4×D4—611no—
398C2×#407—611no—
399C2×#407D6111yescharacteristic, complemented
400#1465—614no—
401#1463—612no—
402#1462—612no—
403#1459—614no—
404C2×C61—22no—
405C2×C61—22no—
406C2×C61—22no—
407C2×C61—22no—
408C2×C61—22no—
409C2×C61—41no—
410C2×C61—41no—
411C2×C61C2×#40711yescharacteristic
412C2×C61C22×#9911yescharacteristic
413C2×C61C2×#41311yescharacteristic
414D61—44no—
415C23×D4—611no—
416C24×C4—611no—
417C24×C4C2×D6111yescharacteristic
418C22×M16—21no—
419C22×M16—1221no—
420C2×C4×D4—612no—
421C2×C4×D4—612no—
422C2×C4×D4—612no—
423C2×C4×D4—612no—
424C2×C4×D4—1221no—
425C2×C4×D4—1221no—
426C2×C4×D4—1221no—
427C2×C4×D4—1221no—
428C2×C4×D4—1221no—
429C2×C4×D4—1221no—
430C2×C4×D4—1221no—
431C2×C4×D4—1221no—
432C22×C4⋊C4—611no—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—611no—
435C22×C42—611no—
436#407—21no—
437#407—21no—
438#407—612no—
439#407—612no—
440#407—1221no—
441#407—1221no—
442#407C2×D6112yes—
443#407C2×D6112yescomplemented
444C2×C22⋊C8—21no—
445C2×C22⋊C8—612no—
446C2×C22⋊C8—1221no—
447C2×C22⋊C8C2×D6112yescomplemented
448#324—618no—
449#323—618no—
450C61#1736211yescharacteristic, complemented, Sylow
451C25—611no—
452C25C4×D6111yescharacteristic
453C22×D4—612no—
454C22×D4—612no—
455C22×D4—1228no—
456C22×D4—1221no—
457C22×D4—1221no—
458C22×D4—1221no—
459C22×D4—1221no—
460C23×C4—44no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—612no—
465C23×C4—612no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4—2444no—
471C23×C4C4×D6111yescharacteristic
472C23×C4C4×D6111yescharacteristic
473C23×C4C4×D6111yescharacteristic
474C23×C4D24411yescharacteristic
475C23×C4D24411yescharacteristic
476C23×C4D24411yescharacteristic
477C23×C4D24411yescharacteristic
478C23×C4C22⋊D6111yescharacteristic
479C23×C4C22⋊D6111yescharacteristic
480C23×C4C22⋊D6111yescharacteristic
481C23×C4C22⋊D6111yescharacteristic
482C23×C4C22×D6111yescharacteristic
483C23×C4C22×D6111yescharacteristic
484C23×C4C22×D6111yescharacteristic
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—44no—
488C2×M16—1222no—
489C2×M16—1222no—
490C2×M16—2444no—
491C22×C8—22no—
492C22×C8—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—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C2×C4⋊C4—612no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C22⋊C4—612no—
516C2×C22⋊C4—612no—
517C2×C22⋊C4—612no—
518C2×C22⋊C4—612no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C42—612no—
528C2×C42—612no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42—1221no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—614no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—1222no—
540C22⋊C8C22×D6114yes—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—612no—
545C24—1224no—
546C24—1221no—
547C24—1221no—
548C24—2442no—
549C24—2442no—
550C24#1175819811yescharacteristic
551C24#1175819811yescharacteristic
552C24#1175819811yescharacteristic
553C24#1175819811yescharacteristic
554C24C2×C4×D6111yescharacteristic
555C24C2×C4×D6111yescharacteristic
556C24C2×C4×D6111yescharacteristic
557C2×D4—618no—
558C2×D4—1224no—
559C2×D4—1224no—
560C2×D4—1228no—
561C2×D4—1228no—
562C2×D4—1228no—
563C2×D4—1228no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1224no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—1224no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—2444no—
598C22×C4—2444no—
599C22×C4—2444no—
600C22×C4—2444no—
601C22×C4—2444no—
602C22×C4—2444no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4#1175819811yescharacteristic
606C22×C4#1175819811yescharacteristic
607C22×C4#1175819811yescharacteristic
608C22×C4#1175819811yescharacteristic
609C22×C4#1175819811yescharacteristic
610C22×C4#1175819811yescharacteristic
611C22×C4#1175819811yescharacteristic
612C22×C4#1175819811yescharacteristic
613C22×C4#1175819811yescharacteristic
614C22×C4#1175819811yescharacteristic
615C22×C4#1175819811yescharacteristic
616C22×C4#1175819811yescharacteristic
617C22×C4C2×C4×D6111yescharacteristic
618C22×C4C2×C4×D6111yescharacteristic
619C22×C4C2×C4×D6111yescharacteristic
620C22×C4C2×D24411yescharacteristic
621C22×C4C2×D24411yescharacteristic
622C22×C4C2×D24411yescharacteristic
623C22×C4C2×D24411yescharacteristic
624C22×C4C2×D24411yescharacteristic
625C22×C4C2×D24411yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C22×C4C2×C22⋊D6111yescharacteristic
629C22×C4C2×C22⋊D6111yescharacteristic
630C22×C4C2×C22⋊D6111yescharacteristic
631C22×C4C2×C22⋊D6111yescharacteristic
632C22×C4C23×D6111yescharacteristic
633M16—44no—
634M16—44no—
635M16—2444no—
636M16—2444no—
637C2×C8—24no—
638C2×C8—44no—
639C2×C8—1224no—
640C2×C8—2444no—
641C4⋊C4—1222no—
642C4⋊C4—1222no—
643C4⋊C4—1222no—
644C4⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C42—1222no—
654C42—1222no—
655C42—1222no—
656C42—1222no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—416no—
678C23—614no—
679C23—1224no—
680C23—1224no—
681C23—1222no—
682C23—1222no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—24416no—
687C23—2442no—
688C23—2442no—
689C23—2442no—
690C23C2×#1175819811yescharacteristic
691C23C2×#1175819811yescharacteristic
692C23C2×#1175819811yescharacteristic
693C23C2×#1175819811yescharacteristic
694C23C2×#1175819811yescharacteristic
695C23C2×#1175819811yescharacteristic
696C23M16×D6114yes—
697C23C22×C4×D6111yescharacteristic
698D4—1228no—
699D4—1228no—
700D4—1228no—
701D4—1228no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—614no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—2444no—
737C2×C4—2444no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2444no—
743C2×C4—2444no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4#1451969114yes—
747C2×C4C2×#1175819811yescharacteristic
748C2×C4C2×#1175819811yescharacteristic
749C2×C4C2×#1175819811yescharacteristic
750C2×C4C2×#1175819811yescharacteristic
751C2×C4C2×#1175819811yescharacteristic
752C2×C4C2×#1175819811yescharacteristic
753C2×C4C22×C22⋊D6111yescharacteristic
754C2×C4C22×D24411yescharacteristic
755C8—44no—
756C8—2444no—
757C22—28no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—1224no—
781C22—2444no—
782C22—2448no—
783C22—2448no—
784C22—2444no—
785C22—2442no—
786C22—2442no—
787C22#1683972512yes—
788C22#1683972512yes—
789C22C2×#1451969112yes—
790C22#1683974412yes—
791C22C22×#1175819811yescharacteristic
792C22C2×M16×D6112yes—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—1224no—
800C4—2442no—
801C4—2442no—
802C4C2×#1451969112yes—
803C4C2×#1451969112yes—
804C2—22no—
805C2—22no—
806C2—22no—
807C2—22no—
808C2—22no—
809C2—41no—
810C2—41no—
811C2—2444no—
812C2C2×#1683972511yescharacteristic
813C2C22×#1451969111yescharacteristic
814C2C2×#1683974411yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#407C2
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC22×C4×C61C24
hypercenterC2×#407D61
hypocenterC61#17362
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#16839726C2semidirect
3. #21444155C2semidirect
4. #21444148C2semidirect
5. #21444145C2semidirect
6. #21444135C2semidirect
7. C2×C61×#407C2semidirect
30. #16839726C22semidirect
32. C2×C22⋊#92418C22semidirect
33. #16839487C22semidirect
34. #16839485C22semidirect
40. C61×#407C22semidirect
42. C2×C22⋊C8×C61C22semidirect
202. C2×C22⋊D61M16semidirect
289. C22×D61C2×M16semidirect
342. C2×Dic61C2×M16semidirect
399. C2×#407D61semidirect
443. #407C2×D61semidirect
447. C2×C22⋊C8C2×D61semidirect
450. C61#17362semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C2×#168397262
#214441552
#214441482
#214441452
#214441352
C2×C61×#4072
#1736261