Finite Group Databasebeta

← C2×#21448614 #29838912

Subgroups — C2×#21448614 #29838912

Order 15616.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519761C211yesmaximal, characteristic
2#21448614C2116yesmaximal, direct product factor
3C2×#16839662C211yesmaximal, characteristic
4C2×#16839658C211yesmaximal, characteristic, complemented
5C2×#16839655C211yesmaximal, characteristic, complemented
6C2×#16839653C211yesmaximal, characteristic, complemented
7C2×#16839652C211yesmaximal, characteristic, complemented
8C2×#16839647C211yesmaximal, characteristic, complemented
9C2×#16839645C211yesmaximal, characteristic, complemented
10C2×#16839638C211yesmaximal, characteristic
11C2×#16839636C211yesmaximal, characteristic, complemented
12C2×#16839620C211yesmaximal, characteristic, complemented
13C2×C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519761C4116yescomplemented
21C2×#14519761C2218yes—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839662C2218yes—
40#16839658C2218yescomplemented
41#16839655C2218yescomplemented
42#16839653C2218yescomplemented
43#16839652C2218yescomplemented
44#16839647C2218yescomplemented
45#16839645C2218yescomplemented
46#16839638C2218yes—
47#16839636C2218yescomplemented
48#16839620C2218yescomplemented
49C4×C4⋊Dic61C2218yescomplemented
50C22⋊C4×Dic61C2218yescomplemented
51#16839609C2218yescomplemented
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C61×#388C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C24×D61C2311yescharacteristic
69C22×C22⋊D61—42no—
70C22×C22⋊D61—42no—
71C22×C22⋊D61C2×C418yes—
72C22×C22⋊D61C2314yes—
73C23×Dic61—42no—
74C23×Dic61—42no—
75C23×Dic61C2×C418yescomplemented
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2314yes—
84C22×C4×D61—24no—
85C22×C4×D61—42no—
86C22×C4×D61—42no—
87C22×C4×D61C2314yes—
88#14519761C2×C4164yescomplemented
89C2×C4⋊Dic61—24no—
90C2×C4⋊Dic61C2×C418yescomplemented
91C2×C4⋊Dic61C2×C418yescomplemented
92C2×C4⋊Dic61C2314yes—
93C2×C4⋊Dic61C2314yes—
94C2×C4⋊Dic61C2314yes—
95C2×#11758196—42no—
96C2×#11758196—42no—
97C2×#11758196—42no—
98C2×#11758196C2314yes—
99C2×#11758196C2314yes—
100C2×#11758196C2314yes—
101C2×C22⋊Dic61—24no—
102C2×C22⋊Dic61—42no—
103C2×C22⋊Dic61C2314yes—
104C2×C22⋊Dic61C2314yes—
105C2×#11758198—24no—
106C2×#11758198—42no—
107C2×#11758198—42no—
108C2×#11758198C2×C418yes—
109C2×#11758198C2×C418yes—
110C2×#11758198C2314yes—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×C4×Dic61—42no—
116C2×C4×Dic61—42no—
117C2×C4×Dic61—42no—
118C2×C4×Dic61—42no—
119C2×C4×Dic61C2314yes—
120C2×C4×Dic61C2314yes—
121C2×C4×Dic61C2314yes—
122C2×C4×Dic61C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131C25×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61—42no—
139C2×C4⋊C4×C61C2314yes—
140C2×C22⋊C4×C61—24no—
141C2×C22⋊C4×C61—42no—
142C2×C22⋊C4×C61C2×C418yescomplemented
143C2×C22⋊C4×C61C2314yes—
144C2×C22⋊C4×C61C2314yes—
145C2×C22⋊C4×C61C2314yes—
146C2×C42×C61—24no—
147C2×C42×C61C2314yes—
148#95×C61C2314yes—
149#95×C61C2314yes—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61C22×C414yes—
157C24×C61C2412yes—
158C24×C61C2411yescharacteristic
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61C22×C414yes—
166C23×D61C2412yes—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61C22×C414yes—
183C22×C4×C61C22×C414yes—
184C22×C4×C61#4114yes—
185C22×C4×C61C2412yes—
186C22×C4×C61C2412yes—
187C22×C4×C61C2412yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C2×C22⋊D61—416no—
192C2×C22⋊D61—44no—
193C2×C22⋊D61—44no—
194C2×C22⋊D61C22×C4116yes—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—416no—
213C22×Dic61—44no—
214C22×Dic61—44no—
215C22×Dic61C22×C414yes—
216C22×Dic61C22×C414yes—
217C22×Dic61C22×C414yes—
218C22×Dic61C22×C4116yescomplemented
219C22×Dic61#4114yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C2×C4×D61—28no—
228C2×C4×D61—44no—
229C2×C4×D61—44no—
230C2×C4×D61—416no—
231C4⋊C4×C61—44no—
232C22⋊C4×C61—28no—
233C22⋊C4×C61—44no—
234C22⋊C4×C61C22×C4116yescomplemented
235C42×C61—28no—
236C22⋊Dic61—28no—
237C22⋊Dic61—44no—
238#11758198—28no—
239#11758198—44no—
240#11758198—44no—
241#11758198C22×C4116yes—
242#11758198C22×C4116yes—
243C4⋊Dic61—28no—
244C4⋊Dic61C22×C4116yescomplemented
245C4⋊Dic61C22×C4116yescomplemented
246#11758196—44no—
247#11758196—44no—
248#11758196—44no—
249C4×Dic61—44no—
250C4×Dic61—44no—
251C4×Dic61—44no—
252C4×Dic61—44no—
253C23×C61—28no—
254C23×C61—28no—
255C23×C61—28no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—44no—
263C23×C61—44no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61C23×C414yes—
267C23×C61C23×C412yes—
268C23×C61C2×#4112yes—
269C23×C61C2×#4112yes—
270C23×C61H(5,𝔽2)12yes—
271C23×C61H(5,𝔽2)12yes—
272C23×C61H(5,𝔽2)12yes—
273C23×C612−1+412yes—
274C23×C61C2511yescharacteristic
275C22×D61—28no—
276C22×D61—28no—
277C22×D61—28no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—44no—
285C22×D61—44no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61C23×C414yes—
289C2×C4×C61—28no—
290C2×C4×C61—28no—
291C2×C4×C61—28no—
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—22no—
306C2×C4×C61—22no—
307C2×C4×C61—44no—
308C2×C4×C61—44no—
309C2×C4×C61—44no—
310C2×C4×C61C23×C414yes—
311C2×C4×C61C23×C414yes—
312C2×C4×C61C2×#4114yes—
313C22⋊D61—416no—
314C2×Dic61—28no—
315C2×Dic61—28no—
316C2×Dic61—28no—
317C2×Dic61—28no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—416no—
336C2×Dic61—44no—
337C2×Dic61—44no—
338C2×Dic61—44no—
339C2×Dic61C23×C414yes—
340C2×Dic61C23×C414yes—
341C2×Dic61C23×C414yes—
342C2×Dic61C2×#4114yes—
343C4×D61—416no—
344C2×#2335—611nomaximal, Sylow
345C22×C61—24no—
346C22×C61—24no—
347C22×C61—24no—
348C22×C61—416no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61C4×#4114yes—
354C22×C61#51814yes—
355C22×C61#52014yes—
356C22×C61#53814yes—
357C22×C61#53914yes—
358C22×C61#54014yes—
359C22×C61#54214yes—
360C22×C61C24×C411yescharacteristic
361C22×C61C22×#4111yescharacteristic
362C22×C61C22×#4111yescharacteristic
363C22×C61C2×H(5,𝔽2)11yescharacteristic
364C22×C61C2×H(5,𝔽2)11yescharacteristic
365C22×C61C2×H(5,𝔽2)11yescharacteristic
366C22×C61C2×2−1+411yescharacteristic
367C2×D61—24no—
368C2×D61—24no—
369C2×D61—24no—
370C2×D61—416no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C4×C61—24no—
376C4×C61—24no—
377C4×C61—24no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61—42no—
381Dic61—24no—
382Dic61—24no—
383Dic61—24no—
384Dic61—24no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C22×#123—611no—
389#2335—6116no—
390C2×#390—611no—
391C2×#389—611no—
392C2×#388—611no—
393C2×#388—611no—
394C2×#388—611no—
395C2×#388D6111yescharacteristic, complemented
396C2×#387—611no—
397C2×#387—611no—
398C2×#386—611no—
399C2×#385—611no—
400C2×#380—611no—
401C2×C4×C4⋊C4—611no—
402C2×C4×C22⋊C4—611no—
403C2×C4×C22⋊C4—611no—
404C2×C61—44no—
405C2×C61#233518yescomplemented
406C2×C61C2×C4×#4111yescharacteristic
407C2×C61C2×#51811yescharacteristic
408C2×C61C2×#52011yescharacteristic
409C2×C61C2×#53811yescharacteristic
410C2×C61C2×#53911yescharacteristic
411C2×C61C2×#54011yescharacteristic
412C2×C61C2×#54211yescharacteristic
413D61—44no—
414C23×D4—611no—
415C24×C4—611no—
416C24×C4—611no—
417C2×#123—6116no—
418C2×#123—618no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—611no—
421C22×C4⋊C4—611no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4C2×D6111yescharacteristic
426C22×C22⋊C4—611no—
427C22×C22⋊C4—611no—
428C22×C22⋊C4—611no—
429C22×C22⋊C4—611no—
430C22×C22⋊C4—611no—
431C22×C22⋊C4—611no—
432C22×C22⋊C4—611no—
433C22×C22⋊C4C2×D6111yescharacteristic
434C22×C22⋊C4C2×D6111yescharacteristic
435C22×C22⋊C4C2×D6111yescharacteristic
436C22×C42—611no—
437C22×C42—611no—
438C22×C42—611no—
439C22×C42—611no—
440C22×C42C2×D6111yescharacteristic
441#390—618no—
442#389—618no—
443#388—618no—
444#388—618no—
445#388—618no—
446#388C2×D6118yescomplemented
447#387—618no—
448#387—618no—
449#386—618no—
450#385—618no—
451#380—618no—
452C4×C4⋊C4—618no—
453C4×C22⋊C4—618no—
454C4×C22⋊C4—618no—
455C2×#95—611no—
456C2×#95—611no—
457C2×#95—611no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95C2×D6111yescharacteristic
464C2×#95C2×D6111yescharacteristic
465C61C2×#233511yescharacteristic, complemented, Sylow
466C25—611no—
467C25C22×D6111yescharacteristic
468C22×D4—618no—
469C22×D4—614no—
470C22×D4—2442no—
471C22×D4—2442no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—618no—
477C23×C4—614no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—614no—
482C23×C4—1224no—
483C23×C4—2442no—
484C23×C4—2442no—
485C23×C4—2442no—
486C23×C4—2442no—
487C23×C4C22×D6111yescharacteristic
488C23×C4C22×D6111yescharacteristic
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6111yescharacteristic
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6111yescharacteristic
493#123—6164no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—618no—
496C2×C4⋊C4—618no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—614no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—614no—
503C2×C4⋊C4—1224no—
504C2×C4⋊C4—2442no—
505C2×C4⋊C4—2442no—
506C2×C4⋊C4—2442no—
507C2×C4⋊C4C22×D6114yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—618no—
511C2×C22⋊C4—618no—
512C2×C22⋊C4—614no—
513C2×C22⋊C4—614no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—614no—
516C2×C22⋊C4—614no—
517C2×C22⋊C4—614no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—2442no—
522C2×C22⋊C4—2442no—
523C2×C22⋊C4—2442no—
524C2×C22⋊C4C4×D6118yescomplemented
525C2×C22⋊C4C22×D6114yes—
526C2×C22⋊C4C22×D6114yes—
527C2×C22⋊C4C22×D6114yes—
528C2×C42—24no—
529C2×C42—614no—
530C2×C42—614no—
531C2×C42—614no—
532C2×C42—614no—
533C2×C42—2442no—
534C2×C42—2442no—
535C2×C42—2442no—
536C2×C42—2442no—
537C2×C42C22×D6114yes—
538#95—614no—
539#95—614no—
540#95—614no—
541#95—614no—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95C22×D6114yes—
547#95C22×D6114yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—614no—
555C24—612no—
556C24—1222no—
557C24—1222no—
558C24—1222no—
559C24—1222no—
560C24—1222no—
561C24—1222no—
562C24C2×C4×D6114yes—
563C24C23×D6112yes—
564C24C23×D6111yescharacteristic
565C2×D4—6116no—
566C2×D4—24416no—
567C2×D4—2444no—
568C2×D4—2444no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—614no—
585C22×C4—614no—
586C22×C4—614no—
587C22×C4—614no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—6116no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—1228no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—2444no—
615C22×C4—2444no—
616C22×C4—24416no—
617C22×C4—24416no—
618C22×C4—2444no—
619C22×C4—2444no—
620C22×C4C2×C4×D6114yes—
621C22×C4C2×C4×D6114yes—
622C22×C4#1175822414yes—
623C22×C4C23×D6112yes—
624C22×C4C23×D6112yes—
625C22×C4C23×D6112yes—
626C22×C4C23×D6112yes—
627C22×C4C23×D6112yes—
628C22×C4C23×D6112yes—
629C4⋊C4—44no—
630C4⋊C4—6116no—
631C4⋊C4—6116no—
632C4⋊C4—1228no—
633C4⋊C4—2444no—
634C4⋊C4—2444no—
635C4⋊C4—2444no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—6116no—
639C22⋊C4—6116no—
640C22⋊C4—1228no—
641C22⋊C4—1228no—
642C22⋊C4—2444no—
643C22⋊C4—2444no—
644C22⋊C4—2444no—
645C22⋊C4C2×C4×D61116yescomplemented
646C42—28no—
647C42—2444no—
648C42—2444no—
649C42—2444no—
650C42—2444no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—614no—
665C23—1228no—
666C23—1228no—
667C23—1228no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—2444no—
675C23—2444no—
676C23—2444no—
677C23—2444no—
678C23C22×C4×D6114yes—
679C23C22×C4×D6112yes—
680C23#41×D6112yes—
681C23C2×#1175822412yes—
682C23#1451982212yes—
683C23#1451982312yes—
684C23#1451982312yes—
685C23#1451982412yes—
686C23C24×D6111yescharacteristic
687D4—24416no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—614no—
710C2×C4—614no—
711C2×C4—614no—
712C2×C4—614no—
713C2×C4—1228no—
714C2×C4—1228no—
715C2×C4—1228no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1228no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—24416no—
735C2×C4—24416no—
736C2×C4—2444no—
737C2×C4—2444no—
738C2×C4—2444no—
739C2×C4C22×C4×D6114yes—
740C2×C4C22×C4×D6114yes—
741C2×C4C2×#1175822414yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—1224no—
751C22—1224no—
752C22—1224no—
753C22—24416no—
754C22—2442no—
755C22—2442no—
756C22—2442no—
757C22—2442no—
758C22C4×#1175822414yes—
759C22#1684023614yes—
760C22#1684024114yes—
761C22#1684034614yes—
762C22#1684035614yes—
763C22#1684036514yes—
764C22#1684037814yes—
765C22C23×C4×D6111yescharacteristic
766C22C2×#41×D6111yescharacteristic
767C22C22×#1175822411yescharacteristic
768C22C2×#1451982211yescharacteristic
769C22C2×#1451982311yescharacteristic
770C22C2×#1451982311yescharacteristic
771C22C2×#1451982411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—1224no—
779C4—1224no—
780C4—1224no—
781C4—1224no—
782C4—2442no—
783C4—2442no—
784C4—2442no—
785C2—44no—
786C2—2444no—
787C2#2144861418yesdirect product factor
788C2C2×C4×#1175822411yescharacteristic
789C2C2×#1684023611yescharacteristic
790C2C2×#1684024111yescharacteristic
791C2C2×#1684034611yescharacteristic
792C2C2×#1684035611yescharacteristic
793C2C2×#1684036511yescharacteristic
794C2C2×#1684037811yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2335
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #21448614C2direct (N × H)
4. C2×#16839658C2semidirect
5. C2×#16839655C2semidirect
6. C2×#16839653C2semidirect
7. C2×#16839652C2semidirect
8. C2×#16839647C2semidirect
9. C2×#16839645C2semidirect
11. C2×#16839636C2semidirect
12. C2×#16839620C2semidirect
13. C2×C4×C4⋊Dic61C2semidirect
14. C2×C22⋊C4×Dic61C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#388C2semidirect
20. C2×#14519761C4semidirect
40. #16839658C22semidirect
41. #16839655C22semidirect
42. #16839653C22semidirect
43. #16839652C22semidirect
44. #16839647C22semidirect
45. #16839645C22semidirect
47. #16839636C22semidirect
48. #16839620C22semidirect
49. C4×C4⋊Dic61C22semidirect
50. C22⋊C4×Dic61C22semidirect
51. #16839609C22semidirect
65. C61×#388C22semidirect
75. C23×Dic61C2×C4semidirect
88. #14519761C2×C4semidirect
90. C2×C4⋊Dic61C2×C4semidirect
91. C2×C4⋊Dic61C2×C4semidirect
142. C2×C22⋊C4×C61C2×C4semidirect
218. C22×Dic61C22×C4semidirect
234. C22⋊C4×C61C22×C4semidirect
244. C4⋊Dic61C22×C4semidirect
245. C4⋊Dic61C22×C4semidirect
395. C2×#388D61semidirect
405. C2×C61#2335semidirect
446. #388C2×D61semidirect
465. C61C2×#2335semidirect
524. C2×C22⋊C4C4×D61semidirect
645. C22⋊C4C2×C4×D61semidirect
787. C2#21448614direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197612
#214486142
C2×#168396622
C2×#168396582
C2×#168396552
C2×#168396532
C2×#168396522
C2×#168396472
C2×#168396452
C2×#168396382
C2×#168396362
C2×#168396202
C2×C4×C4⋊Dic612
C2×C22⋊C4×Dic612
C2×#168396092
C2×C61×#3882
C2×#233561