Finite Group Databasebeta

← C2×#21448613 #29838911

Subgroups — C2×#21448613 #29838911

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
1#21448613C2116yesmaximal, direct product factor
2C2×#16839665C211yesmaximal, characteristic
3C2×#16839661C211yesmaximal, characteristic, complemented
4C2×#16839655C211yesmaximal, characteristic, complemented
5C2×#16839655C211yesmaximal, characteristic, complemented
6C2×#16839655C211yesmaximal, characteristic, complemented
7C2×#16839655C211yesmaximal, characteristic, complemented
8C2×#16839648C211yesmaximal, characteristic, complemented
9C2×#16839648C211yesmaximal, characteristic, complemented
10C2×#16839642C211yesmaximal, characteristic
11C2×#16839637C211yesmaximal, characteristic, complemented
12C2×#16839622C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
16C22×#123×C61C211yesmaximal, characteristic
17C24×Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839665C2218yes—
36#16839661C2218yescomplemented
37#16839655C2218yescomplemented
38#16839655C2218yescomplemented
39#16839655C2218yescomplemented
40#16839655C2218yescomplemented
41#16839648C2218yescomplemented
42#16839648C2218yescomplemented
43#16839642C2218yes—
44#16839637C2218yescomplemented
45#16839622C2218yescomplemented
46C4⋊C4×Dic61C2218yescomplemented
47C22⋊C4×Dic61C2218yescomplemented
48C4×C22⋊Dic61C2218yescomplemented
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C23×D4×C61C2211yescharacteristic
60C24×C4×C61C2211yescharacteristic
61C2×#123×C61C4116yescomplemented
62C2×#123×C61C2218yes—
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C23×Dic61—24no—
69C23×Dic61—42no—
70C23×Dic61—42no—
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2314yes—
80C2×C4⋊Dic61—24no—
81C2×C4⋊Dic61—42no—
82C2×C4⋊Dic61—42no—
83C2×C4⋊Dic61—42no—
84C2×C4⋊Dic61—42no—
85C2×C4⋊Dic61C2314yes—
86C2×C4⋊Dic61C2314yes—
87C2×C4⋊Dic61C2314yes—
88C2×C4⋊Dic61C2314yes—
89C2×C4⋊Dic61C2314yes—
90C2×C22⋊Dic61—24no—
91C2×C22⋊Dic61—24no—
92C2×C22⋊Dic61—24no—
93C2×C22⋊Dic61—42no—
94C2×C22⋊Dic61—42no—
95C2×C22⋊Dic61—42no—
96C2×C22⋊Dic61—42no—
97C2×C22⋊Dic61C2314yes—
98C2×C22⋊Dic61C2314yes—
99C2×C22⋊Dic61C2314yes—
100C2×C22⋊Dic61C2314yes—
101C2×C22⋊Dic61C2314yes—
102C2×C22⋊Dic61C2314yes—
103C2×C22⋊Dic61C2314yes—
104C2×C4×Dic61—24no—
105C2×C4×Dic61—42no—
106C2×C4×Dic61—42no—
107C2×C4×Dic61—42no—
108C2×C4×Dic61—42no—
109C2×C4×Dic61C2314yes—
110C2×C4×Dic61C2314yes—
111C2×C4×Dic61C2314yes—
112C2×C4×Dic61C2314yes—
113C2×C4×Dic61C2314yes—
114#14519684C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124C25×C61C2311yescharacteristic
125C25×C61C2311yescharacteristic
126C22×D4×C61—42no—
127C22×D4×C61—42no—
128C22×D4×C61C2×C418yes—
129C22×D4×C61C2314yes—
130C23×C4×C61—42no—
131C23×C4×C61—42no—
132C23×C4×C61C2×C418yescomplemented
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2314yes—
139#123×C61C2×C4164yescomplemented
140C2×C4⋊C4×C61C2×C418yescomplemented
141C2×C4⋊C4×C61C2×C418yescomplemented
142C2×C4⋊C4×C61C2314yes—
143C2×C4⋊C4×C61C2314yes—
144C2×C22⋊C4×C61C2×C418yes—
145C2×C22⋊C4×C61C2×C418yes—
146C2×C22⋊C4×C61C2×C418yescomplemented
147C2×C22⋊C4×C61C2314yes—
148C2×C22⋊C4×C61C2314yes—
149C2×C22⋊C4×C61C2314yes—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61C22×C414yes—
163C24×C61C22×C414yes—
164C24×C61C2412yes—
165C24×C61C2412yes—
166C24×C61C2411yescharacteristic
167C2×D4×C61—416no—
168C2×D4×C61—44no—
169C2×D4×C61—44no—
170C2×D4×C61C22×C4116yes—
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—416no—
182C22×C4×C61—44no—
183C22×C4×C61—44no—
184C22×C4×C61C22×C414yes—
185C22×C4×C61C22×C414yes—
186C22×C4×C61C22×C414yes—
187C22×C4×C61C22×C414yes—
188C22×C4×C61C22×C414yes—
189C22×C4×C61C22×C4116yescomplemented
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
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—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—28no—
218C22×Dic61—44no—
219C22×Dic61—44no—
220C22×Dic61—416no—
221C22×Dic61#4114yes—
222C22×Dic61#4114yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C4⋊C4×C61C22×C4116yescomplemented
232C4⋊C4×C61C22×C4116yescomplemented
233C22⋊C4×C61C22×C4116yes—
234C22⋊C4×C61C22×C4116yes—
235C22⋊C4×C61C22×C4116yescomplemented
236C22⋊Dic61—28no—
237C22⋊Dic61—28no—
238C22⋊Dic61—28no—
239C22⋊Dic61—44no—
240C22⋊Dic61—44no—
241C22⋊Dic61—44no—
242C22⋊Dic61—44no—
243C4⋊Dic61—28no—
244C4⋊Dic61—44no—
245C4⋊Dic61—44no—
246C4⋊Dic61—44no—
247C4⋊Dic61—44no—
248C4×Dic61—28no—
249C4×Dic61—44no—
250C4×Dic61—44no—
251C4×Dic61—44no—
252C4×Dic61—44no—
253C23×C61—28no—
254C23×C61—28no—
255C23×C61—28no—
256C23×C61—28no—
257C23×C61—28no—
258C23×C61—28no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—44no—
272C23×C61—44no—
273C23×C61—44no—
274C23×C61—44no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61C23×C414yes—
280C23×C61C23×C414yes—
281C23×C61C23×C412yes—
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61H(5,𝔽2)12yes—
285C23×C61H(5,𝔽2)12yes—
286C23×C61H(5,𝔽2)12yes—
287C23×C612−1+412yes—
288C23×C61C2511yescharacteristic
289D4×C61—416no—
290C2×C4×C61—28no—
291C2×C4×C61—28no—
292C2×C4×C61—28no—
293C2×C4×C61—28no—
294C2×C4×C61—28no—
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—416no—
306C2×C4×C61C23×C414yes—
307C2×C4×C61C23×C414yes—
308C2×C4×C61C23×C414yes—
309C2×C4×C61C23×C414yes—
310C2×C4×C61C23×C414yes—
311C2×Dic61—28no—
312C2×Dic61—28no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
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×Dic61—44no—
340C2×Dic61—44no—
341C2×Dic61—44no—
342C2×Dic61C2×#4114yes—
343C2×Dic61C2×#4114yes—
344C2×#2335—611nomaximal, Sylow
345C22×C61—24no—
346C22×C61—24no—
347C22×C61—24no—
348C22×C61—24no—
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—416no—
352C22×C61—416no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61C4×#4114yes—
362C22×C61#51814yes—
363C22×C61#52014yes—
364C22×C61#53814yes—
365C22×C61#53914yes—
366C22×C61#54014yes—
367C22×C61#54214yes—
368C22×C61C24×C411yescharacteristic
369C22×C61C22×#4111yescharacteristic
370C22×C61C22×#4111yescharacteristic
371C22×C61C2×H(5,𝔽2)11yescharacteristic
372C22×C61C2×H(5,𝔽2)11yescharacteristic
373C22×C61C2×H(5,𝔽2)11yescharacteristic
374C22×C61C2×2−1+411yescharacteristic
375C4×C61—24no—
376C4×C61—24no—
377C4×C61—24no—
378C4×C61—24no—
379C4×C61—24no—
380Dic61—24no—
381Dic61—24no—
382Dic61—42no—
383Dic61—42no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C22×#123D6111yescharacteristic
389#2335—6116no—
390C2×#390—611no—
391C2×#389—611no—
392C2×#388—611no—
393C2×#388—611no—
394C2×#388—611no—
395C2×#388—611no—
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—44no—
406C2×C61#233518yescomplemented
407C2×C61C2×C4×#4111yescharacteristic
408C2×C61C2×#51811yescharacteristic
409C2×C61C2×#52011yescharacteristic
410C2×C61C2×#53811yescharacteristic
411C2×C61C2×#53911yescharacteristic
412C2×C61C2×#54011yescharacteristic
413C2×C61C2×#54211yescharacteristic
414C23×D4C2×D6111yescharacteristic
415C24×C4—611no—
416C24×C4C2×D6111yescharacteristic
417C2×#123Dic61116yescomplemented
418C2×#123C2×D6118yes—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—611no—
421C22×C4⋊C4—611no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4C2×D6111yescharacteristic
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×C42—611no—
441#390—618no—
442#389—618no—
443#388—618no—
444#388—618no—
445#388—618no—
446#388—618no—
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×#95—611no—
464C2×#95—611no—
465C61C2×#233511yescharacteristic, complemented, Sylow
466C25C22×D6111yescharacteristic
467C25C22×D6111yescharacteristic
468C22×D4—42no—
469C22×D4—42no—
470C22×D4C2×Dic6118yes—
471C22×D4C22×D6114yes—
472C23×C4—42no—
473C23×C4—42no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—614no—
483C23×C4—1224no—
484C23×C4—2442no—
485C23×C4—2442no—
486C23×C4C2×Dic6118yescomplemented
487C23×C4C22×D6111yescharacteristic
488C23×C4C22×D6111yescharacteristic
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6111yescharacteristic
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6114yes—
493#123C2×Dic61164yescomplemented
494C2×C4⋊C4—614no—
495C2×C4⋊C4—614no—
496C2×C4⋊C4—614no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—1224no—
500C2×C4⋊C4—2442no—
501C2×C4⋊C4—2442no—
502C2×C4⋊C4—2442no—
503C2×C4⋊C4—2442no—
504C2×C4⋊C4C2×Dic6118yescomplemented
505C2×C4⋊C4C2×Dic6118yescomplemented
506C2×C4⋊C4C22×D6114yes—
507C2×C4⋊C4C22×D6114yes—
508C2×C22⋊C4—614no—
509C2×C22⋊C4—614no—
510C2×C22⋊C4—614no—
511C2×C22⋊C4—614no—
512C2×C22⋊C4—614no—
513C2×C22⋊C4—614no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—1224no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—1224no—
518C2×C22⋊C4—2442no—
519C2×C22⋊C4—2442no—
520C2×C22⋊C4—2442no—
521C2×C22⋊C4—2442no—
522C2×C22⋊C4C2×Dic6118yes—
523C2×C22⋊C4C2×Dic6118yes—
524C2×C22⋊C4C2×Dic6118yescomplemented
525C2×C22⋊C4C22×D6114yes—
526C2×C22⋊C4C22×D6114yes—
527C2×C22⋊C4C22×D6114yes—
528C2×C42—614no—
529C2×C42—614no—
530C2×C42—614no—
531C2×C42—614no—
532C2×C42—614no—
533C2×C42—1224no—
534C2×C42—2442no—
535C2×C42—2442no—
536C2×C42—2442no—
537C2×C42—2442no—
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#95—614no—
547#95—614no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24C22×Dic6114yes—
561C24C22×Dic6114yes—
562C24C23×D6112yes—
563C24C23×D6112yes—
564C24C23×D6111yescharacteristic
565C2×D4—416no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4C22×Dic61116yes—
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—416no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—614no—
583C22×C4—614no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—1228no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
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—1222no—
615C22×C4—2444no—
616C22×C4—2444no—
617C22×C4—24416no—
618C22×C4C22×Dic6114yes—
619C22×C4C22×Dic6114yes—
620C22×C4C22×Dic6114yes—
621C22×C4C22×Dic6114yes—
622C22×C4C22×Dic6114yes—
623C22×C4C22×Dic61116yescomplemented
624C22×C4C23×D6112yes—
625C22×C4C23×D6112yes—
626C22×C4C23×D6112yes—
627C22×C4C23×D6112yes—
628C22×C4C23×D6112yes—
629C4⋊C4—1228no—
630C4⋊C4—2444no—
631C4⋊C4—2444no—
632C4⋊C4—2444no—
633C4⋊C4—2444no—
634C4⋊C4C22×Dic61116yescomplemented
635C4⋊C4C22×Dic61116yescomplemented
636C22⋊C4—1228no—
637C22⋊C4—1228no—
638C22⋊C4—1228no—
639C22⋊C4—2444no—
640C22⋊C4—2444no—
641C22⋊C4—2444no—
642C22⋊C4—2444no—
643C22⋊C4C22×Dic61116yes—
644C22⋊C4C22×Dic61116yes—
645C22⋊C4C22×Dic61116yescomplemented
646C42—1228no—
647C42—2444no—
648C42—2444no—
649C42—2444no—
650C42—2444no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—28no—
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—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23C23×Dic6114yes—
678C23C23×Dic6114yes—
679C23C23×Dic6112yes—
680C23#41×D6112yes—
681C23#41×D6112yes—
682C23#1451982212yes—
683C23#1451982212yes—
684C23#1451982312yes—
685C23#1451982412yes—
686C23C24×D6111yescharacteristic
687D4—416no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—416no—
704C2×C4—614no—
705C2×C4—614no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1228no—
711C2×C4—1228no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
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—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—24416no—
731C2×C4—2444no—
732C2×C4—2444no—
733C2×C4—2444no—
734C2×C4—2444no—
735C2×C4—2444no—
736C2×C4—2444no—
737C2×C4C23×Dic6114yes—
738C2×C4C23×Dic6114yes—
739C2×C4C23×Dic6114yes—
740C2×C4C23×Dic6114yes—
741C2×C4C23×Dic6114yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—416no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22#41×Dic6114yes—
759C22#1684023714yes—
760C22#1684024514yes—
761C22#1684034814yes—
762C22#1684035514yes—
763C22#1684036414yes—
764C22#1684038014yes—
765C22C24×Dic6111yescharacteristic
766C22C2×#41×D6111yescharacteristic
767C22C2×#41×D6111yescharacteristic
768C22C2×#1451982211yescharacteristic
769C22C2×#1451982211yescharacteristic
770C22C2×#1451982311yescharacteristic
771C22C2×#1451982411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—24no—
777C4—1224no—
778C4—1224no—
779C4—2442no—
780C4—2442no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4—2442no—
785C2—44no—
786C2—44no—
787C2#2144861318yesdirect product factor
788C2C2×#41×Dic6111yescharacteristic
789C2C2×#1684023711yescharacteristic
790C2C2×#1684024511yescharacteristic
791C2C2×#1684034811yescharacteristic
792C2C2×#1684035511yescharacteristic
793C2C2×#1684036411yescharacteristic
794C2C2×#1684038011yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC22×#123×C61C2
socleC24×C61C24
prime radicalC23×D4×C61C22
cosocleC23×C61C25
hypercenterC22×#123D61
hypocenterC61C2×#2335
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #21448613C2direct (N × H)
3. C2×#16839661C2semidirect
4. C2×#16839655C2semidirect
5. C2×#16839655C2semidirect
6. C2×#16839655C2semidirect
7. C2×#16839655C2semidirect
8. C2×#16839648C2semidirect
9. C2×#16839648C2semidirect
11. C2×#16839637C2semidirect
12. C2×#16839622C2semidirect
13. C2×C4⋊C4×Dic61C2semidirect
14. C2×C22⋊C4×Dic61C2semidirect
15. C2×C4×C22⋊Dic61C2semidirect
36. #16839661C22semidirect
37. #16839655C22semidirect
38. #16839655C22semidirect
39. #16839655C22semidirect
40. #16839655C22semidirect
41. #16839648C22semidirect
42. #16839648C22semidirect
44. #16839637C22semidirect
45. #16839622C22semidirect
46. C4⋊C4×Dic61C22semidirect
47. C22⋊C4×Dic61C22semidirect
48. C4×C22⋊Dic61C22semidirect
61. C2×#123×C61C4semidirect
132. C23×C4×C61C2×C4semidirect
139. #123×C61C2×C4semidirect
140. C2×C4⋊C4×C61C2×C4semidirect
141. C2×C4⋊C4×C61C2×C4semidirect
146. C2×C22⋊C4×C61C2×C4semidirect
189. C22×C4×C61C22×C4semidirect
231. C4⋊C4×C61C22×C4semidirect
232. C4⋊C4×C61C22×C4semidirect
235. C22⋊C4×C61C22×C4semidirect
406. C2×C61#2335semidirect
417. C2×#123Dic61semidirect
465. C61C2×#2335semidirect
486. C23×C4C2×Dic61semidirect
493. #123C2×Dic61semidirect
504. C2×C4⋊C4C2×Dic61semidirect
505. C2×C4⋊C4C2×Dic61semidirect
524. C2×C22⋊C4C2×Dic61semidirect
623. C22×C4C22×Dic61semidirect
634. C4⋊C4C22×Dic61semidirect
635. C4⋊C4C22×Dic61semidirect
645. C22⋊C4C22×Dic61semidirect
787. C2#21448613direct (N × H)

Maximal subgroups

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

subgroupindex
#214486132
C2×#168396652
C2×#168396612
C2×#168396552
C2×#168396482
C2×#168396422
C2×#168396372
C2×#168396222
C2×C4⋊C4×Dic612
C2×C22⋊C4×Dic612
C2×C4×C22⋊Dic612
C22×#123×C612
C2×#233561