Finite Group Databasebeta

← C2×#21448413 #29838591

Subgroups — C2×#21448413 #29838591

Order 15616.

4142 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D61C211yesmaximal, characteristic
2#21448413C2116yesmaximal, direct product factor
3C2×#16839656C211yesmaximal, characteristic, complemented
4C2×#16839655C211yesmaximal, characteristic, complemented
5C2×#16839654C211yesmaximal, characteristic, complemented
6C2×#16839653C211yesmaximal, characteristic, complemented
7C2×#16839652C211yesmaximal, characteristic, complemented
8C2×#16839651C211yesmaximal, characteristic, complemented
9C2×#16839650C211yesmaximal, characteristic, complemented
10C2×#16839621C211yesmaximal, characteristic, complemented
11C2×#16839619C211yesmaximal, characteristic, complemented
12C2×#16839617C211yesmaximal, characteristic
13C2×#16839617C211yesmaximal, characteristic
14C2×C4×#11758198C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C25×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic, complemented
21C22×#11758196C2211yescharacteristic, complemented
22C22×#11758196C2211yescharacteristic, complemented
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C2×C22⋊C4×D61C4116yescomplemented
37C2×C22⋊C4×D61C2218yes—
38C22×C4×Dic61C2211yescharacteristic, complemented
39C22×C4×Dic61C2211yescharacteristic, complemented
40C22×C4×Dic61C2211yescharacteristic, complemented
41#16839656C2218yescomplemented
42#16839655C2218yescomplemented
43#16839654C2218yescomplemented
44#16839653C2218yescomplemented
45#16839652C2218yescomplemented
46#16839651C2218yescomplemented
47#16839650C2218yescomplemented
48#16839621C2218yescomplemented
49#16839619C2218yescomplemented
50#16839617C2218yes—
51#16839617C2218yes—
52C4×#11758198C2218yescomplemented
53#16839609C2218yescomplemented
54C2×#14519684C2211yescharacteristic, complemented
55C2×#14519684C2211yescharacteristic, complemented
56C2×#14519684C2211yescharacteristic, complemented
57C2×#14519684C2211yescharacteristic, complemented
58C2×#14519684C2211yescharacteristic, complemented
59C2×#14519684C2211yescharacteristic, complemented
60C22×C4⋊C4×C61C2211yescharacteristic, complemented
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic, complemented
65C61×#388C2218yescomplemented
66C2×#95×C61C2211yescharacteristic, complemented
67C2×#95×C61C2211yescharacteristic, complemented
68C24×D61—24no—
69C24×D61—24no—
70C24×D61—42no—
71C24×D61—42no—
72C24×D61—42no—
73C24×D61—42no—
74C24×D61C2×C418yes—
75C24×D61C2311yescharacteristic
76C24×D61C2311yescharacteristic
77C24×D61C2314yes—
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C22×C4×D61—42no—
85C22×C4×D61—42no—
86C22×C4×D61—42no—
87C22×C4×D61—42no—
88C22×C4×D61C2×C418yes—
89C22×C4×D61C2×C418yes—
90C22×C4×D61C2314yes—
91C22×C4×D61C2314yes—
92C2×C4⋊Dic61—42no—
93C2×C4⋊Dic61C2314yescomplemented
94C2×#11758196—42no—
95C2×#11758196—42no—
96C2×#11758196C2314yescomplemented
97C2×#11758196C2314yescomplemented
98C2×C22⋊Dic61—42no—
99C2×C22⋊Dic61—42no—
100C2×C22⋊Dic61C2×C418yes—
101C2×C22⋊Dic61C2314yes—
102C2×C22⋊Dic61C2314yes—
103C2×C22⋊Dic61C2314yes—
104C2×#11758198—24no—
105C2×#11758198—24no—
106C2×#11758198—24no—
107C2×#11758198—24no—
108C2×#11758198—42no—
109C2×#11758198—42no—
110C2×#11758198—42no—
111C2×#11758198—42no—
112C2×#11758198C2×C418yes—
113C2×#11758198C2×C418yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×#11758198C2314yes—
120C2×#11758198C2314yes—
121C2×#11758198C2314yes—
122C2×#11758198C2314yes—
123C2×#11758198C2314yes—
124C22⋊C4×D61C2×C4164yescomplemented
125C2×C4×Dic61—42no—
126C2×C4×Dic61—42no—
127C2×C4×Dic61—42no—
128C2×C4×Dic61C2314yescomplemented
129C2×C4×Dic61C2314yescomplemented
130C2×C4×Dic61C2314yescomplemented
131#14519684C2314yescomplemented
132#14519684C2314yescomplemented
133#14519684C2314yescomplemented
134#14519684C2314yescomplemented
135#14519684C2314yescomplemented
136#14519684C2314yescomplemented
137C25×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61—42no—
145C2×C4⋊C4×C61C2314yescomplemented
146C2×C22⋊C4×C61—42no—
147C2×C22⋊C4×C61—42no—
148C2×C22⋊C4×C61C2×C418yes—
149C2×C22⋊C4×C61C2314yes—
150C2×C22⋊C4×C61C2314yes—
151C2×C22⋊C4×C61C2314yes—
152C2×C42×C61—42no—
153C2×C42×C61C2314yescomplemented
154#95×C61C2314yescomplemented
155#95×C61C2314yescomplemented
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61C22×C414yes—
163C24×C61C2412yes—
164C24×C61C2411yescharacteristic
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
173C23×D61—22no—
174C23×D61—22no—
175C23×D61—232no—
176C23×D61—28no—
177C23×D61—28no—
178C23×D61—416no—
179C23×D61—416no—
180C23×D61—44no—
181C23×D61—44no—
182C23×D61—44no—
183C23×D61—44no—
184C23×D61—416no—
185C23×D61—416no—
186C23×D61—416no—
187C23×D61—416no—
188C23×D61C22×C414yes—
189C23×D61C22×C414yes—
190C23×D61C22×C4116yes—
191C23×D61#4114yes—
192C23×D61#4114yes—
193C23×D61C2412yes—
194C23×D61C2412yes—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61C22×C414yes—
212C22×C4×C61C22×C414yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2412yes—
215C22×C4×C61C2412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2412yes—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61—22no—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61C22×C414yes—
236C22×Dic61C22×C414yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
239C22×Dic61C2412yes—
240C22×Dic61C2412yes—
241C22×Dic61C2412yes—
242C22×Dic61C2412yes—
243C2×C4×D61—416no—
244C2×C4×D61—416no—
245C2×C4×D61—44no—
246C2×C4×D61—44no—
247C2×C4×D61—44no—
248C2×C4×D61—44no—
249C2×C4×D61C22×C4116yes—
250C2×C4×D61C22×C4116yes—
251C4⋊C4×C61—44no—
252C22⋊C4×C61—44no—
253C22⋊C4×C61—44no—
254C22⋊C4×C61C22×C4116yes—
255C42×C61—44no—
256C22⋊Dic61—44no—
257C22⋊Dic61—44no—
258C22⋊Dic61C22×C4116yes—
259#11758198—28no—
260#11758198—28no—
261#11758198—28no—
262#11758198—28no—
263#11758198—44no—
264#11758198—44no—
265#11758198—44no—
266#11758198—44no—
267#11758198C22×C4116yes—
268#11758198C22×C4116yes—
269C4⋊Dic61—44no—
270#11758196—44no—
271#11758196—44no—
272C4×Dic61—44no—
273C4×Dic61—44no—
274C4×Dic61—44no—
275C23×C61—28no—
276C23×C61—28no—
277C23×C61—28no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—44no—
285C23×C61—44no—
286C23×C61—44no—
287C23×C61—44no—
288C23×C61C23×C414yes—
289C23×C61C23×C412yes—
290C23×C61C2×#4112yes—
291C23×C61C2×#4112yes—
292C23×C61H(5,𝔽2)12yes—
293C23×C61H(5,𝔽2)12yes—
294C23×C61H(5,𝔽2)12yes—
295C23×C61H(5,𝔽2)12yes—
296C23×C61C2511yescharacteristic
297C22×D61—28no—
298C22×D61—28no—
299C22×D61—28no—
300C22×D61—28no—
301C22×D61—28no—
302C22×D61—28no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—28no—
308C22×D61—28no—
309C22×D61—28no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—232no—
317C22×D61—416no—
318C22×D61—416no—
319C22×D61—4128no—
320C22×D61—416no—
321C22×D61—416no—
322C22×D61—416no—
323C22×D61—416no—
324C22×D61—44no—
325C22×D61—44no—
326C22×D61—44no—
327C22×D61—44no—
328C22×D61#117116yes—
329C22×D61C23×C414yes—
330C22×D61C23×C414yes—
331C22×D61C2×#4114yes—
332C22×D61C2×#4114yes—
333C2×C4×C61—28no—
334C2×C4×C61—28no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—44no—
352C2×C4×C61—44no—
353C2×C4×C61—44no—
354C2×C4×C61—44no—
355C2×C4×C61C23×C414yes—
356C2×C4×C61C23×C414yes—
357C2×Dic61—28no—
358C2×Dic61—28no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—44no—
376C2×Dic61—44no—
377C2×Dic61—44no—
378C2×Dic61—44no—
379C2×Dic61C23×C414yes—
380C2×Dic61C23×C414yes—
381C4×D61—416no—
382C4×D61—416no—
383C2×#2312—611nomaximal, Sylow
384C22×C61—24no—
385C22×C61—24no—
386C22×C61—24no—
387C22×C61—416no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61C2×#11714yes—
393C22×C61#51814yes—
394C22×C61#51814yes—
395C22×C61#53814yes—
396C22×C61#53814yes—
397C22×C61#53814yes—
398C22×C61#53814yes—
399C22×C61C24×C411yescharacteristic
400C22×C61C22×#4111yescharacteristic
401C22×C61C22×#4111yescharacteristic
402C22×C61C2×H(5,𝔽2)11yescharacteristic
403C22×C61C2×H(5,𝔽2)11yescharacteristic
404C22×C61C2×H(5,𝔽2)11yescharacteristic
405C22×C61C2×H(5,𝔽2)11yescharacteristic
406C2×D61—232no—
407C2×D61—24no—
408C2×D61—24no—
409C2×D61—24no—
410C2×D61—24no—
411C2×D61—24no—
412C2×D61—24no—
413C2×D61—24no—
414C2×D61—24no—
415C2×D61—24no—
416C2×D61—464no—
417C2×D61—416no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61C2×#11718yes—
423C4×C61—24no—
424C4×C61—24no—
425C4×C61—42no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61—42no—
429Dic61—24no—
430Dic61—24no—
431Dic61—42no—
432Dic61—42no—
433Dic61—42no—
434Dic61—42no—
435C23×C22⋊C4—611no—
436#2312—6116no—
437C2×#388—611no—
438C2×#388—611no—
439C2×#388—611no—
440C2×#388—611no—
441C2×#388—611no—
442C2×#388—611no—
443C2×#388—611no—
444C2×#388D6111yescharacteristic, complemented
445C2×#380—611no—
446C2×#380—611no—
447C2×#379—611no—
448C2×#379—611no—
449C2×C4×C22⋊C4—611no—
450C2×C4×C22⋊C4—611no—
451C2×C61—44no—
452C2×C61#231218yescomplemented
453C2×C61C22×#11711yescharacteristic
454C2×C61C2×#51811yescharacteristic
455C2×C61C2×#51811yescharacteristic
456C2×C61C2×#53811yescharacteristic
457C2×C61C2×#53811yescharacteristic
458C2×C61C2×#53811yescharacteristic
459C2×C61C2×#53811yescharacteristic
460D61—28no—
461D61—44no—
462C26—611no—
463C24×C4—611no—
464C24×C4—611no—
465C22×C4⋊C4—611no—
466C22×C4⋊C4—611no—
467C22×C4⋊C4—611no—
468C22×C4⋊C4C2×D6111yescharacteristic, complemented
469C22×C22⋊C4—611no—
470C22×C22⋊C4—611no—
471C22×C22⋊C4—611no—
472C22×C22⋊C4—6116no—
473C22×C22⋊C4—618no—
474C22×C22⋊C4—611no—
475C22×C22⋊C4—611no—
476C22×C22⋊C4—611no—
477C22×C22⋊C4—611no—
478C22×C22⋊C4—611no—
479C22×C22⋊C4—611no—
480C22×C22⋊C4—611no—
481C22×C22⋊C4—611no—
482C22×C22⋊C4—611no—
483C22×C22⋊C4—611no—
484C22×C22⋊C4C2×D6111yescharacteristic
485C22×C22⋊C4C2×D6111yescharacteristic
486C22×C22⋊C4C2×D6111yescharacteristic
487C22×C42—611no—
488C22×C42—611no—
489C22×C42—611no—
490C22×C42C2×D6111yescharacteristic, complemented
491#388—618no—
492#388—618no—
493#388—618no—
494#388—618no—
495#388—618no—
496#388—618no—
497#388—618no—
498#388C2×D6118yescomplemented
499#380—618no—
500#380—618no—
501#379—618no—
502#379—618no—
503C4×C22⋊C4—618no—
504C4×C22⋊C4—618no—
505C2×#95—611no—
506C2×#95—611no—
507C2×#95—611no—
508C2×#95—611no—
509C2×#95—611no—
510C2×#95—611no—
511C2×#95C2×D6111yescharacteristic, complemented
512C2×#95C2×D6111yescharacteristic, complemented
513C61C2×#231211yescharacteristic, complemented, Sylow
514C25—611no—
515C25—611no—
516C25—618no—
517C25—614no—
518C25—1224no—
519C25—1224no—
520C25—2442no—
521C25—2442no—
522C25—2442no—
523C25—2442no—
524C25C22×D6111yescharacteristic
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—618no—
528C23×C4—618no—
529C23×C4—614no—
530C23×C4—614no—
531C23×C4—611no—
532C23×C4—611no—
533C23×C4—611no—
534C23×C4—611no—
535C23×C4—2442no—
536C23×C4—2442no—
537C23×C4—2442no—
538C23×C4—2442no—
539C23×C4C22×D6111yescharacteristic
540C23×C4C22×D6111yescharacteristic
541C23×C4C22×D6111yescharacteristic
542C23×C4C22×D6111yescharacteristic
543C23×C4C22×D6111yescharacteristic
544C23×C4C22×D6111yescharacteristic
545C2×C4⋊C4—42no—
546C2×C4⋊C4—614no—
547C2×C4⋊C4—614no—
548C2×C4⋊C4—614no—
549C2×C4⋊C4—2442no—
550C2×C4⋊C4—2442no—
551C2×C4⋊C4—2442no—
552C2×C4⋊C4C22×D6114yescomplemented
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—618no—
556C2×C22⋊C4—614no—
557C2×C22⋊C4—618no—
558C2×C22⋊C4—618no—
559C2×C22⋊C4—614no—
560C2×C22⋊C4—614no—
561C2×C22⋊C4—6164no—
562C2×C22⋊C4—614no—
563C2×C22⋊C4—614no—
564C2×C22⋊C4—614no—
565C2×C22⋊C4—614no—
566C2×C22⋊C4—614no—
567C2×C22⋊C4—614no—
568C2×C22⋊C4—614no—
569C2×C22⋊C4—614no—
570C2×C22⋊C4—614no—
571C2×C22⋊C4—614no—
572C2×C22⋊C4—1224no—
573C2×C22⋊C4—1224no—
574C2×C22⋊C4—1224no—
575C2×C22⋊C4—1224no—
576C2×C22⋊C4—2442no—
577C2×C22⋊C4—2442no—
578C2×C22⋊C4—2442no—
579C2×C22⋊C4—2442no—
580C2×C22⋊C4—2442no—
581C2×C22⋊C4—2442no—
582C2×C22⋊C4C4×D6118yes—
583C2×C22⋊C4C22×D6114yes—
584C2×C22⋊C4C22×D6114yes—
585C2×C22⋊C4C22×D6114yes—
586C2×C42—42no—
587C2×C42—614no—
588C2×C42—614no—
589C2×C42—614no—
590C2×C42—2442no—
591C2×C42—2442no—
592C2×C42—2442no—
593C2×C42C22×D6114yescomplemented
594#95—614no—
595#95—614no—
596#95—614no—
597#95—614no—
598#95—614no—
599#95—614no—
600#95C22×D6114yescomplemented
601#95C22×D6114yescomplemented
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—614no—
609C24—614no—
610C24—614no—
611C24—612no—
612C24—614no—
613C24—612no—
614C24—6116no—
615C24—12232no—
616C24—1228no—
617C24—1228no—
618C24—1222no—
619C24—1222no—
620C24—1222no—
621C24—1222no—
622C24—1222no—
623C24—1222no—
624C24—1222no—
625C24—1222no—
626C24—1222no—
627C24—1222no—
628C24—24416no—
629C24—24416no—
630C24—2444no—
631C24—2444no—
632C24—2444no—
633C24—2444no—
634C24—24416no—
635C24—24416no—
636C24—24416no—
637C24—24416no—
638C24C2×C4×D6114yes—
639C24C23×D6112yes—
640C24C23×D6111yescharacteristic
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—614no—
658C22×C4—614no—
659C22×C4—612no—
660C22×C4—612no—
661C22×C4—6116no—
662C22×C4—6116no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1222no—
681C22×C4—1222no—
682C22×C4—1222no—
683C22×C4—24416no—
684C22×C4—24416no—
685C22×C4—2444no—
686C22×C4—2444no—
687C22×C4—2444no—
688C22×C4—2444no—
689C22×C4C2×C4×D6114yes—
690C22×C4C2×C4×D6114yes—
691C22×C4C23×D6112yes—
692C22×C4C23×D6112yes—
693C22×C4C23×D6112yes—
694C22×C4C23×D6112yes—
695C22×C4C23×D6112yes—
696C22×C4C23×D6112yes—
697C4⋊C4—44no—
698C4⋊C4—2444no—
699C4⋊C4—2444no—
700C4⋊C4—2444no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—6116no—
704C22⋊C4—6116no—
705C22⋊C4—6116no—
706C22⋊C4—1228no—
707C22⋊C4—1228no—
708C22⋊C4—1228no—
709C22⋊C4—1228no—
710C22⋊C4—2444no—
711C22⋊C4—2444no—
712C22⋊C4—2444no—
713C22⋊C4—2444no—
714C22⋊C4—2444no—
715C22⋊C4—2444no—
716C22⋊C4C2×C4×D61116yes—
717C42—44no—
718C42—2444no—
719C42—2444no—
720C42—2444no—
721C23—28no—
722C23—28no—
723C23—28no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—6116no—
735C23—614no—
736C23—614no—
737C23—614no—
738C23—614no—
739C23—12232no—
740C23—1228no—
741C23—1228no—
742C23—1222no—
743C23—1222no—
744C23—1222no—
745C23—1222no—
746C23—1228no—
747C23—1228no—
748C23—1228no—
749C23—1228no—
750C23—1228no—
751C23—1228no—
752C23—1228no—
753C23—1222no—
754C23—1222no—
755C23—1222no—
756C23—1222no—
757C23—1222no—
758C23—1222no—
759C23—24416no—
760C23—24416no—
761C23—24416no—
762C23—24416no—
763C23—24416no—
764C23—24416no—
765C23—244128no—
766C23—2444no—
767C23—2444no—
768C23—2444no—
769C23—2444no—
770C23C22×C4×D6114yes—
771C23C22×C4×D6112yes—
772C23#41×D6112yes—
773C23#41×D6112yes—
774C23#1451982212yes—
775C23#1451982212yes—
776C23#1451982312yes—
777C23#1451982312yes—
778C23C24×D6111yescharacteristic
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—614no—
802C2×C4—614no—
803C2×C4—1228no—
804C2×C4—1228no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—24416no—
822C2×C4—24416no—
823C2×C4—2444no—
824C2×C4—2444no—
825C2×C4—2444no—
826C2×C4—2444no—
827C2×C4C22×C4×D6114yes—
828C2×C4C22×C4×D6114yes—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—416no—
837C22—618no—
838C22—1224no—
839C22—1224no—
840C22—1224no—
841C22—1224no—
842C22—1224no—
843C22—1224no—
844C22—12232no—
845C22—1224no—
846C22—1224no—
847C22—1224no—
848C22—24464no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22—24416no—
854C22#117×D6114yes—
855C22#1684023414yes—
856C22#1684023414yes—
857C22#1684034414yes—
858C22#1684034614yes—
859C22#1684034814yes—
860C22#1684035114yes—
861C22C23×C4×D6111yescharacteristic
862C22C2×#41×D6111yescharacteristic
863C22C2×#41×D6111yescharacteristic
864C22C2×#1451982211yescharacteristic
865C22C2×#1451982211yescharacteristic
866C22C2×#1451982311yescharacteristic
867C22C2×#1451982311yescharacteristic
868C4—24no—
869C4—24no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1224no—
875C4—1224no—
876C4—2442no—
877C4—2442no—
878C4—2442no—
879C4—2442no—
880C2—44no—
881C2—1228no—
882C2—2444no—
883C2#2144841318yesdirect product factor
884C2C2×#117×D6111yescharacteristic
885C2C2×#1684023411yescharacteristic
886C2C2×#1684023411yescharacteristic
887C2C2×#1684034411yescharacteristic
888C2C2×#1684034611yescharacteristic
889C2C2×#1684034811yescharacteristic
890C2C2×#1684035111yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC25×D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2312
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #21448413C2direct (N × H)
3. C2×#16839656C2semidirect
4. C2×#16839655C2semidirect
5. C2×#16839654C2semidirect
6. C2×#16839653C2semidirect
7. C2×#16839652C2semidirect
8. C2×#16839651C2semidirect
9. C2×#16839650C2semidirect
10. C2×#16839621C2semidirect
11. C2×#16839619C2semidirect
14. C2×C4×#11758198C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#388C2semidirect
20. C22×C4⋊Dic61C22semidirect
21. C22×#11758196C22semidirect
22. C22×#11758196C22semidirect
36. C2×C22⋊C4×D61C4semidirect
38. C22×C4×Dic61C22semidirect
39. C22×C4×Dic61C22semidirect
40. C22×C4×Dic61C22semidirect
41. #16839656C22semidirect
42. #16839655C22semidirect
43. #16839654C22semidirect
44. #16839653C22semidirect
45. #16839652C22semidirect
46. #16839651C22semidirect
47. #16839650C22semidirect
48. #16839621C22semidirect
49. #16839619C22semidirect
52. C4×#11758198C22semidirect
53. #16839609C22semidirect
54. C2×#14519684C22semidirect
55. C2×#14519684C22semidirect
56. C2×#14519684C22semidirect
57. C2×#14519684C22semidirect
58. C2×#14519684C22semidirect
59. C2×#14519684C22semidirect
60. C22×C4⋊C4×C61C22semidirect
64. C22×C42×C61C22semidirect
65. C61×#388C22semidirect
66. C2×#95×C61C22semidirect
67. C2×#95×C61C22semidirect
93. C2×C4⋊Dic61C23semidirect
96. C2×#11758196C23semidirect
97. C2×#11758196C23semidirect
124. C22⋊C4×D61C2×C4semidirect
128. C2×C4×Dic61C23semidirect
129. C2×C4×Dic61C23semidirect
130. C2×C4×Dic61C23semidirect
131. #14519684C23semidirect
132. #14519684C23semidirect
133. #14519684C23semidirect
134. #14519684C23semidirect
135. #14519684C23semidirect
136. #14519684C23semidirect
145. C2×C4⋊C4×C61C23semidirect
153. C2×C42×C61C23semidirect
154. #95×C61C23semidirect
155. #95×C61C23semidirect
444. C2×#388D61semidirect
452. C2×C61#2312semidirect
468. C22×C4⋊C4C2×D61semidirect
490. C22×C42C2×D61semidirect
498. #388C2×D61semidirect
511. C2×#95C2×D61semidirect
512. C2×#95C2×D61semidirect
513. C61C2×#2312semidirect
552. C2×C4⋊C4C22×D61semidirect
593. C2×C42C22×D61semidirect
600. #95C22×D61semidirect
601. #95C22×D61semidirect
883. C2#21448413direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D612
#214484132
C2×#168396562
C2×#168396552
C2×#168396542
C2×#168396532
C2×#168396522
C2×#168396512
C2×#168396502
C2×#168396212
C2×#168396192
C2×#168396172
C2×C4×#117581982
C2×#168396092
C2×C61×#3882
C2×#231261