Finite Group Databasebeta

← C2×#21448279 #29838370

Subgroups — C2×#21448279 #29838370

Order 15616.

3790 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C22×#14519735C211yesmaximal, characteristic, complemented
3C22×#14519733C211yesmaximal, characteristic, complemented
4#21448279C2116yesmaximal, direct product factor
5C2×#16839662C211yesmaximal, characteristic
6C2×#16839662C211yesmaximal, characteristic
7C2×#16839659C211yesmaximal, characteristic, complemented
8C2×#16839657C211yesmaximal, characteristic, complemented
9C2×#16839655C211yesmaximal, characteristic, complemented
10C2×#16839653C211yesmaximal, characteristic, complemented
11C2×#16839651C211yesmaximal, characteristic, complemented
12C2×#16839613C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C2×#16839609C211yesmaximal, characteristic, complemented
15C2×C42×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519737C4116yescomplemented
21C2×#14519737C2218yes—
22C2×#14519735—28no—
23C2×#14519735C2218yescomplemented
24C2×#14519733—28no—
25C2×#14519733C2218yescomplemented
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43C22×C4×Dic61C2211yescharacteristic
44C22×C4×Dic61C2211yescharacteristic
45C22×C4×Dic61C2211yescharacteristic
46C22×C4×Dic61C2211yescharacteristic
47#16839662C2218yes—
48#16839662C2218yes—
49#16839659C2218yescomplemented
50#16839657C2218yescomplemented
51#16839655C2218yescomplemented
52#16839653C2218yescomplemented
53#16839651C2218yescomplemented
54#16839613C2218yescomplemented
55C22⋊C4×Dic61C2218yescomplemented
56#16839609C2218yescomplemented
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C42×Dic61C2218yescomplemented
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C42×C61C2211yescharacteristic
67C61×#388C2218yescomplemented
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C24×D61C2311yescharacteristic
71C22×C22⋊D61—24no—
72C22×C22⋊D61—24no—
73C22×C22⋊D61C2×C418yes—
74C22×C22⋊D61C2314yes—
75C23×Dic61—24no—
76C23×Dic61—24no—
77C23×Dic61C2×C418yes—
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2314yes—
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61C2×C418yes—
89C22×C4×D61C2314yes—
90#14519737C2×C4164yescomplemented
91#14519735—232no—
92#14519733—232no—
93C2×C4⋊Dic61—24no—
94C2×C4⋊Dic61C2314yes—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196—24no—
98C2×#11758196—24no—
99C2×#11758196C2×C418yes—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×C22⋊Dic61—24no—
106C2×C22⋊Dic61—24no—
107C2×C22⋊Dic61C2314yes—
108C2×C22⋊Dic61C2314yes—
109C2×#11758198—24no—
110C2×#11758198—24no—
111C2×#11758198—24no—
112C2×#11758198—24no—
113C2×#11758198C2×C418yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61—24no—
122C2×C4×Dic61—24no—
123C2×C4×Dic61—24no—
124C2×C4×Dic61—24no—
125C2×C4×Dic61C2×C418yes—
126C2×C4×Dic61D418yescomplemented
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131C2×C4×Dic61C2314yes—
132C2×C4×Dic61C2314yes—
133C2×C4×Dic61C2314yes—
134C2×C4×Dic61C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137#14519684C2314yes—
138#14519684C2314yes—
139C25×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61—24no—
147C2×C4⋊C4×C61C2314yes—
148C2×C22⋊C4×C61—24no—
149C2×C22⋊C4×C61—24no—
150C2×C22⋊C4×C61C2×C418yes—
151C2×C22⋊C4×C61C2314yes—
152C2×C22⋊C4×C61C2314yes—
153C2×C22⋊C4×C61C2314yes—
154C2×C42×C61—24no—
155C2×C42×C61C2314yes—
156#95×C61C2314yes—
157#95×C61C2314yes—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61C22×C414yes—
165C24×C61C2412yes—
166C24×C61C2411yescharacteristic
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
173C23×D61C22×C414yes—
174C23×D61C2412yes—
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×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61C22×C414yes—
190C22×C4×C61C22×C414yes—
191C22×C4×C61C2×D414yes—
192C22×C4×C61#4114yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C2×C22⋊D61—232no—
200C2×C22⋊D61—28no—
201C2×C22⋊D61—28no—
202C2×C22⋊D61C22×C4116yes—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—232no—
210C22×Dic61—28no—
211C22×Dic61—28no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61C22×C414yes—
219C22×Dic61C22×C4116yes—
220C22×Dic61C22×C414yes—
221C22×Dic61C22×C414yes—
222C22×Dic61C2×D414yes—
223C22×Dic61C2×D414yes—
224C22×Dic61#4114yes—
225C22×Dic61#4114yes—
226C22×Dic61#4114yes—
227C22×Dic61#4114yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C2×C4×D61—232no—
236C2×C4×D61—28no—
237C2×C4×D61—28no—
238C2×C4×D61C22×C4116yes—
239C4⋊C4×C61—28no—
240C22⋊C4×C61—28no—
241C22⋊C4×C61—28no—
242C22⋊C4×C61C22×C4116yes—
243C42×C61—28no—
244C22⋊Dic61—28no—
245C22⋊Dic61—28no—
246#11758198—28no—
247#11758198—28no—
248#11758198—28no—
249#11758198—28no—
250#11758198C22×C4116yes—
251C4⋊Dic61—28no—
252#11758196—28no—
253#11758196—28no—
254#11758196—28no—
255#11758196—28no—
256#11758196C22×C4116yes—
257C4×Dic61—28no—
258C4×Dic61—28no—
259C4×Dic61—28no—
260C4×Dic61—28no—
261C4×Dic61—28no—
262C4×Dic61—28no—
263C4×Dic61C22×C4116yes—
264C4×Dic61C2×D4116yescomplemented
265C23×C61—28no—
266C23×C61—28no—
267C23×C61—28no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—44no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61C23×C414yes—
279C23×C61C23×C412yes—
280C23×C61C22×D412yes—
281C23×C61C2×#4112yes—
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61C2×#4112yes—
285C23×C61C2×#4112yes—
286C23×C61C2511yescharacteristic
287C22×D61—28no—
288C22×D61—28no—
289C22×D61—28no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—44no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61C23×C414yes—
301C2×C4×C61—28no—
302C2×C4×C61—28no—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—44no—
320C2×C4×C61—44no—
321C2×C4×C61C23×C414yes—
322C2×C4×C61C23×C414yes—
323C2×C4×C61C22×D414yes—
324C2×C4×C61C2×#4114yes—
325C22⋊D61—232no—
326C2×Dic61—28no—
327C2×Dic61—28no—
328C2×Dic61—28no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—232no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—44no—
343C2×Dic61—44no—
344C2×Dic61#117116yescomplemented
345C2×Dic61C4×D4116yes—
346C2×Dic61C23×C414yes—
347C2×Dic61C23×C414yes—
348C2×Dic61C23×C414yes—
349C2×Dic61C22×D414yes—
350C2×Dic61C22×D414yes—
351C2×Dic61C2×#4114yes—
352C2×Dic61C2×#4114yes—
353C2×Dic61C2×#4114yes—
354C2×Dic61C2×#4114yes—
355C4×D61—232no—
356C2×#2293—611nomaximal, Sylow
357C22×C61—24no—
358C22×C61—24no—
359C22×C61—24no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—416no—
365C22×C61C2×#11714yes—
366C22×C61C2×C4×D414yes—
367C22×C61C4×#4114yes—
368C22×C61#52914yes—
369C22×C61#52914yes—
370C22×C61#53214yes—
371C22×C61#53214yes—
372C22×C61C24×C411yescharacteristic
373C22×C61C23×D411yescharacteristic
374C22×C61C22×#4111yescharacteristic
375C22×C61C22×#4111yescharacteristic
376C22×C61C22×#4111yescharacteristic
377C22×C61C22×#4111yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C2×D61—24no—
380C2×D61—24no—
381C2×D61—24no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—416no—
387C4×C61—24no—
388C4×C61—24no—
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—42no—
392C4×C61—42no—
393Dic61—24no—
394Dic61—24no—
395Dic61—24no—
396Dic61—42no—
397Dic61—42no—
398Dic61C2×#11718yescomplemented
399Dic61C2×C4×D418yes—
400C22×C4×D4—611no—
401C22×#117—611no—
402C22×#117—611no—
403#2293—6116no—
404C2×#390—611no—
405C2×#390—611no—
406C2×#389—611no—
407C2×#389—611no—
408C2×#388—611no—
409C2×#388—611no—
410C2×#388—611no—
411C2×#388D6111yescharacteristic, complemented
412C2×C4×C4⋊C4—611no—
413C2×C4×C22⋊C4—611no—
414C2×C4×C22⋊C4—611no—
415C2×C43—611no—
416C2×C61—44no—
417C2×C61#229318yescomplemented
418C2×C61C22×#11711yescharacteristic
419C2×C61C22×C4×D411yescharacteristic
420C2×C61C2×C4×#4111yescharacteristic
421C2×C61C2×#52911yescharacteristic
422C2×C61C2×#52911yescharacteristic
423C2×C61C2×#53211yescharacteristic
424C2×C61C2×#53211yescharacteristic
425D61—44no—
426C23×D4—611no—
427C24×C4—611no—
428C24×C4—611no—
429C2×C4×D4—6116no—
430C2×C4×D4—618no—
431C2×#117—618no—
432C2×#117—618no—
433C2×#117—1228no—
434C2×#117—1228no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—611no—
437C22×C4⋊C4—611no—
438C22×C4⋊C4—611no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4C2×D6111yescharacteristic
442C22×C22⋊C4—611no—
443C22×C22⋊C4—611no—
444C22×C22⋊C4—611no—
445C22×C22⋊C4—611no—
446C22×C22⋊C4—611no—
447C22×C22⋊C4—611no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4C2×D6111yescharacteristic
450C22×C22⋊C4C2×D6111yescharacteristic
451C22×C22⋊C4C2×D6111yescharacteristic
452C22×C42—611no—
453C22×C42—611no—
454C22×C42—611no—
455C22×C42—611no—
456C22×C42—611no—
457C22×C42—611no—
458C22×C42—611no—
459C22×C42—611no—
460C22×C42C2×D6111yescharacteristic
461#390—618no—
462#390—618no—
463#389—618no—
464#389—618no—
465#388—618no—
466#388—618no—
467#388—618no—
468#388C2×D6118yescomplemented
469C4×C4⋊C4—618no—
470C4×C22⋊C4—618no—
471C4×C22⋊C4—618no—
472C2×#95—611no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95C2×D6111yescharacteristic
477C2×#95C2×D6111yescharacteristic
478C43—618no—
479C61C2×#229311yescharacteristic, complemented, Sylow
480C25—611no—
481C25C22×D6111yescharacteristic
482C22×D4—618no—
483C22×D4—614no—
484C22×D4—1224no—
485C22×D4—1224no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—618no—
489C23×C4—614no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—618no—
494C23×C4—614no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—1224no—
498C23×C4—1224no—
499C23×C4—1224no—
500C23×C4—1224no—
501C23×C4C22×D6111yescharacteristic
502C23×C4C22×D6111yescharacteristic
503C23×C4C22×D6111yescharacteristic
504C23×C4C22×D6111yescharacteristic
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507C4×D4—6164no—
508#117—12232no—
509#117—12232no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—618no—
512C2×C4⋊C4—614no—
513C2×C4⋊C4—614no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—614no—
516C2×C4⋊C4—614no—
517C2×C4⋊C4—614no—
518C2×C4⋊C4—1224no—
519C2×C4⋊C4—1224no—
520C2×C4⋊C4—1224no—
521C2×C4⋊C4—1224no—
522C2×C4⋊C4—1224no—
523C2×C4⋊C4C22×D6114yes—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—618no—
527C2×C22⋊C4—614no—
528C2×C22⋊C4—614no—
529C2×C22⋊C4—614no—
530C2×C22⋊C4—614no—
531C2×C22⋊C4—614no—
532C2×C22⋊C4—614no—
533C2×C22⋊C4—614no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1224no—
536C2×C22⋊C4—1224no—
537C2×C22⋊C4—1224no—
538C2×C22⋊C4—1224no—
539C2×C22⋊C4—1224no—
540C2×C22⋊C4C4×D6118yes—
541C2×C22⋊C4C22×D6114yes—
542C2×C22⋊C4C22×D6114yes—
543C2×C22⋊C4C22×D6114yes—
544C2×C42—24no—
545C2×C42—618no—
546C2×C42—618no—
547C2×C42—614no—
548C2×C42—614no—
549C2×C42—614no—
550C2×C42—614no—
551C2×C42—614no—
552C2×C42—614no—
553C2×C42—614no—
554C2×C42—614no—
555C2×C42—1224no—
556C2×C42—1224no—
557C2×C42—1224no—
558C2×C42—1224no—
559C2×C42—1224no—
560C2×C42—1224no—
561C2×C42C22×D6114yes—
562#95—614no—
563#95—614no—
564#95—614no—
565#95—614no—
566#95C22×D6114yes—
567#95C22×D6114yes—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—614no—
575C24—612no—
576C24—1222no—
577C24—1222no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24C2×C4×D6114yes—
583C24C23×D6112yes—
584C24C23×D6111yescharacteristic
585C2×D4—6116no—
586C2×D4—12232no—
587C2×D4—1228no—
588C2×D4—1228no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—614no—
604C22×C4—614no—
605C22×C4—614no—
606C22×C4—614no—
607C22×C4—614no—
608C22×C4—614no—
609C22×C4—612no—
610C22×C4—612no—
611C22×C4—614no—
612C22×C4—6116no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—6116no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—1228no—
622C22×C4—12232no—
623C22×C4—1228no—
624C22×C4—1228no—
625C22×C4—12232no—
626C22×C4—1228no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4C2×C4×D6114yes—
640C22×C4C2×C4×D6114yes—
641C22×C4D4×D6114yes—
642C22×C4#1175822414yes—
643C22×C4C23×D6112yes—
644C22×C4C23×D6112yes—
645C22×C4C23×D6112yes—
646C22×C4C23×D6112yes—
647C22×C4C23×D6112yes—
648C22×C4C23×D6112yes—
649C4⋊C4—28no—
650C4⋊C4—6116no—
651C4⋊C4—1228no—
652C4⋊C4—1228no—
653C4⋊C4—1228no—
654C4⋊C4—1228no—
655C4⋊C4—1228no—
656C22⋊C4—28no—
657C22⋊C4—28no—
658C22⋊C4—6116no—
659C22⋊C4—1228no—
660C22⋊C4—1228no—
661C22⋊C4—1228no—
662C22⋊C4—1228no—
663C22⋊C4—1228no—
664C22⋊C4—1228no—
665C22⋊C4C2×C4×D61116yes—
666C42—28no—
667C42—6116no—
668C42—6116no—
669C42—1228no—
670C42—1228no—
671C42—1228no—
672C42—1228no—
673C42—1228no—
674C42—1228no—
675C23—28no—
676C23—28no—
677C23—28no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—614no—
689C23—1228no—
690C23—1228no—
691C23—1228no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—2444no—
699C23—2444no—
700C23—2444no—
701C23—2444no—
702C23C22×C4×D6114yes—
703C23C22×C4×D6112yes—
704C23C2×D4×D6112yes—
705C23#41×D6112yes—
706C23#41×D6112yes—
707C23#41×D6112yes—
708C23#41×D6112yes—
709C23C2×#1175822412yes—
710C23C24×D6111yescharacteristic
711D4—12232no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—6116no—
733C2×C4—6116no—
734C2×C4—614no—
735C2×C4—614no—
736C2×C4—614no—
737C2×C4—614no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—12232no—
744C2×C4—12232no—
745C2×C4—1228no—
746C2×C4—1228no—
747C2×C4—1228no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—2444no—
761C2×C4—2444no—
762C2×C4C22×C4×D6114yes—
763C2×C4C22×C4×D6114yes—
764C2×C4C2×D4×D6114yes—
765C2×C4C2×#1175822414yes—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—416no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—1224no—
775C22—1224no—
776C22—1224no—
777C22—24416no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22#117×D6114yes—
783C22C4×D4×D6114yes—
784C22C4×#1175822414yes—
785C22#1684028914yes—
786C22#1684029514yes—
787C22#1684030714yes—
788C22#1684031114yes—
789C22C23×C4×D6111yescharacteristic
790C22C22×D4×D6111yescharacteristic
791C22C2×#41×D6111yescharacteristic
792C22C2×#41×D6111yescharacteristic
793C22C2×#41×D6111yescharacteristic
794C22C2×#41×D6111yescharacteristic
795C22C22×#1175822411yescharacteristic
796C4—24no—
797C4—24no—
798C4—24no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—618no—
803C4—618no—
804C4—1224no—
805C4—1224no—
806C4—1224no—
807C4—2442no—
808C4—2442no—
809C2—44no—
810C2—2444no—
811C2#2144827918yesdirect product factor
812C2C2×#117×D6111yescharacteristic
813C2C2×C4×D4×D6111yescharacteristic
814C2C2×C4×#1175822411yescharacteristic
815C2C2×#1684028911yescharacteristic
816C2C2×#1684029511yescharacteristic
817C2C2×#1684030711yescharacteristic
818C2C2×#1684031111yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2293
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14519735C2semidirect
3. C22×#14519733C2semidirect
4. #21448279C2direct (N × H)
7. C2×#16839659C2semidirect
8. C2×#16839657C2semidirect
9. C2×#16839655C2semidirect
10. C2×#16839653C2semidirect
11. C2×#16839651C2semidirect
12. C2×#16839613C2semidirect
13. C2×C22⋊C4×Dic61C2semidirect
14. C2×#16839609C2semidirect
15. C2×C42×Dic61C2semidirect
16. C2×C61×#388C2semidirect
20. C2×#14519737C4semidirect
23. C2×#14519735C22semidirect
25. C2×#14519733C22semidirect
49. #16839659C22semidirect
50. #16839657C22semidirect
51. #16839655C22semidirect
52. #16839653C22semidirect
53. #16839651C22semidirect
54. #16839613C22semidirect
55. C22⋊C4×Dic61C22semidirect
56. #16839609C22semidirect
61. C42×Dic61C22semidirect
67. C61×#388C22semidirect
90. #14519737C2×C4semidirect
126. C2×C4×Dic61D4semidirect
264. C4×Dic61C2×D4semidirect
344. C2×Dic61#117semidirect
398. Dic61C2×#117semidirect
411. C2×#388D61semidirect
417. C2×C61#2293semidirect
468. #388C2×D61semidirect
479. C61C2×#2293semidirect
811. C2#21448279direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197372
C22×#145197352
C22×#145197332
#214482792
C2×#168396622
C2×#168396592
C2×#168396572
C2×#168396552
C2×#168396532
C2×#168396512
C2×#168396132
C2×C22⋊C4×Dic612
C2×#168396092
C2×C42×Dic612
C2×C61×#3882
C2×#229361