Finite Group Databasebeta

← C2×#21448360 #29838483

Subgroups — C2×#21448360 #29838483

Order 15616.

3790 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C22×#14519742C211yesmaximal, characteristic, complemented
3C22×#14519737C211yesmaximal, characteristic
4#21448360C2116yesmaximal, direct product factor
5C2×#16839666C211yesmaximal, characteristic, complemented
6C2×#16839662C211yesmaximal, characteristic
7C2×#16839656C211yesmaximal, characteristic, complemented
8C2×#16839653C211yesmaximal, characteristic, complemented
9C2×#16839652C211yesmaximal, characteristic, complemented
10C2×#16839626C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
13C2×#16839609C211yesmaximal, characteristic, complemented
14C2×#16839609C211yesmaximal, characteristic, complemented
15C2×C42×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519763C4116yescomplemented
22C2×#14519763C2218yes—
23C2×#14519742—28no—
24C2×#14519742C2218yescomplemented
25C2×#14519737—28no—
26C2×#14519737C2218yes—
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43C22×C4×Dic61C2211yescharacteristic
44C22×C4×Dic61C2211yescharacteristic
45#16839666C2218yescomplemented
46#16839662C2218yes—
47#16839656C2218yescomplemented
48#16839653C2218yescomplemented
49#16839652C2218yescomplemented
50#16839626C2218yescomplemented
51C22⋊C4×Dic61C2218yescomplemented
52C22⋊C4×Dic61C2218yescomplemented
53#16839609C2218yescomplemented
54#16839609C2218yescomplemented
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
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×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122C2×C418yescomplemented
74C22×Dic122C2314yes—
75C22×C22⋊D61—24no—
76C22×C22⋊D61—24no—
77C22×C22⋊D61C2×C418yes—
78C22×C22⋊D61C2314yes—
79C23×Dic61—24no—
80C23×Dic61—24no—
81C23×Dic61—24no—
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2314yes—
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61—24no—
93C22×C4×D61C2314yes—
94#14519763C2×C4164yescomplemented
95#14519742—232no—
96#14519737—232no—
97C2×#11758196—24no—
98C2×#11758196—24no—
99C2×#11758196—24no—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×C22⋊Dic61—24no—
104C2×C22⋊Dic61C2×C418yescomplemented
105C2×C22⋊Dic61C2314yes—
106C2×C22⋊Dic61C2314yes—
107C2×#11758198—24no—
108C2×#11758198—24no—
109C2×#11758198—24no—
110C2×#11758198C2×C418yescomplemented
111C2×#11758198C2×C418yescomplemented
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×C4×Dic61—24no—
118C2×C4×Dic61—24no—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61—24no—
122C2×C4×Dic61—24no—
123C2×C4×Dic61C2×C418yescomplemented
124C2×C4×Dic61D418yes—
125C2×C4×Dic61C2314yes—
126C2×C4×Dic61C2314yes—
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131C2×C4×Dic61C2314yes—
132C2×C4×Dic61C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
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×C418yescomplemented
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—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—28no—
216C22×Dic61—28no—
217C22×Dic61—28no—
218C22×Dic61—416no—
219C22×Dic61C22×C414yes—
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—28no—
236C2×C4×D61—28no—
237C2×C4×D61—28no—
238C2×C4×D61—416no—
239C2×Dic122—232no—
240C2×Dic122—28no—
241C2×Dic122—28no—
242C2×Dic122C22×C4116yescomplemented
243C4⋊C4×C61—28no—
244C22⋊C4×C61—28no—
245C22⋊C4×C61—28no—
246C22⋊C4×C61C22×C4116yescomplemented
247C42×C61—28no—
248C22⋊Dic61—28no—
249C22⋊Dic61C22×C4116yescomplemented
250#11758198—28no—
251#11758198—28no—
252#11758198—28no—
253#11758198C22×C4116yescomplemented
254#11758198C22×C4116yescomplemented
255#11758196—28no—
256#11758196—28no—
257#11758196—28no—
258C4×Dic61—28no—
259C4×Dic61—28no—
260C4×Dic61—28no—
261C4×Dic61—28no—
262C4×Dic61—28no—
263C4×Dic61—28no—
264C4×Dic61C22×C4116yescomplemented
265C4×Dic61C2×D4116yes—
266C23×C61—28no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61C23×C414yes—
280C23×C61C23×C412yes—
281C23×C61C22×D412yes—
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61C2×#4112yes—
285C23×C61C2×#4112yes—
286C23×C61C2×#4112yes—
287C23×C61C2511yescharacteristic
288C22×D61—28no—
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61C23×C414yes—
302C2×C4×C61—28no—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—28no—
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—22no—
320C2×C4×C61—44no—
321C2×C4×C61—44no—
322C2×C4×C61C23×C414yes—
323C2×C4×C61C23×C414yes—
324C2×C4×C61C22×D414yes—
325C2×C4×C61C2×#4114yes—
326C22⋊D61—232no—
327C2×Dic61—28no—
328C2×Dic61—28no—
329C2×Dic61—28no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
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—416no—
345C2×Dic61C4×D4116yes—
346C2×Dic61#124116yescomplemented
347C2×Dic61C23×C414yes—
348C2×Dic61C23×C414yes—
349C2×Dic61C23×C414yes—
350C2×Dic61C22×D414yes—
351C2×Dic61C22×D414yes—
352C2×Dic61C2×#4114yes—
353C2×Dic61C2×#4114yes—
354C2×Dic61C2×#4114yes—
355C2×Dic61C2×#4114yes—
356C4×D61—416no—
357Dic122—232no—
358C2×C4×#124—611nomaximal, Sylow
359C22×C61—24no—
360C22×C61—24no—
361C22×C61—24no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—416no—
367C22×C61C2×C4×D414yes—
368C22×C61C4×#4114yes—
369C22×C61C4×#4114yes—
370C22×C61C2×#12414yes—
371C22×C61#52914yes—
372C22×C61#52914yes—
373C22×C61#53214yes—
374C22×C61C24×C411yescharacteristic
375C22×C61C23×D411yescharacteristic
376C22×C61C22×#4111yescharacteristic
377C22×C61C22×#4111yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C22×#4111yescharacteristic
380C22×C61C22×#4111yescharacteristic
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—416no—
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—42no—
394C4×C61—42no—
395Dic61—24no—
396Dic61—24no—
397Dic61—24no—
398Dic61—42no—
399Dic61—42no—
400Dic61C2×C4×D418yes—
401Dic61C2×#12418yescomplemented
402C22×#124—611no—
403C22×C4×Q8—611no—
404C22×C4×D4—611no—
405C4×#124—6116no—
406C2×#391—611no—
407C2×#390—611no—
408C2×#388—611no—
409C2×#388—611no—
410C2×#388—611no—
411C2×#388D6111yescharacteristic, complemented
412C2×#382—611no—
413C2×C4×C22⋊C4—611no—
414C2×C4×C22⋊C4—611no—
415C2×C4×C22⋊C4—611no—
416C2×C4×C22⋊C4—611no—
417C2×C43—611no—
418C2×C61—44no—
419C2×C61C4×#12418yescomplemented
420C2×C61C22×C4×D411yescharacteristic
421C2×C61C2×C4×#4111yescharacteristic
422C2×C61C2×C4×#4111yescharacteristic
423C2×C61C22×#12411yescharacteristic
424C2×C61C2×#52911yescharacteristic
425C2×C61C2×#52911yescharacteristic
426C2×C61C2×#53211yescharacteristic
427D61—44no—
428C23×Q8—611no—
429C23×D4—611no—
430C24×C4—611no—
431C24×C4—611no—
432C2×#124—6116no—
433C2×#124—618no—
434C2×C4×Q8—618no—
435C2×C4×Q8—1228no—
436C2×C4×D4—618no—
437C2×C4×D4—1228no—
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#391—618no—
462#390—618no—
463#388—618no—
464#388—618no—
465#388—618no—
466#388C2×D6118yescomplemented
467#382—618no—
468C4×C22⋊C4—618no—
469C4×C22⋊C4—618no—
470C4×C22⋊C4—618no—
471C4×C22⋊C4—618no—
472C2×#95—611no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95C2×D6111yescharacteristic
479C2×#95C2×D6111yescharacteristic
480C43—618no—
481C61C2×C4×#12411yescharacteristic, complemented, Sylow
482C25—611no—
483C25C22×D6111yescharacteristic
484C22×Q8—618no—
485C22×Q8—614no—
486C22×Q8—1224no—
487C22×Q8—1224no—
488C22×D4—618no—
489C22×D4—614no—
490C22×D4—1224no—
491C22×D4—1224no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—614no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—614no—
501C23×C4—1224no—
502C23×C4—1224no—
503C23×C4—1224no—
504C23×C4—1224no—
505C23×C4—1224no—
506C23×C4—1224no—
507C23×C4C22×D6111yescharacteristic
508C23×C4C22×D6111yescharacteristic
509C23×C4C22×D6111yescharacteristic
510C23×C4C22×D6111yescharacteristic
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513#124—6164no—
514C4×Q8—12232no—
515C4×D4—12232no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—614no—
518C2×C4⋊C4—614no—
519C2×C4⋊C4—614no—
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—618no—
529C2×C22⋊C4—618no—
530C2×C22⋊C4—614no—
531C2×C22⋊C4—614no—
532C2×C22⋊C4—614no—
533C2×C22⋊C4—614no—
534C2×C22⋊C4—614no—
535C2×C22⋊C4—614no—
536C2×C22⋊C4—1224no—
537C2×C22⋊C4—1224no—
538C2×C22⋊C4—1224no—
539C2×C22⋊C4—1224no—
540C2×C22⋊C4C4×D6118yescomplemented
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#95—614no—
567#95—614no—
568#95C22×D6114yes—
569#95C22×D6114yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—614no—
577C24—612no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24C2×C4×D6114yes—
585C24C23×D6112yes—
586C24C23×D6111yescharacteristic
587C2×Q8—6116no—
588C2×Q8—1228no—
589C2×Q8—12232no—
590C2×Q8—1228no—
591C2×D4—6116no—
592C2×D4—1228no—
593C2×D4—12232no—
594C2×D4—1228no—
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—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—614no—
610C22×C4—614no—
611C22×C4—614no—
612C22×C4—614no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—614no—
618C22×C4—614no—
619C22×C4—614no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—1228no—
626C22×C4—1228no—
627C22×C4—1228no—
628C22×C4—1228no—
629C22×C4—1228no—
630C22×C4—1228no—
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×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—24416no—
644C22×C4—24416no—
645C22×C4C2×C4×D6114yes—
646C22×C4C2×C4×D6114yes—
647C22×C4D4×D6114yes—
648C22×C4#1175822414yes—
649C22×C4C23×D6112yes—
650C22×C4C23×D6112yes—
651C22×C4C23×D6112yes—
652C22×C4C23×D6112yes—
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C4⋊C4—28no—
656C4⋊C4—1228no—
657C4⋊C4—1228no—
658C4⋊C4—1228no—
659C22⋊C4—28no—
660C22⋊C4—28no—
661C22⋊C4—6116no—
662C22⋊C4—6116no—
663C22⋊C4—6116no—
664C22⋊C4—1228no—
665C22⋊C4—1228no—
666C22⋊C4—1228no—
667C22⋊C4—1228no—
668C22⋊C4C2×C4×D61116yescomplemented
669C42—28no—
670C42—6116no—
671C42—6116no—
672C42—1228no—
673C42—1228no—
674C42—1228no—
675C42—1228no—
676C42—1228no—
677C42—1228no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—614no—
692C23—1228no—
693C23—1228no—
694C23—1228no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—2444no—
702C23—2444no—
703C23—2444no—
704C23—2444no—
705C23C22×C4×D6114yes—
706C23C22×C4×D6112yes—
707C23C2×D4×D6112yes—
708C23#41×D6112yes—
709C23#41×D6112yes—
710C23#41×D6112yes—
711C23#41×D6112yes—
712C23C2×#1175822412yes—
713C23C24×D6111yescharacteristic
714Q8—12232no—
715D4—12232no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
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—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—6116no—
737C2×C4—6116no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—614no—
744C2×C4—614no—
745C2×C4—614no—
746C2×C4—614no—
747C2×C4—1228no—
748C2×C4—1228no—
749C2×C4—1228no—
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—1222no—
761C2×C4—1222no—
762C2×C4—24416no—
763C2×C4—24416no—
764C2×C4—2444no—
765C2×C4—2444no—
766C2×C4C22×C4×D6114yes—
767C2×C4C22×C4×D6114yes—
768C2×C4C2×D4×D6114yes—
769C2×C4C2×#1175822414yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—416no—
778C22—1224no—
779C22—1224no—
780C22—1224no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—24416no—
786C22C4×D4×D6114yes—
787C22C4×#1175822414yes—
788C22#1684023014yes—
789C22#124×D6114yes—
790C22#1684028914yes—
791C22#1684029514yes—
792C22#1684030714yes—
793C22C23×C4×D6111yescharacteristic
794C22C22×D4×D6111yescharacteristic
795C22C2×#41×D6111yescharacteristic
796C22C2×#41×D6111yescharacteristic
797C22C2×#41×D6111yescharacteristic
798C22C2×#41×D6111yescharacteristic
799C22C22×#1175822411yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—618no—
807C4—618no—
808C4—1224no—
809C4—1224no—
810C4—1224no—
811C4—2442no—
812C4—2442no—
813C2—44no—
814C2—2444no—
815C2#2144836018yesdirect product factor
816C2C2×C4×D4×D6111yescharacteristic
817C2C2×C4×#1175822411yescharacteristic
818C2C2×#1684023011yescharacteristic
819C2C2×#124×D6111yescharacteristic
820C2C2×#1684028911yescharacteristic
821C2C2×#1684029511yescharacteristic
822C2C2×#1684030711yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×C4×#124
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14519742C2semidirect
4. #21448360C2direct (N × H)
5. C2×#16839666C2semidirect
7. C2×#16839656C2semidirect
8. C2×#16839653C2semidirect
9. C2×#16839652C2semidirect
10. C2×#16839626C2semidirect
11. C2×C22⋊C4×Dic61C2semidirect
12. C2×C22⋊C4×Dic61C2semidirect
13. C2×#16839609C2semidirect
14. C2×#16839609C2semidirect
15. C2×C42×Dic61C2semidirect
16. C2×C61×#388C2semidirect
21. C2×#14519763C4semidirect
24. C2×#14519742C22semidirect
45. #16839666C22semidirect
47. #16839656C22semidirect
48. #16839653C22semidirect
49. #16839652C22semidirect
50. #16839626C22semidirect
51. C22⋊C4×Dic61C22semidirect
52. C22⋊C4×Dic61C22semidirect
53. #16839609C22semidirect
54. #16839609C22semidirect
61. C42×Dic61C22semidirect
67. C61×#388C22semidirect
73. C22×Dic122C2×C4semidirect
94. #14519763C2×C4semidirect
104. C2×C22⋊Dic61C2×C4semidirect
110. C2×#11758198C2×C4semidirect
111. C2×#11758198C2×C4semidirect
123. C2×C4×Dic61C2×C4semidirect
150. C2×C22⋊C4×C61C2×C4semidirect
242. C2×Dic122C22×C4semidirect
246. C22⋊C4×C61C22×C4semidirect
249. C22⋊Dic61C22×C4semidirect
253. #11758198C22×C4semidirect
254. #11758198C22×C4semidirect
264. C4×Dic61C22×C4semidirect
346. C2×Dic61#124semidirect
401. Dic61C2×#124semidirect
411. C2×#388D61semidirect
419. C2×C61C4×#124semidirect
466. #388C2×D61semidirect
481. C61C2×C4×#124semidirect
540. C2×C22⋊C4C4×D61semidirect
668. C22⋊C4C2×C4×D61semidirect
815. C2#21448360direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197632
C22×#145197422
C22×#145197372
#214483602
C2×#168396662
C2×#168396622
C2×#168396562
C2×#168396532
C2×#168396522
C2×#168396262
C2×C22⋊C4×Dic612
C2×#168396092
C2×C42×Dic612
C2×C61×#3882
C2×C4×#12461