Finite Group Databasebeta

← C2×#21449666 #29847922

Subgroups — C2×#21449666 #29847922

Order 15616.

3614 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519776C211yesmaximal, characteristic, complemented
2C22×#14519756C211yesmaximal, characteristic, complemented
3C22×#14519755C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D61C211yesmaximal, characteristic
5#21449666C2116yesmaximal, direct product factor
6C2×#16839685C211yesmaximal, characteristic, complemented
7C2×#16839684C211yesmaximal, characteristic, complemented
8C2×#16839675C211yesmaximal, characteristic, complemented
9C2×#16839674C211yesmaximal, characteristic, complemented
10C2×#16839662C211yesmaximal, characteristic
11C2×#16839662C211yesmaximal, characteristic
12C2×#16839659C211yesmaximal, characteristic, complemented
13C2×#16839657C211yesmaximal, characteristic, complemented
14C2×#16839636C211yesmaximal, characteristic, complemented
15C2×#16839613C211yesmaximal, characteristic, complemented
16C2×C61×#385C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C23×C22⋊D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519776—28no—
22C2×#14519776C2218yescomplemented
23C2×#14519756—28no—
24C2×#14519756C2218yescomplemented
25C2×#14519755—28no—
26C2×#14519755C2218yescomplemented
27C2×C4×C22⋊D61—28no—
28C2×C4×C22⋊D61C2218yes—
29C22×C4⋊Dic61C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758196C2211yescharacteristic
37C22×#11758196C2211yescharacteristic
38C22×C22⋊Dic61C2211yescharacteristic
39C22×C22⋊Dic61C2211yescharacteristic
40C22×C22⋊Dic61C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×#11758198C2211yescharacteristic
43C22×#11758198C2211yescharacteristic
44C22×#11758198C2211yescharacteristic
45C22×#11758198C2211yescharacteristic
46C22×C4×Dic61C2211yescharacteristic
47C22×C4×Dic61C2211yescharacteristic
48C22×C4×Dic61C2211yescharacteristic
49#16839685C2218yescomplemented
50#16839684C2218yescomplemented
51#16839675C2218yescomplemented
52#16839674C2218yescomplemented
53#16839662C2218yes—
54#16839662C2218yes—
55#16839659C2218yescomplemented
56#16839657C2218yescomplemented
57#16839636C2218yescomplemented
58#16839613C2218yescomplemented
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C2×#14519684C2211yescharacteristic
63C24×C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C61×#385C2218yescomplemented
69C2×#95×C61C2211yescharacteristic
70C2×#95×C61C2211yescharacteristic
71C24×D61C2311yescharacteristic
72C22×Dic122—24no—
73C22×Dic122—24no—
74C22×Dic122—24no—
75C22×Dic122—24no—
76C22×Dic122—42no—
77C22×Dic122—42no—
78C22×Dic122C2314yes—
79C22×Dic122C2314yes—
80C22×C22⋊D61—24no—
81C22×C22⋊D61—24no—
82C22×C22⋊D61Q818yescomplemented
83C22×C22⋊D61C2314yes—
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C22×C4×D61—24no—
92C22×C4×D61—24no—
93C22×C4×D61—42no—
94C22×C4×D61C2314yes—
95#14519776—232no—
96#14519756—232no—
97#14519755—232no—
98C4×C22⋊D61—232no—
99C2×C4⋊Dic61—24no—
100C2×C4⋊Dic61—24no—
101C2×C4⋊Dic61C2314yes—
102C2×C4⋊Dic61C2314yes—
103C2×#11758196—24no—
104C2×#11758196—24no—
105C2×#11758196—24no—
106C2×#11758196—24no—
107C2×#11758196—24no—
108C2×#11758196D418yes—
109C2×#11758196D418yescomplemented
110C2×#11758196C2314yes—
111C2×#11758196C2314yes—
112C2×#11758196C2314yes—
113C2×#11758196C2314yes—
114C2×#11758196C2314yes—
115C2×#11758196C2314yes—
116C2×#11758196C2314yes—
117C2×C22⋊Dic61—24no—
118C2×C22⋊Dic61—24no—
119C2×C22⋊Dic61—24no—
120C2×C22⋊Dic61C2314yes—
121C2×C22⋊Dic61C2314yes—
122C2×C22⋊Dic61C2314yes—
123C2×#11758198—24no—
124C2×#11758198—24no—
125C2×#11758198—24no—
126C2×#11758198—24no—
127C2×#11758198—42no—
128C2×#11758198C2314yes—
129C2×#11758198C2314yes—
130C2×#11758198C2314yes—
131C2×#11758198C2314yes—
132C2×#11758198C2314yes—
133C2×C4×Dic61—24no—
134C2×C4×Dic61—24no—
135C2×C4×Dic61—24no—
136C2×C4×Dic61C2314yes—
137C2×C4×Dic61C2314yes—
138C2×C4×Dic61C2314yes—
139#14519684C2314yes—
140#14519684C2314yes—
141#14519684C2314yes—
142#14519684C2314yes—
143C25×C61C2311yescharacteristic
144C23×C4×C61—24no—
145C23×C4×C61—24no—
146C23×C4×C61—42no—
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2314yes—
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61—24no—
155C2×C4⋊C4×C61—24no—
156C2×C4⋊C4×C61C2314yes—
157C2×C4⋊C4×C61C2314yes—
158C2×C22⋊C4×C61—24no—
159C2×C22⋊C4×C61—42no—
160C2×C22⋊C4×C61C2314yes—
161C2×C22⋊C4×C61C2314yes—
162#95×C61C2314yes—
163#95×C61C2314yes—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61C2×Q814yes—
171C24×C61C2412yes—
172C24×C61C2411yescharacteristic
173C23×D61—22no—
174C23×D61—22no—
175C23×D61—22no—
176C23×D61—22no—
177C23×D61—22no—
178C23×D61—22no—
179C23×D61C2×Q814yes—
180C23×D61C2412yes—
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×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—28no—
197C22×C4×C61—28no—
198C22×C4×C61—44no—
199C22×C4×C61—416no—
200C22×C4×C61C2×D414yes—
201C22×C4×C61C2×D414yes—
202C22×C4×C61#4114yes—
203C22×C4×C61C2412yes—
204C22×C4×C61C2412yes—
205C22×C4×C61C2412yes—
206C22×C4×C61C2412yes—
207C22×C4×C61C2412yes—
208C22×C4×C61C2412yes—
209C2×C22⋊D61—232no—
210C2×C22⋊D61—28no—
211C2×C22⋊D61—28no—
212C2×C22⋊D61C2×Q8116yescomplemented
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
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×Dic61C2×D414yes—
229C22×Dic61C2×D414yes—
230C22×Dic61C2×D414yes—
231C22×Dic61C2×D414yes—
232C22×Dic61C2×Q814yes—
233C22×Dic61#4114yes—
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236C22×Dic61C2412yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
239C22×Dic61C2412yes—
240C22×Dic61C2412yes—
241C2×C4×D61—28no—
242C2×C4×D61—28no—
243C2×C4×D61—44no—
244C2×C4×D61—416no—
245C2×Dic122—28no—
246C2×Dic122—28no—
247C2×Dic122—28no—
248C2×Dic122—28no—
249C2×Dic122—44no—
250C2×Dic122—44no—
251C2×Dic122—416no—
252C2×Dic122—416no—
253C4⋊C4×C61—28no—
254C4⋊C4×C61—28no—
255C22⋊C4×C61—28no—
256C22⋊C4×C61—44no—
257C22⋊Dic61—28no—
258C22⋊Dic61—28no—
259C22⋊Dic61—28no—
260#11758198—28no—
261#11758198—28no—
262#11758198—28no—
263#11758198—28no—
264#11758198—44no—
265C4⋊Dic61—28no—
266C4⋊Dic61—28no—
267#11758196—28no—
268#11758196—28no—
269#11758196—28no—
270#11758196—28no—
271#11758196—28no—
272#11758196C2×D4116yes—
273#11758196C2×D4116yescomplemented
274C4×Dic61—28no—
275C4×Dic61—28no—
276C4×Dic61—28no—
277C23×C61—28no—
278C23×C61—28no—
279C23×C61—28no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—44no—
287C23×C61—44no—
288C23×C61—44no—
289C23×C61—44no—
290C23×C61C22×D412yes—
291C23×C61C22×D412yes—
292C23×C61C22×Q814yes—
293C23×C61C22×Q812yes—
294C23×C61C2×#4112yes—
295C23×C61C2×#4112yes—
296C23×C61H(5,𝔽2)12yes—
297C23×C612−1+412yes—
298C23×C61C2511yescharacteristic
299C22×D61—28no—
300C22×D61—28no—
301C22×D61—28no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—44no—
309C22×D61—44no—
310C22×D61—44no—
311C22×D61—44no—
312C22×D61C22×Q814yes—
313C2×C4×C61—28no—
314C2×C4×C61—28no—
315C2×C4×C61—28no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—416no—
332C2×C4×C61—44no—
333C2×C4×C61—44no—
334C2×C4×C61—44no—
335C2×C4×C61C22×D414yes—
336C2×C4×C61C22×D414yes—
337C2×C4×C61C2×#4114yes—
338C22⋊D61—232no—
339C2×Dic61—28no—
340C2×Dic61—28no—
341C2×Dic61—28no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—44no—
358C2×Dic61—44no—
359C2×Dic61—44no—
360C2×Dic61C22⋊Q8116yescomplemented
361C2×Dic61C22×D414yes—
362C2×Dic61C22×D414yes—
363C2×Dic61C22×D414yes—
364C2×Dic61C22×D414yes—
365C2×Dic61C22×Q814yes—
366C2×Dic61C2×#4114yes—
367C4×D61—416no—
368Dic122—416no—
369Dic122—416no—
370C2×#2452—611nomaximal, Sylow
371C22×C61—24no—
372C22×C61—24no—
373C22×C61—24no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—416no—
379C22×C61C2×C22⋊Q814yes—
380C22×C61#53214yes—
381C22×C61#54214yes—
382C22×C61D4214yes—
383C22×C61#54814yes—
384C22×C61D4×Q814yes—
385C22×C61#55414yes—
386C22×C61C23×D411yescharacteristic
387C22×C61C23×D411yescharacteristic
388C22×C61C23×Q811yescharacteristic
389C22×C61C22×#4111yescharacteristic
390C22×C61C22×#4111yescharacteristic
391C22×C61C2×H(5,𝔽2)11yescharacteristic
392C22×C61C2×2−1+411yescharacteristic
393C2×D61—24no—
394C2×D61—24no—
395C2×D61—24no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—416no—
401C4×C61—24no—
402C4×C61—24no—
403C4×C61—24no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—42no—
407Dic61—24no—
408Dic61—24no—
409Dic61—24no—
410Dic61—42no—
411Dic61—42no—
412Dic61—42no—
413Dic61C2×C22⋊Q818yescomplemented
414C22×C4⋊Q8—611no—
415C22×C22⋊Q8—611no—
416C22×C22⋊Q8—611no—
417C22×C4×D4—611no—
418#2452—6116no—
419C2×#396—611no—
420C2×#396—611no—
421C2×#393—611no—
422C2×#393—611no—
423C2×#390—611no—
424C2×#390—611no—
425C2×#389—611no—
426C2×#389—611no—
427C2×#385—611no—
428C2×#385D6111yescharacteristic, complemented
429C2×C4×C4⋊C4—611no—
430C2×C61—44no—
431C2×C61#245218yescomplemented
432C2×C61C22×C22⋊Q811yescharacteristic
433C2×C61C2×#53211yescharacteristic
434C2×C61C2×#54211yescharacteristic
435C2×C61C2×D4211yescharacteristic
436C2×C61C2×#54811yescharacteristic
437C2×C61C2×D4×Q811yescharacteristic
438C2×C61C2×#55411yescharacteristic
439D61—44no—
440C23×Q8—611no—
441C23×Q8—611no—
442C23×D4—611no—
443C24×C4—611no—
444C24×C4C2×D6111yescharacteristic
445C2×C4⋊Q8—618no—
446C2×C4⋊Q8—1228no—
447C2×C22⋊Q8—618no—
448C2×C22⋊Q8—618no—
449C2×C22⋊Q8—1228no—
450C2×C22⋊Q8—1228no—
451C2×C4×D4—618no—
452C2×C4×D4—1228no—
453C22×C4⋊C4—611no—
454C22×C4⋊C4—611no—
455C22×C4⋊C4—611no—
456C22×C4⋊C4—611no—
457C22×C4⋊C4—611no—
458C22×C4⋊C4—611no—
459C22×C4⋊C4—611no—
460C22×C4⋊C4—611no—
461C22×C4⋊C4—611no—
462C22×C4⋊C4C2×D6111yescharacteristic
463C22×C4⋊C4C2×D6111yescharacteristic
464C22×C22⋊C4—611no—
465C22×C22⋊C4—611no—
466C22×C22⋊C4—611no—
467C22×C22⋊C4—611no—
468C22×C22⋊C4—611no—
469C22×C22⋊C4—611no—
470C22×C22⋊C4—611no—
471C22×C22⋊C4—611no—
472C22×C22⋊C4C2×D6111yescharacteristic
473C22×C22⋊C4C2×D6111yescharacteristic
474C22×C42—611no—
475C22×C42—611no—
476C22×C42—611no—
477#396—618no—
478#396—618no—
479#393—618no—
480#393—618no—
481#390—618no—
482#390—618no—
483#389—618no—
484#389—618no—
485#385—618no—
486#385C2×D6118yescomplemented
487C4×C4⋊C4—618no—
488C2×#95—611no—
489C2×#95—611no—
490C2×#95—611no—
491C2×#95—611no—
492C2×#95C2×D6111yescharacteristic
493C2×#95C2×D6111yescharacteristic
494C61C2×#245211yescharacteristic, complemented, Sylow
495C25—611no—
496C25C22×D6111yescharacteristic
497C22×Q8—614no—
498C22×Q8—614no—
499C22×Q8—1224no—
500C22×Q8—1224no—
501C22×Q8—1224no—
502C22×Q8—1224no—
503C22×Q8—2442no—
504C22×Q8—2442no—
505C22×D4—618no—
506C22×D4—614no—
507C22×D4—1224no—
508C22×D4—1224no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—42no—
512C23×C4—611no—
513C23×C4—611no—
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—611no—
518C23×C4—611no—
519C23×C4—614no—
520C23×C4—1224no—
521C23×C4—1224no—
522C23×C4—2442no—
523C23×C4C22×D6111yescharacteristic
524C23×C4C22×D6111yescharacteristic
525C23×C4C22×D6111yescharacteristic
526C23×C4C22×D6114yes—
527C23×C4C22×D6111yescharacteristic
528C23×C4C22×D6111yescharacteristic
529C23×C4C22×D6111yescharacteristic
530C4⋊Q8—12232no—
531C22⋊Q8—12232no—
532C22⋊Q8—12232no—
533C4×D4—12232no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—618no—
537C2×C4⋊C4—618no—
538C2×C4⋊C4—614no—
539C2×C4⋊C4—614no—
540C2×C4⋊C4—614no—
541C2×C4⋊C4—614no—
542C2×C4⋊C4—614no—
543C2×C4⋊C4—614no—
544C2×C4⋊C4—614no—
545C2×C4⋊C4—614no—
546C2×C4⋊C4—614no—
547C2×C4⋊C4—1224no—
548C2×C4⋊C4—1224no—
549C2×C4⋊C4—1224no—
550C2×C4⋊C4—1224no—
551C2×C4⋊C4—1224no—
552C2×C4⋊C4—1224no—
553C2×C4⋊C4—1224no—
554C2×C4⋊C4C22×D6114yes—
555C2×C4⋊C4C22×D6114yes—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—614no—
559C2×C22⋊C4—614no—
560C2×C22⋊C4—614no—
561C2×C22⋊C4—614no—
562C2×C22⋊C4—614no—
563C2×C22⋊C4—614no—
564C2×C22⋊C4—614no—
565C2×C22⋊C4—614no—
566C2×C22⋊C4—1224no—
567C2×C22⋊C4—1224no—
568C2×C22⋊C4—1224no—
569C2×C22⋊C4—1224no—
570C2×C22⋊C4—1224no—
571C2×C22⋊C4—1224no—
572C2×C22⋊C4—1224no—
573C2×C22⋊C4—2442no—
574C2×C22⋊C4C22×D6114yes—
575C2×C22⋊C4C22×D6114yes—
576C2×C42—614no—
577C2×C42—614no—
578C2×C42—614no—
579C2×C42—1224no—
580C2×C42—1224no—
581C2×C42—1224no—
582#95—614no—
583#95—614no—
584#95—614no—
585#95—614no—
586#95C22×D6114yes—
587#95C22×D6114yes—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—614no—
595C24—612no—
596C24—1222no—
597C24—1222no—
598C24—1222no—
599C24—1222no—
600C24—1222no—
601C24—1222no—
602C24Q8×D6114yes—
603C24C23×D6112yes—
604C24C23×D6111yescharacteristic
605C2×Q8—1228no—
606C2×Q8—1228no—
607C2×Q8—1228no—
608C2×Q8—1228no—
609C2×Q8—2444no—
610C2×Q8—2444no—
611C2×Q8—24416no—
612C2×Q8—24416no—
613C2×D4—6116no—
614C2×D4—1228no—
615C2×D4—12232no—
616C2×D4—1228no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—44no—
635C22×C4—416no—
636C22×C4—614no—
637C22×C4—614no—
638C22×C4—614no—
639C22×C4—612no—
640C22×C4—614no—
641C22×C4—614no—
642C22×C4—614no—
643C22×C4—612no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—1228no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1228no—
666C22×C4—2444no—
667C22×C4—24416no—
668C22×C4#1175822214yes—
669C22×C4D4×D6114yes—
670C22×C4D4×D6114yes—
671C22×C4C23×D6112yes—
672C22×C4C23×D6112yes—
673C22×C4C23×D6112yes—
674C22×C4C23×D6112yes—
675C22×C4C23×D6112yes—
676C22×C4C23×D6112yes—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—6116no—
680C4⋊C4—6116no—
681C4⋊C4—1228no—
682C4⋊C4—1228no—
683C4⋊C4—1228no—
684C4⋊C4—1228no—
685C4⋊C4—1228no—
686C4⋊C4—1228no—
687C4⋊C4—1228no—
688C22⋊C4—28no—
689C22⋊C4—44no—
690C22⋊C4—1228no—
691C22⋊C4—1228no—
692C22⋊C4—1228no—
693C22⋊C4—1228no—
694C22⋊C4—1228no—
695C22⋊C4—1228no—
696C22⋊C4—1228no—
697C22⋊C4—2444no—
698C42—1228no—
699C42—1228no—
700C42—1228no—
701C23—28no—
702C23—28no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—28no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—614no—
715C23—1228no—
716C23—1228no—
717C23—1222no—
718C23—1222no—
719C23—1222no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1228no—
724C23—2444no—
725C23—2444no—
726C23—2444no—
727C23—2444no—
728C23C2×D4×D6112yes—
729C23C2×D4×D6112yes—
730C23C2×Q8×D6114yes—
731C23C2×Q8×D6112yes—
732C23#41×D6112yes—
733C23C2×#1175822212yes—
734C23#1451982212yes—
735C23#1451982412yes—
736C23C24×D6111yescharacteristic
737Q8—24416no—
738Q8—24416no—
739D4—12232no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—416no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—6116no—
763C2×C4—614no—
764C2×C4—614no—
765C2×C4—614no—
766C2×C4—614no—
767C2×C4—614no—
768C2×C4—614no—
769C2×C4—1228no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1228no—
777C2×C4—1228no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—24416no—
788C2×C4—2444no—
789C2×C4—2444no—
790C2×C4—2444no—
791C2×C4C2×D4×D6114yes—
792C2×C4C2×D4×D6114yes—
793C2×C4C2×#1175822214yes—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—416no—
801C22—42no—
802C22—1224no—
803C22—1224no—
804C22—1224no—
805C22—2442no—
806C22—2442no—
807C22—2442no—
808C22—24416no—
809C22—2442no—
810C22C22⋊Q8×D6114yes—
811C22#1684030914yes—
812C22#1684038014yes—
813C22#1684039414yes—
814C22#1684042114yes—
815C22#1684042514yes—
816C22#1684046714yes—
817C22C22×D4×D6111yescharacteristic
818C22C22×D4×D6111yescharacteristic
819C22C22×Q8×D6111yescharacteristic
820C22C2×#41×D6111yescharacteristic
821C22C22×#1175822211yescharacteristic
822C22C2×#1451982211yescharacteristic
823C22C2×#1451982411yescharacteristic
824C4—24no—
825C4—24no—
826C4—24no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—618no—
831C4—1224no—
832C4—1224no—
833C4—1224no—
834C4—2442no—
835C4—2442no—
836C4—2442no—
837C2—44no—
838C2—2444no—
839C2#2144966618yesdirect product factor
840C2C2×C22⋊Q8×D6111yescharacteristic
841C2C2×#1684030911yescharacteristic
842C2C2×#1684038011yescharacteristic
843C2C2×#1684039411yescharacteristic
844C2C2×#1684042111yescharacteristic
845C2C2×#1684042511yescharacteristic
846C2C2×#1684046711yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#385D61
hypocenterC61C2×#2452
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14519776C2semidirect
2. C22×#14519756C2semidirect
3. C22×#14519755C2semidirect
5. #21449666C2direct (N × H)
6. C2×#16839685C2semidirect
7. C2×#16839684C2semidirect
8. C2×#16839675C2semidirect
9. C2×#16839674C2semidirect
12. C2×#16839659C2semidirect
13. C2×#16839657C2semidirect
14. C2×#16839636C2semidirect
15. C2×#16839613C2semidirect
16. C2×C61×#385C2semidirect
22. C2×#14519776C22semidirect
24. C2×#14519756C22semidirect
26. C2×#14519755C22semidirect
49. #16839685C22semidirect
50. #16839684C22semidirect
51. #16839675C22semidirect
52. #16839674C22semidirect
55. #16839659C22semidirect
56. #16839657C22semidirect
57. #16839636C22semidirect
58. #16839613C22semidirect
68. C61×#385C22semidirect
82. C22×C22⋊D61Q8semidirect
109. C2×#11758196D4semidirect
212. C2×C22⋊D61C2×Q8semidirect
273. #11758196C2×D4semidirect
360. C2×Dic61C22⋊Q8semidirect
413. Dic61C2×C22⋊Q8semidirect
428. C2×#385D61semidirect
431. C2×C61#2452semidirect
486. #385C2×D61semidirect
494. C61C2×#2452semidirect
839. C2#21449666direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197762
C22×#145197562
C22×#145197552
C22×C4×C22⋊D612
#214496662
C2×#168396852
C2×#168396842
C2×#168396752
C2×#168396742
C2×#168396622
C2×#168396592
C2×#168396572
C2×#168396362
C2×#168396132
C2×C61×#3852
C2×#245261