Finite Group Databasebeta

← C2×#21448838 #29839545

Subgroups — C2×#21448838 #29839545

Order 15616.

4782 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519750C211yesmaximal, characteristic
2C22×#14519739C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D61C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D61C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
6#21448838C2116yesmaximal, direct product factor
7C2×#16839662C211yesmaximal, characteristic, complemented
8C2×#16839657C211yesmaximal, characteristic, complemented
9C2×#16839655C211yesmaximal, characteristic, complemented
10C2×#16839652C211yesmaximal, characteristic, complemented
11C2×#16839640C211yesmaximal, characteristic, complemented
12C2×#16839638C211yesmaximal, characteristic, complemented
13C2×#16839636C211yesmaximal, characteristic, complemented
14C2×#16839613C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#385C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C22⋊D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C23×C4×D61C2211yescharacteristic
24C2×#14519750C4116yescomplemented
25C2×#14519750C2218yes—
26C2×#14519739—28no—
27C2×#14519739C2218yescomplemented
28C2×C4×C22⋊D61—28no—
29C2×C4×C22⋊D61—28no—
30C2×C4×C22⋊D61C2218yescomplemented
31C2×C4×C22⋊D61C2218yescomplemented
32C22×C4⋊Dic61C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758196C2211yescharacteristic
37C2×C4⋊C4×D61—28no—
38C2×C4⋊C4×D61C2218yescomplemented
39C22×C22⋊Dic61C2211yescharacteristic
40C22×C22⋊Dic61C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×#11758198C2211yescharacteristic
43C22×#11758198C2211yescharacteristic
44C22×#11758198C2211yescharacteristic
45C22×#11758198C2211yescharacteristic
46C22×#11758198C2211yescharacteristic
47C22×C4×Dic61C2211yescharacteristic
48C22×C4×Dic61C2211yescharacteristic
49C22×C4×Dic61C2211yescharacteristic
50C22×C4×Dic61C2211yescharacteristic
51#16839662C2218yescomplemented
52#16839657C2218yescomplemented
53#16839655C2218yescomplemented
54#16839652C2218yescomplemented
55#16839640C2218yescomplemented
56#16839638C2218yescomplemented
57#16839636C2218yescomplemented
58#16839613C2218yescomplemented
59#16839609C2218yescomplemented
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C2×#14519684C2211yescharacteristic
63C2×#14519684C2211yescharacteristic
64C24×C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C4⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C22×C22⋊C4×C61C2211yescharacteristic
69C61×#385C2218yescomplemented
70C2×#95×C61C2211yescharacteristic
71C2×#95×C61C2211yescharacteristic
72C24×D61C2311yescharacteristic
73C24×D61C2311yescharacteristic
74C22×D244—24no—
75C22×D244—24no—
76C22×D244C2×C418yescomplemented
77C22×D244C2314yes—
78C22×C22⋊D61—24no—
79C22×C22⋊D61—24no—
80C22×C22⋊D61—24no—
81C22×C22⋊D61—24no—
82C22×C22⋊D61C2×C418yescomplemented
83C22×C22⋊D61C2×C418yescomplemented
84C22×C22⋊D61C2314yes—
85C22×C22⋊D61C2314yes—
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C23×Dic61C2311yescharacteristic
92C22×C4×D61—24no—
93C22×C4×D61—24no—
94C22×C4×D61—24no—
95C22×C4×D61—24no—
96C22×C4×D61—24no—
97C22×C4×D61—24no—
98C22×C4×D61—24no—
99C22×C4×D61—24no—
100C22×C4×D61—42no—
101C22×C4×D61—42no—
102C22×C4×D61—42no—
103C22×C4×D61C2×C418yescomplemented
104C22×C4×D61C2314yes—
105C22×C4×D61C2314yes—
106C22×C4×D61C2314yes—
107C22×C4×D61C2314yes—
108#14519750C2×C4164yescomplemented
109#14519739—232no—
110C4×C22⋊D61—232no—
111C4×C22⋊D61—232no—
112C2×C4⋊Dic61—24no—
113C2×C4⋊Dic61C2314yes—
114C2×#11758196—24no—
115C2×#11758196—24no—
116C2×#11758196C2×C418yescomplemented
117C2×#11758196D418yescomplemented
118C2×#11758196C2314yes—
119C2×#11758196C2314yes—
120C2×#11758196C2314yes—
121C2×#11758196C2314yes—
122C4⋊C4×D61—232no—
123C2×C22⋊Dic61—24no—
124C2×C22⋊Dic61—24no—
125C2×C22⋊Dic61C2314yes—
126C2×C22⋊Dic61C2314yes—
127C2×#11758198—24no—
128C2×#11758198—24no—
129C2×#11758198—24no—
130C2×#11758198—42no—
131C2×#11758198C2×C418yescomplemented
132C2×#11758198D418yescomplemented
133C2×#11758198C2314yes—
134C2×#11758198C2314yes—
135C2×#11758198C2314yes—
136C2×#11758198C2314yes—
137C2×#11758198C2314yes—
138C2×#11758198C2314yes—
139C2×C4×Dic61—24no—
140C2×C4×Dic61—24no—
141C2×C4×Dic61—24no—
142C2×C4×Dic61—24no—
143C2×C4×Dic61C2314yes—
144C2×C4×Dic61C2314yes—
145C2×C4×Dic61C2314yes—
146C2×C4×Dic61C2314yes—
147#14519684C2314yes—
148#14519684C2314yes—
149#14519684C2314yes—
150#14519684C2314yes—
151C25×C61C2311yescharacteristic
152C23×C4×C61—24no—
153C23×C4×C61—24no—
154C23×C4×C61—42no—
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2314yes—
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C2×C4⋊C4×C61—24no—
163C2×C4⋊C4×C61—24no—
164C2×C4⋊C4×C61C2314yes—
165C2×C4⋊C4×C61C2314yes—
166C2×C22⋊C4×C61—42no—
167C2×C22⋊C4×C61C2×C418yescomplemented
168C2×C22⋊C4×C61C2314yes—
169C2×C22⋊C4×C61C2314yes—
170#95×C61C2314yes—
171#95×C61C2314yes—
172C24×C61—22no—
173C24×C61—22no—
174C24×C61—22no—
175C24×C61—22no—
176C24×C61—22no—
177C24×C61—22no—
178C24×C61C22×C414yes—
179C24×C61C2412yes—
180C24×C61C2411yescharacteristic
181C23×D61—22no—
182C23×D61—22no—
183C23×D61—22no—
184C23×D61—22no—
185C23×D61—22no—
186C23×D61—22no—
187C23×D61—22no—
188C23×D61—22no—
189C23×D61—22no—
190C23×D61—22no—
191C23×D61C22×C414yes—
192C23×D61C22×C414yes—
193C23×D61C2×D414yes—
194C23×D61#4114yes—
195C23×D61C2412yes—
196C23×D61C2412yes—
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×C61—28no—
212C22×C4×C61—28no—
213C22×C4×C61—44no—
214C22×C4×C61—416no—
215C22×C4×C61C22×C414yes—
216C22×C4×C61C22×C414yes—
217C22×C4×C61C2×D414yes—
218C22×C4×C61C2×D414yes—
219C22×C4×C61C2412yes—
220C22×C4×C61C2412yes—
221C22×C4×C61C2412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2412yes—
224C22×C4×C61C2412yes—
225C2×C22⋊D61—232no—
226C2×C22⋊D61—28no—
227C2×C22⋊D61—28no—
228C2×C22⋊D61—232no—
229C2×C22⋊D61—28no—
230C2×C22⋊D61—28no—
231C2×C22⋊D61C22×C4116yescomplemented
232C2×C22⋊D61C22×C4116yescomplemented
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61—22no—
236C22×Dic61—22no—
237C22×Dic61—22no—
238C22×Dic61—22no—
239C22×Dic61—22no—
240C22×Dic61—22no—
241C22×Dic61—22no—
242C22×Dic61—22no—
243C22×Dic61—22no—
244C22×Dic61—22no—
245C22×Dic61C22×C414yes—
246C22×Dic61C22×C414yes—
247C22×Dic61C2×D414yes—
248C22×Dic61C2×D414yes—
249C22×Dic61C2×D414yes—
250C22×Dic61#4114yes—
251C22×Dic61C2412yes—
252C22×Dic61C2412yes—
253C22×Dic61C2412yes—
254C22×Dic61C2412yes—
255C22×Dic61C2412yes—
256C22×Dic61C2412yes—
257C2×D244—232no—
258C2×D244—28no—
259C2×D244—28no—
260C2×D244C22×C4116yescomplemented
261C2×C4×D61—232no—
262C2×C4×D61—28no—
263C2×C4×D61—28no—
264C2×C4×D61—28no—
265C2×C4×D61—28no—
266C2×C4×D61—28no—
267C2×C4×D61—28no—
268C2×C4×D61—28no—
269C2×C4×D61—28no—
270C2×C4×D61—44no—
271C2×C4×D61—44no—
272C2×C4×D61—44no—
273C2×C4×D61—416no—
274C2×C4×D61—416no—
275C2×C4×D61—416no—
276C2×C4×D61C22×C4116yescomplemented
277C4⋊C4×C61—28no—
278C4⋊C4×C61—28no—
279C22⋊C4×C61—44no—
280C22⋊C4×C61C22×C4116yescomplemented
281C22⋊Dic61—28no—
282C22⋊Dic61—28no—
283#11758198—28no—
284#11758198—28no—
285#11758198—28no—
286#11758198—44no—
287#11758198C22×C4116yescomplemented
288#11758198C2×D4116yescomplemented
289C4⋊Dic61—28no—
290#11758196—28no—
291#11758196—28no—
292#11758196C22×C4116yescomplemented
293#11758196C2×D4116yescomplemented
294C4×Dic61—28no—
295C4×Dic61—28no—
296C4×Dic61—28no—
297C4×Dic61—28no—
298C23×C61—28no—
299C23×C61—28no—
300C23×C61—28no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—44no—
308C23×C61—44no—
309C23×C61—44no—
310C23×C61—44no—
311C23×C61C23×C414yes—
312C23×C61C23×C412yes—
313C23×C61C22×D412yes—
314C23×C61C22×D412yes—
315C23×C61C2×#4112yes—
316C23×C61C2×#4112yes—
317C23×C61H(5,𝔽2)12yes—
318C23×C612−1+412yes—
319C23×C61C2511yescharacteristic
320C22×D61—28no—
321C22×D61—28no—
322C22×D61—28no—
323C22×D61—28no—
324C22×D61—28no—
325C22×D61—28no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—28no—
331C22×D61—28no—
332C22×D61—28no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—44no—
340C22×D61—44no—
341C22×D61—44no—
342C22×D61—44no—
343C22×D61C4×D4116yescomplemented
344C22×D61C23×C414yes—
345C22×D61C23×C414yes—
346C22×D61C22×D414yes—
347C22×D61C2×#4114yes—
348C2×C4×C61—28no—
349C2×C4×C61—28no—
350C2×C4×C61—28no—
351C2×C4×C61—28no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—416no—
367C2×C4×C61—44no—
368C2×C4×C61—44no—
369C2×C4×C61C23×C414yes—
370C2×C4×C61C23×C414yes—
371C2×C4×C61C22×D414yes—
372C2×C4×C61C22×D414yes—
373C22⋊D61—232no—
374C22⋊D61—232no—
375C2×Dic61—28no—
376C2×Dic61—28no—
377C2×Dic61—28no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—44no—
391C2×Dic61—44no—
392C2×Dic61C4×D4116yescomplemented
393C2×Dic61C23×C414yes—
394C2×Dic61C23×C414yes—
395C2×Dic61C22×D414yes—
396C2×Dic61C22×D414yes—
397C2×Dic61C22×D414yes—
398C2×Dic61C2×#4114yes—
399D244—232no—
400C4×D61—232no—
401C4×D61—416no—
402C4×D61—416no—
403C4×D61—416no—
404C2×#2361—611nomaximal, Sylow
405C22×C61—24no—
406C22×C61—24no—
407C22×C61—24no—
408C22×C61—416no—
409C22×C61—42no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61C2×C4×D414yes—
414C22×C61C2×C4×D414yes—
415C22×C61#52014yes—
416C22×C61D4214yes—
417C22×C61#54714yes—
418C22×C61#54814yes—
419C22×C61#55314yes—
420C22×C61C24×C411yescharacteristic
421C22×C61C23×D411yescharacteristic
422C22×C61C23×D411yescharacteristic
423C22×C61C22×#4111yescharacteristic
424C22×C61C22×#4111yescharacteristic
425C22×C61C2×H(5,𝔽2)11yescharacteristic
426C22×C61C2×2−1+411yescharacteristic
427C2×D61—232no—
428C2×D61—24no—
429C2×D61—24no—
430C2×D61—24no—
431C2×D61—24no—
432C2×D61—24no—
433C2×D61—24no—
434C2×D61—24no—
435C2×D61—24no—
436C2×D61—24no—
437C2×D61—416no—
438C2×D61—42no—
439C2×D61—42no—
440C2×D61—42no—
441C2×D61—42no—
442C2×D61C2×C4×D418yescomplemented
443C4×C61—24no—
444C4×C61—24no—
445C4×C61—24no—
446C4×C61—24no—
447C4×C61—42no—
448C4×C61—42no—
449Dic61—24no—
450Dic61—24no—
451Dic61—24no—
452Dic61—42no—
453Dic61—42no—
454Dic61C2×C4×D418yescomplemented
455C22×#121—611no—
456C22×C4×D4—611no—
457C22×C4×D4—611no—
458C22×C4×D4—611no—
459C23×C4⋊C4—611no—
460#2361—6116no—
461C2×#390—611no—
462C2×#389—611no—
463C2×#388—611no—
464C2×#388—611no—
465C2×#386—611no—
466C2×#386—611no—
467C2×#385—611no—
468C2×#385D6111yescharacteristic, complemented
469C2×C4×C4⋊C4—611no—
470C2×C4×C22⋊C4—611no—
471C2×C61—44no—
472C2×C61#236118yescomplemented
473C2×C61C22×C4×D411yescharacteristic
474C2×C61C22×C4×D411yescharacteristic
475C2×C61C2×#52011yescharacteristic
476C2×C61C2×D4211yescharacteristic
477C2×C61C2×#54711yescharacteristic
478C2×C61C2×#54811yescharacteristic
479C2×C61C2×#55311yescharacteristic
480D61—28no—
481D61—44no—
482C23×D4—611no—
483C23×D4—611no—
484C23×D4—611no—
485C24×C4—611no—
486C24×C4—611no—
487C24×C4—611no—
488C24×C4—611no—
489C24×C4C2×D6111yescharacteristic
490C2×#121—6116no—
491C2×#121—618no—
492C2×C4×D4—618no—
493C2×C4×D4—618no—
494C2×C4×D4—618no—
495C2×C4×D4—1228no—
496C2×C4×D4—1228no—
497C2×C4×D4—1228no—
498C22×C4⋊C4—611no—
499C22×C4⋊C4—611no—
500C22×C4⋊C4—611no—
501C22×C4⋊C4—611no—
502C22×C4⋊C4—611no—
503C22×C4⋊C4—618no—
504C22×C4⋊C4—1228no—
505C22×C4⋊C4C2×D6111yescharacteristic
506C22×C4⋊C4C2×D6111yescharacteristic
507C22×C22⋊C4—611no—
508C22×C22⋊C4—611no—
509C22×C22⋊C4—611no—
510C22×C22⋊C4—611no—
511C22×C22⋊C4—611no—
512C22×C22⋊C4—611no—
513C22×C22⋊C4—611no—
514C22×C22⋊C4—611no—
515C22×C22⋊C4C2×D6111yescharacteristic
516C22×C22⋊C4C2×D6111yescharacteristic
517C22×C42—611no—
518C22×C42—611no—
519C22×C42—611no—
520C22×C42—611no—
521#390—618no—
522#389—618no—
523#388—618no—
524#388—618no—
525#386—618no—
526#386—618no—
527#385—618no—
528#385C2×D6118yescomplemented
529C4×C4⋊C4—618no—
530C4×C22⋊C4—618no—
531C2×#95—611no—
532C2×#95—611no—
533C2×#95—611no—
534C2×#95—611no—
535C2×#95C2×D6111yescharacteristic
536C2×#95C2×D6111yescharacteristic
537C61C2×#236111yescharacteristic, complemented, Sylow
538C25—611no—
539C25—611no—
540C25C22×D6111yescharacteristic
541C22×D4—618no—
542C22×D4—618no—
543C22×D4—614no—
544C22×D4—614no—
545C22×D4—618no—
546C22×D4—614no—
547C22×D4—1224no—
548C22×D4—1224no—
549C22×D4—1224no—
550C22×D4—1224no—
551C22×D4—1224no—
552C22×D4—1224no—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—42no—
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—618no—
561C23×C4—614no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—614no—
565C23×C4—614no—
566C23×C4—614no—
567C23×C4—1224no—
568C23×C4—1224no—
569C23×C4—1224no—
570C23×C4—1224no—
571C23×C4—1224no—
572C23×C4—1224no—
573C23×C4—1224no—
574C23×C4—1224no—
575C23×C4—2442no—
576C23×C4—2442no—
577C23×C4—2442no—
578C23×C4C22×D6111yescharacteristic
579C23×C4C22×D6111yescharacteristic
580C23×C4C22×D6114yes—
581C23×C4C22×D6111yescharacteristic
582C23×C4C22×D6111yescharacteristic
583C23×C4C22×D6111yescharacteristic
584C23×C4C22×D6111yescharacteristic
585#121—6164no—
586C4×D4—12232no—
587C4×D4—12232no—
588C4×D4—12232no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—618no—
592C2×C4⋊C4—618no—
593C2×C4⋊C4—614no—
594C2×C4⋊C4—614no—
595C2×C4⋊C4—614no—
596C2×C4⋊C4—614no—
597C2×C4⋊C4—614no—
598C2×C4⋊C4—12232no—
599C2×C4⋊C4—1224no—
600C2×C4⋊C4—1224no—
601C2×C4⋊C4—1224no—
602C2×C4⋊C4C22×D6114yes—
603C2×C4⋊C4C22×D6114yes—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—618no—
606C2×C22⋊C4—618no—
607C2×C22⋊C4—614no—
608C2×C22⋊C4—614no—
609C2×C22⋊C4—614no—
610C2×C22⋊C4—614no—
611C2×C22⋊C4—614no—
612C2×C22⋊C4—614no—
613C2×C22⋊C4—614no—
614C2×C22⋊C4—614no—
615C2×C22⋊C4—1224no—
616C2×C22⋊C4—1224no—
617C2×C22⋊C4—1224no—
618C2×C22⋊C4—1224no—
619C2×C22⋊C4—1224no—
620C2×C22⋊C4—2442no—
621C2×C22⋊C4C4×D6118yescomplemented
622C2×C22⋊C4C22×D6114yes—
623C2×C22⋊C4C22×D6114yes—
624C2×C42—614no—
625C2×C42—614no—
626C2×C42—614no—
627C2×C42—614no—
628C2×C42—1224no—
629C2×C42—1224no—
630C2×C42—1224no—
631C2×C42—1224no—
632#95—614no—
633#95—614no—
634#95—614no—
635#95—614no—
636#95C22×D6114yes—
637#95C22×D6114yes—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—614no—
645C24—614no—
646C24—614no—
647C24—612no—
648C24—614no—
649C24—612no—
650C24—1222no—
651C24—1222no—
652C24—1222no—
653C24—1222no—
654C24—1222no—
655C24—1222no—
656C24—1222no—
657C24—1222no—
658C24—1222no—
659C24—1222no—
660C24C2×C4×D6114yes—
661C24C23×D6112yes—
662C24C23×D6111yescharacteristic
663C2×D4—6116no—
664C2×D4—6116no—
665C2×D4—6116no—
666C2×D4—1228no—
667C2×D4—12232no—
668C2×D4—1228no—
669C2×D4—1228no—
670C2×D4—12232no—
671C2×D4—1228no—
672C2×D4—1228no—
673C2×D4—12232no—
674C2×D4—1228no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—44no—
692C22×C4—416no—
693C22×C4—614no—
694C22×C4—614no—
695C22×C4—614no—
696C22×C4—612no—
697C22×C4—614no—
698C22×C4—614no—
699C22×C4—614no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—6116no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—1228no—
707C22×C4—12232no—
708C22×C4—1228no—
709C22×C4—1228no—
710C22×C4—1228no—
711C22×C4—1228no—
712C22×C4—1228no—
713C22×C4—1222no—
714C22×C4—1222no—
715C22×C4—1222no—
716C22×C4—1222no—
717C22×C4—1222no—
718C22×C4—1222no—
719C22×C4—1222no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1222no—
723C22×C4—1222no—
724C22×C4—1222no—
725C22×C4—1228no—
726C22×C4—1228no—
727C22×C4—2444no—
728C22×C4—2444no—
729C22×C4—2444no—
730C22×C4—24416no—
731C22×C4—24416no—
732C22×C4—24416no—
733C22×C4C2×C4×D6114yes—
734C22×C4C2×C4×D6114yes—
735C22×C4D4×D6114yes—
736C22×C4D4×D6114yes—
737C22×C4C23×D6112yes—
738C22×C4C23×D6112yes—
739C22×C4C23×D6112yes—
740C22×C4C23×D6112yes—
741C22×C4C23×D6112yes—
742C22×C4C23×D6112yes—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—6116no—
746C4⋊C4—6116no—
747C4⋊C4—1228no—
748C4⋊C4—1228no—
749C4⋊C4—1228no—
750C22⋊C4—44no—
751C22⋊C4—6116no—
752C22⋊C4—6116no—
753C22⋊C4—1228no—
754C22⋊C4—1228no—
755C22⋊C4—1228no—
756C22⋊C4—1228no—
757C22⋊C4—1228no—
758C22⋊C4—2444no—
759C22⋊C4C2×C4×D61116yescomplemented
760C42—1228no—
761C42—1228no—
762C42—1228no—
763C42—1228no—
764C23—28no—
765C23—28no—
766C23—28no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—6116no—
778C23—614no—
779C23—614no—
780C23—614no—
781C23—614no—
782C23—1228no—
783C23—1228no—
784C23—1228no—
785C23—1222no—
786C23—1222no—
787C23—1222no—
788C23—1222no—
789C23—1228no—
790C23—1228no—
791C23—1228no—
792C23—1228no—
793C23—1228no—
794C23—1228no—
795C23—1222no—
796C23—1222no—
797C23—1222no—
798C23—1222no—
799C23—1222no—
800C23—1222no—
801C23—2444no—
802C23—2444no—
803C23—2444no—
804C23—2444no—
805C23C22×C4×D6114yes—
806C23C22×C4×D6112yes—
807C23C2×D4×D6112yes—
808C23C2×D4×D6112yes—
809C23#41×D6112yes—
810C23#41×D6112yes—
811C23#1451982212yes—
812C23#1451982512yes—
813C23C24×D6111yescharacteristic
814D4—12232no—
815D4—12232no—
816D4—12232no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—416no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—6116no—
839C2×C4—614no—
840C2×C4—614no—
841C2×C4—614no—
842C2×C4—614no—
843C2×C4—614no—
844C2×C4—614no—
845C2×C4—12232no—
846C2×C4—1228no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—1228no—
854C2×C4—1228no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—24416no—
862C2×C4—24416no—
863C2×C4—24416no—
864C2×C4—2444no—
865C2×C4—2444no—
866C2×C4C22×C4×D6114yes—
867C2×C4C22×C4×D6114yes—
868C2×C4C2×D4×D6114yes—
869C2×C4C2×D4×D6114yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—416no—
877C22—42no—
878C22—618no—
879C22—1224no—
880C22—1224no—
881C22—1224no—
882C22—1224no—
883C22—1224no—
884C22—12232no—
885C22—1224no—
886C22—1224no—
887C22—1224no—
888C22—1224no—
889C22—2442no—
890C22—2442no—
891C22—2442no—
892C22—24416no—
893C22—2442no—
894C22C4×D4×D6114yes—
895C22C4×D4×D6114yes—
896C22#1684024314yes—
897C22#1684039414yes—
898C22#1684041414yes—
899C22#1684042214yes—
900C22#1684045714yes—
901C22C23×C4×D6111yescharacteristic
902C22C22×D4×D6111yescharacteristic
903C22C22×D4×D6111yescharacteristic
904C22C2×#41×D6111yescharacteristic
905C22C2×#41×D6111yescharacteristic
906C22C2×#1451982211yescharacteristic
907C22C2×#1451982511yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—42no—
914C4—618no—
915C4—1224no—
916C4—1224no—
917C4—1224no—
918C4—2442no—
919C4—2442no—
920C2—44no—
921C2—1228no—
922C2—2444no—
923C2#2144883818yesdirect product factor
924C2C2×C4×D4×D6111yescharacteristic
925C2C2×C4×D4×D6111yescharacteristic
926C2C2×#1684024311yescharacteristic
927C2C2×#1684039411yescharacteristic
928C2C2×#1684041411yescharacteristic
929C2C2×#1684042211yescharacteristic
930C2C2×#1684045711yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC22×#14519750C2
cosocleC23×C61C25
hypercenterC2×#385D61
hypocenterC61C2×#2361
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#14519739C2semidirect
3. C22×C4×C22⋊D61C2semidirect
4. C22×C4×C22⋊D61C2semidirect
5. C22×C4⋊C4×D61C2semidirect
6. #21448838C2direct (N × H)
7. C2×#16839662C2semidirect
8. C2×#16839657C2semidirect
9. C2×#16839655C2semidirect
10. C2×#16839652C2semidirect
11. C2×#16839640C2semidirect
12. C2×#16839638C2semidirect
13. C2×#16839636C2semidirect
14. C2×#16839613C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#385C2semidirect
24. C2×#14519750C4semidirect
27. C2×#14519739C22semidirect
30. C2×C4×C22⋊D61C22semidirect
31. C2×C4×C22⋊D61C22semidirect
38. C2×C4⋊C4×D61C22semidirect
51. #16839662C22semidirect
52. #16839657C22semidirect
53. #16839655C22semidirect
54. #16839652C22semidirect
55. #16839640C22semidirect
56. #16839638C22semidirect
57. #16839636C22semidirect
58. #16839613C22semidirect
59. #16839609C22semidirect
69. C61×#385C22semidirect
76. C22×D244C2×C4semidirect
82. C22×C22⋊D61C2×C4semidirect
83. C22×C22⋊D61C2×C4semidirect
103. C22×C4×D61C2×C4semidirect
108. #14519750C2×C4semidirect
116. C2×#11758196C2×C4semidirect
117. C2×#11758196D4semidirect
131. C2×#11758198C2×C4semidirect
132. C2×#11758198D4semidirect
167. C2×C22⋊C4×C61C2×C4semidirect
231. C2×C22⋊D61C22×C4semidirect
232. C2×C22⋊D61C22×C4semidirect
260. C2×D244C22×C4semidirect
276. C2×C4×D61C22×C4semidirect
280. C22⋊C4×C61C22×C4semidirect
287. #11758198C22×C4semidirect
288. #11758198C2×D4semidirect
292. #11758196C22×C4semidirect
293. #11758196C2×D4semidirect
343. C22×D61C4×D4semidirect
392. C2×Dic61C4×D4semidirect
442. C2×D61C2×C4×D4semidirect
454. Dic61C2×C4×D4semidirect
468. C2×#385D61semidirect
472. C2×C61#2361semidirect
528. #385C2×D61semidirect
537. C61C2×#2361semidirect
621. C2×C22⋊C4C4×D61semidirect
759. C22⋊C4C2×C4×D61semidirect
923. C2#21448838direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197502
C22×#145197392
C22×C4×C22⋊D612
C22×C4⋊C4×D612
#214488382
C2×#168396622
C2×#168396572
C2×#168396552
C2×#168396522
C2×#168396402
C2×#168396382
C2×#168396362
C2×#168396132
C2×#168396092
C2×C61×#3852
C2×#236161