Finite Group Databasebeta

← C2×#20291238 #28328766

Subgroups — C2×#20291238 #28328766

Order 13568.

3830 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×#6157C211yesmaximal, characteristic
2C22×#13133296C211yesmaximal, characteristic, complemented
3#20291238C2116yesmaximal, direct product factor
4C2×#16811574C211yesmaximal, characteristic, complemented
5C2×#16811573C211yesmaximal, characteristic, complemented
6C2×#16811573C211yesmaximal, characteristic, complemented
7C2×#16811572C211yesmaximal, characteristic, complemented
8C2×#16811572C211yesmaximal, characteristic, complemented
9C2×#16811571C211yesmaximal, characteristic
10C2×#16811570C211yesmaximal, characteristic, complemented
11C2×#16811570C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×#6157C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×#6157C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×#6157C211yesmaximal, characteristic, complemented
15C22×(C2×#6157)⋊C4C211yesmaximal, characteristic, complemented
16C2×#123×D53C211yesmaximal, characteristic
17C24×#6157C2211yescharacteristic
18C24×#6157C2211yescharacteristic
19C24×#6157C2211yescharacteristic
20C2×D4×#6157—28no—
21C2×D4×#6157C2218yes—
22C2×#13133296—28no—
23C2×#13133296C2218yescomplemented
24C22×C4⋊#6157C2211yescharacteristic
25C22×C4⋊#6157C2211yescharacteristic
26C22×C4⋊#6157C2211yescharacteristic
27C22×C4⋊#6157C2211yescharacteristic
28C22×C4⋊#6157C2211yescharacteristic
29C22×C22⋊#6157C2211yescharacteristic
30C22×C22⋊#6157C2211yescharacteristic
31C22×C22⋊#6157C2211yescharacteristic
32C22×C22⋊#6157C2211yescharacteristic
33C22×C22⋊#6157C2211yescharacteristic
34C22×C4×#6157C2211yescharacteristic
35C22×C4×#6157C2211yescharacteristic
36C22×C4×#6157C2211yescharacteristic
37C22×C4×#6157C2211yescharacteristic
38C22×C4×#6157C2211yescharacteristic
39#16811574C2218yescomplemented
40#16811573C2218yescomplemented
41#16811573C2218yescomplemented
42#16811572C2218yescomplemented
43#16811572C2218yescomplemented
44#16811571C2218yes—
45#16811570C2218yescomplemented
46#16811570C2218yescomplemented
47C4⋊C4×#6157C2218yescomplemented
48C22⋊C4×#6157C2218yescomplemented
49C22⋊C4×#6157C2218yescomplemented
50C2×(C2×#6157)⋊C4C2211yescharacteristic
51C2×(C2×#6157)⋊C4C2211yescharacteristic
52C2×(C2×#6157)⋊C4C2211yescharacteristic
53C2×(C2×#6157)⋊C4C2211yescharacteristic
54C2×(C2×#6157)⋊C4C2211yescharacteristic
55C2×(C2×#6157)⋊C4C2211yescharacteristic
56C2×(C2×#6157)⋊C4C2211yescharacteristic
57C2×(C2×#6157)⋊C4C2211yescharacteristic
58C2×(C2×#6157)⋊C4C2211yescharacteristic
59C2×(C2×#6157)⋊C4C2211yescharacteristic
60C2×(C2×#6157)⋊C4C2218yescomplemented
61C22×D4×D53C2211yescharacteristic
62C23×C4×D53C2211yescharacteristic
63C2×#13133202C411yescharacteristic, complemented
64C2×#13133202C411yescharacteristic, complemented
65C2×#13133201C411yescharacteristic, complemented
66C2×#13133200C411yescharacteristic, complemented
67C2×#13133199C411yescharacteristic, complemented
68C2×#13133199C411yescharacteristic, complemented
69C2×#13133198C411yescharacteristic, complemented
70#123×D53C418yescomplemented
71#123×D53C2218yes—
72C2×C4⋊C4×D53C2211yescharacteristic
73C2×C4⋊C4×D53C2211yescharacteristic
74C2×C22⋊C4×D53C2211yescharacteristic
75C2×C22⋊C4×D53C2211yescharacteristic
76C2×C22⋊C4×D53C2211yescharacteristic
77C2×#123×C53C411yescharacteristic, complemented
78C23×#6157—24no—
79C23×#6157—24no—
80C23×#6157—24no—
81C23×#6157—24no—
82C23×#6157—24no—
83C23×#6157—24no—
84C23×#6157—42no—
85C23×#6157—42no—
86C23×#6157—42no—
87C23×#6157C2311yescharacteristic
88C23×#6157C2311yescharacteristic
89C23×#6157C2311yescharacteristic
90C23×#6157C2311yescharacteristic
91C23×#6157C2314yes—
92C23×#6157C2314yes—
93C23×#6157C2314yes—
94C23×#6157C2311yescharacteristic
95C23×#6157C2311yescharacteristic
96C23×#6157C2311yescharacteristic
97C23×#6157C2311yescharacteristic
98D4×#6157—232no—
99#13133296—232no—
100C2×C4⋊#6157—24no—
101C2×C4⋊#6157—24no—
102C2×C4⋊#6157—24no—
103C2×C4⋊#6157—24no—
104C2×C4⋊#6157—42no—
105C2×C4⋊#6157C2314yes—
106C2×C4⋊#6157C2314yes—
107C2×C4⋊#6157C2314yes—
108C2×C4⋊#6157C2314yes—
109C2×C4⋊#6157C2314yes—
110C2×C22⋊#6157—24no—
111C2×C22⋊#6157—24no—
112C2×C22⋊#6157—24no—
113C2×C22⋊#6157—42no—
114C2×C22⋊#6157D418yes—
115C2×C22⋊#6157C2314yes—
116C2×C22⋊#6157C2314yes—
117C2×C22⋊#6157C2314yes—
118C2×C22⋊#6157C2314yes—
119C2×C22⋊#6157C2314yes—
120C2×C4×#6157—24no—
121C2×C4×#6157—24no—
122C2×C4×#6157—24no—
123C2×C4×#6157—24no—
124C2×C4×#6157—42no—
125C2×C4×#6157C2314yes—
126C2×C4×#6157C2314yes—
127C2×C4×#6157C2314yes—
128C2×C4×#6157C2314yes—
129C2×C4×#6157C2314yes—
130(C2×#6157)⋊C4C2314yes—
131(C2×#6157)⋊C4C2314yes—
132(C2×#6157)⋊C4C2314yes—
133(C2×#6157)⋊C4C2314yes—
134(C2×#6157)⋊C4C2314yes—
135(C2×#6157)⋊C4C2314yes—
136(C2×#6157)⋊C4C2314yes—
137(C2×#6157)⋊C4C2314yes—
138(C2×#6157)⋊C4C2314yes—
139(C2×#6157)⋊C4C2314yes—
140C24×D53C2311yescharacteristic
141C24×D53C2311yescharacteristic
142C22×D212C2×C411yescharacteristic
143C22×C22⋊D53C2×C411yescharacteristic
144C22×C22⋊D53C2×C411yescharacteristic
145C2×D4×D53—24no—
146C2×D4×D53—24no—
147C2×D4×D53C2×C414yes—
148C2×D4×D53C2314yes—
149C23×Dic53C2×C411yescharacteristic, complemented
150C22×C4×D53—24no—
151C22×C4×D53—24no—
152C22×C4×D53C2×C414yescomplemented
153C22×C4×D53C2×C411yescharacteristic, complemented
154C22×C4×D53C2×C411yescharacteristic, complemented
155C22×C4×D53C2311yescharacteristic
156C22×C4×D53C2311yescharacteristic
157C22×C4×D53C2311yescharacteristic
158C22×C4×D53C2311yescharacteristic
159C22×C4×D53C2311yescharacteristic
160C22×C4×D53C2314yes—
161#13133202C2×C418yescomplemented
162#13133202C2×C418yescomplemented
163#13133201C2×C418yescomplemented
164#13133200C2×C418yescomplemented
165#13133199C2×C418yescomplemented
166#13133199C2×C418yescomplemented
167#13133198C2×C418yescomplemented
168C2×C4⋊Dic53C2×C411yescharacteristic, complemented
169C2×C4⋊Dic53C2×C411yescharacteristic, complemented
170C2×#11719919C2×C411yescharacteristic, complemented
171C2×#11719919C2×C411yescharacteristic, complemented
172C2×#11719919C2×C411yescharacteristic, complemented
173C2×#11719919C2×C411yescharacteristic, complemented
174C4⋊C4×D53C2×C414yescomplemented
175C4⋊C4×D53C2×C414yescomplemented
176C4⋊C4×D53C2314yes—
177C4⋊C4×D53C2314yes—
178C2×C22⋊Dic53C2×C411yescharacteristic, complemented
179C2×C22⋊Dic53C2×C411yescharacteristic, complemented
180C2×C22⋊Dic53C2×C411yescharacteristic, complemented
181C2×#11719921C2×C411yescharacteristic, complemented
182C2×#11719921C2×C411yescharacteristic, complemented
183C2×#11719921C2×C411yescharacteristic, complemented
184C2×#11719921C2×C411yescharacteristic, complemented
185C2×#11719921C2×C411yescharacteristic, complemented
186C2×#11719921C2×C411yescharacteristic, complemented
187C22⋊C4×D53C2×C414yescomplemented
188C22⋊C4×D53C2×C414yescomplemented
189C22⋊C4×D53C2×C414yescomplemented
190C22⋊C4×D53C2314yes—
191C22⋊C4×D53C2314yes—
192C22⋊C4×D53C2314yes—
193C22×D4×C53C2×C411yescharacteristic
194C23×C4×C53C2×C411yescharacteristic, complemented
195#123×C53C2×C418yescomplemented
196C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
197C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
198C2×C22⋊C4×C53C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C53C2×C411yescharacteristic, complemented
200C2×C22⋊C4×C53C2×C411yescharacteristic, complemented
201C24×C53C22×C411yescharacteristic
202C24×C53C22×C411yescharacteristic
203C23×D53—22no—
204C23×D53—22no—
205C23×D53—22no—
206C23×D53—22no—
207C23×D53—22no—
208C23×D53—22no—
209C23×D53—22no—
210C23×D53—22no—
211C23×D53—22no—
212C23×D53—22no—
213C23×D53C22×C412yes—
214C23×D53C22×C411yescharacteristic
215C23×D53C22×C412yes—
216C23×D53C22×C411yescharacteristic
217C23×D53C2×D414yes—
218C23×D53#4114yes—
219C23×D53C2412yes—
220C23×D53C2412yes—
221C23×D53C2411yescharacteristic
222C22×#6157—22no—
223C22×#6157—22no—
224C22×#6157—22no—
225C22×#6157—22no—
226C22×#6157—22no—
227C22×#6157—22no—
228C22×#6157—22no—
229C22×#6157—22no—
230C22×#6157—22no—
231C22×#6157—22no—
232C22×#6157—22no—
233C22×#6157—28no—
234C22×#6157—22no—
235C22×#6157—22no—
236C22×#6157—28no—
237C22×#6157—22no—
238C22×#6157—22no—
239C22×#6157—22no—
240C22×#6157—22no—
241C22×#6157—22no—
242C22×#6157—22no—
243C22×#6157—22no—
244C22×#6157—28no—
245C22×#6157—28no—
246C22×#6157—28no—
247C22×#6157—28no—
248C22×#6157—44no—
249C22×#6157—44no—
250C22×#6157—44no—
251C22×#6157—416no—
252C22×#6157—416no—
253C22×#6157—416no—
254C22×#6157C2×D414yes—
255C22×#6157C2×D414yes—
256C22×#6157#4114yes—
257C22×#6157#4114yes—
258C22×#6157C2412yes—
259C22×#6157C2412yes—
260C22×#6157C2412yes—
261C22×#6157C2412yes—
262C22×#6157C2412yes—
263C22×#6157C2412yes—
264C22×#6157C2412yes—
265C22×#6157C2412yes—
266C2×D4×C53—24no—
267C2×D4×C53C22×C414yes—
268C22×C4×C53—24no—
269C22×C4×C53C22×C411yescharacteristic
270C22×C4×C53C22×C411yescharacteristic
271C22×C4×C53C22×C411yescharacteristic
272C22×C4×C53C22×C411yescharacteristic
273C22×C4×C53C22×C411yescharacteristic
274C22×C4×C53C22×C414yescomplemented
275C2×C22⋊D53—24no—
276C2×C22⋊D53—24no—
277C2×C22⋊D53C22×C414yes—
278C2×C22⋊D53C22×C414yes—
279C22×Dic53—24no—
280C22×Dic53C22×C411yescharacteristic
281C22×Dic53C22×C411yescharacteristic
282C22×Dic53C22×C411yescharacteristic
283C22×Dic53C22×C411yescharacteristic
284C22×Dic53C22×C411yescharacteristic
285C22×Dic53C22×C414yescomplemented
286D4×D53—216no—
287D4×D53—28no—
288D4×D53—28no—
289C2×D212—24no—
290C2×D212C22×C414yes—
291C2×C4×D53—216no—
292C2×C4×D53—24no—
293C2×C4×D53—24no—
294C2×C4×D53—22no—
295C2×C4×D53—22no—
296C2×C4×D53—28no—
297C2×C4×D53—22no—
298C2×C4×D53—22no—
299C2×C4×D53—22no—
300C2×C4×D53—28no—
301C2×C4×D53—22no—
302C2×C4×D53—22no—
303C2×C4×D53—22no—
304C2×C4×D53—22no—
305C2×C4×D53—22no—
306C2×C4×D53C22×C412yes—
307C2×C4×D53C22×C412yes—
308C2×C4×D53C22×C412yes—
309C2×C4×D53C22×C412yes—
310C2×C4×D53C22×C412yes—
311C2×C4×D53C22×C414yescomplemented
312C2×C4×D53C22×C414yescomplemented
313C2×C4×D53C2412yes—
314C2×C4×D53C2412yes—
315C2×C4×D53C2412yes—
316C2×C4×D53C2412yes—
317C2×C4×D53C2412yes—
318C22⋊#6157—28no—
319C22⋊#6157—28no—
320C22⋊#6157—28no—
321C22⋊#6157—44no—
322C22⋊#6157C2×D4116yes—
323C4⋊#6157—28no—
324C4⋊#6157—28no—
325C4⋊#6157—28no—
326C4⋊#6157—28no—
327C4⋊#6157—44no—
328C4×#6157—28no—
329C4×#6157—28no—
330C4×#6157—28no—
331C4×#6157—28no—
332C4×#6157—44no—
333C4⋊C4×C53C22×C414yescomplemented
334C4⋊C4×C53C22×C414yescomplemented
335C22⋊C4×C53C22×C414yescomplemented
336C22⋊C4×C53C22×C414yescomplemented
337C22⋊C4×C53C22×C414yescomplemented
338C22⋊Dic53C22×C414yescomplemented
339C22⋊Dic53C22×C414yescomplemented
340C22⋊Dic53C22×C414yescomplemented
341#11719921C22×C414yescomplemented
342#11719921C22×C414yescomplemented
343#11719921C22×C414yescomplemented
344#11719921C22×C414yescomplemented
345#11719921C22×C414yescomplemented
346#11719921C22×C414yescomplemented
347C4⋊Dic53C22×C414yescomplemented
348C4⋊Dic53C22×C414yescomplemented
349#11719919C22×C414yescomplemented
350#11719919C22×C414yescomplemented
351#11719919C22×C414yescomplemented
352#11719919C22×C414yescomplemented
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53C4×D414yes—
359C23×C53C23×C412yes—
360C23×C53C23×C412yes—
361C23×C53C23×C411yescharacteristic
362C22×D53—22no—
363C22×D53—22no—
364C22×D53—24no—
365C22×D53—24no—
366C22×D53—28no—
367C22×D53—28no—
368C22×D53—28no—
369C22×D53—28no—
370C22×D53—22no—
371C22×D53—22no—
372C22×D53—22no—
373C22×D53—22no—
374C22×D53—22no—
375C22×D53—22no—
376C22×D53—22no—
377C22×D53—24no—
378C22×D53—24no—
379C22×D53—24no—
380C22×D53—22no—
381C22×D53—22no—
382C22×D53—22no—
383C22×D53—22no—
384C22×D53—22no—
385C22×D53—22no—
386C22×D53—44no—
387C22×D53—44no—
388C22×D53—44no—
389C22×D53—44no—
390C22×D53C4×D414yes—
391C22×D53C4×D418yes—
392C22×D53C23×C412yes—
393C22×D53C23×C412yes—
394C22×D53C23×C411yescharacteristic
395C22×D53C22×D414yes—
396C22×D53C22×D412yes—
397C22×D53C2×#4114yes—
398C22×D53C2×#4112yes—
399C22×D53C2×#4112yes—
400C22×D53C2×#4112yes—
401C22×D53H(5,𝔽2)12yes—
402C22×D532−1+412yes—
403C22×D53C2511yescharacteristic
404C2×#6157—28no—
405C2×#6157—28no—
406C2×#6157—28no—
407C2×#6157—28no—
408C2×#6157—22no—
409C2×#6157—22no—
410C2×#6157—22no—
411C2×#6157—22no—
412C2×#6157—22no—
413C2×#6157—22no—
414C2×#6157—22no—
415C2×#6157—22no—
416C2×#6157—22no—
417C2×#6157—22no—
418C2×#6157—22no—
419C2×#6157—22no—
420C2×#6157—22no—
421C2×#6157—22no—
422C2×#6157—22no—
423C2×#6157—22no—
424C2×#6157—22no—
425C2×#6157—22no—
426C2×#6157—22no—
427C2×#6157—22no—
428C2×#6157—416no—
429C2×#6157—416no—
430C2×#6157—416no—
431C2×#6157—44no—
432C2×#6157—44no—
433C2×#6157—44no—
434C2×#6157—44no—
435C2×#6157C22×D414yes—
436C2×#6157C22×D414yes—
437C2×#6157C2×#4114yes—
438C2×#6157C2×#4114yes—
439D4×C53—28no—
440C2×C4×C53—22no—
441C2×C4×C53—22no—
442C2×C4×C53—28no—
443C2×C4×C53—22no—
444C2×C4×C53—22no—
445C2×C4×C53—22no—
446C2×C4×C53C23×C412yes—
447C2×C4×C53C23×C412yes—
448C2×C4×C53C23×C412yes—
449C2×C4×C53C23×C412yes—
450C2×C4×C53C23×C412yes—
451C22⋊D53—28no—
452C22⋊D53—28no—
453C2×Dic53—22no—
454C2×Dic53—22no—
455C2×Dic53—28no—
456C2×Dic53—22no—
457C2×Dic53—22no—
458C2×Dic53—22no—
459C2×Dic53C23×C412yes—
460C2×Dic53C23×C412yes—
461C2×Dic53C23×C412yes—
462C2×Dic53C23×C412yes—
463C2×Dic53C23×C412yes—
464D212—28no—
465C4×D53—24no—
466C4×D53—24no—
467C4×D53—28no—
468C4×D53—28no—
469C4×D53—24no—
470C4×D53—24no—
471C4×D53—24no—
472C4×D53—22no—
473C4×D53—22no—
474C4×D53—22no—
475C4×D53—22no—
476C4×D53—22no—
477C4×D53—22no—
478C4×D53—22no—
479C4×D53—22no—
480C4×D53—22no—
481C4×D53—22no—
482C2×#2359—531nomaximal, Sylow
483C22×C53—28no—
484C22×C53—22no—
485C22×C53—22no—
486C22×C53—22no—
487C22×C53—22no—
488C22×C53—22no—
489C22×C53—44no—
490C22×C53C2×C4×D414yes—
491C22×C53C2×C4×D412yes—
492C22×C53C4×#4112yes—
493C22×C53#52012yes—
494C22×C53C24×C411yescharacteristic
495C2×D53—28no—
496C2×D53—22no—
497C2×D53—22no—
498C2×D53—216no—
499C2×D53—24no—
500C2×D53—24no—
501C2×D53—24no—
502C2×D53—24no—
503C2×D53—22no—
504C2×D53—22no—
505C2×D53—22no—
506C2×D53—44no—
507C2×D53—48no—
508C2×D53—42no—
509C2×D53—42no—
510C2×D53—42no—
511C2×D53—42no—
512C2×D53C2×C4×D414yes—
513C2×D53C2×C4×D412yes—
514C2×D53C4×#4112yes—
515C2×D53#52012yes—
516C2×D53#54614yes—
517C2×D53#54714yes—
518C2×D53#55114yes—
519C2×D53#55214yes—
520C2×D53C23×D411yescharacteristic
521C2×D53C22×#4111yescharacteristic
522C2×D53C22×#4111yescharacteristic
523C2×D53C22×#4111yescharacteristic
524C2×D53C2×H(5,𝔽2)11yescharacteristic
525C2×D53C2×2−1+411yescharacteristic
526#6157—24no—
527#6157—24no—
528#6157—24no—
529#6157—24no—
530#6157—42no—
531#6157—42no—
532#6157—42no—
533#6157—42no—
534C4×C53—22no—
535C4×C53—22no—
536C4×C53—22no—
537C4×C53—22no—
538C4×C53—22no—
539Dic53—22no—
540Dic53—22no—
541Dic53—22no—
542Dic53—22no—
543Dic53—22no—
544C22×#123—531no—
545C22×C4×D4—531no—
546C22×#117—531no—
547#2359—5316no—
548C2×#389—531no—
549C2×#388—531no—
550C2×#388—531no—
551C2×#387—531no—
552C2×#387—531no—
553C2×#386—531no—
554C2×#385—531no—
555C2×#385—531no—
556C2×C4×C4⋊C4—531no—
557C2×C4×C22⋊C4—531no—
558C2×C4×C22⋊C4—531no—
559C22×#95—531no—
560C2×C53—24no—
561C2×C53—42no—
562C2×C53#235914yescomplemented
563C2×C53C22×C4×D411yescharacteristic
564C2×C53C2×C4×#4111yescharacteristic
565C2×C53C2×#52011yescharacteristic
566D53—24no—
567D53—42no—
568D53#235914yescomplemented
569D53C2×#54611yescharacteristic
570D53C2×#54711yescharacteristic
571D53C2×#55111yescharacteristic
572D53C2×#55211yescharacteristic
573C23×D4—531no—
574C24×C4—531no—
575C24×C4—531no—
576C24×C4—531no—
577C24×C4—531no—
578C2×#123—531no—
579C2×#123—531no—
580C2×#123—538no—
581C2×#123—538no—
582C2×#123—531no—
583C2×#123—531no—
584C2×#123—531no—
585C2×#123—531no—
586C2×#123—531no—
587C2×#123#615711yescharacteristic, complemented
588C2×C4×D4—538no—
589C2×C4×D4—1068no—
590C2×#117—538no—
591C2×#117—1068no—
592C22×C4⋊C4—531no—
593C22×C4⋊C4—531no—
594C22×C4⋊C4—531no—
595C22×C4⋊C4—531no—
596C22×C4⋊C4—531no—
597C22×C4⋊C4—531no—
598C22×C4⋊C4—531no—
599C22×C22⋊C4—531no—
600C22×C22⋊C4—531no—
601C22×C22⋊C4—531no—
602C22×C22⋊C4—531no—
603C22×C22⋊C4—531no—
604C22×C22⋊C4—531no—
605C22×C22⋊C4—531no—
606C22×C22⋊C4—531no—
607C22×C42—531no—
608C22×C42—531no—
609C22×C42—531no—
610C22×C42—531no—
611C22×C42—531no—
612#389—538no—
613#388—538no—
614#388—538no—
615#387—538no—
616#387—538no—
617#386—538no—
618#385—538no—
619#385—538no—
620C4×C4⋊C4—538no—
621C4×C22⋊C4—538no—
622C4×C22⋊C4—538no—
623C2×#95—531no—
624C2×#95—531no—
625C2×#95—531no—
626C2×#95—531no—
627C2×#95—531no—
628C2×#95—531no—
629C2×#95—531no—
630C2×#95—531no—
631C2×#95—531no—
632C2×#95—531no—
633C2×#95—538no—
634C53C2×#235911yescharacteristic, complemented, Sylow
635C25—531no—
636C25—531no—
637C22×D4—531no—
638C22×D4—531no—
639C22×D4—534no—
640C22×D4—534no—
641C22×D4—531no—
642C22×D4—1064no—
643C22×D4—1064no—
644C22×D4C2×#615711yescharacteristic
645C23×C4—531no—
646C23×C4—531no—
647C23×C4—531no—
648C23×C4—531no—
649C23×C4—531no—
650C23×C4—531no—
651C23×C4—531no—
652C23×C4—531no—
653C23×C4—531no—
654C23×C4—531no—
655C23×C4—531no—
656C23×C4—531no—
657C23×C4—534no—
658C23×C4—534no—
659C23×C4—531no—
660C23×C4—531no—
661C23×C4—531no—
662C23×C4—531no—
663C23×C4—534no—
664C23×C4—534no—
665C23×C4—534no—
666C23×C4—1064no—
667C23×C4—1064no—
668C23×C4—1064no—
669C23×C4—1064no—
670C23×C4—1064no—
671C23×C4—1064no—
672C23×C4—1064no—
673C23×C4—1064no—
674C23×C4—2122no—
675C23×C4—2122no—
676C23×C4—2122no—
677C23×C4C2×#615711yescharacteristic, complemented
678#123—538no—
679#123—538no—
680#123—538no—
681#123—538no—
682#123—538no—
683#123—538no—
684#123—538no—
685#123C2×#615718yescomplemented
686C4×D4—10632no—
687#117—10632no—
688C2×C4⋊C4—531no—
689C2×C4⋊C4—531no—
690C2×C4⋊C4—531no—
691C2×C4⋊C4—531no—
692C2×C4⋊C4—531no—
693C2×C4⋊C4—531no—
694C2×C4⋊C4—534no—
695C2×C4⋊C4—534no—
696C2×C4⋊C4—534no—
697C2×C4⋊C4—534no—
698C2×C4⋊C4—534no—
699C2×C4⋊C4—534no—
700C2×C4⋊C4—534no—
701C2×C4⋊C4—534no—
702C2×C4⋊C4—534no—
703C2×C4⋊C4—1064no—
704C2×C4⋊C4—1064no—
705C2×C4⋊C4—1064no—
706C2×C4⋊C4—1064no—
707C2×C4⋊C4—2122no—
708C2×C4⋊C4C2×#615711yescharacteristic, complemented
709C2×C4⋊C4C2×#615711yescharacteristic, complemented
710C2×C22⋊C4—534no—
711C2×C22⋊C4—538no—
712C2×C22⋊C4—531no—
713C2×C22⋊C4—531no—
714C2×C22⋊C4—531no—
715C2×C22⋊C4—531no—
716C2×C22⋊C4—531no—
717C2×C22⋊C4—531no—
718C2×C22⋊C4—531no—
719C2×C22⋊C4—531no—
720C2×C22⋊C4—531no—
721C2×C22⋊C4—534no—
722C2×C22⋊C4—534no—
723C2×C22⋊C4—534no—
724C2×C22⋊C4—534no—
725C2×C22⋊C4—534no—
726C2×C22⋊C4—534no—
727C2×C22⋊C4—534no—
728C2×C22⋊C4—534no—
729C2×C22⋊C4—534no—
730C2×C22⋊C4—534no—
731C2×C22⋊C4—1064no—
732C2×C22⋊C4—1064no—
733C2×C22⋊C4—1064no—
734C2×C22⋊C4—2122no—
735C2×C22⋊C4C2×#615711yescharacteristic, complemented
736C2×C22⋊C4C2×#615711yescharacteristic, complemented
737C2×C22⋊C4C2×#615711yescharacteristic, complemented
738C2×C42—534no—
739C2×C42—534no—
740C2×C42—534no—
741C2×C42—534no—
742C2×C42—534no—
743C2×C42—1064no—
744C2×C42—1064no—
745C2×C42—1064no—
746C2×C42—1064no—
747C2×C42—2122no—
748#95—534no—
749#95—534no—
750#95—534no—
751#95—534no—
752#95—534no—
753#95—534no—
754#95—534no—
755#95—534no—
756#95—534no—
757#95—534no—
758C24—531no—
759C24—534no—
760C24—534no—
761C24—532no—
762C24—532no—
763C24—531no—
764C24—532no—
765C24—532no—
766C24—531no—
767C24—1062no—
768C24—1062no—
769C24—1062no—
770C24—1062no—
771C24—1062no—
772C24—1062no—
773C24—1062no—
774C24—1062no—
775C24—1062no—
776C24—1062no—
777C24C22×#615711yescharacteristic
778C24C22×#615711yescharacteristic
779C2×D4—24no—
780C2×D4—534no—
781C2×D4—534no—
782C2×D4—534no—
783C2×D4—1064no—
784C2×D4—1068no—
785C2×D4—10616no—
786C2×D4—1068no—
787C2×D4—1064no—
788C2×D4—1064no—
789C2×D4C22×#615714yes—
790C22×C4—24no—
791C22×C4—534no—
792C22×C4—534no—
793C22×C4—534no—
794C22×C4—534no—
795C22×C4—532no—
796C22×C4—532no—
797C22×C4—532no—
798C22×C4—532no—
799C22×C4—534no—
800C22×C4—531no—
801C22×C4—531no—
802C22×C4—531no—
803C22×C4—531no—
804C22×C4—531no—
805C22×C4—532no—
806C22×C4—532no—
807C22×C4—532no—
808C22×C4—532no—
809C22×C4—532no—
810C22×C4—534no—
811C22×C4—534no—
812C22×C4—532no—
813C22×C4—532no—
814C22×C4—532no—
815C22×C4—532no—
816C22×C4—532no—
817C22×C4—532no—
818C22×C4—532no—
819C22×C4—532no—
820C22×C4—532no—
821C22×C4—1062no—
822C22×C4—1062no—
823C22×C4—1062no—
824C22×C4—1062no—
825C22×C4—1062no—
826C22×C4—1062no—
827C22×C4—1068no—
828C22×C4—1062no—
829C22×C4—1062no—
830C22×C4—1062no—
831C22×C4—1064no—
832C22×C4—1064no—
833C22×C4—10616no—
834C22×C4—1068no—
835C22×C4—1062no—
836C22×C4—1068no—
837C22×C4—1068no—
838C22×C4—1068no—
839C22×C4—1068no—
840C22×C4—1062no—
841C22×C4—1062no—
842C22×C4—1062no—
843C22×C4—1062no—
844C22×C4—1062no—
845C22×C4—1062no—
846C22×C4—1062no—
847C22×C4—1062no—
848C22×C4—1064no—
849C22×C4—1062no—
850C22×C4—1062no—
851C22×C4—1062no—
852C22×C4—1062no—
853C22×C4—1062no—
854C22×C4—1062no—
855C22×C4—1062no—
856C22×C4—1062no—
857C22×C4—1068no—
858C22×C4—1062no—
859C22×C4—1068no—
860C22×C4—1062no—
861C22×C4—1062no—
862C22×C4—1062no—
863C22×C4—2124no—
864C22×C4—2124no—
865C22×C4—2124no—
866C22×C4—21216no—
867C22×C4—21216no—
868C22×C4—21216no—
869C22×C4C22×#615711yescharacteristic
870C22×C4C22×#615711yescharacteristic
871C22×C4C22×#615711yescharacteristic
872C22×C4C22×#615711yescharacteristic
873C22×C4C22×#615711yescharacteristic
874C22×C4C22×#615714yescomplemented
875C4⋊C4—534no—
876C4⋊C4—534no—
877C4⋊C4—534no—
878C4⋊C4—534no—
879C4⋊C4—534no—
880C4⋊C4—534no—
881C4⋊C4—1068no—
882C4⋊C4—1068no—
883C4⋊C4—1068no—
884C4⋊C4—1068no—
885C4⋊C4—2124no—
886C4⋊C4C22×#615714yescomplemented
887C4⋊C4C22×#615714yescomplemented
888C22⋊C4—5316no—
889C22⋊C4—534no—
890C22⋊C4—534no—
891C22⋊C4—534no—
892C22⋊C4—534no—
893C22⋊C4—534no—
894C22⋊C4—534no—
895C22⋊C4—534no—
896C22⋊C4—534no—
897C22⋊C4—534no—
898C22⋊C4—1068no—
899C22⋊C4—1068no—
900C22⋊C4—1068no—
901C22⋊C4—2124no—
902C22⋊C4C22×#615714yescomplemented
903C22⋊C4C22×#615714yescomplemented
904C22⋊C4C22×#615714yescomplemented
905C42—1068no—
906C42—1068no—
907C42—1068no—
908C42—1068no—
909C42—2124no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—532no—
916C23—532no—
917C23—532no—
918C23—532no—
919C23—532no—
920C23—532no—
921C23—531no—
922C23—531no—
923C23—538no—
924C23—534no—
925C23—534no—
926C23—534no—
927C23—532no—
928C23—532no—
929C23—1062no—
930C23—1062no—
931C23—1062no—
932C23—1068no—
933C23—1068no—
934C23—1064no—
935C23—1062no—
936C23—1064no—
937C23—1068no—
938C23—1068no—
939C23—1062no—
940C23—1062no—
941C23—1062no—
942C23—1062no—
943C23—1062no—
944C23—1064no—
945C23—1064no—
946C23—1062no—
947C23—1064no—
948C23—1062no—
949C23—1062no—
950C23—1062no—
951C23—1062no—
952C23—1062no—
953C23—2124no—
954C23—2124no—
955C23—2124no—
956C23—2124no—
957C23D4×#615714yes—
958C23C23×#615712yes—
959C23C23×#615712yes—
960C23C23×#615711yescharacteristic
961D4—28no—
962D4—1068no—
963D4—1068no—
964D4—1068no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—534no—
972C2×C4—534no—
973C2×C4—534no—
974C2×C4—534no—
975C2×C4—532no—
976C2×C4—532no—
977C2×C4—532no—
978C2×C4—532no—
979C2×C4—532no—
980C2×C4—1062no—
981C2×C4—1062no—
982C2×C4—1062no—
983C2×C4—1062no—
984C2×C4—1062no—
985C2×C4—1062no—
986C2×C4—1064no—
987C2×C4—1062no—
988C2×C4—1064no—
989C2×C4—1062no—
990C2×C4—1062no—
991C2×C4—1064no—
992C2×C4—1064no—
993C2×C4—1068no—
994C2×C4—1068no—
995C2×C4—1062no—
996C2×C4—1064no—
997C2×C4—1062no—
998C2×C4—1062no—
999C2×C4—1062no—
1000C2×C4—1062no—
1001C2×C4—1062no—
1002C2×C4—1068no—
1003C2×C4—1062no—
1004C2×C4—1062no—
1005C2×C4—1068no—
1006C2×C4—1068no—
1007C2×C4—1062no—
1008C2×C4—1068no—
1009C2×C4—1068no—
1010C2×C4—1062no—
1011C2×C4—1062no—
1012C2×C4—1062no—
1013C2×C4—1062no—
1014C2×C4—1062no—
1015C2×C4—1062no—
1016C2×C4—1062no—
1017C2×C4—1062no—
1018C2×C4—1062no—
1019C2×C4—1062no—
1020C2×C4—1062no—
1021C2×C4—1062no—
1022C2×C4—1062no—
1023C2×C4—1062no—
1024C2×C4—1062no—
1025C2×C4—1062no—
1026C2×C4—1062no—
1027C2×C4—21216no—
1028C2×C4—21216no—
1029C2×C4—21216no—
1030C2×C4—2124no—
1031C2×C4—2124no—
1032C2×C4—2124no—
1033C2×C4—2124no—
1034C2×C4C23×#615712yes—
1035C2×C4C23×#615712yes—
1036C2×C4C23×#615712yes—
1037C2×C4C23×#615712yes—
1038C2×C4C23×#615712yes—
1039C22—22no—
1040C22—22no—
1041C22—28no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—44no—
1046C22—531no—
1047C22—531no—
1048C22—532no—
1049C22—531no—
1050C22—531no—
1051C22—532no—
1052C22—531no—
1053C22—531no—
1054C22—532no—
1055C22—534no—
1056C22—534no—
1057C22—534no—
1058C22—534no—
1059C22—534no—
1060C22—1064no—
1061C22—1064no—
1062C22—1064no—
1063C22—10616no—
1064C22—1064no—
1065C22—1062no—
1066C22—1062no—
1067C22—1068no—
1068C22—1062no—
1069C22—1062no—
1070C22—1062no—
1071C22—2122no—
1072C22—2122no—
1073C22—2122no—
1074C22—2128no—
1075C22—2122no—
1076C22—2124no—
1077C22C2×D4×#615714yes—
1078C22C2×D4×#615712yes—
1079C22#41×#615712yes—
1080C22#1681169212yes—
1081C22C24×#615711yescharacteristic
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—1064no—
1088C4—1064no—
1089C4—1064no—
1090C4—1064no—
1091C4—1062no—
1092C4—1062no—
1093C4—1062no—
1094C4—1062no—
1095C4—1062no—
1096C4—2122no—
1097C4—2122no—
1098C4—2122no—
1099C4—2122no—
1100C2—24no—
1101C2—42no—
1102C2—531no—
1103C2—531no—
1104C2—531no—
1105C2—534no—
1106C2—531no—
1107C2—1064no—
1108C2—2122no—
1109C2#2029123814yesdirect product factor
1110C2C22×D4×#615711yescharacteristic
1111C2C2×#41×#615711yescharacteristic
1112C2C2×#1681169211yescharacteristic
subgroupG/H
centerC23C23×#6157
commutatorC22×C53C24×C4
FrattiniC22C24×#6157
FittingC2×#123×C53C4
socleC23×C53C23×C4
prime radicalC22×D4×D53C22
cosocleC22×D53C25
hypercenterC2×#123#6157
hypocenterC53C2×#2359
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C22×#13133296C2semidirect
3. #20291238C2direct (N × H)
4. C2×#16811574C2semidirect
5. C2×#16811573C2semidirect
6. C2×#16811573C2semidirect
7. C2×#16811572C2semidirect
8. C2×#16811572C2semidirect
10. C2×#16811570C2semidirect
11. C2×#16811570C2semidirect
12. C2×C4⋊C4×#6157C2semidirect
13. C2×C22⋊C4×#6157C2semidirect
14. C2×C22⋊C4×#6157C2semidirect
15. C22×(C2×#6157)⋊C4C2semidirect
23. C2×#13133296C22semidirect
39. #16811574C22semidirect
40. #16811573C22semidirect
41. #16811573C22semidirect
42. #16811572C22semidirect
43. #16811572C22semidirect
45. #16811570C22semidirect
46. #16811570C22semidirect
47. C4⋊C4×#6157C22semidirect
48. C22⋊C4×#6157C22semidirect
49. C22⋊C4×#6157C22semidirect
60. C2×(C2×#6157)⋊C4C22semidirect
63. C2×#13133202C4semidirect
64. C2×#13133202C4semidirect
65. C2×#13133201C4semidirect
66. C2×#13133200C4semidirect
67. C2×#13133199C4semidirect
68. C2×#13133199C4semidirect
69. C2×#13133198C4semidirect
70. #123×D53C4semidirect
77. C2×#123×C53C4semidirect
149. C23×Dic53C2×C4semidirect
152. C22×C4×D53C2×C4semidirect
153. C22×C4×D53C2×C4semidirect
154. C22×C4×D53C2×C4semidirect
161. #13133202C2×C4semidirect
162. #13133202C2×C4semidirect
163. #13133201C2×C4semidirect
164. #13133200C2×C4semidirect
165. #13133199C2×C4semidirect
166. #13133199C2×C4semidirect
167. #13133198C2×C4semidirect
168. C2×C4⋊Dic53C2×C4semidirect
169. C2×C4⋊Dic53C2×C4semidirect
170. C2×#11719919C2×C4semidirect
171. C2×#11719919C2×C4semidirect
172. C2×#11719919C2×C4semidirect
173. C2×#11719919C2×C4semidirect
174. C4⋊C4×D53C2×C4semidirect
175. C4⋊C4×D53C2×C4semidirect
178. C2×C22⋊Dic53C2×C4semidirect
179. C2×C22⋊Dic53C2×C4semidirect
180. C2×C22⋊Dic53C2×C4semidirect
181. C2×#11719921C2×C4semidirect
182. C2×#11719921C2×C4semidirect
183. C2×#11719921C2×C4semidirect
184. C2×#11719921C2×C4semidirect
185. C2×#11719921C2×C4semidirect
186. C2×#11719921C2×C4semidirect
187. C22⋊C4×D53C2×C4semidirect
188. C22⋊C4×D53C2×C4semidirect
189. C22⋊C4×D53C2×C4semidirect
194. C23×C4×C53C2×C4semidirect
195. #123×C53C2×C4semidirect
196. C2×C4⋊C4×C53C2×C4semidirect
197. C2×C4⋊C4×C53C2×C4semidirect
198. C2×C22⋊C4×C53C2×C4semidirect
199. C2×C22⋊C4×C53C2×C4semidirect
200. C2×C22⋊C4×C53C2×C4semidirect
274. C22×C4×C53C22×C4semidirect
285. C22×Dic53C22×C4semidirect
311. C2×C4×D53C22×C4semidirect
312. C2×C4×D53C22×C4semidirect
333. C4⋊C4×C53C22×C4semidirect
334. C4⋊C4×C53C22×C4semidirect
335. C22⋊C4×C53C22×C4semidirect
336. C22⋊C4×C53C22×C4semidirect
337. C22⋊C4×C53C22×C4semidirect
338. C22⋊Dic53C22×C4semidirect
339. C22⋊Dic53C22×C4semidirect
340. C22⋊Dic53C22×C4semidirect
341. #11719921C22×C4semidirect
342. #11719921C22×C4semidirect
343. #11719921C22×C4semidirect
344. #11719921C22×C4semidirect
345. #11719921C22×C4semidirect
346. #11719921C22×C4semidirect
347. C4⋊Dic53C22×C4semidirect
348. C4⋊Dic53C22×C4semidirect
349. #11719919C22×C4semidirect
350. #11719919C22×C4semidirect
351. #11719919C22×C4semidirect
352. #11719919C22×C4semidirect
562. C2×C53#2359semidirect
568. D53#2359semidirect
587. C2×#123#6157semidirect
634. C53C2×#2359semidirect
677. C23×C4C2×#6157semidirect
685. #123C2×#6157semidirect
708. C2×C4⋊C4C2×#6157semidirect
709. C2×C4⋊C4C2×#6157semidirect
735. C2×C22⋊C4C2×#6157semidirect
736. C2×C22⋊C4C2×#6157semidirect
737. C2×C22⋊C4C2×#6157semidirect
874. C22×C4C22×#6157semidirect
886. C4⋊C4C22×#6157semidirect
887. C4⋊C4C22×#6157semidirect
902. C22⋊C4C22×#6157semidirect
903. C22⋊C4C22×#6157semidirect
904. C22⋊C4C22×#6157semidirect
1109. C2#20291238direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×#61572
C22×#131332962
#202912382
C2×#168115742
C2×#168115732
C2×#168115722
C2×#168115712
C2×#168115702
C2×C4⋊C4×#61572
C2×C22⋊C4×#61572
C22×(C2×#6157)⋊C42
C2×#123×D532
C2×#235953