Finite Group Databasebeta

← C2×#20291214 #28328713

Subgroups — C2×#20291214 #28328713

Order 13568.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20291214C2116yesmaximal, direct product factor
2C2×#16811575C211yesmaximal, characteristic
3C2×#16811574C211yesmaximal, characteristic, complemented
4C2×#16811573C211yesmaximal, characteristic, complemented
5C2×#16811573C211yesmaximal, characteristic, complemented
6C2×#16811573C211yesmaximal, characteristic, complemented
7C2×#16811573C211yesmaximal, characteristic, complemented
8C2×#16811572C211yesmaximal, characteristic, complemented
9C2×#16811572C211yesmaximal, characteristic, complemented
10C2×#16811571C211yesmaximal, characteristic
11C2×#16811570C211yesmaximal, characteristic, complemented
12C2×#16811565C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×#6157C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×#6157C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊#6157C211yesmaximal, characteristic, complemented
16C2×#123×D53C211yesmaximal, characteristic
17C24×#6157C2211yescharacteristic
18C22×C4⋊#6157C2211yescharacteristic
19C22×C4⋊#6157C2211yescharacteristic
20C22×C4⋊#6157C2211yescharacteristic
21C22×C4⋊#6157C2211yescharacteristic
22C22×C4⋊#6157C2211yescharacteristic
23C22×C22⋊#6157C2211yescharacteristic
24C22×C22⋊#6157C2211yescharacteristic
25C22×C22⋊#6157C2211yescharacteristic
26C22×C22⋊#6157C2211yescharacteristic
27C22×C22⋊#6157C2211yescharacteristic
28C22×C22⋊#6157C2211yescharacteristic
29C22×C22⋊#6157C2211yescharacteristic
30C22×C4×#6157C2211yescharacteristic
31C22×C4×#6157C2211yescharacteristic
32C22×C4×#6157C2211yescharacteristic
33C22×C4×#6157C2211yescharacteristic
34C22×C4×#6157C2211yescharacteristic
35#16811575C2218yes—
36#16811574C2218yescomplemented
37#16811573C2218yescomplemented
38#16811573C2218yescomplemented
39#16811573C2218yescomplemented
40#16811573C2218yescomplemented
41#16811572C2218yescomplemented
42#16811572C2218yescomplemented
43#16811571C2218yes—
44#16811570C2218yescomplemented
45#16811565C2218yescomplemented
46C4⋊C4×#6157C2218yescomplemented
47C22⋊C4×#6157C2218yescomplemented
48C4×C22⋊#6157C2218yescomplemented
49C2×(C2×#6157)⋊C4C2211yescharacteristic
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
59C22×D4×D53C2211yescharacteristic
60C23×C4×D53C2211yescharacteristic
61C2×#13133202C411yescharacteristic, complemented
62C2×#13133202C411yescharacteristic, complemented
63C2×#13133201C411yescharacteristic, complemented
64C2×#13133200C411yescharacteristic, complemented
65C2×#13133199C411yescharacteristic, complemented
66C2×#13133199C411yescharacteristic, complemented
67C2×#13133198C411yescharacteristic, complemented
68#123×D53C418yescomplemented
69#123×D53C2218yes—
70C2×C4⋊C4×D53C2211yescharacteristic
71C2×C4⋊C4×D53C2211yescharacteristic
72C2×C22⋊C4×D53C2211yescharacteristic
73C2×C22⋊C4×D53C2211yescharacteristic
74C2×C22⋊C4×D53C2211yescharacteristic
75C2×#123×C53C411yescharacteristic, complemented
76C23×#6157—24no—
77C23×#6157—42no—
78C23×#6157—42no—
79C23×#6157C2311yescharacteristic
80C23×#6157C2311yescharacteristic
81C23×#6157C2311yescharacteristic
82C23×#6157C2311yescharacteristic
83C23×#6157C2311yescharacteristic
84C23×#6157C2311yescharacteristic
85C23×#6157C2311yescharacteristic
86C23×#6157C2311yescharacteristic
87C23×#6157C2314yes—
88C2×C4⋊#6157—24no—
89C2×C4⋊#6157—42no—
90C2×C4⋊#6157—42no—
91C2×C4⋊#6157—42no—
92C2×C4⋊#6157—42no—
93C2×C4⋊#6157C2314yes—
94C2×C4⋊#6157C2314yes—
95C2×C4⋊#6157C2314yes—
96C2×C4⋊#6157C2314yes—
97C2×C4⋊#6157C2314yes—
98C2×C22⋊#6157—24no—
99C2×C22⋊#6157—24no—
100C2×C22⋊#6157—24no—
101C2×C22⋊#6157—42no—
102C2×C22⋊#6157—42no—
103C2×C22⋊#6157—42no—
104C2×C22⋊#6157—42no—
105C2×C22⋊#6157C2314yes—
106C2×C22⋊#6157C2314yes—
107C2×C22⋊#6157C2314yes—
108C2×C22⋊#6157C2314yes—
109C2×C22⋊#6157C2314yes—
110C2×C22⋊#6157C2314yes—
111C2×C22⋊#6157C2314yes—
112C2×C4×#6157—24no—
113C2×C4×#6157—42no—
114C2×C4×#6157—42no—
115C2×C4×#6157—42no—
116C2×C4×#6157—42no—
117C2×C4×#6157C2314yes—
118C2×C4×#6157C2314yes—
119C2×C4×#6157C2314yes—
120C2×C4×#6157C2314yes—
121C2×C4×#6157C2314yes—
122(C2×#6157)⋊C4C2314yes—
123(C2×#6157)⋊C4C2314yes—
124(C2×#6157)⋊C4C2314yes—
125(C2×#6157)⋊C4C2314yes—
126(C2×#6157)⋊C4C2314yes—
127(C2×#6157)⋊C4C2314yes—
128(C2×#6157)⋊C4C2314yes—
129(C2×#6157)⋊C4C2314yes—
130(C2×#6157)⋊C4C2314yes—
131(C2×#6157)⋊C4C2314yes—
132C24×D53C2311yescharacteristic
133C24×D53C2311yescharacteristic
134C22×D212C2×C411yescharacteristic
135C22×C22⋊D53C2×C411yescharacteristic
136C22×C22⋊D53C2×C411yescharacteristic
137C2×D4×D53—42no—
138C2×D4×D53—42no—
139C2×D4×D53C2×C414yes—
140C2×D4×D53C2314yes—
141C23×Dic53C2×C411yescharacteristic, complemented
142C22×C4×D53—42no—
143C22×C4×D53—42no—
144C22×C4×D53C2×C414yescomplemented
145C22×C4×D53C2×C411yescharacteristic, complemented
146C22×C4×D53C2×C411yescharacteristic, complemented
147C22×C4×D53C2311yescharacteristic
148C22×C4×D53C2311yescharacteristic
149C22×C4×D53C2311yescharacteristic
150C22×C4×D53C2311yescharacteristic
151C22×C4×D53C2311yescharacteristic
152C22×C4×D53C2314yes—
153#13133202C2×C418yescomplemented
154#13133202C2×C418yescomplemented
155#13133201C2×C418yescomplemented
156#13133200C2×C418yescomplemented
157#13133199C2×C418yescomplemented
158#13133199C2×C418yescomplemented
159#13133198C2×C418yescomplemented
160C2×C4⋊Dic53C2×C411yescharacteristic, complemented
161C2×C4⋊Dic53C2×C411yescharacteristic, complemented
162C2×#11719919C2×C411yescharacteristic, complemented
163C2×#11719919C2×C411yescharacteristic, complemented
164C2×#11719919C2×C411yescharacteristic, complemented
165C2×#11719919C2×C411yescharacteristic, complemented
166C4⋊C4×D53C2×C414yescomplemented
167C4⋊C4×D53C2×C414yescomplemented
168C4⋊C4×D53C2314yes—
169C4⋊C4×D53C2314yes—
170C2×C22⋊Dic53C2×C411yescharacteristic
171C2×C22⋊Dic53C2×C411yescharacteristic
172C2×C22⋊Dic53C2×C411yescharacteristic, complemented
173C2×#11719921C2×C411yescharacteristic
174C2×#11719921C2×C411yescharacteristic
175C2×#11719921C2×C411yescharacteristic
176C2×#11719921C2×C411yescharacteristic
177C2×#11719921C2×C411yescharacteristic, complemented
178C2×#11719921C2×C411yescharacteristic, complemented
179C22⋊C4×D53C2×C414yes—
180C22⋊C4×D53C2×C414yes—
181C22⋊C4×D53C2×C414yescomplemented
182C22⋊C4×D53C2314yes—
183C22⋊C4×D53C2314yes—
184C22⋊C4×D53C2314yes—
185C22×D4×C53C2×C411yescharacteristic
186C23×C4×C53C2×C411yescharacteristic, complemented
187#123×C53C2×C418yescomplemented
188C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
189C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
190C2×C22⋊C4×C53C2×C411yescharacteristic
191C2×C22⋊C4×C53C2×C411yescharacteristic
192C2×C22⋊C4×C53C2×C411yescharacteristic, complemented
193C24×C53C22×C411yescharacteristic
194C24×C53C22×C411yescharacteristic
195C23×D53—22no—
196C23×D53—22no—
197C23×D53—22no—
198C23×D53—22no—
199C23×D53—22no—
200C23×D53—22no—
201C23×D53—22no—
202C23×D53—22no—
203C23×D53—22no—
204C23×D53—22no—
205C23×D53—22no—
206C23×D53—22no—
207C23×D53C22×C412yes—
208C23×D53C22×C412yes—
209C23×D53C22×C411yescharacteristic
210C23×D53C22×C411yescharacteristic
211C23×D53C2412yes—
212C23×D53C2412yes—
213C23×D53C2411yescharacteristic
214C22×#6157—22no—
215C22×#6157—22no—
216C22×#6157—22no—
217C22×#6157—22no—
218C22×#6157—22no—
219C22×#6157—22no—
220C22×#6157—22no—
221C22×#6157—22no—
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—22no—
234C22×#6157—22no—
235C22×#6157—22no—
236C22×#6157—28no—
237C22×#6157—44no—
238C22×#6157—44no—
239C22×#6157—416no—
240C22×#6157#4114yes—
241C22×#6157#4114yes—
242C22×#6157C2412yes—
243C22×#6157C2412yes—
244C22×#6157C2412yes—
245C22×#6157C2412yes—
246C22×#6157C2412yes—
247C22×#6157C2412yes—
248C22×#6157C2412yes—
249C22×#6157C2412yes—
250C2×D4×C53—42no—
251C2×D4×C53C22×C414yes—
252C22×C4×C53—42no—
253C22×C4×C53C22×C411yescharacteristic
254C22×C4×C53C22×C411yescharacteristic
255C22×C4×C53C22×C411yescharacteristic
256C22×C4×C53C22×C411yescharacteristic
257C22×C4×C53C22×C411yescharacteristic
258C22×C4×C53C22×C414yescomplemented
259C2×C22⋊D53—42no—
260C2×C22⋊D53—42no—
261C2×C22⋊D53C22×C414yes—
262C2×C22⋊D53C22×C414yes—
263C22×Dic53—42no—
264C22×Dic53C22×C411yescharacteristic
265C22×Dic53C22×C411yescharacteristic
266C22×Dic53C22×C411yescharacteristic
267C22×Dic53C22×C411yescharacteristic
268C22×Dic53C22×C411yescharacteristic
269C22×Dic53C22×C414yescomplemented
270D4×D53—48no—
271D4×D53—44no—
272D4×D53—44no—
273C2×D212—42no—
274C2×D212C22×C414yes—
275C2×C4×D53—22no—
276C2×C4×D53—22no—
277C2×C4×D53—22no—
278C2×C4×D53—22no—
279C2×C4×D53—22no—
280C2×C4×D53—22no—
281C2×C4×D53—22no—
282C2×C4×D53—22no—
283C2×C4×D53—22no—
284C2×C4×D53—22no—
285C2×C4×D53—48no—
286C2×C4×D53—44no—
287C2×C4×D53—44no—
288C2×C4×D53—42no—
289C2×C4×D53—42no—
290C2×C4×D53C22×C412yes—
291C2×C4×D53C22×C412yes—
292C2×C4×D53C22×C412yes—
293C2×C4×D53C22×C412yes—
294C2×C4×D53C22×C412yes—
295C2×C4×D53C22×C414yescomplemented
296C2×C4×D53C22×C414yescomplemented
297C2×C4×D53C2412yes—
298C2×C4×D53C2412yes—
299C2×C4×D53C2412yes—
300C2×C4×D53C2412yes—
301C2×C4×D53C2412yes—
302C22⋊#6157—28no—
303C22⋊#6157—28no—
304C22⋊#6157—28no—
305C22⋊#6157—44no—
306C22⋊#6157—44no—
307C22⋊#6157—44no—
308C22⋊#6157—44no—
309C4⋊#6157—28no—
310C4⋊#6157—44no—
311C4⋊#6157—44no—
312C4⋊#6157—44no—
313C4⋊#6157—44no—
314C4×#6157—28no—
315C4×#6157—44no—
316C4×#6157—44no—
317C4×#6157—44no—
318C4×#6157—44no—
319C4⋊C4×C53C22×C414yescomplemented
320C4⋊C4×C53C22×C414yescomplemented
321C22⋊C4×C53C22×C414yes—
322C22⋊C4×C53C22×C414yes—
323C22⋊C4×C53C22×C414yescomplemented
324C22⋊Dic53C22×C414yes—
325C22⋊Dic53C22×C414yes—
326C22⋊Dic53C22×C414yescomplemented
327#11719921C22×C414yes—
328#11719921C22×C414yes—
329#11719921C22×C414yes—
330#11719921C22×C414yes—
331#11719921C22×C414yescomplemented
332#11719921C22×C414yescomplemented
333C4⋊Dic53C22×C414yescomplemented
334C4⋊Dic53C22×C414yescomplemented
335#11719919C22×C414yescomplemented
336#11719919C22×C414yescomplemented
337#11719919C22×C414yescomplemented
338#11719919C22×C414yescomplemented
339C23×C53—22no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53C23×C412yes—
346C23×C53C23×C412yes—
347C23×C53C23×C411yescharacteristic
348C22×D53—22no—
349C22×D53—22no—
350C22×D53—22no—
351C22×D53—22no—
352C22×D53—22no—
353C22×D53—22no—
354C22×D53—24no—
355C22×D53—24no—
356C22×D53—24no—
357C22×D53—24no—
358C22×D53—24no—
359C22×D53—24no—
360C22×D53—22no—
361C22×D53—22no—
362C22×D53—22no—
363C22×D53—22no—
364C22×D53—22no—
365C22×D53—22no—
366C22×D53—22no—
367C22×D53—22no—
368C22×D53—22no—
369C22×D53—22no—
370C22×D53—22no—
371C22×D53—22no—
372C22×D53—44no—
373C22×D53—44no—
374C22×D53—44no—
375C22×D53—44no—
376C22×D53—44no—
377C22×D53—44no—
378C22×D53—44no—
379C22×D53—44no—
380C22×D53C23×C412yes—
381C22×D53C23×C412yes—
382C22×D53C23×C411yescharacteristic
383C22×D53C2×#4112yes—
384C22×D53C2×#4112yes—
385C22×D53H(5,𝔽2)12yes—
386C22×D53H(5,𝔽2)12yes—
387C22×D53H(5,𝔽2)12yes—
388C22×D532−1+412yes—
389C22×D53C2511yescharacteristic
390C2×#6157—28no—
391C2×#6157—28no—
392C2×#6157—22no—
393C2×#6157—22no—
394C2×#6157—22no—
395C2×#6157—22no—
396C2×#6157—22no—
397C2×#6157—22no—
398C2×#6157—22no—
399C2×#6157—22no—
400C2×#6157—22no—
401C2×#6157—22no—
402C2×#6157—22no—
403C2×#6157—22no—
404C2×#6157—22no—
405C2×#6157—22no—
406C2×#6157—22no—
407C2×#6157—22no—
408C2×#6157—22no—
409C2×#6157—22no—
410C2×#6157—22no—
411C2×#6157—22no—
412C2×#6157—22no—
413C2×#6157—22no—
414C2×#6157—416no—
415C2×#6157—44no—
416C2×#6157—44no—
417C2×#6157—44no—
418C2×#6157—44no—
419C2×#6157—44no—
420C2×#6157—44no—
421C2×#6157C2×#4114yes—
422C2×#6157C2×#4114yes—
423D4×C53—44no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—44no—
430C2×C4×C53C23×C412yes—
431C2×C4×C53C23×C412yes—
432C2×C4×C53C23×C412yes—
433C2×C4×C53C23×C412yes—
434C2×C4×C53C23×C412yes—
435C22⋊D53—44no—
436C22⋊D53—44no—
437C2×Dic53—22no—
438C2×Dic53—22no—
439C2×Dic53—22no—
440C2×Dic53—22no—
441C2×Dic53—22no—
442C2×Dic53—44no—
443C2×Dic53C23×C412yes—
444C2×Dic53C23×C412yes—
445C2×Dic53C23×C412yes—
446C2×Dic53C23×C412yes—
447C2×Dic53C23×C412yes—
448D212—44no—
449C4×D53—24no—
450C4×D53—24no—
451C4×D53—24no—
452C4×D53—24no—
453C4×D53—24no—
454C4×D53—22no—
455C4×D53—22no—
456C4×D53—22no—
457C4×D53—22no—
458C4×D53—22no—
459C4×D53—22no—
460C4×D53—22no—
461C4×D53—22no—
462C4×D53—22no—
463C4×D53—22no—
464C4×D53—44no—
465C4×D53—44no—
466C2×#2335—531nomaximal, Sylow
467C22×C53—22no—
468C22×C53—22no—
469C22×C53—22no—
470C22×C53—22no—
471C22×C53—22no—
472C22×C53—22no—
473C22×C53—44no—
474C22×C53—44no—
475C22×C53C4×#4112yes—
476C22×C53#51812yes—
477C22×C53#52012yes—
478C22×C53C24×C411yescharacteristic
479C2×D53—22no—
480C2×D53—22no—
481C2×D53—22no—
482C2×D53—22no—
483C2×D53—22no—
484C2×D53—22no—
485C2×D53—44no—
486C2×D53—44no—
487C2×D53—48no—
488C2×D53—48no—
489C2×D53—42no—
490C2×D53—42no—
491C2×D53—42no—
492C2×D53—42no—
493C2×D53—42no—
494C2×D53—42no—
495C2×D53—42no—
496C2×D53—42no—
497C2×D53C4×#4112yes—
498C2×D53#51812yes—
499C2×D53#52012yes—
500C2×D53#53814yes—
501C2×D53#53914yes—
502C2×D53#54014yes—
503C2×D53#54214yes—
504C2×D53C22×#4111yescharacteristic
505C2×D53C22×#4111yescharacteristic
506C2×D53C2×H(5,𝔽2)11yescharacteristic
507C2×D53C2×H(5,𝔽2)11yescharacteristic
508C2×D53C2×H(5,𝔽2)11yescharacteristic
509C2×D53C2×2−1+411yescharacteristic
510#6157—24no—
511#6157—24no—
512#6157—42no—
513#6157—42no—
514#6157—42no—
515#6157—42no—
516#6157—42no—
517#6157—42no—
518C4×C53—22no—
519C4×C53—22no—
520C4×C53—22no—
521C4×C53—22no—
522C4×C53—22no—
523Dic53—22no—
524Dic53—22no—
525Dic53—22no—
526Dic53—22no—
527Dic53—22no—
528C22×#123—531no—
529#2335—5316no—
530C2×#390—531no—
531C2×#389—531no—
532C2×#388—531no—
533C2×#388—531no—
534C2×#388—531no—
535C2×#388—531no—
536C2×#387—531no—
537C2×#387—531no—
538C2×#386—531no—
539C2×#385—531no—
540C2×#380—531no—
541C2×C4×C4⋊C4—531no—
542C2×C4×C22⋊C4—531no—
543C2×C4×C22⋊C4—531no—
544C2×C53—42no—
545C2×C53—42no—
546C2×C53#233514yescomplemented
547C2×C53C2×C4×#4111yescharacteristic
548C2×C53C2×#51811yescharacteristic
549C2×C53C2×#52011yescharacteristic
550D53—42no—
551D53—42no—
552D53#233514yescomplemented
553D53C2×#53811yescharacteristic
554D53C2×#53911yescharacteristic
555D53C2×#54011yescharacteristic
556D53C2×#54211yescharacteristic
557C23×D4—531no—
558C24×C4—531no—
559C24×C4—531no—
560C2×#123—531no—
561C2×#123—531no—
562C2×#123—538no—
563C2×#123—538no—
564C2×#123—531no—
565C2×#123—531no—
566C2×#123—531no—
567C2×#123—531no—
568C2×#123—531no—
569C2×#123#615711yescharacteristic, complemented
570C22×C4⋊C4—531no—
571C22×C4⋊C4—531no—
572C22×C4⋊C4—531no—
573C22×C4⋊C4—531no—
574C22×C4⋊C4—531no—
575C22×C4⋊C4—531no—
576C22×C4⋊C4—531no—
577C22×C22⋊C4—531no—
578C22×C22⋊C4—531no—
579C22×C22⋊C4—531no—
580C22×C22⋊C4—531no—
581C22×C22⋊C4—531no—
582C22×C22⋊C4—531no—
583C22×C22⋊C4—531no—
584C22×C22⋊C4—531no—
585C22×C22⋊C4—531no—
586C22×C22⋊C4—531no—
587C22×C42—531no—
588C22×C42—531no—
589C22×C42—531no—
590C22×C42—531no—
591C22×C42—531no—
592#390—538no—
593#389—538no—
594#388—538no—
595#388—538no—
596#388—538no—
597#388—538no—
598#387—538no—
599#387—538no—
600#386—538no—
601#385—538no—
602#380—538no—
603C4×C4⋊C4—538no—
604C4×C22⋊C4—538no—
605C4×C22⋊C4—538no—
606C2×#95—531no—
607C2×#95—531no—
608C2×#95—531no—
609C2×#95—531no—
610C2×#95—531no—
611C2×#95—531no—
612C2×#95—531no—
613C2×#95—531no—
614C2×#95—531no—
615C2×#95—531no—
616C53C2×#233511yescharacteristic, complemented, Sylow
617C25—531no—
618C25—531no—
619C22×D4—531no—
620C22×D4—531no—
621C22×D4—534no—
622C22×D4—534no—
623C22×D4—531no—
624C22×D4—2122no—
625C22×D4—2122no—
626C22×D4C2×#615711yescharacteristic
627C23×C4—531no—
628C23×C4—531no—
629C23×C4—531no—
630C23×C4—531no—
631C23×C4—531no—
632C23×C4—531no—
633C23×C4—531no—
634C23×C4—531no—
635C23×C4—531no—
636C23×C4—531no—
637C23×C4—534no—
638C23×C4—534no—
639C23×C4—531no—
640C23×C4—531no—
641C23×C4—531no—
642C23×C4—531no—
643C23×C4—531no—
644C23×C4—531no—
645C23×C4—534no—
646C23×C4—1064no—
647C23×C4—2122no—
648C23×C4—2122no—
649C23×C4—2122no—
650C23×C4—2122no—
651C23×C4C2×#615711yescharacteristic, complemented
652#123—538no—
653#123—538no—
654#123—538no—
655#123—538no—
656#123—538no—
657#123—538no—
658#123—538no—
659#123C2×#615718yescomplemented
660C2×C4⋊C4—531no—
661C2×C4⋊C4—531no—
662C2×C4⋊C4—531no—
663C2×C4⋊C4—531no—
664C2×C4⋊C4—531no—
665C2×C4⋊C4—531no—
666C2×C4⋊C4—534no—
667C2×C4⋊C4—534no—
668C2×C4⋊C4—534no—
669C2×C4⋊C4—534no—
670C2×C4⋊C4—534no—
671C2×C4⋊C4—534no—
672C2×C4⋊C4—534no—
673C2×C4⋊C4—534no—
674C2×C4⋊C4—534no—
675C2×C4⋊C4—1064no—
676C2×C4⋊C4—2122no—
677C2×C4⋊C4—2122no—
678C2×C4⋊C4—2122no—
679C2×C4⋊C4—2122no—
680C2×C4⋊C4C2×#615711yescharacteristic, complemented
681C2×C4⋊C4C2×#615711yescharacteristic, complemented
682C2×C22⋊C4—531no—
683C2×C22⋊C4—531no—
684C2×C22⋊C4—531no—
685C2×C22⋊C4—531no—
686C2×C22⋊C4—531no—
687C2×C22⋊C4—531no—
688C2×C22⋊C4—531no—
689C2×C22⋊C4—531no—
690C2×C22⋊C4—531no—
691C2×C22⋊C4—534no—
692C2×C22⋊C4—534no—
693C2×C22⋊C4—534no—
694C2×C22⋊C4—534no—
695C2×C22⋊C4—534no—
696C2×C22⋊C4—534no—
697C2×C22⋊C4—534no—
698C2×C22⋊C4—534no—
699C2×C22⋊C4—534no—
700C2×C22⋊C4—534no—
701C2×C22⋊C4—534no—
702C2×C22⋊C4—534no—
703C2×C22⋊C4—534no—
704C2×C22⋊C4—1064no—
705C2×C22⋊C4—1064no—
706C2×C22⋊C4—1064no—
707C2×C22⋊C4—2122no—
708C2×C22⋊C4—2122no—
709C2×C22⋊C4—2122no—
710C2×C22⋊C4—2122no—
711C2×C22⋊C4C2×#615711yescharacteristic
712C2×C22⋊C4C2×#615711yescharacteristic
713C2×C22⋊C4C2×#615711yescharacteristic, complemented
714C2×C42—534no—
715C2×C42—534no—
716C2×C42—534no—
717C2×C42—534no—
718C2×C42—534no—
719C2×C42—1064no—
720C2×C42—2122no—
721C2×C42—2122no—
722C2×C42—2122no—
723C2×C42—2122no—
724#95—534no—
725#95—534no—
726#95—534no—
727#95—534no—
728#95—534no—
729#95—534no—
730#95—534no—
731#95—534no—
732#95—534no—
733#95—534no—
734C24—531no—
735C24—532no—
736C24—532no—
737C24—532no—
738C24—532no—
739C24—531no—
740C24—531no—
741C24—1062no—
742C24—1062no—
743C24—1062no—
744C24—1062no—
745C24—1062no—
746C24—1062no—
747C24—1062no—
748C24—1062no—
749C24—1062no—
750C24—1062no—
751C24—1062no—
752C24—1062no—
753C24C22×#615711yescharacteristic
754C24C22×#615711yescharacteristic
755C2×D4—42no—
756C2×D4—534no—
757C2×D4—534no—
758C2×D4—534no—
759C2×D4—2122no—
760C2×D4—2124no—
761C2×D4—2124no—
762C2×D4—2128no—
763C2×D4—2122no—
764C2×D4—2122no—
765C2×D4C22×#615714yes—
766C22×C4—42no—
767C22×C4—534no—
768C22×C4—534no—
769C22×C4—532no—
770C22×C4—532no—
771C22×C4—531no—
772C22×C4—531no—
773C22×C4—531no—
774C22×C4—531no—
775C22×C4—531no—
776C22×C4—534no—
777C22×C4—532no—
778C22×C4—532no—
779C22×C4—532no—
780C22×C4—532no—
781C22×C4—532no—
782C22×C4—532no—
783C22×C4—532no—
784C22×C4—532no—
785C22×C4—532no—
786C22×C4—532no—
787C22×C4—534no—
788C22×C4—534no—
789C22×C4—532no—
790C22×C4—532no—
791C22×C4—532no—
792C22×C4—532no—
793C22×C4—532no—
794C22×C4—532no—
795C22×C4—1062no—
796C22×C4—1062no—
797C22×C4—1062no—
798C22×C4—1062no—
799C22×C4—1062no—
800C22×C4—1062no—
801C22×C4—1062no—
802C22×C4—1062no—
803C22×C4—1062no—
804C22×C4—1062no—
805C22×C4—1068no—
806C22×C4—1062no—
807C22×C4—1062no—
808C22×C4—1062no—
809C22×C4—1062no—
810C22×C4—1062no—
811C22×C4—1062no—
812C22×C4—1062no—
813C22×C4—1062no—
814C22×C4—1062no—
815C22×C4—1062no—
816C22×C4—1062no—
817C22×C4—1062no—
818C22×C4—1062no—
819C22×C4—1062no—
820C22×C4—1062no—
821C22×C4—1062no—
822C22×C4—1062no—
823C22×C4—1062no—
824C22×C4—1062no—
825C22×C4—1062no—
826C22×C4—1062no—
827C22×C4—1062no—
828C22×C4—2122no—
829C22×C4—2122no—
830C22×C4—2124no—
831C22×C4—2124no—
832C22×C4—2128no—
833C22×C4—2122no—
834C22×C4—2124no—
835C22×C4—2124no—
836C22×C4—21216no—
837C22×C4C22×#615711yescharacteristic
838C22×C4C22×#615711yescharacteristic
839C22×C4C22×#615711yescharacteristic
840C22×C4C22×#615711yescharacteristic
841C22×C4C22×#615711yescharacteristic
842C22×C4C22×#615714yescomplemented
843C4⋊C4—534no—
844C4⋊C4—534no—
845C4⋊C4—534no—
846C4⋊C4—534no—
847C4⋊C4—534no—
848C4⋊C4—534no—
849C4⋊C4—1068no—
850C4⋊C4—2124no—
851C4⋊C4—2124no—
852C4⋊C4—2124no—
853C4⋊C4—2124no—
854C4⋊C4C22×#615714yescomplemented
855C4⋊C4C22×#615714yescomplemented
856C22⋊C4—534no—
857C22⋊C4—534no—
858C22⋊C4—534no—
859C22⋊C4—534no—
860C22⋊C4—534no—
861C22⋊C4—534no—
862C22⋊C4—534no—
863C22⋊C4—534no—
864C22⋊C4—534no—
865C22⋊C4—1068no—
866C22⋊C4—1068no—
867C22⋊C4—1068no—
868C22⋊C4—2124no—
869C22⋊C4—2124no—
870C22⋊C4—2124no—
871C22⋊C4—2124no—
872C22⋊C4C22×#615714yes—
873C22⋊C4C22×#615714yes—
874C22⋊C4C22×#615714yescomplemented
875C42—1068no—
876C42—2124no—
877C42—2124no—
878C42—2124no—
879C42—2124no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—532no—
887C23—532no—
888C23—532no—
889C23—532no—
890C23—532no—
891C23—532no—
892C23—531no—
893C23—531no—
894C23—532no—
895C23—532no—
896C23—1062no—
897C23—1062no—
898C23—1062no—
899C23—1062no—
900C23—1062no—
901C23—1062no—
902C23—1062no—
903C23—1062no—
904C23—1062no—
905C23—1064no—
906C23—1062no—
907C23—1064no—
908C23—1064no—
909C23—1064no—
910C23—1062no—
911C23—1062no—
912C23—1064no—
913C23—1064no—
914C23—1062no—
915C23—1062no—
916C23—1062no—
917C23—1062no—
918C23—1062no—
919C23—1062no—
920C23—2124no—
921C23—2124no—
922C23—2124no—
923C23—2124no—
924C23—2124no—
925C23—2124no—
926C23—2124no—
927C23—2124no—
928C23C23×#615712yes—
929C23C23×#615712yes—
930C23C23×#615711yescharacteristic
931D4—44no—
932D4—2124no—
933D4—2124no—
934D4—2124no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—44no—
941C2×C4—534no—
942C2×C4—534no—
943C2×C4—532no—
944C2×C4—532no—
945C2×C4—532no—
946C2×C4—532no—
947C2×C4—532no—
948C2×C4—1062no—
949C2×C4—1062no—
950C2×C4—1062no—
951C2×C4—1062no—
952C2×C4—1062no—
953C2×C4—1062no—
954C2×C4—1062no—
955C2×C4—1062no—
956C2×C4—1062no—
957C2×C4—1064no—
958C2×C4—1062no—
959C2×C4—1064no—
960C2×C4—1064no—
961C2×C4—1064no—
962C2×C4—1064no—
963C2×C4—1062no—
964C2×C4—1062no—
965C2×C4—1062no—
966C2×C4—1062no—
967C2×C4—1068no—
968C2×C4—1068no—
969C2×C4—1062no—
970C2×C4—1062no—
971C2×C4—1062no—
972C2×C4—1062no—
973C2×C4—1062no—
974C2×C4—1062no—
975C2×C4—1062no—
976C2×C4—1062no—
977C2×C4—1062no—
978C2×C4—1062no—
979C2×C4—1062no—
980C2×C4—1062no—
981C2×C4—1062no—
982C2×C4—1062no—
983C2×C4—1062no—
984C2×C4—1062no—
985C2×C4—1062no—
986C2×C4—1062no—
987C2×C4—1062no—
988C2×C4—1062no—
989C2×C4—1062no—
990C2×C4—1062no—
991C2×C4—1062no—
992C2×C4—2124no—
993C2×C4—2124no—
994C2×C4—2124no—
995C2×C4—21216no—
996C2×C4—2124no—
997C2×C4—2124no—
998C2×C4—2124no—
999C2×C4—2124no—
1000C2×C4—2124no—
1001C2×C4—2124no—
1002C2×C4C23×#615712yes—
1003C2×C4C23×#615712yes—
1004C2×C4C23×#615712yes—
1005C2×C4C23×#615712yes—
1006C2×C4C23×#615712yes—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—44no—
1014C22—44no—
1015C22—531no—
1016C22—531no—
1017C22—532no—
1018C22—531no—
1019C22—531no—
1020C22—532no—
1021C22—531no—
1022C22—531no—
1023C22—532no—
1024C22—534no—
1025C22—534no—
1026C22—534no—
1027C22—534no—
1028C22—1062no—
1029C22—1062no—
1030C22—1062no—
1031C22—1062no—
1032C22—1062no—
1033C22—1062no—
1034C22—2122no—
1035C22—2122no—
1036C22—2122no—
1037C22—2122no—
1038C22—2122no—
1039C22—2122no—
1040C22—2122no—
1041C22—2122no—
1042C22—2128no—
1043C22—2128no—
1044C22—2124no—
1045C22—2124no—
1046C22#41×#615712yes—
1047C22#1681169012yes—
1048C22#1681169212yes—
1049C22C24×#615711yescharacteristic
1050C4—22no—
1051C4—22no—
1052C4—22no—
1053C4—22no—
1054C4—22no—
1055C4—1064no—
1056C4—1064no—
1057C4—1062no—
1058C4—1062no—
1059C4—1062no—
1060C4—1062no—
1061C4—1062no—
1062C4—2122no—
1063C4—2122no—
1064C4—2122no—
1065C4—2122no—
1066C4—2122no—
1067C4—2122no—
1068C2—42no—
1069C2—42no—
1070C2—531no—
1071C2—531no—
1072C2—531no—
1073C2—531no—
1074C2—534no—
1075C2—2122no—
1076C2—2122no—
1077C2#2029121414yesdirect product factor
1078C2C2×#41×#615711yescharacteristic
1079C2C2×#1681169011yescharacteristic
1080C2C2×#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×#2335
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #20291214C2direct (N × H)
3. C2×#16811574C2semidirect
4. C2×#16811573C2semidirect
5. C2×#16811573C2semidirect
6. C2×#16811573C2semidirect
7. C2×#16811573C2semidirect
8. C2×#16811572C2semidirect
9. C2×#16811572C2semidirect
11. C2×#16811570C2semidirect
12. C2×#16811565C2semidirect
13. C2×C4⋊C4×#6157C2semidirect
14. C2×C22⋊C4×#6157C2semidirect
15. C2×C4×C22⋊#6157C2semidirect
36. #16811574C22semidirect
37. #16811573C22semidirect
38. #16811573C22semidirect
39. #16811573C22semidirect
40. #16811573C22semidirect
41. #16811572C22semidirect
42. #16811572C22semidirect
44. #16811570C22semidirect
45. #16811565C22semidirect
46. C4⋊C4×#6157C22semidirect
47. C22⋊C4×#6157C22semidirect
48. C4×C22⋊#6157C22semidirect
61. C2×#13133202C4semidirect
62. C2×#13133202C4semidirect
63. C2×#13133201C4semidirect
64. C2×#13133200C4semidirect
65. C2×#13133199C4semidirect
66. C2×#13133199C4semidirect
67. C2×#13133198C4semidirect
68. #123×D53C4semidirect
75. C2×#123×C53C4semidirect
141. C23×Dic53C2×C4semidirect
144. C22×C4×D53C2×C4semidirect
145. C22×C4×D53C2×C4semidirect
146. C22×C4×D53C2×C4semidirect
153. #13133202C2×C4semidirect
154. #13133202C2×C4semidirect
155. #13133201C2×C4semidirect
156. #13133200C2×C4semidirect
157. #13133199C2×C4semidirect
158. #13133199C2×C4semidirect
159. #13133198C2×C4semidirect
160. C2×C4⋊Dic53C2×C4semidirect
161. C2×C4⋊Dic53C2×C4semidirect
162. C2×#11719919C2×C4semidirect
163. C2×#11719919C2×C4semidirect
164. C2×#11719919C2×C4semidirect
165. C2×#11719919C2×C4semidirect
166. C4⋊C4×D53C2×C4semidirect
167. C4⋊C4×D53C2×C4semidirect
172. C2×C22⋊Dic53C2×C4semidirect
177. C2×#11719921C2×C4semidirect
178. C2×#11719921C2×C4semidirect
181. C22⋊C4×D53C2×C4semidirect
186. C23×C4×C53C2×C4semidirect
187. #123×C53C2×C4semidirect
188. C2×C4⋊C4×C53C2×C4semidirect
189. C2×C4⋊C4×C53C2×C4semidirect
192. C2×C22⋊C4×C53C2×C4semidirect
258. C22×C4×C53C22×C4semidirect
269. C22×Dic53C22×C4semidirect
295. C2×C4×D53C22×C4semidirect
296. C2×C4×D53C22×C4semidirect
319. C4⋊C4×C53C22×C4semidirect
320. C4⋊C4×C53C22×C4semidirect
323. C22⋊C4×C53C22×C4semidirect
326. C22⋊Dic53C22×C4semidirect
331. #11719921C22×C4semidirect
332. #11719921C22×C4semidirect
333. C4⋊Dic53C22×C4semidirect
334. C4⋊Dic53C22×C4semidirect
335. #11719919C22×C4semidirect
336. #11719919C22×C4semidirect
337. #11719919C22×C4semidirect
338. #11719919C22×C4semidirect
546. C2×C53#2335semidirect
552. D53#2335semidirect
569. C2×#123#6157semidirect
616. C53C2×#2335semidirect
651. C23×C4C2×#6157semidirect
659. #123C2×#6157semidirect
680. C2×C4⋊C4C2×#6157semidirect
681. C2×C4⋊C4C2×#6157semidirect
713. C2×C22⋊C4C2×#6157semidirect
842. C22×C4C22×#6157semidirect
854. C4⋊C4C22×#6157semidirect
855. C4⋊C4C22×#6157semidirect
874. C22⋊C4C22×#6157semidirect
1077. C2#20291214direct (N × H)

Maximal subgroups

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

subgroupindex
#202912142
C2×#168115752
C2×#168115742
C2×#168115732
C2×#168115722
C2×#168115712
C2×#168115702
C2×#168115652
C2×C4⋊C4×#61572
C2×C22⋊C4×#61572
C2×C4×C22⋊#61572
C2×#123×D532
C2×#233553