Finite Group Databasebeta

← C2×#20291213 #28328712

Subgroups — C2×#20291213 #28328712

Order 13568.

2614 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20291213C2116yesmaximal, direct product factor
2C2×#16811574C211yesmaximal, characteristic, complemented
3C2×#16811574C211yesmaximal, characteristic, complemented
4C2×#16811573C211yesmaximal, characteristic
5C2×#16811573C211yesmaximal, characteristic
6C2×#16811573C211yesmaximal, characteristic
7C2×#16811572C211yesmaximal, characteristic, complemented
8C2×#16811572C211yesmaximal, characteristic, complemented
9C2×#16811572C211yesmaximal, characteristic, complemented
10C2×#16811570C211yesmaximal, characteristic
11C2×#16811570C211yesmaximal, characteristic
12C2×#16811567C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×#6157C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊#6157C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×#6157C211yesmaximal, characteristic
16C2×#126×D53C211yesmaximal, characteristic
17C24×#6157C2211yescharacteristic
18C22×C4⋊#6157C2211yescharacteristic
19C22×C4⋊#6157C2211yescharacteristic
20C22×C4⋊#6157C2211yescharacteristic
21C22×C4⋊#6157C2211yescharacteristic
22C22×C4⋊#6157C2211yescharacteristic
23C22×C4⋊#6157C2211yescharacteristic
24C22×C4⋊#6157C2211yescharacteristic
25C22×C22⋊#6157C2211yescharacteristic
26C22×C22⋊#6157C2211yescharacteristic
27C22×C22⋊#6157C2211yescharacteristic
28C22×C4×#6157C2211yescharacteristic
29C22×C4×#6157C2211yescharacteristic
30C22×C4×#6157C2211yescharacteristic
31C22×C4×#6157C2211yescharacteristic
32C22×C4×#6157C2211yescharacteristic
33#16811574C2218yescomplemented
34#16811574C2218yescomplemented
35#16811573C2218yes—
36#16811573C2218yes—
37#16811573C2218yes—
38#16811572C2218yescomplemented
39#16811572C2218yescomplemented
40#16811572C2218yescomplemented
41#16811570C2218yes—
42#16811570C2218yes—
43#16811567C2218yescomplemented
44C4⋊C4×#6157C2218yescomplemented
45C4×C4⋊#6157C2218yescomplemented
46C22⋊C4×#6157C2218yes—
47C2×(C2×#6157)⋊C4C2211yescharacteristic
48C2×(C2×#6157)⋊C4C2211yescharacteristic
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
59C2×#13133212C411yescharacteristic, complemented
60C2×#13133212C411yescharacteristic, complemented
61C2×#13133212C411yescharacteristic, complemented
62C2×#13133211C411yescharacteristic, complemented
63C2×#13133210C411yescharacteristic, complemented
64C2×#13133210C411yescharacteristic, complemented
65C2×#13133210C411yescharacteristic, complemented
66#126×D53C418yescomplemented
67#126×D53C2218yes—
68C2×C4⋊C4×D53C2211yescharacteristic
69C2×C4⋊C4×D53C2211yescharacteristic
70C2×C4⋊C4×D53C2211yescharacteristic
71C2×C22⋊C4×D53C2211yescharacteristic
72C2×C22⋊C4×D53C2211yescharacteristic
73C2×C22⋊C4×D53C2211yescharacteristic
74C2×C42×D53C2211yescharacteristic
75C2×#126×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—24no—
90C2×C4⋊#6157—24no—
91C2×C4⋊#6157—42no—
92C2×C4⋊#6157—42no—
93C2×C4⋊#6157—42no—
94C2×C4⋊#6157—42no—
95C2×C4⋊#6157C2314yes—
96C2×C4⋊#6157C2314yes—
97C2×C4⋊#6157C2314yes—
98C2×C4⋊#6157C2314yes—
99C2×C4⋊#6157C2314yes—
100C2×C4⋊#6157C2314yes—
101C2×C4⋊#6157C2314yes—
102C2×C22⋊#6157—24no—
103C2×C22⋊#6157—42no—
104C2×C22⋊#6157—42no—
105C2×C22⋊#6157C2314yes—
106C2×C22⋊#6157C2314yes—
107C2×C22⋊#6157C2314yes—
108C2×C4×#6157—24no—
109C2×C4×#6157—42no—
110C2×C4×#6157—42no—
111C2×C4×#6157—42no—
112C2×C4×#6157—42no—
113C2×C4×#6157C2314yes—
114C2×C4×#6157C2314yes—
115C2×C4×#6157C2314yes—
116C2×C4×#6157C2314yes—
117C2×C4×#6157C2314yes—
118(C2×#6157)⋊C4C2314yes—
119(C2×#6157)⋊C4C2314yes—
120(C2×#6157)⋊C4C2314yes—
121(C2×#6157)⋊C4C2314yes—
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—
130C24×D53C2311yescharacteristic
131C22×C4×D53C2311yescharacteristic
132C22×C4×D53C2311yescharacteristic
133C22×C4×D53C2311yescharacteristic
134C22×C4×D53C2311yescharacteristic
135C22×C4×D53C2311yescharacteristic
136C22×C4×D53C2311yescharacteristic
137#13133212C2×C418yescomplemented
138#13133212C2×C418yescomplemented
139#13133212C2×C418yescomplemented
140#13133211C2×C418yescomplemented
141#13133210C2×C418yescomplemented
142#13133210C2×C418yescomplemented
143#13133210C2×C418yescomplemented
144C2×C4⋊Dic53C2×C411yescharacteristic, complemented
145C2×C4⋊Dic53C2×C411yescharacteristic, complemented
146C2×C4⋊Dic53C2×C411yescharacteristic, complemented
147C2×#11719919C2×C411yescharacteristic, complemented
148C2×#11719919C2×C411yescharacteristic, complemented
149C2×#11719919C2×C411yescharacteristic, complemented
150C2×#11719919C2×C411yescharacteristic, complemented
151C2×#11719919C2×C411yescharacteristic, complemented
152C2×#11719919C2×C411yescharacteristic, complemented
153C4⋊C4×D53C2×C414yescomplemented
154C4⋊C4×D53C2×C414yescomplemented
155C4⋊C4×D53C2×C414yescomplemented
156C4⋊C4×D53C2314yes—
157C4⋊C4×D53C2314yes—
158C4⋊C4×D53C2314yes—
159C2×C22⋊Dic53C2×C411yescharacteristic
160C2×C22⋊Dic53C2×C411yescharacteristic
161C2×C22⋊Dic53C2×C411yescharacteristic
162C2×#11719921C2×C411yescharacteristic
163C2×#11719921C2×C411yescharacteristic
164C2×#11719921C2×C411yescharacteristic
165C2×#11719921C2×C411yescharacteristic
166C2×#11719921C2×C411yescharacteristic
167C2×#11719921C2×C411yescharacteristic
168C22⋊C4×D53C2×C414yes—
169C22⋊C4×D53C2×C414yes—
170C22⋊C4×D53C2×C414yes—
171C22⋊C4×D53C2314yes—
172C22⋊C4×D53C2314yes—
173C22⋊C4×D53C2314yes—
174C2×C4×Dic53C2×C411yescharacteristic, complemented
175C2×C4×Dic53C2×C411yescharacteristic, complemented
176C2×C4×Dic53C2×C411yescharacteristic, complemented
177C42×D53C2×C414yescomplemented
178C42×D53C2314yes—
179#126×C53C2×C418yescomplemented
180C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
181C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
182C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
183C2×C22⋊C4×C53C2×C411yescharacteristic
184C2×C22⋊C4×C53C2×C411yescharacteristic
185C2×C22⋊C4×C53C2×C411yescharacteristic
186C2×C42×C53C2×C411yescharacteristic, complemented
187C24×C53C22×C411yescharacteristic
188C23×D53—22no—
189C23×D53—22no—
190C23×D53—22no—
191C23×D53—22no—
192C23×D53—22no—
193C23×D53—22no—
194C23×D53C22×C412yes—
195C23×D53C22×C411yescharacteristic
196C23×D53C2412yes—
197C23×D53C2411yescharacteristic
198C22×#6157—22no—
199C22×#6157—22no—
200C22×#6157—22no—
201C22×#6157—22no—
202C22×#6157—22no—
203C22×#6157—22no—
204C22×#6157—22no—
205C22×#6157—22no—
206C22×#6157—22no—
207C22×#6157—22no—
208C22×#6157—22no—
209C22×#6157—22no—
210C22×#6157—22no—
211C22×#6157—22no—
212C22×#6157—22no—
213C22×#6157—22no—
214C22×#6157—22no—
215C22×#6157—22no—
216C22×#6157—22no—
217C22×#6157—22no—
218C22×#6157—22no—
219C22×#6157—22no—
220C22×#6157—28no—
221C22×#6157—44no—
222C22×#6157—44no—
223C22×#6157—416no—
224C22×#6157#4114yes—
225C22×#6157#4114yes—
226C22×#6157C2412yes—
227C22×#6157C2412yes—
228C22×#6157C2412yes—
229C22×#6157C2412yes—
230C22×#6157C2412yes—
231C22×#6157C2412yes—
232C22×#6157C2412yes—
233C22×#6157C2412yes—
234C22×C4×C53C22×C411yescharacteristic
235C22×C4×C53C22×C411yescharacteristic
236C22×C4×C53C22×C411yescharacteristic
237C22×C4×C53C22×C411yescharacteristic
238C22×C4×C53C22×C411yescharacteristic
239C22×C4×C53C22×C411yescharacteristic
240C22×Dic53C22×C411yescharacteristic
241C22×Dic53C22×C411yescharacteristic
242C22×Dic53C22×C411yescharacteristic
243C22×Dic53C22×C411yescharacteristic
244C22×Dic53C22×C411yescharacteristic
245C22×Dic53C22×C411yescharacteristic
246C2×C4×D53—22no—
247C2×C4×D53—22no—
248C2×C4×D53—22no—
249C2×C4×D53—22no—
250C2×C4×D53—22no—
251C2×C4×D53—22no—
252C2×C4×D53—22no—
253C2×C4×D53—22no—
254C2×C4×D53—22no—
255C2×C4×D53—22no—
256C2×C4×D53—22no—
257C2×C4×D53—22no—
258C2×C4×D53C22×C412yes—
259C2×C4×D53C22×C412yes—
260C2×C4×D53C22×C412yes—
261C2×C4×D53C22×C412yes—
262C2×C4×D53C22×C412yes—
263C2×C4×D53C22×C412yes—
264C2×C4×D53C2412yes—
265C2×C4×D53C2412yes—
266C2×C4×D53C2412yes—
267C2×C4×D53C2412yes—
268C2×C4×D53C2412yes—
269C2×C4×D53C2412yes—
270C22⋊#6157—28no—
271C22⋊#6157—44no—
272C22⋊#6157—44no—
273C4⋊#6157—28no—
274C4⋊#6157—28no—
275C4⋊#6157—28no—
276C4⋊#6157—44no—
277C4⋊#6157—44no—
278C4⋊#6157—44no—
279C4⋊#6157—44no—
280C4×#6157—28no—
281C4×#6157—44no—
282C4×#6157—44no—
283C4×#6157—44no—
284C4×#6157—44no—
285C4⋊C4×C53C22×C414yescomplemented
286C4⋊C4×C53C22×C414yescomplemented
287C4⋊C4×C53C22×C414yescomplemented
288C22⋊C4×C53C22×C414yes—
289C22⋊C4×C53C22×C414yes—
290C22⋊C4×C53C22×C414yes—
291C42×C53C22×C414yescomplemented
292C22⋊Dic53C22×C414yes—
293C22⋊Dic53C22×C414yes—
294C22⋊Dic53C22×C414yes—
295#11719921C22×C414yes—
296#11719921C22×C414yes—
297#11719921C22×C414yes—
298#11719921C22×C414yes—
299#11719921C22×C414yes—
300#11719921C22×C414yes—
301C4⋊Dic53C22×C414yescomplemented
302C4⋊Dic53C22×C414yescomplemented
303C4⋊Dic53C22×C414yescomplemented
304#11719919C22×C414yescomplemented
305#11719919C22×C414yescomplemented
306#11719919C22×C414yescomplemented
307#11719919C22×C414yescomplemented
308#11719919C22×C414yescomplemented
309#11719919C22×C414yescomplemented
310C4×Dic53C22×C414yescomplemented
311C4×Dic53C22×C414yescomplemented
312C4×Dic53C22×C414yescomplemented
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53C23×C412yes—
317C23×C53C23×C411yescharacteristic
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—24no—
322C22×D53—24no—
323C22×D53—24no—
324C22×D53—22no—
325C22×D53—22no—
326C22×D53—22no—
327C22×D53—22no—
328C22×D53—22no—
329C22×D53—22no—
330C22×D53—44no—
331C22×D53—44no—
332C22×D53—44no—
333C22×D53—44no—
334C22×D53C23×C412yes—
335C22×D53C23×C411yescharacteristic
336C22×D53C2×#4112yes—
337C22×D53C2×#4112yes—
338C22×D53H(5,𝔽2)12yes—
339C22×D53H(5,𝔽2)12yes—
340C22×D532−1+412yes—
341C22×D532−1+412yes—
342C22×D53C2511yescharacteristic
343C2×#6157—28no—
344C2×#6157—28no—
345C2×#6157—22no—
346C2×#6157—22no—
347C2×#6157—22no—
348C2×#6157—22no—
349C2×#6157—22no—
350C2×#6157—22no—
351C2×#6157—22no—
352C2×#6157—22no—
353C2×#6157—22no—
354C2×#6157—22no—
355C2×#6157—22no—
356C2×#6157—22no—
357C2×#6157—22no—
358C2×#6157—22no—
359C2×#6157—22no—
360C2×#6157—22no—
361C2×#6157—22no—
362C2×#6157—22no—
363C2×#6157—22no—
364C2×#6157—22no—
365C2×#6157—22no—
366C2×#6157—22no—
367C2×#6157—416no—
368C2×#6157—44no—
369C2×#6157—44no—
370C2×#6157—44no—
371C2×#6157—44no—
372C2×#6157—44no—
373C2×#6157—44no—
374C2×#6157C2×#4114yes—
375C2×#6157C2×#4114yes—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—22no—
381C2×C4×C53—22no—
382C2×C4×C53C23×C412yes—
383C2×C4×C53C23×C412yes—
384C2×C4×C53C23×C412yes—
385C2×C4×C53C23×C412yes—
386C2×C4×C53C23×C412yes—
387C2×C4×C53C23×C412yes—
388C2×Dic53—22no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—22no—
393C2×Dic53—22no—
394C2×Dic53C23×C412yes—
395C2×Dic53C23×C412yes—
396C2×Dic53C23×C412yes—
397C2×Dic53C23×C412yes—
398C2×Dic53C23×C412yes—
399C2×Dic53C23×C412yes—
400C4×D53—24no—
401C4×D53—24no—
402C4×D53—24no—
403C4×D53—24no—
404C4×D53—24no—
405C4×D53—24no—
406C4×D53—22no—
407C4×D53—22no—
408C4×D53—22no—
409C4×D53—22no—
410C4×D53—22no—
411C4×D53—22no—
412C4×D53—22no—
413C4×D53—22no—
414C4×D53—22no—
415C4×D53—22no—
416C4×D53—22no—
417C4×D53—22no—
418C2×#2334—531nomaximal, Sylow
419C22×C53—22no—
420C22×C53—22no—
421C22×C53—22no—
422C22×C53—44no—
423C22×C53C4×#4112yes—
424C22×C53#52012yes—
425C22×C53#52012yes—
426C22×C53C24×C411yescharacteristic
427C2×D53—22no—
428C2×D53—22no—
429C2×D53—22no—
430C2×D53—44no—
431C2×D53—48no—
432C2×D53—42no—
433C2×D53—42no—
434C2×D53—42no—
435C2×D53—42no—
436C2×D53C4×#4112yes—
437C2×D53#52012yes—
438C2×D53#52012yes—
439C2×D53#53814yes—
440C2×D53#53914yes—
441C2×D53#54114yes—
442C2×D53#54214yes—
443C2×D53C22×#4111yescharacteristic
444C2×D53C22×#4111yescharacteristic
445C2×D53C2×H(5,𝔽2)11yescharacteristic
446C2×D53C2×H(5,𝔽2)11yescharacteristic
447C2×D53C2×2−1+411yescharacteristic
448C2×D53C2×2−1+411yescharacteristic
449#6157—24no—
450#6157—24no—
451#6157—42no—
452#6157—42no—
453#6157—42no—
454#6157—42no—
455#6157—42no—
456#6157—42no—
457C4×C53—22no—
458C4×C53—22no—
459C4×C53—22no—
460C4×C53—22no—
461C4×C53—22no—
462C4×C53—22no—
463Dic53—22no—
464Dic53—22no—
465Dic53—22no—
466Dic53—22no—
467Dic53—22no—
468Dic53—22no—
469C22×#126—531no—
470#2334—5316no—
471C2×#389—531no—
472C2×#389—531no—
473C2×#388—531no—
474C2×#388—531no—
475C2×#388—531no—
476C2×#387—531no—
477C2×#387—531no—
478C2×#387—531no—
479C2×#385—531no—
480C2×#385—531no—
481C2×#382—531no—
482C2×C4×C4⋊C4—531no—
483C2×C4×C4⋊C4—531no—
484C2×C4×C22⋊C4—531no—
485C2×C53—42no—
486C2×C53#233414yescomplemented
487C2×C53C2×C4×#4111yescharacteristic
488C2×C53C2×#52011yescharacteristic
489C2×C53C2×#52011yescharacteristic
490D53—42no—
491D53#233414yescomplemented
492D53C2×#53811yescharacteristic
493D53C2×#53911yescharacteristic
494D53C2×#54111yescharacteristic
495D53C2×#54211yescharacteristic
496C24×C4—531no—
497C2×#126—538no—
498C2×#126—538no—
499C2×#126—531no—
500C2×#126—531no—
501C2×#126—531no—
502C2×#126—531no—
503C2×#126—531no—
504C2×#126—531no—
505C2×#126—531no—
506C2×#126#615711yescharacteristic, complemented
507C22×C4⋊C4—531no—
508C22×C4⋊C4—531no—
509C22×C4⋊C4—531no—
510C22×C4⋊C4—531no—
511C22×C4⋊C4—531no—
512C22×C4⋊C4—531no—
513C22×C4⋊C4—531no—
514C22×C4⋊C4—531no—
515C22×C4⋊C4—531no—
516C22×C4⋊C4—531no—
517C22×C22⋊C4—531no—
518C22×C22⋊C4—531no—
519C22×C22⋊C4—531no—
520C22×C22⋊C4—531no—
521C22×C22⋊C4—531no—
522C22×C22⋊C4—531no—
523C22×C42—531no—
524C22×C42—531no—
525C22×C42—531no—
526C22×C42—531no—
527C22×C42—531no—
528C22×C42—531no—
529#389—538no—
530#389—538no—
531#388—538no—
532#388—538no—
533#388—538no—
534#387—538no—
535#387—538no—
536#387—538no—
537#385—538no—
538#385—538no—
539#382—538no—
540C4×C4⋊C4—538no—
541C4×C4⋊C4—538no—
542C4×C22⋊C4—538no—
543C2×#95—531no—
544C2×#95—531no—
545C2×#95—531no—
546C2×#95—531no—
547C2×#95—531no—
548C2×#95—531no—
549C2×#95—531no—
550C2×#95—531no—
551C2×#95—531no—
552C2×#95—531no—
553C2×#95—531no—
554C2×#95—531no—
555C53C2×#233411yescharacteristic, complemented, Sylow
556C25—531no—
557C23×C4—531no—
558C23×C4—531no—
559C23×C4—531no—
560C23×C4—531no—
561C23×C4—531no—
562C23×C4—531no—
563C23×C4—531no—
564C23×C4—531no—
565C23×C4—531no—
566C23×C4—531no—
567C23×C4—531no—
568C23×C4—531no—
569C23×C4—531no—
570C23×C4—531no—
571C23×C4—534no—
572C23×C4—1064no—
573C23×C4—2122no—
574C23×C4—2122no—
575#126—538no—
576#126—538no—
577#126—538no—
578#126—538no—
579#126—538no—
580#126—538no—
581#126—538no—
582#126C2×#615718yescomplemented
583C2×C4⋊C4—531no—
584C2×C4⋊C4—531no—
585C2×C4⋊C4—531no—
586C2×C4⋊C4—531no—
587C2×C4⋊C4—531no—
588C2×C4⋊C4—531no—
589C2×C4⋊C4—531no—
590C2×C4⋊C4—531no—
591C2×C4⋊C4—531no—
592C2×C4⋊C4—534no—
593C2×C4⋊C4—534no—
594C2×C4⋊C4—534no—
595C2×C4⋊C4—534no—
596C2×C4⋊C4—534no—
597C2×C4⋊C4—534no—
598C2×C4⋊C4—534no—
599C2×C4⋊C4—534no—
600C2×C4⋊C4—534no—
601C2×C4⋊C4—534no—
602C2×C4⋊C4—534no—
603C2×C4⋊C4—534no—
604C2×C4⋊C4—534no—
605C2×C4⋊C4—1064no—
606C2×C4⋊C4—1064no—
607C2×C4⋊C4—1064no—
608C2×C4⋊C4—2122no—
609C2×C4⋊C4—2122no—
610C2×C4⋊C4—2122no—
611C2×C4⋊C4—2122no—
612C2×C4⋊C4C2×#615711yescharacteristic, complemented
613C2×C4⋊C4C2×#615711yescharacteristic, complemented
614C2×C4⋊C4C2×#615711yescharacteristic, complemented
615C2×C22⋊C4—531no—
616C2×C22⋊C4—531no—
617C2×C22⋊C4—531no—
618C2×C22⋊C4—531no—
619C2×C22⋊C4—531no—
620C2×C22⋊C4—531no—
621C2×C22⋊C4—531no—
622C2×C22⋊C4—531no—
623C2×C22⋊C4—531no—
624C2×C22⋊C4—534no—
625C2×C22⋊C4—534no—
626C2×C22⋊C4—534no—
627C2×C22⋊C4—534no—
628C2×C22⋊C4—534no—
629C2×C22⋊C4—534no—
630C2×C22⋊C4—534no—
631C2×C22⋊C4—534no—
632C2×C22⋊C4—534no—
633C2×C22⋊C4—1064no—
634C2×C22⋊C4—2122no—
635C2×C22⋊C4—2122no—
636C2×C22⋊C4C2×#615711yescharacteristic
637C2×C22⋊C4C2×#615711yescharacteristic
638C2×C22⋊C4C2×#615711yescharacteristic
639C2×C42—531no—
640C2×C42—531no—
641C2×C42—531no—
642C2×C42—534no—
643C2×C42—534no—
644C2×C42—534no—
645C2×C42—534no—
646C2×C42—534no—
647C2×C42—534no—
648C2×C42—534no—
649C2×C42—1064no—
650C2×C42—2122no—
651C2×C42—2122no—
652C2×C42—2122no—
653C2×C42—2122no—
654C2×C42C2×#615711yescharacteristic, complemented
655#95—534no—
656#95—534no—
657#95—534no—
658#95—534no—
659#95—534no—
660#95—534no—
661#95—534no—
662#95—534no—
663#95—534no—
664#95—534no—
665#95—534no—
666#95—534no—
667C24—531no—
668C24—532no—
669C24—532no—
670C24—531no—
671C24—1062no—
672C24—1062no—
673C24—1062no—
674C24—1062no—
675C24—1062no—
676C24—1062no—
677C24C22×#615711yescharacteristic
678C22×C4—534no—
679C22×C4—534no—
680C22×C4—532no—
681C22×C4—532no—
682C22×C4—531no—
683C22×C4—531no—
684C22×C4—531no—
685C22×C4—531no—
686C22×C4—531no—
687C22×C4—531no—
688C22×C4—532no—
689C22×C4—532no—
690C22×C4—532no—
691C22×C4—532no—
692C22×C4—532no—
693C22×C4—532no—
694C22×C4—532no—
695C22×C4—532no—
696C22×C4—532no—
697C22×C4—532no—
698C22×C4—532no—
699C22×C4—532no—
700C22×C4—532no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—532no—
706C22×C4—1062no—
707C22×C4—1062no—
708C22×C4—1062no—
709C22×C4—1062no—
710C22×C4—1062no—
711C22×C4—1062no—
712C22×C4—1062no—
713C22×C4—1062no—
714C22×C4—1062no—
715C22×C4—1062no—
716C22×C4—1062no—
717C22×C4—1062no—
718C22×C4—1068no—
719C22×C4—1062no—
720C22×C4—1062no—
721C22×C4—1062no—
722C22×C4—1062no—
723C22×C4—1062no—
724C22×C4—1062no—
725C22×C4—1062no—
726C22×C4—1062no—
727C22×C4—1062no—
728C22×C4—1062no—
729C22×C4—1062no—
730C22×C4—1062no—
731C22×C4—1062no—
732C22×C4—1062no—
733C22×C4—1062no—
734C22×C4—1062no—
735C22×C4—1062no—
736C22×C4—1062no—
737C22×C4—1062no—
738C22×C4—1062no—
739C22×C4—1062no—
740C22×C4—1062no—
741C22×C4—2124no—
742C22×C4—2124no—
743C22×C4—21216no—
744C22×C4C22×#615711yescharacteristic
745C22×C4C22×#615711yescharacteristic
746C22×C4C22×#615711yescharacteristic
747C22×C4C22×#615711yescharacteristic
748C22×C4C22×#615711yescharacteristic
749C22×C4C22×#615711yescharacteristic
750C4⋊C4—534no—
751C4⋊C4—534no—
752C4⋊C4—534no—
753C4⋊C4—534no—
754C4⋊C4—534no—
755C4⋊C4—534no—
756C4⋊C4—534no—
757C4⋊C4—534no—
758C4⋊C4—534no—
759C4⋊C4—1068no—
760C4⋊C4—1068no—
761C4⋊C4—1068no—
762C4⋊C4—2124no—
763C4⋊C4—2124no—
764C4⋊C4—2124no—
765C4⋊C4—2124no—
766C4⋊C4C22×#615714yescomplemented
767C4⋊C4C22×#615714yescomplemented
768C4⋊C4C22×#615714yescomplemented
769C22⋊C4—534no—
770C22⋊C4—534no—
771C22⋊C4—534no—
772C22⋊C4—534no—
773C22⋊C4—534no—
774C22⋊C4—534no—
775C22⋊C4—534no—
776C22⋊C4—534no—
777C22⋊C4—534no—
778C22⋊C4—1068no—
779C22⋊C4—2124no—
780C22⋊C4—2124no—
781C22⋊C4C22×#615714yes—
782C22⋊C4C22×#615714yes—
783C22⋊C4C22×#615714yes—
784C42—534no—
785C42—534no—
786C42—534no—
787C42—1068no—
788C42—2124no—
789C42—2124no—
790C42—2124no—
791C42—2124no—
792C42C22×#615714yescomplemented
793C23—22no—
794C23—22no—
795C23—22no—
796C23—532no—
797C23—532no—
798C23—532no—
799C23—532no—
800C23—532no—
801C23—532no—
802C23—531no—
803C23—531no—
804C23—532no—
805C23—1062no—
806C23—1062no—
807C23—1062no—
808C23—1062no—
809C23—1064no—
810C23—1062no—
811C23—1062no—
812C23—1064no—
813C23—1064no—
814C23—1062no—
815C23—1062no—
816C23—1062no—
817C23—2124no—
818C23—2124no—
819C23—2124no—
820C23—2124no—
821C23C23×#615712yes—
822C23C23×#615711yescharacteristic
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—534no—
830C2×C4—534no—
831C2×C4—532no—
832C2×C4—532no—
833C2×C4—532no—
834C2×C4—532no—
835C2×C4—532no—
836C2×C4—532no—
837C2×C4—1062no—
838C2×C4—1062no—
839C2×C4—1062no—
840C2×C4—1062no—
841C2×C4—1062no—
842C2×C4—1062no—
843C2×C4—1062no—
844C2×C4—1062no—
845C2×C4—1064no—
846C2×C4—1064no—
847C2×C4—1062no—
848C2×C4—1062no—
849C2×C4—1062no—
850C2×C4—1062no—
851C2×C4—1064no—
852C2×C4—1064no—
853C2×C4—1064no—
854C2×C4—1064no—
855C2×C4—1062no—
856C2×C4—1062no—
857C2×C4—1062no—
858C2×C4—1062no—
859C2×C4—1068no—
860C2×C4—1068no—
861C2×C4—1062no—
862C2×C4—1062no—
863C2×C4—1062no—
864C2×C4—1062no—
865C2×C4—1062no—
866C2×C4—1062no—
867C2×C4—1062no—
868C2×C4—1062no—
869C2×C4—1062no—
870C2×C4—1062no—
871C2×C4—1062no—
872C2×C4—1062no—
873C2×C4—1062no—
874C2×C4—1062no—
875C2×C4—1062no—
876C2×C4—1062no—
877C2×C4—1062no—
878C2×C4—1062no—
879C2×C4—1062no—
880C2×C4—1062no—
881C2×C4—1062no—
882C2×C4—1062no—
883C2×C4—1062no—
884C2×C4—1062no—
885C2×C4—21216no—
886C2×C4—2124no—
887C2×C4—2124no—
888C2×C4—2124no—
889C2×C4—2124no—
890C2×C4—2124no—
891C2×C4—2124no—
892C2×C4C23×#615712yes—
893C2×C4C23×#615712yes—
894C2×C4C23×#615712yes—
895C2×C4C23×#615712yes—
896C2×C4C23×#615712yes—
897C2×C4C23×#615712yes—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—44no—
902C22—531no—
903C22—531no—
904C22—532no—
905C22—531no—
906C22—531no—
907C22—531no—
908C22—531no—
909C22—532no—
910C22—532no—
911C22—534no—
912C22—534no—
913C22—534no—
914C22—534no—
915C22—1062no—
916C22—1062no—
917C22—1062no—
918C22—2122no—
919C22—2122no—
920C22—2122no—
921C22—2128no—
922C22—2122no—
923C22—2124no—
924C22#41×#615712yes—
925C22#1681169212yes—
926C22#1681169212yes—
927C22C24×#615711yescharacteristic
928C4—22no—
929C4—22no—
930C4—22no—
931C4—22no—
932C4—22no—
933C4—22no—
934C4—1064no—
935C4—1064no—
936C4—1062no—
937C4—1062no—
938C4—1062no—
939C4—1062no—
940C4—1062no—
941C4—1062no—
942C4—2122no—
943C4—2122no—
944C4—2122no—
945C4—2122no—
946C4—2122no—
947C4—2122no—
948C2—42no—
949C2—531no—
950C2—531no—
951C2—531no—
952C2—534no—
953C2—531no—
954C2—2122no—
955C2#2029121314yesdirect product factor
956C2C2×#41×#615711yescharacteristic
957C2C2×#1681169211yescharacteristic
958C2C2×#1681169211yescharacteristic
subgroupG/H
centerC23C23×#6157
commutatorC22×C53C24×C4
FrattiniC22C24×#6157
FittingC2×#126×C53C4
socleC23×C53C23×C4
prime radicalC24×D53C23
cosocleC22×D53C25
hypercenterC2×#126#6157
hypocenterC53C2×#2334
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #20291213C2direct (N × H)
2. C2×#16811574C2semidirect
3. C2×#16811574C2semidirect
7. C2×#16811572C2semidirect
8. C2×#16811572C2semidirect
9. C2×#16811572C2semidirect
12. C2×#16811567C2semidirect
13. C2×C4⋊C4×#6157C2semidirect
14. C2×C4×C4⋊#6157C2semidirect
33. #16811574C22semidirect
34. #16811574C22semidirect
38. #16811572C22semidirect
39. #16811572C22semidirect
40. #16811572C22semidirect
43. #16811567C22semidirect
44. C4⋊C4×#6157C22semidirect
45. C4×C4⋊#6157C22semidirect
59. C2×#13133212C4semidirect
60. C2×#13133212C4semidirect
61. C2×#13133212C4semidirect
62. C2×#13133211C4semidirect
63. C2×#13133210C4semidirect
64. C2×#13133210C4semidirect
65. C2×#13133210C4semidirect
66. #126×D53C4semidirect
75. C2×#126×C53C4semidirect
137. #13133212C2×C4semidirect
138. #13133212C2×C4semidirect
139. #13133212C2×C4semidirect
140. #13133211C2×C4semidirect
141. #13133210C2×C4semidirect
142. #13133210C2×C4semidirect
143. #13133210C2×C4semidirect
144. C2×C4⋊Dic53C2×C4semidirect
145. C2×C4⋊Dic53C2×C4semidirect
146. C2×C4⋊Dic53C2×C4semidirect
147. C2×#11719919C2×C4semidirect
148. C2×#11719919C2×C4semidirect
149. C2×#11719919C2×C4semidirect
150. C2×#11719919C2×C4semidirect
151. C2×#11719919C2×C4semidirect
152. C2×#11719919C2×C4semidirect
153. C4⋊C4×D53C2×C4semidirect
154. C4⋊C4×D53C2×C4semidirect
155. C4⋊C4×D53C2×C4semidirect
174. C2×C4×Dic53C2×C4semidirect
175. C2×C4×Dic53C2×C4semidirect
176. C2×C4×Dic53C2×C4semidirect
177. C42×D53C2×C4semidirect
179. #126×C53C2×C4semidirect
180. C2×C4⋊C4×C53C2×C4semidirect
181. C2×C4⋊C4×C53C2×C4semidirect
182. C2×C4⋊C4×C53C2×C4semidirect
186. C2×C42×C53C2×C4semidirect
285. C4⋊C4×C53C22×C4semidirect
286. C4⋊C4×C53C22×C4semidirect
287. C4⋊C4×C53C22×C4semidirect
291. C42×C53C22×C4semidirect
301. C4⋊Dic53C22×C4semidirect
302. C4⋊Dic53C22×C4semidirect
303. C4⋊Dic53C22×C4semidirect
304. #11719919C22×C4semidirect
305. #11719919C22×C4semidirect
306. #11719919C22×C4semidirect
307. #11719919C22×C4semidirect
308. #11719919C22×C4semidirect
309. #11719919C22×C4semidirect
310. C4×Dic53C22×C4semidirect
311. C4×Dic53C22×C4semidirect
312. C4×Dic53C22×C4semidirect
486. C2×C53#2334semidirect
491. D53#2334semidirect
506. C2×#126#6157semidirect
555. C53C2×#2334semidirect
582. #126C2×#6157semidirect
612. C2×C4⋊C4C2×#6157semidirect
613. C2×C4⋊C4C2×#6157semidirect
614. C2×C4⋊C4C2×#6157semidirect
654. C2×C42C2×#6157semidirect
766. C4⋊C4C22×#6157semidirect
767. C4⋊C4C22×#6157semidirect
768. C4⋊C4C22×#6157semidirect
792. C42C22×#6157semidirect
955. C2#20291213direct (N × H)

Maximal subgroups

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

subgroupindex
#202912132
C2×#168115742
C2×#168115732
C2×#168115722
C2×#168115702
C2×#168115672
C2×C4⋊C4×#61572
C2×C4×C4⋊#61572
C2×C22⋊C4×#61572
C2×#126×D532
C2×#233453