Finite Group Databasebeta

← C2×#13131359 #16807593

Subgroups — C2×#13131359 #16807593

Order 3328.

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×#261C211yesmaximal, characteristic
2C22×#88237C211yesmaximal, characteristic, complemented
3#13131359C2116yesmaximal, direct product factor
4C2×#11719083C211yesmaximal, characteristic, complemented
5C2×#11719071C211yesmaximal, characteristic, complemented
6C2×#11719071C211yesmaximal, characteristic, complemented
7C2×#11719082C211yesmaximal, characteristic, complemented
8C2×#11719082C211yesmaximal, characteristic, complemented
9C2×#11719150C211yesmaximal, characteristic
10C2×#11719070C211yesmaximal, characteristic, complemented
11C2×#11719070C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×#261C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×#261C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×#261C211yesmaximal, characteristic, complemented
15C22×(C2×#261)⋊C4C211yesmaximal, characteristic, complemented
16C2×D13×#123C211yesmaximal, characteristic
17C24×#261C2211yescharacteristic
18C24×#261C2211yescharacteristic
19C24×#261C2211yescharacteristic
20C22×D4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C22×C22⋊#261C2211yescharacteristic
23C22×C22⋊#261C2211yescharacteristic
24C22×C22⋊#261C2211yescharacteristic
25C22×C22⋊#261C2211yescharacteristic
26C22×C22⋊#261C2211yescharacteristic
27C2×D4×#261—28no—
28C2×D4×#261C2218yes—
29C2×#88237—28no—
30C2×#88237C2218yescomplemented
31C22×C4⋊#261C2211yescharacteristic
32C22×C4⋊#261C2211yescharacteristic
33C22×C4⋊#261C2211yescharacteristic
34C22×C4⋊#261C2211yescharacteristic
35C22×C4⋊#261C2211yescharacteristic
36C22×C4×#261C2211yescharacteristic
37C22×C4×#261C2211yescharacteristic
38C22×C4×#261C2211yescharacteristic
39C22×C4×#261C2211yescharacteristic
40C22×C4×#261C2211yescharacteristic
41C2×C13×#123C411yescharacteristic, complemented
42C2×#88189C411yescharacteristic, complemented
43C2×#88183C411yescharacteristic, complemented
44D13×#123C418yescomplemented
45D13×#123C2218yes—
46C2×#88148C411yescharacteristic, complemented
47C2×#88148C411yescharacteristic, complemented
48C2×C4⋊C4×D13C2211yescharacteristic
49C2×C4⋊C4×D13C2211yescharacteristic
50C2×#88140C411yescharacteristic, complemented
51C2×#88137C411yescharacteristic, complemented
52C2×#88137C411yescharacteristic, complemented
53C2×C22⋊C4×D13C2211yescharacteristic
54C2×C22⋊C4×D13C2211yescharacteristic
55C2×C22⋊C4×D13C2211yescharacteristic
56#11719150C2218yes—
57C2×(C2×#261)⋊C4C2211yescharacteristic
58C2×(C2×#261)⋊C4C2211yescharacteristic
59C2×(C2×#261)⋊C4C2211yescharacteristic
60C2×(C2×#261)⋊C4C2211yescharacteristic
61C2×(C2×#261)⋊C4C2211yescharacteristic
62C2×(C2×#261)⋊C4C2211yescharacteristic
63C2×(C2×#261)⋊C4C2211yescharacteristic
64C2×(C2×#261)⋊C4C2211yescharacteristic
65C2×(C2×#261)⋊C4C2211yescharacteristic
66C2×(C2×#261)⋊C4C2211yescharacteristic
67C2×(C2×#261)⋊C4C2218yescomplemented
68#11719083C2218yescomplemented
69#11719082C2218yescomplemented
70#11719082C2218yescomplemented
71C4⋊C4×#261C2218yescomplemented
72#11719071C2218yescomplemented
73#11719071C2218yescomplemented
74#11719070C2218yescomplemented
75#11719070C2218yescomplemented
76C22⋊C4×#261C2218yescomplemented
77C22⋊C4×#261C2218yescomplemented
78C24×D13C2311yescharacteristic
79C24×D13C2311yescharacteristic
80C23×#261—24no—
81C23×#261—24no—
82C23×#261—24no—
83C23×#261—24no—
84C23×#261—24no—
85C23×#261—24no—
86C23×#261—42no—
87C23×#261—42no—
88C23×#261—42no—
89C23×#261C2311yescharacteristic
90C23×#261C2311yescharacteristic
91C23×#261C2311yescharacteristic
92C23×#261C2311yescharacteristic
93C23×#261C2314yes—
94C23×#261C2314yes—
95C23×#261C2314yes—
96C23×#261C2311yescharacteristic
97C23×#261C2311yescharacteristic
98C23×#261C2311yescharacteristic
99C23×#261C2311yescharacteristic
100C22×D4×C13C2×C411yescharacteristic
101C23×C4×C13C2×C411yescharacteristic, complemented
102C22×C22⋊D13C2×C411yescharacteristic
103C22×C22⋊D13C2×C411yescharacteristic
104C23×Dic13C2×C411yescharacteristic, complemented
105C2×D4×D13—24no—
106C2×D4×D13—24no—
107C2×D4×D13C2×C414yes—
108C2×D4×D13C2314yes—
109C22×D52C2×C411yescharacteristic
110C22×C4×D13—24no—
111C22×C4×D13—24no—
112C22×C4×D13C2×C414yescomplemented
113C22×C4×D13C2×C411yescharacteristic, complemented
114C22×C4×D13C2×C411yescharacteristic, complemented
115C22×C4×D13C2311yescharacteristic
116C22×C4×D13C2311yescharacteristic
117C22×C4×D13C2311yescharacteristic
118C22×C4×D13C2311yescharacteristic
119C22×C4×D13C2311yescharacteristic
120C22×C4×D13C2314yes—
121C2×C22⋊#261—24no—
122C2×C22⋊#261—24no—
123C2×C22⋊#261—24no—
124C2×C22⋊#261—42no—
125C2×C22⋊#261D418yes—
126C2×C22⋊#261C2314yes—
127C2×C22⋊#261C2314yes—
128C2×C22⋊#261C2314yes—
129C2×C22⋊#261C2314yes—
130C2×C22⋊#261C2314yes—
131D4×#261—232no—
132#88237—232no—
133C2×C4⋊#261—24no—
134C2×C4⋊#261—24no—
135C2×C4⋊#261—24no—
136C2×C4⋊#261—24no—
137C2×C4⋊#261—42no—
138C2×C4⋊#261C2314yes—
139C2×C4⋊#261C2314yes—
140C2×C4⋊#261C2314yes—
141C2×C4⋊#261C2314yes—
142C2×C4⋊#261C2314yes—
143C2×C4×#261—24no—
144C2×C4×#261—24no—
145C2×C4×#261—24no—
146C2×C4×#261—24no—
147C2×C4×#261—42no—
148C2×C4×#261C2314yes—
149C2×C4×#261C2314yes—
150C2×C4×#261C2314yes—
151C2×C4×#261C2314yes—
152C2×C4×#261C2314yes—
153C13×#123C2×C418yescomplemented
154C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
155C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
156C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
157C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
158C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
159C2×C22⋊Dic13C2×C411yescharacteristic, complemented
160C2×C22⋊Dic13C2×C411yescharacteristic, complemented
161C2×C22⋊Dic13C2×C411yescharacteristic, complemented
162#88189C2×C418yescomplemented
163#88183C2×C418yescomplemented
164C2×#6103C2×C411yescharacteristic, complemented
165C2×#6103C2×C411yescharacteristic, complemented
166C2×#6103C2×C411yescharacteristic, complemented
167C2×#6103C2×C411yescharacteristic, complemented
168C2×#6103C2×C411yescharacteristic, complemented
169C2×#6103C2×C411yescharacteristic, complemented
170C2×C4⋊Dic13C2×C411yescharacteristic, complemented
171C2×C4⋊Dic13C2×C411yescharacteristic, complemented
172C2×#6101C2×C411yescharacteristic, complemented
173C2×#6101C2×C411yescharacteristic, complemented
174C2×#6101C2×C411yescharacteristic, complemented
175C2×#6101C2×C411yescharacteristic, complemented
176#88148C2×C418yescomplemented
177#88148C2×C418yescomplemented
178C4⋊C4×D13C2×C414yescomplemented
179C4⋊C4×D13C2×C414yescomplemented
180C4⋊C4×D13C2314yes—
181C4⋊C4×D13C2314yes—
182#88140C2×C418yescomplemented
183#88137C2×C418yescomplemented
184#88137C2×C418yescomplemented
185C22⋊C4×D13C2×C414yescomplemented
186C22⋊C4×D13C2×C414yescomplemented
187C22⋊C4×D13C2×C414yescomplemented
188C22⋊C4×D13C2314yes—
189C22⋊C4×D13C2314yes—
190C22⋊C4×D13C2314yes—
191(C2×#261)⋊C4C2314yes—
192(C2×#261)⋊C4C2314yes—
193(C2×#261)⋊C4C2314yes—
194(C2×#261)⋊C4C2314yes—
195(C2×#261)⋊C4C2314yes—
196(C2×#261)⋊C4C2314yes—
197(C2×#261)⋊C4C2314yes—
198(C2×#261)⋊C4C2314yes—
199(C2×#261)⋊C4C2314yes—
200(C2×#261)⋊C4C2314yes—
201C2×#2359—131nomaximal, Sylow
202C24×C13C22×C411yescharacteristic
203C24×C13C22×C411yescharacteristic
204C23×D13—22no—
205C23×D13—22no—
206C23×D13—22no—
207C23×D13—22no—
208C23×D13—22no—
209C23×D13—22no—
210C23×D13—22no—
211C23×D13—22no—
212C23×D13—22no—
213C23×D13—22no—
214C23×D13C22×C412yes—
215C23×D13C22×C411yescharacteristic
216C23×D13C22×C412yes—
217C23×D13C22×C411yescharacteristic
218C23×D13C2×D414yes—
219C23×D13#4114yes—
220C23×D13C2412yes—
221C23×D13C2412yes—
222C23×D13C2411yescharacteristic
223C22×#261—22no—
224C22×#261—22no—
225C22×#261—22no—
226C22×#261—22no—
227C22×#261—22no—
228C22×#261—22no—
229C22×#261—22no—
230C22×#261—22no—
231C22×#261—22no—
232C22×#261—22no—
233C22×#261—22no—
234C22×#261—28no—
235C22×#261—22no—
236C22×#261—22no—
237C22×#261—28no—
238C22×#261—22no—
239C22×#261—22no—
240C22×#261—22no—
241C22×#261—22no—
242C22×#261—22no—
243C22×#261—22no—
244C22×#261—22no—
245C22×#261—28no—
246C22×#261—28no—
247C22×#261—28no—
248C22×#261—28no—
249C22×#261—44no—
250C22×#261—44no—
251C22×#261—44no—
252C22×#261—416no—
253C22×#261—416no—
254C22×#261—416no—
255C22×#261C2×D414yes—
256C22×#261C2×D414yes—
257C22×#261#4114yes—
258C22×#261#4114yes—
259C22×#261C2412yes—
260C22×#261C2412yes—
261C22×#261C2412yes—
262C22×#261C2412yes—
263C22×#261C2412yes—
264C22×#261C2412yes—
265C22×#261C2412yes—
266C22×#261C2412yes—
267C2×D4×C13—24no—
268C2×D4×C13C22×C414yes—
269C22×C4×C13—24no—
270C22×C4×C13C22×C411yescharacteristic
271C22×C4×C13C22×C411yescharacteristic
272C22×C4×C13C22×C411yescharacteristic
273C22×C4×C13C22×C411yescharacteristic
274C22×C4×C13C22×C411yescharacteristic
275C22×C4×C13C22×C414yescomplemented
276C2×C22⋊D13—24no—
277C2×C22⋊D13—24no—
278C2×C22⋊D13C22×C414yes—
279C2×C22⋊D13C22×C414yes—
280C22×Dic13—24no—
281C22×Dic13C22×C411yescharacteristic
282C22×Dic13C22×C411yescharacteristic
283C22×Dic13C22×C411yescharacteristic
284C22×Dic13C22×C411yescharacteristic
285C22×Dic13C22×C411yescharacteristic
286C22×Dic13C22×C414yescomplemented
287D4×D13—216no—
288D4×D13—28no—
289D4×D13—28no—
290C2×D52—24no—
291C2×D52C22×C414yes—
292C2×C4×D13—216no—
293C2×C4×D13—24no—
294C2×C4×D13—24no—
295C2×C4×D13—22no—
296C2×C4×D13—22no—
297C2×C4×D13—22no—
298C2×C4×D13—28no—
299C2×C4×D13—22no—
300C2×C4×D13—22no—
301C2×C4×D13—22no—
302C2×C4×D13—22no—
303C2×C4×D13—28no—
304C2×C4×D13—22no—
305C2×C4×D13—22no—
306C2×C4×D13—22no—
307C2×C4×D13C22×C412yes—
308C2×C4×D13C22×C412yes—
309C2×C4×D13C22×C412yes—
310C2×C4×D13C22×C412yes—
311C2×C4×D13C22×C412yes—
312C2×C4×D13C22×C414yescomplemented
313C2×C4×D13C22×C414yescomplemented
314C2×C4×D13C2412yes—
315C2×C4×D13C2412yes—
316C2×C4×D13C2412yes—
317C2×C4×D13C2412yes—
318C2×C4×D13C2412yes—
319C22⋊#261—28no—
320C22⋊#261—28no—
321C22⋊#261—28no—
322C22⋊#261—44no—
323C22⋊#261C2×D4116yes—
324C4⋊#261—28no—
325C4⋊#261—28no—
326C4⋊#261—28no—
327C4⋊#261—28no—
328C4⋊#261—44no—
329C4×#261—28no—
330C4×#261—28no—
331C4×#261—28no—
332C4×#261—28no—
333C4×#261—44no—
334C13×C4⋊C4C22×C414yescomplemented
335C13×C4⋊C4C22×C414yescomplemented
336C13×C22⋊C4C22×C414yescomplemented
337C13×C22⋊C4C22×C414yescomplemented
338C13×C22⋊C4C22×C414yescomplemented
339C22⋊Dic13C22×C414yescomplemented
340C22⋊Dic13C22×C414yescomplemented
341C22⋊Dic13C22×C414yescomplemented
342#6103C22×C414yescomplemented
343#6103C22×C414yescomplemented
344#6103C22×C414yescomplemented
345#6103C22×C414yescomplemented
346#6103C22×C414yescomplemented
347#6103C22×C414yescomplemented
348C4⋊Dic13C22×C414yescomplemented
349C4⋊Dic13C22×C414yescomplemented
350#6101C22×C414yescomplemented
351#6101C22×C414yescomplemented
352#6101C22×C414yescomplemented
353#6101C22×C414yescomplemented
354C22×#123—131no—
355C22×C4×D4—131no—
356C22×#117—131no—
357#2359—1316no—
358C2×#389—131no—
359C2×#388—131no—
360C2×#388—131no—
361C2×#387—131no—
362C2×#387—131no—
363C2×#386—131no—
364C2×#385—131no—
365C2×#385—131no—
366C2×C4×C4⋊C4—131no—
367C2×C4×C22⋊C4—131no—
368C2×C4×C22⋊C4—131no—
369C22×#95—131no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—22no—
374C23×C13—22no—
375C23×C13C4×D414yes—
376C23×C13C23×C412yes—
377C23×C13C23×C412yes—
378C23×C13C23×C411yescharacteristic
379C22×D13—22no—
380C22×D13—22no—
381C22×D13—24no—
382C22×D13—24no—
383C22×D13—28no—
384C22×D13—28no—
385C22×D13—28no—
386C22×D13—28no—
387C22×D13—22no—
388C22×D13—22no—
389C22×D13—22no—
390C22×D13—22no—
391C22×D13—22no—
392C22×D13—22no—
393C22×D13—22no—
394C22×D13—24no—
395C22×D13—24no—
396C22×D13—24no—
397C22×D13—22no—
398C22×D13—22no—
399C22×D13—22no—
400C22×D13—22no—
401C22×D13—22no—
402C22×D13—22no—
403C22×D13—44no—
404C22×D13—44no—
405C22×D13—44no—
406C22×D13—44no—
407C22×D13C4×D414yes—
408C22×D13C4×D418yes—
409C22×D13C23×C412yes—
410C22×D13C23×C412yes—
411C22×D13C23×C411yescharacteristic
412C22×D13C22×D414yes—
413C22×D13C22×D412yes—
414C22×D13C2×#4114yes—
415C22×D13C2×#4112yes—
416C22×D13C2×#4112yes—
417C22×D13C2×#4112yes—
418C22×D13H(5,𝔽2)12yes—
419C22×D132−1+412yes—
420C22×D13C2511yescharacteristic
421C2×#261—28no—
422C2×#261—28no—
423C2×#261—28no—
424C2×#261—28no—
425C2×#261—22no—
426C2×#261—22no—
427C2×#261—22no—
428C2×#261—22no—
429C2×#261—22no—
430C2×#261—22no—
431C2×#261—22no—
432C2×#261—22no—
433C2×#261—22no—
434C2×#261—22no—
435C2×#261—22no—
436C2×#261—22no—
437C2×#261—22no—
438C2×#261—22no—
439C2×#261—22no—
440C2×#261—22no—
441C2×#261—22no—
442C2×#261—22no—
443C2×#261—22no—
444C2×#261—22no—
445C2×#261—416no—
446C2×#261—416no—
447C2×#261—416no—
448C2×#261—44no—
449C2×#261—44no—
450C2×#261—44no—
451C2×#261—44no—
452C2×#261C22×D414yes—
453C2×#261C22×D414yes—
454C2×#261C2×#4114yes—
455C2×#261C2×#4114yes—
456D4×C13—28no—
457C2×C4×C13—22no—
458C2×C4×C13—22no—
459C2×C4×C13—28no—
460C2×C4×C13—22no—
461C2×C4×C13—22no—
462C2×C4×C13—22no—
463C2×C4×C13C23×C412yes—
464C2×C4×C13C23×C412yes—
465C2×C4×C13C23×C412yes—
466C2×C4×C13C23×C412yes—
467C2×C4×C13C23×C412yes—
468C22⋊D13—28no—
469C22⋊D13—28no—
470C2×Dic13—22no—
471C2×Dic13—22no—
472C2×Dic13—28no—
473C2×Dic13—22no—
474C2×Dic13—22no—
475C2×Dic13—22no—
476C2×Dic13C23×C412yes—
477C2×Dic13C23×C412yes—
478C2×Dic13C23×C412yes—
479C2×Dic13C23×C412yes—
480C2×Dic13C23×C412yes—
481D52—28no—
482C4×D13—24no—
483C4×D13—24no—
484C4×D13—28no—
485C4×D13—28no—
486C4×D13—24no—
487C4×D13—24no—
488C4×D13—24no—
489C4×D13—22no—
490C4×D13—22no—
491C4×D13—22no—
492C4×D13—22no—
493C4×D13—22no—
494C4×D13—22no—
495C4×D13—22no—
496C4×D13—22no—
497C4×D13—22no—
498C4×D13—22no—
499C23×D4—131no—
500C24×C4—131no—
501C24×C4—131no—
502C24×C4—131no—
503C24×C4—131no—
504C2×#123—131no—
505C2×#123—131no—
506C2×#123—138no—
507C2×#123—138no—
508C2×#123—131no—
509C2×#123—131no—
510C2×#123—131no—
511C2×#123—131no—
512C2×#123—131no—
513C2×#123#26111yescharacteristic, complemented
514C2×C4×D4—138no—
515C2×C4×D4—268no—
516C2×#117—138no—
517C2×#117—268no—
518C22×C4⋊C4—131no—
519C22×C4⋊C4—131no—
520C22×C4⋊C4—131no—
521C22×C4⋊C4—131no—
522C22×C4⋊C4—131no—
523C22×C4⋊C4—131no—
524C22×C4⋊C4—131no—
525C22×C22⋊C4—131no—
526C22×C22⋊C4—131no—
527C22×C22⋊C4—131no—
528C22×C22⋊C4—131no—
529C22×C22⋊C4—131no—
530C22×C22⋊C4—131no—
531C22×C22⋊C4—131no—
532C22×C22⋊C4—131no—
533C22×C42—131no—
534C22×C42—131no—
535C22×C42—131no—
536C22×C42—131no—
537C22×C42—131no—
538#389—138no—
539#388—138no—
540#388—138no—
541#387—138no—
542#387—138no—
543#386—138no—
544#385—138no—
545#385—138no—
546C4×C4⋊C4—138no—
547C4×C22⋊C4—138no—
548C4×C22⋊C4—138no—
549C2×#95—138no—
550C2×#95—131no—
551C2×#95—131no—
552C2×#95—131no—
553C2×#95—131no—
554C2×#95—131no—
555C2×#95—131no—
556C2×#95—131no—
557C2×#95—131no—
558C2×#95—131no—
559C2×#95—131no—
560C22×C13—28no—
561C22×C13—22no—
562C22×C13—22no—
563C22×C13—22no—
564C22×C13—22no—
565C22×C13—22no—
566C22×C13—44no—
567C22×C13C2×C4×D414yes—
568C22×C13C2×C4×D412yes—
569C22×C13C4×#4112yes—
570C22×C13#52012yes—
571C22×C13C24×C411yescharacteristic
572C2×D13—28no—
573C2×D13—22no—
574C2×D13—22no—
575C2×D13—216no—
576C2×D13—24no—
577C2×D13—24no—
578C2×D13—24no—
579C2×D13—24no—
580C2×D13—22no—
581C2×D13—22no—
582C2×D13—22no—
583C2×D13—44no—
584C2×D13—48no—
585C2×D13—42no—
586C2×D13—42no—
587C2×D13—42no—
588C2×D13—42no—
589C2×D13C2×C4×D414yes—
590C2×D13C2×C4×D412yes—
591C2×D13C4×#4112yes—
592C2×D13#52012yes—
593C2×D13#54614yes—
594C2×D13#54714yes—
595C2×D13#55114yes—
596C2×D13#55214yes—
597C2×D13C23×D411yescharacteristic
598C2×D13C22×#4111yescharacteristic
599C2×D13C22×#4111yescharacteristic
600C2×D13C22×#4111yescharacteristic
601C2×D13C2×H(5,𝔽2)11yescharacteristic
602C2×D13C2×2−1+411yescharacteristic
603#261—24no—
604#261—24no—
605#261—24no—
606#261—24no—
607#261—42no—
608#261—42no—
609#261—42no—
610#261—42no—
611C4×C13—22no—
612C4×C13—22no—
613C4×C13—22no—
614C4×C13—22no—
615C4×C13—22no—
616Dic13—22no—
617Dic13—22no—
618Dic13—22no—
619Dic13—22no—
620Dic13—22no—
621C25—131no—
622C25—131no—
623C22×D4—131no—
624C22×D4—131no—
625C22×D4—134no—
626C22×D4—134no—
627C22×D4—131no—
628C22×D4—264no—
629C22×D4—264no—
630C22×D4C2×#26111yescharacteristic
631C23×C4—131no—
632C23×C4—131no—
633C23×C4—131no—
634C23×C4—131no—
635C23×C4—131no—
636C23×C4—131no—
637C23×C4—131no—
638C23×C4—131no—
639C23×C4—131no—
640C23×C4—131no—
641C23×C4—131no—
642C23×C4—131no—
643C23×C4—134no—
644C23×C4—134no—
645C23×C4—131no—
646C23×C4—131no—
647C23×C4—131no—
648C23×C4—131no—
649C23×C4—134no—
650C23×C4—134no—
651C23×C4—134no—
652C23×C4—264no—
653C23×C4—264no—
654C23×C4—264no—
655C23×C4—264no—
656C23×C4—264no—
657C23×C4—264no—
658C23×C4—264no—
659C23×C4—264no—
660C23×C4—522no—
661C23×C4—522no—
662C23×C4—522no—
663C23×C4C2×#26111yescharacteristic, complemented
664#123—138no—
665#123—138no—
666#123—138no—
667#123—138no—
668#123—138no—
669#123—138no—
670#123—138no—
671#123C2×#26118yescomplemented
672C4×D4—2632no—
673#117—2632no—
674C2×C4⋊C4—131no—
675C2×C4⋊C4—131no—
676C2×C4⋊C4—131no—
677C2×C4⋊C4—131no—
678C2×C4⋊C4—131no—
679C2×C4⋊C4—131no—
680C2×C4⋊C4—134no—
681C2×C4⋊C4—134no—
682C2×C4⋊C4—134no—
683C2×C4⋊C4—134no—
684C2×C4⋊C4—134no—
685C2×C4⋊C4—134no—
686C2×C4⋊C4—134no—
687C2×C4⋊C4—134no—
688C2×C4⋊C4—134no—
689C2×C4⋊C4—264no—
690C2×C4⋊C4—264no—
691C2×C4⋊C4—264no—
692C2×C4⋊C4—264no—
693C2×C4⋊C4—522no—
694C2×C4⋊C4C2×#26111yescharacteristic, complemented
695C2×C4⋊C4C2×#26111yescharacteristic, complemented
696C2×C22⋊C4—134no—
697C2×C22⋊C4—138no—
698C2×C22⋊C4—131no—
699C2×C22⋊C4—131no—
700C2×C22⋊C4—131no—
701C2×C22⋊C4—131no—
702C2×C22⋊C4—131no—
703C2×C22⋊C4—131no—
704C2×C22⋊C4—131no—
705C2×C22⋊C4—131no—
706C2×C22⋊C4—131no—
707C2×C22⋊C4—134no—
708C2×C22⋊C4—134no—
709C2×C22⋊C4—134no—
710C2×C22⋊C4—134no—
711C2×C22⋊C4—134no—
712C2×C22⋊C4—134no—
713C2×C22⋊C4—134no—
714C2×C22⋊C4—134no—
715C2×C22⋊C4—134no—
716C2×C22⋊C4—134no—
717C2×C22⋊C4—264no—
718C2×C22⋊C4—264no—
719C2×C22⋊C4—264no—
720C2×C22⋊C4—522no—
721C2×C22⋊C4C2×#26111yescharacteristic, complemented
722C2×C22⋊C4C2×#26111yescharacteristic, complemented
723C2×C22⋊C4C2×#26111yescharacteristic, complemented
724C2×C42—134no—
725C2×C42—134no—
726C2×C42—134no—
727C2×C42—134no—
728C2×C42—134no—
729C2×C42—264no—
730C2×C42—264no—
731C2×C42—264no—
732C2×C42—264no—
733C2×C42—522no—
734#95—134no—
735#95—134no—
736#95—134no—
737#95—134no—
738#95—134no—
739#95—134no—
740#95—134no—
741#95—134no—
742#95—134no—
743#95—134no—
744C2×C13—24no—
745C2×C13—42no—
746C2×C13#235914yescomplemented
747C2×C13C22×C4×D411yescharacteristic
748C2×C13C2×C4×#4111yescharacteristic
749C2×C13C2×#52011yescharacteristic
750D13—24no—
751D13—42no—
752D13#235914yescomplemented
753D13C2×#54611yescharacteristic
754D13C2×#54711yescharacteristic
755D13C2×#55111yescharacteristic
756D13C2×#55211yescharacteristic
757C24—131no—
758C24—134no—
759C24—134no—
760C24—132no—
761C24—132no—
762C24—131no—
763C24—132no—
764C24—132no—
765C24—131no—
766C24—262no—
767C24—262no—
768C24—262no—
769C24—262no—
770C24—262no—
771C24—262no—
772C24—262no—
773C24—262no—
774C24—262no—
775C24—262no—
776C24C22×#26111yescharacteristic
777C24C22×#26111yescharacteristic
778C2×D4—24no—
779C2×D4—134no—
780C2×D4—134no—
781C2×D4—134no—
782C2×D4—264no—
783C2×D4—268no—
784C2×D4—268no—
785C2×D4—2616no—
786C2×D4—264no—
787C2×D4—264no—
788C2×D4C22×#26114yes—
789C22×C4—24no—
790C22×C4—132no—
791C22×C4—132no—
792C22×C4—132no—
793C22×C4—132no—
794C22×C4—134no—
795C22×C4—134no—
796C22×C4—134no—
797C22×C4—134no—
798C22×C4—134no—
799C22×C4—131no—
800C22×C4—131no—
801C22×C4—131no—
802C22×C4—131no—
803C22×C4—131no—
804C22×C4—132no—
805C22×C4—132no—
806C22×C4—132no—
807C22×C4—132no—
808C22×C4—132no—
809C22×C4—132no—
810C22×C4—132no—
811C22×C4—132no—
812C22×C4—132no—
813C22×C4—132no—
814C22×C4—134no—
815C22×C4—134no—
816C22×C4—132no—
817C22×C4—132no—
818C22×C4—132no—
819C22×C4—132no—
820C22×C4—262no—
821C22×C4—262no—
822C22×C4—262no—
823C22×C4—262no—
824C22×C4—262no—
825C22×C4—262no—
826C22×C4—268no—
827C22×C4—262no—
828C22×C4—262no—
829C22×C4—264no—
830C22×C4—264no—
831C22×C4—268no—
832C22×C4—2616no—
833C22×C4—262no—
834C22×C4—262no—
835C22×C4—268no—
836C22×C4—268no—
837C22×C4—268no—
838C22×C4—268no—
839C22×C4—262no—
840C22×C4—262no—
841C22×C4—262no—
842C22×C4—262no—
843C22×C4—262no—
844C22×C4—262no—
845C22×C4—262no—
846C22×C4—262no—
847C22×C4—264no—
848C22×C4—262no—
849C22×C4—262no—
850C22×C4—262no—
851C22×C4—262no—
852C22×C4—262no—
853C22×C4—262no—
854C22×C4—262no—
855C22×C4—262no—
856C22×C4—268no—
857C22×C4—268no—
858C22×C4—262no—
859C22×C4—262no—
860C22×C4—262no—
861C22×C4—262no—
862C22×C4—524no—
863C22×C4—524no—
864C22×C4—524no—
865C22×C4—5216no—
866C22×C4—5216no—
867C22×C4—5216no—
868C22×C4C22×#26111yescharacteristic
869C22×C4C22×#26111yescharacteristic
870C22×C4C22×#26111yescharacteristic
871C22×C4C22×#26111yescharacteristic
872C22×C4C22×#26111yescharacteristic
873C22×C4C22×#26114yescomplemented
874C4⋊C4—134no—
875C4⋊C4—134no—
876C4⋊C4—134no—
877C4⋊C4—134no—
878C4⋊C4—134no—
879C4⋊C4—134no—
880C4⋊C4—268no—
881C4⋊C4—268no—
882C4⋊C4—268no—
883C4⋊C4—268no—
884C4⋊C4—524no—
885C4⋊C4C22×#26114yescomplemented
886C4⋊C4C22×#26114yescomplemented
887C22⋊C4—1316no—
888C22⋊C4—134no—
889C22⋊C4—134no—
890C22⋊C4—134no—
891C22⋊C4—134no—
892C22⋊C4—134no—
893C22⋊C4—134no—
894C22⋊C4—134no—
895C22⋊C4—134no—
896C22⋊C4—134no—
897C22⋊C4—268no—
898C22⋊C4—268no—
899C22⋊C4—268no—
900C22⋊C4—524no—
901C22⋊C4C22×#26114yescomplemented
902C22⋊C4C22×#26114yescomplemented
903C22⋊C4C22×#26114yescomplemented
904C42—268no—
905C42—268no—
906C42—268no—
907C42—268no—
908C42—524no—
909C13C2×#235911yescharacteristic, complemented, Sylow
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—132no—
916C23—132no—
917C23—132no—
918C23—132no—
919C23—132no—
920C23—132no—
921C23—131no—
922C23—131no—
923C23—134no—
924C23—134no—
925C23—138no—
926C23—134no—
927C23—132no—
928C23—132no—
929C23—262no—
930C23—262no—
931C23—262no—
932C23—268no—
933C23—268no—
934C23—264no—
935C23—264no—
936C23—262no—
937C23—268no—
938C23—268no—
939C23—262no—
940C23—262no—
941C23—262no—
942C23—262no—
943C23—264no—
944C23—262no—
945C23—264no—
946C23—264no—
947C23—262no—
948C23—262no—
949C23—262no—
950C23—262no—
951C23—262no—
952C23—262no—
953C23—524no—
954C23—524no—
955C23—524no—
956C23—524no—
957C23D4×#26114yes—
958C23C23×#26112yes—
959C23C23×#26112yes—
960C23C23×#26111yescharacteristic
961D4—28no—
962D4—268no—
963D4—268no—
964D4—268no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—134no—
972C2×C4—134no—
973C2×C4—134no—
974C2×C4—134no—
975C2×C4—132no—
976C2×C4—132no—
977C2×C4—132no—
978C2×C4—132no—
979C2×C4—132no—
980C2×C4—262no—
981C2×C4—262no—
982C2×C4—262no—
983C2×C4—262no—
984C2×C4—262no—
985C2×C4—262no—
986C2×C4—264no—
987C2×C4—264no—
988C2×C4—262no—
989C2×C4—264no—
990C2×C4—264no—
991C2×C4—262no—
992C2×C4—262no—
993C2×C4—268no—
994C2×C4—268no—
995C2×C4—264no—
996C2×C4—262no—
997C2×C4—262no—
998C2×C4—262no—
999C2×C4—262no—
1000C2×C4—262no—
1001C2×C4—262no—
1002C2×C4—262no—
1003C2×C4—262no—
1004C2×C4—268no—
1005C2×C4—268no—
1006C2×C4—268no—
1007C2×C4—262no—
1008C2×C4—268no—
1009C2×C4—268no—
1010C2×C4—262no—
1011C2×C4—262no—
1012C2×C4—262no—
1013C2×C4—262no—
1014C2×C4—262no—
1015C2×C4—262no—
1016C2×C4—262no—
1017C2×C4—262no—
1018C2×C4—262no—
1019C2×C4—262no—
1020C2×C4—262no—
1021C2×C4—262no—
1022C2×C4—262no—
1023C2×C4—262no—
1024C2×C4—262no—
1025C2×C4—262no—
1026C2×C4—262no—
1027C2×C4—5216no—
1028C2×C4—5216no—
1029C2×C4—5216no—
1030C2×C4—524no—
1031C2×C4—524no—
1032C2×C4—524no—
1033C2×C4—524no—
1034C2×C4C23×#26112yes—
1035C2×C4C23×#26112yes—
1036C2×C4C23×#26112yes—
1037C2×C4C23×#26112yes—
1038C2×C4C23×#26112yes—
1039C22—22no—
1040C22—22no—
1041C22—28no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—44no—
1046C22—132no—
1047C22—131no—
1048C22—131no—
1049C22—132no—
1050C22—131no—
1051C22—131no—
1052C22—132no—
1053C22—131no—
1054C22—131no—
1055C22—134no—
1056C22—134no—
1057C22—134no—
1058C22—134no—
1059C22—134no—
1060C22—264no—
1061C22—264no—
1062C22—264no—
1063C22—2616no—
1064C22—264no—
1065C22—262no—
1066C22—262no—
1067C22—268no—
1068C22—262no—
1069C22—262no—
1070C22—262no—
1071C22—522no—
1072C22—522no—
1073C22—522no—
1074C22—528no—
1075C22—522no—
1076C22—524no—
1077C22C2×D4×#26114yes—
1078C22C2×D4×#26112yes—
1079C22#41×#26112yes—
1080C22#1171963112yes—
1081C22C24×#26111yescharacteristic
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—264no—
1088C4—264no—
1089C4—264no—
1090C4—264no—
1091C4—262no—
1092C4—262no—
1093C4—262no—
1094C4—262no—
1095C4—262no—
1096C4—522no—
1097C4—522no—
1098C4—522no—
1099C4—522no—
1100C2—24no—
1101C2—42no—
1102C2—131no—
1103C2—131no—
1104C2—131no—
1105C2—134no—
1106C2—131no—
1107C2—264no—
1108C2—522no—
1109C2#1313135914yesdirect product factor
1110C2C22×D4×#26111yescharacteristic
1111C2C2×#41×#26111yescharacteristic
1112C2C2×#1171963111yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C13×#123C4
socleC23×C13C23×C4
prime radicalC22×D4×D13C22
cosocleC22×D13C25
hypercenterC2×#123#261
hypocenterC13C2×#2359
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C22×#88237C2semidirect
3. #13131359C2direct (N × H)
4. C2×#11719083C2semidirect
5. C2×#11719071C2semidirect
6. C2×#11719071C2semidirect
7. C2×#11719082C2semidirect
8. C2×#11719082C2semidirect
10. C2×#11719070C2semidirect
11. C2×#11719070C2semidirect
12. C2×C4⋊C4×#261C2semidirect
13. C2×C22⋊C4×#261C2semidirect
14. C2×C22⋊C4×#261C2semidirect
15. C22×(C2×#261)⋊C4C2semidirect
30. C2×#88237C22semidirect
41. C2×C13×#123C4semidirect
42. C2×#88189C4semidirect
43. C2×#88183C4semidirect
44. D13×#123C4semidirect
46. C2×#88148C4semidirect
47. C2×#88148C4semidirect
50. C2×#88140C4semidirect
51. C2×#88137C4semidirect
52. C2×#88137C4semidirect
67. C2×(C2×#261)⋊C4C22semidirect
68. #11719083C22semidirect
69. #11719082C22semidirect
70. #11719082C22semidirect
71. C4⋊C4×#261C22semidirect
72. #11719071C22semidirect
73. #11719071C22semidirect
74. #11719070C22semidirect
75. #11719070C22semidirect
76. C22⋊C4×#261C22semidirect
77. C22⋊C4×#261C22semidirect
101. C23×C4×C13C2×C4semidirect
104. C23×Dic13C2×C4semidirect
112. C22×C4×D13C2×C4semidirect
113. C22×C4×D13C2×C4semidirect
114. C22×C4×D13C2×C4semidirect
153. C13×#123C2×C4semidirect
154. C2×C13×C4⋊C4C2×C4semidirect
155. C2×C13×C4⋊C4C2×C4semidirect
156. C2×C13×C22⋊C4C2×C4semidirect
157. C2×C13×C22⋊C4C2×C4semidirect
158. C2×C13×C22⋊C4C2×C4semidirect
159. C2×C22⋊Dic13C2×C4semidirect
160. C2×C22⋊Dic13C2×C4semidirect
161. C2×C22⋊Dic13C2×C4semidirect
162. #88189C2×C4semidirect
163. #88183C2×C4semidirect
164. C2×#6103C2×C4semidirect
165. C2×#6103C2×C4semidirect
166. C2×#6103C2×C4semidirect
167. C2×#6103C2×C4semidirect
168. C2×#6103C2×C4semidirect
169. C2×#6103C2×C4semidirect
170. C2×C4⋊Dic13C2×C4semidirect
171. C2×C4⋊Dic13C2×C4semidirect
172. C2×#6101C2×C4semidirect
173. C2×#6101C2×C4semidirect
174. C2×#6101C2×C4semidirect
175. C2×#6101C2×C4semidirect
176. #88148C2×C4semidirect
177. #88148C2×C4semidirect
178. C4⋊C4×D13C2×C4semidirect
179. C4⋊C4×D13C2×C4semidirect
182. #88140C2×C4semidirect
183. #88137C2×C4semidirect
184. #88137C2×C4semidirect
185. C22⋊C4×D13C2×C4semidirect
186. C22⋊C4×D13C2×C4semidirect
187. C22⋊C4×D13C2×C4semidirect
275. C22×C4×C13C22×C4semidirect
286. C22×Dic13C22×C4semidirect
312. C2×C4×D13C22×C4semidirect
313. C2×C4×D13C22×C4semidirect
334. C13×C4⋊C4C22×C4semidirect
335. C13×C4⋊C4C22×C4semidirect
336. C13×C22⋊C4C22×C4semidirect
337. C13×C22⋊C4C22×C4semidirect
338. C13×C22⋊C4C22×C4semidirect
339. C22⋊Dic13C22×C4semidirect
340. C22⋊Dic13C22×C4semidirect
341. C22⋊Dic13C22×C4semidirect
342. #6103C22×C4semidirect
343. #6103C22×C4semidirect
344. #6103C22×C4semidirect
345. #6103C22×C4semidirect
346. #6103C22×C4semidirect
347. #6103C22×C4semidirect
348. C4⋊Dic13C22×C4semidirect
349. C4⋊Dic13C22×C4semidirect
350. #6101C22×C4semidirect
351. #6101C22×C4semidirect
352. #6101C22×C4semidirect
353. #6101C22×C4semidirect
513. C2×#123#261semidirect
663. C23×C4C2×#261semidirect
671. #123C2×#261semidirect
694. C2×C4⋊C4C2×#261semidirect
695. C2×C4⋊C4C2×#261semidirect
721. C2×C22⋊C4C2×#261semidirect
722. C2×C22⋊C4C2×#261semidirect
723. C2×C22⋊C4C2×#261semidirect
746. C2×C13#2359semidirect
752. D13#2359semidirect
873. C22×C4C22×#261semidirect
885. C4⋊C4C22×#261semidirect
886. C4⋊C4C22×#261semidirect
901. C22⋊C4C22×#261semidirect
902. C22⋊C4C22×#261semidirect
903. C22⋊C4C22×#261semidirect
909. C13C2×#2359semidirect
1109. C2#13131359direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×#2612
C22×#882372
#131313592
C2×#117190832
C2×#117190712
C2×#117190822
C2×#117191502
C2×#117190702
C2×C4⋊C4×#2612
C2×C22⋊C4×#2612
C22×(C2×#261)⋊C42
C2×D13×#1232
C2×#235913