Finite Group Databasebeta

← D13×#2974 #16727648

Subgroups — D13×#2974 #16727648

Order 3328.

2654 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
1C2×C4×D4×D13C211yesmaximal, characteristic
2#13123873C211yesmaximal, characteristic, complemented
3#13123872C212yesmaximal, complemented
4#13123871C211yesmaximal, characteristic, complemented
5#13123870C211yesmaximal, characteristic, complemented
6#13123869C212yesmaximal, complemented
7#13123868C212yesmaximal, complemented
8#13123867C212yesmaximal, complemented
9#13123866C214yesmaximal, complemented
10D13×#436C212yesmaximal, complemented
11D13×#435C214yesmaximal, complemented
12C8×D4×D13C212yesmaximal, complemented
13D13×#432C211yesmaximal, characteristic, complemented
14D13×#431C211yesmaximal, characteristic, complemented
15D13×#407C212yesmaximal, complemented
16C2×D13×C22⋊C8C212yesmaximal, complemented
17C13×#2974C211yesmaximal, characteristic, complemented
18C22×D4×D13C411yescharacteristic
19C23×C4×D13C2212yes—
20C2×C4×D4×C13C2211yescharacteristic
21C2×D4×Dic13C411yescharacteristic
22C2×C4×C22⋊D13C2212yes—
23C2×M16×D13C2214yescomplemented
24C22×C8×D13C2214yescomplemented
25C4×D4×D13C412yes—
26C4×D4×D13C411yescharacteristic
27C4×D4×D13C412yes—
28C4×D4×D13C411yescharacteristic
29C4×D4×D13C411yescharacteristic
30C4×D4×D13C411yescharacteristic
31C4×D4×D13C2212yes—
32C4×D4×D13C2211yescharacteristic
33C4×D4×D13C2211yescharacteristic
34C4×D4×D13C2211yescharacteristic
35C4×D4×D13C2212yes—
36C4×D4×D13C2211yescharacteristic
37C2×#88147C411yescharacteristic
38C2×C4⋊C4×D13C411yescharacteristic
39C2×#88135C412yes—
40C2×C22⋊C4×D13C412yes—
41C2×C4×D52C2211yescharacteristic
42C2×C42×D13C2211yescharacteristic
43C13×#436C2212yescomplemented
44C13×#435C2214yescomplemented
45C8×D4×C13C2212yescomplemented
46C13×#432C2211yescharacteristic, complemented
47C13×#431C2211yescharacteristic, complemented
48C13×#407C2212yescomplemented
49C2×C13×C22⋊C8C2212yescomplemented
50#11718868C2212yescomplemented
51C2×C22⋊#1055C2212yescomplemented
52#11718789C2214yescomplemented
53#11718788C2214yescomplemented
54#11718787C2214yescomplemented
55#11718772C2214yescomplemented
56C8×C22⋊D13C2214yescomplemented
57C2×#88060C2214yescomplemented
58#11718673C2212yescomplemented
59#11718672C2214yescomplemented
60D4×#1055C2212yescomplemented
61#11718587C2211yescharacteristic, complemented
62#11718586C2211yescharacteristic, complemented
63#11718499C2212yescomplemented
64#11718497C2214yescomplemented
65#11718496C2212yescomplemented
66#11718495C2212yescomplemented
67#11718494C2212yescomplemented
68D13×C4⋊C8C2212yescomplemented
69D13×C4⋊C8C2212yescomplemented
70#11718391C2214yescomplemented
71#11718390C2214yescomplemented
72#11718389C2214yescomplemented
73#11718387C2212yescomplemented
74#11718387C2212yescomplemented
75#11718387C2214yescomplemented
76#11718386C2214yescomplemented
77D13×C22⋊C8C2211yescharacteristic
78D13×C22⋊C8C2211yescharacteristic
79D13×C22⋊C8C2212yes—
80D13×C22⋊C8C2212yescomplemented
81D13×C22⋊C8C2212yescomplemented
82D13×C22⋊C8C2214yescomplemented
83D13×C22⋊C8C2214yescomplemented
84D13×C22⋊C8C2214yescomplemented
85#11718380C2212yescomplemented
86#11718379C2211yescharacteristic, complemented
87#11718379C2211yescharacteristic, complemented
88#11718367C2214yescomplemented
89#11718366C2212yescomplemented
90D13×#97C2212yescomplemented
91#11718349C2212yescomplemented
92C8×D52C2212yescomplemented
93#11718346C2212yescomplemented
94C4×C8×D13C2212yescomplemented
95C24×D13C2×C412yes—
96C22×D4×C13C2×C411yescharacteristic
97C23×C4×C13C2312yes—
98C22×C22⋊D13C2×C412yes—
99C23×Dic13C2×C412yes—
100C2×D4×D13—28no—
101C2×D4×D13C2×C412yes—
102C2×D4×D13C2×C411yescharacteristic
103C2×D4×D13C2×C412yes—
104C2×D4×D13C2×C411yescharacteristic
105C2×D4×D13C2×C411yescharacteristic
106C2×D4×D13C2×C411yescharacteristic
107C22×D52C2×C411yescharacteristic
108C22×C4×D13—48no—
109C22×C4×D13C2×C411yescharacteristic
110C22×C4×D13C2×C411yescharacteristic
111C22×C4×D13C2×C412yes—
112C22×C4×D13C2×C412yes—
113C22×C4×D13C2×C412yes—
114C22×C4×D13C2×C412yes—
115C22×C4×D13C2×C412yes—
116C22×C4×D13C2×C412yes—
117C22×C4×D13C2311yescharacteristic
118C22×C4×D13C2312yes—
119C22×C4×D13C2312yes—
120C22×C4×D13C2312yes—
121C22×C4×D13C2312yes—
122C22×C4×D13C2312yes—
123C2×C13×M16C2314yescomplemented
124C22×C8×C13C2314yescomplemented
125C4×D4×C13C2×C412yes—
126C4×D4×C13C2×C411yescharacteristic
127C4×D4×C13C2×C411yescharacteristic
128C4×D4×C13C2311yescharacteristic
129C4×D4×C13C2312yes—
130C4×D4×C13C2311yescharacteristic
131C2×C13×C4⋊C4C2×C411yescharacteristic
132C2×C13×C22⋊C4C2×C412yes—
133C2×C42×C13C2311yescharacteristic
134C2×C22⋊Dic13C2×C412yes—
135D4×Dic13C2×C412yes—
136D4×Dic13C2×C411yescharacteristic
137D4×Dic13C2×C411yescharacteristic
138D4×Dic13C2×C412yes—
139D4×Dic13C2×C411yescharacteristic
140D4×Dic13C2×C411yescharacteristic
141C4×C22⋊D13C2×C412yes—
142C4×C22⋊D13C2×C412yes—
143C4×C22⋊D13C2×C412yes—
144C4×C22⋊D13C2×C412yes—
145C4×C22⋊D13C2312yes—
146C4×C22⋊D13C2312yes—
147C4×C22⋊D13C2312yes—
148C4×C22⋊D13C2312yes—
149C2×#6103C2×C412yes—
150C2×#6103C2×C412yes—
151C2×C4⋊Dic13C2×C411yescharacteristic
152C2×#6101C2×C412yes—
153C2×C4×Dic13C2×C411yescharacteristic
154C2×C4×Dic13C2×C411yescharacteristic
155C2×C4×Dic13C2311yescharacteristic
156C2×#6099C2314yescomplemented
157C22×#1055C2314yescomplemented
158M16×D13—48no—
159C2×#6094C2314yescomplemented
160C2×#6094C2314yescomplemented
161C2×C8×D13—48no—
162C2×C8×D13C2312yes—
163C2×C8×D13C2314yes—
164C2×C8×D13C2312yes—
165C2×C8×D13C2314yescomplemented
166C2×C8×D13C2314yescomplemented
167#88147C2×C412yes—
168#88147C2×C411yescharacteristic
169#88147C2×C411yescharacteristic
170#88147C2×C412yes—
171#88147C2×C411yescharacteristic
172#88147C2×C411yescharacteristic
173C4⋊C4×D13C2×C412yes—
174C4⋊C4×D13C2×C412yes—
175C4⋊C4×D13C2×C411yescharacteristic
176C4⋊C4×D13C2×C411yescharacteristic
177C4⋊C4×D13C2×C411yescharacteristic
178C4⋊C4×D13C2×C411yescharacteristic
179#88135C2×C412yes—
180#88135C2×C412yes—
181#88135C2×C412yes—
182#88135C2×C412yes—
183#88135C2×C412yes—
184#88135C2×C412yes—
185#88135C2×C412yes—
186#88135C2×C412yes—
187C22⋊C4×D13C2×C412yes—
188C22⋊C4×D13C2×C412yes—
189C22⋊C4×D13C2×C412yes—
190C22⋊C4×D13C2×C412yes—
191C22⋊C4×D13C2×C412yes—
192C22⋊C4×D13C2×C412yes—
193C22⋊C4×D13C2×C412yes—
194C22⋊C4×D13C2×C412yes—
195C4×D52C2×C412yes—
196C4×D52C2×C411yescharacteristic
197C4×D52C2×C411yescharacteristic
198C4×D52C2311yescharacteristic
199C4×D52C2312yes—
200C4×D52C2311yescharacteristic
201C42×D13C2×C411yescharacteristic
202C42×D13C2×C411yescharacteristic
203C42×D13C2×C411yescharacteristic
204C42×D13C2×C411yescharacteristic
205C42×D13C2311yescharacteristic
206C42×D13C2311yescharacteristic
207C42×D13C2311yescharacteristic
208C42×D13C2311yescharacteristic
209C13×C4⋊C8C2312yescomplemented
210C13×C4⋊C8C2312yescomplemented
211C13×C22⋊C8C2311yescharacteristic
212C13×C22⋊C8C2312yes—
213C13×C22⋊C8C2311yescharacteristic
214C13×C22⋊C8C2314yescomplemented
215C13×C22⋊C8C2314yescomplemented
216C13×#97C2312yescomplemented
217C4×C8×C13C2312yescomplemented
218C22⋊#1055C2311yescharacteristic
219C22⋊#1055C2311yescharacteristic
220C22⋊#1055C2312yes—
221C22⋊#1055C2314yescomplemented
222C22⋊#1055C2314yescomplemented
223#88060C2312yes—
224#88060C2312yes—
225#88060C2314yes—
226#88060C2314yescomplemented
227#88060C2314yescomplemented
228#88060C2314yescomplemented
229#88060C2314yescomplemented
230#88055C2314yescomplemented
231#88054C2314yescomplemented
232#88054C2312yescomplemented
233#88054C2312yescomplemented
234C8×Dic13C2312yescomplemented
235C8×Dic13C2312yescomplemented
236C4⋊#1055C2312yescomplemented
237C4⋊#1055C2312yescomplemented
238#88043C2312yescomplemented
239C4×#1055C2312yescomplemented
240C2×#2974—131nomaximal, Sylow
241C24×C13C22×C412yes—
242C23×D13—28no—
243C23×D13—28no—
244C23×D13—44no—
245C23×D13C22×C412yes—
246C23×D13C22×C412yes—
247C23×D13C22×C412yes—
248C23×D13C22×C412yes—
249C23×D13C22×C412yes—
250C23×D13C22×C411yescharacteristic
251C2×D4×C13—24no—
252C2×D4×C13C22×C412yes—
253C2×D4×C13C22×C411yescharacteristic
254C2×D4×C13C22×C411yescharacteristic
255C22×C4×C13—44no—
256C22×C4×C13C22×C411yescharacteristic
257C22×C4×C13C22×C411yescharacteristic
258C22×C4×C13C22×C412yes—
259C22×C4×C13C22×C412yes—
260C22×C4×C13C22×C412yes—
261C22×C4×C13C2411yescharacteristic
262C22×C4×C13C2412yes—
263C22×C4×C13C2412yes—
264C2×C22⋊D13—28no—
265C2×C22⋊D13C22×C412yes—
266C2×C22⋊D13C22×C412yes—
267C2×C22⋊D13C22×C412yes—
268C2×C22⋊D13C22×C412yes—
269C22×Dic13—44no—
270C22×Dic13C22×C412yes—
271C22×Dic13C22×C412yes—
272C22×Dic13C22×C411yescharacteristic
273C22×Dic13C22×C411yescharacteristic
274C22×Dic13C22×C411yescharacteristic
275C22×Dic13C22×C412yes—
276C22×Dic13C22×C412yes—
277C22×Dic13C22×C412yes—
278D4×D13—28no—
279D4×D13—24no—
280D4×D13—28no—
281D4×D13—24no—
282D4×D13—24no—
283D4×D13M1618yescomplemented
284C2×D52—24no—
285C2×D52C22×C412yes—
286C2×D52C22×C411yescharacteristic
287C2×D52C22×C411yescharacteristic
288C2×C4×D13—24no—
289C2×C4×D13—24no—
290C2×C4×D13—28no—
291C2×C4×D13—28no—
292C2×C4×D13—24no—
293C2×C4×D13—44no—
294C2×C4×D13—44no—
295C2×C4×D13—44no—
296C2×C4×D13—44no—
297C2×C4×D13—44no—
298C2×C4×D13—44no—
299C2×C4×D13—44no—
300C2×C4×D13—44no—
301C2×C4×D13—44no—
302C2×C4×D13C22×C411yescharacteristic
303C2×C4×D13C22×C411yescharacteristic
304C2×C4×D13C22×C411yescharacteristic
305C2×C4×D13C22×C411yescharacteristic
306C2×C4×D13C22×C411yescharacteristic
307C2×C4×D13C22×C411yescharacteristic
308C2×C4×D13C22×C411yescharacteristic
309C2×C4×D13C22×C411yescharacteristic
310C2×C4×D13C22×C411yescharacteristic
311C2×C4×D13C22×C412yes—
312C2×C4×D13C22×C412yes—
313C2×C4×D13C22×C412yes—
314C2×C4×D13C22×C412yes—
315C2×C4×D13C22×C412yes—
316C2×C4×D13C22×C412yes—
317C2×C4×D13C22×C412yes—
318C2×C4×D13C22×C412yes—
319C2×C4×D13C22×C412yes—
320C2×C4×D13C22×C412yes—
321C2×C4×D13C22×C411yescharacteristic
322C2×C4×D13C2411yescharacteristic
323C2×C4×D13C2412yes—
324C2×C4×D13C2412yes—
325C2×C4×D13C2411yescharacteristic
326C13×M16—44no—
327C2×C8×C13—44no—
328C2×C8×C13C2412yes—
329C2×C8×C13C2412yes—
330C2×C8×C13C2414yes—
331C13×C4⋊C4C22×C412yes—
332C13×C4⋊C4C22×C411yescharacteristic
333C13×C4⋊C4C22×C411yescharacteristic
334C13×C22⋊C4C22×C412yes—
335C13×C22⋊C4C22×C412yes—
336C13×C22⋊C4C22×C412yes—
337C13×C22⋊C4C22×C412yes—
338C42×C13C22×C411yescharacteristic
339C42×C13C22×C411yescharacteristic
340C42×C13C2411yescharacteristic
341C42×C13C2411yescharacteristic
342C22⋊Dic13C22×C412yes—
343C22⋊Dic13C22×C412yes—
344C22⋊Dic13C22×C412yes—
345C22⋊Dic13C22×C412yes—
346#6103C22×C412yes—
347#6103C22×C412yes—
348#6103C22×C412yes—
349#6103C22×C412yes—
350#6103C22×C412yes—
351#6103C22×C412yes—
352#6103C22×C412yes—
353#6103C22×C412yes—
354C4⋊Dic13C22×C412yes—
355C4⋊Dic13C22×C411yescharacteristic
356C4⋊Dic13C22×C411yescharacteristic
357#6101C22×C412yes—
358#6101C22×C412yes—
359#6101C22×C412yes—
360#6101C22×C412yes—
361C4×Dic13C22×C411yescharacteristic
362C4×Dic13C22×C411yescharacteristic
363C4×Dic13C22×C411yescharacteristic
364C4×Dic13C22×C411yescharacteristic
365C4×Dic13C22×C411yescharacteristic
366C4×Dic13C22×C411yescharacteristic
367C4×Dic13C22×C411yescharacteristic
368C4×Dic13C22×C411yescharacteristic
369C4×Dic13C22×C411yescharacteristic
370C4×Dic13C22×C411yescharacteristic
371C4×Dic13C2411yescharacteristic
372C4×Dic13C2411yescharacteristic
373#6099—44no—
374C2×#1055—44no—
375C2×#1055C2412yes—
376C2×#1055C2414yes—
377C2×#1055C2412yes—
378#6094—44no—
379#6094—44no—
380C8×D13—24no—
381C8×D13—28no—
382C8×D13—24no—
383C8×D13—44no—
384C8×D13—44no—
385C22×C4×D4—131no—
386#2974—132no—
387#2974—134no—
388#2974—132no—
389#2974—131no—
390#2974—131no—
391#2974—132no—
392#2974—132no—
393#2974—131no—
394#2974D1311yescharacteristic, direct product factor
395C2×#436—132no—
396C2×#435—134no—
397C2×C8×D4—132no—
398C2×#432—131no—
399C2×#431—131no—
400C2×#407—132no—
401C22×C22⋊C8—132no—
402C23×C13—24no—
403C23×C13—24no—
404C23×C13—42no—
405C23×C13C23×C412yes—
406C23×C13C23×C412yes—
407C23×C13C23×C411yescharacteristic
408C22×D13—22no—
409C22×D13—24no—
410C22×D13—22no—
411C22×D13—24no—
412C22×D13—24no—
413C22×D13—24no—
414C22×D13—24no—
415C22×D13—24no—
416C22×D13—24no—
417C22×D13—24no—
418C22×D13—24no—
419C22×D13—24no—
420C22×D13—24no—
421C22×D13—42no—
422C22×D13—42no—
423C22×D13—42no—
424C22×D13—432no—
425C22×D13C2×M1618yes—
426C22×D13#13114yes—
427C22×D13C23×C412yes—
428C22×D13C23×C412yes—
429C22×D13C23×C411yescharacteristic
430C22×D13C23×C411yescharacteristic
431D4×C13—24no—
432D4×C13—22no—
433D4×C13C2×M1614yescomplemented
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—24no—
437C2×C4×C13—24no—
438C2×C4×C13—22no—
439C2×C4×C13—42no—
440C2×C4×C13—42no—
441C2×C4×C13—42no—
442C2×C4×C13C23×C411yescharacteristic
443C2×C4×C13C23×C411yescharacteristic
444C2×C4×C13C23×C411yescharacteristic
445C2×C4×C13C23×C411yescharacteristic
446C2×C4×C13C23×C412yes—
447C2×C4×C13C23×C412yes—
448C2×C4×C13C23×C411yescharacteristic
449C2×C4×C13C2511yescharacteristic
450C22⋊D13—24no—
451C22⋊D13—24no—
452C22⋊D13—24no—
453C22⋊D13C2×M1618yescomplemented
454C2×Dic13—22no—
455C2×Dic13—22no—
456C2×Dic13—24no—
457C2×Dic13—24no—
458C2×Dic13—22no—
459C2×Dic13—42no—
460C2×Dic13—42no—
461C2×Dic13—42no—
462C2×Dic13C23×C411yescharacteristic
463C2×Dic13C23×C411yescharacteristic
464C2×Dic13C23×C411yescharacteristic
465C2×Dic13C23×C411yescharacteristic
466C2×Dic13C23×C412yes—
467C2×Dic13C23×C412yes—
468C2×Dic13C23×C411yescharacteristic
469C2×Dic13C23×C411yescharacteristic
470D52—24no—
471D52—22no—
472D52C2×M1614yescomplemented
473C4×D13—22no—
474C4×D13—24no—
475C4×D13—24no—
476C4×D13—22no—
477C4×D13—22no—
478C4×D13—22no—
479C4×D13—22no—
480C4×D13—22no—
481C4×D13—22no—
482C4×D13—24no—
483C4×D13—24no—
484C4×D13—22no—
485C4×D13—22no—
486C4×D13—24no—
487C4×D13—24no—
488C4×D13—22no—
489C4×D13—42no—
490C4×D13—42no—
491C4×D13—42no—
492C4×D13—42no—
493C4×D13—42no—
494C4×D13—42no—
495C4×D13C2×M1614yes—
496C4×D13H(5,𝔽2)14yes—
497C8×C13—22no—
498C8×C13—24no—
499C8×C13—22no—
500#1055—22no—
501#1055—24no—
502#1055—22no—
503C23×D4—131no—
504C24×C4—132no—
505C22×M16—134no—
506C23×C8—134no—
507C2×C4×D4—131no—
508C2×C4×D4—132no—
509C2×C4×D4—131no—
510C2×C4×D4—131no—
511C2×C4×D4—132no—
512C2×C4×D4—132no—
513C2×C4×D4—131no—
514C2×C4×D4—131no—
515C2×C4×D4—131no—
516C2×C4×D4—132no—
517C2×C4×D4—131no—
518C2×C4×D4—132no—
519C2×C4×D4—131no—
520C2×C4×D4—131no—
521C2×C4×D4—131no—
522C2×C4×D4—132no—
523C2×C4×D4—131no—
524C2×C4×D4C2×D1311yescharacteristic
525C22×C4⋊C4—131no—
526C22×C22⋊C4—132no—
527C22×C42—131no—
528#436—134no—
529#436—132no—
530#436—132no—
531#436—134no—
532#436—132no—
533#436C2×D1312yescomplemented
534#435—134no—
535#435—134no—
536#435—134no—
537#435—134no—
538#435—134no—
539#435—134no—
540#435—134no—
541#435C2×D1314yescomplemented
542C8×D4—134no—
543C8×D4—132no—
544C8×D4—132no—
545C8×D4—134no—
546C8×D4—132no—
547C8×D4C2×D1312yescomplemented
548#432—131no—
549#432—132no—
550#432—132no—
551#432—132no—
552#432C2×D1311yescharacteristic, complemented
553#431—131no—
554#431—132no—
555#431—131no—
556#431—131no—
557#431—132no—
558#431C2×D1311yescharacteristic, complemented
559C2×C4⋊C8—132no—
560C2×C4⋊C8—132no—
561#407—132no—
562#407—134no—
563#407—132no—
564#407—132no—
565#407—134no—
566#407C2×D1312yescomplemented
567C2×C22⋊C8—132no—
568C2×C22⋊C8—134no—
569C2×C22⋊C8—131no—
570C2×C22⋊C8—132no—
571C2×C22⋊C8—132no—
572C2×C22⋊C8—132no—
573C2×C22⋊C8—131no—
574C2×C22⋊C8—134no—
575C2×C22⋊C8—134no—
576C2×C22⋊C8—134no—
577C2×C22⋊C8C2×D1312yescomplemented
578C2×#97—132no—
579C2×C4×C8—132no—
580C22×C13—21no—
581C22×C13—22no—
582C22×C13—21no—
583C22×C13—22no—
584C22×C13—22no—
585C22×C13—22no—
586C22×C13—22no—
587C22×C13—48no—
588C22×C13C22×M1614yes—
589C22×C13C2×#13112yes—
590C22×C13C24×C411yescharacteristic
591C2×D13—21no—
592C2×D13—22no—
593C2×D13—21no—
594C2×D13—22no—
595C2×D13—28no—
596C2×D13—216no—
597C2×D13—22no—
598C2×D13—22no—
599C2×D13—22no—
600C2×D13—48no—
601C2×D13—48no—
602C2×D13—48no—
603C2×D13—48no—
604C2×D13#51812yes—
605C2×D13C22×M1614yes—
606C2×D13C22×M1612yes—
607C2×D13C2×#13112yes—
608C2×D13C2×#13112yes—
609C4×C13—21no—
610C4×C13—22no—
611C4×C13—22no—
612C4×C13—21no—
613C4×C13—21no—
614C4×C13—21no—
615C4×C13C22×M1612yes—
616C4×C13C2×H(5,𝔽2)12yes—
617Dic13—21no—
618Dic13—22no—
619Dic13—22no—
620Dic13—21no—
621Dic13—21no—
622Dic13—21no—
623Dic13#51812yes—
624Dic13C22×M1612yes—
625C25—132no—
626C22×D4—131no—
627C22×D4—132no—
628C22×D4—131no—
629C22×D4—132no—
630C22×D4—131no—
631C22×D4—132no—
632C22×D4—131no—
633C22×D4—131no—
634C22×D4—268no—
635C22×D4C4×D1311yescharacteristic
636C23×C4—132no—
637C23×C4—131no—
638C23×C4—131no—
639C23×C4—132no—
640C23×C4—132no—
641C23×C4—131no—
642C23×C4—132no—
643C23×C4—132no—
644C23×C4—132no—
645C23×C4—132no—
646C23×C4—132no—
647C23×C4—132no—
648C23×C4—132no—
649C23×C4—132no—
650C23×C4—132no—
651C23×C4—528no—
652C23×C4C22×D1312yes—
653C2×M16—134no—
654C2×M16—134no—
655C2×M16—134no—
656C2×M16—528no—
657C2×M16C22×D1314yescomplemented
658C22×C8—134no—
659C22×C8—132no—
660C22×C8—134no—
661C22×C8—132no—
662C22×C8—134no—
663C22×C8—134no—
664C22×C8—528no—
665C22×C8C22×D1314yescomplemented
666C4×D4—132no—
667C4×D4—131no—
668C4×D4—131no—
669C4×D4—132no—
670C4×D4—131no—
671C4×D4—131no—
672C4×D4—132no—
673C4×D4—132no—
674C4×D4—132no—
675C4×D4—132no—
676C4×D4—132no—
677C4×D4—132no—
678C4×D4—132no—
679C4×D4—132no—
680C4×D4—131no—
681C4×D4—132no—
682C4×D4—131no—
683C4×D4—131no—
684C4×D4—132no—
685C4×D4—131no—
686C4×D4—132no—
687C4×D4—132no—
688C4×D4—132no—
689C4×D4—132no—
690C4×D4—132no—
691C4×D4—132no—
692C4×D4—132no—
693C4×D4—132no—
694C4×D4—131no—
695C4×D4—132no—
696C4×D4—131no—
697C4×D4—131no—
698C4×D4—132no—
699C4×D4—131no—
700C4×D4C4×D1312yes—
701C4×D4C4×D1311yescharacteristic
702C4×D4C4×D1311yescharacteristic
703C4×D4C22×D1311yescharacteristic
704C4×D4C22×D1312yes—
705C4×D4C22×D1311yescharacteristic
706C2×C4⋊C4—132no—
707C2×C4⋊C4—131no—
708C2×C4⋊C4—131no—
709C2×C4⋊C4—131no—
710C2×C4⋊C4—132no—
711C2×C4⋊C4—132no—
712C2×C4⋊C4—131no—
713C2×C4⋊C4—131no—
714C2×C4⋊C4C4×D1311yescharacteristic
715C2×C22⋊C4—132no—
716C2×C22⋊C4—132no—
717C2×C22⋊C4—132no—
718C2×C22⋊C4—132no—
719C2×C22⋊C4—132no—
720C2×C22⋊C4—132no—
721C2×C22⋊C4—132no—
722C2×C22⋊C4—132no—
723C2×C22⋊C4—132no—
724C2×C22⋊C4—132no—
725C2×C22⋊C4—132no—
726C2×C22⋊C4C4×D1312yes—
727C2×C42—131no—
728C2×C42—131no—
729C2×C42—131no—
730C2×C42—131no—
731C2×C42—131no—
732C2×C42—131no—
733C2×C42—131no—
734C2×C42—131no—
735C2×C42—131no—
736C2×C42—131no—
737C2×C42—131no—
738C2×C42C22×D1311yescharacteristic
739C4⋊C8—132no—
740C4⋊C8—132no—
741C4⋊C8—134no—
742C4⋊C8—132no—
743C4⋊C8—132no—
744C4⋊C8C22×D1312yescomplemented
745C4⋊C8C22×D1312yescomplemented
746C22⋊C8—131no—
747C22⋊C8—132no—
748C22⋊C8—131no—
749C22⋊C8—134no—
750C22⋊C8—134no—
751C22⋊C8—132no—
752C22⋊C8—134no—
753C22⋊C8—134no—
754C22⋊C8—134no—
755C22⋊C8—132no—
756C22⋊C8—134no—
757C22⋊C8—134no—
758C22⋊C8C22×D1311yescharacteristic
759C22⋊C8C22×D1312yes—
760C22⋊C8C22×D1311yescharacteristic
761C22⋊C8C22×D1314yescomplemented
762C22⋊C8C22×D1314yescomplemented
763#97—134no—
764#97—132no—
765#97C22×D1312yescomplemented
766C4×C8—132no—
767C4×C8—132no—
768C4×C8—132no—
769C4×C8C22×D1312yescomplemented
770C2×C13—22no—
771C2×C13—24no—
772C2×C13—42no—
773C2×C13C2×#51811yescharacteristic
774C2×C13C23×M1611yescharacteristic
775C2×C13C22×#13111yescharacteristic
776D13—22no—
777D13—24no—
778D13—42no—
779D13#297414yesdirect product factor
780C24—132no—
781C24—131no—
782C24—132no—
783C24—132no—
784C24—132no—
785C24—132no—
786C24—268no—
787C24—268no—
788C24—524no—
789C24C2×C4×D1312yes—
790C2×D4—24no—
791C2×D4—132no—
792C2×D4—138no—
793C2×D4—132no—
794C2×D4—132no—
795C2×D4—132no—
796C2×D4—131no—
797C2×D4—132no—
798C2×D4—131no—
799C2×D4—264no—
800C2×D4—264no—
801C2×D4—268no—
802C2×D4—264no—
803C2×D4—268no—
804C2×D4—268no—
805C2×D4—264no—
806C2×D4C2×C4×D1312yes—
807C2×D4C2×C4×D1311yescharacteristic
808C2×D4C2×C4×D1311yescharacteristic
809C22×C4—44no—
810C22×C4—131no—
811C22×C4—131no—
812C22×C4—131no—
813C22×C4—131no—
814C22×C4—131no—
815C22×C4—132no—
816C22×C4—132no—
817C22×C4—132no—
818C22×C4—132no—
819C22×C4—132no—
820C22×C4—131no—
821C22×C4—131no—
822C22×C4—131no—
823C22×C4—131no—
824C22×C4—131no—
825C22×C4—131no—
826C22×C4—131no—
827C22×C4—131no—
828C22×C4—131no—
829C22×C4—132no—
830C22×C4—132no—
831C22×C4—132no—
832C22×C4—132no—
833C22×C4—131no—
834C22×C4—132no—
835C22×C4—132no—
836C22×C4—132no—
837C22×C4—132no—
838C22×C4—132no—
839C22×C4—132no—
840C22×C4—132no—
841C22×C4—132no—
842C22×C4—268no—
843C22×C4—268no—
844C22×C4—264no—
845C22×C4—264no—
846C22×C4—264no—
847C22×C4—524no—
848C22×C4—524no—
849C22×C4—524no—
850C22×C4—524no—
851C22×C4—524no—
852C22×C4—524no—
853C22×C4—524no—
854C22×C4—524no—
855C22×C4—524no—
856C22×C4—524no—
857C22×C4C2×C4×D1311yescharacteristic
858C22×C4C2×C4×D1311yescharacteristic
859C22×C4C2×C4×D1312yes—
860C22×C4C2×C4×D1312yes—
861C22×C4C2×C4×D1312yes—
862C22×C4C23×D1311yescharacteristic
863C22×C4C23×D1312yes—
864C22×C4C23×D1312yes—
865M16—44no—
866M16—524no—
867M16—524no—
868M16—524no—
869C2×C8—44no—
870C2×C8—132no—
871C2×C8—132no—
872C2×C8—134no—
873C2×C8—264no—
874C2×C8—268no—
875C2×C8—264no—
876C2×C8—524no—
877C2×C8—524no—
878C2×C8—524no—
879C2×C8C23×D1312yes—
880C2×C8C23×D1312yes—
881C2×C8C23×D1314yes—
882C4⋊C4—132no—
883C4⋊C4—132no—
884C4⋊C4—132no—
885C4⋊C4—132no—
886C4⋊C4—132no—
887C4⋊C4—131no—
888C4⋊C4—131no—
889C4⋊C4C2×C4×D1312yes—
890C4⋊C4C2×C4×D1311yescharacteristic
891C4⋊C4C2×C4×D1311yescharacteristic
892C22⋊C4—132no—
893C22⋊C4—132no—
894C22⋊C4—132no—
895C22⋊C4—132no—
896C22⋊C4—132no—
897C22⋊C4—132no—
898C22⋊C4—132no—
899C22⋊C4—132no—
900C22⋊C4—132no—
901C22⋊C4—132no—
902C22⋊C4—132no—
903C22⋊C4—132no—
904C22⋊C4C2×C4×D1312yes—
905C22⋊C4C2×C4×D1312yes—
906C22⋊C4C2×C4×D1312yes—
907C22⋊C4C2×C4×D1312yes—
908C42—131no—
909C42—131no—
910C42—131no—
911C42—131no—
912C42—131no—
913C42—131no—
914C42—131no—
915C42—131no—
916C42—131no—
917C42—131no—
918C42—131no—
919C42—131no—
920C42C2×C4×D1311yescharacteristic
921C42C2×C4×D1311yescharacteristic
922C42C23×D1311yescharacteristic
923C42C23×D1311yescharacteristic
924C13C2×#297411yescharacteristic, complemented, Sylow
925C23—24no—
926C23—24no—
927C23—42no—
928C23—131no—
929C23—138no—
930C23—134no—
931C23—132no—
932C23—131no—
933C23—132no—
934C23—262no—
935C23—264no—
936C23—262no—
937C23—264no—
938C23—264no—
939C23—264no—
940C23—264no—
941C23—264no—
942C23—264no—
943C23—264no—
944C23—264no—
945C23—264no—
946C23—264no—
947C23—522no—
948C23—522no—
949C23—522no—
950C23—5232no—
951C23C22×C4×D1312yes—
952C23C22×C4×D1312yes—
953C23C22×C4×D1311yescharacteristic
954D4—24no—
955D4—22no—
956D4—138no—
957D4—134no—
958D4—264no—
959D4—264no—
960D4—264no—
961D4—264no—
962D4—262no—
963D4M16×D1314yescomplemented
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—131no—
973C2×C4—131no—
974C2×C4—134no—
975C2×C4—134no—
976C2×C4—131no—
977C2×C4—131no—
978C2×C4—131no—
979C2×C4—131no—
980C2×C4—132no—
981C2×C4—132no—
982C2×C4—264no—
983C2×C4—264no—
984C2×C4—262no—
985C2×C4—262no—
986C2×C4—262no—
987C2×C4—262no—
988C2×C4—262no—
989C2×C4—262no—
990C2×C4—264no—
991C2×C4—264no—
992C2×C4—262no—
993C2×C4—262no—
994C2×C4—264no—
995C2×C4—264no—
996C2×C4—262no—
997C2×C4—262no—
998C2×C4—262no—
999C2×C4—262no—
1000C2×C4—264no—
1001C2×C4—264no—
1002C2×C4—262no—
1003C2×C4—522no—
1004C2×C4—522no—
1005C2×C4—522no—
1006C2×C4—522no—
1007C2×C4—522no—
1008C2×C4—522no—
1009C2×C4—522no—
1010C2×C4—522no—
1011C2×C4—522no—
1012C2×C4C22×C4×D1311yescharacteristic
1013C2×C4C22×C4×D1311yescharacteristic
1014C2×C4C22×C4×D1311yescharacteristic
1015C2×C4C22×C4×D1311yescharacteristic
1016C2×C4C22×C4×D1312yes—
1017C2×C4C22×C4×D1312yes—
1018C2×C4C22×C4×D1311yescharacteristic
1019C2×C4C24×D1311yescharacteristic
1020C8—22no—
1021C8—24no—
1022C8—22no—
1023C8—262no—
1024C8—264no—
1025C8—262no—
1026C22—21no—
1027C22—22no—
1028C22—21no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—22no—
1033C22—48no—
1034C22—132no—
1035C22—132no—
1036C22—132no—
1037C22—134no—
1038C22—132no—
1039C22—2616no—
1040C22—268no—
1041C22—261no—
1042C22—262no—
1043C22—261no—
1044C22—262no—
1045C22—262no—
1046C22—262no—
1047C22—262no—
1048C22—528no—
1049C22—528no—
1050C22—528no—
1051C22—528no—
1052C22C2×M16×D1314yes—
1053C22D13×#13112yes—
1054C22C23×C4×D1311yescharacteristic
1055C4—21no—
1056C4—21no—
1057C4—21no—
1058C4—21no—
1059C4—22no—
1060C4—22no—
1061C4—132no—
1062C4—132no—
1063C4—261no—
1064C4—261no—
1065C4—261no—
1066C4—262no—
1067C4—262no—
1068C4—261no—
1069C4C2×M16×D1312yes—
1070C4D13×H(5,𝔽2)12yes—
1071C2—22no—
1072C2—24no—
1073C2—42no—
1074C2—134no—
1075C2—262no—
1076C2—264no—
1077C2—522no—
1078C2D13×#51811yescharacteristic
1079C2C22×M16×D1311yescharacteristic
1080C2C2×D13×#13111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingC13×#2974C2
prime radicalC22×D4×D13C4
cosocleC2×C4×C13C25
hypercenter#2974D13
hypocenterC13C2×#2974
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13123873C2semidirect
3. #13123872C2semidirect
4. #13123871C2semidirect
5. #13123870C2semidirect
6. #13123869C2semidirect
7. #13123868C2semidirect
8. #13123867C2semidirect
9. #13123866C2semidirect
10. D13×#436C2semidirect
11. D13×#435C2semidirect
12. C8×D4×D13C2semidirect
13. D13×#432C2semidirect
14. D13×#431C2semidirect
15. D13×#407C2semidirect
16. C2×D13×C22⋊C8C2semidirect
17. C13×#2974C2semidirect
23. C2×M16×D13C22semidirect
24. C22×C8×D13C22semidirect
43. C13×#436C22semidirect
44. C13×#435C22semidirect
45. C8×D4×C13C22semidirect
46. C13×#432C22semidirect
47. C13×#431C22semidirect
48. C13×#407C22semidirect
49. C2×C13×C22⋊C8C22semidirect
50. #11718868C22semidirect
51. C2×C22⋊#1055C22semidirect
52. #11718789C22semidirect
53. #11718788C22semidirect
54. #11718787C22semidirect
55. #11718772C22semidirect
56. C8×C22⋊D13C22semidirect
57. C2×#88060C22semidirect
58. #11718673C22semidirect
59. #11718672C22semidirect
60. D4×#1055C22semidirect
61. #11718587C22semidirect
62. #11718586C22semidirect
63. #11718499C22semidirect
64. #11718497C22semidirect
65. #11718496C22semidirect
66. #11718495C22semidirect
67. #11718494C22semidirect
68. D13×C4⋊C8C22semidirect
69. D13×C4⋊C8C22semidirect
70. #11718391C22semidirect
71. #11718390C22semidirect
72. #11718389C22semidirect
73. #11718387C22semidirect
74. #11718387C22semidirect
75. #11718387C22semidirect
76. #11718386C22semidirect
80. D13×C22⋊C8C22semidirect
81. D13×C22⋊C8C22semidirect
82. D13×C22⋊C8C22semidirect
83. D13×C22⋊C8C22semidirect
84. D13×C22⋊C8C22semidirect
85. #11718380C22semidirect
86. #11718379C22semidirect
87. #11718379C22semidirect
88. #11718367C22semidirect
89. #11718366C22semidirect
90. D13×#97C22semidirect
91. #11718349C22semidirect
92. C8×D52C22semidirect
93. #11718346C22semidirect
94. C4×C8×D13C22semidirect
123. C2×C13×M16C23semidirect
124. C22×C8×C13C23semidirect
156. C2×#6099C23semidirect
157. C22×#1055C23semidirect
159. C2×#6094C23semidirect
160. C2×#6094C23semidirect
165. C2×C8×D13C23semidirect
166. C2×C8×D13C23semidirect
209. C13×C4⋊C8C23semidirect
210. C13×C4⋊C8C23semidirect
214. C13×C22⋊C8C23semidirect
215. C13×C22⋊C8C23semidirect
216. C13×#97C23semidirect
217. C4×C8×C13C23semidirect
221. C22⋊#1055C23semidirect
222. C22⋊#1055C23semidirect
226. #88060C23semidirect
227. #88060C23semidirect
228. #88060C23semidirect
229. #88060C23semidirect
230. #88055C23semidirect
231. #88054C23semidirect
232. #88054C23semidirect
233. #88054C23semidirect
234. C8×Dic13C23semidirect
235. C8×Dic13C23semidirect
236. C4⋊#1055C23semidirect
237. C4⋊#1055C23semidirect
238. #88043C23semidirect
239. C4×#1055C23semidirect
283. D4×D13M16semidirect
394. #2974D13direct (N × H)
433. D4×C13C2×M16semidirect
453. C22⋊D13C2×M16semidirect
472. D52C2×M16semidirect
533. #436C2×D13semidirect
541. #435C2×D13semidirect
547. C8×D4C2×D13semidirect
552. #432C2×D13semidirect
558. #431C2×D13semidirect
566. #407C2×D13semidirect
577. C2×C22⋊C8C2×D13semidirect
657. C2×M16C22×D13semidirect
665. C22×C8C22×D13semidirect
744. C4⋊C8C22×D13semidirect
745. C4⋊C8C22×D13semidirect
761. C22⋊C8C22×D13semidirect
762. C22⋊C8C22×D13semidirect
765. #97C22×D13semidirect
769. C4×C8C22×D13semidirect
779. D13#2974direct (N × H)
924. C13C2×#2974semidirect
963. D4M16×D13semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D132
#131238732
#131238722
#131238712
#131238702
#131238692
#131238682
#131238672
#131238662
D13×#4362
D13×#4352
C8×D4×D132
D13×#4322
D13×#4312
D13×#4072
C2×D13×C22⋊C82
C13×#29742
C2×#297413