Finite Group Databasebeta

← C13×#14052 #15700391

Subgroups — C13×#14052 #15700391

Order 3328.

2266 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
1C22×C13×C22⋊Q8C211yesmaximal, characteristic
2C2×C13×#391C211yesmaximal, characteristic, complemented
3C2×C13×#385C211yesmaximal, characteristic
4C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
5C22×C13×#95C211yesmaximal, characteristic
6C13×#1446C211yesmaximal, characteristic, complemented
7C13×#1445C211yesmaximal, characteristic, complemented
8C13×#1441C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1436C211yesmaximal, characteristic, complemented
11C13×#1436C211yesmaximal, characteristic, complemented
12C13×C4⋊#95C211yesmaximal, characteristic, complemented
13C13×C22⋊#95C211yesmaximal, characteristic
14C13×C22⋊#95C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C2×C13×C22⋊Q8—24no—
21C2×C13×C22⋊Q8—24no—
22C2×C13×C22⋊Q8C418yescomplemented
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C13×#391—24no—
35C13×#385—24no—
36C4×C13×C22⋊C4—24no—
37C2×C13×#95—24no—
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C2×C13×#95C2211yescharacteristic
58C25×C13C2311yescharacteristic
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—41no—
64C22×Q8×C13—41no—
65C22×Q8×C13C2×C414yescomplemented
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—22no—
72C23×C4×C13—22no—
73C23×C4×C13—22no—
74C23×C4×C13—22no—
75C23×C4×C13—22no—
76C23×C4×C13—22no—
77C23×C4×C13—22no—
78C23×C4×C13—22no—
79C23×C4×C13—41no—
80C23×C4×C13—41no—
81C23×C4×C13—41no—
82C23×C4×C13—41no—
83C23×C4×C13—41no—
84C23×C4×C13—41no—
85C23×C4×C13C2×C414yes—
86C23×C4×C13Q814yescomplemented
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C23×C4×C13C2311yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C13×C22⋊Q8—232no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—22no—
109C2×C13×C4⋊C4—22no—
110C2×C13×C4⋊C4—22no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—41no—
113C2×C13×C4⋊C4—41no—
114C2×C13×C4⋊C4C2×C414yescomplemented
115C2×C13×C4⋊C4C2×C414yescomplemented
116C2×C13×C4⋊C4C2×C414yescomplemented
117C2×C13×C22⋊C4—22no—
118C2×C13×C22⋊C4—22no—
119C2×C13×C22⋊C4—22no—
120C2×C13×C22⋊C4—22no—
121C2×C13×C22⋊C4—22no—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4—22no—
124C2×C13×C22⋊C4C2×C414yes—
125C2×C13×C22⋊C4C2×C414yes—
126C2×C13×C22⋊C4D414yes—
127C2×C13×C22⋊C4D414yes—
128C2×C13×C22⋊C4Q814yescomplemented
129C2×C42×C13—22no—
130C2×C42×C13—22no—
131C2×C42×C13—22no—
132C2×C42×C13—22no—
133C2×C42×C13—41no—
134C2×C42×C13—41no—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—22no—
138C13×#95—22no—
139C13×#95—22no—
140C13×#95—22no—
141C13×#95—22no—
142C13×#95—22no—
143C13×#95—22no—
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95—22no—
148C13×#95—41no—
149C13×#95—41no—
150C13×#95—41no—
151C13×#95—41no—
152C13×#95—41no—
153C13×#95—41no—
154C13×#95D414yes—
155#14052C1311yesmaximal, characteristic, direct product factor, Sylow
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13C22×C412yes—
165C24×C13C2×D412yes—
166C24×C13C2×D412yes—
167C24×C13C2×Q812yes—
168C24×C13C2×Q812yes—
169C24×C13#4112yes—
170C24×C13#4112yes—
171C24×C13C2411yescharacteristic
172C2×Q8×C13—28no—
173C2×Q8×C13—28no—
174C2×Q8×C13—44no—
175C2×Q8×C13—44no—
176C2×Q8×C13—44no—
177C2×Q8×C13—44no—
178C2×Q8×C13—44no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—28no—
196C22×C4×C13—28no—
197C22×C4×C13—28no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—28no—
247C22×C4×C13—28no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—44no—
263C22×C4×C13—44no—
264C22×C4×C13—44no—
265C22×C4×C13—44no—
266C22×C4×C13—44no—
267C22×C4×C13—44no—
268C22×C4×C13—44no—
269C22×C4×C13—44no—
270C22×C4×C13—44no—
271C22×C4×C13—44no—
272C22×C4×C13—44no—
273C22×C4×C13—44no—
274C22×C4×C13—44no—
275C22×C4×C13—44no—
276C22×C4×C13—44no—
277C22×C4×C13—44no—
278C22×C4×C13C22×C412yes—
279C22×C4×C13C22×C412yes—
280C22×C4×C13C22×C412yes—
281C22×C4×C13C22×C412yes—
282C22×C4×C13C22×C412yes—
283C22×C4×C13C22×C412yes—
284C22×C4×C13C2×D412yes—
285C22×C4×C13C2×D412yes—
286C22×C4×C13C2×D412yes—
287C22×C4×C13C2×D412yes—
288C22×C4×C13C2×D412yes—
289C22×C4×C13C2×D412yes—
290C22×C4×C13C2×D412yes—
291C22×C4×C13C2×Q812yes—
292C22×C4×C13C2×Q812yes—
293C22×C4×C13C2×Q812yes—
294C22×C4×C13C2×Q812yes—
295C22×C4×C13#4112yes—
296C22×C4×C13#4112yes—
297C22×C4×C13#4112yes—
298C13×C4⋊C4—28no—
299C13×C4⋊C4—28no—
300C13×C4⋊C4—28no—
301C13×C4⋊C4—44no—
302C13×C4⋊C4—44no—
303C13×C22⋊C4—28no—
304C13×C22⋊C4—28no—
305C13×C22⋊C4—44no—
306C13×C22⋊C4C22⋊C4116yes—
307C42×C13—44no—
308C42×C13—44no—
309C22×C22⋊Q8C2×C1311yescharacteristic
310C2×#391C2×C1311yescharacteristic, complemented
311C2×#385C2×C1311yescharacteristic
312C2×C4×C22⋊C4C2×C1311yescharacteristic
313C22×#95C2×C1311yescharacteristic
314#1446C2×C1311yescharacteristic, complemented
315#1445C2×C1311yescharacteristic, complemented
316#1441C2×C1311yescharacteristic, complemented
317#1441C2×C1311yescharacteristic, complemented
318#1436C2×C1311yescharacteristic, complemented
319#1436C2×C1311yescharacteristic, complemented
320C4⋊#95C2×C1311yescharacteristic, complemented
321C22⋊#95C2×C1311yescharacteristic
322C22⋊#95C2×C1311yescharacteristic
323C22⋊#95C2×C1311yescharacteristic
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13—22no—
341C23×C13—22no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—22no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—22no—
349C23×C13—22no—
350C23×C13—22no—
351C23×C13—22no—
352C23×C13C2×C22⋊C414yes—
353C23×C13C4×Q814yes—
354C23×C13C4×Q814yes—
355C23×C13C22⋊Q814yes—
356C23×C13C22⋊Q814yes—
357C23×C13#12414yes—
358C23×C13C4⋊Q814yes—
359C23×C13C23×C411yescharacteristic
360C23×C13C22×D411yescharacteristic
361C23×C13C22×D411yescharacteristic
362C23×C13C22×D411yescharacteristic
363C23×C13C22×Q811yescharacteristic
364C23×C13C22×Q811yescharacteristic
365C23×C13C2×#4111yescharacteristic
366C23×C13C2×#4111yescharacteristic
367C23×C13C2×#4111yescharacteristic
368C23×C13C2×#4111yescharacteristic
369C23×C13C2×#4111yescharacteristic
370C23×C13H(5,𝔽2)11yescharacteristic
371C23×C13H(5,𝔽2)11yescharacteristic
372C23×C13H(5,𝔽2)11yescharacteristic
373C23×C132−1+411yescharacteristic
374Q8×C13—416no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—22no—
402C2×C4×C13—22no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—22no—
406C2×C4×C13—22no—
407C2×C4×C13—22no—
408C2×C4×C13—22no—
409C2×C4×C13—22no—
410C2×C4×C13—22no—
411C2×C4×C13—22no—
412C2×C4×C13—22no—
413C2×C4×C13—22no—
414C2×C4×C13—22no—
415C2×C4×C13—22no—
416C2×C4×C13—22no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—22no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
422C2×C4×C13—22no—
423C2×C4×C13—416no—
424C2×C4×C13—416no—
425C2×C4×C13—416no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
453C2×C4×C13—41no—
454C2×C4×C13—41no—
455C2×C4×C13—41no—
456C2×C4×C13—41no—
457C2×C4×C13—41no—
458C2×C4×C13—41no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—41no—
463C2×C4×C13—41no—
464C2×C4×C13—41no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—41no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13C2×C22⋊C414yes—
473C2×C4×C13C2×C22⋊C414yes—
474C2×C4×C13C4×D414yes—
475C2×C4×C13C22⋊Q814yescomplemented
476C23×Q8C22×C1311yescharacteristic
477C24×C4C22×C1311yescharacteristic
478C24×C4C22×C1311yescharacteristic
479C24×C4C22×C1311yescharacteristic
480C2×C22⋊Q8—24no—
481C2×C22⋊Q8—24no—
482C2×C22⋊Q8C4×C1318yescomplemented
483C22×C4⋊C4C22×C1311yescharacteristic
484C22×C4⋊C4C22×C1311yescharacteristic
485C22×C4⋊C4C22×C1311yescharacteristic
486C22×C4⋊C4C22×C1311yescharacteristic
487C22×C4⋊C4C22×C1311yescharacteristic
488C22×C22⋊C4C22×C1311yescharacteristic
489C22×C22⋊C4C22×C1311yescharacteristic
490C22×C22⋊C4C22×C1311yescharacteristic
491C22×C22⋊C4C22×C1311yescharacteristic
492C22×C42C22×C1311yescharacteristic
493C22×C42C22×C1311yescharacteristic
494#391—24no—
495#385—24no—
496C4×C22⋊C4—24no—
497C2×#95—24no—
498C2×#95C22×C1311yescharacteristic
499C2×#95C22×C1311yescharacteristic
500C2×#95C22×C1311yescharacteristic
501C2×#95C22×C1311yescharacteristic
502C2×#95C22×C1311yescharacteristic
503C2×#95C22×C1311yescharacteristic
504C2×#95C22×C1311yescharacteristic
505C2×#95C22×C1311yescharacteristic
506C2×#95C22×C1311yescharacteristic
507C2×#95C22×C1311yescharacteristic
508C2×#95C22×C1311yescharacteristic
509C2×#95C22×C1311yescharacteristic
510C2×#95C22×C1311yescharacteristic
511C2×#95C22×C1311yescharacteristic
512C2×#95C22×C1311yescharacteristic
513C2×#95C22×C1311yescharacteristic
514C2×#95C22×C1311yescharacteristic
515C2×#95C22×C1311yescharacteristic
516C2×#95C22×C1311yescharacteristic
517C2×#95C22×C1311yescharacteristic
518C22×C13—24no—
519C22×C13—24no—
520C22×C13—24no—
521C22×C13—24no—
522C22×C13—24no—
523C22×C13—24no—
524C22×C13—24no—
525C22×C13—24no—
526C22×C13—24no—
527C22×C13—24no—
528C22×C13—24no—
529C22×C13—24no—
530C22×C13—24no—
531C22×C13—24no—
532C22×C13#39118yescomplemented
533C22×C13C22×C22⋊C411yescharacteristic
534C22×C13C2×C4×D411yescharacteristic
535C22×C13C2×C4×Q811yescharacteristic
536C22×C13C2×C4×Q811yescharacteristic
537C22×C13C4×#4111yescharacteristic
538C22×C13#51811yescharacteristic
539C22×C13#52011yescharacteristic
540C22×C13C2×C22⋊Q811yescharacteristic
541C22×C13C2×C22⋊Q811yescharacteristic
542C22×C13C2×C22⋊Q811yescharacteristic
543C22×C13#52511yescharacteristic
544C22×C13C2×#12411yescharacteristic
545C22×C13#52911yescharacteristic
546C22×C13C2×C4⋊Q811yescharacteristic
547C22×C13#53311yescharacteristic
548C22×C13#53811yescharacteristic
549C22×C13#53911yescharacteristic
550C22×C13#54311yescharacteristic
551C22×C13#54411yescharacteristic
552C22×C13D4211yescharacteristic
553C22×C13D4211yescharacteristic
554C22×C13#54611yescharacteristic
555C22×C13#54611yescharacteristic
556C22×C13#54611yescharacteristic
557C22×C13#54611yescharacteristic
558C22×C13#54611yescharacteristic
559C22×C13#54711yescharacteristic
560C22×C13#54711yescharacteristic
561C22×C13D4×Q811yescharacteristic
562C22×C13#55111yescharacteristic
563C22×C13#55111yescharacteristic
564C22×C13#55211yescharacteristic
565C22×C13#55411yescharacteristic
566C22×C13#55411yescharacteristic
567C22×C13#55411yescharacteristic
568C4×C13—24no—
569C4×C13—24no—
570C4×C13—24no—
571C4×C13—24no—
572C4×C13—42no—
573C4×C13—42no—
574C4×C13—42no—
575C4×C13—42no—
576C4×C13—42no—
577C4×C13—42no—
578C4×C13—42no—
579C4×C13—42no—
580C4×C13—81no—
581C4×C13—81no—
582C25C23×C1311yescharacteristic
583C22×Q8—22no—
584C22×Q8—22no—
585C22×Q8—22no—
586C22×Q8—22no—
587C22×Q8—41no—
588C22×Q8—41no—
589C22×Q8C2×C4×C1314yescomplemented
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—22no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—41no—
604C23×C4—41no—
605C23×C4—41no—
606C23×C4—41no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4C2×C4×C1314yes—
610C23×C4Q8×C1314yescomplemented
611C23×C4C23×C1311yescharacteristic
612C23×C4C23×C1311yescharacteristic
613C23×C4C23×C1311yescharacteristic
614C23×C4C23×C1311yescharacteristic
615C23×C4C23×C1311yescharacteristic
616C23×C4C23×C1311yescharacteristic
617C23×C4C23×C1311yescharacteristic
618C23×C4C23×C1311yescharacteristic
619C23×C4C23×C1311yescharacteristic
620C23×C4C23×C1311yescharacteristic
621C23×C4C23×C1311yescharacteristic
622C23×C4C23×C1311yescharacteristic
623C23×C4C23×C1311yescharacteristic
624C23×C4C23×C1311yescharacteristic
625C22⋊Q8—232no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4C2×C4×C1314yescomplemented
639C2×C4⋊C4C2×C4×C1314yescomplemented
640C2×C4⋊C4C2×C4×C1314yescomplemented
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4C2×C4×C1314yes—
649C2×C22⋊C4C2×C4×C1314yes—
650C2×C22⋊C4D4×C1314yes—
651C2×C22⋊C4D4×C1314yes—
652C2×C22⋊C4Q8×C1314yescomplemented
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—22no—
656C2×C42—22no—
657C2×C42—41no—
658C2×C42—41no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—22no—
669#95—22no—
670#95—22no—
671#95—22no—
672#95—41no—
673#95—41no—
674#95—41no—
675#95—41no—
676#95—41no—
677#95—41no—
678#95D4×C1314yes—
679C2×C13—28no—
680C2×C13C2×#39111yescharacteristic
681C2×C13C4×C22⋊Q811yescharacteristic
682C2×C13#232911yescharacteristic
683C2×C13D4×C22⋊C411yescharacteristic
684C2×C13#233911yescharacteristic
685C2×C13#236011yescharacteristic
686C2×C13#236811yescharacteristic
687C2×C13#243711yescharacteristic
688C2×C13#243811yescharacteristic
689C2×C13#244011yescharacteristic
690C2×C13#244911yescharacteristic
691C2×C13#245011yescharacteristic
692C2×C13#247211yescharacteristic
693C2×C13#248811yescharacteristic
694C2×C13#254911yescharacteristic
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C22×C4×C1312yes—
704C24C2×D4×C1312yes—
705C24C2×D4×C1312yes—
706C24C2×Q8×C1312yes—
707C24C2×Q8×C1312yes—
708C24C13×#4112yes—
709C24C13×#4112yes—
710C24C24×C1311yescharacteristic
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—44no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—44no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4C22×C4×C1312yes—
818C22×C4C22×C4×C1312yes—
819C22×C4C22×C4×C1312yes—
820C22×C4C22×C4×C1312yes—
821C22×C4C22×C4×C1312yes—
822C22×C4C22×C4×C1312yes—
823C22×C4C2×D4×C1312yes—
824C22×C4C2×D4×C1312yes—
825C22×C4C2×D4×C1312yes—
826C22×C4C2×D4×C1312yes—
827C22×C4C2×D4×C1312yes—
828C22×C4C2×D4×C1312yes—
829C22×C4C2×D4×C1312yes—
830C22×C4C2×Q8×C1312yes—
831C22×C4C2×Q8×C1312yes—
832C22×C4C2×Q8×C1312yes—
833C22×C4C2×Q8×C1312yes—
834C22×C4C13×#4112yes—
835C22×C4C13×#4112yes—
836C22×C4C13×#4112yes—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—44no—
845C22⋊C4C13×C22⋊C4116yes—
846C42—44no—
847C42—44no—
848C13#1405211yescharacteristic, direct product factor, Sylow
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23C2×C13×C22⋊C414yes—
878C23C4×Q8×C1314yes—
879C23C4×Q8×C1314yes—
880C23C13×C22⋊Q814yes—
881C23C13×C22⋊Q814yes—
882C23C13×#12414yes—
883C23C13×C4⋊Q814yes—
884C23C23×C4×C1311yescharacteristic
885C23C22×D4×C1311yescharacteristic
886C23C22×D4×C1311yescharacteristic
887C23C22×D4×C1311yescharacteristic
888C23C22×Q8×C1311yescharacteristic
889C23C22×Q8×C1311yescharacteristic
890C23C2×C13×#4111yescharacteristic
891C23C2×C13×#4111yescharacteristic
892C23C2×C13×#4111yescharacteristic
893C23C2×C13×#4111yescharacteristic
894C23C2×C13×#4111yescharacteristic
895C23C13×H(5,𝔽2)11yescharacteristic
896C23C13×H(5,𝔽2)11yescharacteristic
897C23C13×H(5,𝔽2)11yescharacteristic
898C23C13×2−1+411yescharacteristic
899Q8—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—416no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4C2×C13×C22⋊C414yes—
998C2×C4C2×C13×C22⋊C414yes—
999C2×C4C4×D4×C1314yes—
1000C2×C4C13×C22⋊Q814yescomplemented
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22C13×#39118yescomplemented
1016C22C22×C13×C22⋊C411yescharacteristic
1017C22C2×C4×D4×C1311yescharacteristic
1018C22C2×C4×Q8×C1311yescharacteristic
1019C22C2×C4×Q8×C1311yescharacteristic
1020C22C4×C13×#4111yescharacteristic
1021C22C13×#51811yescharacteristic
1022C22C13×#52011yescharacteristic
1023C22C2×C13×C22⋊Q811yescharacteristic
1024C22C2×C13×C22⋊Q811yescharacteristic
1025C22C2×C13×C22⋊Q811yescharacteristic
1026C22C13×#52511yescharacteristic
1027C22C2×C13×#12411yescharacteristic
1028C22C13×#52911yescharacteristic
1029C22C2×C13×C4⋊Q811yescharacteristic
1030C22C13×#53311yescharacteristic
1031C22C13×#53811yescharacteristic
1032C22C13×#53911yescharacteristic
1033C22C13×#54311yescharacteristic
1034C22C13×#54411yescharacteristic
1035C22D42×C1311yescharacteristic
1036C22D42×C1311yescharacteristic
1037C22C13×#54611yescharacteristic
1038C22C13×#54611yescharacteristic
1039C22C13×#54611yescharacteristic
1040C22C13×#54611yescharacteristic
1041C22C13×#54611yescharacteristic
1042C22C13×#54711yescharacteristic
1043C22C13×#54711yescharacteristic
1044C22D4×Q8×C1311yescharacteristic
1045C22C13×#55111yescharacteristic
1046C22C13×#55111yescharacteristic
1047C22C13×#55211yescharacteristic
1048C22C13×#55411yescharacteristic
1049C22C13×#55411yescharacteristic
1050C22C13×#55411yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—24no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—81no—
1065C2—28no—
1066C2C2×C13×#39111yescharacteristic
1067C2C4×C13×C22⋊Q811yescharacteristic
1068C2C13×#232911yescharacteristic
1069C2D4×C13×C22⋊C411yescharacteristic
1070C2C13×#233911yescharacteristic
1071C2C13×#236011yescharacteristic
1072C2C13×#236811yescharacteristic
1073C2C13×#243711yescharacteristic
1074C2C13×#243811yescharacteristic
1075C2C13×#244011yescharacteristic
1076C2C13×#244911yescharacteristic
1077C2C13×#245011yescharacteristic
1078C2C13×#247211yescharacteristic
1079C2C13×#248811yescharacteristic
1080C2C13×#254911yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#391C2semidirect
6. C13×#1446C2semidirect
7. C13×#1445C2semidirect
8. C13×#1441C2semidirect
9. C13×#1441C2semidirect
10. C13×#1436C2semidirect
11. C13×#1436C2semidirect
12. C13×C4⋊#95C2semidirect
22. C2×C13×C22⋊Q8C4semidirect
65. C22×Q8×C13C2×C4semidirect
86. C23×C4×C13Q8semidirect
114. C2×C13×C4⋊C4C2×C4semidirect
115. C2×C13×C4⋊C4C2×C4semidirect
116. C2×C13×C4⋊C4C2×C4semidirect
128. C2×C13×C22⋊C4Q8semidirect
155. #14052C13direct (N × H)
310. C2×#391C2×C13semidirect
314. #1446C2×C13semidirect
315. #1445C2×C13semidirect
316. #1441C2×C13semidirect
317. #1441C2×C13semidirect
318. #1436C2×C13semidirect
319. #1436C2×C13semidirect
320. C4⋊#95C2×C13semidirect
475. C2×C4×C13C22⋊Q8semidirect
482. C2×C22⋊Q8C4×C13semidirect
532. C22×C13#391semidirect
589. C22×Q8C2×C4×C13semidirect
610. C23×C4Q8×C13semidirect
638. C2×C4⋊C4C2×C4×C13semidirect
639. C2×C4⋊C4C2×C4×C13semidirect
640. C2×C4⋊C4C2×C4×C13semidirect
652. C2×C22⋊C4Q8×C13semidirect
848. C13#14052direct (N × H)
1000. C2×C4C13×C22⋊Q8semidirect
1015. C22C13×#391semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C22⋊Q82
C2×C13×#3912
C2×C13×#3852
C2×C4×C13×C22⋊C42
C22×C13×#952
C13×#14462
C13×#14452
C13×#14412
C13×#14362
C13×C4⋊#952
C13×C22⋊#952
#1405213