Finite Group Databasebeta

← #16792939

Subgroups — #16792939

Order 3328.

1098 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131735C212yesmaximal, complemented
2#13130099C212yesmaximal, complemented
3#13130098C212yesmaximal, complemented
4#13130090C212yesmaximal
5#13130089C212yesmaximal
6#13130078C212yesmaximal, complemented
7#13130070C212yesmaximal
8C2×#11719277C211yesmaximal, characteristic
9C22×Q8×D13C411yescharacteristic
10C2×C4×Q8×C13C411yescharacteristic
11C2×Q8×Dic13C2211yescharacteristic
12#11719277—28no—
13C2×#88146C411yescharacteristic
14C2×#88146C2211yescharacteristic
15C2×#88146C2211yescharacteristic
16C2×#88141C411yescharacteristic
17C2×#88141C411yescharacteristic
18C2×#88141C2211yescharacteristic
19C2×#88126C411yescharacteristic
20C2×#88126C411yescharacteristic
21C2×#88126C2211yescharacteristic
22C2×C4×Dic26C411yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C2×C4×Dic26C2211yescharacteristic
25#11719130C2214yes—
26#11719128C2214yes—
27#11719125C2214yes—
28#11719078—28no—
29#11718287C2214yes—
30#11718286C2214yes—
31#11718285C2214yes—
32#11718285C2214yes—
33C22×Q8×C13C2×C411yescharacteristic
34C2×Q8×D13—24no—
35C2×Q8×D13—24no—
36C2×Q8×D13—24no—
37C22×C4×D13C2×C411yescharacteristic
38C22×C4×D13C2×C411yescharacteristic
39C22×C4×D13C2×C411yescharacteristic
40C22×Dic26C2×C411yescharacteristic
41C22×Dic26C2×C411yescharacteristic
42C22×Dic26C2×C411yescharacteristic
43C4×Q8×C13—24no—
44C2×C13×C4⋊C4C2×C411yescharacteristic
45C2×C13×C4⋊C4C2×C411yescharacteristic
46C2×C13×C4⋊C4C2×C411yescharacteristic
47C2×C42×C13C2×C411yescharacteristic
48C2×C42×C13C2×C411yescharacteristic
49C2×C42×C13C2×C411yescharacteristic
50Q8×Dic13—24no—
51C2×#6103C2×C411yescharacteristic
52C2×#6103C2×C411yescharacteristic
53C2×#6103C2×C411yescharacteristic
54C2×#6103C2311yescharacteristic
55C2×C4⋊Dic13C2×C411yescharacteristic
56C2×C4⋊Dic13C2311yescharacteristic
57C2×C4⋊Dic13C2311yescharacteristic
58C2×#6101C2×C411yescharacteristic
59C2×#6101C2×C411yescharacteristic
60C2×#6101C2×C411yescharacteristic
61C2×#6101C2×C411yescharacteristic
62C2×#6101C2×C411yescharacteristic
63C2×#6101C2311yescharacteristic
64C2×C4×Dic13C2×C411yescharacteristic
65C2×C4×Dic13C2×C411yescharacteristic
66C2×C4×Dic13C2×C411yescharacteristic
67C2×C4×Dic13C2×C411yescharacteristic
68C2×C4×Dic13C2×C411yescharacteristic
69C2×C4×Dic13C2×C411yescharacteristic
70C2×C4×Dic13C2311yescharacteristic
71C2×C4×Dic13C2311yescharacteristic
72C2×C4×Dic13C2311yescharacteristic
73#88146—24no—
74#88146—24no—
75#88146—24no—
76#88141—24no—
77#88141—24no—
78#88141D418yes—
79#88126—24no—
80#88126—24no—
81#88126—24no—
82C4×Dic26—24no—
83C4×Dic26—24no—
84C4×Dic26—24no—
85C22⋊#1057C2318yes—
86#88112—24no—
87#88112—24no—
88#88110—24no—
89#88110—24no—
90C4⋊#1057—24no—
91C4×#1057—24no—
92#17371—131nomaximal, Sylow
93C23×D13C22×C411yescharacteristic
94C2×Q8×C13—22no—
95C2×Q8×C13—22no—
96C2×Q8×C13—22no—
97C22×C4×C13C22×C411yescharacteristic
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C22×C411yescharacteristic
100C22×C4×C13C22×C411yescharacteristic
101C22×C4×C13C22×C411yescharacteristic
102C22×C4×C13C22×C411yescharacteristic
103C22×C4×C13C22×C411yescharacteristic
104C22×Dic13C22×C411yescharacteristic
105C22×Dic13C22×C411yescharacteristic
106C22×Dic13C22×C411yescharacteristic
107C22×Dic13C22×C411yescharacteristic
108C22×Dic13C22×C411yescharacteristic
109C22×Dic13C22×C411yescharacteristic
110C22×Dic13C2411yescharacteristic
111Q8×D13—232no—
112C2×C4×D13—22no—
113C2×C4×D13—22no—
114C2×C4×D13—22no—
115C2×C4×D13—22no—
116C2×C4×D13—22no—
117C2×C4×D13—22no—
118C2×C4×D13—22no—
119C2×C4×D13—22no—
120C2×C4×D13M1614yes—
121C2×Dic26—22no—
122C2×Dic26—22no—
123C2×Dic26—22no—
124C2×Dic26—22no—
125C2×Dic26—22no—
126C2×Dic26—22no—
127C2×Dic26—22no—
128C2×Dic26C22⋊C414yes—
129C2×Dic26M1614yes—
130C2×#1057—28no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4C22⋊C414yes—
134C42×C13—22no—
135C42×C13—22no—
136C42×C13—22no—
137#6103—22no—
138#6103—22no—
139#6103—22no—
140#6103—22no—
141C4⋊Dic13—22no—
142C4⋊Dic13—22no—
143C4⋊Dic13—22no—
144#6101—22no—
145#6101—22no—
146#6101—22no—
147#6101—22no—
148#6101C22⋊C414yes—
149#6101C22⋊C414yes—
150C4×Dic13—22no—
151C4×Dic13—22no—
152C4×Dic13—22no—
153C4×Dic13—22no—
154C4×Dic13—22no—
155C4×Dic13—22no—
156C4×Dic13C2×D414yes—
157C4×Dic13C2×D414yes—
158C4×Dic13C2×D414yes—
159C2×#519—131no—
160#2983—132no—
161#1467—132no—
162#1467—132no—
163#1464—132no—
164#1464—132no—
165#1461—132no—
166#1458—132no—
167C23×C13C23×C411yescharacteristic
168C22×D13—21no—
169C22×D13—21no—
170C22×D13—41no—
171C22×D13—41no—
172C22×D13C2×M1612yes—
173Q8×C13—28no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13C2×C22⋊C412yes—
187C2×C4×C13C2×C22⋊C412yes—
188C2×C4×C13C2×C22⋊C412yes—
189C2×C4×C13C2×M1612yes—
190C2×C4×C13C2×M1612yes—
191C2×Dic13—21no—
192C2×Dic13—21no—
193C2×Dic13—21no—
194C2×Dic13—21no—
195C2×Dic13—21no—
196C2×Dic13—21no—
197C2×Dic13—41no—
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—41no—
201C2×Dic13C2×C22⋊C412yes—
202C2×Dic13C2×C22⋊C412yes—
203C2×Dic13C2×C22⋊C412yes—
204C2×Dic13C2×M1612yes—
205C2×Dic13C2×M1612yes—
206C2×Dic13C2×M1612yes—
207C2×Dic13C22×D412yes—
208C4×D13—28no—
209C4×D13—28no—
210C4×D13—28no—
211Dic26—28no—
212Dic26—28no—
213Dic26—28no—
214#1057—48no—
215C23×Q8—131no—
216#519—268no—
217C2×C4×Q8—131no—
218C2×C4×Q8—131no—
219C2×C4×Q8—131no—
220C2×C4×Q8—131no—
221C2×C4×Q8—131no—
222C2×C4×Q8—131no—
223C2×C4×Q8—131no—
224C2×C4×Q8#26111yescharacteristic
225C2×#117—131no—
226C2×#117—131no—
227C2×#117—131no—
228C2×#117—131no—
229C2×#117—131no—
230C2×#117—131no—
231#446—268no—
232#432—134no—
233#432—134no—
234#431—134no—
235#324—134no—
236#324—134no—
237#324—134no—
238#323—134no—
239C22×C13—21no—
240C22×C13—21no—
241C22×C13C22×C22⋊C411yescharacteristic
242C22×C13C22×M1611yescharacteristic
243C22×C13C22×M1611yescharacteristic
244C2×D13—22no—
245C2×D13—42no—
246C2×D13—41no—
247C2×D13—41no—
248C2×D13—42no—
249C4×C13—22no—
250C4×C13—22no—
251C4×C13—22no—
252C4×C13—22no—
253C4×C13—22no—
254C4×C13—41no—
255C4×C13—41no—
256Dic13—22no—
257Dic13—22no—
258Dic13—22no—
259Dic13—22no—
260Dic13—41no—
261Dic13—41no—
262Dic13#40714yes—
263C22×Q8—131no—
264C22×Q8—131no—
265C22×Q8—131no—
266C22×Q8—264no—
267C22×Q8—264no—
268C22×Q8—264no—
269C22×Q8C2×#26111yescharacteristic
270C23×C4—131no—
271C23×C4—131no—
272C23×C4—131no—
273C4×Q8—24no—
274C4×Q8—138no—
275C4×Q8—264no—
276C4×Q8—264no—
277C4×Q8—264no—
278C4×Q8—264no—
279C4×Q8—264no—
280C4×Q8—264no—
281#117—264no—
282#117—264no—
283#117—264no—
284#117—264no—
285#117—264no—
286#117—264no—
287C2×C4⋊C4—131no—
288C2×C4⋊C4—131no—
289C2×C4⋊C4—131no—
290C2×C4⋊C4—131no—
291C2×C4⋊C4—131no—
292C2×C4⋊C4—131no—
293C2×C4⋊C4—131no—
294C2×C4⋊C4—131no—
295C2×C4⋊C4—131no—
296C2×C4⋊C4C2×#26111yescharacteristic
297C2×C4⋊C4C2×#26111yescharacteristic
298C2×C4⋊C4C2×#26111yescharacteristic
299C2×C22⋊C4—131no—
300C2×C22⋊C4—131no—
301C2×C22⋊C4—131no—
302C2×C22⋊C4—131no—
303C2×C42—131no—
304C2×C42—131no—
305C2×C42—131no—
306C2×C42—131no—
307C2×C42—131no—
308C2×C42—131no—
309C2×C42—131no—
310C2×C42—131no—
311C2×C42—131no—
312C2×C42C2×#26111yescharacteristic
313C2×C42C2×#26111yescharacteristic
314C2×C42C2×#26111yescharacteristic
315C4⋊C8—264no—
316C4⋊C8—264no—
317C4⋊C8—264no—
318C22⋊C8—138no—
319#97—264no—
320#97—264no—
321C4×C8—264no—
322C2×C13—21no—
323C2×C13—21no—
324C2×C13C2×#40711yescharacteristic
325C2×C13#288411yescharacteristic
326C2×C13#288911yescharacteristic
327D13—42no—
328C24—131no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—134no—
333C2×Q8—134no—
334C2×Q8—262no—
335C2×Q8—262no—
336C2×Q8—262no—
337C2×Q8—262no—
338C2×Q8—262no—
339C2×Q8—262no—
340C2×Q8—2632no—
341C2×Q8—262no—
342C22×C4—131no—
343C22×C4—131no—
344C22×C4—131no—
345C22×C4—131no—
346C22×C4—131no—
347C22×C4—134no—
348C22×C4—131no—
349C22×C4—131no—
350C22×C4—262no—
351C22×C4—262no—
352C22×C4—262no—
353C22×C4—262no—
354C22×C4—262no—
355C22×C4—262no—
356C22×C4—262no—
357C22×C4—262no—
358C22×C4C22×#26111yescharacteristic
359C22×C4C22×#26111yescharacteristic
360C22×C4C22×#26111yescharacteristic
361C22×C4C22×#26111yescharacteristic
362C22×C4C22×#26111yescharacteristic
363C22×C4C22×#26111yescharacteristic
364C22×C4C22×#26111yescharacteristic
365C2×C8—268no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—134no—
369C4⋊C4—134no—
370C4⋊C4—262no—
371C4⋊C4—262no—
372C4⋊C4—262no—
373C4⋊C4—262no—
374C4⋊C4—262no—
375C4⋊C4—262no—
376C4⋊C4—262no—
377C4⋊C4C22⋊#26114yes—
378C22⋊C4—262no—
379C22⋊C4—262no—
380C22⋊C4—262no—
381C22⋊C4—262no—
382C42—22no—
383C42—22no—
384C42—22no—
385C42—134no—
386C42—134no—
387C42—134no—
388C42—262no—
389C42—262no—
390C42—262no—
391C42—262no—
392C42—262no—
393C42—262no—
394C13#1737111yescharacteristic, complemented, Sylow
395C23—132no—
396C23—261no—
397C23—261no—
398C23—521no—
399C23—521no—
400C23C23×#26111yescharacteristic
401Q8—28no—
402Q8—268no—
403Q8—268no—
404Q8—268no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—132no—
418C2×C4—132no—
419C2×C4—132no—
420C2×C4—132no—
421C2×C4—132no—
422C2×C4—132no—
423C2×C4—132no—
424C2×C4—268no—
425C2×C4—268no—
426C2×C4—268no—
427C2×C4—261no—
428C2×C4—261no—
429C2×C4—261no—
430C2×C4—261no—
431C2×C4—261no—
432C2×C4—261no—
433C2×C4—521no—
434C2×C4—521no—
435C2×C4—521no—
436C2×C4—521no—
437C2×C4D13⋊M1612yes—
438C2×C4D13⋊M1612yes—
439C2×C4C2×C22⋊#26112yes—
440C2×C4C2×C22⋊#26112yes—
441C2×C4C2×C22⋊#26112yes—
442C8—528no—
443C22—21no—
444C22—21no—
445C22—262no—
446C22—522no—
447C22—522no—
448C22—521no—
449C22—521no—
450C22C2×D13⋊M1611yescharacteristic
451C22C2×D13⋊M1611yescharacteristic
452C22C22×C22⋊#26111yescharacteristic
453C4—22no—
454C4—22no—
455C4—22no—
456C4—22no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—134no—
461C4—262no—
462C4—262no—
463C4—262no—
464C4—262no—
465C4—521no—
466C4—521no—
467C2—21no—
468C2—21no—
469C2—522no—
470C2D13⋊#40711yescharacteristic
471C2#1313143711yescharacteristic
472C2#1313144811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22×C4
cosocleC22×Dic13C24
hypercenterC2×C4×Q8#261
hypocenterC13#17371
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #13131735C2semidirect
2. #13130099C2semidirect
3. #13130098C2semidirect
6. #13130078C2semidirect
394. C13#17371semidirect

Maximal subgroups

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

subgroupindex
#131317352
#131300992
#131300982
#131300902
#131300892
#131300782
#131300702
C2×#117192772
#1737113