Finite Group Databasebeta

← #15864017

Subgroups — #15864017

Order 3328.

1458 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128039C211yesmaximal, characteristic
2C2×#11718901C211yesmaximal, characteristic
3#13117460C212yesmaximal, complemented
4#13115116C218yesmaximal, complemented
5#13114568C212yesmaximal, complemented
6C13×#2311C211yesmaximal, characteristic
7C22×C13×#41C2211yescharacteristic
8C2×C13×#117C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10#11719532—22no—
11#11719532—22no—
12#41×Dic13—24no—
13#11719517—21no—
14#11719503—21no—
15#11719503C2214yes—
16C2×#88180—22no—
17C2×#88180C2212yes—
18C2×#88180C2212yes—
19C13×#391—21no—
20C13×#390—21no—
21C13×#386C2214yes—
22C13×#380—22no—
23#11718901C418yescomplemented
24C2×#88074C2214yes—
25#11718871C2218yes—
26#11718638—22no—
27#11718637—22no—
28#11718634—24no—
29#11718119C2218yes—
30C2×C13×#41—22no—
31C2×C13×#41—22no—
32C2×C13×#41—24no—
33C2×C13×#41C2×C414yes—
34C2×C13×#41Q814yes—
35C22×Q8×C13D411yescharacteristic
36C22×D4×C13D411yescharacteristic
37C22×D4×C13C2312yes—
38C23×C4×C13D412yes—
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C13×#117—24no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4—22no—
47C2×C13×C22⋊C4—24no—
48C2×C13×C22⋊C4C2312yes—
49C2×C42×C13—21no—
50C2×C22⋊Dic13—24no—
51C2×C22⋊Dic13C2314yes—
52C2×C22⋊Dic13C2314yes—
53Q8×Dic13—24no—
54Q8×Dic13—24no—
55D4×Dic13—24no—
56D4×Dic13—24no—
57D4×Dic13—28no—
58D4×Dic13—28no—
59#88180—24no—
60#88180—24no—
61#88180—22no—
62#88180—24no—
63#88180—22no—
64#88180—22no—
65#88180—22no—
66#88180—24no—
67#88180C2×C418yescomplemented
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13D412yes—
72C2×C4⋊Dic13D412yes—
73C2×#6101—28no—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13D414yes—
77C13×#95—24no—
78#88074C2×C4116yescomplemented
79#88071—28no—
80#20890—131nomaximal, Sylow
81C24×C13C2×D412yes—
82C24×C13C2411yescharacteristic
83C13×#41—28no—
84C13×#41—28no—
85C13×#41—28no—
86C13×#41—28no—
87C2×Q8×C13—22no—
88C2×Q8×C13—22no—
89C2×Q8×C13C4⋊C414yescomplemented
90C2×D4×C13—24no—
91C2×D4×C13—24no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C2×D4×C13C4⋊C414yescomplemented
95C2×D4×C13C22×C414yes—
96C2×D4×C13C2×Q814yes—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—24no—
100C22×C4×C13—24no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—82no—
104C22×C4×C13C4⋊C418yescomplemented
105C22×C4×C13C22×C412yes—
106C22×C4×C13C2×D412yes—
107C22×C4×C13C2×D412yes—
108C22×C4×C13C2×D412yes—
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×Q812yes—
112C22×C4×C13#4114yes—
113C22×Dic13—24no—
114C22×Dic13—24no—
115C22×Dic13—24no—
116C22×Dic13C2×D414yes—
117C22×Dic13C2×D414yes—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—42no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—42no—
122C13×C22⋊C4—24no—
123C13×C22⋊C4—84no—
124C42×C13—42no—
125C22⋊Dic13—28no—
126C22⋊Dic13—24no—
127C22⋊Dic13—24no—
128C22⋊Dic13—24no—
129C22⋊Dic13C22×C418yes—
130C4⋊Dic13—24no—
131C4⋊Dic13—24no—
132C4⋊Dic13—28no—
133C4⋊Dic13—22no—
134C4⋊Dic13—22no—
135C4⋊Dic13—22no—
136C4⋊Dic13—22no—
137#6101—88no—
138C4×Dic13—28no—
139C4×Dic13—28no—
140C4×Dic13—24no—
141C4×Dic13—24no—
142#3428—131no—
143C2×#410—131no—
144#2317—132no—
145#2311D1311yescharacteristic
146#1867—138no—
147#1740—132no—
148C23×C13—22no—
149C23×C13—22no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—42no—
153C23×C13—42no—
154C23×C13C2×C4⋊C414yes—
155C23×C13C23×C411yescharacteristic
156C23×C13C22×D411yescharacteristic
157C23×C13C22×D412yes—
158C23×C13C22×Q811yescharacteristic
159C23×C13C2×#4112yes—
160Q8×C13—28no—
161D4×C13—28no—
162D4×C13—28no—
163D4×C13—28no—
164C2×C4×C13—22no—
165C2×C4×C13—22no—
166C2×C4×C13—28no—
167C2×C4×C13—28no—
168C2×C4×C13—48no—
169C2×C4×C13—42no—
170C2×C4×C13—44no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13C2×C4⋊C414yes—
175C2×C4×C13C2×C4⋊C412yes—
176C2×C4×C13C2×C4⋊C412yes—
177C2×C4×C13C4×D414yes—
178C2×C4×C13C4×D414yes—
179C2×C4×C13#12011yescharacteristic
180C2×C4×C13#12012yes—
181C2×C4×C13#12011yescharacteristic
182C2×C4×C13C22⋊Q814yes—
183C2×C4×C13C22⋊Q814yes—
184C2×C4×C13#12312yes—
185C2×C4×C13#12312yes—
186C2×Dic13—28no—
187C2×Dic13—24no—
188C2×Dic13—24no—
189C2×Dic13—44no—
190C2×Dic13—44no—
191C2×Dic13—44no—
192C2×Dic13—44no—
193C2×Dic13—84no—
194C2×Dic13—84no—
195C22×#41C2×D1311yescharacteristic
196#520—262no—
197#520—262no—
198#519—261no—
199#518—134no—
200#518—261no—
201C4×#41—264no—
202C2×#117—132no—
203C2×#117—132no—
204C2×#117—262no—
205C2×#117C2×D1311yescharacteristic
206C22×C4⋊C4C2×D1311yescharacteristic
207#410—138no—
208C2×#99—134no—
209#391—21no—
210#390—21no—
211#389—264no—
212#386C2×D1314yes—
213#385—138no—
214#384—262no—
215#382—262no—
216#380—22no—
217#342—138no—
218C22×C13—22no—
219C22×C13—21no—
220C22×C13—22no—
221C22×C13—21no—
222C22×C13—24no—
223C22×C13—41no—
224C22×C13—41no—
225C22×C13—42no—
226C22×C13—44no—
227C22×C13—42no—
228C22×C13—42no—
229C22×C13—82no—
230C22×C13C22×C4⋊C411yescharacteristic
231C22×C13C2×C4×D412yes—
232C22×C13C2×#12011yescharacteristic
233C22×C13C2×C22⋊Q812yes—
234C22×C13C2×#12311yescharacteristic
235C4×C13—24no—
236C4×C13—82no—
237C4×C13—82no—
238C4×C13#38512yes—
239C4×C13#38512yes—
240C4×C13#38514yes—
241Dic13—48no—
242Dic13—44no—
243Dic13—44no—
244C2×#41—22no—
245C2×#41—22no—
246C2×#41—24no—
247C2×#41Dic2614yes—
248C2×#41C4×D1314yes—
249C22×Q8C22⋊D1311yescharacteristic
250C22×D4C22⋊D1311yescharacteristic
251C22×D4C22×D1312yes—
252C23×C4C22⋊D1312yes—
253C23×C4C22×D1312yes—
254C23×C4C22×D1311yescharacteristic
255C4×Q8—264no—
256C4×Q8—264no—
257C4×D4—268no—
258C4×D4—268no—
259C4×D4—264no—
260C4×D4—264no—
261#117—24no—
262#117—138no—
263#117—264no—
264#117—264no—
265#117—262no—
266#117—262no—
267#117—264no—
268#117—262no—
269#117—262no—
270#117—264no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—132no—
277C2×C4⋊C4—132no—
278C2×C4⋊C4—262no—
279C2×C4⋊C4—262no—
280C2×C4⋊C4—262no—
281C2×C4⋊C4—268no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—134no—
284C2×C22⋊C4—134no—
285C2×C22⋊C4—264no—
286C2×C22⋊C4C22×D1312yes—
287C2×C42—21no—
288C2×C42—134no—
289C2×C42—264no—
290C2×C42—262no—
291#99—1316no—
292#95—24no—
293#95—268no—
294C2×C13—22no—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—22no—
298C2×C13—44no—
299C2×C13C2×#38511yescharacteristic
300C2×C13#302711yescharacteristic
301C2×C13#302811yescharacteristic
302C24C2×C22⋊D1312yes—
303C24C23×D1311yescharacteristic
304#41—28no—
305#41—28no—
306#41—28no—
307#41—28no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8#610114yescomplemented
311C2×D4—24no—
312C2×D4—24no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4#610114yescomplemented
316C2×D4C2×Dic2614yes—
317C2×D4C2×C4×D1314yes—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—82no—
325C22×C4—134no—
326C22×C4—134no—
327C22×C4—264no—
328C22×C4—264no—
329C22×C4—264no—
330C22×C4#610118yescomplemented
331C22×C4C2×Dic2612yes—
332C22×C4C2×C4×D1312yes—
333C22×C4D4×D1312yes—
334C22×C4D4×D1312yes—
335C22×C4#612914yes—
336C22×C4C2×C22⋊D1312yes—
337C22×C4C2×C22⋊D1311yescharacteristic
338C22×C4C2×C22⋊D1311yescharacteristic
339C4⋊C4—42no—
340C4⋊C4—41no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—264no—
344C4⋊C4—264no—
345C4⋊C4—268no—
346C4⋊C4—262no—
347C4⋊C4—262no—
348C4⋊C4—262no—
349C4⋊C4—262no—
350C4⋊C4—1048no—
351C22⋊C4—24no—
352C22⋊C4—84no—
353C22⋊C4—138no—
354C22⋊C4—268no—
355C22⋊C4—264no—
356C22⋊C4—264no—
357C22⋊C4—264no—
358C42—42no—
359C42—268no—
360C42—268no—
361C42—264no—
362C42—264no—
363C13#2089011yescharacteristic, complemented, Sylow
364C23—22no—
365C23—22no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—42no—
370C23C2×#610114yes—
371C23C22×Dic2611yescharacteristic
372C23C22×C4×D1311yescharacteristic
373C23C2×D4×D1312yes—
374C23C2×#612912yes—
375C23C22×C22⋊D1311yescharacteristic
376Q8—28no—
377D4—28no—
378D4—28no—
379D4—28no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—28no—
383C2×C4—28no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—48no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—268no—
391C2×C4—264no—
392C2×C4—264no—
393C2×C4—524no—
394C2×C4—524no—
395C2×C4—524no—
396C2×C4—524no—
397C2×C4—1044no—
398C2×C4—1044no—
399C2×C4#8813214yes—
400C2×C4#8813214yes—
401C2×C4#8813514yes—
402C2×C4#8813514yes—
403C2×C4C2×#610114yes—
404C2×C4C2×#610112yes—
405C2×C4C2×#610112yes—
406C2×C4#8818912yes—
407C2×C4#8818912yes—
408C2×C4#8819111yescharacteristic
409C2×C4#8819112yes—
410C2×C4#8819111yescharacteristic
411C22—21no—
412C22—22no—
413C22—21no—
414C22—22no—
415C22—24no—
416C22—41no—
417C22—41no—
418C22—42no—
419C22—44no—
420C22—42no—
421C22—42no—
422C22—82no—
423C22C2×#8813212yes—
424C22C2×#8813512yes—
425C22C22×#610111yescharacteristic
426C22C2×#8818911yescharacteristic
427C22C2×#8819111yescharacteristic
428C4—24no—
429C4—82no—
430C4—82no—
431C4—528no—
432C4—524no—
433C4—524no—
434C4#1171860712yes—
435C4#1171860712yes—
436C4#1171860714yes—
437C2—21no—
438C2—22no—
439C2—21no—
440C2—22no—
441C2—44no—
442C2C2×#1171860711yescharacteristic
443C2#1312423711yescharacteristic
444C2#1312424111yescharacteristic
subgroupG/H
centerC22C2×#88191
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC13×#2311C2
socleC22×C13C2×#120
prime radicalC22×C13×#41C22
cosocleC24×C13C24
hypercenter#2311D13
hypocenterC13#20890
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2311

Complements

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

NH ≅ G/Ntype
3. #13117460C2semidirect
4. #13115116C2semidirect
5. #13114568C2semidirect
23. #11718901C4semidirect
67. #88180C2×C4semidirect
78. #88074C2×C4semidirect
89. C2×Q8×C13C4⋊C4semidirect
94. C2×D4×C13C4⋊C4semidirect
104. C22×C4×C13C4⋊C4semidirect
310. C2×Q8#6101semidirect
315. C2×D4#6101semidirect
330. C22×C4#6101semidirect
363. C13#20890semidirect

Maximal subgroups

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

subgroupindex
#131280392
C2×#117189012
#131174602
#131151162
#131145682
C13×#23112
#2089013