Finite Group Databasebeta

← #15864018

Subgroups — #15864018

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
1C2×#11718901C211yesmaximal, characteristic
2#13117456C212yesmaximal, complemented
3#13117428C211yesmaximal, characteristic
4#13115117C218yesmaximal, complemented
5#13114569C212yesmaximal, complemented
6C13×#3428C211yesmaximal, characteristic
7C22×C13×#41C2211yescharacteristic
8C13×#520—22no—
9C13×#520—22no—
10C13×#519—21no—
11C13×#518—21no—
12C13×#518C2214yes—
13C4×C13×#41—24no—
14C2×C13×#117—22no—
15C2×C13×#117C2212yes—
16C2×#88180C2211yescharacteristic
17C2×#88180C2212yes—
18C22×C4⋊Dic13C2211yescharacteristic
19#11718901C418yescomplemented
20#11718891—21no—
21#11718882—21no—
22#11718881C2214yes—
23C2×#88074C2214yes—
24#11718873—22no—
25#11718638—22no—
26#11718637—22no—
27#11718607C2218yes—
28#11718589—24no—
29#11718118C2218yes—
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×C13C2311yescharacteristic
40C23×Dic13C2312yes—
41C4×Q8×C13—24no—
42C4×Q8×C13—24no—
43C4×D4×C13—24no—
44C4×D4×C13—24no—
45C4×D4×C13—28no—
46C4×D4×C13—28no—
47C13×#117—24no—
48C13×#117—24no—
49C13×#117—22no—
50C13×#117—24no—
51C13×#117—22no—
52C13×#117—22no—
53C13×#117—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4D412yes—
57C2×C13×C4⋊C4D412yes—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4C2314yes—
60C2×C42×C13—24no—
61C2×C42×C13D414yes—
62C2×C22⋊Dic13—24no—
63C2×C22⋊Dic13C2312yes—
64C2×C22⋊Dic13C2314yes—
65#88180—24no—
66#88180—24no—
67#88180C2×C418yescomplemented
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13—21no—
74C2×#6101—28no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—21no—
77#88074C2×C4116yescomplemented
78#88071—28no—
79#88071—24no—
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—24no—
102C22×C4×C13C4⋊C418yescomplemented
103C22×C4×C13C22×C412yes—
104C22×C4×C13C2×D412yes—
105C22×C4×C13C2×D414yes—
106C22×C4×C13C2×D414yes—
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D412yes—
110C22×C4×C13C2×D412yes—
111C22×C4×C13C2×Q812yes—
112C22×C4×C13#4114yes—
113C22×Dic13—24no—
114C22×Dic13—22no—
115C22×Dic13—24no—
116C22×Dic13—22no—
117C22×Dic13—82no—
118C13×C4⋊C4—24no—
119C13×C4⋊C4—24no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—22no—
124C13×C22⋊C4—28no—
125C13×C22⋊C4—24no—
126C13×C22⋊C4—24no—
127C42×C13—28no—
128C42×C13—24no—
129C42×C13—24no—
130C22⋊Dic13—24no—
131C22⋊Dic13—24no—
132C22⋊Dic13—84no—
133C22⋊Dic13C22×C418yes—
134C4⋊Dic13—28no—
135C4⋊Dic13—41no—
136C4⋊Dic13—42no—
137C4⋊Dic13—41no—
138C4⋊Dic13—42no—
139#6101—88no—
140C4×Dic13—28no—
141C4×Dic13—42no—
142#3428D1311yescharacteristic
143C2×#410—131no—
144#2317—132no—
145#2311—131no—
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—24no—
169C2×C4×C13—24no—
170C2×C4×C13—44no—
171C2×C4×C13—44no—
172C2×C4×C13—84no—
173C2×C4×C13—84no—
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—44no—
188C2×Dic13—44no—
189C2×Dic13—48no—
190C2×Dic13—42no—
191C2×Dic13—44no—
192C2×Dic13—42no—
193C2×Dic13—42no—
194C2×Dic13—42no—
195C22×#41C2×D1311yescharacteristic
196#520—22no—
197#520—22no—
198#519—21no—
199#518—21no—
200#518C2×D1314yes—
201C4×#41—24no—
202C2×#117—22no—
203C2×#117—132no—
204C2×#117—131no—
205C2×#117C2×D1312yes—
206C22×C4⋊C4—131no—
207#410—138no—
208C2×#99—134no—
209#391—261no—
210#390—261no—
211#389—264no—
212#386—134no—
213#385—138no—
214#384—262no—
215#382—262no—
216#380—262no—
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—44no—
237C4×C13—44no—
238C4×C13#38512yes—
239C4×C13#38512yes—
240C4×C13#38514yes—
241Dic13—48no—
242Dic13—82no—
243Dic13—82no—
244C2×#41—24no—
245C2×#41—22no—
246C2×#41—22no—
247C2×#41Dic2614yes—
248C2×#41C4×D1314yes—
249C22×Q8C22⋊D1311yescharacteristic
250C22×D4C22⋊D1311yescharacteristic
251C22×D4C22×D1312yes—
252C23×C4—132no—
253C23×C4C22⋊D1312yes—
254C23×C4C22×D1311yescharacteristic
255C4×Q8—24no—
256C4×Q8—24no—
257C4×D4—24no—
258C4×D4—24no—
259C4×D4—28no—
260C4×D4—28no—
261#117—24no—
262#117—24no—
263#117—22no—
264#117—24no—
265#117—22no—
266#117—22no—
267#117—22no—
268#117—138no—
269#117—264no—
270#117—264no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—262no—
274C2×C4⋊C4—261no—
275C2×C4⋊C4—262no—
276C2×C4⋊C4—262no—
277C2×C4⋊C4—261no—
278C2×C4⋊C4—261no—
279C2×C4⋊C4—268no—
280C2×C4⋊C4C22⋊D1312yes—
281C2×C4⋊C4C22⋊D1312yes—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—134no—
284C2×C22⋊C4—132no—
285C2×C22⋊C4—264no—
286C2×C22⋊C4C22×D1314yes—
287C2×C42—24no—
288C2×C42—262no—
289C2×C42—261no—
290C2×C42C22⋊D1314yes—
291#99—1316no—
292#95—264no—
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—24no—
323C22×C4—264no—
324C22×C4—262no—
325C22×C4—262no—
326C22×C4—264no—
327C22×C4—1042no—
328C22×C4#610118yescomplemented
329C22×C4C2×Dic2612yes—
330C22×C4C2×C4×D1312yes—
331C22×C4#612714yes—
332C22×C4C2×C22⋊D1312yes—
333C22×C4C2×C22⋊D1314yes—
334C22×C4C2×C22⋊D1314yes—
335C22×C4C2×C22⋊D1311yescharacteristic
336C22×C4C2×C22⋊D1311yescharacteristic
337C22×C4C2×C22⋊D1312yes—
338C22×C4C2×C22⋊D1312yes—
339C4⋊C4—24no—
340C4⋊C4—24no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—268no—
346C4⋊C4—522no—
347C4⋊C4—521no—
348C4⋊C4—522no—
349C4⋊C4—521no—
350C4⋊C4—1048no—
351C22⋊C4—28no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—138no—
355C22⋊C4—264no—
356C22⋊C4—264no—
357C22⋊C4—1044no—
358C42—28no—
359C42—24no—
360C42—24no—
361C42—268no—
362C42—522no—
363C13#2089011yescharacteristic, complemented, Sylow
364C23—22no—
365C23—22no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—42no—
370C23C2×#610114yes—
371C23C22×Dic2611yescharacteristic
372C23C22×C4×D1311yescharacteristic
373C23C2×#612712yes—
374C23C22×C22⋊D1311yescharacteristic
375C23C22×C22⋊D1312yes—
376Q8—28no—
377D4—28no—
378D4—28no—
379D4—28no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—28no—
383C2×C4—28no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—84no—
389C2×C4—84no—
390C2×C4—268no—
391C2×C4—524no—
392C2×C4—524no—
393C2×C4—522no—
394C2×C4—524no—
395C2×C4—528no—
396C2×C4—522no—
397C2×C4—522no—
398C2×C4—522no—
399C2×C4C2×#610114yes—
400C2×C4C2×#610112yes—
401C2×C4C2×#610112yes—
402C2×C4#8817814yes—
403C2×C4#8817814yes—
404C2×C4C4×C22⋊D1314yes—
405C2×C4C4×C22⋊D1314yes—
406C2×C4#8818312yes—
407C2×C4#8818312yes—
408C2×C4#8820711yescharacteristic
409C2×C4#8820712yes—
410C2×C4#8820711yescharacteristic
411C22—22no—
412C22—21no—
413C22—22no—
414C22—21no—
415C22—24no—
416C22—41no—
417C22—41no—
418C22—42no—
419C22—44no—
420C22—42no—
421C22—42no—
422C22—82no—
423C22C22×#610111yescharacteristic
424C22C2×#8817812yes—
425C22C2×C4×C22⋊D1312yes—
426C22C2×#8818311yescharacteristic
427C22C2×#8820711yescharacteristic
428C4—24no—
429C4—44no—
430C4—44no—
431C4—528no—
432C4—1042no—
433C4—1042no—
434C4#1171887112yes—
435C4#1171887112yes—
436C4#1171887114yes—
437C2—22no—
438C2—21no—
439C2—21no—
440C2—22no—
441C2—44no—
442C2C2×#1171887111yescharacteristic
443C2#1312423811yescharacteristic
444C2#1312424211yescharacteristic
subgroupG/H
centerC22C2×#88207
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC13×#3428C2
socleC22×C13C2×#120
prime radicalC22×C13×#41C22
cosocleC24×C13C24
hypercenter#3428D13
hypocenterC13#20890
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3428

Complements

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

NH ≅ G/Ntype
2. #13117456C2semidirect
4. #13115117C2semidirect
5. #13114569C2semidirect
19. #11718901C4semidirect
67. #88180C2×C4semidirect
77. #88074C2×C4semidirect
89. C2×Q8×C13C4⋊C4semidirect
94. C2×D4×C13C4⋊C4semidirect
102. C22×C4×C13C4⋊C4semidirect
310. C2×Q8#6101semidirect
315. C2×D4#6101semidirect
328. 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
C2×#117189012
#131174562
#131174282
#131151172
#131145692
C13×#34282
#2089013