Finite Group Databasebeta

← #15880590

Subgroups — #15880590

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88048C211yesmaximal, characteristic
2#13117715C211yesmaximal, characteristic
3#13117705C211yesmaximal, characteristic
4#13115578C212yesmaximal, complemented
5#13115424C212yesmaximal, complemented
6#13115412C212yesmaximal, complemented
7#13114927C211yesmaximal, characteristic
8#13114863C211yesmaximal, characteristic
9#13114732C212yesmaximal, complemented
10#13114615C211yesmaximal, characteristic
11C13×#1823C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C2×#88180—21no—
14C22×C4⋊Dic13C2211yescharacteristic
15C23×#1055C2211yescharacteristic
16C2×C13×C22⋊C8C2211yescharacteristic
17C13×#380C2211yescharacteristic
18#11718873C2211yescharacteristic
19#11718872—21no—
20C4×C22⋊Dic13C2211yescharacteristic
21C2×#88055C2212yes—
22#11718646C2212yes—
23#11718642—22no—
24C4⋊C4×Dic13C2212yes—
25C4⋊C4×Dic13C2212yes—
26#11718634C2212yes—
27C2×#88048C418yescomplemented
28C2×#88048C2211yescharacteristic
29C2×#88048C2211yescharacteristic
30C2×#88048C2211yescharacteristic
31C2×#88048C2211yescharacteristic
32C2×#88047C2212yes—
33#11718603—21no—
34C22⋊C4×Dic13—21no—
35#11718314—22no—
36C13×#340C2212yes—
37C13×#340C2212yes—
38#11718143C2212yes—
39#11718143C2212yes—
40#11718142C2212yes—
41#11718121C2212yes—
42C23×C4×C13—21no—
43C23×C4×C13C2311yescharacteristic
44C23×Dic13—21no—
45C22×C8×C13C2312yes—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—22no—
48C2×C13×C4⋊C4C2×C414yes—
49C2×C13×C4⋊C4C2312yes—
50C2×C13×C4⋊C4C2311yescharacteristic
51C2×C13×C4⋊C4C2311yescharacteristic
52C2×C13×C22⋊C4—21no—
53C2×C22⋊Dic13—21no—
54C2×C22⋊Dic13D411yescharacteristic
55C2×C22⋊Dic13D411yescharacteristic
56#88180—44no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—22no—
60C2×C4⋊Dic13C2×C414yes—
61C2×C4⋊Dic13C2312yes—
62C2×C4⋊Dic13C2311yescharacteristic
63C2×C4⋊Dic13C2311yescharacteristic
64C2×#6101—22no—
65C2×C4×Dic13—22no—
66C2×C4×Dic13—22no—
67C2×C4×Dic13C2312yes—
68C22×#1055—24no—
69C22×#1055C2×C414yes—
70C22×#1055C2311yescharacteristic
71C22×#1055C2311yescharacteristic
72C13×C22⋊C8—22no—
73C13×#95—21no—
74#88071—21no—
75#88071—22no—
76#88071—22no—
77#88071—22no—
78#88071—22no—
79#88071D412yes—
80#88055—24no—
81#88048C2×C414yes—
82#88048C2×C414yes—
83#88048C2×C414yes—
84#88048C2×C414yes—
85#88047—24no—
86#22615—131nomaximal, Sylow
87C24×C13C2×D411yescharacteristic
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—24no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—22no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13C22×C412yes—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13#4112yes—
99C22×C4×C13C2411yescharacteristic
100C22×Dic13—21no—
101C22×Dic13—21no—
102C22×Dic13—24no—
103C22×Dic13—22no—
104C22×Dic13—82no—
105C22×Dic13C2×D412yes—
106C22×Dic13C2×D412yes—
107C2×C8×C13—22no—
108C2×C8×C13—22no—
109C2×C8×C13—22no—
110C13×C4⋊C4—24no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—22no—
115C13×C4⋊C4C22×C412yes—
116C13×C4⋊C4C22×C412yes—
117C13×C22⋊C4—42no—
118C22⋊Dic13—22no—
119C22⋊Dic13—22no—
120C22⋊Dic13—42no—
121C4⋊Dic13—24no—
122C4⋊Dic13—21no—
123C4⋊Dic13—21no—
124C4⋊Dic13—22no—
125C4⋊Dic13—22no—
126C4⋊Dic13—44no—
127C4⋊Dic13C22×C412yes—
128C4⋊Dic13C22×C412yes—
129#6101—82no—
130C4×Dic13—22no—
131C4×Dic13—22no—
132C4×Dic13—44no—
133C4×Dic13—82no—
134C2×#1055—22no—
135C2×#1055—28no—
136C2×#1055C22×C412yes—
137C2×#1055C22×C412yes—
138C2×#1055#4114yes—
139C22×#106—131no—
140#2345—131no—
141#2344—131no—
142#1944—132no—
143#1920—132no—
144#1919—132no—
145#1824—131no—
146#1823D1311yescharacteristic
147#1808—131no—
148#1776—132no—
149#1752—131no—
150C23×C13—22no—
151C23×C13—22no—
152C23×C13C4×D412yes—
153C23×C13AGL(1,ℤ/8)12yes—
154C23×C13#13712yes—
155C23×C13C22×D411yescharacteristic
156C2×C4×C13—22no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—24no—
160C2×C4×C13—22no—
161C2×C4×C13—22no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—48no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13C4×D412yes—
171C2×C4×C13C23×C411yescharacteristic
172C2×C4×C13C2×#4112yes—
173C2×C4×C13C2×#4111yescharacteristic
174C2×C4×C132−1+412yes—
175C2×Dic13—22no—
176C2×Dic13—22no—
177C2×Dic13—22no—
178C2×Dic13—22no—
179C2×Dic13—22no—
180C2×Dic13—22no—
181C2×Dic13—22no—
182C2×Dic13—22no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187C2×Dic13—42no—
188C2×Dic13—84no—
189C8×C13—42no—
190#1055—22no—
191#1055#11714yescomplemented
192C23×C8—131no—
193C2×#117—261no—
194C22×C4⋊C4—131no—
195C22×C4⋊C4C2×D1311yescharacteristic
196C2×#107—132no—
197C2×#106—138no—
198C2×#106—131no—
199C2×#106—131no—
200C2×#106—131no—
201C2×#106—131no—
202C2×C22⋊C8C2×D1311yescharacteristic
203C2×#97—132no—
204#389—132no—
205#389—132no—
206#387—262no—
207#387—262no—
208#381—261no—
209#380—131no—
210#380—261no—
211#380C2×D1311yescharacteristic
212C4×C4⋊C4—132no—
213C4×C4⋊C4—132no—
214C4×C22⋊C4—131no—
215C4×C22⋊C4—261no—
216#340—132no—
217#340—132no—
218#340—132no—
219#340C2×D1312yes—
220#340C2×D1312yes—
221#336—132no—
222C22×C13—24no—
223C22×C13—24no—
224C22×C13—22no—
225C22×C13—22no—
226C22×C13#44014yes—
227C22×C13C2×C4×D411yescharacteristic
228C22×C13#54712yes—
229C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
230C22×C13C2×#13711yescharacteristic
231C22×C13#57712yes—
232C4×C13—22no—
233C4×C13—42no—
234C4×C13—42no—
235C4×C13—82no—
236C4×C13C2×#11711yescharacteristic
237C4×C13#51911yescharacteristic
238C4×C13#55212yes—
239Dic13—42no—
240Dic13—42no—
241Dic13—42no—
242Dic13—42no—
243Dic13—82no—
244C23×C4—21no—
245C23×C4—261no—
246C23×C4C22×D1311yescharacteristic
247C22×C8—131no—
248C22×C8—134no—
249C22×C8—131no—
250C22×C8—264no—
251C22×C8C22×D1312yes—
252#117—524no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—134no—
256C2×C4⋊C4—131no—
257C2×C4⋊C4—131no—
258C2×C4⋊C4—132no—
259C2×C4⋊C4—261no—
260C2×C4⋊C4—262no—
261C2×C4⋊C4—262no—
262C2×C4⋊C4—262no—
263C2×C4⋊C4C4×D1314yes—
264C2×C4⋊C4C22×D1312yes—
265C2×C4⋊C4C22×D1311yescharacteristic
266C2×C4⋊C4C22×D1311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—131no—
269C2×C22⋊C4—131no—
270C2×C22⋊C4—261no—
271C2×C42—132no—
272C2×C42—262no—
273C2×C42—262no—
274#107—264no—
275#106—134no—
276#106—134no—
277#106—134no—
278#106—134no—
279C22⋊C8—22no—
280#97—264no—
281#95—21no—
282#95—132no—
283#95—262no—
284#95—262no—
285#95—262no—
286#95—262no—
287#95—261no—
288C2×C13—24no—
289C2×C13#234411yescharacteristic
290C2×C13C2×#44011yescharacteristic
291C2×C13#294911yescharacteristic
292C2×C13#334412yes—
293C2×C13#334512yes—
294C24D4×D1311yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—132no—
304C22×C4—132no—
305C22×C4—261no—
306C22×C4—261no—
307C22×C4—264no—
308C22×C4—262no—
309C22×C4—1042no—
310C22×C4C2×C4×D1312yes—
311C22×C4D4×D1311yescharacteristic
312C22×C4#612912yes—
313C22×C4C23×D1311yescharacteristic
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—132no—
318C2×C8—134no—
319C2×C8—132no—
320C2×C8—268no—
321C2×C8—262no—
322C4⋊C4—24no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—132no—
328C4⋊C4—132no—
329C4⋊C4—264no—
330C4⋊C4—261no—
331C4⋊C4—261no—
332C4⋊C4—262no—
333C4⋊C4—262no—
334C4⋊C4—524no—
335C4⋊C4—1042no—
336C4⋊C4C2×C4×D1312yes—
337C4⋊C4C2×C4×D1312yes—
338C22⋊C4—42no—
339C22⋊C4—262no—
340C22⋊C4—262no—
341C22⋊C4—522no—
342C42—262no—
343C42—262no—
344C42—524no—
345C42—1042no—
346C13#2261511yescharacteristic, complemented, Sylow
347C23—22no—
348C23—22no—
349C23#8813512yes—
350C23#8816512yes—
351C23#8816912yes—
352C23C2×D4×D1311yescharacteristic
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—48no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—262no—
368C2×C4—262no—
369C2×C4—262no—
370C2×C4—262no—
371C2×C4—262no—
372C2×C4—262no—
373C2×C4—262no—
374C2×C4—262no—
375C2×C4—522no—
376C2×C4—522no—
377C2×C4—522no—
378C2×C4—522no—
379C2×C4—522no—
380C2×C4—1044no—
381C2×C4#8813512yes—
382C2×C4C22×C4×D1311yescharacteristic
383C2×C4C2×#612911yescharacteristic
384C2×C4#41×D1312yes—
385C2×C4#8825712yes—
386C8—42no—
387C8—134no—
388C8—262no—
389C22—22no—
390C22—22no—
391C22—24no—
392C22—24no—
393C22#1171841814yes—
394C22C2×#8813511yescharacteristic
395C22#1171936012yes—
396C22C2×#8816511yescharacteristic
397C22C2×#8816911yescharacteristic
398C22#1171948312yes—
399C4—22no—
400C4—42no—
401C4—42no—
402C4—82no—
403C4—522no—
404C4—522no—
405C4—522no—
406C4—522no—
407C4—1042no—
408C4#1171922111yescharacteristic
409C4D13×#11711yescharacteristic
410C4#1171935512yes—
411C2—24no—
412C2#1311770011yescharacteristic
413C2C2×#1171841811yescharacteristic
414C2#1312369111yescharacteristic
415C2#1312729512yes—
416C2#1312731012yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1823C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1823D13
hypocenterC13#22615
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #13115578C2semidirect
5. #13115424C2semidirect
6. #13115412C2semidirect
9. #13114732C2semidirect
27. C2×#88048C4semidirect
191. #1055#117semidirect
346. C13#22615semidirect

Maximal subgroups

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

subgroupindex
C22×#880482
#131177152
#131177052
#131155782
#131154242
#131154122
#131149272
#131148632
#131147322
#131146152
C13×#18232
#2261513