Finite Group Databasebeta

← #15881810

Subgroups — #15881810

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1M16×Dic26C211yesmaximal, characteristic
2#13123787C211yesmaximal, characteristic
3C2×#11718491C211yesmaximal, characteristic
4#13115612C211yesmaximal, characteristic
5#13115610C212yesmaximal
6#13115608C212yesmaximal
7#13115007C211yesmaximal, characteristic
8#13115006C212yesmaximal
9C4×#88062C211yesmaximal, characteristic
10#13114737C212yesmaximal
11C13×#1950C211yesmaximal, characteristic
12C2×C4×Dic26C2211yescharacteristic
13C2×C13×#108C2212yes—
14C13×#423C2211yescharacteristic
15C2×C13×C4⋊C8C2211yescharacteristic
16C4×C13×M16C2211yescharacteristic
17C2×#88062C2212yes—
18C2×#88062C2211yescharacteristic
19C2×#88062C2212yes—
20C2×#88062C2211yescharacteristic
21#11718779C2212yes—
22#11718779C2212yes—
23M16×Dic13C2212yes—
24M16×Dic13C2212yes—
25C2×#88059C2212yes—
26C2×#88054C2212yes—
27C2×C8×Dic13C2212yes—
28#11718585C2211yescharacteristic
29C4×#6099C2211yescharacteristic
30C2×C4×#1055C2211yescharacteristic
31#11718492—21no—
32#11718491—21no—
33#11718491C414yes—
34#11718491C412yes—
35#11718491C412yes—
36#11718489—22no—
37#11718362—22no—
38#11718340—21no—
39C8×Dic26—21no—
40C13×#341C2212yes—
41#11718150C2211yescharacteristic
42#11718150C2211yescharacteristic
43#11718144C2212yes—
44C22×Dic26Q811yescharacteristic
45C2×C13×M16C2311yescharacteristic
46C2×C13×M16C2312yes—
47C2×C13×M16C2311yescharacteristic
48C22×C8×C13C2312yes—
49C2×C42×C13C2311yescharacteristic
50C2×C4⋊Dic13Q811yescharacteristic
51C2×#6101Q812yes—
52C2×C4×Dic13C2312yes—
53C2×#6099C2312yes—
54C2×#6099C2311yescharacteristic
55C2×#6099C2311yescharacteristic
56C22×#1055C2311yescharacteristic
57C22×#1055C2311yescharacteristic
58C4×Dic26C2×C411yescharacteristic
59C4×Dic26C2×C412yes—
60C4×Dic26C2×C411yescharacteristic
61C4×Dic26D412yes—
62C4×Dic26D411yescharacteristic
63C4×Dic26D411yescharacteristic
64C13×#108—42no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8—21no—
67C13×C4⋊C8C2×C412yes—
68C13×C4⋊C8C2×C412yes—
69C13×#97—21no—
70C4×C8×C13—21no—
71#88062—24no—
72#88062—22no—
73#88062—42no—
74#88062Q814yescomplemented
75#88059—42no—
76#88055—22no—
77#88055—22no—
78#88054—22no—
79#88054—22no—
80#88054—22no—
81#88054—22no—
82#88054C2×C414yes—
83#88054C2×C414yes—
84C8×Dic13—22no—
85C8×Dic13—22no—
86C8×Dic13C2×C414yes—
87C8×Dic13C2×C414yes—
88C4⋊#1055—21no—
89C4⋊#1055—21no—
90#88043—21no—
91C4×#1055—21no—
92C4×#1055C2×C412yes—
93C4×#1055C2×C412yes—
94Q8×#108—131nomaximal, Sylow
95C22×C4×C13C2×Q811yescharacteristic
96C22×C4×C13C2×Q811yescharacteristic
97C22×C4×C13C2411yescharacteristic
98C22×Dic13C2×Q812yes—
99C22×Dic13C2×Q812yes—
100C2×Dic26—24no—
101C2×Dic26C4⋊C411yescharacteristic
102C2×Dic26C4⋊C412yes—
103C2×Dic26C4⋊C411yescharacteristic
104C13×M16—21no—
105C13×M16—21no—
106C13×M16—22no—
107C13×M16—21no—
108C13×M16—22no—
109C13×M16C2×Q812yes—
110C2×C8×C13—21no—
111C2×C8×C13—22no—
112C2×C8×C13—22no—
113C2×C8×C13—21no—
114C2×C8×C13—22no—
115C2×C8×C13C22×C414yes—
116C42×C13C22×C411yescharacteristic
117C42×C13C22×C411yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13C2×D411yescharacteristic
120C4⋊Dic13C4⋊C412yes—
121C4⋊Dic13C4⋊C411yescharacteristic
122C4⋊Dic13C4⋊C411yescharacteristic
123#6101C4⋊C412yes—
124#6101C4⋊C412yes—
125#6101C4⋊C412yes—
126#6101C4⋊C412yes—
127C4×Dic13C22×C412yes—
128C4×Dic13C22×C412yes—
129C4×Dic13C2×D412yes—
130C4×Dic13C2×D412yes—
131#6099—21no—
132#6099—22no—
133#6099—21no—
134#6099—21no—
135#6099—22no—
136#6099C2×Q812yes—
137C2×#1055—21no—
138C2×#1055—21no—
139C2×#1055—21no—
140C2×#1055—21no—
141C2×#1055—22no—
142C2×#1055C22×C412yes—
143C2×#1055C22×C412yes—
144C2×#1055C2×Q812yes—
145C2×#1055#4112yes—
146Q8×M16—131no—
147Q8×M16—131no—
148C2×C8×Q8—131no—
149#1950—132no—
150#1950—131no—
151#1950—132no—
152#1950D1311yescharacteristic
153#1848—132no—
154#1848—131no—
155C4×#108—131no—
156C4×#108—132no—
157C23×C13C22×Q811yescharacteristic
158C2×C4×C13—22no—
159C2×C4×C13—41no—
160C2×C4×C13C2×C4⋊C411yescharacteristic
161C2×C4×C13C2×C4⋊C411yescharacteristic
162C2×C4×C13C2×C4⋊C411yescharacteristic
163C2×C4×C13C2×C4⋊C411yescharacteristic
164C2×C4×C13C23×C411yescharacteristic
165C2×C4×C13C22×D411yescharacteristic
166C2×C4×C13C22×Q811yescharacteristic
167C2×C4×C13C2×#4111yescharacteristic
168C2×C4×C13H(5,𝔽2)11yescharacteristic
169C2×C4×C132−1+411yescharacteristic
170C2×Dic13—24no—
171C2×Dic13—42no—
172C2×Dic13C2×C4⋊C412yes—
173C2×Dic13C2×C4⋊C412yes—
174C2×Dic13C2×C4⋊C412yes—
175C2×Dic13C2×C4⋊C412yes—
176Dic26—22no—
177Dic26—24no—
178Dic26#10814yescomplemented
179C8×C13—24no—
180C8×C13—22no—
181C8×C13—41no—
182C8×C13—42no—
183#1055—22no—
184#1055—22no—
185#1055—41no—
186#1055—42no—
187#1055C4×Q814yes—
188C2×C4×Q8—131no—
189#446—261no—
190#446—262no—
191#446—262no—
192#446—261no—
193C8×Q8—132no—
194C8×Q8—134no—
195C8×Q8—132no—
196C8×Q8—261no—
197C8×Q8—261no—
198C2×#108—131no—
199C2×#108—131no—
200C2×#108—132no—
201C2×#108—132no—
202C2×#108—132no—
203C2×#108C2×D1312yes—
204#423—132no—
205#423—132no—
206#423—131no—
207#423C2×D1311yescharacteristic
208C2×C4⋊C8—132no—
209C2×C4⋊C8C2×D1311yescharacteristic
210C4×M16—132no—
211C4×M16—132no—
212C4×M16—131no—
213C4×M16C2×D1311yescharacteristic
214C2×C4×C8—132no—
215C2×C4×C8—131no—
216#341—131no—
217#341—131no—
218#341—132no—
219#341C2×D1312yes—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13C22×C4⋊C411yescharacteristic
223C22×C13#55711yescharacteristic
224C22×C13Q8211yescharacteristic
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—21no—
228C4×C13C2×#10812yes—
229C4×C13C2×C4×Q811yescharacteristic
230C4×C13#52011yescharacteristic
231C4×C13D4×Q811yescharacteristic
232C4×C13#55011yescharacteristic
233Dic13—22no—
234Dic13—22no—
235Dic13—22no—
236Dic13C2×#10814yes—
237C22×Q8—131no—
238C2×M16—131no—
239C2×M16—131no—
240C2×M16—132no—
241C2×M16C22×D1311yescharacteristic
242C2×M16C22×D1312yes—
243C2×M16C22×D1311yescharacteristic
244C22×C8—131no—
245C22×C8—131no—
246C22×C8C22×D1312yes—
247C4×Q8—131no—
248C4×Q8—132no—
249C4×Q8—131no—
250C4×Q8—131no—
251C4×Q8—132no—
252C4×Q8—131no—
253C2×C4⋊C4—132no—
254C2×C4⋊C4—131no—
255C2×C42—132no—
256C2×C42C22×D1311yescharacteristic
257#108—42no—
258#108—134no—
259#108—262no—
260#108—264no—
261#108—522no—
262#108—522no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—134no—
266C4⋊C8—134no—
267C4⋊C8—262no—
268C4⋊C8—262no—
269C4⋊C8—262no—
270C4⋊C8—262no—
271C4⋊C8—261no—
272C4⋊C8—261no—
273C4⋊C8C4×D1312yes—
274C4⋊C8C4×D1312yes—
275#97—21no—
276#97—262no—
277#97—262no—
278#97—261no—
279C4×C8—21no—
280C4×C8—134no—
281C4×C8—134no—
282C4×C8—132no—
283C4×C8—132no—
284C4×C8—262no—
285C4×C8—262no—
286C4×C8—261no—
287C2×C13—21no—
288C2×C13—21no—
289C2×C13Q8×C4⋊C411yescharacteristic
290C2×C13C22×#10811yescharacteristic
291C2×C13#291611yescharacteristic
292C2×Q8—131no—
293C2×Q8—132no—
294C2×Q8—131no—
295C2×Q8—264no—
296C22×C4—132no—
297C22×C4—132no—
298C22×C4Q8×D1311yescharacteristic
299C22×C4Q8×D1311yescharacteristic
300C22×C4C23×D1311yescharacteristic
301M16—21no—
302M16—21no—
303M16—22no—
304M16—21no—
305M16—22no—
306M16—132no—
307M16—261no—
308M16—261no—
309M16—262no—
310M16—261no—
311M16—262no—
312M16Q8×D1312yes—
313C2×C8—21no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—21no—
317C2×C8—22no—
318C2×C8—132no—
319C2×C8—132no—
320C2×C8—132no—
321C2×C8—132no—
322C2×C8—261no—
323C2×C8—261no—
324C2×C8—261no—
325C2×C8—262no—
326C2×C8—261no—
327C2×C8C2×C4×D1314yes—
328C4⋊C4—132no—
329C4⋊C4—132no—
330C4⋊C4—132no—
331C4⋊C4—132no—
332C4⋊C4—132no—
333C4⋊C4—131no—
334C4⋊C4—131no—
335C42—132no—
336C42—132no—
337C42—132no—
338C42—132no—
339C42C2×C4×D1311yescharacteristic
340C42C2×C4×D1311yescharacteristic
341C42D4×D1311yescharacteristic
342C42D4×D1311yescharacteristic
343C13Q8×#10811yescharacteristic, complemented, Sylow
344C23C2×Q8×D1311yescharacteristic
345Q8—134no—
346Q8—264no—
347Q8—262no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—132no—
351C2×C4—132no—
352C2×C4—132no—
353C2×C4—132no—
354C2×C4—264no—
355C2×C4—522no—
356C2×C4C4⋊C4×D1311yescharacteristic
357C2×C4C4⋊C4×D1311yescharacteristic
358C2×C4C4⋊C4×D1311yescharacteristic
359C2×C4C4⋊C4×D1311yescharacteristic
360C2×C4C22×C4×D1311yescharacteristic
361C2×C4C2×D4×D1311yescharacteristic
362C2×C4#8825111yescharacteristic
363C2×C4C2×Q8×D1311yescharacteristic
364C2×C4#41×D1311yescharacteristic
365C2×C4#8825711yescharacteristic
366C8—24no—
367C8—22no—
368C8—41no—
369C8—42no—
370C8—134no—
371C8—262no—
372C8—262no—
373C8—521no—
374C8—522no—
375C22—21no—
376C22—21no—
377C22C2×C4⋊C4×D1311yescharacteristic
378C22#1171939011yescharacteristic
379C22#1171942711yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—134no—
384C4—262no—
385C4—262no—
386C4—262no—
387C4D13×#10812yes—
388C4#1171925111yescharacteristic
389C4C4×Q8×D1311yescharacteristic
390C4#1171930411yescharacteristic
391C4#1171933711yescharacteristic
392C2—21no—
393C2—21no—
394C2#1311775011yescharacteristic
395C2C2×D13×#10811yescharacteristic
396C2#1312344611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1950C2
socleC22×C13C22×C4⋊C4
prime radicalC23×C13C22×Q8
cosocleC22×C4×C13C24
hypercenter#1950D13
hypocenterC13Q8×#108
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
74. #88062Q8semidirect
178. Dic26#108semidirect
343. C13Q8×#108semidirect

Maximal subgroups

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

subgroupindex
M16×Dic262
#131237872
C2×#117184912
#131156122
#131156102
#131156082
#131150072
#131150062
C4×#880622
#131147372
C13×#19502
Q8×#10813