Finite Group Databasebeta

← #15891039

Subgroups — #15891039

Order 3328.

1074 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719205C211yesmaximal, characteristic
2#13123426C212yesmaximal
3#13117460C211yesmaximal, characteristic
4#13116187C214yesmaximal, complemented
5#13116182C214yesmaximal, complemented
6#13114547C212yesmaximal
7C2×C13×#343C211yesmaximal, characteristic
8C22×C13×M16C2212yes—
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×#88180C2212yes—
11C2×#88180C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C2×#88178—22no—
14#11719205—22no—
15#11719205—24no—
16#11719205C2214yes—
17C2×#88144—22no—
18C2×#88142—22no—
19#11718871—22no—
20#11718782—22no—
21#11718782—22no—
22#11718782C2214yes—
23#11718782C2214yes—
24#11718767—24no—
25#11718638C2212yes—
26#11718637C2212yes—
27#11718634—22no—
28C13×#343C2214yes—
29#11718147C2218yes—
30C23×C4×C13D412yes—
31C23×C4×C13C2311yescharacteristic
32C22×Dic26—22no—
33C2×C13×M16—22no—
34C2×C13×M16—24no—
35C2×C13×M16Q818yescomplemented
36C2×C13×M16C2314yes—
37C22×C8×C13—22no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4—22no—
40C2×C13×C4⋊C4D412yes—
41C2×C13×C4⋊C4C2312yes—
42C2×C22⋊Dic13—22no—
43C2×C22⋊Dic13—21no—
44C2×C22⋊Dic13—21no—
45#88180—22no—
46#88180—22no—
47#88180—22no—
48#88180—22no—
49#88180—22no—
50#88180D414yes—
51#88180Q814yescomplemented
52#88180C2314yes—
53C2×C4⋊Dic13—22no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13D412yes—
56C2×C4⋊Dic13D412yes—
57C2×C4⋊Dic13C2311yescharacteristic
58C2×C4⋊Dic13C2311yescharacteristic
59#88178—28no—
60#88178—28no—
61C2×#6101—24no—
62C2×#6101—24no—
63C2×C4×Dic13—22no—
64C2×C4×Dic13—21no—
65C2×C4×Dic13C2312yes—
66#88144—28no—
67#88144—28no—
68#88142—28no—
69#88142—28no—
70#88071—24no—
71#88058—24no—
72#88058—24no—
73#88057—24no—
74#88057—24no—
75#23561—131nomaximal, Sylow
76C24×C13C2×D411yescharacteristic
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—82no—
80C22×C4×C13C2×D414yes—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×Q814yes—
85C22×C4×C13C2×Q812yes—
86C22×C4×C13#4112yes—
87C22×C4×C13C2411yescharacteristic
88C22×Dic13—22no—
89C22×Dic13—22no—
90C22×Dic13—22no—
91C22×Dic13—21no—
92C22×Dic13—21no—
93C2×Dic26—28no—
94C2×Dic26—84no—
95C13×M16—28no—
96C13×M16—24no—
97C13×M16C2×Q818yescomplemented
98C2×C8×C13—28no—
99C2×C8×C13—24no—
100C13×C4⋊C4—24no—
101C13×C4⋊C4—24no—
102C22⋊Dic13—24no—
103C22⋊Dic13—24no—
104C22⋊Dic13—24no—
105C22⋊Dic13—41no—
106C22⋊Dic13—41no—
107C4⋊Dic13—28no—
108C4⋊Dic13—22no—
109C4⋊Dic13—22no—
110C4⋊Dic13—24no—
111C4⋊Dic13—22no—
112C4⋊Dic13—22no—
113C4⋊Dic13C2×D414yes—
114C4⋊Dic13C2×D414yes—
115#6101—216no—
116#6101—84no—
117C4×Dic13—24no—
118C4×Dic13—24no—
119C4×Dic13—22no—
120C4×Dic13—42no—
121C4×Dic13C2×Q814yescomplemented
122C2×#544—131no—
123#2911—132no—
124#2317—131no—
125#2061—134no—
126#2060—134no—
127C2×#343D1311yescharacteristic
128#1733—132no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13#12011yescharacteristic
132C23×C13#12011yescharacteristic
133C23×C13C22⋊Q812yes—
134C23×C13C4⋊Q812yes—
135C23×C13C22×D411yescharacteristic
136C2×C4×C13—24no—
137C2×C4×C13—44no—
138C2×C4×C13—44no—
139C2×C4×C13—82no—
140C2×C4×C13#12012yes—
141C2×C4×C13C22⋊Q814yes—
142C2×C4×C13C22⋊Q814yes—
143C2×C4×C13C22⋊Q812yes—
144C2×C4×C13C4⋊Q814yes—
145C2×C4×C13C4⋊Q814yes—
146C2×C4×C13C4⋊Q812yes—
147C2×C4×C13C22×D412yes—
148C2×C4×C13C22×Q812yes—
149C2×C4×C13C22×Q811yescharacteristic
150C2×C4×C13C2×#4111yescharacteristic
151C2×Dic13—24no—
152C2×Dic13—24no—
153C2×Dic13—24no—
154C2×Dic13—42no—
155C2×Dic13—44no—
156C2×Dic13—42no—
157C2×Dic13—44no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162Dic26—88no—
163C8×C13—28no—
164C22×M16C2×D1312yes—
165#544—134no—
166#544—264no—
167#544—262no—
168C2×C4⋊Q8—262no—
169C2×#125—262no—
170C2×C22⋊Q8—262no—
171C2×#117—131no—
172C2×#117—132no—
173C2×#117—131no—
174C22×C4⋊C4C2×D1311yescharacteristic
175#428—134no—
176#428—134no—
177#428—262no—
178#428—262no—
179#427—264no—
180#389—262no—
181#385—262no—
182#384—132no—
183#382—132no—
184#343C2×D1314yes—
185#339—138no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13#39512yes—
195C22×C13#39512yes—
196C22×C13C2×#12011yescharacteristic
197C22×C13C2×C22⋊Q811yescharacteristic
198C22×C13C2×C4⋊Q811yescharacteristic
199C4×C13—44no—
200C4×C13#39514yes—
201C4×C13C2×C22⋊Q812yes—
202C4×C13C2×C4⋊Q812yes—
203Dic13—44no—
204Dic13—44no—
205Dic13—44no—
206Dic13—81no—
207Dic13—81no—
208C22×Q8—262no—
209C23×C4D5212yes—
210C23×C4C22×D1311yescharacteristic
211C2×M16—22no—
212C2×M16—24no—
213C2×M16Dic2618yescomplemented
214C2×M16C22×D1314yes—
215C22×C8—22no—
216C4⋊Q8—268no—
217C4⋊Q8—268no—
218#125—268no—
219#125—268no—
220C22⋊Q8—268no—
221C22⋊Q8—268no—
222#117—134no—
223#117—134no—
224#117—134no—
225#117—262no—
226#117—262no—
227#117—262no—
228#117—262no—
229#117—262no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—132no—
233C2×C4⋊C4—132no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—262no—
237C2×C4⋊C4—264no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—264no—
240C2×C4⋊C4D5212yes—
241C2×C4⋊C4C22×D1312yes—
242C2×C22⋊C4—262no—
243C2×C22⋊C4—261no—
244C2×C22⋊C4—261no—
245C2×C42—132no—
246C2×C42—262no—
247C2×C42—261no—
248#107—264no—
249#107—264no—
250#106—264no—
251#106—264no—
252#95—264no—
253C2×C13—21no—
254C2×C13—21no—
255C2×C13—22no—
256C2×C13—22no—
257C2×C13C2×#39511yescharacteristic
258C2×C13#301911yescharacteristic
259C2×C13#302011yescharacteristic
260C24C2×D5211yescharacteristic
261C2×Q8—268no—
262C2×Q8—1044no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—82no—
266C22×C4—262no—
267C22×C4—262no—
268C22×C4—262no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4C2×Dic2614yes—
272C22×C4C2×D5214yes—
273C22×C4C2×D5211yescharacteristic
274C22×C4D4×D1312yes—
275C22×C4D4×D1312yes—
276C22×C4#612912yes—
277C22×C4Q8×D1312yes—
278C22×C4C23×D1311yescharacteristic
279M16—28no—
280M16—24no—
281M16C2×Dic2618yescomplemented
282C2×C8—28no—
283C2×C8—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—134no—
287C4⋊C4—134no—
288C4⋊C4—268no—
289C4⋊C4—2616no—
290C4⋊C4—262no—
291C4⋊C4—262no—
292C4⋊C4—264no—
293C4⋊C4—262no—
294C4⋊C4—262no—
295C4⋊C4—1044no—
296C22⋊C4—264no—
297C22⋊C4—264no—
298C22⋊C4—264no—
299C22⋊C4—521no—
300C22⋊C4—521no—
301C42—134no—
302C42—264no—
303C42—264no—
304C42—262no—
305C42—522no—
306C13#2356111yescharacteristic, complemented, Sylow
307C23—41no—
308C23—41no—
309C23#8812312yes—
310C23#8813611yescharacteristic
311C23#8813611yescharacteristic
312C23#8815112yes—
313C23C22×D5211yescharacteristic
314Q8—1048no—
315C2×C4—24no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—82no—
319C2×C4—264no—
320C2×C4—264no—
321C2×C4—264no—
322C2×C4—522no—
323C2×C4—522no—
324C2×C4—524no—
325C2×C4—524no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4#8812312yes—
331C2×C4#8813214yes—
332C2×C4#8813214yes—
333C2×C4#8813612yes—
334C2×C4#8814214yes—
335C2×C4#8814214yes—
336C2×C4#8815112yes—
337C2×C4C22×Dic2612yes—
338C2×C4C2×D4×D1312yes—
339C2×C4C2×#612911yescharacteristic
340C2×C4C2×Q8×D1311yescharacteristic
341C8—28no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22#1171831712yes—
351C22#1171831712yes—
352C22C2×#8812311yescharacteristic
353C22C2×#8813611yescharacteristic
354C22C2×#8815111yescharacteristic
355C4—44no—
356C4—524no—
357C4—524no—
358C4—524no—
359C4—1041no—
360C4—1041no—
361C4#1171831714yes—
362C4C2×#8813212yes—
363C4C2×#8814212yes—
364C2—21no—
365C2—21no—
366C2—22no—
367C2—22no—
368C2C2×#1171831711yescharacteristic
369C2#1312419611yescharacteristic
370C2#1312420311yescharacteristic
subgroupG/H
centerC22C2×#88136
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#343C2
socleC22×C13C2×#120
prime radicalC24×C13C2×D4
hypercenterC2×#343D13
hypocenterC13#23561
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. #13116187C2semidirect
5. #13116182C2semidirect
35. C2×C13×M16Q8semidirect
51. #88180Q8semidirect
97. C13×M16C2×Q8semidirect
121. C4×Dic13C2×Q8semidirect
213. C2×M16Dic26semidirect
281. M16C2×Dic26semidirect
306. C13#23561semidirect

Maximal subgroups

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

subgroupindex
C2×#117192052
#131234262
#131174602
#131161872
#131161822
#131145472
C2×C13×#3432
#2356113