Finite Group Databasebeta

← #15765743

Subgroups — #15765743

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718343C211yesmaximal, characteristic
2C2×#11718342C211yesmaximal, characteristic
3C2×#11718342C211yesmaximal, characteristic
4#13115797C211yesmaximal, characteristic
5#13115797C211yesmaximal, characteristic
6#13115638C211yesmaximal, characteristic
7C13×#1273C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88058—22no—
15C2×#88056—22no—
16C2×#88056—22no—
17C2×#88056—22no—
18#11718596C2211yescharacteristic
19#11718343—22no—
20#11718343—22no—
21#11718342—22no—
22#11718342—22no—
23#11718342—22no—
24#11718342—22no—
25#11718143—22no—
26#11718143—22no—
27C22×Dic26—21no—
28C22×Dic26—21no—
29C22×Dic26—21no—
30C22×C8×C13D412yes—
31C22×C8×C13D412yes—
32C22×C8×C13D412yes—
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43#88123—21no—
44#88123—21no—
45#88123—21no—
46#88123—21no—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123—21no—
52#88123D412yes—
53#88123D412yes—
54#88123D412yes—
55C4×C8×C13—21no—
56C4×C8×C13—21no—
57C4×C8×C13—21no—
58C4×C8×C13—21no—
59C4×C8×C13—21no—
60C4×C8×C13—21no—
61#88058—28no—
62#88056—28no—
63#88056—28no—
64#88056—44no—
65#10313—131nomaximal, Sylow
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—41no—
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13—41no—
73C2×Dic26—22no—
74C2×Dic26—22no—
75C2×Dic26—22no—
76C2×Dic26—42no—
77C2×Dic26—42no—
78C2×Dic26—42no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×C8×C13—22no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C2×C8×C13—22no—
89C2×C8×C13—22no—
90C2×C8×C13—22no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13Q1614yes—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13#4111yescharacteristic
98C4⋊Dic13—22no—
99C4⋊Dic13—22no—
100C4⋊Dic13—22no—
101C4⋊Dic13—22no—
102C4⋊Dic13—22no—
103C4⋊Dic13—22no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4⋊Dic13—42no—
111C4⋊Dic13—42no—
112C4⋊Dic13—42no—
113C2×#500—131no—
114C2×#487—131no—
115C2×#487—131no—
116#1990—131no—
117#1990—131no—
118#1956—131no—
119#1273D1311yescharacteristic
120C23×C13#12711yescharacteristic
121C2×C4×C13#12011yescharacteristic
122C2×C4×C13#12011yescharacteristic
123C2×C4×C13#12011yescharacteristic
124C2×C4×C13#12111yescharacteristic
125C2×C4×C13#12111yescharacteristic
126C2×C4×C13#12111yescharacteristic
127C2×C4×C13C2×Q1612yes—
128C2×C4×C13#13512yes—
129C2×C4×C13#13512yes—
130C2×C4×C13AGL(1,ℤ/8)12yes—
131C2×C4×C13#13712yes—
132C2×C4×C13#13712yes—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140C2×Dic13—81no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145Dic26—44no—
146Dic26—44no—
147Dic26—44no—
148Dic26—82no—
149Dic26—82no—
150Dic26—82no—
151C8×C13—24no—
152C8×C13—42no—
153C8×C13—42no—
154C2×C4⋊Q8—131no—
155C2×C4⋊Q8—131no—
156C2×C4⋊Q8—131no—
157#500—262no—
158#500—262no—
159#487—262no—
160#487—262no—
161#487—262no—
162#487—262no—
163C2×#107—262no—
164C2×#103—262no—
165C2×#103—262no—
166C2×#103—262no—
167C2×C4×C8C2×D1311yescharacteristic
168C2×C4×C8C2×D1311yescharacteristic
169C2×C4×C8C2×D1311yescharacteristic
170#384—131no—
171#340—262no—
172#340—262no—
173C22×C13#39211yescharacteristic
174C22×C13#49411yescharacteristic
175C22×C13#49511yescharacteristic
176C22×C13#49511yescharacteristic
177C22×C13#49611yescharacteristic
178C22×C13#49711yescharacteristic
179C22×C13#49711yescharacteristic
180C4×C13#44912yes—
181C4×C13#45112yes—
182C4×C13#45212yes—
183C4×C13#46212yes—
184C4×C13#46312yes—
185C4×C13#46412yes—
186Dic13—82no—
187Dic13—82no—
188Dic13—82no—
189Dic13—161no—
190C22×Q8—261no—
191C22×Q8—261no—
192C22×Q8—261no—
193C22×C8D5212yes—
194C22×C8D5212yes—
195C22×C8D5212yes—
196C4⋊Q8—132no—
197C4⋊Q8—132no—
198C4⋊Q8—132no—
199C4⋊Q8—261no—
200C4⋊Q8—261no—
201C4⋊Q8—261no—
202C4⋊Q8—261no—
203C4⋊Q8—261no—
204C4⋊Q8—261no—
205C4⋊Q8—261no—
206C4⋊Q8—261no—
207C4⋊Q8—261no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C42C22×D1311yescharacteristic
218#107—268no—
219#103—268no—
220#103—268no—
221#103—524no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—21no—
225C4×C8—21no—
226C4×C8—21no—
227C4×C8—21no—
228C2×C13#171011yescharacteristic
229C2×C13#171811yescharacteristic
230C2×C13#171911yescharacteristic
231C2×C13#172311yescharacteristic
232C2×C13#201211yescharacteristic
233C2×C13#201511yescharacteristic
234C2×C13#201611yescharacteristic
235C2×Q8—262no—
236C2×Q8—262no—
237C2×Q8—262no—
238C2×Q8—521no—
239C2×Q8—521no—
240C2×Q8—521no—
241C2×Q8—522no—
242C2×Q8—522no—
243C2×Q8—522no—
244C2×Q8—522no—
245C2×Q8—522no—
246C2×Q8—522no—
247C22×C4—521no—
248C22×C4—521no—
249C22×C4—521no—
250C22×C4—521no—
251C22×C4C2×D5211yescharacteristic
252C22×C4C2×D5211yescharacteristic
253C22×C4C2×D5211yescharacteristic
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8Dic5214yes—
263C4⋊C4—262no—
264C4⋊C4—262no—
265C4⋊C4—262no—
266C4⋊C4—262no—
267C4⋊C4—262no—
268C4⋊C4—262no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—522no—
276C4⋊C4—522no—
277C4⋊C4—522no—
278C42D4×D1311yescharacteristic
279C42D4×D1311yescharacteristic
280C42D4×D1311yescharacteristic
281C42#613111yescharacteristic
282C13#1031311yescharacteristic, complemented, Sylow
283C23#8812811yescharacteristic
284Q8—524no—
285Q8—524no—
286Q8—524no—
287Q8—1042no—
288Q8—1042no—
289Q8—1042no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—522no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4—1041no—
296C2×C4—1041no—
297C2×C4—1041no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4—1041no—
302C2×C4#8813611yescharacteristic
303C2×C4#8813611yescharacteristic
304C2×C4#8813611yescharacteristic
305C2×C4#8814911yescharacteristic
306C2×C4#8814911yescharacteristic
307C2×C4#8814911yescharacteristic
308C2×C4#8815812yes—
309C2×C4#8815812yes—
310C2×C4C2×Dic5212yes—
311C2×C4#8816212yes—
312C2×C4#8816312yes—
313C2×C4#8816312yes—
314C8—24no—
315C8—42no—
316C8—42no—
317C22#1171833211yescharacteristic
318C22#1171835711yescharacteristic
319C22#1171835711yescharacteristic
320C22#1171836011yescharacteristic
321C22#1171837311yescharacteristic
322C22#1171837611yescharacteristic
323C22#1171837611yescharacteristic
324C4—1042no—
325C4—1042no—
326C4—1042no—
327C4—2081no—
328C4#1171839412yes—
329C4#1171839512yes—
330C4#1171840012yes—
331C4#1171850512yes—
332C4#1171850612yes—
333C4#1171851012yes—
334C2#1311444611yescharacteristic
335C2#1311448211yescharacteristic
336C2#1311448911yescharacteristic
337C2#1311451311yescharacteristic
338C2#1311591611yescharacteristic
339C2#1311593311yescharacteristic
340C2#1311593811yescharacteristic
subgroupG/H
centerC23#88128
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1273C2
socle, prime radicalC23×C13#127
hypercenter#1273D13
hypocenterC13#10313
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1273

Complements

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

NH ≅ G/Ntype
282. C13#10313semidirect

Maximal subgroups

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

subgroupindex
C2×#117183432
C2×#117183422
#131157972
#131156382
C13×#12732
#1031313