Finite Group Databasebeta

← #15765770

Subgroups — #15765770

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718341C211yesmaximal, characteristic
2C2×#11718360C211yesmaximal, characteristic
3C2×#11718342C211yesmaximal, characteristic
4#13115797C211yesmaximal, characteristic
5#13115797C211yesmaximal, characteristic
6#13115797C211yesmaximal, characteristic
7C13×#1273C211yesmaximal, characteristic
8C22×Dic52—22no—
9C2×#88123C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×C4×C8×C13C2211yescharacteristic
15C2×#88057—22no—
16C2×#88056—22no—
17#11718596C2211yescharacteristic
18#11718360—22no—
19#11718360—22no—
20#11718342—22no—
21#11718342—22no—
22#11718341—22no—
23#11718341—22no—
24#11718143—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—
43C2×Dic52—28no—
44C2×Dic52—44no—
45C2×Dic52—44no—
46#88123—21no—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123—21no—
52#88123—21no—
53#88123—21no—
54#88123—21no—
55#88123D412yes—
56#88123D412yes—
57#88123D412yes—
58C4×C8×C13—21no—
59C4×C8×C13—21no—
60C4×C8×C13—21no—
61C4×C8×C13—21no—
62C4×C8×C13—21no—
63C4×C8×C13—21no—
64#88057—28no—
65#88056—28no—
66#10318—131nomaximal, Sylow
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C2×Dic26—22no—
75C2×Dic26—22no—
76C2×Dic26—22no—
77C2×Dic26—42no—
78C2×Dic26—42no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×Dic26—42no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×Dic26—41no—
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×C13SD1614yes—
94C2×C8×C13Q1614yescomplemented
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13#4111yescharacteristic
99C4⋊Dic13—22no—
100C4⋊Dic13—22no—
101C4⋊Dic13—22no—
102C4⋊Dic13—22no—
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111C4⋊Dic13—42no—
112C4⋊Dic13—42no—
113C4⋊Dic13—42no—
114Dic52—416no—
115C2×#498—131no—
116C2×#494—131no—
117C2×#487—131no—
118#1990—131no—
119#1990—131no—
120#1990—131no—
121#1273D1311yescharacteristic
122C23×C13#12711yescharacteristic
123C2×C4×C13#12011yescharacteristic
124C2×C4×C13#12011yescharacteristic
125C2×C4×C13#12011yescharacteristic
126C2×C4×C13#12111yescharacteristic
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13C2×SD1612yes—
130C2×C4×C13C2×Q1612yes—
131C2×C4×C13#13512yes—
132C2×C4×C13AGL(1,ℤ/8)12yes—
133C2×C4×C13#13712yes—
134C2×C4×C13#13712yes—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140C2×Dic13—81no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147Dic26—44no—
148Dic26—44no—
149Dic26—44no—
150Dic26—82no—
151Dic26—82no—
152Dic26—82no—
153C8×C13—24no—
154C8×C13—24no—
155C8×C13—42no—
156C22×Q16—262no—
157C2×C4⋊Q8—131no—
158C2×C4⋊Q8—131no—
159C2×C4⋊Q8—131no—
160#498—262no—
161#498—262no—
162#494—262no—
163#494—262no—
164#487—262no—
165#487—262no—
166C2×#106—262no—
167C2×#103—262no—
168C2×C4×C8C2×D1311yescharacteristic
169C2×C4×C8C2×D1311yescharacteristic
170C2×C4×C8C2×D1311yescharacteristic
171#384—131no—
172#340—262no—
173#340—262no—
174#340—262no—
175C22×C13#39211yescharacteristic
176C22×C13#49211yescharacteristic
177C22×C13#49411yescharacteristic
178C22×C13#49511yescharacteristic
179C22×C13#49611yescharacteristic
180C22×C13#49711yescharacteristic
181C22×C13#49711yescharacteristic
182C4×C13#45012yes—
183C4×C13#45112yes—
184C4×C13#45212yes—
185C4×C13#46012yes—
186C4×C13#46212yes—
187C4×C13#46412yes—
188Dic13—82no—
189Dic13—82no—
190Dic13—82no—
191Dic13—161no—
192C22×Q8—261no—
193C22×Q8—261no—
194C22×Q8—261no—
195C2×Q16—268no—
196C2×Q16—524no—
197C2×Q16—524no—
198C22×C8D5212yes—
199C22×C8D5212yes—
200C22×C8D5212yes—
201C4⋊Q8—132no—
202C4⋊Q8—132no—
203C4⋊Q8—132no—
204C4⋊Q8—261no—
205C4⋊Q8—261no—
206C4⋊Q8—261no—
207C4⋊Q8—261no—
208C4⋊Q8—261no—
209C4⋊Q8—261no—
210C4⋊Q8—261no—
211C4⋊Q8—261no—
212C4⋊Q8—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C42C22×D1311yescharacteristic
223#106—268no—
224#103—268no—
225C4×C8—21no—
226C4×C8—21no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—21no—
231C2×C13#170711yescharacteristic
232C2×C13#171611yescharacteristic
233C2×C13#172011yescharacteristic
234C2×C13#172311yescharacteristic
235C2×C13#201411yescharacteristic
236C2×C13#201511yescharacteristic
237C2×C13#201611yescharacteristic
238C2×Q8—262no—
239C2×Q8—262no—
240C2×Q8—262no—
241C2×Q8—521no—
242C2×Q8—521no—
243C2×Q8—521no—
244C2×Q8—522no—
245C2×Q8—522no—
246C2×Q8—522no—
247C2×Q8—522no—
248C2×Q8—522no—
249C2×Q8—522no—
250C22×C4—521no—
251C22×C4—521no—
252C22×C4—521no—
253C22×C4—521no—
254C22×C4C2×D5211yescharacteristic
255C22×C4C2×D5211yescharacteristic
256C22×C4C2×D5211yescharacteristic
257Q16—5216no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8#609514yes—
266C2×C8Dic5214yescomplemented
267C4⋊C4—262no—
268C4⋊C4—262no—
269C4⋊C4—262no—
270C4⋊C4—262no—
271C4⋊C4—262no—
272C4⋊C4—262no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C4⋊C4—521no—
279C4⋊C4—522no—
280C4⋊C4—522no—
281C4⋊C4—522no—
282C42D4×D1311yescharacteristic
283C42D4×D1311yescharacteristic
284C42D4×D1311yescharacteristic
285C42#613111yescharacteristic
286C13#1031811yescharacteristic, complemented, Sylow
287C23#8812811yescharacteristic
288Q8—524no—
289Q8—524no—
290Q8—524no—
291Q8—1042no—
292Q8—1042no—
293Q8—1042no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—1041no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4—1041no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4#8813611yescharacteristic
307C2×C4#8813611yescharacteristic
308C2×C4#8813611yescharacteristic
309C2×C4#8814911yescharacteristic
310C2×C4#8814911yescharacteristic
311C2×C4#8814911yescharacteristic
312C2×C4C2×#609512yes—
313C2×C4#8815812yes—
314C2×C4C2×Dic5212yes—
315C2×C4#8816212yes—
316C2×C4#8816312yes—
317C2×C4#8816312yes—
318C8—24no—
319C8—24no—
320C8—42no—
321C22#1171833211yescharacteristic
322C22#1171835411yescharacteristic
323C22#1171835711yescharacteristic
324C22#1171836011yescharacteristic
325C22#1171837311yescharacteristic
326C22#1171837611yescharacteristic
327C22#1171837611yescharacteristic
328C4—1042no—
329C4—1042no—
330C4—1042no—
331C4—2081no—
332C4#1171839212yes—
333C4#1171839412yes—
334C4#1171840012yes—
335C4#1171850612yes—
336C4#1171850912yes—
337C4#1171851012yes—
338C2#1311443311yescharacteristic
339C2#1311446911yescharacteristic
340C2#1311449611yescharacteristic
341C2#1311451311yescharacteristic
342C2#1311592611yescharacteristic
343C2#1311593311yescharacteristic
344C2#1311593811yescharacteristic
subgroupG/H
centerC23#88128
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1273C2
socle, prime radicalC23×C13#127
hypercenter#1273D13
hypocenterC13#10318
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
94. C2×C8×C13Q16semidirect
266. C2×C8Dic52semidirect
286. C13#10318semidirect

Maximal subgroups

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

subgroupindex
C2×#117183412
C2×#117183602
C2×#117183422
#131157972
C13×#12732
#1031813