Finite Group Databasebeta

← #16752968

Subgroups — #16752968

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128646C211yesmaximal, characteristic
2#13127768C218yesmaximal, complemented
3#13127639C218yesmaximal, complemented
4#13126042C214yesmaximal
5#13125980C212yesmaximal
6#13124966C214yesmaximal
7#13124875C212yesmaximal
8#13123921C211yesmaximal, characteristic
9C2×C13×#557C211yesmaximal, characteristic
10C13×#557—24no—
11C13×#557C2218yes—
12C2×C13×C4⋊Q8—21no—
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C13×#125—22no—
15C2×C13×#125C2212yes—
16C2×C4×Q8×C13—21no—
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2212yes—
19C2×C4×Q8×C13C2211yescharacteristic
20#11719517—21no—
21#11719275C2214yes—
22#11719274—24no—
23Q8×Dic26C2214yes—
24#11719205—21no—
25#11719205—22no—
26#11719175C2212yes—
27#11719175C2214yes—
28#11718889C2214yes—
29#11718755C2218yes—
30#11718754C2214yes—
31#11718740C2214yes—
32#11718730C2218yes—
33#11718726C2218yes—
34#11718724C22116yes—
35#11718692C2214yes—
36#11718692C2218yes—
37#11718691C22116yes—
38C4×#6107C2218yes—
39#11718685C2218yes—
40#11718682C2214yes—
41#11718681C2218yes—
42#11718632C2218yes—
43#11718631C2214yes—
44#11718587C2214yes—
45#11718586C2212yes—
46C22×Q8×C13—21no—
47C22×Q8×C13D411yescharacteristic
48C22×Q8×C13C2311yescharacteristic
49C13×C4⋊Q8—28no—
50C13×C4⋊Q8—22no—
51C13×C4⋊Q8C2314yes—
52C13×#125—216no—
53C13×#125—24no—
54C13×#125C2318yes—
55C4×Q8×C13—28no—
56C4×Q8×C13—24no—
57C4×Q8×C13—22no—
58C4×Q8×C13D414yes—
59C4×Q8×C13C2318yes—
60C4×Q8×C13C2314yes—
61C4×Q8×C13C2314yes—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4D412yes—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2312yes—
71C2×C42×C13—22no—
72C2×C42×C13—21no—
73C2×C42×C13C2312yes—
74C2×C42×C13C2311yescharacteristic
75Q8×Dic13—24no—
76Q8×Dic13—24no—
77C2×#6107C2318yes—
78#88180—24no—
79#88180—22no—
80#88178—24no—
81#88178—22no—
82#88178C2314yes—
83#88144—24no—
84#88144—28no—
85#88142—24no—
86#88142—28no—
87#88124—24no—
88#88124—22no—
89#88123C2314yes—
90#88123C2312yes—
91#88123C2314yes—
92#88123C2312yes—
93C4×Dic26—24no—
94C4×Dic26—22no—
95C4×Dic26C2314yes—
96C4×Dic26C2318yes—
97#88075C2318yes—
98C22⋊#1055C2314yes—
99#88050C2318yes—
100#88050C23116yes—
101#88048C23116yes—
102#88047C2318yes—
103C4⋊#1055C2318yes—
104C4⋊#1055C2314yes—
105#88043C2318yes—
106C4×#1055C2314yes—
107#61829—131nomaximal, Sylow
108C2×Q8×C13—24no—
109C2×Q8×C13—24no—
110C2×Q8×C13—21no—
111C2×Q8×C13—24no—
112C2×Q8×C13—44no—
113C2×Q8×C13C2×D414yes—
114C2×Q8×C13C2412yes—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13C2×D412yes—
119C22×C4×C13C2×D412yes—
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2411yescharacteristic
123C2×Dic26—24no—
124C2×Dic26—22no—
125C2×Dic26C2414yes—
126C13×C4⋊C4—28no—
127C13×C4⋊C4—24no—
128C13×C4⋊C4—28no—
129C13×C4⋊C4—24no—
130C13×C4⋊C4—28no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4C2×D414yes—
134C13×C4⋊C4C2×D418yes—
135C13×C4⋊C4C2412yes—
136C13×C4⋊C4C2414yes—
137C42×C13—28no—
138C42×C13—24no—
139C42×C13C2×D414yes—
140C42×C13C2×D412yes—
141C42×C13C2414yes—
142C42×C13C2412yes—
143C22⋊Dic13—24no—
144#6107—216no—
145C4⋊Dic13—24no—
146C4⋊Dic13—22no—
147C4⋊Dic13—24no—
148C4⋊Dic13—22no—
149C4⋊Dic13—24no—
150C4⋊Dic13—22no—
151C4⋊Dic13C2414yes—
152#6101—24no—
153#6101—28no—
154#6101—24no—
155C4×Dic13—28no—
156C4×Dic13—24no—
157C2×#1055C2418yes—
158#3502—131no—
159C2×#557D1311yescharacteristic
160#3387—138no—
161#3374—138no—
162#3236—134no—
163#3229—132no—
164#3113—134no—
165#3104—132no—
166#2983—131no—
167C23×C13C22×D411yescharacteristic
168Q8×C13—24no—
169Q8×C13—28no—
170Q8×C13—22no—
171Q8×C13—48no—
172Q8×C132−1+414yes—
173C2×C4×C13—24no—
174C2×C4×C13—24no—
175C2×C4×C13—22no—
176C2×C4×C13—22no—
177C2×C4×C13—22no—
178C2×C4×C13—24no—
179C2×C4×C13—42no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—44no—
183C2×C4×C13#13714yes—
184C2×C4×C13C22×D414yes—
185C2×C4×C13C22×D411yescharacteristic
186C2×C4×C13C22×D414yes—
187C2×C4×C13C22×D412yes—
188C2×C4×C13C22×D412yes—
189C2×C4×C13C2511yescharacteristic
190C2×Dic13—24no—
191C2×Dic13—24no—
192Dic26—28no—
193Dic26—84no—
194Dic26—82no—
195#1055—28no—
196Q82—134no—
197#557—24no—
198#557—134no—
199#557—264no—
200#557C2×D1318yes—
201#544—261no—
202#544—262no—
203#533—132no—
204#533—134no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2×D1311yescharacteristic
207C2×#125—22no—
208C2×#125C2×D1312yes—
209#519—261no—
210C2×C4×Q8—21no—
211C2×C4×Q8C2×D1311yescharacteristic
212C2×C4×Q8C2×D1312yes—
213C2×C4×Q8C2×D1311yescharacteristic
214#501—138no—
215#498—134no—
216#491—138no—
217#487—134no—
218#484—134no—
219#483—138no—
220#479—1316no—
221#477—134no—
222#475—138no—
223#475—138no—
224#462—134no—
225#462—138no—
226#451—134no—
227#446—138no—
228#441—1316no—
229C4×Q16—138no—
230#432—134no—
231#431—132no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13C2×#13712yes—
235C22×C13C23×D411yescharacteristic
236C4×C13—24no—
237C4×C13—22no—
238C4×C13—24no—
239C4×C13—21no—
240C4×C13—24no—
241C4×C13—42no—
242C4×C13—44no—
243C4×C13C2×#13714yes—
244C4×C13C2×2−1+412yes—
245Dic13—44no—
246Dic13—44no—
247C22×Q8—21no—
248C22×Q8C22⋊D1311yescharacteristic
249C22×Q8C22×D1311yescharacteristic
250C2×Q16—138no—
251C4⋊Q8—28no—
252C4⋊Q8—22no—
253C4⋊Q8—134no—
254C4⋊Q8—132no—
255C4⋊Q8—132no—
256C4⋊Q8—134no—
257C4⋊Q8—264no—
258C4⋊Q8—268no—
259C4⋊Q8C22×D1314yes—
260#125—216no—
261#125—24no—
262#125—264no—
263#125—268no—
264#125—264no—
265#125—262no—
266#125C22×D1318yes—
267C22⋊Q8—134no—
268C22⋊Q8—264no—
269C22⋊Q8—262no—
270C4×Q8—28no—
271C4×Q8—24no—
272C4×Q8—22no—
273C4×Q8—134no—
274C4×Q8—138no—
275C4×Q8—264no—
276C4×Q8—264no—
277C4×Q8—264no—
278C4×Q8—262no—
279C4×Q8C22⋊D1314yes—
280C4×Q8C22×D1314yes—
281C4×Q8C22×D1318yes—
282C4×Q8C22×D1314yes—
283#117—264no—
284#117—262no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4C22⋊D1311yescharacteristic
291C2×C4⋊C4C22⋊D1312yes—
292C2×C4⋊C4C22×D1311yescharacteristic
293C2×C4⋊C4C22×D1312yes—
294C2×C42—22no—
295C2×C42—21no—
296C2×C42C22×D1312yes—
297C2×C42C22×D1311yescharacteristic
298#107—138no—
299#106—1316no—
300C4⋊C8—134no—
301C4⋊C8—138no—
302#103—138no—
303#103—138no—
304#103—1316no—
305C22⋊C8—134no—
306#97—138no—
307C4×C8—134no—
308C2×C13—22no—
309C2×C13#348611yescharacteristic
310C2×C13C22×#13711yescharacteristic
311C2×C13#358611yescharacteristic
312C2×Q8—24no—
313C2×Q8—24no—
314C2×Q8—21no—
315C2×Q8—24no—
316C2×Q8—44no—
317C2×Q8—134no—
318C2×Q8—264no—
319C2×Q8—262no—
320C2×Q8C2×C22⋊D1314yes—
321C2×Q8C23×D1312yes—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4C2×C22⋊D1312yes—
326C22×C4C2×C22⋊D1312yes—
327C22×C4C2×C22⋊D1311yescharacteristic
328C22×C4C2×C22⋊D1311yescharacteristic
329C22×C4C23×D1311yescharacteristic
330Q16—2616no—
331C2×C8—138no—
332C4⋊C4—28no—
333C4⋊C4—24no—
334C4⋊C4—28no—
335C4⋊C4—24no—
336C4⋊C4—28no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—134no—
340C4⋊C4—264no—
341C4⋊C4—262no—
342C4⋊C4—264no—
343C4⋊C4—262no—
344C4⋊C4—268no—
345C4⋊C4—264no—
346C4⋊C4—264no—
347C4⋊C4—264no—
348C4⋊C4—262no—
349C4⋊C4C2×C22⋊D1314yes—
350C4⋊C4C2×C22⋊D1318yes—
351C4⋊C4C23×D1314yes—
352C4⋊C4C23×D1312yes—
353C22⋊C4—264no—
354C42—28no—
355C42—24no—
356C42—268no—
357C42—264no—
358C42C2×C22⋊D1314yes—
359C42C2×C22⋊D1312yes—
360C42C23×D1312yes—
361C42C23×D1314yes—
362C13#6182911yescharacteristic, complemented, Sylow
363C23C22×C22⋊D1311yescharacteristic
364Q8—24no—
365Q8—28no—
366Q8—22no—
367Q8—48no—
368Q8—268no—
369Q8—1044no—
370Q8—1042no—
371Q8#8825414yes—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—264no—
383C2×C4—264no—
384C2×C4#8820514yes—
385C2×C4C22×C22⋊D1314yes—
386C2×C4C22×C22⋊D1314yes—
387C2×C4C22×C22⋊D1311yescharacteristic
388C2×C4C22×C22⋊D1312yes—
389C2×C4C22×C22⋊D1312yes—
390C2×C4C24×D1311yescharacteristic
391C8—268no—
392C22—21no—
393C22—21no—
394C22C2×#8820512yes—
395C22C23×C22⋊D1311yescharacteristic
396C4—24no—
397C4—21no—
398C4—24no—
399C4—24no—
400C4—22no—
401C4—44no—
402C4—42no—
403C4—524no—
404C4—524no—
405C4C2×#8820514yes—
406C4C2×#8825412yes—
407C2—22no—
408C2#1312848711yescharacteristic
409C2C22×#8820511yescharacteristic
410C2#1312962311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#557C2
socleC22×C13C23×D4
prime radicalC23×C13C22×D4
hypercenterC2×#557D13
hypocenterC13#61829
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13127768C2semidirect
3. #13127639C2semidirect
362. C13#61829semidirect

Maximal subgroups

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

subgroupindex
#131286462
#131277682
#131276392
#131260422
#131259802
#131249662
#131248752
#131239212
C2×C13×#5572
#6182913