Finite Group Databasebeta

← #16752963

Subgroups — #16752963

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
1C2×#11719272C211yesmaximal, characteristic
2#13127764C218yesmaximal, complemented
3#13127635C218yesmaximal, complemented
4#13126038C214yesmaximal
5#13125977C212yesmaximal
6#13124962C214yesmaximal
7#13124871C212yesmaximal
8#13123921C211yesmaximal, characteristic
9C13×#3502C211yesmaximal, characteristic
10Q82×C13C2214yes—
11C13×#557—24no—
12C13×#557C2214yes—
13C13×#544—21no—
14C13×#544—22no—
15C13×#533C2212yes—
16C13×#533C2214yes—
17C13×#519—21no—
18C2×C4×Q8×C13C2211yescharacteristic
19C2×#88198—21no—
20#11719272—24no—
21#11719272C2218yes—
22C2×#88143—22no—
23C2×#88141—21no—
24C2×#88124C2212yes—
25C2×#88123C2211yescharacteristic
26C2×C4×Dic26C2211yescharacteristic
27C2×C4×Dic26C2212yes—
28#11718755C2218yes—
29#11718752C2214yes—
30#11718751C2214yes—
31#11718751C2218yes—
32#11718743C2218yes—
33#11718742C2214yes—
34#11718741C2218yes—
35#11718740C2214yes—
36#11718711C2214yes—
37#11718705C2214yes—
38#11718704C2218yes—
39#11718691C22116yes—
40C4×#6107C2218yes—
41#11718685C2218yes—
42#11718683C22116yes—
43#11718681C2218yes—
44#11718587C2214yes—
45#11718586C2212yes—
46C22×Q8×C13D411yescharacteristic
47C22×Dic26—21no—
48C22×Dic26C2311yescharacteristic
49C13×C4⋊Q8—24no—
50C13×C4⋊Q8—28no—
51C13×C4⋊Q8C2312yes—
52C13×C4⋊Q8C2314yes—
53C13×C4⋊Q8C2312yes—
54C13×C4⋊Q8C2314yes—
55C13×#125—24no—
56C13×#125—28no—
57C13×#125—22no—
58C13×#125—24no—
59C13×C22⋊Q8—24no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8C2314yes—
62C4×Q8×C13—24no—
63C4×Q8×C13—24no—
64C4×Q8×C13—22no—
65C4×Q8×C13—24no—
66C4×Q8×C13D414yes—
67C4×Q8×C13C2314yes—
68C4×Q8×C13C2318yes—
69C4×Q8×C13C2314yes—
70C13×#117—24no—
71C13×#117—22no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D412yes—
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2312yes—
76#88198—28no—
77C2×#6107C2318yes—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2312yes—
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—22no—
83C2×#6101—22no—
84C2×#6101—22no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—21no—
87#88143—216no—
88#88141—28no—
89#88124—24no—
90#88124C2318yes—
91#88123—22no—
92#88123C2314yes—
93C4×Dic26—24no—
94C4×Dic26—22no—
95C4×Dic26C2314yes—
96C4×Dic26C2318yes—
97#88075C23116yes—
98#88075C2318yes—
99C22⋊#1055C2314yes—
100#88050C2318yes—
101#88048C23116yes—
102#88047C2318yes—
103C4⋊#1055C2314yes—
104C4⋊#1055C2318yes—
105#88043C2318yes—
106C4×#1055C2314yes—
107#61829—131nomaximal, Sylow
108C2×Q8×C13—24no—
109C2×Q8×C13—24no—
110C2×Q8×C13—22no—
111C2×Q8×C13C2×D414yes—
112C2×Q8×C13C2414yes—
113C22×C4×C13C2×D412yes—
114C22×C4×C13C2×D412yes—
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2411yescharacteristic
118C22×Dic13—21no—
119C22×Dic13—21no—
120C22×Dic13—22no—
121C2×Dic26—21no—
122C2×Dic26—24no—
123C2×Dic26—24no—
124C2×Dic26—44no—
125C2×Dic26C2412yes—
126C13×C4⋊C4—24no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—24no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—24no—
131C13×C4⋊C4—24no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—28no—
134C13×C4⋊C4—24no—
135C13×C4⋊C4C2×D414yes—
136C13×C4⋊C4C2×D418yes—
137C13×C4⋊C4C2414yes—
138C13×C22⋊C4—24no—
139C42×C13—28no—
140C42×C13—24no—
141C42×C13C2×D412yes—
142C42×C13C2×D414yes—
143C42×C13C2412yes—
144C42×C13C2414yes—
145#6107—216no—
146C4⋊Dic13—22no—
147C4⋊Dic13—21no—
148C4⋊Dic13—24no—
149C4⋊Dic13C2414yes—
150C4⋊Dic13C2412yes—
151#6101—24no—
152#6101—28no—
153#6101—28no—
154#6101—28no—
155C4×Dic13—28no—
156C4×Dic13—24no—
157C2×#1055C2418yes—
158#3502D1311yescharacteristic
159C2×#557—131no—
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—28no—
169Q8×C13—28no—
170Q8×C13—84no—
171Q8×C13—82no—
172C2×C4×C13—24no—
173C2×C4×C13—22no—
174C2×C4×C13—24no—
175C2×C4×C13—24no—
176C2×C4×C13—42no—
177C2×C4×C13—41no—
178C2×C4×C13#13714yes—
179C2×C4×C13C22×D414yes—
180C2×C4×C13C22×D414yes—
181C2×C4×C13C22×D412yes—
182C2×C4×C13C22×D411yescharacteristic
183C2×C4×C13C22×D412yes—
184C2×C4×C13C2511yescharacteristic
185C2×Dic13—24no—
186C2×Dic13—22no—
187C2×Dic13—22no—
188C2×Dic13—24no—
189C2×Dic13—42no—
190C2×Dic13—44no—
191Dic26—24no—
192Dic26—22no—
193Dic26—48no—
194Dic262−1+414yes—
195#1055—28no—
196Q82C2×D1314yes—
197#557—24no—
198#557—138no—
199#557—264no—
200#557C2×D1314yes—
201#544—21no—
202#544—22no—
203#533C2×D1312yes—
204#533C2×D1314yes—
205C2×C4⋊Q8—131no—
206C2×C4⋊Q8—261no—
207C2×#125—132no—
208C2×#125—262no—
209#519—21no—
210C2×C4×Q8—131no—
211C2×C4×Q8—132no—
212C2×C4×Q8—261no—
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—21no—
239C4×C13—24no—
240C4×C13—44no—
241C4×C13—44no—
242C4×C13C2×#13714yes—
243C4×C13C2×2−1+412yes—
244Dic13—24no—
245Dic13—42no—
246Dic13—44no—
247C22×Q8—131no—
248C22×Q8—261no—
249C22×Q8C22⋊D1311yescharacteristic
250C2×Q16—138no—
251C4⋊Q8—24no—
252C4⋊Q8—28no—
253C4⋊Q8—134no—
254C4⋊Q8—268no—
255C4⋊Q8—262no—
256C4⋊Q8C22×D1312yes—
257C4⋊Q8C22×D1314yes—
258C4⋊Q8C22×D1314yes—
259C4⋊Q8C22×D1312yes—
260#125—24no—
261#125—28no—
262#125—24no—
263#125—22no—
264#125—138no—
265#125—2616no—
266#125—264no—
267C22⋊Q8—24no—
268C22⋊Q8—22no—
269C22⋊Q8C22×D1314yes—
270C4×Q8—24no—
271C4×Q8—24no—
272C4×Q8—24no—
273C4×Q8—22no—
274C4×Q8—134no—
275C4×Q8—138no—
276C4×Q8—268no—
277C4×Q8—264no—
278C4×Q8—262no—
279C4×Q8C22⋊D1314yes—
280C4×Q8C22×D1314yes—
281C4×Q8C22×D1318yes—
282C4×Q8C22×D1314yes—
283#117—24no—
284#117—22no—
285C2×C4⋊C4—131no—
286C2×C4⋊C4—132no—
287C2×C4⋊C4—261no—
288C2×C4⋊C4—262no—
289C2×C4⋊C4—262no—
290C2×C4⋊C4—262no—
291C2×C4⋊C4—261no—
292C2×C4⋊C4C22⋊D1311yescharacteristic
293C2×C4⋊C4C22⋊D1312yes—
294C2×C42—262no—
295C2×C42—261no—
296C2×C42C22×D1312yes—
297C2×C42C22×D1311yescharacteristic
298#107—138no—
299#106—1316no—
300C4⋊C8—134no—
301C4⋊C8—138no—
302#103—138no—
303#103—1316no—
304#103—138no—
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—22no—
315C2×Q8—132no—
316C2×Q8—264no—
317C2×Q8—261no—
318C2×Q8—264no—
319C2×Q8—524no—
320C2×Q8C2×C22⋊D1314yes—
321C2×Q8C23×D1314yes—
322C22×C4—261no—
323C22×C4—261no—
324C22×C4—262no—
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—24no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—28no—
340C4⋊C4—24no—
341C4⋊C4—134no—
342C4⋊C4—132no—
343C4⋊C4—261no—
344C4⋊C4—262no—
345C4⋊C4—264no—
346C4⋊C4—268no—
347C4⋊C4—268no—
348C4⋊C4—268no—
349C4⋊C4—264no—
350C4⋊C4C2×C22⋊D1314yes—
351C4⋊C4C2×C22⋊D1318yes—
352C4⋊C4C23×D1314yes—
353C22⋊C4—24no—
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—28no—
365Q8—28no—
366Q8—84no—
367Q8—82no—
368Q8—134no—
369Q8—264no—
370Q8—262no—
371Q8—528no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—264no—
379C2×C4—262no—
380C2×C4—262no—
381C2×C4—264no—
382C2×C4—522no—
383C2×C4—524no—
384C2×C4#8819614yes—
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×#8819612yes—
395C22C23×C22⋊D1311yescharacteristic
396C4—21no—
397C4—24no—
398C4—24no—
399C4—22no—
400C4—44no—
401C4—44no—
402C4—264no—
403C4—524no—
404C4—522no—
405C4C2×#8819614yes—
406C4D13×2−1+412yes—
407C2—22no—
408C2#1312848411yescharacteristic
409C2C22×#8819611yescharacteristic
410C2#1312962211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3502C2
socleC22×C13C23×D4
prime radicalC23×C13C22×D4
hypercenter#3502D13
hypocenterC13#61829
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #3502

Complements

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

NH ≅ G/Ntype
2. #13127764C2semidirect
3. #13127635C2semidirect
362. C13#61829semidirect

Maximal subgroups

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

subgroupindex
C2×#117192722
#131277642
#131276352
#131260382
#131259772
#131249622
#131248712
#131239212
C13×#35022
#6182913