Finite Group Databasebeta

← #15836911

Subgroups — #15836911

Order 3328.

912 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125781C212yesmaximal, complemented
2#13120657C211yesmaximal, characteristic
3#13113810C214yesmaximal, complemented
4#13113793C214yesmaximal
5#13113400C212yesmaximal, complemented
6#13113150C211yesmaximal, characteristic
7C13×#3458C211yesmaximal, characteristic
8C13×#544—22no—
9C13×#544—22no—
10C13×#544—21no—
11C13×#544C2212yes—
12C13×#543—21no—
13C13×#543C2212yes—
14C13×#533—24no—
15C13×#533—21no—
16C13×#533C2212yes—
17C2×C13×#117—21no—
18C2×C13×#117C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20#11718873—21no—
21#11718754—22no—
22#11718753—22no—
23#11718711C2218yes—
24#11718692—24no—
25#11718647—21no—
26#11718640C2212yes—
27#11718610—21no—
28#11718608C2212yes—
29#11718597C2211yescharacteristic
30#11718589—21no—
31#11718586C2212yes—
32#11718130C2218yes—
33#11718120C2212yes—
34#11718117C2212yes—
35C23×C4×C13D411yescharacteristic
36C22×Dic26C2312yes—
37C13×C4⋊Q8—24no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—24no—
41C13×C4⋊Q8D412yes—
42C13×C4⋊Q8D412yes—
43C13×#125—24no—
44C13×#125—22no—
45C13×#125—24no—
46C13×#125—22no—
47C13×C22⋊Q8—24no—
48C13×C22⋊Q8—24no—
49C13×C22⋊Q8—24no—
50C13×C22⋊Q8—22no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8—24no—
54C13×C22⋊Q8C2314yes—
55C4×Q8×C13—22no—
56C4×Q8×C13—22no—
57C4×Q8×C13—22no—
58C4×Q8×C13D414yes—
59C13×#117—22no—
60C13×#117—22no—
61C13×#117—22no—
62C13×#117—22no—
63C13×#117—22no—
64C13×#117—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C13×C22⋊C4C2311yescharacteristic
72C2×C42×C13—22no—
73C2×C42×C13D411yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—22no—
76C2×#6107—28no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×#6101—22no—
81#88123—22no—
82#88123—22no—
83#88071—22no—
84#88071—21no—
85#88071—22no—
86#88071C2312yes—
87C22⋊#1055C2314yes—
88#88050—28no—
89C4⋊#1055—22no—
90C4×#1055—22no—
91#18303—131nomaximal, Sylow
92C24×C13C2×D411yescharacteristic
93C2×Q8×C13—22no—
94C2×Q8×C13—22no—
95C2×Q8×C13—22no—
96C2×Q8×C13C2×D414yes—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13Q1614yescomplemented
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2411yescharacteristic
109C22×Dic13—22no—
110C22×Dic13—22no—
111C2×Dic26—24no—
112C2×Dic26—82no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—22no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—24no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—24no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—24no—
126C13×C4⋊C4C2×D414yes—
127C13×C22⋊C4—24no—
128C13×C22⋊C4—24no—
129C13×C22⋊C4—22no—
130C13×C22⋊C4—22no—
131C42×C13—24no—
132C42×C13—24no—
133C42×C13—21no—
134C42×C13—21no—
135C42×C13C2×D412yes—
136C42×C13C2×D412yes—
137C22⋊Dic13—82no—
138#6107—88no—
139C4⋊Dic13—42no—
140C4⋊Dic13—41no—
141C4⋊Dic13—41no—
142C4⋊Dic13—42no—
143#6101—82no—
144C2×#1055—24no—
145#3458D1311yescharacteristic
146#3209—132no—
147#2628—131no—
148#1605—134no—
149#1602—134no—
150#1518—132no—
151#1458—131no—
152C23×C13—21no—
153C23×C13—21no—
154C23×C13—41no—
155C23×C13—41no—
156C23×C13C2×Q1612yes—
157C23×C13C22×D411yescharacteristic
158Q8×C13—44no—
159Q8×C13—82no—
160Q8×C13—82no—
161Q8×C13—82no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—24no—
165C2×C4×C13—24no—
166C2×C4×C13—24no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—24no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—82no—
175C2×C4×C13—82no—
176C2×C4×C13#12012yes—
177C2×C4×C13#12011yescharacteristic
178C2×C4×C13#12011yescharacteristic
179C2×C4×C13C2×Q1612yes—
180C2×C4×C13C2×Q1612yes—
181C2×C4×C13#13712yes—
182C2×C4×C13C22×D412yes—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189Dic26—48no—
190#1055—44no—
191#544—22no—
192#544—22no—
193#544—21no—
194#544C2×D1312yes—
195#543—21no—
196#543C2×D1312yes—
197#533—24no—
198#533—21no—
199#533C2×D1312yes—
200C2×C4⋊Q8—131no—
201C2×#117—21no—
202C2×#117C2×D1311yescharacteristic
203#494—262no—
204#487—262no—
205#462—264no—
206#451—138no—
207#431—132no—
208#400—261no—
209#399—261no—
210#395—132no—
211#393—132no—
212#389—261no—
213#382—131no—
214#380—261no—
215#328—138no—
216#324—132no—
217#323—132no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—22no—
221C22×C13—42no—
222C22×C13—41no—
223C22×C13—41no—
224C22×C13—81no—
225C22×C13C2×#12011yescharacteristic
226C22×C13C22×Q1611yescharacteristic
227C22×C13C2×#13711yescharacteristic
228C4×C13—22no—
229C4×C13—22no—
230C4×C13—22no—
231C4×C13—41no—
232C4×C13—44no—
233C4×C13—41no—
234C4×C13—44no—
235C4×C13#45112yes—
236C4×C13#45112yes—
237Dic13—82no—
238Dic13—82no—
239C22×Q8—132no—
240C23×C4C22⋊D1311yescharacteristic
241C2×Q16—268no—
242C4⋊Q8—24no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—24no—
246C4⋊Q8—262no—
247C4⋊Q8—262no—
248C4⋊Q8C22⋊D1312yes—
249C4⋊Q8C22⋊D1312yes—
250#125—24no—
251#125—22no—
252#125—24no—
253#125—22no—
254C22⋊Q8—24no—
255C22⋊Q8—24no—
256C22⋊Q8—24no—
257C22⋊Q8—22no—
258C22⋊Q8—22no—
259C22⋊Q8—22no—
260C22⋊Q8—24no—
261C22⋊Q8C22×D1314yes—
262C4×Q8—22no—
263C4×Q8—22no—
264C4×Q8—22no—
265C4×Q8C22⋊D1314yes—
266#117—22no—
267#117—22no—
268#117—22no—
269#117—22no—
270#117—22no—
271#117—22no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—261no—
275C2×C4⋊C4—261no—
276C2×C4⋊C4—261no—
277C2×C4⋊C4—262no—
278C2×C4⋊C4C22⋊D1311yescharacteristic
279C2×C4⋊C4C22×D1311yescharacteristic
280C2×C22⋊C4—22no—
281C2×C22⋊C4—262no—
282C2×C22⋊C4C22⋊D1311yescharacteristic
283C2×C22⋊C4C22×D1311yescharacteristic
284C2×C42—22no—
285C2×C42C22⋊D1311yescharacteristic
286C2×C42C22×D1311yescharacteristic
287C4⋊C8—262no—
288#103—268no—
289C22⋊C8—134no—
290C4×C8—262no—
291#95—132no—
292#95—262no—
293#95—261no—
294#95—262no—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—42no—
298C2×C13C2×#45111yescharacteristic
299C2×C13#302211yescharacteristic
300C2×C13#302711yescharacteristic
301C24C2×C22⋊D1311yescharacteristic
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—264no—
306C2×Q8—1042no—
307C2×Q8C2×C22⋊D1314yes—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—262no—
314C22×C4—262no—
315C22×C4#610714yescomplemented
316C22×C4C2×C22⋊D1311yescharacteristic
317C22×C4C2×C22⋊D1311yescharacteristic
318C22×C4C2×C22⋊D1311yescharacteristic
319C22×C4C2×C22⋊D1311yescharacteristic
320C22×C4C2×C22⋊D1311yescharacteristic
321C22×C4C23×D1311yescharacteristic
322Q16—1048no—
323C2×C8—264no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—24no—
337C4⋊C4—522no—
338C4⋊C4—522no—
339C4⋊C4—521no—
340C4⋊C4—521no—
341C4⋊C4—1042no—
342C4⋊C4C2×C22⋊D1314yes—
343C22⋊C4—24no—
344C22⋊C4—24no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—1042no—
348C42—24no—
349C42—24no—
350C42—21no—
351C42—21no—
352C42C2×C22⋊D1312yes—
353C42C2×C22⋊D1312yes—
354C13#1830311yescharacteristic, complemented, Sylow
355C23—21no—
356C23—21no—
357C23—41no—
358C23—41no—
359C23C2×#610712yes—
360C23C22×C22⋊D1311yescharacteristic
361Q8—44no—
362Q8—82no—
363Q8—82no—
364Q8—82no—
365Q8—528no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—24no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—522no—
381C2×C4—522no—
382C2×C4—522no—
383C2×C4—522no—
384C2×C4—522no—
385C2×C4—522no—
386C2×C4#8819612yes—
387C2×C4C2×#610712yes—
388C2×C4C2×#610712yes—
389C2×C4#8820712yes—
390C2×C4#8820711yescharacteristic
391C2×C4#8820711yescharacteristic
392C2×C4C22×C22⋊D1312yes—
393C8—524no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22C2×#8819611yescharacteristic
402C22C22×#610711yescharacteristic
403C22C2×#8820711yescharacteristic
404C4—22no—
405C4—22no—
406C4—22no—
407C4—41no—
408C4—44no—
409C4—41no—
410C4—44no—
411C4—1042no—
412C4—1042no—
413C4#1171888912yes—
414C4#1171888912yes—
415C2—21no—
416C2—21no—
417C2—42no—
418C2C2×#1171888911yescharacteristic
419C2#1312421511yescharacteristic
420C2#1312423811yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3458C2
socleC22×C13C2×#120
prime radicalC24×C13C2×D4
hypercenter#3458D13
hypocenterC13#18303
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3458

Complements

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

NH ≅ G/Ntype
1. #13125781C2semidirect
3. #13113810C2semidirect
5. #13113400C2semidirect
102. C22×C4×C13Q16semidirect
315. C22×C4#6107semidirect
354. C13#18303semidirect

Maximal subgroups

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

subgroupindex
#131257812
#131206572
#131138102
#131137932
#131134002
#131131502
C13×#34582
#1830313