Finite Group Databasebeta

← #15836828

Subgroups — #15836828

Order 3328.

1220 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125593C212yesmaximal, complemented
2#13120649C211yesmaximal, characteristic, complemented
3#13113873C214yesmaximal, complemented
4#13113805C214yesmaximal, complemented
5#13113404C212yesmaximal, complemented
6C2×#11718120C211yesmaximal, characteristic, complemented
7C2×C13×#537C211yesmaximal, characteristic
8C22×C13×#41—21no—
9C13×#537—24no—
10C13×#537—22no—
11C13×#537C2214yes—
12C2×C13×C22⋊Q8—22no—
13C2×C13×#121—22no—
14C2×C13×#121—21no—
15C2×C13×#121C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18#11718879—22no—
19#11718873C2211yescharacteristic
20#11718872—21no—
21#11718871—21no—
22C2×C22⋊#1055C2212yes—
23#11718702—24no—
24#11718701C2214yescomplemented
25#11718695C2214yescomplemented
26#11718647C2212yescomplemented
27#11718645—22no—
28#11718640C2212yescomplemented
29#11718632—22no—
30#11718129C2218yescomplemented
31#11718120C2214yescomplemented
32C2×C13×#41—24no—
33C2×C13×#41—24no—
34C2×C13×#41—44no—
35C2×C13×#41—44no—
36C22×Q8×C13—21no—
37C22×D4×C13—21no—
38C22×D4×C13—22no—
39C22×D4×C13—21no—
40C22×D4×C13D412yes—
41C23×C4×C13—22no—
42C23×C4×C13D411yescharacteristic
43C23×C4×C13D411yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C22×Dic26C2311yescharacteristic
46C13×C22⋊Q8—28no—
47C13×C22⋊Q8—28no—
48C13×#121—24no—
49C13×#121—28no—
50C13×#121—28no—
51C13×#121—24no—
52C13×#121—22no—
53C13×#121—22no—
54C13×#121D414yes—
55C13×#121C2314yes—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4D412yes—
60C2×C13×C4⋊C4D412yes—
61C2×C13×C4⋊C4C2312yes—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—22no—
64C2×C22⋊Dic13—21no—
65C2×C22⋊Dic13—21no—
66C2×#6105—24no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13C2311yescharacteristic
69#88178—22no—
70#88178—22no—
71C2×#6101—21no—
72C2×#6101—22no—
73C22×#1055—22no—
74#88072—24no—
75#88071—22no—
76#88071—22no—
77#88071—22no—
78#88071C2312yes—
79C22⋊#1055—22no—
80C22⋊#1055C2314yes—
81#88050—24no—
82#88048—24no—
83#18293—131nomaximal, Sylow
84C24×C13—22no—
85C24×C13C2×D411yescharacteristic
86C13×#41—48no—
87C13×#41—416no—
88C13×#41—48no—
89C2×Q8×C13—24no—
90C2×Q8×C13—44no—
91C2×D4×C13—24no—
92C2×D4×C13—24no—
93C2×D4×C13—24no—
94C2×D4×C13—24no—
95C2×D4×C13—22no—
96C2×D4×C13—44no—
97C2×D4×C13—44no—
98C2×D4×C13—44no—
99C2×D4×C13—82no—
100C2×D4×C13—82no—
101C2×D4×C13C2×D414yes—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—28no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—48no—
110C22×C4×C13—81no—
111C22×C4×C13—81no—
112C22×C4×C13SD1614yescomplemented
113C22×C4×C13C2×D412yes—
114C22×C4×C13C2×D412yes—
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D412yes—
117C22×C4×C13C2×D412yes—
118C22×C4×C13C2411yescharacteristic
119C22×Dic13—21no—
120C22×Dic13—22no—
121C22×Dic13—21no—
122C2×Dic26—22no—
123C2×Dic26—81no—
124C13×C4⋊C4—24no—
125C13×C4⋊C4—24no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—24no—
128C13×C4⋊C4C2×D414yes—
129C13×C22⋊C4—28no—
130C13×C22⋊C4—24no—
131C13×C22⋊C4—24no—
132C22⋊Dic13—41no—
133C22⋊Dic13—41no—
134C22⋊Dic13—42no—
135#6105—84no—
136C4⋊Dic13—22no—
137C4⋊Dic13—81no—
138#6101—42no—
139#6101—82no—
140C2×#1055—24no—
141C2×#1055—82no—
142C2×#537D1311yescharacteristic
143#3187—132no—
144#2627—131no—
145#1616—134no—
146#1604—134no—
147#1519—132no—
148C2×#324—131no—
149C23×C13—24no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—44no—
153C23×C13—44no—
154C23×C13—44no—
155C23×C13#12011yescharacteristic
156C23×C13#12011yescharacteristic
157C23×C13C2×SD1612yes—
158C23×C13AGL(1,ℤ/8)12yes—
159C23×C13C22×D411yescharacteristic
160Q8×C13—48no—
161D4×C13—48no—
162D4×C13—44no—
163D4×C13—44no—
164D4×C13—44no—
165D4×C13—48no—
166D4×C13—82no—
167D4×C13—84no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—24no—
171C2×C4×C13—24no—
172C2×C4×C13—22no—
173C2×C4×C13—24no—
174C2×C4×C13—42no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—42no—
178C2×C4×C13—416no—
179C2×C4×C13—42no—
180C2×C4×C13—44no—
181C2×C4×C13—42no—
182C2×C4×C13—81no—
183C2×C4×C13#12012yes—
184C2×C4×C13C2×SD1614yes—
185C2×C4×C13C22×D412yes—
186C2×Dic13—42no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189C2×Dic13—42no—
190C2×Dic13—41no—
191C2×Dic13—41no—
192C2×Dic13—42no—
193Dic26—44no—
194#1055—44no—
195C22×#41—21no—
196#537—24no—
197#537—22no—
198#537C2×D1314yes—
199C2×C22⋊Q8—22no—
200C2×C22⋊Q8—131no—
201C2×#121—22no—
202C2×#121—21no—
203C2×#121C2×D1312yes—
204C22×C4⋊C4C2×D1311yescharacteristic
205#483—262no—
206#481—134no—
207#465—264no—
208#450—262no—
209#448—134no—
210C2×C22⋊C8—132no—
211#400—132no—
212#398—262no—
213#395—132no—
214#385—261no—
215#381—261no—
216#380—131no—
217#327—138no—
218#324—134no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—42no—
226C22×C13—42no—
227C22×C13—44no—
228C22×C13—44no—
229C22×C13—44no—
230C22×C13—88no—
231C22×C13#45012yes—
232C22×C13#45012yes—
233C22×C13C2×#12011yescharacteristic
234C22×C13C22×SD1611yescharacteristic
235C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
236C4×C13—24no—
237C4×C13—22no—
238C4×C13—22no—
239C4×C13—44no—
240C4×C13—42no—
241Dic13—82no—
242Dic13—81no—
243Dic13—81no—
244C2×#41—24no—
245C2×#41—24no—
246C2×#41—44no—
247C2×#41—44no—
248C22×Q8—21no—
249C22×Q8—131no—
250C22×D4—21no—
251C22×D4—22no—
252C22×D4—21no—
253C22×D4C22⋊D1312yes—
254C23×C4—22no—
255C23×C4C22⋊D1311yescharacteristic
256C23×C4C22⋊D1311yescharacteristic
257C23×C4C22×D1311yescharacteristic
258C2×SD16—264no—
259C22×C8—262no—
260C22⋊Q8—28no—
261C22⋊Q8—28no—
262C22⋊Q8—262no—
263C22⋊Q8—262no—
264#121—24no—
265#121—28no—
266#121—28no—
267#121—24no—
268#121—22no—
269#121—22no—
270#121C22⋊D1314yes—
271#121C22×D1314yes—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—131no—
276C2×C4⋊C4—261no—
277C2×C4⋊C4—262no—
278C2×C4⋊C4—261no—
279C2×C4⋊C4C22⋊D1312yes—
280C2×C4⋊C4C22⋊D1312yes—
281C2×C4⋊C4C22×D1312yes—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—261no—
285C2×C22⋊C4—261no—
286#106—264no—
287#103—264no—
288#102—264no—
289C22⋊C8—134no—
290C22⋊C8—262no—
291#95—132no—
292#95—262no—
293#95—262no—
294#95—262no—
295C2×C13—21no—
296C2×C13—22no—
297C2×C13—21no—
298C2×C13—22no—
299C2×C13—84no—
300C2×C13C2×#45011yescharacteristic
301C2×C13#302011yescharacteristic
302C2×C13#302611yescharacteristic
303C24—22no—
304C24C2×C22⋊D1311yescharacteristic
305#41—48no—
306#41—416no—
307#41—48no—
308C2×Q8—24no—
309C2×Q8—44no—
310C2×Q8—262no—
311C2×Q8—1041no—
312C2×D4—24no—
313C2×D4—24no—
314C2×D4—24no—
315C2×D4—24no—
316C2×D4—22no—
317C2×D4—44no—
318C2×D4—44no—
319C2×D4—44no—
320C2×D4—82no—
321C2×D4—82no—
322C2×D4C2×C22⋊D1314yes—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—28no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—48no—
331C22×C4—81no—
332C22×C4—81no—
333C22×C4—262no—
334C22×C4—261no—
335C22×C4—261no—
336C22×C4#610514yescomplemented
337C22×C4C2×C22⋊D1312yes—
338C22×C4C2×C22⋊D1312yes—
339C22×C4C2×C22⋊D1311yescharacteristic
340C22×C4C2×C22⋊D1312yes—
341C22×C4C2×C22⋊D1312yes—
342C22×C4C23×D1311yescharacteristic
343SD16—1044no—
344C2×C8—264no—
345C2×C8—1042no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—22no—
349C4⋊C4—24no—
350C4⋊C4—262no—
351C4⋊C4—522no—
352C4⋊C4—1042no—
353C4⋊C4—1041no—
354C4⋊C4C2×C22⋊D1314yes—
355C22⋊C4—28no—
356C22⋊C4—24no—
357C22⋊C4—24no—
358C22⋊C4—522no—
359C22⋊C4—521no—
360C22⋊C4—521no—
361C13#1829311yescharacteristic, complemented, Sylow
362C23—24no—
363C23—41no—
364C23—41no—
365C23—44no—
366C23—44no—
367C23—44no—
368C23#8818612yes—
369C23C2×#610512yes—
370C23#8820711yescharacteristic
371C23#8820711yescharacteristic
372C23C22×C22⋊D1311yescharacteristic
373Q8—48no—
374Q8—524no—
375D4—44no—
376D4—48no—
377D4—44no—
378D4—44no—
379D4—48no—
380D4—82no—
381D4—84no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—416no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—81no—
397C2×C4—522no—
398C2×C4—522no—
399C2×C4—522no—
400C2×C4—522no—
401C2×C4—522no—
402C2×C4—521no—
403C2×C4—521no—
404C2×C4C2×#610514yes—
405C2×C4#8820712yes—
406C2×C4C22×C22⋊D1312yes—
407C8—524no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22—44no—
417C22—44no—
418C22—44no—
419C22—88no—
420C22#1171887912yes—
421C22#1171887912yes—
422C22C2×#8818611yescharacteristic
423C22C22×#610511yescharacteristic
424C22C2×#8820711yescharacteristic
425C4—22no—
426C4—22no—
427C4—24no—
428C4—42no—
429C4—44no—
430C4—1042no—
431C4—1041no—
432C4—1041no—
433C2—21no—
434C2—22no—
435C2—21no—
436C2—22no—
437C2—84no—
438C2C2×#1171887911yescharacteristic
439C2#1312420011yescharacteristic
440C2#1312423311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#537C2
socleC22×C13C2×#120
hypercenterC2×#537D13
hypocenterC13#18293
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13125593C2semidirect
2. #13120649C2semidirect
3. #13113873C2semidirect
4. #13113805C2semidirect
5. #13113404C2semidirect
6. C2×#11718120C2semidirect
24. #11718701C22semidirect
25. #11718695C22semidirect
26. #11718647C22semidirect
28. #11718640C22semidirect
30. #11718129C22semidirect
31. #11718120C22semidirect
112. C22×C4×C13SD16semidirect
336. C22×C4#6105semidirect
361. C13#18293semidirect

Maximal subgroups

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

subgroupindex
#131255932
#131206492
#131138732
#131138052
#131134042
C2×#117181202
C2×C13×#5372
#1829313