Finite Group Databasebeta

← #15836835

Subgroups — #15836835

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125589C212yesmaximal
2#13120578C211yesmaximal, characteristic
3#13113844C214yesmaximal, complemented
4#13113776C214yesmaximal, complemented
5#13113408C212yesmaximal, complemented
6C2×#11718120C211yesmaximal, characteristic, complemented
7C2×C13×#544C211yesmaximal, characteristic, complemented
8C13×#544—24no—
9C13×#544—22no—
10C13×#544C2214yes—
11C2×C13×C4⋊Q8—22no—
12C2×C13×#125—22no—
13C2×C13×C22⋊Q8—21no—
14C2×C13×C22⋊Q8C2212yes—
15C2×C13×#117—21no—
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88184C2211yescharacteristic
18C2×#88183—21no—
19#11718888—22no—
20#11718874—21no—
21#11718873C2211yescharacteristic
22C2×C22⋊#1055C2212yes—
23#11718709—24no—
24#11718707C2214yes—
25#11718704C2214yes—
26#11718655—22no—
27#11718652C2212yes—
28#11718644C2212yes—
29#11718629—22no—
30#11718130C2218yes—
31#11718120C2214yes—
32C22×Q8×C13—21no—
33C22×Q8×C13D412yes—
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C22×C22⋊D13—21no—
38C22×D52C2311yescharacteristic
39C13×C4⋊Q8—28no—
40C13×C4⋊Q8—28no—
41C13×#125—28no—
42C13×#125—28no—
43C13×C22⋊Q8—24no—
44C13×C22⋊Q8—24no—
45C13×C22⋊Q8—22no—
46C13×C22⋊Q8—22no—
47C13×C22⋊Q8D414yes—
48C13×C22⋊Q8C2314yes—
49C13×#117—24no—
50C13×#117—24no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4D412yes—
59C2×C13×C4⋊C4D412yes—
60C2×C13×C4⋊C4C2312yes—
61C2×C13×C22⋊C4—22no—
62C2×C42×C13—22no—
63C2×C22⋊Dic13—21no—
64C2×#6106—24no—
65#88184—22no—
66#88184—22no—
67#88183—44no—
68C2×#6103—22no—
69C2×#6103—21no—
70C2×#6103—22no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13C2311yescharacteristic
73C2×#6101—22no—
74C22×#1055—22no—
75#88075—24no—
76#88071—22no—
77#88071C2312yes—
78C22⋊#1055—22no—
79C22⋊#1055C2314yes—
80#88049—24no—
81#88048—24no—
82#18294—131nomaximal, Sylow
83C24×C13C2×D411yescharacteristic
84C23×D13—21no—
85C2×Q8×C13—24no—
86C2×Q8×C13—22no—
87C2×Q8×C13—82no—
88C2×Q8×C13—82no—
89C2×Q8×C13C2×D414yes—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—81no—
98C22×C4×C13—81no—
99C22×C4×C13SD1614yescomplemented
100C22×C4×C13C2×D412yes—
101C22×C4×C13C2×D412yes—
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D412yes—
104C22×C4×C13C2×D412yes—
105C22×C4×C13C2411yescharacteristic
106C2×C22⋊D13—41no—
107C2×C22⋊D13—41no—
108C2×C22⋊D13—42no—
109C2×C22⋊D13—42no—
110C22×Dic13—21no—
111C22×Dic13—22no—
112C2×D52—22no—
113C2×D52—81no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4—24no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—28no—
118C13×C4⋊C4—24no—
119C13×C4⋊C4—24no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—24no—
122C13×C4⋊C4—24no—
123C13×C4⋊C4C2×D414yes—
124C13×C22⋊C4—24no—
125C13×C22⋊C4—24no—
126C42×C13—28no—
127C22⋊Dic13—42no—
128#6106—84no—
129#6103—42no—
130#6103—44no—
131#6103—82no—
132C4⋊Dic13—22no—
133C4⋊Dic13—81no—
134#6101—44no—
135C2×#1055—24no—
136C2×#1055—82no—
137C2×#544D1311yescharacteristic, complemented
138#3187—132no—
139#2618—131no—
140#1611—134no—
141#1599—134no—
142#1520—132no—
143C2×#324—131no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13#12011yescharacteristic
147C23×C13#12011yescharacteristic
148C23×C13C2×SD1612yes—
149C23×C13#13712yes—
150C23×C13C22×D411yescharacteristic
151C22×D13—42no—
152C22×D13—42no—
153C22×D13—41no—
154C22×D13—41no—
155C22×D13—41no—
156Q8×C13—44no—
157Q8×C13—82no—
158Q8×C13—84no—
159C2×C4×C13—22no—
160C2×C4×C13—22no—
161C2×C4×C13—24no—
162C2×C4×C13—24no—
163C2×C4×C13—24no—
164C2×C4×C13—24no—
165C2×C4×C13—22no—
166C2×C4×C13—42no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—42no—
170C2×C4×C13—44no—
171C2×C4×C13—42no—
172C2×C4×C13—44no—
173C2×C4×C13—42no—
174C2×C4×C13—81no—
175C2×C4×C13#12012yes—
176C2×C4×C13C2×SD1614yes—
177C2×C4×C13C22×D412yes—
178C22⋊D13—82no—
179C22⋊D13—82no—
180C2×Dic13—42no—
181C2×Dic13—42no—
182C2×Dic13—41no—
183C2×Dic13—41no—
184C2×Dic13—42no—
185C2×Dic13—41no—
186D52—44no—
187#1055—44no—
188#544—24no—
189#544—22no—
190#544C2×D1314yes—
191C2×C4⋊Q8—22no—
192C2×#125—22no—
193C2×#123—261no—
194C2×C22⋊Q8—21no—
195C2×C22⋊Q8C2×D1312yes—
196C2×#121—131no—
197C2×#117—21no—
198C22×C4⋊C4C2×D1311yescharacteristic
199#483—134no—
200#481—262no—
201#465—264no—
202#450—134no—
203#448—262no—
204C2×C22⋊C8—132no—
205#398—132no—
206#396—262no—
207#394—132no—
208#386—261no—
209#380—131no—
210#328—138no—
211#324—134no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—42no—
219C22×C13—42no—
220C22×C13#44812yes—
221C22×C13#44812yes—
222C22×C13C2×#12011yescharacteristic
223C22×C13C22×SD1611yescharacteristic
224C22×C13C2×#13711yescharacteristic
225C2×D13—82no—
226C2×D13—82no—
227C2×D13—81no—
228C2×D13—81no—
229C2×D13—81no—
230C4×C13—24no—
231C4×C13—22no—
232C4×C13—22no—
233C4×C13—44no—
234C4×C13—42no—
235C4×C13—44no—
236Dic13—82no—
237Dic13—81no—
238C22×Q8—21no—
239C22×Q8C22⋊D1312yes—
240C22×D4—131no—
241C22×D4—261no—
242C23×C4C22⋊D1311yescharacteristic
243C23×C4C22⋊D1311yescharacteristic
244C23×C4C22×D1311yescharacteristic
245C2×SD16—264no—
246C22×C8—262no—
247C4⋊Q8—28no—
248C4⋊Q8—28no—
249#125—28no—
250#125—28no—
251#123—524no—
252C22⋊Q8—24no—
253C22⋊Q8—24no—
254C22⋊Q8—22no—
255C22⋊Q8—22no—
256C22⋊Q8C22⋊D1314yes—
257C22⋊Q8C22×D1314yes—
258#121—262no—
259#121—262no—
260#117—24no—
261#117—24no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—131no—
270C2×C4⋊C4—262no—
271C2×C4⋊C4—261no—
272C2×C4⋊C4C22⋊D1312yes—
273C2×C4⋊C4C22⋊D1312yes—
274C2×C4⋊C4C22×D1312yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—261no—
277C2×C22⋊C4—261no—
278C2×C22⋊C4—262no—
279C2×C22⋊C4—262no—
280C2×C42—22no—
281#106—264no—
282#103—264no—
283#102—264no—
284C22⋊C8—134no—
285C22⋊C8—262no—
286#95—132no—
287#95—262no—
288C2×C13—21no—
289C2×C13—21no—
290C2×C13—22no—
291C2×C13—22no—
292C2×C13C2×#44811yescharacteristic
293C2×C13#302011yescharacteristic
294C2×C13#302611yescharacteristic
295D13—161no—
296C24—261no—
297C24C2×C22⋊D1311yescharacteristic
298C2×Q8—24no—
299C2×Q8—22no—
300C2×Q8—82no—
301C2×Q8—82no—
302C2×Q8C2×C22⋊D1314yes—
303C2×D4—262no—
304C2×D4—522no—
305C2×D4—522no—
306C2×D4—521no—
307C2×D4—521no—
308C2×D4—1041no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—81no—
317C22×C4—81no—
318C22×C4—262no—
319C22×C4—261no—
320C22×C4#610614yescomplemented
321C22×C4C2×C22⋊D1312yes—
322C22×C4C2×C22⋊D1312yes—
323C22×C4C2×C22⋊D1311yescharacteristic
324C22×C4C2×C22⋊D1312yes—
325C22×C4C2×C22⋊D1312yes—
326C22×C4C23×D1311yescharacteristic
327SD16—1044no—
328C2×C8—264no—
329C2×C8—1042no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—28no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—22no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—262no—
340C4⋊C4—524no—
341C4⋊C4—1041no—
342C4⋊C4C2×C22⋊D1314yes—
343C22⋊C4—24no—
344C22⋊C4—24no—
345C22⋊C4—522no—
346C22⋊C4—524no—
347C22⋊C4—522no—
348C22⋊C4—1042no—
349C42—28no—
350C13#1829411yescharacteristic, complemented, Sylow
351C23—41no—
352C23—41no—
353C23—522no—
354C23—522no—
355C23—521no—
356C23—521no—
357C23—521no—
358C23C2×#610612yes—
359C23#8819612yes—
360C23#8820711yescharacteristic
361C23#8820711yescharacteristic
362C23C22×C22⋊D1311yescharacteristic
363Q8—44no—
364Q8—82no—
365Q8—84no—
366D4—524no—
367D4—1042no—
368D4—1042no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—81no—
385C2×C4—522no—
386C2×C4—522no—
387C2×C4—522no—
388C2×C4—521no—
389C2×C4—521no—
390C2×C4—521no—
391C2×C4C2×#610614yes—
392C2×C4#8820712yes—
393C2×C4C22×C22⋊D1312yes—
394C8—524no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—1042no—
404C22—1042no—
405C22—1041no—
406C22—1041no—
407C22—1041no—
408C22#1171888812yes—
409C22#1171888812yes—
410C22C22×#610611yescharacteristic
411C22C2×#8819611yescharacteristic
412C22C2×#8820711yescharacteristic
413C4—22no—
414C4—22no—
415C4—24no—
416C4—44no—
417C4—42no—
418C4—44no—
419C4—1042no—
420C4—1041no—
421C2—21no—
422C2—21no—
423C2—22no—
424C2—22no—
425C2—2081no—
426C2C2×#1171888811yescharacteristic
427C2#1312420011yescharacteristic
428C2#1312423311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC22×C13C2×#120
prime radicalC2×#88184C22
hypercenterC2×#544D13
hypocenterC13#18294
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13113844C2semidirect
4. #13113776C2semidirect
5. #13113408C2semidirect
6. C2×#11718120C2semidirect
7. C2×C13×#544C2semidirect
99. C22×C4×C13SD16semidirect
137. C2×#544D13semidirect
320. C22×C4#6106semidirect
350. C13#18294semidirect

Maximal subgroups

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

subgroupindex
#131255892
#131205782
#131138442
#131137762
#131134082
C2×#117181202
C2×C13×#5442
#1829413