Finite Group Databasebeta

← #15758281

Subgroups — #15758281

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6099C211yesmaximal, characteristic
2#13114816C211yesmaximal, characteristic
3C2×Q8⋊#1055C212yesmaximal, complemented
4#13112677C212yesmaximal, complemented
5C4×C13×C22⋊Q8C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C22×#6099—21no—
10C13×#391C411yescharacteristic
11C13×#389C411yescharacteristic
12C13×#387—21no—
13C13×#385—21no—
14C13×#380C411yescharacteristic
15C4×C13×C4⋊C4—21no—
16C4×C13×C4⋊C4C2211yescharacteristic
17C4×C13×C22⋊C4—21no—
18C2×C22⋊#1055—21no—
19C2×C4⋊#1055C2212yes—
20C4×#6099—24no—
21C2×#88043—21no—
22C2×C4×#1055C2212yes—
23Q8⋊#1055—24no—
24#11718116—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C13×C22⋊Q8—22no—
30C13×C22⋊Q8—22no—
31C4×Q8×C13—22no—
32C4×Q8×C13—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C42×C13—22no—
42C2×C42×C13—22no—
43C2×C42×C13—21no—
44C2×C42×C13—21no—
45C2×C42×C13C2×C411yescharacteristic
46C2×C42×C13D411yescharacteristic
47C2×C42×C13D411yescharacteristic
48C2×C42×C13C2311yescharacteristic
49C2×#6099—24no—
50C2×#6099—24no—
51C2×#6099—24no—
52C22×#1055—22no—
53C22×#1055—22no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95—21no—
59C22⋊#1055—42no—
60C4⋊#1055—22no—
61C4⋊#1055—22no—
62#88043—24no—
63C4×#1055—22no—
64C4×#1055D414yes—
65#9077—131nomaximal, Sylow
66C24×C13C22⋊C411yescharacteristic
67C2×Q8×C13—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13M1612yescomplemented
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—22no—
82C22×C4×C13—21no—
83C22×C4×C13—22no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22×C411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C13×C4⋊C4—24no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4M1612yescomplemented
101C13×C22⋊C4—24no—
102C13×C22⋊C4—42no—
103C42×C13—22no—
104C42×C13—21no—
105C42×C13—22no—
106C42×C13—21no—
107C42×C13—42no—
108C42×C13—41no—
109C42×C13—41no—
110C42×C13C2×D412yes—
111C42×C13#4112yes—
112#6099—216no—
113C2×#1055—24no—
114C2×#1055—24no—
115C2×#1055—24no—
116C2×#1055—42no—
117C2×#1055—42no—
118C2×#1055—42no—
119C2×C4×M16—131no—
120C4×C22⋊Q8D1311yescharacteristic
121#1797—131no—
122C2×Q8⋊C8—132no—
123#1279—132no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13#10412yes—
131C23×C13C2×C22⋊C411yescharacteristic
132Q8×C13—24no—
133Q8×C13—42no—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13#10412yes—
163C2×C4×C13C4×D412yes—
164C2×C4×C13#12011yescharacteristic
165C2×C4×C13#12112yes—
166C2×C4×C13#12311yescharacteristic
167C2×C4×C13C2×M1611yescharacteristic
168C2×C4×C13C2×M1611yescharacteristic
169C2×C4×C13#13112yes—
170C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C13#13712yes—
172C2×C4×C13#13711yescharacteristic
173#1055—28no—
174#1055—82no—
175C22×M16—261no—
176C2×C22⋊Q8Dic1311yescharacteristic
177C2×C4×Q8C2×D1311yescharacteristic
178C22×C42C2×D1311yescharacteristic
179C2×C4⋊C8—132no—
180C2×C22⋊C8—261no—
181C4×M16—264no—
182C2×#97—261no—
183C2×C4×C8—132no—
184#391Dic1311yescharacteristic
185#389Dic1311yescharacteristic
186#387—21no—
187#385—21no—
188#380Dic1311yescharacteristic
189C4×C4⋊C4—21no—
190C4×C4⋊C4C2×D1311yescharacteristic
191C4×C22⋊C4—21no—
192#336—261no—
193Q8⋊C8—264no—
194C22×C13—22no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13#38611yescharacteristic
202C22×C13#40711yescharacteristic
203C22×C13#40811yescharacteristic
204C22×C13#41711yescharacteristic
205C22×C13#41911yescharacteristic
206C22×C13C2×#10411yescharacteristic
207C22×C13C2×#10411yescharacteristic
208C4×C13—21no—
209C4×C13—22no—
210C4×C13—21no—
211C4×C13—41no—
212C4×C13—42no—
213C4×C13—41no—
214C4×C13—42no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13#43512yes—
218C4×C13#43612yes—
219C4×C13#46812yes—
220C4×C13#47012yes—
221C22×Q8C2×Dic1311yescharacteristic
222C23×C4C2×Dic1311yescharacteristic
223C23×C4C22⋊D1311yescharacteristic
224C23×C4C22⋊D1311yescharacteristic
225C2×M16—264no—
226C2×M16—264no—
227C2×M16—264no—
228C22×C8—262no—
229C22×C8—262no—
230C22⋊Q8—22no—
231C22⋊Q8—22no—
232C4×Q8—22no—
233C4×Q8—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C2×Dic1311yescharacteristic
238C2×C4⋊C4C2×Dic1311yescharacteristic
239C2×C4⋊C4C2×Dic1311yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C42—22no—
243C2×C42—22no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42C2×Dic1311yescharacteristic
247C2×C42C22⋊D1311yescharacteristic
248C2×C42C22⋊D1311yescharacteristic
249C2×C42C22×D1311yescharacteristic
250C4⋊C8—262no—
251C4⋊C8—262no—
252C22⋊C8—522no—
253#97—264no—
254C4×C8—134no—
255C4×C8—262no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261C2×C13—42no—
262C2×C13#148311yescharacteristic
263C2×C13#148511yescharacteristic
264C2×C13#148911yescharacteristic
265C2×C13#149111yescharacteristic
266C2×C13#187011yescharacteristic
267C2×C13#189411yescharacteristic
268C2×C13#189611yescharacteristic
269C24C22⋊Dic1311yescharacteristic
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8#609912yescomplemented
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4C22⋊Dic1311yescharacteristic
291C22×C4C22⋊Dic1311yescharacteristic
292C22×C4C22⋊Dic1311yescharacteristic
293C22×C4C22×Dic1311yescharacteristic
294C22×C4C2×C22⋊D1311yescharacteristic
295C22×C4C2×C22⋊D1311yescharacteristic
296M16—2616no—
297C2×C8—264no—
298C2×C8—264no—
299C2×C8—264no—
300C2×C8—522no—
301C2×C8—522no—
302C2×C8—522no—
303C4⋊C4—24no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4#609912yescomplemented
311C22⋊C4—24no—
312C22⋊C4—42no—
313C42—22no—
314C42—21no—
315C42—21no—
316C42—22no—
317C42—42no—
318C42—41no—
319C42—41no—
320C42D4×D1312yes—
321C42#612912yes—
322C13#907711yescharacteristic, complemented, Sylow
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23#8807712yes—
330C23C2×C22⋊Dic1311yescharacteristic
331Q8—24no—
332Q8—42no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4#8807712yes—
362C2×C4C2×#609911yescharacteristic
363C2×C4C2×#609911yescharacteristic
364C2×C4D4×Dic1312yes—
365C2×C4#8818911yescharacteristic
366C2×C4#8819111yescharacteristic
367C2×C4#8819312yes—
368C2×C4#8819612yes—
369C2×C4#8820212yes—
370C2×C4#8820311yescharacteristic
371C2×C4#8820511yescharacteristic
372C8—268no—
373C8—1042no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22#1171886811yescharacteristic
382C22#1171888111yescharacteristic
383C22#1171888611yescharacteristic
384C22#1171889311yescharacteristic
385C22#1171889511yescharacteristic
386C22C2×#8807711yescharacteristic
387C22C2×#8807711yescharacteristic
388C4—21no—
389C4—22no—
390C4—21no—
391C4—41no—
392C4—42no—
393C4—41no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4#1171867212yes—
398C4#1171867312yes—
399C4#1171871012yes—
400C4#1171871312yes—
401C2—42no—
402C2#1311324911yescharacteristic
403C2#1311325711yescharacteristic
404C2#1311327511yescharacteristic
405C2#1311328311yescharacteristic
406C2#1311513411yescharacteristic
407C2#1311527011yescharacteristic
408C2#1311528011yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×C22⋊Q8C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenterC4×C22⋊Q8D13
hypocenterC13#9077
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×Q8⋊#1055C2semidirect
4. #13112677C2semidirect
70. C2×Q8×C13M16semidirect
100. C13×C4⋊C4M16semidirect
273. C2×Q8#6099semidirect
310. C4⋊C4#6099semidirect
322. C13#9077semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#60992
#131148162
C2×Q8⋊#10552
#131126772
C4×C13×C22⋊Q82
#907713