Finite Group Databasebeta

← #15846074

Subgroups — #15846074

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125758C211yesmaximal, characteristic, complemented
2C2×#11718731C211yesmaximal, characteristic, complemented
3#13123548C211yesmaximal, characteristic, complemented
4#13114395C214yesmaximal, complemented
5#13114271C214yesmaximal, complemented
6#13113582C211yesmaximal, characteristic, complemented
7#13113520C211yesmaximal, characteristic, complemented
8#13113504C211yesmaximal, characteristic, complemented
9C13×#3205C211yesmaximal, characteristic
10C13×#532C2211yescharacteristic
11C2×C13×#127C2211yescharacteristic
12C2×#88202—21no—
13C2×#88123C2211yescharacteristic
14C13×#493—21no—
15C13×#486—21no—
16C13×#459C2214yes—
17C13×#447—22no—
18C13×#431C2211yescharacteristic
19#11718895—21no—
20C2×#88072—21no—
21C2×#88072—21no—
22#11718754—21no—
23#11718737—21no—
24#11718731—21no—
25#11718731—21no—
26#11718731C2212yes—
27#11718731C2212yes—
28#11718701—22no—
29#11718680C2214yescomplemented
30#11718673—21no—
31#11718673C2212yescomplemented
32D4×#1055—21no—
33D4×#1055C2212yescomplemented
34#11718586C2211yescharacteristic
35#11718585C2211yescharacteristic
36C2×C4×#1055C2211yescharacteristic
37#11718136C2214yes—
38#11718074C2214yescomplemented
39#11718072C2212yescomplemented
40#11718071C2212yescomplemented
41C2×C13×#41—21no—
42C22×D4×C13—21no—
43C22×D4×C13—21no—
44C22×D4×C13—21no—
45C22×Dic26—21no—
46C2×C13×D8—24no—
47C13×C4⋊Q8D411yescharacteristic
48C13×#127—21no—
49C13×#127—21no—
50C13×#127—21no—
51C13×#127D411yescharacteristic
52C13×#127C2312yes—
53C13×#124—21no—
54C13×#121—21no—
55C13×#121D412yes—
56C4×D4×C13—21no—
57C4×D4×C13C2312yes—
58C2×C42×C13C2311yescharacteristic
59#88202—44no—
60C2×#6105—24no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13—21no—
63C2×#6099—21no—
64C2×#6099—22no—
65C22×#1055—22no—
66C22×#1055D411yescharacteristic
67C22×#1055D411yescharacteristic
68#88123—21no—
69#88123—21no—
70#88123—21no—
71#88123C2312yes—
72C13×C4⋊C8C2312yes—
73C13×#102—24no—
74C13×C22⋊C8—21no—
75C4×C8×C13—21no—
76#88072—22no—
77#88072—22no—
78#88072—22no—
79#88072—22no—
80C22⋊#1055—21no—
81C22⋊#1055—22no—
82C22⋊#1055—22no—
83#88050—24no—
84C4⋊#1055—21no—
85C4⋊#1055C2312yes—
86C4⋊#1055C2312yes—
87C4×#1055—21no—
88C4×#1055D411yescharacteristic
89C4×#1055D411yescharacteristic
90C4×#1055C2311yescharacteristic
91C4×#1055C2311yescharacteristic
92#19198—131nomaximal, Sylow
93C24×C13—41no—
94C13×#41—42no—
95C13×#41—42no—
96C2×Q8×C13—21no—
97C2×D4×C13—22no—
98C2×D4×C13—21no—
99C2×D4×C13—21no—
100C2×D4×C13—22no—
101C2×D4×C13—22no—
102C2×D4×C13—22no—
103C2×D4×C13—41no—
104C2×D4×C13—41no—
105C2×D4×C13—41no—
106C2×D4×C13—42no—
107C2×D4×C13—42no—
108C2×D4×C13—82no—
109C2×D4×C13—82no—
110C2×D4×C13C2×D412yes—
111C22×C4×C13—22no—
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×Dic13—41no—
116C2×Dic26—22no—
117C2×Dic26—41no—
118C2×Dic26—82no—
119C13×D8—84no—
120C2×C8×C13—22no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4C2×D412yes—
123C13×C22⋊C4—22no—
124C13×C22⋊C4—22no—
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13#4111yescharacteristic
128C42×C13C2411yescharacteristic
129#6105—84no—
130C4⋊Dic13—22no—
131C4⋊Dic13—22no—
132C4⋊Dic13—41no—
133C4⋊Dic13—41no—
134#6099—44no—
135#6099—42no—
136C2×#1055—22no—
137C2×#1055—22no—
138C2×#1055—22no—
139C2×#1055—22no—
140C2×#1055—44no—
141C2×#1055C2×D411yescharacteristic
142C2×#1055C2×D411yescharacteristic
143C2×#1055C2×D411yescharacteristic
144C2×#1055C2×D411yescharacteristic
145#3206—131no—
146#3205D1311yescharacteristic
147C2×#486—131no—
148#2931—131no—
149#1701—134no—
150#1681—134no—
151#1564—131no—
152#1549—131no—
153#1545—131no—
154C23×C13—22no—
155C23×C13—42no—
156C23×C13—82no—
157C23×C13—82no—
158C23×C13—82no—
159C23×C13#12111yescharacteristic
160Q8×C13—42no—
161D4×C13—24no—
162D4×C13—44no—
163D4×C13—42no—
164D4×C13—42no—
165D4×C13—44no—
166D4×C13—42no—
167D4×C13—42no—
168D4×C13—82no—
169D4×C13—82no—
170D4×C13—82no—
171D4×C13—82no—
172C2×C4×C13—22no—
173C2×C4×C13—22no—
174C2×C4×C13—22no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13#12111yescharacteristic
178C2×C4×C13#12111yescharacteristic
179C2×C4×C13#12111yescharacteristic
180C2×C4×C13#13512yes—
181C2×C4×C13AGL(1,ℤ/8)12yes—
182C2×C4×C13C22×D411yescharacteristic
183C2×C4×C13C22×D411yescharacteristic
184C2×C4×C13C2×#4111yescharacteristic
185C2×Dic13—42no—
186C2×Dic13—82no—
187Dic26—44no—
188Dic26—82no—
189C8×C13—42no—
190#1055—21no—
191#1055—21no—
192#1055—21no—
193#1055—21no—
194#1055—42no—
195#1055—42no—
196C2×#131—261no—
197#532C2×D1311yescharacteristic
198C2×C4⋊Q8—131no—
199C2×#127C2×D1311yescharacteristic
200#493—21no—
201#492—261no—
202#487—261no—
203#486—21no—
204#486—132no—
205#486—132no—
206#486—261no—
207#486—261no—
208#461—134no—
209#459C2×D1314yes—
210#448—262no—
211#447—22no—
212#436—132no—
213#436—261no—
214C8×D4—132no—
215C8×D4—261no—
216#431—131no—
217#431C2×D1311yescharacteristic
218#423—131no—
219C2×#102—261no—
220C2×#102—261no—
221#408—261no—
222C2×C4×C8—131no—
223#335—132no—
224#334—132no—
225#332—134no—
226#331—134no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—42no—
230C22×C13—42no—
231C22×C13—42no—
232C22×C13—82no—
233C22×C13—82no—
234C22×C13—82no—
235C22×C13—164no—
236C22×C13#46312yes—
237C22×C13C2×#12111yescharacteristic
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—42no—
241C4×C13#46312yes—
242C4×C13#47112yes—
243C4×C13C2×#13511yescharacteristic
244C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C13#57612yes—
246Dic13—82no—
247C2×#41—21no—
248C22×Q8—261no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—21no—
252C2×SD16—264no—
253C2×D8—24no—
254#131—524no—
255C2×M16—262no—
256C2×M16—261no—
257C22×C8—131no—
258C22×C8—131no—
259C22×C8—262no—
260C4⋊Q8—132no—
261C4⋊Q8—261no—
262C4⋊Q8—261no—
263C4⋊Q8—261no—
264C4⋊Q8C22⋊D1311yescharacteristic
265#127—21no—
266#127—21no—
267#127—21no—
268#127C22⋊D1311yescharacteristic
269#127C22×D1312yes—
270#124—21no—
271#121—21no—
272#121C22⋊D1312yes—
273C4×D4—21no—
274C4×D4C22×D1312yes—
275C2×C4⋊C4—261no—
276C2×C4⋊C4—261no—
277C2×C42C22×D1311yescharacteristic
278C4⋊C8—132no—
279C4⋊C8—132no—
280C4⋊C8—261no—
281C4⋊C8C22×D1312yes—
282#103—264no—
283#102—24no—
284#102—262no—
285#102—262no—
286#102—262no—
287#102—262no—
288C22⋊C8—21no—
289C22⋊C8—262no—
290C22⋊C8—262no—
291C22⋊C8—261no—
292C4×C8—21no—
293C4×C8—131no—
294C4×C8—131no—
295C4×C8—131no—
296C4×C8—131no—
297C4×C8—261no—
298C2×C13—22no—
299C2×C13—82no—
300C2×C13—162no—
301C2×C13C2×#46311yescharacteristic
302C2×C13#305811yescharacteristic
303C2×C13C2×#47111yescharacteristic
304C24—41no—
305#41—42no—
306#41—42no—
307C2×Q8—21no—
308C2×Q8—262no—
309C2×Q8—521no—
310C2×Q8—1042no—
311C2×D4—22no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—82no—
323C2×D4—82no—
324C2×D4C2×C22⋊D1312yes—
325C22×C4—22no—
326C22×C4—521no—
327C22×C4D4×D1311yescharacteristic
328C22×C4#612911yescharacteristic
329C22×C4C2×C22⋊D1311yescharacteristic
330SD16—1044no—
331D8—84no—
332M16—524no—
333M16—522no—
334C2×C8—22no—
335C2×C8—131no—
336C2×C8—131no—
337C2×C8—131no—
338C2×C8—131no—
339C2×C8—262no—
340C2×C8—262no—
341C2×C8—262no—
342C2×C8—262no—
343C2×C8—524no—
344C4⋊C4—21no—
345C4⋊C4—262no—
346C4⋊C4—262no—
347C4⋊C4—521no—
348C4⋊C4—521no—
349C4⋊C4C2×C22⋊D1312yes—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C42D4×D1311yescharacteristic
353C42#612911yescharacteristic
354C42C2×C22⋊D1311yescharacteristic
355C42C23×D1311yescharacteristic
356C13#1919811yescharacteristic, complemented, Sylow
357C23—22no—
358C23—42no—
359C23—82no—
360C23—82no—
361C23—82no—
362C23#8819311yescharacteristic
363Q8—42no—
364Q8—524no—
365Q8—1042no—
366D4—24no—
367D4—44no—
368D4—42no—
369D4—42no—
370D4—44no—
371D4—42no—
372D4—42no—
373D4—82no—
374D4—82no—
375D4—82no—
376D4—82no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—522no—
383C2×C4—1042no—
384C2×C4#8816512yes—
385C2×C4#8816612yes—
386C2×C4#8819311yescharacteristic
387C2×C4#8819311yescharacteristic
388C2×C4#8819311yescharacteristic
389C2×C4C2×D4×D1311yescharacteristic
390C2×C4C2×#612911yescharacteristic
391C2×C4C22×C22⋊D1311yescharacteristic
392C8—42no—
393C8—261no—
394C8—261no—
395C8—261no—
396C8—261no—
397C8—522no—
398C8—522no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—82no—
405C22—82no—
406C22—82no—
407C22—164no—
408C22#1171881412yes—
409C22C2×#8819311yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—1042no—
414C4#1171881412yes—
415C4#1171886112yes—
416C4C2×#8816511yescharacteristic
417C4C2×#8816611yescharacteristic
418C4#1171954012yes—
419C2—22no—
420C2—82no—
421C2—162no—
422C2C2×#1171881411yescharacteristic
423C2#1312448111yescharacteristic
424C2C2×#1171886111yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3205C2
socleC22×C13C2×#121
hypercenter#3205D13
hypocenterC13#19198
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13125758C2semidirect
2. C2×#11718731C2semidirect
3. #13123548C2semidirect
4. #13114395C2semidirect
5. #13114271C2semidirect
6. #13113582C2semidirect
7. #13113520C2semidirect
8. #13113504C2semidirect
29. #11718680C22semidirect
31. #11718673C22semidirect
33. D4×#1055C22semidirect
38. #11718074C22semidirect
39. #11718072C22semidirect
40. #11718071C22semidirect
356. C13#19198semidirect

Maximal subgroups

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

subgroupindex
#131257582
C2×#117187312
#131235482
#131143952
#131142712
#131135822
#131135202
#131135042
C13×#32052
#1919813