Finite Group Databasebeta

← #16781752

Subgroups — #16781752

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130769C211yesmaximal, characteristic
2C4×#88112C211yesmaximal, characteristic
3C2×#11718244C212yesmaximal
4#13129672C212yesmaximal
5C4×#88141C211yesmaximal, characteristic
6C2×#88141C411yescharacteristic
7C2×#88141C2211yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C2×#88112—21no—
10C2×#88112—21no—
11C2×#88112—21no—
12C2×C4⋊#1057C2212yes—
13C2×C4×#1057C2212yes—
14C4×C13×C4⋊C4C411yescharacteristic
15C4⋊C4×Dic13C411yescharacteristic
16C4⋊C4×Dic13C2211yescharacteristic
17C4×#6101—21no—
18C42×Dic13—21no—
19C42×Dic13C2211yescharacteristic
20#11718310—21no—
21#11718310—21no—
22#11718290—21no—
23#11718244—24no—
24C22×Dic26C2×C411yescharacteristic
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C42×C13—21no—
30C2×C42×C13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×#6101—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13C2311yescharacteristic
46#88141—22no—
47#88141—21no—
48#88141—21no—
49#88141C814yescomplemented
50#88141D412yes—
51#88141Q812yes—
52C4×Dic26—22no—
53C4×Dic26—22no—
54#88112—24no—
55#88112—42no—
56#88112—42no—
57C4⋊#1057—22no—
58C4⋊#1057—22no—
59C4×#1057—22no—
60C4×#1057—22no—
61C13×#95—21no—
62#88071—21no—
63#88071—21no—
64#8564—131nomaximal, Sylow
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C2×D411yescharacteristic
75C22×Dic13C2×D411yescharacteristic
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26—21no—
79C2×Dic26C4⋊C412yes—
80C2×Dic26C2×C812yes—
81C2×Dic26M1612yes—
82C2×#1057—24no—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C2×#1057—42no—
87C2×#1057—42no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4C4⋊C412yes—
91C13×C4⋊C4C2×C812yes—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—42no—
95C4⋊Dic13—21no—
96C4⋊Dic13M1612yes—
97#6101—24no—
98#6101—24no—
99#6101—22no—
100#6101—22no—
101C4×Dic13—24no—
102C4×Dic13—24no—
103C4×Dic13—22no—
104C4×Dic13—22no—
105C4×Dic13—22no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13—41no—
109C4×Dic13—42no—
110C4×Dic13—41no—
111C4×Dic13—41no—
112C4×Dic13C2×C812yes—
113C4×Dic13M1612yes—
114C4×Dic13SD1612yes—
115C4×Dic13Q1612yes—
116C4×Dic13C2×D411yescharacteristic
117C4×Dic13C2×Q811yescharacteristic
118C4×Dic13#4111yescharacteristic
119C4×Dic13#4111yescharacteristic
120C42×Q8—131no—
121#1842—131no—
122C4×C4⋊C8—131no—
123C2×Q8⋊C8—132no—
124#1279—132no—
125C23×C13C2×C22⋊C411yescharacteristic
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13#10312yes—
138C2×C4×C13C2×C4⋊C411yescharacteristic
139C2×C4×C13#11711yescharacteristic
140C2×C4×C13C22×C811yescharacteristic
141C2×C4×C13C2×M1611yescharacteristic
142C2×C4×C13C2×M1611yescharacteristic
143C2×C4×C13C2×M1611yescharacteristic
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13—22no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—22no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13C22⋊C812yes—
155C2×Dic13C22⋊C812yes—
156C2×Dic13#10312yes—
157C2×Dic13#10412yes—
158C2×Dic13#12111yescharacteristic
159C2×Dic13#12111yescharacteristic
160C2×Dic13C22⋊Q811yescharacteristic
161C2×Dic13C22⋊Q811yescharacteristic
162C2×Dic13C2×SD1611yescharacteristic
163C2×Dic13C2×Q1611yescharacteristic
164C2×Dic13AGL(1,ℤ/8)11yescharacteristic
165C2×Dic13#13711yescharacteristic
166Dic26—22no—
167Dic26—22no—
168Dic26—22no—
169Dic26C4⋊C814yescomplemented
170#1057—44no—
171#1057—82no—
172C2×C4×Q8—131no—
173C2×C4×Q8—131no—
174C2×C4×Q8—131no—
175C2×C4⋊C8—132no—
176C2×C4⋊C8—261no—
177C2×C4⋊C8—261no—
178C2×C4⋊C8—261no—
179C2×C4×C8—132no—
180C4×C4⋊C4—131no—
181C4×C4⋊C4—131no—
182C4×C4⋊C4—261no—
183C4×C4⋊C4—261no—
184C4×C4⋊C4—261no—
185C4×C4⋊C4#26111yescharacteristic
186C43—131no—
187C43—261no—
188#336—261no—
189Q8⋊C8—264no—
190C22×C13#38011yescharacteristic
191C22×C13C2×C22⋊C811yescharacteristic
192C22×C13#40711yescharacteristic
193C22×C13C2×#10311yescharacteristic
194C22×C13#41711yescharacteristic
195C22×C13C2×#10411yescharacteristic
196C22×C13#42111yescharacteristic
197C4×C13—22no—
198C4×C13—42no—
199C4×C13—42no—
200C4×C13—41no—
201C4×C13C2×C4⋊C811yescharacteristic
202C4×C13#42311yescharacteristic
203C4×C13#43111yescharacteristic
204C4×C13#43211yescharacteristic
205Dic13—24no—
206Dic13—21no—
207Dic13—21no—
208Dic13—22no—
209Dic13—42no—
210Dic13Q8⋊C814yescomplemented
211Dic13#46011yescharacteristic
212Dic13#46211yescharacteristic
213Dic13#47511yescharacteristic
214Dic13#47711yescharacteristic
215C22×Q8—131no—
216C22×C8—262no—
217C22×C8—262no—
218C4×Q8—134no—
219C4×Q8—132no—
220C4×Q8—132no—
221C4×Q8—262no—
222C4×Q8—262no—
223C4×Q8—262no—
224C4×Q8—261no—
225C4×Q8—261no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4C2×#26111yescharacteristic
231C2×C4⋊C4C2×#26111yescharacteristic
232C2×C42—21no—
233C2×C42—131no—
234C2×C42—131no—
235C2×C42—131no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—261no—
240C2×C42—261no—
241C2×C42—261no—
242C2×C42—261no—
243C2×C42—261no—
244C2×C42C2×#26111yescharacteristic
245C4⋊C8—262no—
246C4⋊C8—262no—
247C4⋊C8—264no—
248C4⋊C8—522no—
249C4⋊C8—522no—
250C4×C8—262no—
251C4×C8—262no—
252#95—21no—
253#95—261no—
254#95—261no—
255C2×C13C2×Q8⋊C811yescharacteristic
256C2×C13#147711yescharacteristic
257C2×C13#148711yescharacteristic
258C2×C13#148911yescharacteristic
259C2×C13#179711yescharacteristic
260C2×C13#180311yescharacteristic
261C2×C13#180611yescharacteristic
262C2×Q8—132no—
263C2×Q8—132no—
264C2×Q8—132no—
265C2×Q8—261no—
266C2×Q8—261no—
267C2×Q8—261no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—131no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4C22⋊#26111yescharacteristic
277C22×C4C22⋊#26111yescharacteristic
278C22×C4C22×#26111yescharacteristic
279C2×C8—264no—
280C2×C8—522no—
281C2×C8—522no—
282C2×C8—522no—
283C2×C8—522no—
284C2×C8—522no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—132no—
288C4⋊C4—264no—
289C4⋊C4—262no—
290C4⋊C4—262no—
291C4⋊C4—264no—
292C4⋊C4—261no—
293C4⋊C4D13⋊C812yes—
294C4⋊C4C4⋊#26112yes—
295C42—21no—
296C42—21no—
297C42—42no—
298C42—132no—
299C42—132no—
300C42—132no—
301C42—132no—
302C42—131no—
303C42—131no—
304C42—131no—
305C42—131no—
306C42—262no—
307C42—261no—
308C42—261no—
309C42—264no—
310C42—262no—
311C42—262no—
312C42—264no—
313C42—521no—
314C42—522no—
315C42—521no—
316C42—521no—
317C13#856411yescharacteristic, complemented, Sylow
318C23C2×C22⋊#26111yescharacteristic
319Q8—134no—
320Q8—262no—
321Q8—262no—
322Q8—262no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—132no—
335C2×C4—131no—
336C2×C4—131no—
337C2×C4—131no—
338C2×C4—132no—
339C2×C4—131no—
340C2×C4—132no—
341C2×C4—131no—
342C2×C4—131no—
343C2×C4—132no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—262no—
347C2×C4—262no—
348C2×C4—262no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—262no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4#8811712yes—
357C2×C4C2×D13⋊C811yescharacteristic
358C2×C4D13⋊M1611yescharacteristic
359C2×C4D13⋊M1611yescharacteristic
360C2×C4D13⋊M1611yescharacteristic
361C2×C4C2×C4⋊#26111yescharacteristic
362C2×C4#8823711yescharacteristic
363C8—524no—
364C8—1042no—
365C22D13⋊(C22⋊C8)11yescharacteristic
366C22#1171912611yescharacteristic
367C22#1171913611yescharacteristic
368C22#1171914011yescharacteristic
369C22C2×#8811711yescharacteristic
370C22D13⋊#10411yescharacteristic
371C22#1171916411yescharacteristic
372C4—22no—
373C4—42no—
374C4—41no—
375C4—42no—
376C4—134no—
377C4—131no—
378C4—131no—
379C4—131no—
380C4—131no—
381C4—262no—
382C4—264no—
383C4—261no—
384C4—261no—
385C4—522no—
386C4#1171904911yescharacteristic
387C4D13⋊(C4⋊C8)11yescharacteristic
388C4#1171905311yescharacteristic
389C4#1171905511yescharacteristic
390C2D13⋊(Q8⋊C8)11yescharacteristic
391C2#1313013211yescharacteristic
392C2#1313016611yescharacteristic
393C2#1313017311yescharacteristic
394C2#1313069311yescharacteristic
395C2#1313070511yescharacteristic
396C2#1313071011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#8564
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
49. #88141C8semidirect
169. Dic26C4⋊C8semidirect
210. Dic13Q8⋊C8semidirect
317. C13#8564semidirect

Maximal subgroups

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

subgroupindex
#131307692
C4×#881122
C2×#117182442
#131296722
C4×#881412
#856413