Finite Group Databasebeta

← #16781758

Subgroups — #16781758

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130751C211yesmaximal, characteristic
2C4×C4⋊#1057C211yesmaximal, characteristic
3C2×#11718244C212yesmaximal
4#13129672C212yesmaximal
5C4×#88141C211yesmaximal, characteristic
6C2×#88141C411yescharacteristic
7C2×#88141C2211yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C2×C4⋊#1057—21no—
10C2×C4⋊#1057C2212yes—
11C2×C4×#1057C2212yes—
12C4×C13×C4⋊C4C411yescharacteristic
13C4⋊C4×Dic13C411yescharacteristic
14C4⋊C4×Dic13C2211yescharacteristic
15C4×#6101—21no—
16C42×Dic13—21no—
17C42×Dic13C2211yescharacteristic
18#11718310—21no—
19#11718310—21no—
20#11718290—21no—
21#11718290—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—22no—
48#88141—21no—
49#88141—21no—
50#88141D412yes—
51#88141Q812yes—
52C4×Dic26—22no—
53C4×Dic26C814yescomplemented
54C4⋊#1057—24no—
55C4⋊#1057—22no—
56C4⋊#1057—22no—
57C4×#1057—22no—
58C4×#1057—22no—
59C13×#95—21no—
60#88071—21no—
61#88071—21no—
62#8566—131nomaximal, Sylow
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C2×Dic26—21no—
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26C4⋊C412yes—
78C2×Dic26C2×C812yes—
79C2×Dic26M1612yes—
80C2×#1057—24no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4C4⋊C412yes—
89C13×C4⋊C4M1612yes—
90C42×C13—42no—
91C42×C13C2×C812yes—
92C42×C13M1612yes—
93C4⋊Dic13—21no—
94C4⋊Dic13C2×C812yes—
95#6101—24no—
96#6101—24no—
97#6101—22no—
98#6101—22no—
99C4×Dic13—24no—
100C4×Dic13—24no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—22no—
104C4×Dic13—22no—
105C4×Dic13—22no—
106C4×Dic13—22no—
107C4×Dic13—22no—
108C4×Dic13—41no—
109C4×Dic13—42no—
110C4×Dic13—42no—
111C4×Dic13C2×D411yescharacteristic
112C4×Dic13C2×Q811yescharacteristic
113C4×Dic13#4111yescharacteristic
114C4×Dic13#4111yescharacteristic
115C42×Q8—131no—
116#1831—131no—
117C4×C4⋊C8—131no—
118C2×Q8⋊C8—132no—
119#1279—132no—
120C23×C13C2×C22⋊C411yescharacteristic
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13C22⋊C812yes—
132C2×C4×C13C22⋊C812yes—
133C2×C4×C13C2×C4⋊C411yescharacteristic
134C2×C4×C13#11711yescharacteristic
135C2×C4×C13C22×C811yescharacteristic
136C2×C4×C13C2×M1611yescharacteristic
137C2×C4×C13C2×M1611yescharacteristic
138C2×C4×C13C2×M1611yescharacteristic
139C2×Dic13—22no—
140C2×Dic13—22no—
141C2×Dic13—21no—
142C2×Dic13—22no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—22no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13#10412yes—
153C2×Dic13#12111yescharacteristic
154C2×Dic13#12111yescharacteristic
155C2×Dic13C22⋊Q811yescharacteristic
156C2×Dic13C22⋊Q811yescharacteristic
157C2×Dic13#13512yes—
158C2×Dic13#13712yes—
159Dic26—22no—
160Dic26—22no—
161Dic26—22no—
162Dic26C4⋊C814yescomplemented
163#1057—44no—
164#1057—82no—
165C2×C4×Q8—131no—
166C2×C4×Q8—131no—
167C2×C4×Q8—131no—
168C2×C4⋊C8—132no—
169C2×C4⋊C8—261no—
170C2×C4×C8—132no—
171C4×C4⋊C4—131no—
172C4×C4⋊C4—131no—
173C4×C4⋊C4—261no—
174C4×C4⋊C4—261no—
175C4×C4⋊C4—261no—
176C4×C4⋊C4#26111yescharacteristic
177C43—131no—
178C43—261no—
179#336—261no—
180#336—261no—
181#336—261no—
182Q8⋊C8—264no—
183C22×C13#38011yescharacteristic
184C22×C13C2×C22⋊C811yescharacteristic
185C22×C13#40711yescharacteristic
186C22×C13#41611yescharacteristic
187C22×C13#41911yescharacteristic
188C22×C13C2×#10411yescharacteristic
189C22×C13#42111yescharacteristic
190C4×C13—22no—
191C4×C13—22no—
192C4×C13—42no—
193C4×C13—42no—
194C4×C13C2×C4⋊C811yescharacteristic
195C4×C13#42311yescharacteristic
196C4×C13#43111yescharacteristic
197C4×C13#43211yescharacteristic
198Dic13—24no—
199Dic13—21no—
200Dic13—21no—
201Dic13—22no—
202Dic13—42no—
203Dic13—41no—
204Dic13#46412yes—
205Dic13#47912yes—
206C22×Q8—131no—
207C22×C8—262no—
208C22×C8—262no—
209C4×Q8—132no—
210C4×Q8—132no—
211C4×Q8—134no—
212C4×Q8—261no—
213C4×Q8—261no—
214C4×Q8—262no—
215C4×Q8—262no—
216C4×Q8—262no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4C2×#26111yescharacteristic
222C2×C4⋊C4C2×#26111yescharacteristic
223C2×C42—21no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—131no—
228C2×C42—131no—
229C2×C42—131no—
230C2×C42—261no—
231C2×C42—261no—
232C2×C42—261no—
233C2×C42—261no—
234C2×C42—261no—
235C2×C42C2×#26111yescharacteristic
236C4⋊C8—262no—
237C4⋊C8—262no—
238C4⋊C8—264no—
239C4×C8—262no—
240C4×C8—262no—
241#95—21no—
242#95—261no—
243#95—261no—
244C2×C13#147611yescharacteristic
245C2×C13#147911yescharacteristic
246C2×C13#148811yescharacteristic
247C2×C13#149111yescharacteristic
248C2×C13#179711yescharacteristic
249C2×C13#180511yescharacteristic
250C2×C13#180611yescharacteristic
251C2×Q8—132no—
252C2×Q8—132no—
253C2×Q8—132no—
254C2×Q8—261no—
255C2×Q8—261no—
256C2×Q8—261no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—131no—
262C22×C4—131no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4C22⋊#26111yescharacteristic
266C22×C4C22⋊#26111yescharacteristic
267C22×C4C22×#26111yescharacteristic
268C2×C8—264no—
269C2×C8—522no—
270C2×C8—522no—
271C2×C8—522no—
272C2×C8—522no—
273C2×C8—522no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—132no—
277C4⋊C4—262no—
278C4⋊C4—262no—
279C4⋊C4—264no—
280C4⋊C4—264no—
281C4⋊C4—261no—
282C4⋊C4#611812yes—
283C4⋊C4C4⋊#26112yes—
284C42—42no—
285C42—131no—
286C42—131no—
287C42—131no—
288C42—131no—
289C42—262no—
290C42—262no—
291C42—262no—
292C42—262no—
293C42—262no—
294C42—264no—
295C42—264no—
296C42—261no—
297C42—261no—
298C42—521no—
299C42—522no—
300C42—522no—
301C42D13⋊C812yes—
302C42#611812yes—
303C13#856611yescharacteristic, complemented, Sylow
304C23C2×C22⋊#26111yescharacteristic
305Q8—134no—
306Q8—262no—
307Q8—262no—
308Q8—262no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—131no—
320C2×C4—131no—
321C2×C4—132no—
322C2×C4—132no—
323C2×C4—131no—
324C2×C4—131no—
325C2×C4—132no—
326C2×C4—262no—
327C2×C4—261no—
328C2×C4—262no—
329C2×C4—262no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—262no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4#8811112yes—
340C2×C4#8811112yes—
341C2×C4C2×D13⋊C811yescharacteristic
342C2×C4C2×#611811yescharacteristic
343C2×C4C2×#611811yescharacteristic
344C2×C4D13⋊M1611yescharacteristic
345C2×C4C2×C4⋊#26111yescharacteristic
346C2×C4#8823711yescharacteristic
347C8—524no—
348C8—1042no—
349C22C2×#8811111yescharacteristic
350C22#1171912711yescharacteristic
351C22#1171913611yescharacteristic
352C22#1171914011yescharacteristic
353C22#1171915311yescharacteristic
354C22D13⋊#10411yescharacteristic
355C22#1171916511yescharacteristic
356C4—22no—
357C4—22no—
358C4—42no—
359C4—42no—
360C4—132no—
361C4—132no—
362C4—262no—
363C4—264no—
364C4—261no—
365C4—261no—
366C4—522no—
367C4—521no—
368C4D13⋊(C4⋊C8)11yescharacteristic
369C4#1171905111yescharacteristic
370C4#1171905211yescharacteristic
371C4#1171905411yescharacteristic
372C2#1313012911yescharacteristic
373C2#1313014011yescharacteristic
374C2#1313016811yescharacteristic
375C2#1313017911yescharacteristic
376C2#1313069111yescharacteristic
377C2#1313070711yescharacteristic
378C2#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#8566
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
53. C4×Dic26C8semidirect
162. Dic26C4⋊C8semidirect
303. C13#8566semidirect

Maximal subgroups

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

subgroupindex
#131307512
C4×C4⋊#10572
C2×#117182442
#131296722
C4×#881412
#856613