Finite Group Databasebeta

← #15754607

Subgroups — #15754607

Order 3328.

818 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#13114926C212yesmaximal, complemented
2#13114824C211yesmaximal, characteristic
3#13113408C212yesmaximal, complemented
4#13113154C211yesmaximal, characteristic
5C2×C13×#554C211yesmaximal, characteristic
6C13×#554—24no—
7C13×#554—24no—
8C2×C13×C4⋊Q8C411yescharacteristic, complemented
9C2×C13×#125—21no—
10C2×C13×C22⋊Q8—21no—
11C2×C13×C22⋊Q8—21no—
12C2×C13×C22⋊Q8C411yescharacteristic, complemented
13C2×C13×C22⋊Q8C2211yescharacteristic
14C2×C4×Q8×C13C411yescharacteristic, complemented
15C2×C4×D4×C13—21no—
16C2×C4×D4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C411yescharacteristic, complemented
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88074—21no—
20#11718873C2212yes—
21C2×C22⋊#1055C2212yes—
22#11718130—24no—
23#11718121—24no—
24#11718120—21no—
25#11718118—21no—
26#11718117—21no—
27C22×Q8×C13—21no—
28C22×Q8×C13C2×C411yescharacteristic
29C22×D4×C13D411yescharacteristic
30C23×C4×C13—21no—
31C23×C4×C13—21no—
32C23×C4×C13C2×C411yescharacteristic
33C23×C4×C13C2311yescharacteristic
34C13×C4⋊Q8—22no—
35C13×C4⋊Q8—22no—
36C13×#125—28no—
37C13×C22⋊Q8—28no—
38C13×C22⋊Q8—28no—
39C13×C22⋊Q8—22no—
40C13×C22⋊Q8—22no—
41C13×C22⋊Q8—22no—
42C13×C22⋊Q8D414yes—
43C4×Q8×C13—22no—
44C4×Q8×C13—22no—
45C4×D4×C13—28no—
46C4×D4×C13—22no—
47C4×D4×C13—22no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C13×C4⋊C4C2×C411yescharacteristic
60C2×C13×C4⋊C4D411yescharacteristic
61C2×C13×C4⋊C4D414yes—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C13×C22⋊C4D411yescharacteristic
66C2×C42×C13—21no—
67C2×C42×C13C2×C411yescharacteristic
68C2×C22⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C22×#1055—22no—
71#88074—42no—
72#88071—22no—
73C22⋊#1055—22no—
74C22⋊#1055—22no—
75#8380—131nomaximal, Sylow
76C24×C13C22⋊C411yescharacteristic
77C24×C13C2×D411yescharacteristic
78C2×Q8×C13—24no—
79C2×Q8×C13—21no—
80C2×Q8×C13—42no—
81C2×Q8×C13—82no—
82C2×Q8×C13C22⋊C412yes—
83C2×D4×C13—22no—
84C2×D4×C13—22no—
85C2×D4×C13SD1612yes—
86C2×D4×C13Q1612yes—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—24no—
92C22×C4×C13—24no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—42no—
96C22×C4×C13—42no—
97C22×C4×C13—82no—
98C22×C4×C13—82no—
99C22×C4×C13C22⋊C411yescharacteristic
100C22×C4×C13C22⋊C411yescharacteristic
101C22×C4×C13C22⋊C411yescharacteristic
102C22×C4×C13C22×C411yescharacteristic
103C22×C4×C13C2×D412yes—
104C22×C4×C13C2×D412yes—
105C22×C4×C13C2×D411yescharacteristic
106C22×Dic13—42no—
107C13×C4⋊C4—24no—
108C13×C4⋊C4—24no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—24no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4—24no—
116C13×C4⋊C4—22no—
117C13×C4⋊C4C22⋊C412yes—
118C13×C4⋊C4C22⋊C412yes—
119C13×C4⋊C4C22⋊C412yes—
120C13×C22⋊C4—24no—
121C13×C22⋊C4—24no—
122C13×C22⋊C4—22no—
123C13×C22⋊C4—22no—
124C42×C13—24no—
125C42×C13—21no—
126C42×C13—21no—
127C22⋊Dic13—42no—
128C22⋊Dic13—42no—
129C4⋊Dic13—44no—
130C2×#1055—44no—
131C2×#1055—42no—
132C2×#554D1311yescharacteristic
133#1824—132no—
134#1799—131no—
135#1520—132no—
136#1459—131no—
137C23×C13—21no—
138C23×C13—21no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13#10312yes—
144C23×C13C2×C22⋊C411yescharacteristic
145C23×C13#12012yes—
146C23×C13C2×SD1611yescharacteristic
147C23×C13C2×Q1611yescharacteristic
148C23×C13#13712yes—
149Q8×C13—42no—
150Q8×C13—42no—
151Q8×C13—84no—
152D4×C13—24no—
153D4×C13—24no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—24no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—21no—
160C2×C4×C13—22no—
161C2×C4×C13—21no—
162C2×C4×C13—22no—
163C2×C4×C13—22no—
164C2×C4×C13—41no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—84no—
175C2×C4×C13—84no—
176C2×C4×C13#10312yes—
177C2×C4×C13C2×C22⋊C411yescharacteristic
178C2×C4×C13C2×C22⋊C411yescharacteristic
179C2×C4×C13#12012yes—
180C2×Dic13—82no—
181C2×Dic13—82no—
182C2×Dic13—82no—
183#1055—82no—
184#554—24no—
185#554—24no—
186C2×C4⋊Q8Dic1311yescharacteristic, complemented
187C2×#125—21no—
188C2×C22⋊Q8—21no—
189C2×C22⋊Q8—21no—
190C2×C22⋊Q8Dic1311yescharacteristic, complemented
191C2×C22⋊Q8C2×D1311yescharacteristic
192C2×C4×Q8Dic1311yescharacteristic, complemented
193C2×C4×D4—21no—
194C2×C4×D4C2×D1311yescharacteristic
195C22×C4⋊C4Dic1311yescharacteristic, complemented
196C22×C4⋊C4C2×D1311yescharacteristic
197C2×#99—261no—
198C2×C22⋊C8—132no—
199#380—132no—
200#342—261no—
201#340—264no—
202#328—264no—
203#324—261no—
204#323—261no—
205C22×C13—22no—
206C22×C13—21no—
207C22×C13—22no—
208C22×C13—21no—
209C22×C13—22no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—42no—
213C22×C13—42no—
214C22×C13—42no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13#37911yescharacteristic
218C22×C13C2×#10311yescharacteristic
219C22×C13#41911yescharacteristic
220C22×C13#44812yes—
221C22×C13#45112yes—
222C4×C13—22no—
223C4×C13—21no—
224C4×C13—22no—
225C4×C13—42no—
226C4×C13—42no—
227C4×C13—42no—
228C4×C13—41no—
229C4×C13—41no—
230C4×C13—42no—
231C4×C13#41012yes—
232Dic13—162no—
233C22×Q8—21no—
234C22×Q8C2×Dic1311yescharacteristic
235C22×D4C22⋊D1311yescharacteristic
236C23×C4—21no—
237C23×C4—21no—
238C23×C4C2×Dic1311yescharacteristic
239C23×C4C22×D1311yescharacteristic
240C22×C8—262no—
241C4⋊Q8—22no—
242C4⋊Q8—22no—
243#125—28no—
244C22⋊Q8—28no—
245C22⋊Q8—28no—
246C22⋊Q8—22no—
247C22⋊Q8—22no—
248C22⋊Q8—22no—
249C22⋊Q8C22⋊D1314yes—
250C4×Q8—22no—
251C4×Q8—22no—
252C4×D4—28no—
253C4×D4—22no—
254C4×D4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—262no—
265C2×C4⋊C4C2×Dic1311yescharacteristic
266C2×C4⋊C4C2×Dic1311yescharacteristic
267C2×C4⋊C4C2×Dic1311yescharacteristic
268C2×C4⋊C4C22⋊D1311yescharacteristic
269C2×C4⋊C4C22⋊D1314yes—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—262no—
273C2×C22⋊C4C22⋊D1311yescharacteristic
274C2×C22⋊C4C22⋊D1311yescharacteristic
275C2×C42—21no—
276C2×C42C2×Dic1311yescharacteristic
277#99—522no—
278C22⋊C8—262no—
279C22⋊C8—262no—
280#95—262no—
281C2×C13—22no—
282C2×C13—21no—
283C2×C13—21no—
284C2×C13—22no—
285C2×C13—42no—
286C2×C13#178211yescharacteristic
287C2×C13#178711yescharacteristic
288C2×C13#179511yescharacteristic
289C24C22⋊Dic1311yescharacteristic
290C24C2×C22⋊D1311yescharacteristic
291C2×Q8—24no—
292C2×Q8—21no—
293C2×Q8—42no—
294C2×Q8—82no—
295C2×Q8C22⋊Dic1312yes—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4#610612yes—
299C2×D4#610712yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—82no—
311C22×C4—82no—
312C22×C4—522no—
313C22×C4C22⋊Dic1311yescharacteristic
314C22×C4C22⋊Dic1311yescharacteristic
315C22×C4C22⋊Dic1311yescharacteristic
316C22×C4C22×Dic1311yescharacteristic
317C22×C4C2×C22⋊D1312yes—
318C22×C4C2×C22⋊D1312yes—
319C22×C4C2×C22⋊D1311yescharacteristic
320C2×C8—524no—
321C2×C8—522no—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—24no—
330C4⋊C4—24no—
331C4⋊C4—22no—
332C4⋊C4—524no—
333C4⋊C4C22⋊Dic1312yes—
334C4⋊C4C22⋊Dic1312yes—
335C4⋊C4C22⋊Dic1312yes—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—522no—
341C22⋊C4—522no—
342C42—24no—
343C42—21no—
344C42—21no—
345C13#838011yescharacteristic, complemented, Sylow
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23#8807512yes—
353C23C2×#610611yescharacteristic
354C23#8819612yes—
355C23C2×#610711yescharacteristic
356C23C2×C22⋊Dic1311yescharacteristic
357C23#8820712yes—
358Q8—42no—
359Q8—42no—
360Q8—84no—
361D4—24no—
362D4—24no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—84no—
384C2×C4—84no—
385C2×C4—1042no—
386C2×C4—1042no—
387C2×C4—1042no—
388C2×C4#8807512yes—
389C2×C4C2×C22⋊Dic1311yescharacteristic
390C2×C4C2×C22⋊Dic1311yescharacteristic
391C2×C4#8820712yes—
392C8—1042no—
393C22—21no—
394C22—22no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—42no—
400C22—41no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22C2×#8807511yescharacteristic
406C22#1171888611yescharacteristic
407C22#1171888812yes—
408C22#1171888912yes—
409C22#1171890811yescharacteristic
410C4—22no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—42no—
415C4—42no—
416C4—42no—
417C4—42no—
418C4—41no—
419C4—2082no—
420C4#1171890112yes—
421C2—22no—
422C2—21no—
423C2—21no—
424C2—22no—
425C2—42no—
426C2#1311475411yescharacteristic
427C2#1311477111yescharacteristic
428C2#1311480611yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#554C2
socleC22×C13#379
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenterC2×#554D13
hypocenterC13#8380
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #13114926C2semidirect
3. #13113408C2semidirect
8. C2×C13×C4⋊Q8C4semidirect
12. C2×C13×C22⋊Q8C4semidirect
14. C2×C4×Q8×C13C4semidirect
17. C22×C13×C4⋊C4C4semidirect
186. C2×C4⋊Q8Dic13semidirect
190. C2×C22⋊Q8Dic13semidirect
192. C2×C4×Q8Dic13semidirect
195. C22×C4⋊C4Dic13semidirect
345. C13#8380semidirect

Maximal subgroups

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

subgroupindex
#131149262
#131148242
#131134082
#131131542
C2×C13×#5542
#838013