Finite Group Databasebeta

← #13117537

Subgroups — #13117537

Order 1664.

696 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88193C211yesmaximal, characteristic
2C2×D4×Dic13C211yesmaximal, characteristic, complemented
3C2×#88135C211yesmaximal, characteristic, complemented
4C13×#386C211yesmaximal, characteristic, complemented
5#11718874C211yesmaximal, characteristic, complemented
6C2×#88071C211yesmaximal, characteristic, complemented
7#11718619C211yesmaximal, characteristic, complemented
8#11718617C211yesmaximal, characteristic, complemented
9#11718607C211yesmaximal, characteristic, complemented
10#11718606C211yesmaximal, characteristic, complemented
11#11718603C211yesmaximal, characteristic, complemented
12#11718330C211yesmaximal, characteristic, complemented
13#11718329C211yesmaximal, characteristic, complemented
14#11718316C211yesmaximal, characteristic, complemented
15#11718313C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic
21C23×Dic13C2211yescharacteristic
22C23×Dic13C2211yescharacteristic
23C22×C4×D13C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30#88193C418yescomplemented
31D4×Dic13—24no—
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×C4×Dic13C2211yescharacteristic
42C2×C4×Dic13C2211yescharacteristic
43#88135—24no—
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54C24×C13C2311yescharacteristic
55C24×C13C2311yescharacteristic
56C23×D13C2311yescharacteristic
57C2×D4×C13—22no—
58C2×D4×C13—22no—
59C2×D4×C13C2×C414yescomplemented
60C22×C4×C13—22no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—22no—
69C2×C22⋊D13—22no—
70C2×C22⋊D13—41no—
71C2×C22⋊D13—41no—
72C2×C22⋊D13C2×C414yescomplemented
73C2×C22⋊D13C2×C414yescomplemented
74C22×Dic13—22no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C22×Dic13—41no—
78C22×Dic13—41no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13C2×C414yescomplemented
82C22×Dic13D414yescomplemented
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C22×Dic13C2311yescharacteristic
88C22×Dic13C2311yescharacteristic
89C22×Dic13C2311yescharacteristic
90C2×C4×D13—22no—
91C2×C4×D13—41no—
92C2×C4×D13—41no—
93C13×C22⋊C4—22no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C22⋊Dic13—22no—
97C22⋊Dic13—22no—
98C22⋊Dic13C2×C414yescomplemented
99#6103—22no—
100#6103—41no—
101#6103—41no—
102#6103C2×C414yescomplemented
103C4⋊Dic13—22no—
104#6101—22no—
105#6101—41no—
106#6101—41no—
107#6101C2×C414yescomplemented
108C4×Dic13—22no—
109C4×Dic13—22no—
110#2325—131nomaximal, Sylow
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13C22×C412yes—
122C23×C13C22×C412yes—
123C23×C13C2×D412yes—
124C23×C13#4112yes—
125C23×C13C2411yescharacteristic
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—21no—
132C22×D13C22×C412yes—
133D4×C13—28no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
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—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—44no—
149C2×C4×C13C22×C412yes—
150C22⋊D13—28no—
151C22⋊D13—44no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—44no—
169C2×Dic13—44no—
170C2×Dic13—44no—
171C2×Dic13C22×C412yes—
172C2×Dic13C22×C412yes—
173C2×Dic13C22×C412yes—
174C2×Dic13C2×D412yes—
175C2×Dic13C2×D412yes—
176C4×D13—44no—
177C2×#121—131no—
178C2×C4×D4—131no—
179C2×C4×D4—131no—
180#388—131no—
181#388—131no—
182#387—131no—
183#387—131no—
184#386—131no—
185#386—131no—
186#386—131no—
187#386D1311yescharacteristic, complemented
188#385—131no—
189#385—131no—
190#380—131no—
191C2×#95—131no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13—22no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13C4×D414yes—
206C22×C13C23×C411yescharacteristic
207C22×C13C22×D411yescharacteristic
208C22×C13C2×#4111yescharacteristic
209C22×C13H(5,𝔽2)11yescharacteristic
210C22×C13H(5,𝔽2)11yescharacteristic
211C22×C13H(5,𝔽2)11yescharacteristic
212C22×C132−1+411yescharacteristic
213C2×D13—22no—
214C2×D13—22no—
215C2×D13—22no—
216C2×D13—41no—
217C2×D13—41no—
218C2×D13—41no—
219C2×D13—41no—
220C4×C13—22no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13—41no—
225Dic13—22no—
226Dic13—22no—
227Dic13—22no—
228Dic13—22no—
229Dic13—22no—
230Dic13—41no—
231Dic13—41no—
232C22×D4—131no—
233C22×D4—131no—
234C22×D4C2×D1311yescharacteristic
235C23×C4—131no—
236C23×C4—131no—
237C23×C4—131no—
238C23×C4—131no—
239C23×C4C2×D1311yescharacteristic
240#121—138no—
241C4×D4—264no—
242C4×D4—264no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—131no—
245C2×C4⋊C4—131no—
246C2×C4⋊C4—131no—
247C2×C4⋊C4—131no—
248C2×C22⋊C4—131no—
249C2×C22⋊C4—131no—
250C2×C22⋊C4—131no—
251C2×C22⋊C4—131no—
252C2×C22⋊C4—131no—
253C2×C22⋊C4—131no—
254C2×C22⋊C4—131no—
255C2×C22⋊C4C2×D1311yescharacteristic
256C2×C22⋊C4C2×D1311yescharacteristic
257C2×C22⋊C4C2×D1311yescharacteristic
258C2×C42—131no—
259C2×C42—131no—
260#95—131no—
261#95—131no—
262#95—131no—
263#95—131no—
264#95—131no—
265#95—131no—
266#95—131no—
267#95—131no—
268#95C2×D1311yescharacteristic
269#95C2×D1311yescharacteristic
270C2×C13—24no—
271C2×C13—42no—
272C2×C13C2×C4×D411yescharacteristic
273C2×C13#51811yescharacteristic
274C2×C13#52011yescharacteristic
275C2×C13#53411yescharacteristic
276C2×C13#53711yescharacteristic
277C2×C13#53811yescharacteristic
278C2×C13#53911yescharacteristic
279D13—42no—
280C24—131no—
281C24C22×D1311yescharacteristic
282C24C22×D1311yescharacteristic
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—134no—
286C2×D4—134no—
287C2×D4—262no—
288C2×D4—262no—
289C2×D4—521no—
290C2×D4—521no—
291C2×D4C4×D1314yescomplemented
292C22×C4—22no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—131no—
299C22×C4—131no—
300C22×C4—134no—
301C22×C4—134no—
302C22×C4—131no—
303C22×C4—131no—
304C22×C4—262no—
305C22×C4—262no—
306C22×C4—521no—
307C22×C4—521no—
308C22×C4—521no—
309C22×C4—521no—
310C22×C4—521no—
311C22×C4—521no—
312C22×C4—521no—
313C22×C4—521no—
314C22×C4C22×D1311yescharacteristic
315C22×C4C22×D1311yescharacteristic
316C22×C4C22×D1311yescharacteristic
317C22×C4C22×D1311yescharacteristic
318C22×C4C22×D1311yescharacteristic
319C4⋊C4—134no—
320C4⋊C4—262no—
321C4⋊C4—262no—
322C4⋊C4—521no—
323C4⋊C4—521no—
324C22⋊C4—22no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—134no—
328C22⋊C4—134no—
329C22⋊C4—262no—
330C22⋊C4—262no—
331C22⋊C4—262no—
332C22⋊C4—521no—
333C22⋊C4—521no—
334C42—262no—
335C42—262no—
336C13#232511yescharacteristic, complemented, Sylow
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—132no—
348C23—261no—
349C23—261no—
350C23—261no—
351C23—261no—
352C23—261no—
353C23—261no—
354C23C2×C4×D1312yes—
355C23C2×C4×D1312yes—
356C23D4×D1312yes—
357C23#612912yes—
358C23C23×D1311yescharacteristic
359D4—28no—
360D4—268no—
361D4—524no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—44no—
377C2×C4—132no—
378C2×C4—132no—
379C2×C4—132no—
380C2×C4—132no—
381C2×C4—132no—
382C2×C4—261no—
383C2×C4—261no—
384C2×C4—261no—
385C2×C4—261no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—261no—
389C2×C4—261no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—261no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—524no—
399C2×C4—524no—
400C2×C4—524no—
401C2×C4—524no—
402C2×C4C2×C4×D1312yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—262no—
417C22—262no—
418C22—262no—
419C22—521no—
420C22—521no—
421C22—521no—
422C22—521no—
423C22#8813514yes—
424C22C22×C4×D1311yescharacteristic
425C22C2×D4×D1311yescharacteristic
426C22C2×#612911yescharacteristic
427C22#8825111yescharacteristic
428C22#8825111yescharacteristic
429C22#8825611yescharacteristic
430C22#8825711yescharacteristic
431C4—22no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—262no—
437C4—262no—
438C4—262no—
439C4—262no—
440C4—262no—
441C4—521no—
442C4—521no—
443C2—24no—
444C2—42no—
445C2—522no—
446C2C2×#8813511yescharacteristic
447C2#1171925011yescharacteristic
448C2#1171925111yescharacteristic
449C2#1171929811yescharacteristic
450C2#1171930211yescharacteristic
451C2#1171931011yescharacteristic
452C2#1171937011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#386C2
socle, cosocleC23×C13C24
prime radicalC2×#88193C2
hypercenter#386D13
hypocenterC13#2325
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic13C2semidirect
3. C2×#88135C2semidirect
4. C13×#386C2semidirect
5. #11718874C2semidirect
6. C2×#88071C2semidirect
7. #11718619C2semidirect
8. #11718617C2semidirect
9. #11718607C2semidirect
10. #11718606C2semidirect
11. #11718603C2semidirect
12. #11718330C2semidirect
13. #11718329C2semidirect
14. #11718316C2semidirect
15. #11718313C2semidirect
30. #88193C4semidirect
59. C2×D4×C13C2×C4semidirect
72. C2×C22⋊D13C2×C4semidirect
73. C2×C22⋊D13C2×C4semidirect
81. C22×Dic13C2×C4semidirect
82. C22×Dic13D4semidirect
98. C22⋊Dic13C2×C4semidirect
102. #6103C2×C4semidirect
107. #6101C2×C4semidirect
187. #386D13semidirect
291. C2×D4C4×D13semidirect
336. C13#2325semidirect

Maximal subgroups

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

subgroupindex
C2×#881932
C2×D4×Dic132
C2×#881352
C13×#3862
#117188742
C2×#880712
#117186192
#117186172
#117186072
#117186062
#117186032
#117183302
#117183292
#117183162
#117183132
#232513