Finite Group Databasebeta

← #13118665

Subgroups — #13118665

Order 1664.

584 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D13C211yesmaximal, characteristic
2C2×#88151C211yesmaximal, characteristic, complemented
3C13×#385C211yesmaximal, characteristic, complemented
4#11718873C211yesmaximal, characteristic, complemented
5#11718650C211yesmaximal, characteristic, complemented
6#11718645C211yesmaximal, characteristic, complemented
7#11718642C211yesmaximal, characteristic, complemented
8#11718617C211yesmaximal, characteristic
9#11718617C211yesmaximal, characteristic
10#11718609C211yesmaximal, characteristic, complemented
11#11718608C211yesmaximal, characteristic, complemented
12#11718329C211yesmaximal, characteristic, complemented
13D13×#95C211yesmaximal, characteristic, complemented
14#11718320C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C23×C4×C13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C22×Dic26C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C4×C22⋊D13—24no—
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×C4⋊Dic13C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40#88151—24no—
41C13×#95C2211yescharacteristic
42C13×#95C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C24×C13C2311yescharacteristic
54C23×D13C2311yescharacteristic
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—41no—
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—22no—
65C2×C22⋊D13—22no—
66C2×C22⋊D13Q814yescomplemented
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C2×C4×D13—22no—
75C2×C4×D13—22no—
76C2×C4×D13—22no—
77C2×C4×D13—22no—
78C2×C4×D13—22no—
79C2×C4×D13—41no—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×Dic26—22no—
84C2×Dic26—22no—
85C2×Dic26—41no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—41no—
90C22⋊Dic13—22no—
91C22⋊Dic13—41no—
92C22⋊Dic13—41no—
93#6103—22no—
94#6103—22no—
95#6103D414yes—
96C4⋊Dic13—22no—
97C4⋊Dic13—22no—
98C4⋊Dic13—41no—
99#6101—22no—
100#6101—41no—
101#6101—41no—
102C4×Dic13—22no—
103#2450—131nomaximal, Sylow
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13C2×Q812yes—
111C23×C13C2411yescharacteristic
112C22×D13—21no—
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13C2×D412yes—
117C22×D13C2×Q812yes—
118C22×D13#4112yes—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—44no—
135C2×C4×C13C2×D412yes—
136C2×C4×C13#4112yes—
137C2×C4×C13#4112yes—
138C22⋊D13—28no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13C2×D412yes—
159C2×Dic13C2×Q812yes—
160C4×D13—44no—
161C4×D13—44no—
162C4×D13—44no—
163Dic26—44no—
164C2×C22⋊Q8—131no—
165C2×C4×D4—131no—
166#400—131no—
167#398—131no—
168#396—131no—
169#393—131no—
170#391—131no—
171#387—131no—
172#386—131no—
173#386—131no—
174#385—131no—
175#385—131no—
176#385D1311yescharacteristic, complemented
177#380—131no—
178C2×#95—131no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13C22×D411yescharacteristic
187C22×C13C22×Q811yescharacteristic
188C22×C13C2×#4111yescharacteristic
189C22×C13C2×#4111yescharacteristic
190C22×C13C2×#4111yescharacteristic
191C22×C13H(5,𝔽2)11yescharacteristic
192C22×C13H(5,𝔽2)11yescharacteristic
193C2×D13—22no—
194C2×D13—22no—
195C2×D13—22no—
196C2×D13—22no—
197C2×D13—22no—
198C2×D13—22no—
199C2×D13C22⋊Q814yes—
200C4×C13—22no—
201C4×C13—22no—
202C4×C13—22no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—41no—
206Dic13—22no—
207Dic13—22no—
208Dic13—41no—
209Dic13—41no—
210Dic13—41no—
211Dic13—41no—
212Dic13—41no—
213C22×Q8—131no—
214C22×D4—131no—
215C23×C4—131no—
216C23×C4—131no—
217C23×C4—131no—
218C23×C4C2×D1311yescharacteristic
219C22⋊Q8—264no—
220C4×D4—264no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4C2×D1311yescharacteristic
228C2×C4⋊C4C2×D1311yescharacteristic
229C2×C22⋊C4—131no—
230C2×C22⋊C4—131no—
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4—131no—
234C2×C22⋊C4—131no—
235C2×C22⋊C4C2×D1311yescharacteristic
236C2×C22⋊C4C2×D1311yescharacteristic
237C2×C42—131no—
238#95—131no—
239#95—131no—
240#95—131no—
241#95—131no—
242#95—131no—
243#95—131no—
244#95—131no—
245#95—131no—
246#95—131no—
247#95—131no—
248#95C2×D1311yescharacteristic
249#95C2×D1311yescharacteristic
250C2×C13—42no—
251C2×C13C2×C22⋊Q811yescharacteristic
252C2×C13#52911yescharacteristic
253C2×C13#53811yescharacteristic
254C2×C13#54611yescharacteristic
255C2×C13#54611yescharacteristic
256C2×C13#55411yescharacteristic
257C2×C13#55411yescharacteristic
258D13—24no—
259C24—131no—
260C24C22×D1311yescharacteristic
261C2×Q8—262no—
262C2×Q8—262no—
263C2×Q8—521no—
264C2×D4—134no—
265C2×D4—262no—
266C2×D4—262no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—41no—
270C22×C4—131no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—262no—
278C22×C4—262no—
279C22×C4—262no—
280C22×C4—262no—
281C22×C4—262no—
282C22×C4—521no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4C22×D1311yescharacteristic
287C22×C4C22×D1311yescharacteristic
288C22×C4C22×D1311yescharacteristic
289C22×C4C22×D1311yescharacteristic
290C22×C4C22×D1311yescharacteristic
291C22×C4C22×D1311yescharacteristic
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—262no—
295C4⋊C4—262no—
296C4⋊C4—262no—
297C4⋊C4—521no—
298C4⋊C4—521no—
299C4⋊C4—521no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—134no—
303C22⋊C4—262no—
304C22⋊C4—262no—
305C22⋊C4—262no—
306C22⋊C4—521no—
307C22⋊C4—521no—
308C42—262no—
309C13#245011yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—132no—
317C23—132no—
318C23—132no—
319C23—261no—
320C23—261no—
321C23—261no—
322C23—261no—
323C23Q8×D1312yes—
324C23C23×D1311yescharacteristic
325Q8—524no—
326D4—268no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—132no—
344C2×C4—132no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—524no—
365C2×C4—524no—
366C2×C4—524no—
367C2×C4#612712yes—
368C2×C4D4×D1312yes—
369C2×C4#612912yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—134no—
378C22—262no—
379C22—262no—
380C22—262no—
381C22—262no—
382C22—262no—
383C22—262no—
384C22C2×#612711yescharacteristic
385C22C2×D4×D1311yescharacteristic
386C22C2×#612911yescharacteristic
387C22#8825111yescharacteristic
388C22C2×Q8×D1311yescharacteristic
389C22#41×D1311yescharacteristic
390C22#8825611yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—262no—
398C4—262no—
399C4—521no—
400C4—521no—
401C4—521no—
402C4—521no—
403C4—521no—
404C2—42no—
405C2—264no—
406C2#1171921611yescharacteristic
407C2#1171925511yescharacteristic
408C2#1171926211yescharacteristic
409C2#1171929611yescharacteristic
410C2D13×C22⋊Q811yescharacteristic
411C2#1171934011yescharacteristic
412C2#1171936211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#385C2
prime radicalC22×C22⋊D13C22
hypercenter#385D13
hypocenterC13#2450
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#88151C2semidirect
3. C13×#385C2semidirect
4. #11718873C2semidirect
5. #11718650C2semidirect
6. #11718645C2semidirect
7. #11718642C2semidirect
10. #11718609C2semidirect
11. #11718608C2semidirect
12. #11718329C2semidirect
13. D13×#95C2semidirect
14. #11718320C2semidirect
15. #11718307C2semidirect
66. C2×C22⋊D13Q8semidirect
176. #385D13semidirect
309. C13#2450semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D132
C2×#881512
C13×#3852
#117188732
#117186502
#117186452
#117186422
#117186172
#117186092
#117186082
#117183292
D13×#952
#117183202
#117183072
#245013