Finite Group Databasebeta

← #13118258

Subgroups — #13118258

Order 1664.

604 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×D4×Dic13C211yesmaximal, characteristic
2C2×#88132C211yesmaximal, characteristic, complemented
3C2×#88132C211yesmaximal, characteristic, complemented
4C2×#88131C211yesmaximal, characteristic, complemented
5C13×#394C211yesmaximal, characteristic
6#11718883C211yesmaximal, characteristic
7#11718646C211yesmaximal, characteristic, complemented
8#11718633C211yesmaximal, characteristic, complemented
9#11718614C211yesmaximal, characteristic, complemented
10#11718613C211yesmaximal, characteristic, complemented
11#11718612C211yesmaximal, characteristic, complemented
12#11718605C211yesmaximal, characteristic, complemented
13#11718603C211yesmaximal, characteristic, complemented
14#11718308C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C23×Dic13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31D4×Dic13—24no—
32C2×C4⋊Dic13C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×C4×Dic13C2211yescharacteristic
42C2×C4×Dic13C2211yescharacteristic
43C2×C4×Dic13C2211yescharacteristic
44#88132—24no—
45#88132—24no—
46#88131—24no—
47C13×#95C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55C24×C13C2311yescharacteristic
56C24×C13C2311yescharacteristic
57C2×D4×C13—22no—
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13D414yes—
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C2×Dic26—22no—
80C2×Dic26—22no—
81C2×Dic26—22no—
82C13×C4⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—22no—
87C22⋊Dic13—22no—
88C22⋊Dic13—22no—
89C22⋊Dic13—22no—
90C22⋊Dic13—22no—
91C22⋊Dic13—22no—
92C22⋊Dic13—22no—
93C4⋊Dic13—22no—
94C4⋊Dic13—22no—
95C4⋊Dic13—22no—
96#6101—22no—
97#6101—22no—
98#6101—22no—
99#6101—22no—
100#6101—22no—
101#6101D414yescomplemented
102C4×Dic13—22no—
103C4×Dic13—22no—
104C4×Dic13—22no—
105#2415—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13C2×D412yes—
119C23×C13#4112yes—
120C23×C13C2411yescharacteristic
121D4×C13—28no—
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—21no—
135C2×C4×C13C2×D412yes—
136C2×C4×C13#4112yes—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—28no—
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—44no—
158C2×Dic13C2×D412yes—
159C2×Dic13C2×D412yes—
160C2×Dic13C2×D412yes—
161C2×Dic13C2×D412yes—
162C2×Dic13#4112yes—
163Dic26—44no—
164C2×C22⋊Q8—131no—
165C2×C22⋊Q8—131no—
166C2×C4×D4—131no—
167C2×#117—131no—
168#397—131no—
169#397—131no—
170#394—131no—
171#394D1311yescharacteristic
172#391—131no—
173#389—131no—
174#389—131no—
175#389—131no—
176#388—131no—
177#388—131no—
178#380—131no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13C22×D411yescharacteristic
194C22×C13C22×D411yescharacteristic
195C22×C13C2×#4111yescharacteristic
196C22×C13C2×#4111yescharacteristic
197C22×C13C2×#4111yescharacteristic
198C22×C132−1+411yescharacteristic
199C22×C132−1+411yescharacteristic
200C4×C13—22no—
201C4×C13—22no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13—41no—
205Dic13—22no—
206Dic13—22no—
207Dic13—41no—
208Dic13—41no—
209Dic13—41no—
210Dic13—41no—
211Dic13—41no—
212Dic13#12114yes—
213C22×Q8—131no—
214C22×D4C2×D1311yescharacteristic
215C23×C4—131no—
216C23×C4—131no—
217C22⋊Q8—264no—
218C22⋊Q8—264no—
219C4×D4—264no—
220#117—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⋊C4—131no—
228C2×C4⋊C4—131no—
229C2×C4⋊C4—131no—
230C2×C4⋊C4C2×D1311yescharacteristic
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4—131no—
234C2×C22⋊C4—131no—
235C2×C22⋊C4—131no—
236C2×C22⋊C4—131no—
237C2×C22⋊C4C2×D1311yescharacteristic
238C2×C22⋊C4C2×D1311yescharacteristic
239C2×C22⋊C4C2×D1311yescharacteristic
240C2×C22⋊C4C2×D1311yescharacteristic
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244#95—131no—
245#95—131no—
246#95—131no—
247#95—131no—
248#95—131no—
249#95—131no—
250#95—131no—
251#95C2×D1311yescharacteristic
252C2×C13—42no—
253C2×C13—42no—
254C2×C13C2×#12111yescharacteristic
255C2×C13#52511yescharacteristic
256C2×C13#53611yescharacteristic
257C2×C13#54711yescharacteristic
258C2×C13#54811yescharacteristic
259C2×C13#55211yescharacteristic
260C2×C13#55611yescharacteristic
261C24C22×D1311yescharacteristic
262C24C22×D1311yescharacteristic
263C2×Q8—262no—
264C2×Q8—262no—
265C2×Q8—262no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C22×C4—131no—
270C22×C4—134no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—262no—
279C22×C4—262no—
280C22×C4—262no—
281C22×C4—262no—
282C22×C4—262no—
283C22×C4C22×D1311yescharacteristic
284C22×C4C22×D1311yescharacteristic
285C22×C4C22×D1311yescharacteristic
286C22×C4C22×D1311yescharacteristic
287C22×C4C22×D1311yescharacteristic
288C4⋊C4—22no—
289C4⋊C4—134no—
290C4⋊C4—262no—
291C4⋊C4—262no—
292C4⋊C4—262no—
293C4⋊C4—262no—
294C4⋊C4—262no—
295C4⋊C4—262no—
296C4⋊C4—262no—
297C4⋊C4—262no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—262no—
303C22⋊C4—262no—
304C22⋊C4—262no—
305C22⋊C4—262no—
306C22⋊C4—262no—
307C22⋊C4—262no—
308C42—262no—
309C42—262no—
310C42—262no—
311C13#241511yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23D4×D1312yes—
325C23#612912yes—
326C23C23×D1311yescharacteristic
327Q8—524no—
328D4—28no—
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—132no—
343C2×C4—132no—
344C2×C4—132no—
345C2×C4—132no—
346C2×C4—132no—
347C2×C4—268no—
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—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—524no—
368C2×C4D4×D1312yes—
369C2×C4#612912yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22C2×D4×D1311yescharacteristic
385C22C2×D4×D1311yescharacteristic
386C22C2×#612911yescharacteristic
387C22C2×#612911yescharacteristic
388C22#41×D1311yescharacteristic
389C22#8825711yescharacteristic
390C22#8825711yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—134no—
397C4—262no—
398C4—262no—
399C4—521no—
400C4—521no—
401C4—521no—
402C4—521no—
403C4—521no—
404C2—42no—
405C2—42no—
406C2#1171929111yescharacteristic
407C2#1171930311yescharacteristic
408C2D13×#12111yescharacteristic
409C2#1171931611yescharacteristic
410C2#1171935311yescharacteristic
411C2#1171935511yescharacteristic
412C2#1171937611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC22×D4×C13C22
hypercenter#394D13
hypocenterC13#2415
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88132C2semidirect
3. C2×#88132C2semidirect
4. C2×#88131C2semidirect
7. #11718646C2semidirect
8. #11718633C2semidirect
9. #11718614C2semidirect
10. #11718613C2semidirect
11. #11718612C2semidirect
12. #11718605C2semidirect
13. #11718603C2semidirect
14. #11718308C2semidirect
15. #11718307C2semidirect
101. #6101D4semidirect
311. C13#2415semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881322
C2×#881312
C13×#3942
#117188832
#117186462
#117186332
#117186142
#117186132
#117186122
#117186052
#117186032
#117183082
#117183072
#241513