Finite Group Databasebeta

← #13118284

Subgroups — #13118284

Order 1664.

648 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic13C211yesmaximal, characteristic
2C22×#6101C211yesmaximal, characteristic, complemented
3C2×#88132C211yesmaximal, characteristic, complemented
4C2×#88132C211yesmaximal, characteristic, complemented
5C13×#386C211yesmaximal, characteristic
6#11718881C211yesmaximal, characteristic
7#11718873C211yesmaximal, characteristic, complemented
8#11718609C211yesmaximal, characteristic, complemented
9#11718609C211yesmaximal, characteristic, complemented
10#11718603C211yesmaximal, characteristic, complemented
11#11718603C211yesmaximal, characteristic, complemented
12#11718322C211yesmaximal, characteristic, complemented
13#11718318C211yesmaximal, characteristic, complemented
14#11718308C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C23×Dic13C2211yescharacteristic
19C23×Dic13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic
21C22×Dic26C2211yescharacteristic
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
30D4×Dic13—24no—
31C2×C4⋊Dic13C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6101—24no—
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×#6101C2211yescharacteristic
44C2×C4×Dic13C2211yescharacteristic
45#88132—24no—
46#88132—24no—
47C13×#95C2211yescharacteristic
48C13×#95C2211yescharacteristic
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×C13Q814yescomplemented
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—41no—
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—22no—
75C22×Dic13—41no—
76C22×Dic13D414yes—
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C2×Dic26—22no—
86C2×Dic26—22no—
87C2×Dic26—22no—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—41no—
91C22⋊Dic13—22no—
92C22⋊Dic13—22no—
93C22⋊Dic13—22no—
94C22⋊Dic13—22no—
95C22⋊Dic13—41no—
96C4⋊Dic13—22no—
97C4⋊Dic13—22no—
98C4⋊Dic13—22no—
99C4⋊Dic13—41no—
100#6101—22no—
101#6101—22no—
102#6101—22no—
103#6101—22no—
104#6101—22no—
105#6101—22no—
106#6101—41no—
107#6101D414yescomplemented
108C4×Dic13—22no—
109#2417—131nomaximal, Sylow
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×C13—21no—
119C23×C13—21no—
120C23×C13C2×D412yes—
121C23×C13C2×Q812yes—
122C23×C13C2×Q812yes—
123C23×C13#4112yes—
124C23×C13C2411yescharacteristic
125D4×C13—28no—
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×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—44no—
140C2×C4×C13C2×D412yes—
141C2×C4×C13C2×Q812yes—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—28no—
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×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—44no—
163C2×Dic13—44no—
164C2×Dic13C2×D412yes—
165C2×Dic13C2×D412yes—
166C2×Dic13C2×D412yes—
167C2×Dic13C2×D412yes—
168C2×Dic13#4112yes—
169Dic26—44no—
170C2×C22⋊Q8—131no—
171C2×C22⋊Q8—131no—
172C2×C4×D4—131no—
173C22×C4⋊C4—131no—
174#398—131no—
175#398—131no—
176#396—131no—
177#396—131no—
178#391—131no—
179#389—131no—
180#386—131no—
181#386D1311yescharacteristic
182#380—131no—
183#380—131no—
184#380—131no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13C22⋊Q814yescomplemented
199C22×C13C22×D411yescharacteristic
200C22×C13C22×D411yescharacteristic
201C22×C13C22×Q811yescharacteristic
202C22×C13C2×#4111yescharacteristic
203C22×C13C2×#4111yescharacteristic
204C22×C13H(5,𝔽2)11yescharacteristic
205C22×C132−1+411yescharacteristic
206C4×C13—22no—
207C4×C13—22no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211Dic13—22no—
212Dic13—22no—
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216Dic13—41no—
217Dic13—41no—
218Dic13#12114yes—
219C22×Q8—131no—
220C22×D4C2×D1311yescharacteristic
221C23×C4—131no—
222C23×C4—131no—
223C23×C4—131no—
224C23×C4C2×D1311yescharacteristic
225C22⋊Q8—264no—
226C22⋊Q8—264no—
227C4×D4—264no—
228C2×C4⋊C4—131no—
229C2×C4⋊C4—131no—
230C2×C4⋊C4—131no—
231C2×C4⋊C4—131no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—131no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—131no—
239C2×C4⋊C4—131no—
240C2×C4⋊C4—264no—
241C2×C22⋊C4—131no—
242C2×C22⋊C4—131no—
243C2×C22⋊C4—131no—
244C2×C22⋊C4—131no—
245C2×C22⋊C4—131no—
246C2×C22⋊C4C2×D1311yescharacteristic
247C2×C22⋊C4C2×D1311yescharacteristic
248C2×C22⋊C4C2×D1311yescharacteristic
249C2×C42—131no—
250#95—131no—
251#95—131no—
252#95—131no—
253#95—131no—
254#95—131no—
255#95—131no—
256#95C2×D1311yescharacteristic
257#95C2×D1311yescharacteristic
258C2×C13—24no—
259C2×C13—42no—
260C2×C13C2×#12111yescharacteristic
261C2×C13C2×C22⋊Q811yescharacteristic
262C2×C13#53711yescharacteristic
263C2×C13#54611yescharacteristic
264C2×C13D4×Q811yescharacteristic
265C2×C13#55211yescharacteristic
266C2×C13#55411yescharacteristic
267C24C22×D1311yescharacteristic
268C24C22×D1311yescharacteristic
269C2×Q8—262no—
270C2×Q8—262no—
271C2×Q8—262no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4Dic2614yescomplemented
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—131no—
279C22×C4—134no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—262no—
288C22×C4—262no—
289C22×C4—262no—
290C22×C4—262no—
291C22×C4—262no—
292C22×C4—262no—
293C22×C4—262no—
294C22×C4—521no—
295C22×C4C22×D1311yescharacteristic
296C22×C4C22×D1311yescharacteristic
297C22×C4C22×D1311yescharacteristic
298C22×C4C22×D1311yescharacteristic
299C22×C4C22×D1311yescharacteristic
300C4⋊C4—134no—
301C4⋊C4—262no—
302C4⋊C4—262no—
303C4⋊C4—262no—
304C4⋊C4—262no—
305C4⋊C4—262no—
306C4⋊C4—262no—
307C4⋊C4—262no—
308C4⋊C4—262no—
309C4⋊C4—262no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—41no—
315C22⋊C4—262no—
316C22⋊C4—262no—
317C22⋊C4—262no—
318C22⋊C4—262no—
319C22⋊C4—521no—
320C42—262no—
321C13#241711yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23C2×Dic2612yes—
333C23C2×Dic2612yes—
334C23D4×D1312yes—
335C23#612912yes—
336C23C23×D1311yescharacteristic
337Q8—524no—
338D4—28no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—44no—
353C2×C4—132no—
354C2×C4—132no—
355C2×C4—132no—
356C2×C4—132no—
357C2×C4—132no—
358C2×C4—268no—
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—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—524no—
379C2×C4—524no—
380C2×C4C2×Dic2612yes—
381C2×C4D4×D1312yes—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22#8813214yescomplemented
396C22C22×Dic2611yescharacteristic
397C22C2×D4×D1311yescharacteristic
398C22C2×D4×D1311yescharacteristic
399C22C2×#612911yescharacteristic
400C22#8825111yescharacteristic
401C22#41×D1311yescharacteristic
402C22#8825711yescharacteristic
403C4—22no—
404C4—22no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—134no—
409C4—262no—
410C4—262no—
411C4—521no—
412C4—521no—
413C4—521no—
414C4—521no—
415C4—521no—
416C2—24no—
417C2—42no—
418C2C2×#8813211yescharacteristic
419C2D4×Dic2611yescharacteristic
420C2#1171924411yescharacteristic
421C2#1171929611yescharacteristic
422C2#1171930211yescharacteristic
423C2D13×#12111yescharacteristic
424C2#1171935511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC22×D4×C13C22
hypercenter#386D13
hypocenterC13#2417
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×#6101C2semidirect
3. C2×#88132C2semidirect
4. C2×#88132C2semidirect
7. #11718873C2semidirect
8. #11718609C2semidirect
9. #11718609C2semidirect
10. #11718603C2semidirect
11. #11718603C2semidirect
12. #11718322C2semidirect
13. #11718318C2semidirect
14. #11718308C2semidirect
15. #11718307C2semidirect
59. C2×D4×C13Q8semidirect
107. #6101D4semidirect
198. C22×C13C22⋊Q8semidirect
274. C2×D4Dic26semidirect
321. C13#2417semidirect
395. C22#88132semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C22×#61012
C2×#881322
C13×#3862
#117188812
#117188732
#117186092
#117186032
#117183222
#117183182
#117183082
#117183072
#241713