Finite Group Databasebeta

← #13123133

Subgroups — #13123133

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
2C22×C4×Dic13C211yesmaximal, characteristic, complemented
3C2×#88139C211yesmaximal, characteristic, complemented
4C2×#88132C211yesmaximal, characteristic, complemented
5C13×#386C211yesmaximal, characteristic, complemented
6#11718881C211yesmaximal, characteristic, complemented
7#11718874C211yesmaximal, characteristic, complemented
8#11718619C211yesmaximal, characteristic, complemented
9#11718618C211yesmaximal, characteristic, complemented
10#11718612C211yesmaximal, characteristic, complemented
11#11718605C211yesmaximal, characteristic, complemented
12#11718331C211yesmaximal, characteristic, complemented
13#11718330C211yesmaximal, characteristic, complemented
14#11718311C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic
21C23×Dic13C2211yescharacteristic
22C22×Dic26C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30#88193—24no—
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×C4×Dic13—24no—
41C2×C4×Dic13C2211yescharacteristic
42C2×C4×Dic13C2211yescharacteristic
43C2×C4×Dic13C2211yescharacteristic
44C2×C4×Dic13C2211yescharacteristic
45#88139—24no—
46#88132—24no—
47C13×#95C2211yescharacteristic
48C13×#95C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55C24×C13C2311yescharacteristic
56C24×C13C2311yescharacteristic
57C23×D13C2311yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C2×C22⋊D13—22no—
70C2×C22⋊D13—22no—
71C2×C22⋊D13—22no—
72C2×C22⋊D13—22no—
73C2×C22⋊D13—22no—
74C2×C22⋊D13—22no—
75C22×Dic13—22no—
76C22×Dic13—22no—
77C22×Dic13—22no—
78C22×Dic13—22no—
79C22×Dic13—22no—
80C22×Dic13D414yes—
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C22×Dic13C2311yescharacteristic
87C22×Dic13C2311yescharacteristic
88C2×Dic26—22no—
89C2×Dic26—22no—
90C2×Dic26—22no—
91C13×C22⋊C4—22no—
92C13×C22⋊C4—22no—
93C13×C22⋊C4—22no—
94C22⋊Dic13—22no—
95C22⋊Dic13—22no—
96C22⋊Dic13—22no—
97C22⋊Dic13—22no—
98#6103—22no—
99#6103—22no—
100#6103—22no—
101#6103—22no—
102#6103—22no—
103C4⋊Dic13—22no—
104#6101—22no—
105#6101—22no—
106#6101—22no—
107C4×Dic13—22no—
108C4×Dic13—22no—
109C4×Dic13—22no—
110C4×Dic13D414yescomplemented
111#2850—131nomaximal, Sylow
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×C13—21no—
122C23×C13—21no—
123C23×C13C2×D412yes—
124C23×C13#4112yes—
125C23×C13#4112yes—
126C23×C13C2411yescharacteristic
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134D4×C13—44no—
135C2×C4×C13—28no—
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—21no—
149C2×C4×C13C2×D412yes—
150C2×C4×C13#4112yes—
151C22⋊D13—44no—
152C22⋊D13—44no—
153C2×Dic13—28no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—28no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—21no—
169C2×Dic13—21no—
170C2×Dic13C2×D412yes—
171C2×Dic13C2×D412yes—
172C2×Dic13C2×D412yes—
173C2×Dic13C2×D412yes—
174C2×Dic13#4112yes—
175C2×Dic13#4112yes—
176Dic26—44no—
177C2×#124—131no—
178C2×C22⋊Q8—131no—
179C2×#121—131no—
180C22×C42—131no—
181#391—131no—
182#390—131no—
183#388—131no—
184#388—131no—
185#388—131no—
186#388—131no—
187#386—131no—
188#386—131no—
189#386—131no—
190#386D1311yescharacteristic, complemented
191#382—131no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13—22no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13#12414yescomplemented
206C22×C13C22×D411yescharacteristic
207C22×C13C22×D411yescharacteristic
208C22×C13C2×#4111yescharacteristic
209C22×C13C2×#4111yescharacteristic
210C22×C13C2×#4111yescharacteristic
211C22×C13C2×#4111yescharacteristic
212C22×C13C2×#4111yescharacteristic
213C2×D13—41no—
214C2×D13—41no—
215C2×D13—41no—
216C2×D13—41no—
217C2×D13—41no—
218C2×D13—41no—
219C2×D13—41no—
220C4×C13—22no—
221C4×C13—22no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13—41no—
225Dic13—22no—
226Dic13—22no—
227Dic13—22no—
228Dic13—41no—
229Dic13—41no—
230Dic13—41no—
231Dic13#12114yes—
232C22×Q8—131no—
233C22×D4—131no—
234C22×D4—131no—
235C22×D4C2×D1311yescharacteristic
236C23×C4—131no—
237C23×C4—131no—
238C23×C4C2×D1311yescharacteristic
239#124—264no—
240C22⋊Q8—264no—
241#121—264no—
242C2×C4⋊C4—131no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—131no—
245C2×C4⋊C4—131no—
246C2×C22⋊C4—131no—
247C2×C22⋊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—
260C2×C42—131no—
261C2×C42—131no—
262C2×C42—264no—
263#95—131no—
264#95—131no—
265#95—131no—
266#95—131no—
267#95—131no—
268#95—131no—
269#95C2×D1311yescharacteristic
270#95C2×D1311yescharacteristic
271C2×C13—24no—
272C2×C13—81no—
273C2×C13C2×#12111yescharacteristic
274C2×C13#52511yescharacteristic
275C2×C13#52511yescharacteristic
276C2×C13C2×#12411yescharacteristic
277C2×C13#52911yescharacteristic
278C2×C13#52911yescharacteristic
279C2×C13#53211yescharacteristic
280D13—81no—
281C24—131no—
282C24C22×D1311yescharacteristic
283C24C22×D1311yescharacteristic
284C2×Q8—262no—
285C2×Q8—262no—
286C2×Q8—262no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—262no—
291C2×D4—262no—
292C2×D4—262no—
293C2×D4—262no—
294C2×D4—262no—
295C2×D4—262no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—131no—
300C22×C4—134no—
301C22×C4—131no—
302C22×C4—131no—
303C22×C4—131no—
304C22×C4—131no—
305C22×C4—131no—
306C22×C4—131no—
307C22×C4—262no—
308C22×C4—262no—
309C22×C4—262no—
310C22×C4—262no—
311C22×C4—262no—
312C22×C4C22×D1311yescharacteristic
313C22×C4C22×D1311yescharacteristic
314C22×C4C22×D1311yescharacteristic
315C22×C4C22×D1311yescharacteristic
316C22×C4C22×D1311yescharacteristic
317C4⋊C4—262no—
318C4⋊C4—262no—
319C4⋊C4—262no—
320C4⋊C4—262no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—262no—
325C22⋊C4—262no—
326C22⋊C4—262no—
327C22⋊C4—262no—
328C22⋊C4—262no—
329C22⋊C4—262no—
330C22⋊C4—262no—
331C22⋊C4—262no—
332C22⋊C4—262no—
333C42—134no—
334C42—262no—
335C42—262no—
336C42—262no—
337C13#285011yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—261no—
350C23—261no—
351C23—261no—
352C23—261no—
353C23—261no—
354C23—261no—
355C23—261no—
356C23#612712yes—
357C23D4×D1312yes—
358C23#612912yes—
359C23C23×D1311yescharacteristic
360Q8—524no—
361D4—44no—
362D4—524no—
363D4—524no—
364C2×C4—28no—
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—21no—
377C2×C4—21no—
378C2×C4—132no—
379C2×C4—132no—
380C2×C4—132no—
381C2×C4—132no—
382C2×C4—132no—
383C2×C4—132no—
384C2×C4—268no—
385C2×C4—268no—
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—261no—
399C2×C4—261no—
400C2×C4—261no—
401C2×C4D4×D1312yes—
402C2×C4#612912yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—521no—
417C22—521no—
418C22—521no—
419C22—521no—
420C22—521no—
421C22—521no—
422C22—521no—
423C22#8813914yescomplemented
424C22C2×#612711yescharacteristic
425C22C2×D4×D1311yescharacteristic
426C22C2×D4×D1311yescharacteristic
427C22C2×#612911yescharacteristic
428C22C2×#612911yescharacteristic
429C22#41×D1311yescharacteristic
430C22#41×D1311yescharacteristic
431C4—22no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—134no—
437C4—262no—
438C4—262no—
439C4—262no—
440C4—521no—
441C4—521no—
442C4—521no—
443C2—24no—
444C2—81no—
445C2—1041no—
446C2C2×#8813911yescharacteristic
447C2#1171924311yescharacteristic
448C2#1171925211yescharacteristic
449C2#1171929111yescharacteristic
450C2#1171930111yescharacteristic
451C2D13×#12111yescharacteristic
452C2#1171935411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC2×#88193C2
hypercenter#386D13
hypocenterC13#2850
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic13C2semidirect
3. C2×#88139C2semidirect
4. C2×#88132C2semidirect
5. C13×#386C2semidirect
6. #11718881C2semidirect
7. #11718874C2semidirect
8. #11718619C2semidirect
9. #11718618C2semidirect
10. #11718612C2semidirect
11. #11718605C2semidirect
12. #11718331C2semidirect
13. #11718330C2semidirect
14. #11718311C2semidirect
15. #11718307C2semidirect
110. C4×Dic13D4semidirect
190. #386D13semidirect
205. C22×C13#124semidirect
337. C13#2850semidirect
423. C22#88139semidirect

Maximal subgroups

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

subgroupindex
C2×#881932
C22×C4×Dic132
C2×#881392
C2×#881322
C13×#3862
#117188812
#117188742
#117186192
#117186182
#117186122
#117186052
#117183312
#117183302
#117183112
#117183072
#285013