Finite Group Databasebeta

← #15835849

Subgroups — #15835849

Order 3328.

1174 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718711C212yesmaximal, complemented
2#13118201C211yesmaximal, characteristic
3#13113810C214yesmaximal, complemented
4#13113793C214yesmaximal, complemented
5#13113408C212yesmaximal, complemented
6#13113154C211yesmaximal, characteristic
7C13×#3501C211yesmaximal, characteristic
8C23×Dic26C2211yescharacteristic
9C13×#554—24no—
10C13×#554—22no—
11D4×Q8×C13—22no—
12C13×#544C2212yes—
13C13×#543—21no—
14C13×#543C2212yes—
15C13×#533—21no—
16C2×C13×C22⋊Q8—21no—
17C2×C13×C22⋊Q8C2212yes—
18C13×#518—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C22×#6107—22no—
21C2×#88178—21no—
22#11718881—21no—
23#11718873C2211yescharacteristic
24C2×C22⋊#1055C2212yes—
25#11718711—24no—
26#11718711C2218yes—
27#11718640C2212yes—
28C2×#88050—22no—
29#11718608C2212yes—
30#11718607—21no—
31#11718590—21no—
32#11718130C2218yes—
33#11718120C2212yes—
34#11718117C2212yes—
35C22×Q8×C13—21no—
36C22×Q8×C13D412yes—
37C22×D4×C13D411yescharacteristic
38C23×C4×C13D411yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×Dic13—21no—
41C22×Dic26—22no—
42C22×Dic26—21no—
43C22×Dic26—22no—
44C22×Dic26—44no—
45C22×Dic26C2312yes—
46C13×C4⋊Q8—21no—
47C13×C4⋊Q8—21no—
48C13×C4⋊Q8—24no—
49C13×#125—22no—
50C13×#125—24no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8—24no—
54C13×C22⋊Q8—24no—
55C13×C22⋊Q8—24no—
56C13×C22⋊Q8—22no—
57C13×C22⋊Q8—22no—
58C13×C22⋊Q8—22no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—24no—
61C13×C22⋊Q8D414yes—
62C13×C22⋊Q8C2314yes—
63C4×Q8×C13—22no—
64C4×Q8×C13—22no—
65C4×D4×C13—24no—
66C4×D4×C13—24no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C13×#117—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4D412yes—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C13×C22⋊C4C2311yescharacteristic
79C2×C42×C13D411yescharacteristic
80C2×C22⋊Dic13—22no—
81C2×C22⋊Dic13—21no—
82C2×#6107—28no—
83C2×#6107—48no—
84C2×C4⋊Dic13—21no—
85#88178—44no—
86C2×#6101—22no—
87C22×#1055—22no—
88#88071—22no—
89#88071—22no—
90#88071C2312yes—
91C22⋊#1055—22no—
92C22⋊#1055C2314yes—
93#88050—28no—
94#18197—131nomaximal, Sylow
95C24×C13C2×D411yescharacteristic
96C24×C13C2×D411yescharacteristic
97C2×Q8×C13—22no—
98C2×Q8×C13—22no—
99C2×Q8×C13—22no—
100C2×Q8×C13—44no—
101C2×Q8×C13—82no—
102C2×Q8×C13C2×D414yes—
103C2×D4×C13—22no—
104C2×D4×C13—22no—
105C2×D4×C13Q1614yescomplemented
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—42no—
113C22×C4×C13—42no—
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D412yes—
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D412yes—
120C22×C4×C13C2411yescharacteristic
121C22×Dic13—22no—
122C22×Dic13—22no—
123C22×Dic13—44no—
124C22×Dic13—42no—
125C2×Dic26—28no—
126C2×Dic26—24no—
127C2×Dic26—24no—
128C2×Dic26—44no—
129C2×Dic26—48no—
130C2×Dic26—44no—
131C2×Dic26—42no—
132C2×Dic26—41no—
133C2×Dic26—41no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—24no—
136C13×C4⋊C4—22no—
137C13×C4⋊C4—22no—
138C13×C4⋊C4—24no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—24no—
141C13×C4⋊C4—22no—
142C13×C4⋊C4—24no—
143C13×C4⋊C4—22no—
144C13×C4⋊C4C2×D414yes—
145C13×C22⋊C4—24no—
146C13×C22⋊C4—24no—
147C13×C22⋊C4—22no—
148C13×C22⋊C4—24no—
149C13×C22⋊C4—22no—
150C42×C13—24no—
151C42×C13—21no—
152C42×C13—21no—
153C22⋊Dic13—44no—
154C22⋊Dic13—42no—
155#6107—416no—
156C4⋊Dic13—42no—
157#6101—44no—
158C2×#1055—24no—
159C2×#1055—44no—
160#3501D1311yescharacteristic
161C2×#451—132no—
162#2409—131no—
163#1605—134no—
164#1602—134no—
165#1520—132no—
166#1459—131no—
167C23×C13—21no—
168C23×C13—21no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13#12012yes—
174C23×C13C2×Q1612yes—
175C23×C13C2×Q1612yescomplemented
176C23×C13#13712yes—
177C23×C13C22×D411yescharacteristic
178Q8×C13—44no—
179Q8×C13—44no—
180Q8×C13—82no—
181Q8×C13—82no—
182D4×C13—28no—
183C2×C4×C13—21no—
184C2×C4×C13—21no—
185C2×C4×C13—24no—
186C2×C4×C13—22no—
187C2×C4×C13—21no—
188C2×C4×C13—24no—
189C2×C4×C13—24no—
190C2×C4×C13—21no—
191C2×C4×C13—42no—
192C2×C4×C13—41no—
193C2×C4×C13—42no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—81no—
197C2×C4×C13—82no—
198C2×C4×C13—82no—
199C2×C4×C13—82no—
200C2×C4×C13—82no—
201C2×C4×C13#12011yescharacteristic
202C2×C4×C13#12011yescharacteristic
203C2×C4×C13C2×Q1612yescomplemented
204C2×C4×C13C22×D412yes—
205C2×Dic13—24no—
206C2×Dic13—48no—
207C2×Dic13—42no—
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211C2×Dic13—42no—
212Dic26—28no—
213Dic26—44no—
214Dic26—44no—
215Dic26—44no—
216#1055—44no—
217C23×Q8—131no—
218C22×Q16—262no—
219#554—24no—
220#554—22no—
221D4×Q8—22no—
222#544C2×D1312yes—
223#543—21no—
224#543C2×D1312yes—
225#533—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—261no—
228C2×C22⋊Q8C2×D1312yes—
229#518—21no—
230C2×C4×D4C2×D1311yescharacteristic
231#451—138no—
232#451—264no—
233C2×#103—262no—
234C2×C22⋊C8—132no—
235#395—132no—
236#393—132no—
237#391—261no—
238#386—261no—
239#385—261no—
240#380—131no—
241#328—138no—
242#324—132no—
243#323—132no—
244C22×C13—21no—
245C22×C13—22no—
246C22×C13—21no—
247C22×C13—22no—
248C22×C13—22no—
249C22×C13—42no—
250C22×C13—42no—
251C22×C13—42no—
252C22×C13—41no—
253C22×C13—41no—
254C22×C13—81no—
255C22×C13#45114yes—
256C22×C13C2×#12011yescharacteristic
257C22×C13C22×Q1611yescharacteristic
258C22×C13C2×#13711yescharacteristic
259C4×C13—22no—
260C4×C13—22no—
261C4×C13—21no—
262C4×C13—41no—
263C4×C13—44no—
264C4×C13—41no—
265C4×C13—44no—
266C4×C13B(4,𝔽2)12yes—
267Dic13—44no—
268Dic13—82no—
269C22×Q8—21no—
270C22×Q8—132no—
271C22×Q8—261no—
272C22×Q8—262no—
273C22×Q8—262no—
274C22×Q8—524no—
275C22×Q8C22⋊D1312yes—
276C22×D4C22⋊D1311yescharacteristic
277C23×C4—261no—
278C23×C4C22⋊D1311yescharacteristic
279C23×C4C22×D1311yescharacteristic
280C2×Q16—268no—
281C2×Q16—528no—
282C22×C8—262no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—24no—
286#125—22no—
287#125—24no—
288C22⋊Q8—22no—
289C22⋊Q8—22no—
290C22⋊Q8—24no—
291C22⋊Q8—24no—
292C22⋊Q8—24no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—24no—
298C22⋊Q8—524no—
299C22⋊Q8C22⋊D1314yes—
300C22⋊Q8C22×D1314yes—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×D4—24no—
304C4×D4—24no—
305C4×D4—22no—
306C4×D4—22no—
307#117—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—262no—
312C2×C4⋊C4—261no—
313C2×C4⋊C4C22⋊D1312yes—
314C2×C4⋊C4C22×D1311yescharacteristic
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—262no—
318C2×C22⋊C4—261no—
319C2×C22⋊C4C22⋊D1311yescharacteristic
320C2×C22⋊C4C22×D1311yescharacteristic
321C2×C42C22⋊D1311yescharacteristic
322#103—268no—
323C22⋊C8—134no—
324C22⋊C8—262no—
325#95—132no—
326#95—262no—
327#95—262no—
328C2×C13—21no—
329C2×C13—21no—
330C2×C13—24no—
331C2×C13—42no—
332C2×C13C2×#45111yescharacteristic
333C2×C13#302211yescharacteristic
334C2×C13C2×B(4,𝔽2)11yescharacteristic
335C24C2×C22⋊D1311yescharacteristic
336C24C2×C22⋊D1311yescharacteristic
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—44no—
341C2×Q8—82no—
342C2×Q8—264no—
343C2×Q8—268no—
344C2×Q8—264no—
345C2×Q8—522no—
346C2×Q8—524no—
347C2×Q8—524no—
348C2×Q8—528no—
349C2×Q8—521no—
350C2×Q8—521no—
351C2×Q8C2×C22⋊D1314yes—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4#610714yescomplemented
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—262no—
364C22×C4—262no—
365C22×C4—524no—
366C22×C4—522no—
367C22×C4C2×C22⋊D1311yescharacteristic
368C22×C4C2×C22⋊D1311yescharacteristic
369C22×C4C2×C22⋊D1312yes—
370C22×C4C2×C22⋊D1311yescharacteristic
371C22×C4C2×C22⋊D1311yescharacteristic
372C22×C4C2×C22⋊D1312yes—
373C22×C4C23×D1311yescharacteristic
374Q16—5216no—
375C2×C8—264no—
376C2×C8—524no—
377C4⋊C4—22no—
378C4⋊C4—24no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—24no—
382C4⋊C4—22no—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4—24no—
386C4⋊C4—22no—
387C4⋊C4—522no—
388C4⋊C4—524no—
389C4⋊C4C2×C22⋊D1314yes—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—22no—
393C22⋊C4—24no—
394C22⋊C4—22no—
395C22⋊C4—524no—
396C22⋊C4—522no—
397C42—24no—
398C42—21no—
399C42—21no—
400C13#1819711yescharacteristic, complemented, Sylow
401C23—21no—
402C23—21no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23#8819612yes—
408C23C2×#610712yes—
409C23C2×#610712yescomplemented
410C23#8820712yes—
411C23C22×C22⋊D1311yescharacteristic
412Q8—44no—
413Q8—44no—
414Q8—82no—
415Q8—82no—
416Q8—268no—
417Q8—524no—
418Q8—524no—
419Q8—524no—
420D4—28no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—21no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—21no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—81no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—264no—
440C2×C4—522no—
441C2×C4—528no—
442C2×C4—522no—
443C2×C4—522no—
444C2×C4—522no—
445C2×C4—522no—
446C2×C4C2×#610712yescomplemented
447C2×C4#8820711yescharacteristic
448C2×C4#8820711yescharacteristic
449C2×C4C22×C22⋊D1312yes—
450C8—524no—
451C22—21no—
452C22—22no—
453C22—21no—
454C22—22no—
455C22—22no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—41no—
460C22—41no—
461C22—81no—
462C22#1171888914yes—
463C22C2×#8819611yescharacteristic
464C22C22×#610711yescharacteristic
465C22C2×#8820711yescharacteristic
466C4—22no—
467C4—21no—
468C4—22no—
469C4—41no—
470C4—44no—
471C4—41no—
472C4—44no—
473C4—524no—
474C4—1042no—
475C4#1171890512yes—
476C2—21no—
477C2—21no—
478C2—24no—
479C2—42no—
480C2C2×#1171888911yescharacteristic
481C2#1312421511yescharacteristic
482C2C2×#1171890511yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3501C2
socleC22×C13C2×#120
prime radicalC22×D4×C13D4
hypercenter#3501D13
hypocenterC13#18197
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. C2×#11718711C2semidirect
3. #13113810C2semidirect
4. #13113793C2semidirect
5. #13113408C2semidirect
105. C2×D4×C13Q16semidirect
175. C23×C13C2×Q16semidirect
203. C2×C4×C13C2×Q16semidirect
354. C2×D4#6107semidirect
400. C13#18197semidirect
409. C23C2×#6107semidirect
446. C2×C4C2×#6107semidirect

Maximal subgroups

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

subgroupindex
C2×#117187112
#131182012
#131138102
#131137932
#131134082
#131131542
C13×#35012
#1819713