Finite Group Databasebeta

← #13127123

Subgroups — #13127123

Order 1664.

386 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D13C211yesmaximal, characteristic, complemented
2#11719321C211yesmaximal, characteristic
3C13×#448C211yesmaximal, characteristic, complemented
4#11718886C211yesmaximal, characteristic, complemented
5#11718835C211yesmaximal, characteristic, complemented
6#11718831C211yesmaximal, characteristic, complemented
7#11718823C211yesmaximal, characteristic, complemented
8SD16×Dic13C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic, complemented
10#11718476C211yesmaximal, characteristic, complemented
11#11718463C211yesmaximal, characteristic, complemented
12#11718455C211yesmaximal, characteristic, complemented
13#11718453C211yesmaximal, characteristic, complemented
14#11718390C211yesmaximal, characteristic, complemented
15#11718384C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C13×#121C2211yescharacteristic
21#88200—21no—
22#88200C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24#88198—21no—
25#88198C2211yescharacteristic
26#88193—21no—
27#88192C2211yescharacteristic
28#88190—21no—
29D4×Dic13C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31C4×C22⋊D13—21no—
32C4×C22⋊D13C2211yescharacteristic
33#88180C2211yescharacteristic
34#88178—21no—
35#88178C2211yescharacteristic
36C2×#6099C2211yescharacteristic
37C2×#6094C2211yescharacteristic
38#88146C2211yescharacteristic
39#88142C2211yescharacteristic
40#88139—21no—
41#88131—21no—
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88072C2211yescharacteristic
50#88060C2211yescharacteristic
51#88058C2211yescharacteristic
52#88057C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88054C2211yescharacteristic
56C8×Dic13C2211yescharacteristic
57#88050C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×Q8×C13C2311yescharacteristic
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13D411yescharacteristic
70C22×Dic13—21no—
71Q8×D13—22no—
72Q8×D13—41no—
73C2×C4×D13—21no—
74C2×C4×D13C2311yescharacteristic
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26C2311yescharacteristic
78C13×SD16—22no—
79C13×SD16—41no—
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13D411yescharacteristic
89#6105—41no—
90#6103—21no—
91#6103—21no—
92#6103D411yescharacteristic
93C4⋊Dic13—21no—
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101D411yescharacteristic
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107#6099—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6094—41no—
111#3329—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—42no—
119Q8×C13#4112yes—
120D4×C13—21no—
121D4×C13—21no—
122D4×C13—81no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—42no—
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C22⋊D13—22no—
132C22⋊D13—81no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—42no—
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140C2×Dic13C2×D411yescharacteristic
141C4×D13—21no—
142C4×D13—21no—
143C4×D13—42no—
144Dic26—21no—
145Dic26—21no—
146Dic26—42no—
147Dic26—81no—
148C8×C13—21no—
149C8×C13—21no—
150#1055—21no—
151#1055—21no—
152#555—131no—
153D4×Q8—131no—
154#487—131no—
155#485—131no—
156#485—131no—
157#477—131no—
158#468—131no—
159#468—131no—
160#461—131no—
161#448—131no—
162#448D1311yescharacteristic, complemented
163C4×SD16—131no—
164#436—131no—
165#419—131no—
166#419—131no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13C22×D411yescharacteristic
174C2×D13—21no—
175C2×D13—21no—
176C2×D13—21no—
177C4×C13—22no—
178C4×C13—21no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13C2×#4111yescharacteristic
182C4×C13H(5,𝔽2)11yescharacteristic
183Dic13—21no—
184Dic13—21no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188Dic13—41no—
189Dic13#13712yes—
190C22×Q8—131no—
191C22×Q8C2×D1311yescharacteristic
192C2×SD16—131no—
193C2×SD16C2×D1311yescharacteristic
194C2×SD16C2×D1311yescharacteristic
195C2×M16—131no—
196C2×M16—131no—
197C4⋊Q8—131no—
198C4⋊Q8—131no—
199C4⋊Q8—261no—
200#124—261no—
201#124—261no—
202C22⋊Q8—131no—
203C22⋊Q8—131no—
204C22⋊Q8—261no—
205C22⋊Q8—261no—
206#121—131no—
207#121—261no—
208#121C2×D1311yescharacteristic
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—131no—
212C4×D4—261no—
213#117—131no—
214#117—131no—
215#117—261no—
216#107—131no—
217#107—131no—
218#106—131no—
219C4⋊C8—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103C2×D1311yescharacteristic
228#103C2×D1311yescharacteristic
229#102—131no—
230C22⋊C8—131no—
231C22⋊C8C2×D1311yescharacteristic
232C4×C8—131no—
233C2×C13—41no—
234C2×C13—81no—
235C2×C13#54611yescharacteristic
236C2×C13C2×#13711yescharacteristic
237C2×C13#57711yescharacteristic
238D13—41no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—131no—
243C2×Q8—261no—
244C2×Q8—261no—
245C2×Q8—262no—
246C2×Q8—521no—
247C2×Q8C22×D1311yescharacteristic
248C2×Q8C22×D1311yescharacteristic
249C2×D4—21no—
250C2×D4—131no—
251C2×D4—261no—
252C2×D4C22×D1311yescharacteristic
253C22×C4—21no—
254C22×C4—131no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4C22×D1311yescharacteristic
258SD16—22no—
259SD16—41no—
260SD16—521no—
261M16—521no—
262M16—521no—
263C2×C8—131no—
264C2×C8—131no—
265C2×C8C22×D1311yescharacteristic
266C2×C8C22×D1311yescharacteristic
267C4⋊C4—131no—
268C4⋊C4—131no—
269C4⋊C4—131no—
270C4⋊C4—131no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4C22×D1311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—131no—
280C22⋊C4—131no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C42—131no—
288C42—261no—
289C42—261no—
290C42—261no—
291C13#332911yescharacteristic, complemented, Sylow
292C23—21no—
293C23—131no—
294C23D4×D1311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—261no—
300Q8—261no—
301Q8—522no—
302Q8—1041no—
303Q8#612912yes—
304D4—21no—
305D4—21no—
306D4—81no—
307D4—262no—
308D4—1041no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—131no—
316C2×C4—131no—
317C2×C4—131no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4D4×D1311yescharacteristic
327C2×C4C23×D1311yescharacteristic
328C8—21no—
329C8—21no—
330C8—261no—
331C8—261no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—261no—
339C22—261no—
340C22—261no—
341C22C2×D4×D1311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—132no—
347C4—261no—
348C4—261no—
349C4—521no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4C2×#612911yescharacteristic
354C4#8825111yescharacteristic
355C2—41no—
356C2—81no—
357C2—521no—
358C2#1171929611yescharacteristic
359C2#1171946711yescharacteristic
360C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#448C2
socleC22×C13C22×D4
prime radical#11719321C2
hypercenter#448D13
hypocenterC13#3329
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D13C2semidirect
3. C13×#448C2semidirect
4. #11718886C2semidirect
5. #11718835C2semidirect
6. #11718831C2semidirect
7. #11718823C2semidirect
8. SD16×Dic13C2semidirect
9. #11718703C2semidirect
10. #11718476C2semidirect
11. #11718463C2semidirect
12. #11718455C2semidirect
13. #11718453C2semidirect
14. #11718390C2semidirect
15. #11718384C2semidirect
162. #448D13semidirect
291. C13#3329semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D132
#117193212
C13×#4482
#117188862
#117188352
#117188312
#117188232
SD16×Dic132
#117187032
#117184762
#117184632
#117184552
#117184532
#117183902
#117183842
#332913