Finite Group Databasebeta

← #15846377

Subgroups — #15846377

Order 3328.

584 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13126173C212yesmaximal
2#13125422C211yesmaximal, characteristic, complemented
3#13114354C211yesmaximal, characteristic, complemented
4#13114349C211yesmaximal, characteristic, complemented
5#13114330C211yesmaximal, characteristic, complemented
6#13114325C211yesmaximal, characteristic, complemented
7#13114266C212yesmaximal, complemented
8#13114259C212yesmaximal, complemented
9C2×#11718049C211yesmaximal, characteristic, complemented
10#13113537C212yesmaximal, complemented
11C13×#2966C211yesmaximal, characteristic
12C13×#529C2211yescharacteristic
13#11719175C2212yes—
14C13×#446C2211yescharacteristic
15C8×Q8×C13C2211yescharacteristic
16C13×#436C2211yescharacteristic
17C13×#435—21no—
18C8×D4×C13—21no—
19C8×D4×C13C2211yescharacteristic
20C13×#433—21no—
21C13×#432C2211yescharacteristic
22C13×#405—21no—
23C2×C4×C8×C13C2211yescharacteristic
24#11718777—21no—
25#11718777—21no—
26#11718724—22no—
27#11718715—22no—
28#11718712—22no—
29#11718702—22no—
30#11718692C2212yes—
31#11718681C2212yes—
32#11718680C2212yes—
33#11718668C2212yes—
34C2×C4⋊#1055C2212yes—
35#11718360C2211yescharacteristic
36C4×Dic52—21no—
37C4×Dic52—21no—
38#11718343C2211yescharacteristic
39#11718342C2212yes—
40#11718078C2212yes—
41#11718078C2212yes—
42#11718074C2212yes—
43#11718074C2212yes—
44#11718049C2212yes—
45#11718049C2211yescharacteristic
46#11718049C2211yescharacteristic
47C2×C13×M16—21no—
48C22×C8×C13—21no—
49C22×C8×C13D411yescharacteristic
50C22×C8×C13D411yescharacteristic
51C13×#126—21no—
52C13×#125D411yescharacteristic
53C13×#124D411yescharacteristic
54C13×#123—21no—
55C13×C22⋊Q8D411yescharacteristic
56C13×#121D411yescharacteristic
57C4×Q8×C13C2311yescharacteristic
58C4×D4×C13—21no—
59C4×D4×C13C2311yescharacteristic
60C13×#117—21no—
61C2×C42×C13C2311yescharacteristic
62C2×#6107—22no—
63C2×#6105—22no—
64#88180—22no—
65#88178—22no—
66#88178—22no—
67C22×#1055—22no—
68C2×Dic52—21no—
69C2×Dic52—21no—
70#88124—22no—
71#88123C2312yes—
72#88123C2312yes—
73C4×Dic26—22no—
74C4×Dic26—22no—
75C13×C4⋊C8—21no—
76C13×C4⋊C8—21no—
77C13×C4⋊C8C2311yescharacteristic
78C13×C4⋊C8C2311yescharacteristic
79C13×C22⋊C8—21no—
80C13×C22⋊C8—21no—
81C13×C22⋊C8—21no—
82C13×#97—21no—
83C13×#97—21no—
84C4×C8×C13—21no—
85C4×C8×C13D411yescharacteristic
86C4×C8×C13D411yescharacteristic
87C4×C8×C13C2311yescharacteristic
88C4×C8×C13C2311yescharacteristic
89#88075—22no—
90#88072—22no—
91#88058—21no—
92#88058—21no—
93#88056—22no—
94#88056—22no—
95#88050—22no—
96#88050—22no—
97#88048—22no—
98#88047—22no—
99C4⋊#1055—22no—
100C4⋊#1055C2312yes—
101C4⋊#1055C2312yes—
102#19228—131nomaximal, Sylow
103C2×Q8×C13C2×D411yescharacteristic
104C2×D4×C13—21no—
105C2×D4×C13C2×D411yescharacteristic
106C22×C4×C13—21no—
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C2×Dic26—22no—
111C2×Dic26—22no—
112C13×M16—42no—
113C2×C8×C13—22no—
114C2×C8×C13—21no—
115C2×C8×C13—21no—
116C2×C8×C13—41no—
117C2×C8×C13—42no—
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13C2×D411yescharacteristic
121C2×C8×C13C2×D411yescharacteristic
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4C2×D411yescharacteristic
127C13×C4⋊C4C2×D411yescharacteristic
128C13×C22⋊C4—21no—
129C13×C22⋊C4—21no—
130C13×C22⋊C4—21no—
131C13×C22⋊C4—21no—
132C13×C22⋊C4—21no—
133C42×C13—21no—
134C42×C13C2×D411yescharacteristic
135C42×C13C2×D411yescharacteristic
136C42×C13#4111yescharacteristic
137C42×C13C2411yescharacteristic
138C22⋊Dic13—42no—
139#6107—82no—
140#6105—82no—
141C4⋊Dic13—22no—
142C4⋊Dic13—22no—
143C4⋊Dic13—22no—
144C4⋊Dic13—22no—
145#6101—42no—
146#6101—42no—
147C4×Dic13—42no—
148C2×#1055—22no—
149C2×#1055—22no—
150C2×#1055—82no—
151Dic52—42no—
152Dic52—42no—
153#3248—132no—
154#3170—131no—
155#2966D1311yescharacteristic
156#1694—131no—
157#1693—131no—
158#1690—131no—
159#1689—131no—
160#1680—132no—
161#1679—132no—
162C2×#334—131no—
163#1552—132no—
164C23×C13—21no—
165C23×C13#12111yescharacteristic
166Q8×C13—22no—
167D4×C13—22no—
168D4×C13—42no—
169C2×C4×C13—22no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—22no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13#12111yescharacteristic
179C2×C4×C13#12111yescharacteristic
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13C22×D411yescharacteristic
182C2×C4×C13C22×D411yescharacteristic
183C2×C4×C13C2×#4111yescharacteristic
184C2×Dic13—42no—
185C2×Dic13—42no—
186Dic26—42no—
187Dic26—42no—
188Dic26—42no—
189Dic26—42no—
190C8×C13—21no—
191C8×C13—21no—
192C8×C13—21no—
193C8×C13—41no—
194C8×C13—41no—
195C8×C13#13512yes—
196#1055—42no—
197#1055—42no—
198#533—132no—
199#529C2×D1311yescharacteristic
200#500—131no—
201#494—131no—
202#487—132no—
203#479—262no—
204#475—132no—
205#474—132no—
206#467—261no—
207#467—261no—
208#467—262no—
209#465—262no—
210#464—262no—
211#462—132no—
212#461—132no—
213#446C2×D1311yescharacteristic
214C8×Q8C2×D1311yescharacteristic
215C4×Q16—261no—
216C4×Q16—261no—
217#436C2×D1311yescharacteristic
218#435—21no—
219C8×D4—21no—
220C8×D4C2×D1311yescharacteristic
221#433—21no—
222#432C2×D1311yescharacteristic
223C2×C4⋊C8—132no—
224#405—21no—
225C2×C4×C8C2×D1311yescharacteristic
226#334—132no—
227#334—131no—
228#334—131no—
229#332—132no—
230#332—132no—
231#332—132no—
232#332—132no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—41no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13#47312yes—
239C22×C13C2×#12111yescharacteristic
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—21no—
243C4×C13—21no—
244C4×C13—41no—
245C4×C13—41no—
246C4×C13—41no—
247C4×C13C2×#13511yescharacteristic
248C4×C13#57511yescharacteristic
249C4×C13#57712yes—
250Dic13—82no—
251Dic13—82no—
252C2×Q16—262no—
253C2×Q16—261no—
254C2×Q16—261no—
255C2×SD16—262no—
256C2×M16—21no—
257C22×C8—21no—
258C22×C8—262no—
259C22×C8C22⋊D1311yescharacteristic
260C22×C8C22⋊D1311yescharacteristic
261C4⋊Q8—132no—
262C4⋊Q8—132no—
263#126—21no—
264#125—262no—
265#125D5211yescharacteristic
266#124D5211yescharacteristic
267#123—21no—
268C22⋊Q8—262no—
269C22⋊Q8—262no—
270C22⋊Q8D5211yescharacteristic
271#121D5211yescharacteristic
272C4×Q8—262no—
273C4×Q8—262no—
274C4×Q8C22×D1311yescharacteristic
275C4×D4—21no—
276C4×D4C22×D1311yescharacteristic
277#117—21no—
278#117—262no—
279C2×C42C22×D1311yescharacteristic
280#107—261no—
281#107—261no—
282#107—262no—
283#106—262no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8—132no—
287C4⋊C8—132no—
288C4⋊C8—262no—
289C4⋊C8C22×D1311yescharacteristic
290C4⋊C8C22×D1311yescharacteristic
291#103—262no—
292#103—262no—
293#103—262no—
294#103—262no—
295#103—262no—
296#102—262no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300#97—21no—
301#97—21no—
302C4×C8—21no—
303C4×C8C22⋊D1311yescharacteristic
304C4×C8C22⋊D1311yescharacteristic
305C4×C8C22×D1311yescharacteristic
306C4×C8C22×D1311yescharacteristic
307C2×C13—22no—
308C2×C13—81no—
309C2×C13#303511yescharacteristic
310C2×C13#306011yescharacteristic
311C2×C13C2×#47311yescharacteristic
312C2×Q8—262no—
313C2×Q8—262no—
314C2×Q8C2×D5211yescharacteristic
315C2×D4—21no—
316C2×D4C2×D5211yescharacteristic
317C22×C4—21no—
318C22×C4C2×D5211yescharacteristic
319C22×C4#612711yescharacteristic
320C22×C4C2×C22⋊D1311yescharacteristic
321Q16—522no—
322Q16—522no—
323Q16—1042no—
324SD16—1042no—
325M16—42no—
326C2×C8—22no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—41no—
330C2×C8—42no—
331C2×C8—262no—
332C2×C8—262no—
333C2×C8—1042no—
334C2×C8C2×C22⋊D1311yescharacteristic
335C2×C8C2×C22⋊D1311yescharacteristic
336C2×C8C2×C22⋊D1311yescharacteristic
337C2×C8C2×C22⋊D1311yescharacteristic
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—262no—
343C4⋊C4—262no—
344C4⋊C4—262no—
345C4⋊C4—262no—
346C4⋊C4—522no—
347C4⋊C4—522no—
348C4⋊C4C2×D5211yescharacteristic
349C4⋊C4C2×D5211yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—522no—
356C42—21no—
357C42—522no—
358C42C2×D5211yescharacteristic
359C42#612711yescharacteristic
360C42C2×C22⋊D1311yescharacteristic
361C42C23×D1311yescharacteristic
362C13#1922811yescharacteristic, complemented, Sylow
363C23—21no—
364C23#8818411yescharacteristic
365Q8—22no—
366Q8—522no—
367Q8—522no—
368Q8—522no—
369Q8—522no—
370D4—22no—
371D4—42no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—522no—
382C2×C4—522no—
383C2×C4#8818411yescharacteristic
384C2×C4#8818411yescharacteristic
385C2×C4#8818411yescharacteristic
386C2×C4C22×D5211yescharacteristic
387C2×C4C2×#612711yescharacteristic
388C2×C4C22×C22⋊D1311yescharacteristic
389C8—21no—
390C8—21no—
391C8—21no—
392C8—41no—
393C8—41no—
394C8—522no—
395C8—522no—
396C8#8820412yes—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22#1171880412yes—
403C22C2×#8818411yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—1042no—
412C4—1042no—
413C4#1171945612yes—
414C4C2×#8820411yescharacteristic
415C4#1171952711yescharacteristic
416C2—22no—
417C2—81no—
418C2#1312429111yescharacteristic
419C2#1312449811yescharacteristic
420C2C2×#1171880411yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2966C2
socleC22×C13C2×#121
prime radicalC13×#121D4
hypercenter#2966D13
hypocenterC13#19228
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #13125422C2semidirect
3. #13114354C2semidirect
4. #13114349C2semidirect
5. #13114330C2semidirect
6. #13114325C2semidirect
7. #13114266C2semidirect
8. #13114259C2semidirect
9. C2×#11718049C2semidirect
10. #13113537C2semidirect
362. C13#19228semidirect

Maximal subgroups

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

subgroupindex
#131261732
#131254222
#131143542
#131143492
#131143302
#131143252
#131142662
#131142592
C2×#117180492
#131135372
C13×#29662
#1922813