Finite Group Databasebeta

← #16798286

Subgroups — #16798286

Order 3328.

954 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719100C212yesmaximal
2C22×#88104C211yesmaximal, characteristic
3C2×D13⋊#108C211yesmaximal, characteristic
4#13131479C212yesmaximal
5#13130778C214yesmaximal, complemented
6#13130777C212yesmaximal, complemented
7#13130776C212yesmaximal, complemented
8D13×#405C211yesmaximal, characteristic
9C2×D13⋊M16C2212yes—
10C22×#6118C2212yes—
11C2×M16×D13C2211yescharacteristic
12C22×C8×D13C2211yescharacteristic
13D13×#117C2211yescharacteristic
14#11719100—28no—
15D13⋊#108—24no—
16C2×#88104—24no—
17C2×#88104C2211yescharacteristic
18C2×#88104C2212yes—
19C2×#88104C2211yescharacteristic
20C2×#88104C2214yes—
21C2×#88104C2212yes—
22C2×#88103C2214yes—
23C2×#88103C2212yes—
24#11719079—24no—
25#11719067—24no—
26#11719053C2214yes—
27#11719052C2214yes—
28C13×#405C411yescharacteristic
29#11718783C411yescharacteristic
30#11718762C411yescharacteristic
31#11718658C411yescharacteristic
32#11718369C412yes—
33D13×#97C2212yes—
34#11718350C412yes—
35C4×C8×D13C2212yes—
36C22×C4×D13C2311yescharacteristic
37C2×#6122—22no—
38C22×#1057—22no—
39D13⋊M16—24no—
40D13⋊M16—24no—
41C2×#6118—24no—
42C2×#6118—24no—
43C2×#6118—22no—
44C2×#6118C2312yes—
45C2×#6118C2314yes—
46C2×#6118C2312yes—
47C2×D13⋊C8—22no—
48C2×C13×M16C2×C411yescharacteristic
49C22×C8×C13C2×C411yescharacteristic
50C13×#117C2×C411yescharacteristic
51#88180C2×C411yescharacteristic
52C2×#6099C2×C411yescharacteristic
53C22×#1055C2×C411yescharacteristic
54M16×D13D414yes—
55M16×D13Q814yes—
56C2×#6094C2×C412yes—
57C2×C8×D13C2×C411yescharacteristic
58C2×C8×D13C2×C411yescharacteristic
59C2×C8×D13D414yes—
60C2×C8×D13Q814yes—
61C2×C8×D13C2311yescharacteristic
62C2×C8×D13C2311yescharacteristic
63C2×C8×D13C2312yes—
64#88146D412yes—
65C4⋊C4×D13Q812yes—
66C22⋊C4×D13Q812yes—
67#88131D412yes—
68#88126C2×C412yes—
69C42×D13C2312yes—
70#88112—28no—
71C4⋊#1057—28no—
72#88104—24no—
73#88104—24no—
74#88104—22no—
75#88104—22no—
76#88104—28no—
77#88103—24no—
78#88103—28no—
79C13×#97C2×C412yes—
80C4×C8×C13C2×C412yes—
81#88055C2×C412yes—
82#88055C2×C412yes—
83C8×Dic13C2×C412yes—
84C8×Dic13C2×C412yes—
85#88043C2×C412yes—
86C4×#1055C2×C412yes—
87#20807—131nomaximal, Sylow
88C23×D13C2×Q811yescharacteristic
89C22×C4×C13C22×C411yescharacteristic
90C22×Dic13C2×D411yescharacteristic
91C2×C4×D13C22×C411yescharacteristic
92C2×C4×D13C2×D412yes—
93C2×C4×D13C2×D412yes—
94C2×C4×D13C2×D411yescharacteristic
95C2×C4×D13C2×Q814yes—
96C2×C4×D13C2×Q812yes—
97C2×C4×D13C2×Q812yes—
98C2×C4×D13C2×Q811yescharacteristic
99C2×C4×D13C2411yescharacteristic
100#6122—44no—
101C2×#1057—22no—
102C2×#1057—24no—
103C2×#1057—22no—
104C2×#1057—44no—
105#6118—22no—
106#6118—24no—
107#6118—22no—
108#6118—22no—
109#6118—24no—
110#6118—22no—
111#6118—44no—
112D13⋊C8—44no—
113C13×M16C4⋊C414yes—
114C2×C8×C13C4⋊C414yes—
115C2×C8×C13C22×C411yescharacteristic
116C2×C8×C13C22×C412yes—
117C2×C8×C13C22×C411yescharacteristic
118C13×C4⋊C4C4⋊C412yes—
119C13×C22⋊C4C4⋊C412yes—
120C42×C13C22×C412yes—
121C22⋊Dic13C4⋊C412yes—
122#6103C4⋊C414yes—
123C4⋊Dic13C4⋊C412yes—
124#6101C4⋊C414yes—
125C4×Dic13C22×C412yes—
126C4×Dic13C2×D414yes—
127#6099C4⋊C414yes—
128C2×#1055C4⋊C414yes—
129C2×#1055C22×C411yescharacteristic
130C2×#1055C22×C411yescharacteristic
131C2×#1055C22×C412yes—
132#6094C4⋊C418yes—
133C8×D13C4⋊C414yes—
134C8×D13C4⋊C414yes—
135C8×D13C2×D412yes—
136C8×D13C2×D414yes—
137C8×D13C2×D412yes—
138C8×D13C2×Q812yes—
139C8×D13C2×Q812yes—
140C8×D13C2×Q814yes—
141C2×#430—132no—
142C22×#108—131no—
143C22×#108—131no—
144#2905—132no—
145C2×#405—131no—
146#1849—134no—
147#1848—132no—
148#1848—132no—
149C23×C13C2×C4⋊C411yescharacteristic
150C22×D13—42no—
151C22×D13C2×C4⋊C411yescharacteristic
152C22×D13C4⋊Q812yes—
153C22×D13C4⋊Q812yes—
154C22×D13C22×Q811yescharacteristic
155C2×C4×C13C2×C4⋊C414yes—
156C2×C4×C13C2×C4⋊C412yes—
157C2×C4×C13C2×C4⋊C412yes—
158C2×C4×C13C2×C4⋊C411yescharacteristic
159C2×C4×C13C23×C411yescharacteristic
160C2×Dic13C2×C4⋊C414yes—
161C2×Dic13C2×C4⋊C411yescharacteristic
162C2×Dic13#12712yes—
163C2×Dic13C4⋊Q812yes—
164C2×Dic13C22×D411yescharacteristic
165C4×D13—44no—
166C4×D13C2×C4⋊C412yes—
167C4×D13C2×C4⋊C412yes—
168C4×D13#12712yes—
169C4×D13C4⋊Q812yes—
170C4×D13C4⋊Q812yes—
171C4×D13C4⋊Q812yes—
172C4×D13C22×D411yescharacteristic
173C4×D13C22×D411yescharacteristic
174C4×D13C22×Q811yescharacteristic
175C4×D13C22×Q811yescharacteristic
176#1057—42no—
177#1057—42no—
178#1057—44no—
179C8×C13C2×C4⋊C412yes—
180C8×C13C2×C4⋊C412yes—
181C8×C13C2×C4⋊C414yes—
182#1055C2×C4⋊C412yes—
183#1055C2×C4⋊C412yes—
184#1055C2×C4⋊C414yes—
185C22×M16—131no—
186C22×M16—132no—
187C22×M16—132no—
188C23×C8—131no—
189C2×#117—131no—
190#430—268no—
191C2×#108—131no—
192C2×#108—132no—
193C2×#108—131no—
194C2×#108—134no—
195C2×#108—134no—
196C2×#108—132no—
197C2×#108—132no—
198C2×#108—264no—
199C2×#108—264no—
200#424—264no—
201#424—264no—
202#423—134no—
203#423—134no—
204#405—131no—
205#405—131no—
206#405—131no—
207#405—132no—
208#405—132no—
209#405#26111yescharacteristic
210C2×#97—132no—
211C2×C4×C8—132no—
212C22×C13—22no—
213C22×C13#38412yes—
214C22×C13C22×C4⋊C411yescharacteristic
215C2×D13—22no—
216C2×D13—22no—
217C2×D13—42no—
218C2×D13—42no—
219C2×D13#38412yes—
220C2×D13C2×C4⋊Q811yescharacteristic
221C2×D13C2×C4⋊Q811yescharacteristic
222C4×C13—24no—
223C4×C13#38412yes—
224C4×C13C22×C4⋊C411yescharacteristic
225C4×C13C22×C4⋊C411yescharacteristic
226Dic13—24no—
227Dic13#38412yes—
228Dic13C2×#12711yescharacteristic
229Dic13C2×C4⋊Q811yescharacteristic
230C23×C4—131no—
231C2×M16—131no—
232C2×M16—134no—
233C2×M16—134no—
234C2×M16—132no—
235C2×M16—134no—
236C2×M16—132no—
237C2×M16—132no—
238C2×M16—262no—
239C2×M16—262no—
240C2×M16—264no—
241C2×M16—264no—
242C2×M16—264no—
243C2×M16—264no—
244C2×M16C2×#26111yescharacteristic
245C22×C8—131no—
246C22×C8—134no—
247C22×C8—134no—
248C22×C8—131no—
249C22×C8—131no—
250C22×C8—131no—
251C22×C8—131no—
252C22×C8—132no—
253C22×C8—262no—
254C22×C8—262no—
255C22×C8C2×#26111yescharacteristic
256#117—131no—
257#117—132no—
258#117—132no—
259#117—132no—
260#117C2×#26111yescharacteristic
261C2×C4⋊C4—132no—
262C2×C22⋊C4—132no—
263C2×C42—132no—
264#108—264no—
265#108—268no—
266#108—264no—
267#108—264no—
268#108—262no—
269#108—262no—
270#108—268no—
271C4⋊C8—268no—
272C4⋊C8—268no—
273#97—132no—
274#97—132no—
275#97—132no—
276#97C2×#26112yes—
277C4×C8—132no—
278C4×C8—132no—
279C4×C8—132no—
280C4×C8C2×#26112yes—
281C2×C13—22no—
282C2×C13C2×#38411yescharacteristic
283C2×C13#291612yes—
284D13—21no—
285D13—21no—
286D13—22no—
287C24—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—132no—
292C22×C4—132no—
293C22×C4—132no—
294C22×C4—132no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—134no—
298C22×C4C22×#26111yescharacteristic
299M16—134no—
300M16—138no—
301M16—262no—
302M16—262no—
303M16—262no—
304M16—264no—
305M16—264no—
306M16—262no—
307M16—524no—
308M16—524no—
309M16C4⋊#26114yes—
310C2×C8—134no—
311C2×C8—131no—
312C2×C8—132no—
313C2×C8—131no—
314C2×C8—132no—
315C2×C8—132no—
316C2×C8—134no—
317C2×C8—134no—
318C2×C8—134no—
319C2×C8—132no—
320C2×C8—132no—
321C2×C8—134no—
322C2×C8—262no—
323C2×C8—264no—
324C2×C8—262no—
325C2×C8—524no—
326C2×C8—524no—
327C2×C8C4⋊#26114yes—
328C2×C8C22×#26111yescharacteristic
329C2×C8C22×#26112yes—
330C2×C8C22×#26111yescharacteristic
331C4⋊C4—134no—
332C4⋊C4—132no—
333C4⋊C4C4⋊#26112yes—
334C22⋊C4—132no—
335C22⋊C4—134no—
336C22⋊C4C4⋊#26112yes—
337C42—134no—
338C42—132no—
339C42C22×#26112yes—
340C13#2080711yescharacteristic, complemented, Sylow
341C23—131no—
342C23—131no—
343C23—132no—
344C23—132no—
345C23—522no—
346C23C2×C4⋊#26111yescharacteristic
347C2×C4—132no—
348C2×C4—132no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—132no—
352C2×C4—132no—
353C2×C4—132no—
354C2×C4—132no—
355C2×C4—131no—
356C2×C4—131no—
357C2×C4—132no—
358C2×C4—131no—
359C2×C4—131no—
360C2×C4—132no—
361C2×C4—134no—
362C2×C4—524no—
363C2×C4C2×C4⋊#26114yes—
364C2×C4C2×C4⋊#26111yescharacteristic
365C2×C4C2×C4⋊#26112yes—
366C2×C4C2×C4⋊#26112yes—
367C2×C4C23×#26111yescharacteristic
368C8—132no—
369C8—132no—
370C8—134no—
371C8—522no—
372C8—522no—
373C8—524no—
374C8C2×C4⋊#26112yes—
375C8C2×C4⋊#26112yes—
376C8C2×C4⋊#26114yes—
377C22—22no—
378C22—131no—
379C22—131no—
380C22—132no—
381C22—262no—
382C22—262no—
383C22—522no—
384C22—522no—
385C22#1171905912yes—
386C22C22×C4⋊#26111yescharacteristic
387C4—24no—
388C4—131no—
389C4—131no—
390C4—132no—
391C4—264no—
392C4#1171905912yes—
393C4C22×C4⋊#26111yescharacteristic
394C4C22×C4⋊#26111yescharacteristic
395C2—22no—
396C2—261no—
397C2—261no—
398C2—262no—
399C2C2×#1171905911yescharacteristic
400C2#1313149812yes—
subgroupG/H
centerC22C22×C4⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#405C4
socleC22×C13C22×C4⋊C4
prime radicalC23×D13C2×Q8
cosocleC2×C4×D13C24
hypercenter#405#261
hypocenterC13#20807
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
5. #13130778C2semidirect
6. #13130777C2semidirect
7. #13130776C2semidirect
340. C13#20807semidirect

Maximal subgroups

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

subgroupindex
C2×#117191002
C22×#881042
C2×D13⋊#1082
#131314792
#131307782
#131307772
#131307762
D13×#4052
#2080713