Finite Group Databasebeta

← C2×#13070176 #14783669

Subgroups — C2×#13070176 #14783669

Order 2816.

998 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
1C2×#10622586C211yesmaximal, characteristic
2C2×#10622589C211yesmaximal, characteristic
3#13070176C218yesmaximal, direct product factor
4C2×#10622189C211yesmaximal, characteristic
5C2×#10622167C211yesmaximal, characteristic
6C2×#10622167C211yesmaximal, characteristic
7C2×#10622188C211yesmaximal, characteristic
8C2×C11×#340C211yesmaximal, characteristic
9C23×C8×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4—21no—
15C22×Dic11⋊C4—21no—
16C22×Dic11⋊C4—21no—
17C22×C4×Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×C11⋊#95—21no—
20#10622589—22no—
21#10622589C2214yes—
22#10622586—22no—
23#10622586C2214yes—
24C11×#340C2214yes—
25#10622189C2214yes—
26#10622188C2214yes—
27#10622167C2214yes—
28#10622167C2214yes—
29C23×C4×C11—21no—
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C23×Dic11—21no—
34C23×Dic11D411yescharacteristic
35C23×Dic11D411yescharacteristic
36C22×C8×C11—22no—
37C22×C8×C11—22no—
38C22×C8×C11—22no—
39C22×C8×C11C2312yes—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11Q814yes—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2312yes—
56C2×Dic11⋊C4—24no—
57C2×Dic11⋊C4—24no—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4—44no—
60C2×Dic11⋊C4—44no—
61C2×Dic11⋊C4—44no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11D412yes—
65C2×C4×Dic11C2312yes—
66C22×C11⋊C8—22no—
67C22×C11⋊C8—22no—
68C22×C11⋊C8—22no—
69C22×C11⋊C8C2312yes—
70C11⋊#95—24no—
71C2×#2099—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×Q812yes—
83C22×C4×C11#4112yes—
84C22×C4×C11#4112yes—
85C22×C4×C11#4112yes—
86C22×C4×C11#4112yes—
87C22×C4×C11#4112yes—
88C22×C4×C11C2411yescharacteristic
89C22×Dic11—24no—
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11D814yes—
102C22×Dic11SD1614yes—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D412yes—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—44no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—42no—
114C11×C4⋊C4—42no—
115C4⋊Dic11—24no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—42no—
120C4⋊Dic11C2×Q814yes—
121Dic11⋊C4—48no—
122Dic11⋊C4—48no—
123Dic11⋊C4—48no—
124C4×Dic11—24no—
125C4×Dic11—22no—
126C4×Dic11—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—44no—
131C2×#389—111no—
132C2×#384—111no—
133#2099—118no—
134C2×#340—111no—
135C2×#340—111no—
136C2×#340—111no—
137C2×#340D1111yescharacteristic
138C2×#336—111no—
139C23×C11C22⋊Q812yes—
140C23×C11#12312yes—
141C23×C11#12412yes—
142C23×C11C2×D812yes—
143C23×C11C2×SD1612yes—
144C23×C11#13712yes—
145C23×C11#13712yes—
146C23×C11C22×D411yescharacteristic
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—84no—
154C2×C4×C11—84no—
155C2×C4×C11C22⋊Q812yes—
156C2×C4×C11#12312yes—
157C2×C4×C11#12412yes—
158C2×C4×C11#12514yes—
159C2×C4×C11#12514yes—
160C2×C4×C11#12614yes—
161C2×C4×C11#12614yes—
162C2×C4×C11C22×Q811yescharacteristic
163C2×C4×C11C2×#4111yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—28no—
173C2×Dic11—28no—
174C2×Dic11—24no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—48no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—84no—
182C2×Dic11C2×D814yes—
183C2×Dic11C2×SD1614yes—
184C8×C11—42no—
185C11⋊C8—42no—
186C23×C8—111no—
187C23×C8C2×D1111yescharacteristic
188C22×C4⋊C4—111no—
189C22×C4⋊C4—111no—
190C22×C4⋊C4—221no—
191C22×C4⋊C4—221no—
192C22×C4⋊C4—221no—
193C22×C4⋊C4C2×D1111yescharacteristic
194C22×C4⋊C4C2×D1111yescharacteristic
195C22×C42—111no—
196#389—114no—
197#389—222no—
198#384—114no—
199#384—222no—
200C2×#95—221no—
201#340—114no—
202#340—114no—
203#340—114no—
204#340C2×D1114yes—
205#336—114no—
206C22×C11#40014yes—
207C22×C11#47414yes—
208C22×C11#47514yes—
209C22×C11#48014yes—
210C22×C11#48314yes—
211C22×C11#48614yes—
212C22×C11#49114yes—
213C22×C11C2×C22⋊Q811yescharacteristic
214C22×C11C2×#12311yescharacteristic
215C22×C11C2×#12411yescharacteristic
216C22×C11C22×D811yescharacteristic
217C22×C11C22×SD1611yescharacteristic
218C22×C11C2×#13711yescharacteristic
219C22×C11C2×#13711yescharacteristic
220C4×C11—82no—
221C4×C11—82no—
222C4×C11#40014yes—
223C4×C11C2×#12511yescharacteristic
224C4×C11C2×#12511yescharacteristic
225C4×C11C2×#12611yescharacteristic
226C4×C11C2×#12611yescharacteristic
227Dic11—24no—
228Dic11—24no—
229Dic11—44no—
230Dic11—82no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—111no—
234C23×C4—111no—
235C23×C4—221no—
236C23×C4—221no—
237C23×C4C22×D1111yescharacteristic
238C22×C8—22no—
239C22×C8—22no—
240C22×C8—22no—
241C22×C8—112no—
242C22×C8—222no—
243C22×C8—222no—
244C22×C8—222no—
245C22×C8C22×D1112yes—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—114no—
253C2×C4⋊C4—112no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—222no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—222no—
259C2×C4⋊C4—224no—
260C2×C4⋊C4—224no—
261C2×C4⋊C4—224no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—444no—
264C2×C4⋊C4—444no—
265C2×C4⋊C4—444no—
266C2×C4⋊C4C22×D1112yes—
267C2×C4⋊C4C22×D1112yes—
268C2×C42—112no—
269C2×C42—112no—
270C2×C42—222no—
271C2×C42—222no—
272#95—224no—
273C2×C11#209918yescomplemented
274C2×C11C2×#40011yescharacteristic
275C2×C11C2×#47411yescharacteristic
276C2×C11C2×#47511yescharacteristic
277C2×C11C2×#48011yescharacteristic
278C2×C11C2×#48311yescharacteristic
279C2×C11C2×#48611yescharacteristic
280C2×C11C2×#49111yescharacteristic
281C24D4×D1111yescharacteristic
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—114no—
291C22×C4—114no—
292C22×C4—112no—
293C22×C4—112no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4—222no—
297C22×C4—222no—
298C22×C4—224no—
299C22×C4—222no—
300C22×C4—222no—
301C22×C4—442no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4—442no—
305C22×C4—442no—
306C22×C4#433912yes—
307C22×C4#433912yes—
308C22×C4#433912yes—
309C22×C4D4×D1111yescharacteristic
310C22×C4#434112yes—
311C22×C4#434112yes—
312C22×C4Q8×D1112yes—
313C22×C4C23×D1111yescharacteristic
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—44no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—444no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—114no—
329C4⋊C4—224no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4—222no—
333C4⋊C4—448no—
334C4⋊C4—448no—
335C4⋊C4—448no—
336C4⋊C4—442no—
337C42—224no—
338C42—222no—
339C42—222no—
340C11C2×#209911yescharacteristic, complemented, Sylow
341C23#6693612yes—
342C23#6693812yes—
343C23#6694912yes—
344C23D8×D1112yes—
345C23SD16×D1112yes—
346C23#6696812yes—
347C23#6697112yes—
348C23C2×D4×D1111yescharacteristic
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—84no—
356C2×C4—84no—
357C2×C4—114no—
358C2×C4—114no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—228no—
364C2×C4—228no—
365C2×C4—224no—
366C2×C4—448no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—884no—
373C2×C4#6692914yes—
374C2×C4#6693214yes—
375C2×C4#6693612yes—
376C2×C4#6693812yes—
377C2×C4#6694214yes—
378C2×C4#6694214yes—
379C2×C4#6694912yes—
380C2×C4C2×#433911yescharacteristic
381C2×C4C2×#433911yescharacteristic
382C2×C4C2×#433911yescharacteristic
383C2×C4C2×#434111yescharacteristic
384C2×C4C2×#434111yescharacteristic
385C2×C4C2×Q8×D1111yescharacteristic
386C8—42no—
387C8—442no—
388C22#1062227114yes—
389C22#1062237314yes—
390C22#1062238714yes—
391C22#1062241014yes—
392C22#1062241814yes—
393C22#1062246714yes—
394C22#1062250314yes—
395C22C2×#6693611yescharacteristic
396C22C2×#6693811yescharacteristic
397C22C2×#6694911yescharacteristic
398C22C2×D8×D1111yescharacteristic
399C22C2×SD16×D1111yescharacteristic
400C22C2×#6696811yescharacteristic
401C22C2×#6697111yescharacteristic
402C4—82no—
403C4—82no—
404C4—224no—
405C4—224no—
406C4—444no—
407C4—882no—
408C4#1062227114yes—
409C4C2×#6692911yescharacteristic
410C4C2×#6693211yescharacteristic
411C4C2×#6694211yescharacteristic
412C4C2×#6694211yescharacteristic
413C2#1307017618yesdirect product factor
414C2C2×#1062227111yescharacteristic
415C2C2×#1062250311yescharacteristic
416C2C2×#1062246711yescharacteristic
417C2C2×#1062238711yescharacteristic
418C2C2×#1062241811yescharacteristic
419C2C2×#1062237311yescharacteristic
420C2C2×#1062241011yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socle, prime radicalC24×C11C2×D4
hypercenterC2×#340D11
hypocenterC11C2×#2099
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #13070176C2direct (N × H)
273. C2×C11#2099semidirect
340. C11C2×#2099semidirect
413. C2#13070176direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225862
C2×#106225892
#130701762
C2×#106221892
C2×#106221672
C2×#106221882
C2×C11×#3402
C2×#209911