Finite Group Databasebeta

← #14908133

Subgroups — #14908133

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622808C211yesmaximal, characteristic, complemented
2#13079111C211yesmaximal, characteristic, complemented
3#13077492C211yesmaximal, characteristic, complemented
4#13070676C212yesmaximal, complemented
5#13070669C212yesmaximal, complemented
6#13070664C212yesmaximal, complemented
7#13070659C212yesmaximal, complemented
8#13070374C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic, complemented
10C2×#10622141C211yesmaximal, characteristic, complemented
11C2×C11×#508C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C2×C11×#135C2211yescharacteristic
14#10623358—21no—
15#10623356—21no—
16C2×#67004—21no—
17C22×Dic44C2211yescharacteristic
18C11×#508—24no—
19C2×C11×Q32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C2×C11×SD32C2211yescharacteristic
22C2×C11×D16C2211yescharacteristic
23C22×C11×C16C2211yescharacteristic
24#10622845—21no—
25#10622808—24no—
26Q16×Dic11C2212yes—
27#10622794C2212yes—
28C2×#66893C2212yes—
29#10622780—22no—
30#10622777—22no—
31#10622768C2212yes—
32D8×Dic11C2212yes—
33C2×#66891C2212yes—
34C2×#66882C2211yescharacteristic
35#10622714C2211yescharacteristic
36C2×#66876C2211yescharacteristic
37#10622202C2212yes—
38#10622200C2212yes—
39#10622141C2212yes—
40#10622141C2212yes—
41Dic11⋊C16C2212yes—
42Dic11⋊C16C2212yes—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C22×Dic22—21no—
46C11×#135—22no—
47C11×#135—22no—
48C11×#135—22no—
49C11×#135D414yes—
50C2×C11×Q16C2311yescharacteristic
51C2×C11×Q16C2311yescharacteristic
52C2×C11×SD16—21no—
53C2×C11×SD16—21no—
54C2×C11×D8C2311yescharacteristic
55C2×C11×D8C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57#67004—44no—
58Q8×Dic11—22no—
59#66997—22no—
60C2×#4326—22no—
61#66989—22no—
62#66988—42no—
63D4×Dic11—22no—
64D4×Dic11—42no—
65C2×#4324—22no—
66#66979—41no—
67#66979D411yescharacteristic
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—41no—
70#66977—41no—
71#66977—41no—
72C2×#4318D411yescharacteristic
73C2×Dic44—22no—
74C2×Dic44—22no—
75C2×Dic44—21no—
76C2×Dic44C2312yes—
77C11×Q32—22no—
78C11×SD32—22no—
79C11×SD32—22no—
80C11×D16—22no—
81C2×C11×C16—22no—
82C2×C11×C16C2311yescharacteristic
83C2×C11×C16C2311yescharacteristic
84#66899—22no—
85#66896—22no—
86#66893—24no—
87#66891—24no—
88#66882—21no—
89#66882C2312yes—
90#66879D412yes—
91C8×Dic11C2312yes—
92#66876—22no—
93C2×C11⋊C16C2312yes—
94#33590—111nomaximal, Sylow
95C11×#41—24no—
96C11×#41—42no—
97C11×#41—42no—
98C11×#41—42no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C22×Dic11—42no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C2×Dic22—22no—
112C2×Dic22—42no—
113C2×Dic22—41no—
114C2×Dic22—42no—
115C11×Q16—21no—
116C11×Q16—21no—
117C11×Q16—21no—
118C11×Q16C2×D412yes—
119C11×SD16—24no—
120C11×SD16—42no—
121C11×D8—21no—
122C11×D8—21no—
123C11×D8—21no—
124C11×D8C2×D412yes—
125C2×C8×C11C2×D412yes—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11#4112yes—
128C2×C8×C11C2411yescharacteristic
129C22⋊Dic11—42no—
130C22⋊Dic11—42no—
131C22⋊Dic11—42no—
132C22⋊Dic11D812yes—
133#4326—44no—
134#4324—44no—
135C4⋊Dic11—22no—
136C4⋊Dic11—42no—
137C4⋊Dic11—41no—
138C4⋊Dic11D811yescharacteristic
139C4⋊Dic11D811yescharacteristic
140Dic11⋊C4—42no—
141Dic11⋊C4—42no—
142C4×Dic11—42no—
143C4×Dic11C2×D412yes—
144#4318—22no—
145C2×C11⋊C8C2×D412yes—
146Dic44—22no—
147Dic44—22no—
148Dic44—42no—
149C11×C16—21no—
150C11×C16—21no—
151C11⋊C16—22no—
152C2×#510—111no—
153C2×#508D1111yescharacteristic
154#3156—111no—
155#2951—111no—
156#2211—112no—
157#2210—112no—
158#2209—112no—
159#2208—112no—
160#2151—111no—
161#2139—111no—
162C2×#358—111no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11C2×D811yescharacteristic
166Q8×C11—22no—
167Q8×C11—41no—
168Q8×C11—41no—
169Q8×C11—41no—
170D4×C11—22no—
171D4×C11—44no—
172D4×C11—41no—
173D4×C11—41no—
174D4×C11—41no—
175D4×C11—82no—
176C2×C4×C11—41no—
177C2×C4×C11—44no—
178C2×C4×C11—41no—
179C2×C4×C11—82no—
180C2×C4×C11#12112yes—
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11C22×D411yescharacteristic
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—82no—
187C2×Dic11—162no—
188C2×Dic11—161no—
189C2×Dic11C2×D812yes—
190C2×Dic11C2×D812yes—
191Dic22—42no—
192Dic22—42no—
193Dic22—82no—
194C8×C11#12112yes—
195C8×C11C22×D411yescharacteristic
196C8×C11C2×#4111yescharacteristic
197C11⋊C8—22no—
198C2×#137—221no—
199C2×#135C2×D1111yescharacteristic
200C2×#135C2×D1111yescharacteristic
201C22×Q16—111no—
202#536—221no—
203#520—221no—
204#510—224no—
205#508—24no—
206C2×Q32—112no—
207C2×Q32C2×D1111yescharacteristic
208C2×SD32—112no—
209C2×SD32C2×D1111yescharacteristic
210C2×SD32C2×D1111yescharacteristic
211C2×D16C2×D1111yescharacteristic
212C2×M32—111no—
213C22×C16C2×D1111yescharacteristic
214#497—222no—
215#495—112no—
216#494—112no—
217#440—222no—
218C4×Q16—112no—
219C4×D8—112no—
220C2×#107—111no—
221#417—221no—
222#405—111no—
223C4⋊C16—112no—
224C4⋊C16—112no—
225#358—112no—
226#358—112no—
227#358—112no—
228#357—112no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—42no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11#45912yes—
238C22×C11C22×D811yescharacteristic
239C4×C11—42no—
240C4×C11—81no—
241C4×C11#45912yes—
242C4×C11C2×#12111yescharacteristic
243C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
244Dic11—22no—
245Dic11—22no—
246Dic11—82no—
247Dic11—82no—
248C2×#41—21no—
249C2×#41—21no—
250C22×Q8—221no—
251#137—444no—
252#135—22no—
253#135—22no—
254#135—22no—
255#135C22⋊D1114yes—
256C2×Q16—112no—
257C2×Q16—222no—
258C2×Q16—221no—
259C2×Q16—222no—
260C2×Q16—222no—
261C2×Q16C22×D1111yescharacteristic
262C2×Q16C22×D1111yescharacteristic
263C2×SD16—21no—
264C2×SD16—21no—
265C2×SD16—222no—
266C2×D8C22×D1111yescharacteristic
267C2×D8C22×D1111yescharacteristic
268C2×M16—111no—
269C22×C8C22×D1111yescharacteristic
270C4⋊Q8—222no—
271#124—222no—
272#123—442no—
273C22⋊Q8—441no—
274C22⋊Q8—441no—
275C4×Q8—222no—
276C4×D4—222no—
277C4×D4—442no—
278#117—111no—
279#117—441no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—441no—
282Q32—22no—
283Q32—224no—
284SD32—22no—
285SD32—22no—
286SD32—224no—
287D16—22no—
288M32—222no—
289C2×C16—22no—
290C2×C16—112no—
291C2×C16C22×D1111yescharacteristic
292C2×C16C22×D1111yescharacteristic
293#107—112no—
294#107—221no—
295#103—222no—
296#102—222no—
297#97—112no—
298C4×C8—112no—
299C2×C11—22no—
300C2×C11—82no—
301C2×C11—161no—
302C2×C11C2×#45911yescharacteristic
303C2×C11#341611yescharacteristic
304C2×C11#341711yescharacteristic
305#41—24no—
306#41—42no—
307#41—42no—
308#41—42no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—222no—
312C2×Q8—441no—
313C2×Q8—442no—
314C2×Q8—442no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—442no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4D4×D1111yescharacteristic
325Q16—21no—
326Q16—21no—
327Q16—21no—
328Q16—222no—
329Q16—222no—
330Q16—444no—
331Q16—442no—
332Q16C2×C22⋊D1112yes—
333SD16—24no—
334SD16—42no—
335SD16—444no—
336D8—21no—
337D8—21no—
338D8—21no—
339D8C2×C22⋊D1112yes—
340M16—222no—
341C2×C8—112no—
342C2×C8D4×D1111yescharacteristic
343C2×C8#434112yes—
344C2×C8C2×C22⋊D1112yes—
345C2×C8C23×D1111yescharacteristic
346C4⋊C4—111no—
347C4⋊C4—111no—
348C4⋊C4—222no—
349C4⋊C4—442no—
350C4⋊C4—442no—
351C4⋊C4—442no—
352C4⋊C4—441no—
353C22⋊C4—112no—
354C22⋊C4—442no—
355C22⋊C4—442no—
356C22⋊C4—442no—
357C42—112no—
358C42—442no—
359C16—21no—
360C16—21no—
361C16—222no—
362C11#3359011yescharacteristic, complemented, Sylow
363C23—41no—
364C23—41no—
365C23D8×D1111yescharacteristic
366Q8—22no—
367Q8—41no—
368Q8—41no—
369Q8—41no—
370Q8—442no—
371Q8—442no—
372Q8—882no—
373D4—22no—
374D4—44no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—82no—
379C2×C4—41no—
380C2×C4—44no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—112no—
384C2×C4—112no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—882no—
388C2×C4—1762no—
389C2×C4—1761no—
390C2×C4D8×D1111yescharacteristic
391C2×C4#6696412yes—
392C2×C4#6699212yes—
393C2×C4C2×D4×D1111yescharacteristic
394C8—222no—
395C8#6699212yes—
396C8C2×#434111yescharacteristic
397C8C22×C22⋊D1111yescharacteristic
398C22—21no—
399C22—21no—
400C22—42no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22#1062276312yes—
407C22C2×D8×D1111yescharacteristic
408C4—42no—
409C4—81no—
410C4—222no—
411C4—222no—
412C4—882no—
413C4—882no—
414C4#1062276312yes—
415C4C2×#6696411yescharacteristic
416C4C2×#6699211yescharacteristic
417C2—22no—
418C2—82no—
419C2—161no—
420C2C2×#1062276311yescharacteristic
421C2#1308175911yescharacteristic
422C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC2×C11×#508C2
socleC22×C11C22×D8
hypercenterC2×#508D11
hypocenterC11#33590
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#10622808C2semidirect
2. #13079111C2semidirect
3. #13077492C2semidirect
4. #13070676C2semidirect
5. #13070669C2semidirect
6. #13070664C2semidirect
7. #13070659C2semidirect
8. #13070374C2semidirect
9. #13070328C2semidirect
10. C2×#10622141C2semidirect
362. C11#33590semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
#130791112
#130774922
#130706762
#130706692
#130706642
#130706592
#130703742
#130703282
C2×#106221412
C2×C11×#5082
#3359011