Finite Group Databasebeta

← #14736524

Subgroups — #14736524

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078681C212yesmaximal
2#13077582C211yesmaximal, characteristic
3#13068167C212yesmaximal, complemented
4#13068160C212yesmaximal, complemented
5#13068131C211yesmaximal, characteristic, complemented
6#13068126C211yesmaximal, characteristic, complemented
7#13068107C211yesmaximal, characteristic, complemented
8#13068102C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067281C212yesmaximal, complemented
11C11×#3170C211yesmaximal, characteristic, complemented
12C11×#533C2212yes—
13C4×#4339C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16C11×#487C2212yes—
17C11×#467—21no—
18C11×#467—21no—
19C4×C11×Q16—21no—
20C4×C11×Q16—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23#10622724—21no—
24#10622707C2212yes—
25#10622703C2212yes—
26#10622700C2212yes—
27#10622696C2212yes—
28#10622660—22no—
29#10622658—22no—
30C4×#4326—22no—
31C4×#4325—22no—
32#10622538C2211yescharacteristic
33#10622538C2212yes—
34#10622301C2211yescharacteristic
35#10622301C2211yescharacteristic
36C4×#4313—21no—
37#10622298—21no—
38#10622292C2211yescharacteristic
39#10622292C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622096C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
47C2×#4339D411yescharacteristic
48C2×C11×Q16—21no—
49C2×C11×Q16—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×C4⋊Q8C2312yes—
53C11×C4⋊Q8C2312yes—
54C11×#125—22no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C11×#117—22no—
60C2×C42×C11C2311yescharacteristic
61C2×#4326—22no—
62C2×#4325—22no—
63C4×C22⋊D11—21no—
64C4×C22⋊D11—21no—
65#66979D411yescharacteristic
66C2×#4313—21no—
67C2×#4313—21no—
68C4×D44D411yescharacteristic
69C4×D44C2311yescharacteristic
70#66925—21no—
71C42×D11—21no—
72C4×Dic22D411yescharacteristic
73C4×Dic22C2311yescharacteristic
74C11×#107—21no—
75C11×#107—21no—
76C11×#103—22no—
77C11×#103—22no—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66899—22no—
83#66899—22no—
84C22⋊(C11⋊C8)—21no—
85C22⋊(C11⋊C8)—22no—
86(C2×D11)⋊C8—21no—
87(C2×D11)⋊C8—21no—
88#66879—21no—
89#66879—21no—
90Dic11⋊C8—21no—
91Dic11⋊C8—21no—
92#66874—22no—
93#66873—22no—
94#66872—22no—
95#66871—22no—
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2312yes—
100C4×C11⋊C8—21no—
101C4×C11⋊C8—22no—
102#19161—111nomaximal, Sylow
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—21no—
109#4339—42no—
110C2×D44C2×D411yescharacteristic
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×Dic22C2×D411yescharacteristic
115C11×Q16—42no—
116C11×Q16—42no—
117C2×C8×C11—22no—
118C2×C8×C11—41no—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C11×C22⋊C4—42no—
130C42×C11—42no—
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134C42×C11C2411yescharacteristic
135C22⋊Dic11—21no—
136#4326—44no—
137#4325—44no—
138(C2×D11)⋊C4—21no—
139(C2×D11)⋊C4—21no—
140C4⋊Dic11C2×D411yescharacteristic
141C4⋊Dic11C2×D411yescharacteristic
142Dic11⋊C4—21no—
143Dic11⋊C4—21no—
144C4×Dic11—21no—
145C4×Dic11—21no—
146C4×Dic11—21no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151#4313—42no—
152#4313—42no—
153#3170D1111yescharacteristic, complemented
154#3107—112no—
155#2965—111no—
156#1700—112no—
157#1699—112no—
158#1694—111no—
159#1693—111no—
160#1690—111no—
161#1689—111no—
162#1564—111no—
163#1544—112no—
164C23×C11#12111yescharacteristic
165C22×D11—21no—
166Q8×C11—42no—
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11—42no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C22⋊D11—42no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186D44—22no—
187C4×D11—42no—
188C4×D11—41no—
189C4×D11—41no—
190C4×D11—42no—
191Dic22—22no—
192C8×C11—21no—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11#13512yes—
196C11⋊C8—41no—
197C11⋊C8—41no—
198C11⋊C8—42no—
199C11⋊C8—42no—
200#533C2×D1112yes—
201C4×#41—111no—
202#500C2×D1111yescharacteristic
203#494C2×D1111yescharacteristic
204#487C2×D1112yes—
205#485—222no—
206#475—112no—
207#474—112no—
208#467—21no—
209#467—21no—
210#462—112no—
211#461—112no—
212#452—222no—
213#446—111no—
214#446—111no—
215C4×Q16—21no—
216C4×Q16—21no—
217C4×Q16—222no—
218C4×SD16—222no—
219#436—111no—
220#436—111no—
221#435—221no—
222#435—221no—
223#431—111no—
224#431—112no—
225#431—221no—
226C4×M16—221no—
227C2×C4×C8C2×D1111yescharacteristic
228#335—112no—
229#334—111no—
230#334—111no—
231#332—112no—
232#332—112no—
233#332—112no—
234#332—112no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11C2×#12111yescharacteristic
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—82no—
246C4×C11—82no—
247C4×C11#47312yes—
248C4×C11C2×#13511yescharacteristic
249C4×C11#57512yes—
250C4×C11#57511yescharacteristic
251Dic11—41no—
252Dic11—41no—
253Dic11—41no—
254C2×#41—111no—
255C2×Q16—21no—
256C2×Q16—21no—
257C2×Q16—222no—
258C2×SD16—222no—
259C2×M16—221no—
260C2×M16—221no—
261C22×C8C22⋊D1111yescharacteristic
262C22×C8C22⋊D1111yescharacteristic
263C4⋊Q8C22×D1112yes—
264C4⋊Q8C22×D1112yes—
265#125—22no—
266C22⋊Q8—22no—
267C22⋊Q8—22no—
268C4×Q8—22no—
269C4×Q8—22no—
270C4×Q8—111no—
271C4×Q8—111no—
272C4×D4—111no—
273C4×D4—111no—
274C4×D4—221no—
275C4×D4—221no—
276#117—22no—
277#117—111no—
278#117—221no—
279C2×C42—221no—
280C2×C42C22×D1111yescharacteristic
281#107—21no—
282#107—21no—
283#107—222no—
284#106—222no—
285C4⋊C8—111no—
286C4⋊C8—111no—
287C4⋊C8—112no—
288C4⋊C8—112no—
289C4⋊C8—221no—
290C4⋊C8—221no—
291#103—22no—
292#103—22no—
293#103—222no—
294#103—222no—
295#103—222no—
296#102—222no—
297C22⋊C8—222no—
298C22⋊C8—221no—
299C22⋊C8—221no—
300C22⋊C8—221no—
301#97—221no—
302#97—221no—
303C4×C8—222no—
304C4×C8—221no—
305C4×C8C22⋊D1111yescharacteristic
306C4×C8C22⋊D1111yescharacteristic
307C4×C8C22×D1111yescharacteristic
308C4×C8C22×D1111yescharacteristic
309C2×C11—41no—
310C2×C11#303511yescharacteristic
311C2×C11#305411yescharacteristic
312C2×C11C2×#47311yescharacteristic
313D11—81no—
314#41—442no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8—111no—
318C2×D4—111no—
319C2×D4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4D4×D1111yescharacteristic
324C22×C4#434111yescharacteristic
325C22×C4C2×C22⋊D1111yescharacteristic
326Q16—42no—
327Q16—42no—
328Q16—444no—
329SD16—444no—
330M16—442no—
331M16—442no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8—221no—
337C2×C8—221no—
338C2×C8C2×C22⋊D1111yescharacteristic
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C2×C22⋊D1111yescharacteristic
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—111no—
349C4⋊C4—111no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C22⋊C4—42no—
353C22⋊C4—221no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C42—42no—
357C42—221no—
358C42—221no—
359C42—221no—
360C42D4×D1111yescharacteristic
361C42#434111yescharacteristic
362C42C2×C22⋊D1111yescharacteristic
363C42C23×D1111yescharacteristic
364C11#1916111yescharacteristic, complemented, Sylow
365C23—221no—
366C23#6699111yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—42no—
370Q8—42no—
371Q8—222no—
372D4—222no—
373D4—442no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4#6699111yescharacteristic
388C2×C4#6699111yescharacteristic
389C2×C4#6699111yescharacteristic
390C2×C4C2×D4×D1111yescharacteristic
391C2×C4C2×#434111yescharacteristic
392C2×C4C22×C22⋊D1111yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—442no—
397C8—442no—
398C8—441no—
399C8—441no—
400C8#6700312yes—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22C2×#6699111yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—82no—
413C4—441no—
414C4—441no—
415C4—441no—
416C4#1062280512yes—
417C4#1062329912yes—
418C4C2×#6700311yescharacteristic
419C4#1062335311yescharacteristic
420C2—41no—
421C2—881no—
422C2#1307806511yescharacteristic
423C2#1307822111yescharacteristic
424C2C2×#1062280511yescharacteristic
subgroupG/H
centerC2×C4#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3170C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#3170D11
hypocenterC11#19161
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13068167C2semidirect
4. #13068160C2semidirect
5. #13068131C2semidirect
6. #13068126C2semidirect
7. #13068107C2semidirect
8. #13068102C2semidirect
9. #13067364C2semidirect
10. #13067281C2semidirect
11. C11×#3170C2semidirect
153. #3170D11semidirect
364. C11#19161semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130775822
#130681672
#130681602
#130681312
#130681262
#130681072
#130681022
#130673642
#130672812
C11×#31702
#1916111