Finite Group Databasebeta

← #14737225

Subgroups — #14737225

Order 2816.

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#13079947C212yesmaximal
2#13077591C211yesmaximal, characteristic
3#13068131C211yesmaximal, characteristic, complemented
4#13068126C211yesmaximal, characteristic, complemented
5#13068107C211yesmaximal, characteristic, complemented
6#13068102C211yesmaximal, characteristic, complemented
7#13068043C212yesmaximal, complemented
8#13068036C212yesmaximal, complemented
9C2×#10622095C211yesmaximal, characteristic, complemented
10#13067316C212yesmaximal, complemented
11C11×#3170C211yesmaximal, characteristic, complemented
12C11×#533C2212yes—
13#10623010C2211yescharacteristic
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—
23C8×C22⋊D11—21no—
24#10622707C2212yes—
25#10622703C2212yes—
26#10622700C2212yes—
27#10622696C2212yes—
28#10622664—22no—
29#10622661—22no—
30#10622641—22no—
31#10622635—22no—
32#10622539C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622095C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C11×C4⋊Q8C2312yes—
52C11×C4⋊Q8C2312yes—
53C11×#125—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C11×#117—22no—
59C2×C42×C11C2311yescharacteristic
60C2×#4326—22no—
61C2×#4325—22no—
62#66983D411yescharacteristic
63#66982—21no—
64C4×C22⋊D11—21no—
65#66977D411yescharacteristic
66C22×C11⋊C8—22no—
67C2×#4313—21no—
68C2×C8×D11—21no—
69#66929—21no—
70#66928D411yescharacteristic
71C4×D44C2311yescharacteristic
72#66925—21no—
73#66923D411yescharacteristic
74C4×Dic22C2311yescharacteristic
75C11×#107—21no—
76C11×#107—21no—
77C11×#103—22no—
78C11×#103—22no—
79C4×C8×C11D411yescharacteristic
80C4×C8×C11D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66899—22no—
84#66899—22no—
85C22⋊(C11⋊C8)—21no—
86(C2×D11)⋊C8—21no—
87(C2×D11)⋊C8—21no—
88#66879—21no—
89Dic11⋊C8—21no—
90Dic11⋊C8—21no—
91C8×Dic11—21no—
92#66874—22no—
93#66873—22no—
94#66872—22no—
95#66871—22no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101#66867—21no—
102#19228—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—
109C2×D44C2×D411yescharacteristic
110C2×C4×D11—21no—
111C2×Dic22C2×D411yescharacteristic
112C11×Q16—42no—
113C11×Q16—42no—
114C2×C8×C11—22no—
115C2×C8×C11—41no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—42no—
126C11×C22⋊C4—42no—
127C42×C11—42no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132C22⋊Dic11—21no—
133#4326—82no—
134#4325—82no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—21no—
137(C2×D11)⋊C4—21no—
138(C2×D11)⋊C4—21no—
139C4⋊Dic11C2×D411yescharacteristic
140C4⋊Dic11C2×D411yescharacteristic
141Dic11⋊C4—21no—
142Dic11⋊C4—21no—
143Dic11⋊C4—21no—
144Dic11⋊C4—21no—
145C4×Dic11—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—82no—
151#4313—42no—
152C8×D11—42no—
153#3248—112no—
154#3170D1111yescharacteristic, complemented
155#2966—111no—
156#1694—111no—
157#1693—111no—
158#1690—111no—
159#1689—111no—
160#1680—112no—
161#1679—112no—
162C2×#334—111no—
163#1552—112no—
164C23×C11#12111yescharacteristic
165C22×D11—21no—
166Q8×C11—42no—
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11—42no—
170C2×C4×C11—22no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
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—41no—
188C4×D11—41no—
189Dic22—22no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—21no—
193C8×C11#13512yes—
194C11⋊C8—41no—
195C11⋊C8—41no—
196C11⋊C8—42no—
197C11⋊C8—42no—
198#533C2×D1112yes—
199#529—111no—
200#500C2×D1111yescharacteristic
201#494C2×D1111yescharacteristic
202#487C2×D1112yes—
203#479—222no—
204#475—112no—
205#474—112no—
206#467—21no—
207#467—21no—
208#467—222no—
209#465—222no—
210#464—222no—
211#462—112no—
212#461—112no—
213#446—111no—
214C8×Q8—111no—
215C4×Q16—21no—
216C4×Q16—21no—
217#436—111no—
218#435—221no—
219C8×D4—111no—
220C8×D4—221no—
221#433—221no—
222#432—111no—
223C2×C4⋊C8—112no—
224#405—221no—
225C2×C4×C8C2×D1111yescharacteristic
226#334—112no—
227#334—111no—
228#334—111no—
229#332—112no—
230#332—112no—
231#332—112no—
232#332—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11#47312yes—
236C22×C11C2×#12111yescharacteristic
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—82no—
245C4×C11—82no—
246C4×C11C2×#13511yescharacteristic
247C4×C11#57511yescharacteristic
248C4×C11#57712yes—
249Dic11—41no—
250Dic11—41no—
251Dic11—41no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×Q16—222no—
255C2×SD16—222no—
256C2×M16—221no—
257C22×C8—222no—
258C22×C8—221no—
259C22×C8C22⋊D1111yescharacteristic
260C22×C8C22⋊D1111yescharacteristic
261C4⋊Q8C22×D1112yes—
262C4⋊Q8C22×D1112yes—
263#126—221no—
264#125—22no—
265#125—111no—
266#124—111no—
267#123—221no—
268C22⋊Q8—22no—
269C22⋊Q8—22no—
270C22⋊Q8—111no—
271#121—111no—
272C4×Q8—22no—
273C4×Q8—22no—
274C4×Q8—111no—
275C4×D4—111no—
276C4×D4—221no—
277#117—22no—
278#117—221no—
279C2×C42C22×D1111yescharacteristic
280#107—21no—
281#107—21no—
282#107—222no—
283#106—222no—
284C4⋊C8—111no—
285C4⋊C8—111no—
286C4⋊C8—112no—
287C4⋊C8—112no—
288C4⋊C8—221no—
289C4⋊C8—221no—
290C4⋊C8—222no—
291#103—22no—
292#103—22no—
293#103—222no—
294#103—222no—
295#103—222no—
296#102—222no—
297C22⋊C8—221no—
298C22⋊C8—221no—
299C22⋊C8—221no—
300#97—221no—
301#97—221no—
302C4×C8—221no—
303C4×C8C22⋊D1111yescharacteristic
304C4×C8C22⋊D1111yescharacteristic
305C4×C8C22×D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C2×C11—22no—
308C2×C11#303511yescharacteristic
309C2×C11#306011yescharacteristic
310C2×C11C2×#47311yescharacteristic
311D11—81no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—111no—
315C2×D4—111no—
316C2×D4—221no—
317C22×C4—221no—
318C22×C4D4×D1111yescharacteristic
319C22×C4#434111yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321Q16—42no—
322Q16—42no—
323Q16—882no—
324SD16—882no—
325M16—442no—
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—221no—
331C2×C8—221no—
332C2×C8—442no—
333C2×C8—882no—
334C2×C8C2×C22⋊D1111yescharacteristic
335C2×C8C2×C22⋊D1111yescharacteristic
336C2×C8C2×C22⋊D1111yescharacteristic
337C2×C8C2×C22⋊D1111yescharacteristic
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—111no—
345C4⋊C4—111no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C22⋊C4—42no—
351C22⋊C4—221no—
352C22⋊C4—221no—
353C22⋊C4—221no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C42—42no—
357C42—221no—
358C42D4×D1111yescharacteristic
359C42#434111yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C42C23×D1111yescharacteristic
362C11#1922811yescharacteristic, complemented, Sylow
363C23—221no—
364C23#6699111yescharacteristic
365Q8—42no—
366Q8—42no—
367Q8—42no—
368Q8—42no—
369Q8—222no—
370D4—222no—
371D4—442no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4#6699111yescharacteristic
384C2×C4#6699111yescharacteristic
385C2×C4#6699111yescharacteristic
386C2×C4C2×D4×D1111yescharacteristic
387C2×C4C2×#434111yescharacteristic
388C2×C4C22×C22⋊D1111yescharacteristic
389C8—21no—
390C8—21no—
391C8—21no—
392C8—442no—
393C8—442no—
394C8—441no—
395C8—441no—
396C8#6700312yes—
397C22—21no—
398C22—21no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22#1062280512yes—
403C22C2×#6699111yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—82no—
409C4—82no—
410C4—441no—
411C4—441no—
412C4—441no—
413C4#1062330112yes—
414C4C2×#6700311yescharacteristic
415C4#1062335311yescharacteristic
416C2—22no—
417C2—881no—
418C2#1307806511yescharacteristic
419C2#1307827411yescharacteristic
420C2C2×#1062280511yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3170C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#3170D11
hypocenterC11#19228
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13068131C2semidirect
4. #13068126C2semidirect
5. #13068107C2semidirect
6. #13068102C2semidirect
7. #13068043C2semidirect
8. #13068036C2semidirect
9. C2×#10622095C2semidirect
10. #13067316C2semidirect
11. C11×#3170C2semidirect
154. #3170D11semidirect
362. C11#19228semidirect

Maximal subgroups

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

subgroupindex
#130799472
#130775912
#130681312
#130681262
#130681072
#130681022
#130680432
#130680362
C2×#106220952
#130673162
C11×#31702
#1922811