Finite Group Databasebeta

← #14724098

Subgroups — #14724098

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078681C211yesmaximal, characteristic
2#13077582C211yesmaximal, characteristic
3#13067523C212yesmaximal, complemented
4#13067516C212yesmaximal, complemented
5#13067466C212yesmaximal, complemented
6#13067459C212yesmaximal, complemented
7#13067407C211yesmaximal, characteristic, complemented
8#13067053C211yesmaximal, characteristic
9#13067037C211yesmaximal, characteristic, complemented
10#13066905C211yesmaximal, characteristic, complemented
11C11×#2960C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C4×#4339C2211yescharacteristic
14C11×#446—21no—
15C11×#446C2212yes—
16C8×Q8×C11—21no—
17C8×Q8×C11C2212yes—
18C11×#424—21no—
19C11×#423C2211yescharacteristic
20C11×#405—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23#10622724—21no—
24#10622707C411yescharacteristic
25#10622703C411yescharacteristic
26#10622700C411yescharacteristic
27#10622696C411yescharacteristic
28#10622660C412yes—
29#10622658C412yes—
30C4×#4326C2212yes—
31C4×#4325C2212yes—
32#10622538C2211yescharacteristic
33#10622538C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622301C2211yescharacteristic
36#10622301C2211yescharacteristic
37C4×#4313—21no—
38#10622298—21no—
39#10622292C2211yescharacteristic
40#10622292C2211yescharacteristic
41Q8⋊(C11⋊C8)C2212yes—
42Q8⋊(C11⋊C8)C2212yes—
43#10622122C2212yes—
44#10622121C2212yes—
45#10622118C2212yes—
46#10622117C2212yes—
47#10622093C2212yes—
48#10622092C2212yes—
49C2×#4339C2×C411yescharacteristic
50C2×C11×M16—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C11×C4⋊Q8C2×C411yescharacteristic
54C11×C4⋊Q8C2×C411yescharacteristic
55C11×#125—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8C2×C412yes—
58C4×Q8×C11—21no—
59C4×Q8×C11C2312yes—
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326C2×C412yes—
63C2×#4325C2×C412yes—
64C4×C22⋊D11—21no—
65C4×C22⋊D11—21no—
66#66979C2×C411yescharacteristic
67C2×#4318—21no—
68C2×#4313—21no—
69C2×#4313—21no—
70C4×D44C2×C411yescharacteristic
71C4×D44C2311yescharacteristic
72#66925—21no—
73C42×D11—21no—
74C4×Dic22C2×C411yescharacteristic
75C4×Dic22C2311yescharacteristic
76C11×C4⋊C8—22no—
77C11×C4⋊C8—22no—
78C11×C4⋊C8—21no—
79C11×C4⋊C8C2312yes—
80C11×#97—22no—
81C4×C8×C11—22no—
82C4×C8×C11D411yescharacteristic
83C4×C8×C11D411yescharacteristic
84C4×C8×C11C2311yescharacteristic
85C4×C8×C11C2311yescharacteristic
86#66899C2×C412yes—
87#66899C2×C412yes—
88C22⋊(C11⋊C8)—21no—
89C22⋊(C11⋊C8)C2×C412yes—
90(C2×D11)⋊C8—21no—
91(C2×D11)⋊C8—21no—
92#66879—21no—
93#66879—21no—
94Dic11⋊C8—21no—
95Dic11⋊C8—21no—
96#66874C2×C412yes—
97#66873C2×C412yes—
98#66872C2×C412yes—
99#66871C2×C412yes—
100C4⋊(C11⋊C8)C2×C411yescharacteristic
101C4⋊(C11⋊C8)C2×C411yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4⋊(C11⋊C8)C2311yescharacteristic
104#66867—21no—
105C4×C11⋊C8—21no—
106C4×C11⋊C8C2312yes—
107C4×C11⋊C8C2312yes—
108#17941—111nomaximal, Sylow
109C2×Q8×C11—21no—
110C2×Q8×C11C22×C412yes—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×C22⋊D11—21no—
115#4339—41no—
116#4339—41no—
117C2×D44C22×C411yescharacteristic
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×Dic22C22×C411yescharacteristic
122C11×M16—42no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—41no—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4C22×C412yes—
136C11×C22⋊C4—22no—
137C42×C11—22no—
138C42×C11C22×C411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11#4111yescharacteristic
141C42×C11C2411yescharacteristic
142C22⋊Dic11—21no—
143#4326—42no—
144#4325—42no—
145(C2×D11)⋊C4—21no—
146(C2×D11)⋊C4—21no—
147C4⋊Dic11C22×C411yescharacteristic
148C4⋊Dic11C22×C411yescharacteristic
149Dic11⋊C4—21no—
150Dic11⋊C4—21no—
151C4×Dic11—21no—
152C4×Dic11—21no—
153C4×Dic11—21no—
154#4318—42no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8C22×C412yes—
159C2×C11⋊C8C22×C412yes—
160#4313—42no—
161#4313—42no—
162#3107—111no—
163#2965—111no—
164#2960D1111yescharacteristic, complemented
165#1593—112no—
166#1592—112no—
167#1584—112no—
168#1583—112no—
169#1574—111no—
170#1489—111no—
171#1485—111no—
172#1451—111no—
173C23×C11C4×D411yescharacteristic
174C22×D11—21no—
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—42no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11C4×D411yescharacteristic
187C2×C4×C11C4×D411yescharacteristic
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C22⋊D11—42no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195D44—21no—
196D44—21no—
197C4×D11—42no—
198C4×D11—41no—
199C4×D11—41no—
200C4×D11—42no—
201Dic22—21no—
202Dic22—21no—
203C8×C11—21no—
204C8×C11—21no—
205C8×C11—21no—
206C8×C11—42no—
207C8×C11#13712yes—
208C11⋊C8—22no—
209C11⋊C8—22no—
210C11⋊C8—42no—
211C11⋊C8—41no—
212C11⋊C8—41no—
213#533C2×D1111yescharacteristic
214C4×#41—111no—
215#485—112no—
216#475—111no—
217#474—111no—
218#462—111no—
219#461—111no—
220#452—112no—
221#446—21no—
222#446—111no—
223#446—111no—
224#446C2×D1112yes—
225C8×Q8—21no—
226C8×Q8C2×D1112yes—
227C4×Q16—112no—
228C4×SD16—112no—
229#436—111no—
230#436—111no—
231#435—221no—
232#435—221no—
233#431—111no—
234#431—111no—
235#431—221no—
236#424—21no—
237#423C2×D1111yescharacteristic
238#405—21no—
239C4×M16—111no—
240C4×M16—221no—
241C2×C4×C8C2×D1111yescharacteristic
242#335—112no—
243#334—112no—
244Q8⋊C8—112no—
245Q8⋊C8—112no—
246Q8⋊C8—112no—
247D4⋊C8—112no—
248#322—112no—
249#322—112no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11C2×C4×D411yescharacteristic
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—41no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11#44412yes—
263C4×C11#56811yescharacteristic
264C4×C11#56811yescharacteristic
265C4×C11C2×#13711yescharacteristic
266C4×C11#57511yescharacteristic
267Dic11—41no—
268Dic11—41no—
269Dic11—41no—
270C2×#41—111no—
271C2×Q16—112no—
272C2×SD16—112no—
273C2×M16—21no—
274C2×M16—221no—
275C2×M16—221no—
276C2×M16—221no—
277C22×C8C22⋊D1111yescharacteristic
278C22×C8C22⋊D1111yescharacteristic
279C4⋊Q8C4×D1111yescharacteristic
280C4⋊Q8C4×D1111yescharacteristic
281#125—21no—
282C22⋊Q8—21no—
283C22⋊Q8C4×D1112yes—
284C4×Q8—21no—
285C4×Q8—111no—
286C4×Q8—111no—
287C4×Q8C22×D1112yes—
288C4×D4—111no—
289C4×D4—111no—
290C4×D4—221no—
291C4×D4—221no—
292#117—21no—
293#117—111no—
294#117—221no—
295C2×C42—221no—
296C2×C42C22×D1111yescharacteristic
297#107—112no—
298#106—112no—
299C4⋊C8—22no—
300C4⋊C8—22no—
301C4⋊C8—21no—
302C4⋊C8—111no—
303C4⋊C8—111no—
304C4⋊C8—111no—
305C4⋊C8—111no—
306C4⋊C8—221no—
307C4⋊C8—221no—
308C4⋊C8C22×D1112yes—
309#103—112no—
310#103—112no—
311#103—112no—
312#102—112no—
313C22⋊C8—112no—
314C22⋊C8—221no—
315C22⋊C8—221no—
316C22⋊C8—221no—
317#97—22no—
318#97—221no—
319#97—221no—
320#97—221no—
321C4×C8—22no—
322C4×C8—112no—
323C4×C8—112no—
324C4×C8—221no—
325C4×C8C22⋊D1111yescharacteristic
326C4×C8C22⋊D1111yescharacteristic
327C4×C8C22×D1111yescharacteristic
328C4×C8C22×D1111yescharacteristic
329C2×C11—41no—
330C2×C11#293011yescharacteristic
331C2×C11C4×#13711yescharacteristic
332C2×C11C2×#44411yescharacteristic
333D11—81no—
334#41—441no—
335#41—441no—
336C2×Q8—21no—
337C2×Q8—111no—
338C2×Q8C2×C4×D1112yes—
339C2×D4—111no—
340C2×D4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4C2×C4×D1111yescharacteristic
345C22×C4#433911yescharacteristic
346C22×C4C2×C22⋊D1111yescharacteristic
347Q16—442no—
348SD16—442no—
349M16—42no—
350M16—442no—
351M16—442no—
352M16—442no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—41no—
356C2×C8—112no—
357C2×C8—112no—
358C2×C8—222no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8C2×C22⋊D1111yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—111no—
371C4⋊C4—111no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4C2×C4×D1112yes—
375C22⋊C4—22no—
376C22⋊C4—221no—
377C22⋊C4—221no—
378C22⋊C4—221no—
379C42—22no—
380C42—221no—
381C42—221no—
382C42—221no—
383C42C2×C4×D1111yescharacteristic
384C42#433911yescharacteristic
385C42C2×C22⋊D1111yescharacteristic
386C42C23×D1111yescharacteristic
387C11#1794111yescharacteristic, complemented, Sylow
388C23—221no—
389C23C4×C22⋊D1111yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—42no—
393Q8—221no—
394Q8—221no—
395D4—221no—
396D4—221no—
397D4—442no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4C4×C22⋊D1111yescharacteristic
413C2×C4C4×C22⋊D1111yescharacteristic
414C2×C4C4×C22⋊D1111yescharacteristic
415C2×C4C22×C4×D1111yescharacteristic
416C2×C4C2×#433911yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—42no—
422C8—222no—
423C8—222no—
424C8—442no—
425C8—441no—
426C8—441no—
427C8#6699512yes—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—441no—
432C22—441no—
433C22—441no—
434C22C2×C4×C22⋊D1111yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—42no—
439C4—42no—
440C4—441no—
441C4—441no—
442C4—441no—
443C4#1062275812yes—
444C4#1062328111yescharacteristic
445C4#1062328111yescharacteristic
446C4C2×#6699511yescharacteristic
447C4#1062335311yescharacteristic
448C2—41no—
449C2—881no—
450C2#1307731711yescharacteristic
451C2C4×#6699511yescharacteristic
452C2C2×#1062275811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#2960D11
hypocenterC11#17941
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2960

Complements

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

NH ≅ G/Ntype
3. #13067523C2semidirect
4. #13067516C2semidirect
5. #13067466C2semidirect
6. #13067459C2semidirect
7. #13067407C2semidirect
9. #13067037C2semidirect
10. #13066905C2semidirect
11. C11×#2960C2semidirect
164. #2960D11semidirect
387. C11#17941semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130775822
#130675232
#130675162
#130674662
#130674592
#130674072
#130670532
#130670372
#130669052
C11×#29602
#1794111