Finite Group Databasebeta

← #14767729

Subgroups — #14767729

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66977C211yesmaximal, characteristic
2#13069550C212yesmaximal, complemented
3#13069336C212yesmaximal, complemented
4#13069181C212yesmaximal, complemented
5#13069170C212yesmaximal, complemented
6#13068798C212yesmaximal
7#13068402C212yesmaximal
8#13068310C211yesmaximal, characteristic
9C11×#1797C211yesmaximal, characteristic
10C22×C42×C11C2211yescharacteristic
11C2×#66977C411yescharacteristic
12C22×#4318C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C22⋊C8C2212yes—
18#10622825C411yescharacteristic
19#10622823C412yes—
20C4×C22⋊Dic11C2212yes—
21C2×#66879C2212yes—
22C2×Dic11⋊C8C2212yes—
23C2×Dic11⋊C8C2212yes—
24C2×C8×Dic11C2212yes—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622546C412yes—
27C4×Dic11⋊C4C2212yes—
28#10622542C411yescharacteristic
29#10622541C411yescharacteristic
30C11×#336C2212yes—
31#10622188C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622162C2212yes—
36#10622162C2212yes—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×Dic22C2×C411yescharacteristic
41C22×C8×C11C2312yes—
42C22×C8×C11C2312yes—
43C2×C42×C11—41no—
44C2×C42×C11—41no—
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11C2×C412yes—
50C2×C22⋊Dic11C2×C412yes—
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×C4⋊Dic11C2×C411yescharacteristic
54#66977—24no—
55C2×Dic11⋊C4C2×C412yes—
56C2×Dic11⋊C4C2×C412yes—
57C2×Dic11⋊C4C2×C412yes—
58C2×C4×Dic11C2312yes—
59C2×C4×Dic11C2312yes—
60C2×#4318—22no—
61C2×#4318—41no—
62C2×#4318—41no—
63C2×#4318—41no—
64C2×#4318—41no—
65C2×#4318Q814yescomplemented
66C22×C11⋊C8C2312yes—
67C22×C11⋊C8C2312yes—
68C4×Dic22—41no—
69C4×Dic22—41no—
70C11×C4⋊C8—41no—
71C11×C4⋊C8—41no—
72C11×C22⋊C8—24no—
73C11⋊#95C2×C412yes—
74C11⋊#95C2×C412yes—
75C11⋊#95C2×C412yes—
76C11⋊#95C2×C412yes—
77C11⋊#95C2×C412yes—
78#66879—42no—
79Dic11⋊C8—42no—
80Dic11⋊C8—42no—
81C8×Dic11—42no—
82#22289—111nomaximal, Sylow
83C24×C11C22×C411yescharacteristic
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×Q812yes—
100C22×C4×C11#4112yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11C22×C412yes—
103C22×Dic11C22×C412yes—
104C22×Dic11C22×C412yes—
105C22×Dic11C22×C412yes—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22M1614yescomplemented
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C42×C11—21no—
116C42×C11—21no—
117C42×C11—21no—
118C42×C11—21no—
119C42×C11—41no—
120C42×C11—41no—
121C22⋊Dic11—24no—
122C22⋊Dic11—42no—
123C4⋊Dic11—22no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126Dic11⋊C4—24no—
127Dic11⋊C4—24no—
128Dic11⋊C4—42no—
129C4×Dic11—22no—
130C4×Dic11—22no—
131C4×Dic11—22no—
132C4×Dic11—22no—
133#4318—44no—
134#4318—44no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8C2×Q814yes—
141C4×C22⋊Q8—111no—
142#1984—112no—
143#1940—112no—
144#1917—112no—
145#1916—112no—
146#1851—112no—
147#1797D1111yescharacteristic
148#1753—112no—
149#1728—111no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11C4×Q812yes—
157C23×C11C23×C411yescharacteristic
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11C4×Q812yes—
177C2×C4×C11C2×M1612yes—
178C2×C4×C11#13112yes—
179C2×C4×C11C22×Q811yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11H(5,𝔽2)11yescharacteristic
182C2×C4×C11H(5,𝔽2)11yescharacteristic
183C2×C4×C11H(5,𝔽2)11yescharacteristic
184C2×C4×C112−1+411yescharacteristic
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11C2×M1614yes—
197Dic22—44no—
198C8×C11—42no—
199C8×C11—42no—
200C11⋊C8—24no—
201C11⋊C8—42no—
202C22×M16—111no—
203C22×M16—111no—
204C2×C22⋊Q8—111no—
205C2×C4×Q8—111no—
206C22×C42C2×D1111yescharacteristic
207C2×C4⋊C8—112no—
208C2×C4⋊C8—112no—
209C2×C4⋊C8C2×D1111yescharacteristic
210C2×C4⋊C8C2×D1111yescharacteristic
211C2×C22⋊C8C2×D1112yes—
212C2×#97—112no—
213C2×C4×C8—112no—
214#391—111no—
215#389—111no—
216#387—112no—
217#385—112no—
218#380—111no—
219C4×C4⋊C4—112no—
220C4×C4⋊C4—111no—
221C4×C22⋊C4—112no—
222#336—112no—
223#336—112no—
224#336—112no—
225#336—112no—
226#336—112no—
227#336—112no—
228#336C2×D1112yes—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11C2×C4×Q811yescharacteristic
237C22×C11#51811yescharacteristic
238C22×C11#52011yescharacteristic
239C22×C11C22×M1611yescharacteristic
240C22×C11C2×#13111yescharacteristic
241C22×C11#56811yescharacteristic
242C22×C11#56811yescharacteristic
243C4×C11—22no—
244C4×C11—22no—
245C4×C11—22no—
246C4×C11—41no—
247C4×C11—41no—
248C4×C11#53811yescharacteristic
249C4×C11#53911yescharacteristic
250C4×C11#54311yescharacteristic
251C4×C11#54411yescharacteristic
252Dic11—24no—
253Dic11—42no—
254Dic11—42no—
255Dic11—42no—
256C22×Q8—111no—
257C23×C4C4×D1111yescharacteristic
258C23×C4C4×D1111yescharacteristic
259C23×C4C22×D1111yescharacteristic
260C2×M16—114no—
261C2×M16—222no—
262C2×M16—441no—
263C2×M16—441no—
264C2×M16—441no—
265C2×M16—441no—
266C22×C8—112no—
267C22×C8—112no—
268C22×C8C22×D1112yes—
269C22×C8C22×D1112yes—
270C22⋊Q8—224no—
271C4×Q8—441no—
272C4×Q8—441no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—111no—
279C2×C22⋊C4—112no—
280C2×C22⋊C4—112no—
281C2×C42—41no—
282C2×C42—41no—
283C2×C42—112no—
284C2×C42—112no—
285C2×C42C4×D1111yescharacteristic
286C2×C42C4×D1111yescharacteristic
287C2×C42C22×D1111yescharacteristic
288C2×C42C22×D1111yescharacteristic
289C4⋊C8—41no—
290C4⋊C8—41no—
291C4⋊C8—442no—
292C4⋊C8—442no—
293C22⋊C8—24no—
294#97—442no—
295C4×C8—442no—
296#95—112no—
297#95—112no—
298#95—112no—
299#95—112no—
300#95—112no—
301C2×C11—42no—
302C2×C11#232911yescharacteristic
303C2×C11#296211yescharacteristic
304C2×C11Q8×M1611yescharacteristic
305C2×C11#297311yescharacteristic
306C2×C11#297611yescharacteristic
307C2×C11#299111yescharacteristic
308C2×C11#299511yescharacteristic
309C24C2×C4×D1111yescharacteristic
310C2×Q8—114no—
311C2×Q8—441no—
312C2×Q8—441no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—112no—
324C22×C4—112no—
325C22×C4—112no—
326C22×C4—112no—
327C22×C4C2×C4×D1111yescharacteristic
328C22×C4C2×C4×D1111yescharacteristic
329C22×C4C2×C4×D1111yescharacteristic
330C22×C4C2×C4×D1111yescharacteristic
331C22×C4C2×C4×D1111yescharacteristic
332C22×C4#434112yes—
333C22×C4Q8×D1112yes—
334C22×C4C23×D1111yescharacteristic
335M16—444no—
336M16—444no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—114no—
344C2×C8—222no—
345C2×C8—222no—
346C2×C8—222no—
347C2×C8—222no—
348C2×C8—222no—
349C4⋊C4—224no—
350C4⋊C4—224no—
351C4⋊C4—222no—
352C4⋊C4—442no—
353C4⋊C4—441no—
354C4⋊C4—441no—
355C22⋊C4—224no—
356C22⋊C4—442no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C42—41no—
362C42—41no—
363C42—222no—
364C42—222no—
365C42—222no—
366C42—222no—
367C11#2228911yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23#6694012yes—
375C23C22×C4×D1111yescharacteristic
376Q8—444no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—114no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4#6694012yes—
408C2×C4#6695412yes—
409C2×C4M16×D1112yes—
410C2×C4C2×#434111yescharacteristic
411C2×C4#6703711yescharacteristic
412C2×C4#6703711yescharacteristic
413C2×C4C2×Q8×D1111yescharacteristic
414C2×C4#6704211yescharacteristic
415C2×C4#6704311yescharacteristic
416C8—42no—
417C8—42no—
418C8—224no—
419C8—442no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22#1062301711yescharacteristic
428C22C2×#6694011yescharacteristic
429C22#1062305411yescharacteristic
430C22C2×#6695411yescharacteristic
431C22C2×M16×D1111yescharacteristic
432C22#1062327611yescharacteristic
433C22#1062327611yescharacteristic
434C4—22no—
435C4—22no—
436C4—22no—
437C4—41no—
438C4—41no—
439C4—224no—
440C4—442no—
441C4—442no—
442C4—442no—
443C4#1062313311yescharacteristic
444C4#1062314811yescharacteristic
445C4#1062315411yescharacteristic
446C4#1062316511yescharacteristic
447C2—42no—
448C2#1307134611yescharacteristic
449C2#1307755911yescharacteristic
450C2#1307756711yescharacteristic
451C2#1307764311yescharacteristic
452C2#1307766111yescharacteristic
453C2#1307774511yescharacteristic
454C2#1307778811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1797C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1797D11
hypocenterC11#22289
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. #13069550C2semidirect
3. #13069336C2semidirect
4. #13069181C2semidirect
5. #13069170C2semidirect
65. C2×#4318Q8semidirect
108. C2×Dic22M16semidirect
367. C11#22289semidirect

Maximal subgroups

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

subgroupindex
C4×#669772
#130695502
#130693362
#130691812
#130691702
#130687982
#130684022
#130683102
C11×#17972
#2228911