Finite Group Databasebeta

← #14803556

Subgroups — #14803556

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C211yesmaximal, characteristic
2C2×#10622696C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13069983C212yesmaximal, complemented
5#13069876C212yesmaximal
6#13069518C212yesmaximal
7#13069461C211yesmaximal, characteristic, complemented
8#13069391C211yesmaximal, characteristic, complemented
9#13069274C212yesmaximal, complemented
10C4×#66887C211yesmaximal, characteristic
11C11×#3139C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C22×#4325C2212yes—
15C2×C4×D44C2211yescharacteristic
16C11×#491—22no—
17C11×#487—21no—
18C11×#487—21no—
19C11×#419C2212yes—
20C11×#419C2212yes—
21C4×C11×M16C2211yescharacteristic
22C2×#66900C2212yes—
23C2×#66900C2212yes—
24C2×#66899C2212yes—
25C2×#66887C2211yescharacteristic
26C2×#66887C2211yescharacteristic
27C2×#66886C2212yes—
28#10622700—21no—
29#10622697—21no—
30#10622696—21no—
31#10622696—22no—
32#10622696—21no—
33#10622679—22no—
34#10622637—21no—
35#10622637—22no—
36Q8×C11⋊C8—21no—
37#10622614C2212yes—
38#10622612C2212yes—
39#10622610C2212yes—
40#10622608C2212yes—
41#10622537C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44#10622196C2212yes—
45#10622192C2211yescharacteristic
46#10622192C2211yescharacteristic
47C22×Q8×C11C2312yes—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C2×C11×M16C2311yescharacteristic
51C2×C11×M16C2311yescharacteristic
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×#125D412yes—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C11×#117C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4325—24no—
68C2×#4325—22no—
69C2×#4325—22no—
70C2×#4325—42no—
71C2×(C2×D11)⋊C4—21no—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×#4318C2312yes—
74C2×#4318C2311yescharacteristic
75C2×#4318C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C4×D44—21no—
78C4×D44—21no—
79C4×D44—21no—
80C4×D44—21no—
81C11×#103—22no—
82C11×#103—22no—
83C11×#103—22no—
84C11×#103—22no—
85C11×#97—21no—
86C4×C8×C11—21no—
87#66900—24no—
88#66900—42no—
89#66899—22no—
90#66899—22no—
91#66887—22no—
92#66887—22no—
93#66886—42no—
94#66873—22no—
95#66873—22no—
96#66872—22no—
97#66871—22no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)D411yescharacteristic
103C4⋊(C11⋊C8)D412yes—
104C4⋊(C11⋊C8)D411yescharacteristic
105#66867—21no—
106#66867—22no—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—22no—
109#25313—111nomaximal, Sylow
110C23×D11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44#4112yes—
130C2×C4×D11—41no—
131C2×C4×D11—41no—
132C2×C4×D11—82no—
133C11×M16—21no—
134C11×M16—21no—
135C11×M16—21no—
136C11×M16—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4C2×D412yes—
148C11×C4⋊C4C2×D412yes—
149C11×C22⋊C4—22no—
150C42×C11—22no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155#4325—44no—
156#4325—44no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161#4318—21no—
162#4318—22no—
163#4318—22no—
164#4318—21no—
165#4318—21no—
166#4318#4112yes—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8C2×D412yes—
173C2×C11⋊C8C2×D412yes—
174#3139D1111yescharacteristic, complemented
175#3077—111no—
176C2×#461—111no—
177#2962—111no—
178#2064—112no—
179#2046—112no—
180#1977—112no—
181#1966—111no—
182#1950—111no—
183#1930—112no—
184C4×#100—111no—
185C23×C11C2×#4111yescharacteristic
186C22×D11—22no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—81no—
190C22×D11—81no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—81no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11H(5,𝔽2)11yescharacteristic
213C2×C4×C112−1+411yescharacteristic
214C2×Dic11—41no—
215C2×Dic11—81no—
216D44—22no—
217D44—22no—
218D44—41no—
219D44—41no—
220C4×D11—82no—
221C4×D11—82no—
222C8×C11—41no—
223C8×C11—41no—
224C11⋊C8—22no—
225C11⋊C8—22no—
226C11⋊C8—22no—
227C11⋊C8—41no—
228C11⋊C8—42no—
229C22×SD16—112no—
230#533C2×D1111yescharacteristic
231C2×C4⋊Q8C2×D1111yescharacteristic
232C2×C4×D4—111no—
233#491—22no—
234#487—21no—
235#487—21no—
236#478—222no—
237#476—221no—
238#474—221no—
239#461—221no—
240#461—222no—
241#461—221no—
242#446—222no—
243#446—221no—
244C8×Q8—221no—
245C2×#108—112no—
246#428—112no—
247#424—112no—
248#423—111no—
249C2×C4⋊C8—111no—
250#419C2×D1112yes—
251#419C2×D1112yes—
252#418—112no—
253C2×#103—112no—
254C2×#101—112no—
255C2×#101—112no—
256C2×#100—111no—
257C2×#100—111no—
258#405—112no—
259C4×M16—111no—
260C4×M16C2×D1111yescharacteristic
261#343—111no—
262#343—111no—
263#341—112no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11C2×#12111yescharacteristic
267C22×C11#52911yescharacteristic
268C22×C11#54211yescharacteristic
269C2×D11—42no—
270C2×D11—82no—
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—82no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—82no—
280C4×C11#47112yes—
281C4×C11#54611yescharacteristic
282C4×C11#54811yescharacteristic
283C4×C11#54811yescharacteristic
284C4×C11#55011yescharacteristic
285Dic11—81no—
286C22×Q8C22×D1112yes—
287C22×D4—111no—
288C23×C4—221no—
289C2×SD16—222no—
290C2×SD16—222no—
291C2×SD16—224no—
292C2×SD16—442no—
293C2×M16—111no—
294C2×M16—112no—
295C2×M16—111no—
296C2×M16C22×D1111yescharacteristic
297C2×M16C22×D1111yescharacteristic
298C22×C8—112no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8C22⋊D1111yescharacteristic
304C4⋊Q8C22⋊D1111yescharacteristic
305#125C22⋊D1112yes—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×D4—221no—
311C4×D4—221no—
312C4×D4—221no—
313C4×D4—221no—
314#117C22×D1112yes—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—111no—
318C2×C22⋊C4—221no—
319C2×C42C22×D1111yescharacteristic
320#108—442no—
321#107—222no—
322#106—222no—
323C4⋊C8—111no—
324C4⋊C8—111no—
325C4⋊C8—112no—
326C4⋊C8—222no—
327C4⋊C8—222no—
328C4⋊C8—221no—
329C4⋊C8—221no—
330#103—22no—
331#103—22no—
332#103—22no—
333#103—22no—
334#103—222no—
335#103—222no—
336#102—222no—
337#102—222no—
338#101—224no—
339#101—442no—
340#100—222no—
341#100—222no—
342#97—21no—
343#97—222no—
344#97—221no—
345C4×C8—21no—
346C4×C8—222no—
347C4×C8—221no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11#242611yescharacteristic
351C2×C11C2×#47111yescharacteristic
352C2×C11#306911yescharacteristic
353D11—82no—
354C24—221no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×D4—112no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—221no—
369C22×C4—22no—
370C22×C4—221no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—882no—
374C22×C4#434111yescharacteristic
375C22×C4#434111yescharacteristic
376C22×C4C23×D1111yescharacteristic
377SD16—444no—
378SD16—444no—
379M16—21no—
380M16—21no—
381M16—21no—
382M16—21no—
383M16—112no—
384M16—221no—
385M16—221no—
386M16—222no—
387M16—221no—
388M16—222no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—112no—
392C2×C8—112no—
393C2×C8—221no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—221no—
397C2×C8—222no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4C2×C22⋊D1112yes—
409C4⋊C4C2×C22⋊D1112yes—
410C22⋊C4—22no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C42—22no—
414C42D4×D1111yescharacteristic
415C42D4×D1111yescharacteristic
416C42C2×C22⋊D1111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C11#2531311yescharacteristic, complemented, Sylow
419C23—222no—
420C23—441no—
421C23—441no—
422C23—881no—
423C23—881no—
424C23C2×#434111yescharacteristic
425Q8—42no—
426Q8—42no—
427Q8—42no—
428Q8—42no—
429Q8—42no—
430Q8—81no—
431D4—222no—
432D4—222no—
433D4—441no—
434D4—441no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—441no—
443C2×C4—882no—
444C2×C4—882no—
445C2×C4—881no—
446C2×C4#6699211yescharacteristic
447C2×C4#6699211yescharacteristic
448C2×C4#6699211yescharacteristic
449C2×C4#6699211yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4#41×D1111yescharacteristic
452C2×C4#41×D1111yescharacteristic
453C2×C4#6704211yescharacteristic
454C2×C4#6704311yescharacteristic
455C2×C4C22×C22⋊D1111yescharacteristic
456C8—41no—
457C8—41no—
458C8—222no—
459C8—222no—
460C8—222no—
461C8—442no—
462C8—441no—
463C22—21no—
464C22—21no—
465C22—442no—
466C22—882no—
467C22—882no—
468C22—881no—
469C22—881no—
470C22#1062321111yescharacteristic
471C22#1062321311yescharacteristic
472C22C2×#6699211yescharacteristic
473C4—21no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—42no—
478C4—82no—
479C4—881no—
480C4#1062281612yes—
481C4#1062320711yescharacteristic
482C4#1062320811yescharacteristic
483C4#1062336211yescharacteristic
484C4#1062336511yescharacteristic
485C2—21no—
486C2—21no—
487C2—882no—
488C2#1307218511yescharacteristic
489C2C2×#1062281611yescharacteristic
490C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3139C2
socleC22×C11C2×#121
prime radicalC22×D44C23
hypercenter#3139D11
hypocenterC11#25313
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
3. #13077565C2semidirect
4. #13069983C2semidirect
7. #13069461C2semidirect
8. #13069391C2semidirect
9. #13069274C2semidirect
11. C11×#3139C2semidirect
174. #3139D11semidirect
418. C11#25313semidirect

Maximal subgroups

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

subgroupindex
#130784092
C2×#106226962
#130775652
#130699832
#130698762
#130695182
#130694612
#130693912
#130692742
C4×#668872
C11×#31392
#2531311