Finite Group Databasebeta

← #14782855

Subgroups — #14782855

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622611C211yesmaximal, characteristic
2C2×#10622612C211yesmaximal, characteristic
3#13071232C211yesmaximal, characteristic
4#13070118C212yesmaximal, complemented
5#13070117C212yesmaximal, complemented
6#13070112C212yesmaximal, complemented
7#13070107C212yesmaximal, complemented
8#13068337C211yesmaximal, characteristic
9#13068335C211yesmaximal, characteristic
10C2×#10622167C211yesmaximal, characteristic
11C11×#2316C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C11×#389—21no—
20C11×#389—21no—
21C11×#389C2212yes—
22C11×#389C2212yes—
23C11×#380—22no—
24#10622612—24no—
25#10622611—24no—
26#10622586—21no—
27#10622586—21no—
28C2×#66872C2211yescharacteristic
29C2×#66872C2211yescharacteristic
30C2×#66871C2211yescharacteristic
31C2×#66871C2211yescharacteristic
32#10622555—22no—
33#10622541C2212yes—
34#10622541C2212yes—
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4⋊(C11⋊C8)C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—21no—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117—22no—
49C11×#117—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4Q814yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4D412yes—
62C2×C42×C11—21no—
63C2×C42×C11C2312yes—
64C2×C22⋊Dic11—21no—
65#66979—22no—
66#66979—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11Q814yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11—21no—
76C2×#4318—22no—
77C2×#4318—22no—
78C2×#4318—22no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8D414yes—
82C22×C11⋊C8C2312yes—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C11×#95—22no—
86C11×#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66872—22no—
90#66872—22no—
91#66871—22no—
92#66871—22no—
93C4⋊(C11⋊C8)—24no—
94C4⋊(C11⋊C8)—24no—
95#23669—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—81no—
102C22×C4×C11—81no—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×Q812yes—
108C22×C4×C11C2×Q812yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—24no—
114C22×Dic11—22no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—81no—
118C22×Dic11—81no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—82no—
128C11×C4⋊C4—82no—
129C11×C4⋊C4C2×Q814yes—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—42no—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11—42no—
135C22⋊Dic11—42no—
136C4⋊Dic11—24no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11C2×Q814yes—
143Dic11⋊C4—82no—
144Dic11⋊C4—82no—
145C4×Dic11—42no—
146#4318—44no—
147C2×C11⋊C8—28no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8C2×D412yes—
156C2×C11⋊C8C2×D412yes—
157C2×#427—111no—
158C2×#424—111no—
159#2316—111no—
160#2316D1111yescharacteristic
161#2088—112no—
162#2088—112no—
163#2087—112no—
164#2086—112no—
165#1736—111no—
166#1736—111no—
167C2×#340—111no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11#12112yes—
173C23×C11C22⋊Q812yes—
174C23×C11C22⋊Q812yes—
175C23×C11C22×D411yescharacteristic
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—84no—
192C2×C4×C11#12112yes—
193C2×C4×C11C22⋊Q812yes—
194C2×C4×C11C22⋊Q812yes—
195C2×C4×C11#12314yes—
196C2×C4×C11#12514yes—
197C2×C4×C11#12514yes—
198C2×C4×C11C4⋊Q814yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×Q811yescharacteristic
201C2×C4×C11C22×Q811yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×Dic11—24no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—84no—
215C11⋊C8—22no—
216C11⋊C8—22no—
217C11⋊C8—42no—
218C22×M16—111no—
219C23×C8—111no—
220C2×#117—111no—
221C2×#117C2×D1111yescharacteristic
222C2×#117C2×D1111yescharacteristic
223C22×C4⋊C4—111no—
224C22×C4⋊C4C2×D1111yescharacteristic
225#427—224no—
226C2×#107—111no—
227C2×#107—111no—
228C2×#106—111no—
229C2×#106—111no—
230#424—224no—
231C2×C4⋊C8—112no—
232C2×C4⋊C8—112no—
233#389—21no—
234#389—21no—
235#389—112no—
236#389—112no—
237#389—221no—
238#389—221no—
239#389C2×D1112yes—
240#389C2×D1112yes—
241#380—22no—
242#380—222no—
243#340—112no—
244#340—112no—
245#340—112no—
246#340—112no—
247#340—112no—
248#340—112no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11#39814yes—
256C22×C11C2×#12111yescharacteristic
257C22×C11C2×C22⋊Q811yescharacteristic
258C22×C11C2×C22⋊Q811yescharacteristic
259C22×C11#57611yescharacteristic
260C22×C11#57711yescharacteristic
261C22×C11#57711yescharacteristic
262C22×C11#57811yescharacteristic
263C4×C11—44no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—81no—
267C4×C11—81no—
268C4×C11#39814yes—
269C4×C11C2×#12311yescharacteristic
270C4×C11C2×#12511yescharacteristic
271C4×C11C2×#12511yescharacteristic
272C4×C11C2×C4⋊Q811yescharacteristic
273Dic11—44no—
274Dic11—81no—
275Dic11—81no—
276C23×C4—21no—
277C23×C4—221no—
278C23×C4C22×D1111yescharacteristic
279C2×M16—222no—
280C2×M16—222no—
281C2×M16—222no—
282C22×C8—114no—
283C22×C8—111no—
284C22×C8—111no—
285C22×C8—112no—
286C22×C8—222no—
287C22×C8—222no—
288#117—22no—
289#117—22no—
290#117—22no—
291#117—22no—
292#117—222no—
293#117—222no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—114no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4Dic2214yes—
307C2×C4⋊C4C22⋊D1111yescharacteristic
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1112yes—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4C22⋊D1112yes—
315C2×C42—21no—
316C2×C42—221no—
317C2×C42C22×D1112yes—
318#107—222no—
319#107—222no—
320#106—222no—
321#106—222no—
322C4⋊C8—224no—
323C4⋊C8—224no—
324#95—22no—
325#95—22no—
326#95—222no—
327#95—222no—
328C2×C11—24no—
329C2×C11C2×#39811yescharacteristic
330C2×C11#306011yescharacteristic
331C2×C11#306111yescharacteristic
332C2×C11#308111yescharacteristic
333C2×C11#308111yescharacteristic
334C2×C11#308211yescharacteristic
335C2×C11#308211yescharacteristic
336C24C2×C22⋊D1111yescharacteristic
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—81no—
342C22×C4—81no—
343C22×C4—222no—
344C22×C4—224no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—881no—
348C22×C4—881no—
349C22×C4C2×Dic2212yes—
350C22×C4#433912yes—
351C22×C4D4×D1112yes—
352C22×C4#434112yes—
353C22×C4Q8×D1112yes—
354C22×C4#434312yes—
355C22×C4C2×C22⋊D1112yes—
356C22×C4C2×C22⋊D1112yes—
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C23×D1111yescharacteristic
359M16—444no—
360C2×C8—112no—
361C2×C8—112no—
362C2×C8—228no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—222no—
370C4⋊C4—24no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—82no—
379C4⋊C4—82no—
380C4⋊C4—114no—
381C4⋊C4—224no—
382C4⋊C4—222no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—882no—
388C4⋊C4—882no—
389C4⋊C4C2×Dic2214yes—
390C22⋊C4—24no—
391C22⋊C4—42no—
392C22⋊C4—442no—
393C42—22no—
394C42—22no—
395C42—42no—
396C42—442no—
397C11#2366911yescharacteristic, complemented, Sylow
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23#6697712yes—
403C23#6699212yes—
404C23#6699912yes—
405C23C22×C22⋊D1111yescharacteristic
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—84no—
422C2×C4—224no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—884no—
432C2×C4#6694114yes—
433C2×C4#6694214yes—
434C2×C4#6694314yes—
435C2×C4#6694714yes—
436C2×C4#6697712yes—
437C2×C4#6699212yes—
438C2×C4#6699912yes—
439C2×C4C22×Dic2211yescharacteristic
440C2×C4C2×#433911yescharacteristic
441C2×C4C2×D4×D1111yescharacteristic
442C2×C4C2×#434111yescharacteristic
443C2×C4C2×Q8×D1111yescharacteristic
444C2×C4C2×#434311yescharacteristic
445C8—222no—
446C8—222no—
447C8—442no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22#1062259714yes—
455C22C2×#6697711yescharacteristic
456C22C2×#6699211yescharacteristic
457C22C2×#6699911yescharacteristic
458C22#1062336611yescharacteristic
459C22#1062336711yescharacteristic
460C22#1062336811yescharacteristic
461C22#1062336911yescharacteristic
462C4—42no—
463C4—42no—
464C4—44no—
465C4—81no—
466C4—81no—
467C4—444no—
468C4—881no—
469C4—881no—
470C4#1062259714yes—
471C4C2×#6694111yescharacteristic
472C4C2×#6694211yescharacteristic
473C4C2×#6694311yescharacteristic
474C4C2×#6694711yescharacteristic
475C2—24no—
476C2C2×#1062259711yescharacteristic
477C2#1307827511yescharacteristic
478C2#1307828311yescharacteristic
479C2#1307844111yescharacteristic
480C2#1307844711yescharacteristic
481C2#1307845211yescharacteristic
482C2#1307845811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2316C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2316D11
hypocenterC11#23669
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2316

Complements

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

NH ≅ G/Ntype
4. #13070118C2semidirect
5. #13070117C2semidirect
6. #13070112C2semidirect
7. #13070107C2semidirect
397. C11#23669semidirect

Maximal subgroups

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

subgroupindex
C2×#106226112
C2×#106226122
#130712322
#130701182
#130701172
#130701122
#130701072
#130683372
#130683352
C2×#106221672
C11×#23162
#2366911