Finite Group Databasebeta

← #14782877

Subgroups — #14782877

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622608C211yesmaximal, characteristic
2C2×#10622612C211yesmaximal, characteristic
3#13071236C211yesmaximal, characteristic
4#13070118C212yesmaximal, complemented
5#13070117C212yesmaximal, complemented
6#13070112C212yesmaximal, complemented
7#13070107C212yesmaximal, complemented
8#13068335C211yesmaximal, characteristic
9#13068332C211yesmaximal, 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#10622608—24no—
26#10622590—21no—
27#10622589—21no—
28C2×#66872C2212yes—
29C2×#66871C2212yes—
30#10622559—22no—
31#10622541C2212yes—
32#10622541C2212yes—
33C2×C4⋊(C11⋊C8)C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35#10622167C2211yescharacteristic
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
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#66979Q814yes—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11—21no—
76C2×#4318—22no—
77C2×#4318—22no—
78C2×#4318D414yes—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C11×#95—22no—
86C11×#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66872—24no—
90#66871—24no—
91C4⋊(C11⋊C8)—24no—
92C4⋊(C11⋊C8)—24no—
93#23671—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—81no—
100C22×C4×C11—81no—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×Q812yes—
106C22×C4×C11C2×Q812yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11—42no—
115C22×Dic11—81no—
116C22×Dic11—81no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—82no—
126C11×C4⋊C4—82no—
127C11×C4⋊C4C2×Q814yes—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—42no—
130C42×C11—22no—
131C42×C11—22no—
132C42×C11—42no—
133C22⋊Dic11—24no—
134C4⋊Dic11—22no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—42no—
139C4⋊Dic11C2×Q812yes—
140C4⋊Dic11C2×Q812yes—
141Dic11⋊C4—82no—
142Dic11⋊C4—82no—
143C4×Dic11—24no—
144#4318—28no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—44no—
154C2×C11⋊C8C2×D414yes—
155C2×#428—111no—
156C2×#424—111no—
157#2317—111no—
158#2316D1111yescharacteristic
159#2088—112no—
160#2088—112no—
161#2087—112no—
162#2086—112no—
163#1736—111no—
164#1735—111no—
165C2×#340—111no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11#12112yes—
171C23×C11C22⋊Q812yes—
172C23×C11C22⋊Q812yes—
173C23×C11C22×D411yescharacteristic
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—84no—
190C2×C4×C11#12112yes—
191C2×C4×C11C22⋊Q812yes—
192C2×C4×C11C22⋊Q812yes—
193C2×C4×C11#12314yes—
194C2×C4×C11#12514yes—
195C2×C4×C11#12514yes—
196C2×C4×C11C4⋊Q814yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×Q811yescharacteristic
199C2×C4×C11C22×Q811yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—84no—
213C11⋊C8—24no—
214C11⋊C8—41no—
215C11⋊C8—41no—
216C22×M16—111no—
217C23×C8—111no—
218C2×#117—111no—
219C2×#117C2×D1111yescharacteristic
220C2×#117C2×D1111yescharacteristic
221C22×C4⋊C4—111no—
222C22×C4⋊C4C2×D1111yescharacteristic
223#428—224no—
224C2×#107—112no—
225C2×#106—112no—
226#424—224no—
227C2×C4⋊C8—112no—
228C2×C4⋊C8—112no—
229#389—21no—
230#389—21no—
231#389—112no—
232#389—112no—
233#389C2×D1112yes—
234#389C2×D1112yes—
235#385—222no—
236#384—221no—
237#382—221no—
238#380—22no—
239#340—111no—
240#340—112no—
241#340—112no—
242#340—111no—
243#340—112no—
244#340—112no—
245#340—111no—
246#340—111no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11#39814yes—
254C22×C11C2×#12111yescharacteristic
255C22×C11C2×C22⋊Q811yescharacteristic
256C22×C11C2×C22⋊Q811yescharacteristic
257C22×C11#57611yescharacteristic
258C22×C11#57711yescharacteristic
259C22×C11#57711yescharacteristic
260C22×C11#57811yescharacteristic
261C4×C11—44no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—81no—
265C4×C11—81no—
266C4×C11#39814yes—
267C4×C11C2×#12311yescharacteristic
268C4×C11C2×#12511yescharacteristic
269C4×C11C2×#12511yescharacteristic
270C4×C11C2×C4⋊Q811yescharacteristic
271Dic11—42no—
272Dic11—42no—
273Dic11—82no—
274C23×C4—21no—
275C23×C4—221no—
276C23×C4C22×D1111yescharacteristic
277C2×M16—114no—
278C2×M16—222no—
279C2×M16—222no—
280C22×C8—112no—
281C22×C8—111no—
282C22×C8—111no—
283C22×C8—222no—
284C22×C8—222no—
285C22×C8—222no—
286#117—22no—
287#117—22no—
288#117—22no—
289#117—22no—
290#117—114no—
291#117—222no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—222no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4Dic2214yes—
305C2×C4⋊C4C22⋊D1111yescharacteristic
306C2×C4⋊C4C22⋊D1111yescharacteristic
307C2×C4⋊C4C22×D1111yescharacteristic
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C4⋊C4C22×D1112yes—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4C22⋊D1112yes—
313C2×C42—21no—
314C2×C42—221no—
315C2×C42C22×D1112yes—
316#107—224no—
317#106—224no—
318C4⋊C8—224no—
319C4⋊C8—224no—
320#95—22no—
321#95—22no—
322#95—222no—
323#95—222no—
324C2×C11—24no—
325C2×C11C2×#39811yescharacteristic
326C2×C11#306211yescharacteristic
327C2×C11#306311yescharacteristic
328C2×C11#308111yescharacteristic
329C2×C11#308211yescharacteristic
330C2×C11#308311yescharacteristic
331C2×C11#308411yescharacteristic
332C24C2×C22⋊D1111yescharacteristic
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—81no—
338C22×C4—81no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—222no—
342C22×C4—442no—
343C22×C4—881no—
344C22×C4—881no—
345C22×C4C2×Dic2212yes—
346C22×C4#433912yes—
347C22×C4D4×D1112yes—
348C22×C4#434112yes—
349C22×C4Q8×D1112yes—
350C22×C4#434312yes—
351C22×C4C2×C22⋊D1112yes—
352C22×C4C2×C22⋊D1112yes—
353C22×C4C2×C22⋊D1111yescharacteristic
354C22×C4C23×D1111yescharacteristic
355M16—228no—
356C2×C8—114no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8—444no—
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—82no—
375C4⋊C4—82no—
376C4⋊C4—112no—
377C4⋊C4—112no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—222no—
381C4⋊C4—222no—
382C4⋊C4—442no—
383C4⋊C4—882no—
384C4⋊C4—882no—
385C4⋊C4C2×Dic2214yes—
386C22⋊C4—24no—
387C22⋊C4—42no—
388C22⋊C4—224no—
389C42—22no—
390C42—22no—
391C42—42no—
392C42—224no—
393C11#2367111yescharacteristic, complemented, Sylow
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23#6697712yes—
399C23#6699212yes—
400C23#6699912yes—
401C23C22×C22⋊D1111yescharacteristic
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—84no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—884no—
428C2×C4#6694114yes—
429C2×C4#6694214yes—
430C2×C4#6694314yes—
431C2×C4#6694714yes—
432C2×C4#6697712yes—
433C2×C4#6699212yes—
434C2×C4#6699912yes—
435C2×C4C22×Dic2211yescharacteristic
436C2×C4C2×#433911yescharacteristic
437C2×C4C2×D4×D1111yescharacteristic
438C2×C4C2×#434111yescharacteristic
439C2×C4C2×Q8×D1111yescharacteristic
440C2×C4C2×#434311yescharacteristic
441C8—224no—
442C8—441no—
443C8—441no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22#1062259714yes—
451C22C2×#6697711yescharacteristic
452C22C2×#6699211yescharacteristic
453C22C2×#6699911yescharacteristic
454C22#1062336611yescharacteristic
455C22#1062336711yescharacteristic
456C22#1062336811yescharacteristic
457C22#1062336911yescharacteristic
458C4—42no—
459C4—42no—
460C4—44no—
461C4—81no—
462C4—81no—
463C4—442no—
464C4—442no—
465C4—882no—
466C4#1062259714yes—
467C4C2×#6694111yescharacteristic
468C4C2×#6694211yescharacteristic
469C4C2×#6694311yescharacteristic
470C4C2×#6694711yescharacteristic
471C2—24no—
472C2C2×#1062259711yescharacteristic
473C2#1307829811yescharacteristic
474C2#1307830911yescharacteristic
475C2#1307844711yescharacteristic
476C2#1307845811yescharacteristic
477C2#1307846311yescharacteristic
478C2#1307847411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2316C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2316D11
hypocenterC11#23671
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
393. C11#23671semidirect

Maximal subgroups

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

subgroupindex
C2×#106226082
C2×#106226122
#130712362
#130701182
#130701172
#130701122
#130701072
#130683352
#130683322
C2×#106221672
C11×#23162
#2367111