Finite Group Databasebeta

← #14782872

Subgroups — #14782872

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×#10622732C211yesmaximal, characteristic
2#13071240C211yesmaximal, characteristic
3#13071232C211yesmaximal, characteristic
4#13070115C212yesmaximal, complemented
5#13070115C212yesmaximal, complemented
6#13070110C212yesmaximal, complemented
7#13070105C212yesmaximal, complemented
8#13068336C211yesmaximal, characteristic
9#13068332C211yesmaximal, characteristic
10C2×#10622167C211yesmaximal, characteristic
11C2×C11×#428C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C11×#428—24no—
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22#10622823—22no—
23#10622732—24no—
24C2×Dic11⋊C8C2212yes—
25C2×Dic11⋊C8C2212yes—
26#10622590—21no—
27#10622589—21no—
28#10622586C2212yes—
29#10622586C2212yes—
30#10622586C2212yes—
31#10622586C2212yes—
32#10622555—22no—
33#10622541—21no—
34#10622541—21no—
35#10622189C2212yes—
36#10622189C2212yes—
37#10622167C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—21no—
46C2×C11×M16—22no—
47C2×C11×M16—22no—
48C2×C11×M16D414yes—
49C22×C8×C11C2312yes—
50C11×#117—22no—
51C11×#117—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11D412yes—
62#66979—22no—
63#66979—22no—
64#66979—22no—
65#66979Q814yes—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11Q814yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11C2312yes—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8—22no—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C11×#107—24no—
86C11×#106—24no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91Dic11⋊C8—24no—
92Dic11⋊C8—24no—
93#23671—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—42no—
99C22×C4×C11—81no—
100C22×C4×C11—81no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11C2×Q812yes—
105C22×C4×C11#4112yes—
106C22×C4×C11#4112yes—
107C22×C4×C11#4112yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—24no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—81no—
114C22×Dic11—81no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C11×M16—28no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11C2×D414yes—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—42no—
128C11×C22⋊C4—42no—
129C42×C11—42no—
130C22⋊Dic11—24no—
131C22⋊Dic11—24no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—24no—
135C4⋊Dic11—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11C2×Q814yes—
139C4⋊Dic11C2×Q812yes—
140C4⋊Dic11C2×Q812yes—
141Dic11⋊C4—82no—
142Dic11⋊C4—82no—
143Dic11⋊C4—82no—
144Dic11⋊C4—82no—
145C4×Dic11—24no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—44no—
155C2×#428D1111yescharacteristic
156C2×#424—111no—
157#2317—111no—
158#2316—111no—
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—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—84no—
184C2×C4×C11#12112yes—
185C2×C4×C11C22⋊Q812yes—
186C2×C4×C11C22⋊Q812yes—
187C2×C4×C11#12314yes—
188C2×C4×C11#12514yes—
189C2×C4×C11#12514yes—
190C2×C4×C11C4⋊Q814yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×Q811yescharacteristic
193C2×C4×C11C22×Q811yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—24no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—84no—
213C8×C11—24no—
214C11⋊C8—41no—
215C11⋊C8—41no—
216C22×M16C2×D1111yescharacteristic
217C23×C8—111no—
218C2×#117—111no—
219C2×#117—111no—
220C2×#117C2×D1111yescharacteristic
221C22×C4⋊C4—111no—
222C22×C4⋊C4C2×D1111yescharacteristic
223#428—24no—
224C2×#107C2×D1112yes—
225C2×#106C2×D1112yes—
226#424—224no—
227C2×C4⋊C8—112no—
228C2×C4⋊C8—112no—
229#389—112no—
230#389—112no—
231#389—112no—
232#389—112no—
233#389—221no—
234#389—221no—
235#385—222no—
236#384—221no—
237#382—221no—
238#380—222no—
239#340—112no—
240#340—112no—
241#340—111no—
242#340—112no—
243#340—111no—
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—81no—
262C4×C11—82no—
263C4×C11—81no—
264C4×C11#39814yes—
265C4×C11C2×#12311yescharacteristic
266C4×C11C2×#12511yescharacteristic
267C4×C11C2×#12511yescharacteristic
268C4×C11C2×C4⋊Q811yescharacteristic
269Dic11—44no—
270Dic11—42no—
271Dic11—42no—
272Dic11—42no—
273Dic11—42no—
274C23×C4—21no—
275C23×C4—221no—
276C23×C4C22×D1111yescharacteristic
277C2×M16—22no—
278C2×M16—22no—
279C2×M16C22⋊D1114yes—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8—222no—
283C22×C8—222no—
284C22×C8—222no—
285C22×C8C22×D1112yes—
286#117—22no—
287#117—22no—
288#117—114no—
289#117—222no—
290#117—222no—
291#117—222no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—114no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4C22×D1112yes—
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—112no—
312C2×C22⋊C4—221no—
313C2×C42—21no—
314C2×C42—112no—
315C2×C42—221no—
316#107—24no—
317#106—24no—
318C4⋊C8—224no—
319C4⋊C8—224no—
320#95—222no—
321#95—222no—
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
332C24D4×D1111yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—42no—
337C22×C4—81no—
338C22×C4—81no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—222no—
344C22×C4—224no—
345C22×C4—881no—
346C22×C4—881no—
347C22×C4#433912yes—
348C22×C4#433912yes—
349C22×C4D4×D1111yescharacteristic
350C22×C4#434112yes—
351C22×C4Q8×D1112yes—
352C22×C4Q8×D1112yes—
353C22×C4C2×C22⋊D1112yes—
354C22×C4C23×D1111yescharacteristic
355M16—28no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—221no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8—444no—
365C2×C8C2×C22⋊D1114yes—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—42no—
373C4⋊C4—114no—
374C4⋊C4—112no—
375C4⋊C4—112no—
376C4⋊C4—224no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—222no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—882no—
383C4⋊C4—882no—
384C4⋊C4—882no—
385C4⋊C4—882no—
386C22⋊C4—42no—
387C22⋊C4—224no—
388C22⋊C4—224no—
389C42—42no—
390C42—224no—
391C42—222no—
392C42—222no—
393C11#2367111yescharacteristic, complemented, Sylow
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23#6694912yes—
399C23#6694912yes—
400C23#6699112yes—
401C23C2×D4×D1111yescharacteristic
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—84no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—224no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—222no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—442no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—884no—
428C2×C4#6694214yes—
429C2×C4#6694214yes—
430C2×C4#6694912yes—
431C2×C4#6694912yes—
432C2×C4#6698214yes—
433C2×C4#6699112yes—
434C2×C4#6699714yes—
435C2×C4C2×#433911yescharacteristic
436C2×C4C2×#433911yescharacteristic
437C2×C4C2×#434111yescharacteristic
438C2×C4C2×Q8×D1111yescharacteristic
439C2×C4C2×Q8×D1111yescharacteristic
440C2×C4C22×C22⋊D1111yescharacteristic
441C8—24no—
442C8—441no—
443C8—441no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22#1062259314yes—
451C22C2×#6694911yescharacteristic
452C22C2×#6694911yescharacteristic
453C22#1062330511yescharacteristic
454C22#1062330611yescharacteristic
455C22#1062330911yescharacteristic
456C22#1062331011yescharacteristic
457C22C2×#6699111yescharacteristic
458C4—82no—
459C4—81no—
460C4—81no—
461C4—442no—
462C4—442no—
463C4—444no—
464C4—442no—
465C4—442no—
466C4#1062259314yes—
467C4C2×#6694211yescharacteristic
468C4C2×#6694211yescharacteristic
469C4C2×#6698211yescharacteristic
470C4C2×#6699711yescharacteristic
471C2—24no—
472C2C2×#1062259311yescharacteristic
473C2#1307829011yescharacteristic
474C2#1307830111yescharacteristic
475C2#1307844511yescharacteristic
476C2#1307845611yescharacteristic
477C2#1307846611yescharacteristic
478C2#1307847711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#428D11
hypocenterC11#23671
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. #13070115C2semidirect
5. #13070115C2semidirect
6. #13070110C2semidirect
7. #13070105C2semidirect
393. C11#23671semidirect

Maximal subgroups

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

subgroupindex
C2×#106227322
#130712402
#130712322
#130701152
#130701102
#130701052
#130683362
#130683322
C2×#106221672
C2×C11×#4282
#2367111