Finite Group Databasebeta

← #14671310

Subgroups — #14671310

Order 2816.

702 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66900C211yesmaximal, characteristic, complemented
2#13072270C211yesmaximal, characteristic
3C2×#10622115C212yesmaximal, complemented
4#13066742C212yesmaximal, complemented
5C11×#1784C211yesmaximal, characteristic, complemented
6C23×Q8×C11C2211yescharacteristic
7C2×#67000C411yescharacteristic
8C2×#67000C2211yescharacteristic
9C2×#66983C411yescharacteristic
10C22×#4318—21no—
11C2×C11×#101—21no—
12C2×C11×#101C2212yes—
13C11×#407—21no—
14#10622844—21no—
15#10622844—21no—
16#10622843C411yescharacteristic
17#10622843C2211yescharacteristic
18C2×#66900—21no—
19C2×#66900—24no—
20C2×#66900C2212yes—
21#10622826—21no—
22#10622826—21no—
23C4×C22⋊Dic11C411yescharacteristic
24#10622115—24no—
25C22×Q8×C11—22no—
26C22×Q8×C11—22no—
27C22×Q8×C11—41no—
28C22×Q8×C11—41no—
29C22×Q8×C11—42no—
30C22×Q8×C11C2×C411yescharacteristic
31C22×Q8×C11D411yescharacteristic
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11C2311yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C22×C22⋊D11—21no—
38C22×D44C2×C411yescharacteristic
39C2×C11×M16—22no—
40C2×C22⋊Dic11—21no—
41#67000—22no—
42#67000—22no—
43#67000—42no—
44#66983—41no—
45#66983—41no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×C4×Dic11C2×C411yescharacteristic
53C2×C4×Dic11C2×C411yescharacteristic
54C2×#4318—24no—
55C2×#4318—22no—
56C2×#4318—41no—
57C2×#4318—42no—
58C22×C11⋊C8—41no—
59C11×#101—22no—
60C11×#101—22no—
61C11×#101—42no—
62C11×C22⋊C8—41no—
63C11×C22⋊C8—41no—
64#66900—24no—
65#66900—22no—
66#66900D414yescomplemented
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72#13092—111nomaximal, Sylow
73C24×C11C22⋊C411yescharacteristic
74C23×D11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—44no—
88C2×Q8×C11—44no—
89C2×Q8×C11—44no—
90C2×Q8×C11—44no—
91C2×Q8×C11C2×D412yes—
92C2×Q8×C11#4112yes—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11C22⋊C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C2×C22⋊D11—44no—
113C2×C22⋊D11—41no—
114C2×C22⋊D11—41no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C2×D44—22no—
119C2×D44—41no—
120C2×D44—41no—
121C11×M16—42no—
122C11×M16—42no—
123C2×C8×C11—42no—
124C22⋊Dic11—42no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—41no—
131C4⋊Dic11—41no—
132C4×Dic11—22no—
133C4×Dic11—41no—
134#4318—24no—
135#4318—44no—
136#4318—42no—
137C2×C11⋊C8—44no—
138C2×C11⋊C8—42no—
139C22×#101—111no—
140#2436—111no—
141C2×#355—112no—
142#1784D1111yescharacteristic, complemented
143#1394—112no—
144C23×C11—22no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—41no—
148C23×C11#9911yescharacteristic
149C23×C11#9911yescharacteristic
150C23×C11C2×C22⋊C411yescharacteristic
151C22×D11—42no—
152C22×D11—42no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156Q8×C11—42no—
157Q8×C11—42no—
158Q8×C11—44no—
159Q8×C11—44no—
160Q8×C11—42no—
161Q8×C11—42no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
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—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11#9912yes—
185C2×C4×C11C4×D412yes—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12112yes—
188C2×C4×C11#12311yescharacteristic
189C22⋊D11—82no—
190C22⋊D11—82no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199D44—82no—
200C8×C11—82no—
201C11⋊C8—44no—
202C23×Q8C2×D1111yescharacteristic
203C22×M16—221no—
204C2×#124—111no—
205C2×#124—111no—
206C2×#121—111no—
207C2×#101—21no—
208C2×#101—112no—
209C2×#101—224no—
210C2×#101—221no—
211C2×#101C2×D1112yes—
212#407—21no—
213#393—221no—
214#393—221no—
215#391—111no—
216#391—111no—
217#386—221no—
218#386—221no—
219C4×C22⋊C4—111no—
220#355—224no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11#35512yescomplemented
231C22×C11#38611yescharacteristic
232C22×C11C2×#9911yescharacteristic
233C22×C11C2×#9911yescharacteristic
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C4×C11—22no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—22no—
243C4×C11—22no—
244C4×C11—41no—
245C4×C11—41no—
246Dic11—81no—
247Dic11—81no—
248Dic11—81no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—41no—
252C22×Q8—41no—
253C22×Q8—42no—
254C22×Q8C4×D1111yescharacteristic
255C22×Q8D4411yescharacteristic
256C22×Q8C22⋊D1111yescharacteristic
257C22×Q8C22×D1111yescharacteristic
258C22×D4—111no—
259C22×D4—221no—
260C23×C4C4×D1111yescharacteristic
261C23×C4D4411yescharacteristic
262C23×C4C22⋊D1111yescharacteristic
263C2×M16—22no—
264C2×M16—224no—
265C2×M16—222no—
266C2×M16—441no—
267C2×M16—442no—
268C22×C8—441no—
269#124—222no—
270#124—222no—
271#124—442no—
272#121—441no—
273#121—441no—
274C2×C4⋊C4—111no—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—221no—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—221no—
281C2×C42—111no—
282C2×C42—111no—
283#101—22no—
284#101—22no—
285#101—42no—
286#101—114no—
287#101—224no—
288#101—222no—
289C22⋊C8—41no—
290C22⋊C8—41no—
291#95—221no—
292#95—221no—
293#95—221no—
294#95—221no—
295#95—221no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—22no—
299C2×C11—41no—
300C2×C11#189811yescharacteristic
301C2×C11C2×#35511yescharacteristic
302C2×C11#213311yescharacteristic
303D11—161no—
304C24—221no—
305C24(C2×D11)⋊C411yescharacteristic
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—22no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—44no—
319C2×Q8—44no—
320C2×Q8—44no—
321C2×Q8—44no—
322C2×Q8D4×D1112yes—
323C2×Q8#434112yes—
324C2×D4—222no—
325C2×D4—441no—
326C2×D4—441no—
327C2×D4—444no—
328C2×D4—441no—
329C2×D4—441no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4(C2×D11)⋊C411yescharacteristic
347C22×C4(C2×D11)⋊C411yescharacteristic
348C22×C4(C2×D11)⋊C411yescharacteristic
349C22×C4C2×C4×D1111yescharacteristic
350C22×C4C2×D4411yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352M16—42no—
353M16—42no—
354M16—224no—
355M16—444no—
356M16—442no—
357C2×C8—42no—
358C2×C8—444no—
359C2×C8—442no—
360C4⋊C4—441no—
361C22⋊C4—442no—
362C22⋊C4—442no—
363C22⋊C4—442no—
364C22⋊C4—442no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—442no—
368C42—222no—
369C42—441no—
370C11#1309211yescharacteristic, complemented, Sylow
371C23—21no—
372C23—21no—
373C23—22no—
374C23—41no—
375C23—442no—
376C23—442no—
377C23—441no—
378C23—441no—
379C23—441no—
380C23#6687011yescharacteristic
381C23#6687011yescharacteristic
382C23C2×(C2×D11)⋊C411yescharacteristic
383Q8—42no—
384Q8—42no—
385Q8—44no—
386Q8—44no—
387Q8—42no—
388Q8—42no—
389D4—882no—
390D4—882no—
391D4—882no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4#6687012yes—
423C2×C4(C22⋊D11)⋊C412yes—
424C2×C4#6693511yescharacteristic
425C2×C4#6693911yescharacteristic
426C2×C4#6699212yes—
427C8—82no—
428C8—444no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—882no—
439C22—882no—
440C22—881no—
441C22—881no—
442C22—881no—
443C22#1062211512yescomplemented
444C22C2×#6687011yescharacteristic
445C22C2×#6687011yescharacteristic
446C22#1062257111yescharacteristic
447C4—22no—
448C4—21no—
449C4—22no—
450C4—21no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—881no—
455C4—881no—
456C4—881no—
457C2—21no—
458C2—21no—
459C2—22no—
460C2—41no—
461C2—1761no—
462C2#1306906711yescharacteristic
463C2C2×#1062211511yescharacteristic
464C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#1784C2
socleC22×C11C2×#99
prime radicalC2×#66983C4
cosocleC22×Q8×C11C23
hypercenter#1784D11
hypocenterC11#13092
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #1784

Complements

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

NH ≅ G/Ntype
1. C22×#66900C2semidirect
3. C2×#10622115C2semidirect
4. #13066742C2semidirect
5. C11×#1784C2semidirect
66. #66900D4semidirect
142. #1784D11semidirect
230. C22×C11#355semidirect
370. C11#13092semidirect
443. C22#10622115semidirect

Maximal subgroups

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

subgroupindex
C22×#669002
#130722702
C2×#106221152
#130667422
C11×#17842
#1309211