Finite Group Databasebeta

← #14654341

Subgroups — #14654341

Order 2816.

658 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#10622581C211yesmaximal, characteristic
2#13074550C211yesmaximal, characteristic
3C2×#10622176C211yesmaximal, characteristic, complemented
4C2×#10622108C211yesmaximal, characteristic
5#13066884C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C2×C11×#484C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66983C2211yescharacteristic
11C11×#484—22no—
12C11×#484—22no—
13C2×C11×#107—21no—
14C2×C11×#103—21no—
15C2×C11×C22⋊C8C2211yescharacteristic
16#10622844—21no—
17C2×C11⋊#95—22no—
18C2×C11⋊#95C2211yescharacteristic
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21#10622606—21no—
22#10622604—21no—
23#10622599—21no—
24#10622581—22no—
25#10622581—22no—
26C2×#66873—21no—
27C2×#66872—21no—
28#10622571—22no—
29#10622176—22no—
30#10622108—22no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C23×Dic11—21no—
36C23×Dic11D412yes—
37C22×D44D411yescharacteristic
38C22×C8×C11—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D412yes—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52#66983—21no—
53#66983—21no—
54#66983—21no—
55#66983—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11D411yescharacteristic
60C22×C11⋊C8—21no—
61C11×#107—24no—
62C11×#103—24no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8D412yes—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—44no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)D412yes—
74#66873—24no—
75#66872—24no—
76#9969—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C23×D11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—42no—
99C2×C22⋊D11—42no—
100C22×Dic11—22no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—42no—
106C22×Dic11—42no—
107C22×Dic11—41no—
108C22×Dic11—42no—
109C22×Dic11—41no—
110C22×Dic11—42no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—42no—
114C2×C8×C11—22no—
115C2×C8×C11—42no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—82no—
129(C2×D11)⋊C4—82no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—42no—
134C2×#484D1111yescharacteristic, complemented
135C2×#481—111no—
136#2639—111no—
137C2×#328—111no—
138C2×#327—111no—
139#1445—111no—
140#1280—111no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—22no—
144C23×C11#12011yescharacteristic
145C23×C11#12111yescharacteristic
146C23×C11#12711yescharacteristic
147C23×C11#13512yes—
148C23×C11#13712yes—
149C22×D11—41no—
150C22×D11—42no—
151C22×D11—41no—
152C22×D11—41no—
153C22×D11—42no—
154Q8×C11—42no—
155Q8×C11—81no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—44no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—82no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C22⋊D11—82no—
177C22⋊D11—81no—
178C22⋊D11—81no—
179C2×Dic11—44no—
180C2×Dic11—42no—
181C2×Dic11—44no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—82no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11—82no—
191D44—42no—
192D44—81no—
193C8×C11—42no—
194C11⋊C8—42no—
195C2×C22⋊Q8C2×D1111yescharacteristic
196C2×#121—111no—
197C22×C4⋊C4C2×D1111yescharacteristic
198#484—22no—
199#484—22no—
200#481—222no—
201#481—222no—
202C2×#107—21no—
203C2×#106—221no—
204C2×#103—21no—
205C2×#102—221no—
206C2×C22⋊C8—111no—
207C2×C22⋊C8C2×D1111yescharacteristic
208#400—221no—
209#397—221no—
210#394—221no—
211#393—221no—
212#386—222no—
213C2×#95—111no—
214C2×#95—111no—
215C2×#95—222no—
216#328—222no—
217#327—222no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11#39211yescharacteristic
227C22×C11#45212yes—
228C22×C11#45311yescharacteristic
229C22×C11#45411yescharacteristic
230C22×C11#45812yes—
231C22×C11#46412yes—
232C22×C11#49511yescharacteristic
233C22×C11#49711yescharacteristic
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—81no—
244C4×C11—82no—
245C4×C11—81no—
246Dic11—82no—
247Dic11—82no—
248Dic11—81no—
249C22×Q8C22⋊D1111yescharacteristic
250C22×D4—111no—
251C22×D4—221no—
252C23×C4—21no—
253C23×C4—112no—
254C23×C4—221no—
255C23×C4C22×D1111yescharacteristic
256C22×C8—21no—
257C22×C8—221no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262#121—221no—
263#121—221no—
264#121—221no—
265#121—221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4C22⋊D1112yes—
274C2×C4⋊C4C22⋊D1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—222no—
278C2×C22⋊C4—222no—
279#107—24no—
280#106—224no—
281#103—24no—
282#102—224no—
283C22⋊C8—21no—
284C22⋊C8—112no—
285C22⋊C8—221no—
286C22⋊C8C22⋊D1112yes—
287#95—222no—
288#95—222no—
289#95—221no—
290#95—221no—
291#95—221no—
292#95—221no—
293#95—444no—
294C2×C11—21no—
295C2×C11—22no—
296C2×C11—21no—
297C2×C11#161512yes—
298C2×C11#161812yes—
299C2×C11#200611yescharacteristic
300C2×C11#201511yescharacteristic
301C2×C11#202211yescharacteristic
302D11—161no—
303C24—221no—
304C24D4×D1111yescharacteristic
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—42no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—442no—
311C2×D4—442no—
312C2×D4—442no—
313C2×D4—441no—
314C2×D4—441no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—222no—
324C22×C4—222no—
325C22×C4—222no—
326C22×C4—221no—
327C22×C4—222no—
328C22×C4—442no—
329C22×C4—442no—
330C22×C4—441no—
331C22×C4—442no—
332C22×C4—442no—
333C22×C4—441no—
334C22×C4D4×D1111yescharacteristic
335C22×C4D4×D1111yescharacteristic
336C22×C4#434111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339C22×C4C2×C22⋊D1111yescharacteristic
340C2×C8—22no—
341C2×C8—42no—
342C2×C8—222no—
343C2×C8—442no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—221no—
353C4⋊C4—221no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C22⋊C4—882no—
359C22⋊C4—882no—
360C11#996911yescharacteristic, complemented, Sylow
361C23—21no—
362C23—21no—
363C23—22no—
364C23—442no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23—442no—
369C23#6697112yes—
370C23#6697212yes—
371C23#6699011yescharacteristic
372C23#6699211yescharacteristic
373C23#6699311yescharacteristic
374Q8—42no—
375Q8—81no—
376D4—442no—
377D4—881no—
378D4—882no—
379D4—881no—
380D4—881no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—442no—
398C2×C4—444no—
399C2×C4—444no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—441no—
404C2×C4—442no—
405C2×C4—882no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4—882no—
409C2×C4#6699011yescharacteristic
410C2×C4#6699111yescharacteristic
411C2×C4#6699211yescharacteristic
412C2×C4#6700611yescharacteristic
413C8—42no—
414C8—442no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—21no—
422C22—21no—
423C22—881no—
424C22—882no—
425C22—881no—
426C22—882no—
427C22—881no—
428C22#1062266612yes—
429C22#1062279812yes—
430C22#1062280012yes—
431C22#1062280311yescharacteristic
432C22#1062280411yescharacteristic
433C22#1062281111yescharacteristic
434C22#1062281411yescharacteristic
435C22#1062283611yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—81no—
442C4—81no—
443C4—882no—
444C4—881no—
445C4—882no—
446C2—21no—
447C2—22no—
448C2—21no—
449C2—1761no—
450C2#1306764612yes—
451C2#1306766312yes—
452C2#1306965611yescharacteristic
453C2#1306970711yescharacteristic
454C2#1306974411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#484C2
socleC23×C11#120
prime radicalC2×#66983C22
hypercenterC2×#484D11
hypocenterC11#9969
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. C2×#10622176C2semidirect
5. #13066884C2semidirect
6. #13066458C2semidirect
7. C2×C11×#484C2semidirect
134. C2×#484D11semidirect
360. C11#9969semidirect

Maximal subgroups

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

subgroupindex
C2×#106225812
#130745502
C2×#106221762
C2×#106221082
#130668842
#130664582
C2×C11×#4842
#996911