Finite Group Databasebeta

← #14654458

Subgroups — #14654458

Order 2816.

724 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 89 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
1#13079422C211yesmaximal, characteristic
2C2×#10622841C211yesmaximal, characteristic, complemented
3#13068540C211yesmaximal, characteristic, complemented
4#13066979C211yesmaximal, characteristic, complemented
5#13066976C211yesmaximal, characteristic
6#13066504C211yesmaximal, characteristic, complemented
7C2×C11×#448C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C22×C11×SD16—21no—
10C2×C11×#121C2211yescharacteristic
11C22×#4326—21no—
12C2×#66977C2211yescharacteristic
13C11×#448—22no—
14C11×#448—22no—
15C2×C11×#103—21no—
16C2×C11×C22⋊C8C2211yescharacteristic
17#10622841—22no—
18#10622841—22no—
19C2×#66900—22no—
20C2×#66899—21no—
21#10622831—21no—
22#10622820C2211yescharacteristic
23#10622820C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622655—22no—
26#10622653—21no—
27#10622646—21no—
28#10622583—21no—
29#10622163—22no—
30#10622107—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—44no—
37C22×Q8×C11D412yes—
38C22×D4×C11—21no—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C22×Dic22D411yescharacteristic
43C2×C11×SD16—24no—
44C2×C11×SD16—44no—
45C22×C8×C11—21no—
46C11×#121—21no—
47C11×#121—21no—
48C11×#121—21no—
49C11×#121—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C22⋊Dic11—21no—
53C2×#4326—24no—
54C2×#4326—44no—
55C2×#4324—22no—
56C2×C4⋊Dic11D411yescharacteristic
57#66977—21no—
58#66977—21no—
59#66977—21no—
60#66977—21no—
61C2×Dic11⋊C4—21no—
62C2×#4318—21no—
63C2×#4318D412yes—
64C22×C11⋊C8—21no—
65C11×#103—24no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8D412yes—
68#66900—44no—
69#66899—24no—
70#66896—22no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yes—
77#66874—22no—
78#66871—22no—
79#9989—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11#4111yescharacteristic
82C2×Q8×C11—24no—
83C2×Q8×C11—24no—
84C2×Q8×C11—24no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—44no—
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C2×Q8×C11—44no—
92C2×Q8×C11—44no—
93C2×Q8×C11—41no—
94C2×Q8×C11—41no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—42no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—82no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—42no—
104C22×C4×C11—44no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—21no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×Dic22—42no—
118C11×SD16—48no—
119C2×C8×C11—22no—
120C2×C8×C11—42no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C22⋊Dic11—41no—
126C22⋊Dic11—41no—
127#4326—48no—
128#4324—82no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133#4318—42no—
134#4318—42no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—42no—
138C2×C11⋊C8—41no—
139#3193—111no—
140C2×#451—111no—
141C2×#448D1111yescharacteristic
142#1784—111no—
143#1472—111no—
144#1471—111no—
145#1298—111no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11#12111yescharacteristic
154C23×C11#12111yescharacteristic
155C23×C11#12111yescharacteristic
156Q8×C11—24no—
157Q8×C11—24no—
158Q8×C11—42no—
159Q8×C11—42no—
160Q8×C11—44no—
161Q8×C11—44no—
162D4×C11—42no—
163D4×C11—42no—
164D4×C11—82no—
165D4×C11—82no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—81no—
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12711yescharacteristic
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—81no—
187Dic22—42no—
188Dic22—42no—
189C8×C11—42no—
190C11⋊C8—42no—
191C11⋊C8—42no—
192C11⋊C8—81no—
193C23×Q8C2×D1111yescharacteristic
194C22×Q16—221no—
195C22×SD16—21no—
196C2×C22⋊Q8—111no—
197C2×#121C2×D1111yescharacteristic
198#484—221no—
199#480—221no—
200#468—222no—
201#451—222no—
202#451—222no—
203#450—221no—
204#448—22no—
205#448—22no—
206#448—221no—
207C2×#103—21no—
208C2×#103—221no—
209C2×#101—222no—
210#407—111no—
211#407—111no—
212C2×C22⋊C8—111no—
213C2×C22⋊C8C2×D1111yescharacteristic
214#324—222no—
215#323—222no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—44no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—162no—
228C22×C11#39211yescharacteristic
229C22×C11#47112yes—
230C22×C11#47312yes—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—44no—
235C4×C11—81no—
236C4×C11B(4,𝔽2)12yes—
237Dic11—81no—
238Dic11—81no—
239C22×Q8—21no—
240C22×Q8—21no—
241C22×Q8—21no—
242C22×Q8—21no—
243C22×Q8—21no—
244C22×Q8—44no—
245C22×Q8—111no—
246C22×Q8C22⋊D1112yes—
247C22×D4—21no—
248C22×D4C22⋊D1111yescharacteristic
249C23×C4—21no—
250C23×C4C22×D1111yescharacteristic
251C2×Q16—224no—
252C2×Q16—444no—
253C2×SD16—24no—
254C2×SD16—44no—
255C2×SD16—222no—
256C2×M16—112no—
257C2×M16—221no—
258C22×C8—21no—
259C22×C8—221no—
260C22⋊Q8—221no—
261C22⋊Q8—221no—
262C22⋊Q8—221no—
263C22⋊Q8—221no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4C22⋊D1111yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—221no—
273#107—222no—
274#103—24no—
275#103—222no—
276#103—224no—
277#102—222no—
278#101—444no—
279C22⋊C8—21no—
280C22⋊C8—112no—
281C22⋊C8—221no—
282C22⋊C8—221no—
283C22⋊C8—221no—
284C22⋊C8—221no—
285C22⋊C8—221no—
286C22⋊C8C22⋊D1112yes—
287C2×C11—22no—
288C2×C11—22no—
289C2×C11—41no—
290C2×C11—161no—
291C2×C11#201911yescharacteristic
292C2×C11#202011yescharacteristic
293C2×C11#202111yescharacteristic
294C24—21no—
295C24#434111yescharacteristic
296C2×Q8—24no—
297C2×Q8—24no—
298C2×Q8—24no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—42no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8—44no—
306C2×Q8—44no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—221no—
310C2×Q8—221no—
311C2×Q8—442no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—42no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—82no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—42no—
321C22×C4—44no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4D4×D1111yescharacteristic
327C22×C4D4×D1111yescharacteristic
328C22×C4D4×D1111yescharacteristic
329C22×C4C2×C22⋊D1111yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332Q16—448no—
333SD16—48no—
334SD16—882no—
335M16—442no—
336M16—442no—
337C2×C8—22no—
338C2×C8—42no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—442no—
342C2×C8—441no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C11#998911yescharacteristic, complemented, Sylow
354C23—22no—
355C23—22no—
356C23—41no—
357C23—41no—
358C23—42no—
359C23—81no—
360C23—81no—
361C23#6699111yescharacteristic
362C23#6699211yescharacteristic
363C23#6699211yescharacteristic
364Q8—24no—
365Q8—24no—
366Q8—42no—
367Q8—42no—
368Q8—44no—
369Q8—44no—
370Q8—442no—
371Q8—442no—
372D4—42no—
373D4—42no—
374D4—82no—
375D4—82no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—81no—
389C2×C4—442no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—881no—
393C2×C4#6699011yescharacteristic
394C2×C4#6699011yescharacteristic
395C2×C4#6699311yescharacteristic
396C2×C4#6700611yescharacteristic
397C8—42no—
398C8—442no—
399C8—442no—
400C8—881no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—44no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—162no—
413C22#1062279012yes—
414C22#1062281712yes—
415C22#1062283611yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—44no—
420C4—81no—
421C4—881no—
422C4—881no—
423C4#1062264512yes—
424C2—22no—
425C2—22no—
426C2—41no—
427C2—161no—
428C2#1306972811yescharacteristic
429C2#1306973411yescharacteristic
430C2#1306973911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#448C2
socleC22×C11#392
prime radicalC2×C11×#121C22
hypercenterC2×#448D11
hypocenterC11#9989
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C2×#10622841C2semidirect
3. #13068540C2semidirect
4. #13066979C2semidirect
6. #13066504C2semidirect
353. C11#9989semidirect

Maximal subgroups

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

subgroupindex
#130794222
C2×#106228412
#130685402
#130669792
#130669762
#130665042
C2×C11×#4482
#998911