Finite Group Databasebeta

← #14654450

Subgroups — #14654450

Order 2816.

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

normal subgroups only

This group has 750 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#13079413C211yesmaximal, characteristic
2C2×#10622840C211yesmaximal, characteristic, complemented
3#13068540C211yesmaximal, characteristic, complemented
4#13066976C211yesmaximal, characteristic, complemented
5#13066975C211yesmaximal, characteristic, complemented
6#13066504C211yesmaximal, characteristic, complemented
7C2×C11×#448C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C22×C11×SD16—21no—
10C2×C11×#121C2211yescharacteristic
11C22×#4325—21no—
12C2×#66983C2211yescharacteristic
13C11×#448—22no—
14C11×#448—22no—
15C2×C11×#103—21no—
16C2×C11×C22⋊C8C2211yescharacteristic
17#10622840—22no—
18#10622840—22no—
19C2×#66900—22no—
20C2×#66899—21no—
21#10622830—21no—
22#10622820C2211yescharacteristic
23#10622820C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622652—22no—
26#10622649—21no—
27#10622647—21no—
28#10622581—21no—
29#10622163—22no—
30#10622106—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×C22⋊D11—21no—
43C22×D44D411yescharacteristic
44C2×C11×SD16—24no—
45C2×C11×SD16—44no—
46C22×C8×C11—21no—
47C11×#121—21no—
48C11×#121—21no—
49C11×#121—21no—
50C11×#121—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×#4325—24no—
54C2×#4325—44no—
55C2×#4323—22no—
56#66983—21no—
57#66983—21no—
58#66983—21no—
59#66983—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×C4⋊Dic11D411yescharacteristic
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#66873—22no—
78#66872—22no—
79#9988—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11#4111yescharacteristic
82C23×D11—21no—
83C2×Q8×C11—24no—
84C2×Q8×C11—24no—
85C2×Q8×C11—24no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—44no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C2×Q8×C11—44no—
93C2×Q8×C11—44no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—42no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—82no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—42no—
105C22×C4×C11—44no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C2×C22⋊D11—41no—
115C2×C22⋊D11—41no—
116C2×C22⋊D11—82no—
117C22×Dic11—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—42no—
121C11×SD16—48no—
122C2×C8×C11—22no—
123C2×C8×C11—42no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128#4325—48no—
129#4323—82no—
130(C2×D11)⋊C4—41no—
131(C2×D11)⋊C4—41no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134#4318—42no—
135#4318—42no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—42no—
139C2×C11⋊C8—41no—
140#3192—111no—
141C2×#448—111no—
142C2×#448D1111yescharacteristic, complemented
143#1784—111no—
144#1471—111no—
145#1471—111no—
146#1298—111no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—42no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11#12111yescharacteristic
155C23×C11#12111yescharacteristic
156C23×C11#12111yescharacteristic
157C22×D11—41no—
158C22×D11—42no—
159C22×D11—81no—
160C22×D11—81no—
161Q8×C11—24no—
162Q8×C11—24no—
163Q8×C11—42no—
164Q8×C11—42no—
165Q8×C11—44no—
166Q8×C11—44no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—82no—
170D4×C11—82no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—44no—
180C2×C4×C11—44no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—81no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12711yescharacteristic
188C22⋊D11—82no—
189C22⋊D11—82no—
190C2×Dic11—41no—
191C2×Dic11—81no—
192D44—42no—
193D44—42no—
194C8×C11—42no—
195C11⋊C8—42no—
196C11⋊C8—42no—
197C11⋊C8—81no—
198C23×Q8C2×D1111yescharacteristic
199C22×SD16—21no—
200C22×SD16—221no—
201C2×#121—111no—
202C2×#121C2×D1111yescharacteristic
203#481—221no—
204#481—221no—
205#469—222no—
206#448—22no—
207#448—22no—
208#448—222no—
209#448—222no—
210#447—221no—
211#447—221no—
212C2×#103—21no—
213C2×#103—221no—
214C2×#101—222no—
215#407—111no—
216#407—111no—
217C2×C22⋊C8—111no—
218C2×C22⋊C8C2×D1111yescharacteristic
219#323—222no—
220#323—222no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—44no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—162no—
233C22×C11#39211yescharacteristic
234C22×C11#47112yes—
235C22×C11#47112yes—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C2×D11—162no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—44no—
244C4×C11—81no—
245C4×C11B(4,𝔽2)12yes—
246Dic11—81no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—44no—
253C22×Q8C22⋊D1112yes—
254C22×D4—21no—
255C22×D4—111no—
256C22×D4—221no—
257C22×D4C22⋊D1111yescharacteristic
258C23×C4—21no—
259C23×C4C22×D1111yescharacteristic
260C2×SD16—24no—
261C2×SD16—44no—
262C2×SD16—224no—
263C2×SD16—444no—
264C2×D8—222no—
265C2×M16—112no—
266C2×M16—221no—
267C22×C8—21no—
268C22×C8—221no—
269#121—21no—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—221no—
274#121—221no—
275#121—221no—
276#121—221no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4C22⋊D1111yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—221no—
281#106—222no—
282#103—24no—
283#103—224no—
284#102—222no—
285#102—222no—
286#101—444no—
287C22⋊C8—21no—
288C22⋊C8—112no—
289C22⋊C8—221no—
290C22⋊C8—221no—
291C22⋊C8—221no—
292C22⋊C8—221no—
293C22⋊C8—221no—
294C22⋊C8C22⋊D1112yes—
295C2×C11—22no—
296C2×C11—22no—
297C2×C11—41no—
298C2×C11—161no—
299C2×C11#201911yescharacteristic
300C2×C11#201911yescharacteristic
301C2×C11#202111yescharacteristic
302D11—161no—
303C24—21no—
304C24—221no—
305C24#434111yescharacteristic
306C2×Q8—24no—
307C2×Q8—24no—
308C2×Q8—24no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—44no—
312C2×Q8—42no—
313C2×Q8—42no—
314C2×Q8—42no—
315C2×Q8—44no—
316C2×Q8—44no—
317C2×Q8—41no—
318C2×Q8—41no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—42no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—82no—
325C2×D4—221no—
326C2×D4—221no—
327C2×D4—442no—
328C2×D4—441no—
329C2×D4—441no—
330C2×D4—882no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—42no—
334C22×C4—44no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—221no—
338C22×C4D4×D1111yescharacteristic
339C22×C4D4×D1111yescharacteristic
340C22×C4D4×D1111yescharacteristic
341C22×C4C2×C22⋊D1111yescharacteristic
342C22×C4C2×C22⋊D1111yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344SD16—48no—
345SD16—448no—
346D8—882no—
347M16—442no—
348M16—442no—
349C2×C8—22no—
350C2×C8—42no—
351C2×C8—222no—
352C2×C8—222no—
353C2×C8—442no—
354C2×C8—441no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—221no—
358C4⋊C4—221no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C11#998811yescharacteristic, complemented, Sylow
364C23—22no—
365C23—22no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—441no—
372C23—442no—
373C23—881no—
374C23—881no—
375C23#6699111yescharacteristic
376C23#6699211yescharacteristic
377C23#6699211yescharacteristic
378Q8—24no—
379Q8—24no—
380Q8—42no—
381Q8—42no—
382Q8—44no—
383Q8—44no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—82no—
388D4—442no—
389D4—442no—
390D4—882no—
391D4—882no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—441no—
406C2×C4—881no—
407C2×C4#6699011yescharacteristic
408C2×C4#6699011yescharacteristic
409C2×C4#6699311yescharacteristic
410C2×C4#6700611yescharacteristic
411C8—42no—
412C8—442no—
413C8—442no—
414C8—881no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—44no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—162no—
427C22—881no—
428C22—881no—
429C22—881no—
430C22—1762no—
431C22#1062279012yes—
432C22#1062281612yes—
433C22#1062283611yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—44no—
438C4—81no—
439C4—881no—
440C4#1062264512yes—
441C2—22no—
442C2—22no—
443C2—41no—
444C2—161no—
445C2—1761no—
446C2#1306972711yescharacteristic
447C2#1306972811yescharacteristic
448C2#1306973911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#448C2
socleC22×C11#392
prime radical#13079413C2
hypercenterC2×#448D11
hypocenterC11#9988
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×#10622840C2semidirect
3. #13068540C2semidirect
4. #13066976C2semidirect
5. #13066975C2semidirect
6. #13066504C2semidirect
7. C2×C11×#448C2semidirect
142. C2×#448D11semidirect
363. C11#9988semidirect

Maximal subgroups

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

subgroupindex
#130794132
C2×#106228402
#130685402
#130669762
#130669752
#130665042
C2×C11×#4482
#998811