Finite Group Databasebeta

← #14652790

Subgroups — #14652790

Order 2816.

482 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076989C211yesmaximal, characteristic
2#13068470C211yesmaximal, characteristic, complemented
3#13068364C211yesmaximal, characteristic, complemented
4C2×#10622181C211yesmaximal, characteristic, complemented
5C2×#10622102C211yesmaximal, characteristic
6C2×#10622102C211yesmaximal, characteristic
7C2×C11×#330C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9C2×#66928C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C2×Dic11⋊C8—21no—
13#10622603—21no—
14#10622603—21no—
15#10622603—21no—
16#10622603—21no—
17#10622601C411yescharacteristic
18#10622601C411yescharacteristic
19#10622587C411yescharacteristic
20#10622587C411yescharacteristic
21C42×Dic11C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23C2×#66867C2211yescharacteristic
24C11×#330—22no—
25#10622188—21no—
26#10622188—21no—
27#10622188—21no—
28#10622181—22no—
29#10622102—22no—
30#10622102—22no—
31C22×D44C2×C411yescharacteristic
32C22×Dic22C2×C411yescharacteristic
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×C4×Dic11C2×C411yescharacteristic
51C2×C4×Dic11C2×C411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C2×C4×Dic11D411yescharacteristic
54C2×C4×Dic11D411yescharacteristic
55C2×C4×Dic11D411yescharacteristic
56C22×C11⋊C8—21no—
57C22×C11⋊C8—21no—
58#66928—21no—
59#66928—21no—
60#66928—21no—
61#66928—21no—
62C11×#97—21no—
63C11×#97—21no—
64C11×#97—21no—
65C11×#97D412yes—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70Dic11⋊C8—24no—
71#66867—21no—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75#9688—111nomaximal, Sylow
76C23×D11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—41no—
90C2×D44—41no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121C4×Dic11—22no—
122C4×Dic11—41no—
123C4×Dic11—41no—
124C4×Dic11—41no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133#2861—111no—
134#1767—111no—
135#1745—111no—
136C2×#330—111no—
137C2×#330D1111yescharacteristic, complemented
138C2×#329—111no—
139C2×#329—111no—
140C23×C11C2×C22⋊C411yescharacteristic
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12411yescharacteristic
165C2×C4×C11#12711yescharacteristic
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11#10412yes—
181D44—81no—
182D44—81no—
183Dic22—81no—
184Dic22—81no—
185C8×C11—42no—
186C8×C11—42no—
187C11⋊C8—42no—
188C11⋊C8—42no—
189C2×#125C2×D1111yescharacteristic
190C2×#124—111no—
191C2×C4⋊C8—221no—
192C2×#97—111no—
193C2×#97—111no—
194C2×#97C2×D1111yescharacteristic
195C2×#97C2×D1111yescharacteristic
196#391—111no—
197#391—111no—
198#390—111no—
199#390—111no—
200#388—221no—
201#388—221no—
202#388—221no—
203#388—221no—
204C43—111no—
205#336—221no—
206#336—221no—
207#336—221no—
208#330—22no—
209#330—222no—
210#329—222no—
211#329—222no—
212C22×C11#39011yescharacteristic
213C22×C11#41311yescharacteristic
214C22×C11#41311yescharacteristic
215C22×C11C2×#10411yescharacteristic
216C22×C11#42111yescharacteristic
217C22×C11#42111yescharacteristic
218C22×C11#42111yescharacteristic
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—81no—
233C4×C11—81no—
234Dic11—22no—
235Dic11—41no—
236Dic11—41no—
237Dic11—41no—
238Dic11—81no—
239C22×Q8—111no—
240C22×D4—111no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—221no—
244C22×C8—221no—
245#125—21no—
246#125—21no—
247#125—21no—
248#125—21no—
249#124—221no—
250#124—221no—
251#124—221no—
252#124—221no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4C4×D1111yescharacteristic
256C2×C4⋊C4C4×D1111yescharacteristic
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C42—111no—
264C2×C42—111no—
265C2×C42—111no—
266C2×C42—111no—
267C2×C42—111no—
268C2×C42—111no—
269C2×C42C22×D1111yescharacteristic
270C4⋊C8—224no—
271#97—21no—
272#97—21no—
273#97—21no—
274#97—112no—
275#97—221no—
276#97—221no—
277#97—221no—
278#97C22⋊D1112yes—
279#95—221no—
280#95—221no—
281#95—221no—
282#95—221no—
283C2×C11#152911yescharacteristic
284C2×C11#153211yescharacteristic
285C2×C11#153511yescharacteristic
286C2×C11#153511yescharacteristic
287C2×C11#196311yescharacteristic
288C2×C11#196711yescharacteristic
289C2×C11#198011yescharacteristic
290D11—161no—
291C24—221no—
292C2×Q8—221no—
293C2×Q8—221no—
294C2×Q8—441no—
295C2×Q8—441no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—441no—
299C2×D4—441no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—221no—
307C22×C4C2×C4×D1111yescharacteristic
308C22×C4D4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—441no—
319C2×C8—441no—
320C2×C8—441no—
321C2×C8—441no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C22⋊C4—442no—
331C22⋊C4—442no—
332C22⋊C4—442no—
333C22⋊C4—442no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C42—222no—
339C42—441no—
340C42—441no—
341C42—441no—
342C42—441no—
343C42—441no—
344C42#433911yescharacteristic
345C42D4×D1111yescharacteristic
346C42#434111yescharacteristic
347C42C2×C22⋊D1111yescharacteristic
348C11#968811yescharacteristic, complemented, Sylow
349C23—441no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23C22⋊C4×D1111yescharacteristic
357Q8—881no—
358Q8—881no—
359D4—881no—
360D4—881no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—112no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4(C22⋊D11)⋊C411yescharacteristic
389C2×C4#6693711yescharacteristic
390C2×C4#6693811yescharacteristic
391C2×C4C4×C22⋊D1111yescharacteristic
392C2×C4#6699211yescharacteristic
393C2×C4#6699311yescharacteristic
394C8—42no—
395C8—42no—
396C8—442no—
397C8—442no—
398C22—881no—
399C22—881no—
400C22—881no—
401C22—881no—
402C22—881no—
403C22—881no—
404C22—881no—
405C22#1062236411yescharacteristic
406C22#1062236411yescharacteristic
407C22D11×#10411yescharacteristic
408C22#1062243411yescharacteristic
409C22#1062243411yescharacteristic
410C22#1062243411yescharacteristic
411C22#1062257011yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—222no—
421C4—441no—
422C4—441no—
423C4—441no—
424C4—881no—
425C2—1761no—
426C2#1306722211yescharacteristic
427C2#1306723511yescharacteristic
428C2#1306724611yescharacteristic
429C2#1306724611yescharacteristic
430C2#1306944611yescharacteristic
431C2#1306946411yescharacteristic
432C2#1306953311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#330C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenterC2×#330D11
hypocenterC11#9688
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. #13068470C2semidirect
3. #13068364C2semidirect
4. C2×#10622181C2semidirect
7. C2×C11×#330C2semidirect
137. C2×#330D11semidirect
348. C11#9688semidirect

Maximal subgroups

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

subgroupindex
#130769892
#130684702
#130683642
C2×#106221812
C2×#106221022
C2×C11×#3302
#968811