Finite Group Databasebeta

← #14648841

Subgroups — #14648841

Order 2816.

534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077644C211yesmaximal, characteristic
2#13071902C211yesmaximal, characteristic
3C4×#66887C211yesmaximal, characteristic
4#13067064C211yesmaximal, characteristic, complemented
5#13067062C211yesmaximal, characteristic, complemented
6#13066509C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C11×#376C2211yescharacteristic
13C2×#66887—21no—
14C4×(C2×D11)⋊C4—21no—
15C4×(C2×D11)⋊C4—21no—
16#10622539C2211yescharacteristic
17C4×#4318C2211yescharacteristic
18#10622449—22no—
19#10622339—21no—
20D11×C22⋊C8—21no—
21#10622319—22no—
22#10622287C411yescharacteristic
23#10622287C411yescharacteristic
24#10622286C411yescharacteristic
25#10622286C411yescharacteristic
26#10622285—21no—
27#10622272—21no—
28#10622192—21no—
29#10622122—22no—
30#10622094—22no—
31C22×D44D411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C22×Dic22C2×C411yescharacteristic
35C2×C11×M16—21no—
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4C2×C411yescharacteristic
43C2×(C2×D11)⋊C4C2×C411yescharacteristic
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11—21no—
48C2×#4318—21no—
49C2×#4313—22no—
50C2×C8×D11—22no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22—21no—
58C4×Dic22—21no—
59C11×C4⋊C8D412yes—
60C11×C22⋊C8—21no—
61C11×#97—21no—
62C11×#97—21no—
63C4×C8×C11—21no—
64C11×#95—21no—
65C11×#95C2×C411yescharacteristic
66C11×#95C2×C411yescharacteristic
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)—21no—
72#66887—24no—
73(C2×D11)⋊C8—22no—
74(C2×D11)⋊C8—22no—
75C4⋊(C11⋊C8)D412yes—
76#66867—21no—
77#66867—21no—
78C4×C11⋊C8—21no—
79#9029—111nomaximal, Sylow
80C23×D11C22⋊C411yescharacteristic
81C23×D11C22⋊C411yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C2×D44—22no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—41no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C2×C4×D11—42no—
100C2×C4×D11—42no—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—42no—
104C11×M16—22no—
105C11×M16—41no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C42×C11—42no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113(C2×D11)⋊C4—21no—
114(C2×D11)⋊C4—21no—
115(C2×D11)⋊C4—21no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—42no—
118(C2×D11)⋊C4—42no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—42no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129#4318—22no—
130#4318—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133#4313—82no—
134C8×D11—82no—
135#2973—111no—
136#2398—111no—
137C4×#100—111no—
138#1491—111no—
139#1491—111no—
140#1300—111no—
141#1300D1111yescharacteristic, complemented
142C23×C11C2×C22⋊C411yescharacteristic
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11#10412yes—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12311yescharacteristic
169C2×Dic11—22no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179D44—42no—
180D44—42no—
181C4×D11—42no—
182C4×D11—42no—
183C4×D11—81no—
184C4×D11—81no—
185Dic22—22no—
186Dic22—22no—
187Dic22—41no—
188Dic22—41no—
189C8×C11—42no—
190C8×C11—42no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C2×C4×Q8—111no—
194C2×C4×D4—111no—
195#435—222no—
196#435—222no—
197#432—111no—
198#432C2×D1111yescharacteristic
199C2×#100—221no—
200#407—221no—
201C2×C22⋊C8—221no—
202C4×M16—111no—
203C4×M16C2×D1111yescharacteristic
204#400—221no—
205#397—111no—
206#397—111no—
207#394—221no—
208#393—111no—
209#393—111no—
210C4×C22⋊C4—221no—
211C4×C22⋊C4—221no—
212#376C2×D1111yescharacteristic
213#343—221no—
214Q8⋊C8—222no—
215Q8⋊C8—222no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11#38611yescharacteristic
219C22×C11C2×#10411yescharacteristic
220C22×C11#42111yescharacteristic
221C2×D11—22no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—81no—
230C2×D11—81no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—81no—
237C4×C11—81no—
238C4×C11#45512yes—
239Dic11—41no—
240Dic11—41no—
241Dic11—42no—
242Dic11—81no—
243C22×Q8—111no—
244C22×D4—111no—
245C23×C4—111no—
246C23×C4—111no—
247C2×M16—21no—
248C2×M16—222no—
249C2×M16—221no—
250C22×C8—222no—
251C4×Q8—221no—
252C4×Q8—221no—
253C4×Q8—221no—
254C4×Q8—221no—
255C4×D4—221no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—221no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—221no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C42—21no—
269C2×C42—221no—
270C2×C42C22×D1111yescharacteristic
271C4⋊C8—112no—
272C4⋊C8D4412yes—
273#100—224no—
274C22⋊C8—21no—
275C22⋊C8—222no—
276C22⋊C8—222no—
277C22⋊C8—221no—
278#97—21no—
279#97—21no—
280#97—221no—
281#97—221no—
282C4×C8—21no—
283C4×C8—221no—
284#95—21no—
285#95—221no—
286#95—221no—
287#95—221no—
288#95—221no—
289#95C4×D1111yescharacteristic
290#95C4×D1111yescharacteristic
291C2×C11—21no—
292C2×C11—21no—
293C2×C11#187111yescharacteristic
294C2×C11#188511yescharacteristic
295C2×C11#189111yescharacteristic
296D11—42no—
297D11—81no—
298C24—111no—
299C24—111no—
300C2×Q8—221no—
301C2×Q8—221no—
302C2×Q8—442no—
303C2×D4—222no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—441no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322M16—22no—
323M16—41no—
324M16—222no—
325M16—441no—
326M16—882no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—222no—
330C2×C8—441no—
331C2×C8—882no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C22⋊C4—221no—
339C22⋊C4—221no—
340C22⋊C4—221no—
341C22⋊C4—221no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—442no—
345C22⋊C4—442no—
346C42—42no—
347C42—441no—
348C42—441no—
349C42C2×D4411yescharacteristic
350C42#433911yescharacteristic
351C42D4×D1111yescharacteristic
352C42#434311yescharacteristic
353C11#902911yescharacteristic, complemented, Sylow
354C23—112no—
355C23—221no—
356C23—221no—
357C23—221no—
358C23—221no—
359C23—221no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23C22⋊C4×D1111yescharacteristic
365Q8—222no—
366Q8—222no—
367Q8—441no—
368Q8—441no—
369D4—442no—
370D4—442no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—222no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—881no—
394C2×C4—881no—
395C2×C4C4×D4411yescharacteristic
396C2×C4#6693511yescharacteristic
397C2×C4#6693711yescharacteristic
398C2×C4#6694611yescharacteristic
399C2×C4#6694711yescharacteristic
400C2×C4#6694811yescharacteristic
401C8—42no—
402C8—42no—
403C8—442no—
404C8—442no—
405C22—21no—
406C22—21no—
407C22—222no—
408C22—442no—
409C22—442no—
410C22—441no—
411C22—441no—
412C22—441no—
413C22—441no—
414C22—441no—
415C22—881no—
416C22—881no—
417C22#1062227811yescharacteristic
418C22D11×#10411yescharacteristic
419C22#1062243411yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—81no—
426C4—81no—
427C4—441no—
428C4—441no—
429C4—442no—
430C4—881no—
431C4#1062243812yes—
432C2—21no—
433C2—21no—
434C2—442no—
435C2—881no—
436C2#1306891711yescharacteristic
437C2#1306900311yescharacteristic
438C2#1306903311yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1300C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1300D11
hypocenterC11#9029
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
4. #13067064C2semidirect
5. #13067062C2semidirect
6. #13066509C2semidirect
7. C11×#1300C2semidirect
141. #1300D11semidirect
353. C11#9029semidirect

Maximal subgroups

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

subgroupindex
#130776442
#130719022
C4×#668872
#130670642
#130670622
#130665092
C11×#13002
#902911