Finite Group Databasebeta

← #14654521

Subgroups — #14654521

Order 2816.

554 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 99 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#13078084C211yesmaximal, characteristic
2#13073982C211yesmaximal, characteristic, complemented
3#13067176C211yesmaximal, characteristic
4#13067045C211yesmaximal, characteristic, complemented
5#13067012C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#3103C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#67004—21no—
11C2×C4×Dic22C2211yescharacteristic
12C11×#481—21no—
13C11×#475—21no—
14C11×#460—21no—
15C11×#448—21no—
16C4×C11×SD16—22no—
17C11×#431C2211yescharacteristic
18#10622845—21no—
19#10622842—21no—
20#10622703—21no—
21#10622688—21no—
22#10622667—22no—
23#10622595—21no—
24#10622591—22no—
25#10622549C2211yescharacteristic
26#10622542—21no—
27#10622541—21no—
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30#10622175—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622094—22no—
33C2×C11×#41—21no—
34C22×Q8×C11D411yescharacteristic
35C22×Dic22D411yescharacteristic
36C2×C11×SD16—22no—
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52#67004—42no—
53#67004—42no—
54C2×#4326—22no—
55C2×#4324—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—21no—
60C2×C4×Dic11—21no—
61C2×#4318—21no—
62C4×Dic22—21no—
63C4×Dic22—21no—
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×#106—22no—
67C11×C4⋊C8—21no—
68C11×#103—22no—
69C11×#102—22no—
70C11×C22⋊C8—21no—
71C4×C8×C11D412yes—
72#66899—22no—
73#66896—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95—21no—
78C11⋊#95D412yes—
79C22⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)D412yes—
83C4×C11⋊C8—21no—
84#9999—111nomaximal, Sylow
85C11×#41—41no—
86C11×#41—41no—
87C11×#41—41no—
88C11×#41—41no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—42no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—41no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11—21no—
106C2×Dic22—21no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22—21no—
110C2×Dic22—21no—
111C2×Dic22SD1612yescomplemented
112C11×SD16—44no—
113C2×C8×C11—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128#4326—44no—
129#4324—44no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134Dic11⋊C4—44no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C4×Dic11—41no—
138C4×Dic11—41no—
139#4318—41no—
140#4318—41no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—41no—
143#3103D1111yescharacteristic
144#3037—111no—
145#2581—111no—
146#1517—111no—
147#1487—111no—
148#1479—111no—
149#1286—111no—
150C23×C11—41no—
151C23×C11#12011yescharacteristic
152Q8×C11—22no—
153Q8×C11—22no—
154Q8×C11—41no—
155Q8×C11—41no—
156Q8×C11—41no—
157Q8×C11—41no—
158D4×C11—42no—
159D4×C11—41no—
160D4×C11—41no—
161D4×C11—81no—
162D4×C11—81no—
163D4×C11—81no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12711yescharacteristic
180C2×C4×C11C2×SD1611yescharacteristic
181C2×C4×C11#13511yescharacteristic
182C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C11#13711yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—41no—
191C2×Dic11—42no—
192Dic22—22no—
193Dic22—22no—
194Dic22—41no—
195Dic22—41no—
196C8×C11—42no—
197C11⋊C8—42no—
198C11⋊C8—81no—
199C2×#137—221no—
200#532C2×D1111yescharacteristic
201C2×C4×Q8—111no—
202C2×C4×Q8C2×D1111yescharacteristic
203#481—21no—
204#475—21no—
205#464—222no—
206#462—221no—
207#460—21no—
208#460—221no—
209#448—21no—
210C4×SD16—22no—
211#431—111no—
212#431C2×D1111yescharacteristic
213#423—111no—
214#417—221no—
215#400—221no—
216#395—221no—
217#391—221no—
218#389—221no—
219#387—222no—
220#382—111no—
221#327—222no—
222Q8⋊C8—222no—
223Q8⋊C8—222no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11#39211yescharacteristic
230C22×C11#44811yescharacteristic
231C22×C11#44911yescharacteristic
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—42no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11#45011yescharacteristic
240C4×C11#45211yescharacteristic
241C4×C11#46511yescharacteristic
242C4×C11#46811yescharacteristic
243Dic11—42no—
244Dic11—82no—
245Dic11—81no—
246C2×#41—21no—
247C22×Q8—111no—
248C22×Q8C22⋊D1111yescharacteristic
249#137—442no—
250#137—442no—
251C2×Q16—222no—
252C2×SD16—22no—
253C2×SD16—222no—
254C2×M16—221no—
255C4⋊Q8C22⋊D1111yescharacteristic
256#127C22⋊D1111yescharacteristic
257#124—21no—
258#121—21no—
259#121—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—221no—
265C4×Q8—221no—
266C4×Q8—221no—
267C4×Q8—221no—
268C4×D4—21no—
269C4×D4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4C22⋊D1111yescharacteristic
276C2×C42—21no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279#106—22no—
280C4⋊C8—21no—
281C4⋊C8—112no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284#103—22no—
285#103—222no—
286#102—22no—
287#102—222no—
288C22⋊C8—21no—
289C22⋊C8—221no—
290C4×C8—221no—
291C4×C8C22⋊D1112yes—
292#95—112no—
293#95—222no—
294#95—222no—
295#95—222no—
296#95—221no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—161no—
300C2×C11#200011yescharacteristic
301C2×C11#200911yescharacteristic
302C2×C11#201011yescharacteristic
303#41—41no—
304#41—41no—
305#41—41no—
306#41—41no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—42no—
311C2×Q8—112no—
312C2×Q8—221no—
313C2×Q8—221no—
314C2×Q8—221no—
315C2×Q8—221no—
316C2×Q8—221no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—221no—
325C22×C4—222no—
326C22×C4—221no—
327C22×C4D4×D1111yescharacteristic
328C22×C4D4×D1111yescharacteristic
329C22×C4C2×C22⋊D1111yescharacteristic
330Q16—444no—
331SD16—44no—
332SD16—444no—
333M16—441no—
334M16—441no—
335C2×C8—22no—
336C2×C8—222no—
337C2×C8—441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—444no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42—41no—
354C42—41no—
355C42—441no—
356C42—441no—
357C42D4×D1111yescharacteristic
358C42#434111yescharacteristic
359C42C2×C22⋊D1111yescharacteristic
360C42C2×C22⋊D1111yescharacteristic
361C11#999911yescharacteristic, complemented, Sylow
362C23—41no—
363C23#6699011yescharacteristic
364Q8—22no—
365Q8—22no—
366Q8—41no—
367Q8—41no—
368Q8—41no—
369Q8—41no—
370Q8—222no—
371Q8—222no—
372Q8—441no—
373Q8—441no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—81no—
378D4—81no—
379D4—81no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—222no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—441no—
398C2×C4SD16×D1111yescharacteristic
399C2×C4#6696711yescharacteristic
400C2×C4#6696811yescharacteristic
401C2×C4#6696911yescharacteristic
402C2×C4#6699011yescharacteristic
403C2×C4#6699111yescharacteristic
404C2×C4#6699211yescharacteristic
405C2×C4#6699211yescharacteristic
406C2×C4#6699311yescharacteristic
407C2×C4#6700611yescharacteristic
408C8—42no—
409C8—442no—
410C8—881no—
411C22—21no—
412C22—21no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22#1062278311yescharacteristic
417C22#1062278511yescharacteristic
418C22#1062283611yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—81no—
425C4—81no—
426C4—442no—
427C4—882no—
428C4—881no—
429C4#1062278211yescharacteristic
430C4#1062278411yescharacteristic
431C4#1062278611yescharacteristic
432C4#1062278711yescharacteristic
433C2—21no—
434C2—21no—
435C2—161no—
436C2#1306961611yescharacteristic
437C2#1306967311yescharacteristic
438C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3103C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3103D11
hypocenterC11#9999
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
2. #13073982C2semidirect
4. #13067045C2semidirect
5. #13067012C2semidirect
6. #13066475C2semidirect
111. C2×Dic22SD16semidirect
361. C11#9999semidirect

Maximal subgroups

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

subgroupindex
#130780842
#130739822
#130671762
#130670452
#130670122
#130664752
C11×#31032
#999911