Finite Group Databasebeta

← #14651574

Subgroups — #14651574

Order 2816.

818 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 97 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#13071947C211yesmaximal, characteristic
2#13070971C211yesmaximal, characteristic, complemented
3#13068560C211yesmaximal, characteristic
4#13066945C211yesmaximal, characteristic, complemented
5#13066470C211yesmaximal, characteristic, complemented
6#13066469C211yesmaximal, characteristic, complemented
7C11×#1789C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C2×#66988—21no—
10C22×Dic11⋊C4C2211yescharacteristic
11C2×#66930—21no—
12C2×C11×#104—22no—
13C11×#407C2211yescharacteristic
14C4×C11×C22⋊C4C2211yescharacteristic
15C2×#66901—22no—
16#10622842C412yescomplemented
17#10622835C412yescomplemented
18#10622833—21no—
19#10622824C2211yescharacteristic
20#10622823—22no—
21C4×C22⋊Dic11C2211yescharacteristic
22#10622820C2211yescharacteristic
23C22⋊C4×Dic11—21no—
24C4×Dic11⋊C4—22no—
25#10622262—22no—
26#10622107—22no—
27C2×C11×#41—21no—
28C2×C11×#41—21no—
29C2×C11×#41—21no—
30C2×C11×#41—21no—
31C2×C11×#41—44no—
32C22×Q8×C11C2×C411yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11C2×C411yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11D411yescharacteristic
38C23×Dic11D411yescharacteristic
39C2×C11×M16—21no—
40C2×C11×C22⋊C4—21no—
41C2×C42×C11D412yes—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11—22no—
46#66988—44no—
47C2×Dic11⋊C4—22no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4C2×C412yes—
54C2×Dic11⋊C4D412yes—
55C2×C4×Dic11—22no—
56C2×C4×Dic11—22no—
57C2×C4×Dic11D412yes—
58C2×#4318—21no—
59#66930—28no—
60C11×#104—44no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×#95—21no—
64#66901—44no—
65C11⋊#95—22no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—22no—
69C11⋊#95C2×C412yes—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#9476—111nomaximal, Sylow
73C24×C11—21no—
74C24×C11C2×D411yescharacteristic
75C11×#41—24no—
76C11×#41—24no—
77C11×#41—42no—
78C11×#41—42no—
79C11×#41—42no—
80C11×#41—42no—
81C11×#41—42no—
82C11×#41—42no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—42no—
86C2×D4×C11—24no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—42no—
90C2×D4×C11—42no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×Dic11—24no—
107C22×Dic11—22no—
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—42no—
114C22×Dic11C22⋊C412yes—
115C22×Dic11C22⋊C412yes—
116C11×M16—42no—
117C2×C8×C11—41no—
118C11×C22⋊C4—24no—
119C42×C11—42no—
120C22⋊Dic11—24no—
121C22⋊Dic11—42no—
122C22⋊Dic11—44no—
123C22⋊Dic11—44no—
124Dic11⋊C4—28no—
125Dic11⋊C4—22no—
126Dic11⋊C4—22no—
127Dic11⋊C4—22no—
128Dic11⋊C4—22no—
129Dic11⋊C4—44no—
130C4×Dic11—28no—
131C4×Dic11—42no—
132C4×Dic11—82no—
133#4318—42no—
134C2×C11⋊C8—41no—
135#2406—111no—
136#2274—111no—
137#1789—111no—
138#1789D1111yescharacteristic
139#1463—111no—
140#1284—111no—
141#1284—111no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—41no—
149C23×C11—42no—
150C23×C11C2×C22⋊C411yescharacteristic
151C23×C11#12011yescharacteristic
152C23×C11#12311yescharacteristic
153Q8×C11—22no—
154Q8×C11—22no—
155Q8×C11—41no—
156Q8×C11—41no—
157D4×C11—22no—
158D4×C11—22no—
159D4×C11—41no—
160D4×C11—41no—
161D4×C11—44no—
162D4×C11—44no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—44no—
172C2×C4×C11—44no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11C4×D411yescharacteristic
178C2×C4×C11C4×D411yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—24no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—24no—
187C2×Dic11—22no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—81no—
196C2×Dic11#10414yescomplemented
197C8×C11—81no—
198C11⋊C8—81no—
199C22×#41C2×D1111yescharacteristic
200C2×#123—221no—
201C2×#117—221no—
202C22×C4⋊C4—111no—
203C2×#104—22no—
204C2×#104—222no—
205#407—111no—
206#407C2×D1111yescharacteristic
207#395—112no—
208#394—112no—
209#386—221no—
210#385—222no—
211#381—111no—
212C4×C4⋊C4—222no—
213C4×C4⋊C4—222no—
214C4×C22⋊C4—111no—
215C4×C22⋊C4—221no—
216C4×C22⋊C4C2×D1111yescharacteristic
217#324—222no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—44no—
226C22×C11—44no—
227C22×C11—42no—
228C22×C11—82no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11#38611yescharacteristic
232C22×C11C2×#10412yes—
233C22×C11B(4,𝔽2)12yes—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—44no—
239C4×C11—42no—
240Dic11—24no—
241Dic11—44no—
242Dic11—42no—
243Dic11—82no—
244C2×#41—21no—
245C2×#41—21no—
246C2×#41—21no—
247C2×#41—21no—
248C2×#41—44no—
249C22×Q8C4×D1111yescharacteristic
250C22×D4—21no—
251C22×D4C4×D1111yescharacteristic
252C23×C4—21no—
253C23×C4—111no—
254C23×C4—111no—
255C23×C4C22×D1111yescharacteristic
256C2×M16—21no—
257C2×M16—221no—
258#123—444no—
259#117—228no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—222no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—221no—
273C2×C42—112no—
274C2×C42—222no—
275C2×C42—222no—
276C2×C42C22⋊D1112yes—
277#104—44no—
278#104—444no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—221no—
282C22⋊C8—221no—
283#95—21no—
284#95—112no—
285#95—222no—
286#95—222no—
287#95—221no—
288#95—221no—
289C2×C11—22no—
290C2×C11—22no—
291C2×C11—41no—
292C2×C11—82no—
293C2×C11#188911yescharacteristic
294C2×C11#189611yescharacteristic
295C2×C11#191211yescharacteristic
296C24—21no—
297C24D4×D1111yescharacteristic
298#41—24no—
299#41—24no—
300#41—42no—
301#41—42no—
302#41—42no—
303#41—42no—
304#41—42no—
305#41—42no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—42no—
309C2×D4—24no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4—41no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—112no—
324C22×C4—112no—
325C22×C4—224no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—222no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—222no—
332C22×C4—442no—
333C22×C4C2×C4×D1111yescharacteristic
334C22×C4#433911yescharacteristic
335C22×C4D4×D1111yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4#434111yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339M16—42no—
340M16—442no—
341C2×C8—41no—
342C2×C8—441no—
343C4⋊C4—228no—
344C4⋊C4—222no—
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—444no—
349C22⋊C4—24no—
350C22⋊C4—224no—
351C22⋊C4—444no—
352C22⋊C4—444no—
353C22⋊C4—442no—
354C42—42no—
355C42—228no—
356C42—442no—
357C42—882no—
358C11#947611yescharacteristic, complemented, Sylow
359C23—22no—
360C23—22no—
361C23—22no—
362C23—41no—
363C23—41no—
364C23—42no—
365C23—41no—
366C23—42no—
367C23C22⋊C4×D1111yescharacteristic
368C23#6693611yescharacteristic
369C23#6699011yescharacteristic
370Q8—22no—
371Q8—22no—
372Q8—41no—
373Q8—41no—
374D4—22no—
375D4—22no—
376D4—41no—
377D4—41no—
378D4—44no—
379D4—44no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—114no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—224no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—224no—
401C2×C4—222no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—881no—
410C2×C4(C22⋊D11)⋊C411yescharacteristic
411C2×C4#6693711yescharacteristic
412C2×C4C4×C22⋊D1111yescharacteristic
413C2×C4#6699111yescharacteristic
414C8—81no—
415C8—881no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—44no—
424C22—44no—
425C22—42no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22D11×#10412yes—
430C22#1062256911yescharacteristic
431C22#1062264512yes—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—44no—
437C4—42no—
438C4—224no—
439C4—444no—
440C4—442no—
441C4—882no—
442C2—22no—
443C2—22no—
444C2—41no—
445C2—82no—
446C2#1306902111yescharacteristic
447C2#1306905611yescharacteristic
448C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1789C2
socleC22×C11#386
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenter#1789D11
hypocenterC11#9476
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #13070971C2semidirect
4. #13066945C2semidirect
5. #13066470C2semidirect
6. #13066469C2semidirect
16. #10622842C4semidirect
17. #10622835C4semidirect
196. C2×Dic11#104semidirect
358. C11#9476semidirect

Maximal subgroups

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

subgroupindex
#130719472
#130709712
#130685602
#130669452
#130664702
#130664692
C11×#17892
#947611