Finite Group Databasebeta

← #14651561

Subgroups — #14651561

Order 2816.

556 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077642C211yesmaximal, characteristic
2#13072934C211yesmaximal, characteristic
3#13068707C211yesmaximal, characteristic, complemented
4#13068704C211yesmaximal, characteristic, complemented
5#13068601C211yesmaximal, characteristic
6#13066483C211yesmaximal, characteristic, complemented
7C11×#1289C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D11C2211yescharacteristic
9C22×C4⋊Dic11C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622825C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2211yescharacteristic
15#10622724—22no—
16#10622600—21no—
17#10622598—21no—
18#10622571—21no—
19C2×#66870—21no—
20#10622563—21no—
21#10622343—22no—
22#10622339—21no—
23#10622332—21no—
24#10622290C412yescomplemented
25#10622272C412yescomplemented
26#10622189—22no—
27#10622167—22no—
28#10622165—21no—
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11D411yescharacteristic
31C23×Dic11—21no—
32C22×C4×D11D411yescharacteristic
33C22×C8×C11D412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11D411yescharacteristic
40C4×C22⋊D11—21no—
41C4×C22⋊D11—21no—
42C4×C22⋊D11—21no—
43C4×C22⋊D11—21no—
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4C2×C411yescharacteristic
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11C2×C412yes—
54C2×Dic11⋊C4C2×C411yescharacteristic
55C2×C4×Dic11D411yescharacteristic
56C22×C11⋊C8D412yes—
57C2×#4313—22no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95C2×C412yes—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—21no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67(C2×D11)⋊C8—22no—
68#66879—22no—
69Dic11⋊C8—22no—
70#66870—42no—
71#9473—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C23×D11C22⋊C411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×C22⋊D11—21no—
84C2×C22⋊D11—21no—
85C2×C22⋊D11—21no—
86C2×C22⋊D11—21no—
87C2×C22⋊D11—21no—
88C2×C22⋊D11—21no—
89C22×Dic11—22no—
90C22×Dic11—41no—
91C22×Dic11—41no—
92C22×Dic11—41no—
93C22×Dic11—82no—
94C22×Dic11C22⋊C411yescharacteristic
95C22×Dic11C22⋊C411yescharacteristic
96C22×Dic11C22⋊C411yescharacteristic
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C2×C4×D11—42no—
100C2×C8×C11—22no—
101C2×C8×C11—42no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C22⋊Dic11—21no—
109C22⋊Dic11—21no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112(C2×D11)⋊C4—21no—
113(C2×D11)⋊C4—21no—
114(C2×D11)⋊C4—82no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11—42no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—82no—
121Dic11⋊C4—21no—
122Dic11⋊C4—21no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127#4313—82no—
128#2973—111no—
129#2487—111no—
130#1824—111no—
131#1824—111no—
132#1799—111no—
133#1289—111no—
134#1289D1111yescharacteristic, complemented
135C23×C11—41no—
136C23×C11—41no—
137C23×C11C2×C22⋊C411yescharacteristic
138C23×C11#12111yescharacteristic
139C23×C11#12111yescharacteristic
140C23×C11AGL(1,ℤ/8)11yescharacteristic
141C23×C11#13711yescharacteristic
142C23×C11#13711yescharacteristic
143C23×C11#13711yescharacteristic
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—41no—
148C22×D11—41no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C22⋊D11—41no—
166C22⋊D11—41no—
167C22⋊D11—41no—
168C22⋊D11—41no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—82no—
180C2×Dic11—82no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184C4×D11—42no—
185C4×D11—81no—
186C8×C11—42no—
187C11⋊C8—42no—
188C2×C4×D4—111no—
189C22×C4⋊C4—111no—
190#435—222no—
191#435—222no—
192#432—221no—
193C2×#99—221no—
194#407—221no—
195C2×C22⋊C8—111no—
196C2×C22⋊C8C2×D1111yescharacteristic
197#400—112no—
198#399—112no—
199#389—221no—
200#386—221no—
201#385—221no—
202#380—111no—
203#380—221no—
204#380C2×D1111yescharacteristic
205#380C2×D1111yescharacteristic
206#342—221no—
207#340—222no—
208#340—222no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11#38611yescharacteristic
220C22×C11#41711yescharacteristic
221C22×C11#41911yescharacteristic
222C22×C11#46811yescharacteristic
223C22×C11#46811yescharacteristic
224C22×C11#47011yescharacteristic
225C22×C11#47011yescharacteristic
226C2×D11—42no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—81no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—82no—
235C4×C11—161no—
236C4×C11#45812yes—
237Dic11—41no—
238Dic11—41no—
239Dic11—41no—
240Dic11—82no—
241Dic11—161no—
242C22×D4—111no—
243C23×C4—111no—
244C23×C4—221no—
245C23×C4C22×D1111yescharacteristic
246C2×M16—222no—
247C22×C8—112no—
248C22×C8D4412yes—
249C4×D4—221no—
250C4×D4—221no—
251C4×D4—221no—
252C4×D4—221no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—222no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—222no—
270C2×C42—111no—
271C4⋊C8—222no—
272#99—442no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—222no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278#97—222no—
279#95—21no—
280#95—222no—
281#95—222no—
282#95—221no—
283#95C4×D1112yes—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11#189011yescharacteristic
291C2×C11#189411yescharacteristic
292C2×C11#191011yescharacteristic
293D11—81no—
294C24—111no—
295C24D4×D1111yescharacteristic
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—221no—
302C22×C4—22no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—222no—
311C22×C4—442no—
312C22×C4—441no—
313C22×C4—441no—
314C22×C4—441no—
315C22×C4—882no—
316C22×C4C2×C4×D1111yescharacteristic
317C22×C4C2×D4411yescharacteristic
318C22×C4#433911yescharacteristic
319C22×C4D4×D1111yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4#434311yescharacteristic
322M16—882no—
323C2×C8—22no—
324C2×C8—42no—
325C2×C8—222no—
326C2×C8—442no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4—222no—
332C4⋊C4—222no—
333C4⋊C4—442no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C4⋊C4—882no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—221no—
342C22⋊C4—221no—
343C22⋊C4—221no—
344C22⋊C4—221no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—882no—
348C42—221no—
349C42—221no—
350C11#947311yescharacteristic, complemented, Sylow
351C23—41no—
352C23—41no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—441no—
357C23—441no—
358C23C22⋊C4×D1111yescharacteristic
359C23#6693711yescharacteristic
360C23#6694811yescharacteristic
361C23#6696411yescharacteristic
362C23#6696811yescharacteristic
363C23#6696811yescharacteristic
364C23#6697111yescharacteristic
365D4—441no—
366D4—441no—
367D4—441no—
368D4—441no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—442no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—881no—
393C2×C4—882no—
394C2×C4—882no—
395C2×C4—881no—
396C2×C4—881no—
397C2×C4—881no—
398C2×C4C4×D4411yescharacteristic
399C2×C4#6693511yescharacteristic
400C2×C4#6694611yescharacteristic
401C2×C4#6694711yescharacteristic
402C8—42no—
403C8—442no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—442no—
415C22—441no—
416C22—441no—
417C22—441no—
418C22—881no—
419C22#1062227811yescharacteristic
420C22#1062238411yescharacteristic
421C22#1062239311yescharacteristic
422C22#1062241511yescharacteristic
423C22#1062242911yescharacteristic
424C22#1062248111yescharacteristic
425C22#1062249911yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—161no—
431C4—441no—
432C4—441no—
433C4—441no—
434C4—882no—
435C4—1761no—
436C4#1062235512yes—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—881no—
444C2#1306902811yescharacteristic
445C2#1306904811yescharacteristic
446C2#1306914211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1289C2
socleC22×C11#386
prime radicalC22×C22⋊D11D4
cosocleC23×C4×C11C23
hypercenter#1289D11
hypocenterC11#9473
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
3. #13068707C2semidirect
4. #13068704C2semidirect
6. #13066483C2semidirect
7. C11×#1289C2semidirect
24. #10622290C4semidirect
25. #10622272C4semidirect
134. #1289D11semidirect
350. C11#9473semidirect

Maximal subgroups

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

subgroupindex
#130776422
#130729342
#130687072
#130687042
#130686012
#130664832
C11×#12892
#947311