Finite Group Databasebeta

← #14651559

Subgroups — #14651559

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#13072927C211yesmaximal, characteristic
3#13068706C211yesmaximal, characteristic, complemented
4#13068601C211yesmaximal, characteristic
5#13066484C211yesmaximal, characteristic, complemented
6#13066483C211yesmaximal, characteristic, complemented
7C11×#1824C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×C4×C22⋊D11C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12#10622826—21no—
13#10622825C2211yescharacteristic
14#10622825C2211yescharacteristic
15#10622823—21no—
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622724—22no—
18#10622605C412yescomplemented
19#10622600—21no—
20#10622595C412yescomplemented
21#10622586—21no—
22C2×#66870—21no—
23#10622343—22no—
24#10622339—21no—
25#10622332—21no—
26C11×#340—22no—
27#10622167—22no—
28#10622165—21no—
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C22×C22⋊D11D411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×C8×C11D412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C412yes—
41C2×C11×C22⋊C4—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11D411yescharacteristic
45C4×C22⋊D11—21no—
46C4×C22⋊D11—21no—
47C4×C22⋊D11—21no—
48C4×C22⋊D11—21no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4C2×C411yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×Dic11⋊C4—22no—
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⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—21no—
64C11⋊#95C2×C412yes—
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×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—82no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×C22⋊D11—21no—
87C2×C22⋊D11—21no—
88C2×C22⋊D11—21no—
89C2×C22⋊D11—21no—
90C2×C22⋊D11—21no—
91C2×C22⋊D11—21no—
92C22×Dic11—22no—
93C22×Dic11—41no—
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—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C22⋊Dic11—21no—
110C22⋊Dic11—21no—
111C22⋊Dic11—41no—
112C22⋊Dic11—41no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115(C2×D11)⋊C4—21no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—82no—
118C4⋊Dic11—42no—
119C4⋊Dic11—42no—
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122Dic11⋊C4—82no—
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#1824D1111yescharacteristic, complemented
132#1799—111no—
133#1289—111no—
134#1289—111no—
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—82no—
159C2×C4×C11—82no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C22⋊D11—41no—
168C22⋊D11—41no—
169C22⋊D11—41no—
170C22⋊D11—41no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
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⋊C4C2×D1111yescharacteristic
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—111no—
204#380—221no—
205#380C2×D1111yescharacteristic
206#342—221no—
207#340—22no—
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—21no—
244C23×C4—111no—
245C23×C4C22×D1111yescharacteristic
246C2×M16—222no—
247C22×C8—112no—
248C22×C8C22⋊D1112yes—
249C4×D4—221no—
250C4×D4—221no—
251C4×D4—221no—
252C4×D4—221no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4C4×D1112yes—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—221no—
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—112no—
281#95—222no—
282#95—222no—
283#95—221no—
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—41no—
306C22×C4—41no—
307C22×C4—82no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—222no—
314C22×C4—442no—
315C22×C4—441no—
316C22×C4C2×C4×D1111yescharacteristic
317C22×C4#433911yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C22×C4D4×D1111yescharacteristic
320C22×C4#434111yescharacteristic
321C22×C4C2×C22⋊D1111yescharacteristic
322M16—882no—
323C2×C8—22no—
324C2×C8—42no—
325C2×C8—222no—
326C2×C8—442no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—42no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—442no—
335C4⋊C4—442no—
336C4⋊C4—882no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—221no—
340C22⋊C4—221no—
341C22⋊C4—221no—
342C22⋊C4—221no—
343C22⋊C4—441no—
344C22⋊C4—441no—
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#6696711yescharacteristic
361C23#6696811yescharacteristic
362C23#6697111yescharacteristic
363C23#6697111yescharacteristic
364C23#6699111yescharacteristic
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—82no—
379C2×C4—82no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—442no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—881no—
395C2×C4—881no—
396C2×C4—881no—
397C2×C4—881no—
398C2×C4(C22⋊D11)⋊C411yescharacteristic
399C2×C4#6693611yescharacteristic
400C2×C4C4×C22⋊D1111yescharacteristic
401C2×C4#6699011yescharacteristic
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#1062241511yescharacteristic
420C22#1062241611yescharacteristic
421C22#1062242511yescharacteristic
422C22#1062242911yescharacteristic
423C22#1062256911yescharacteristic
424C22#1062278711yescharacteristic
425C22#1062280211yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—161no—
431C4—441no—
432C4—441no—
433C4—441no—
434C4—882no—
435C4—1761no—
436C4#1062266612yes—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—881no—
444C2#1306902611yescharacteristic
445C2#1306904611yescharacteristic
446C2#1306914011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1824C2
socleC22×C11#386
prime radicalC22×C22⋊D11D4
cosocleC23×C4×C11C23
hypercenter#1824D11
hypocenterC11#9473
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
3. #13068706C2semidirect
5. #13066484C2semidirect
6. #13066483C2semidirect
7. C11×#1824C2semidirect
18. #10622605C4semidirect
20. #10622595C4semidirect
131. #1824D11semidirect
350. C11#9473semidirect

Maximal subgroups

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

subgroupindex
#130776422
#130729272
#130687062
#130686012
#130664842
#130664832
C11×#18242
#947311