Finite Group Databasebeta

← C11×#11280 #14588473

Subgroups — C11×#11280 #14588473

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2905C211yesmaximal, characteristic
2C2×C11×#344C211yesmaximal, characteristic
3C2×C11×#344C211yesmaximal, characteristic
4C2×C11×#344C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic
6C11×#1742C211yesmaximal, characteristic
7C11×#1740C211yesmaximal, characteristic
8C22×C11×M16C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#424—22no—
16C11×#424—22no—
17C11×#423—22no—
18C11×#344—22no—
19C11×#344—22no—
20C11×#344—22no—
21C11×#344—22no—
22C11×#343—22no—
23C11×#342C414yes—
24C23×C4×C11C2311yescharacteristic
25C2×C11×M16—21no—
26C2×C11×M16—21no—
27C2×C11×M16—21no—
28C2×C11×M16—21no—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C2×C11×M16—21no—
34C2×C11×M16—21no—
35C2×C11×M16—21no—
36C2×C11×M16—21no—
37C2×C11×M16—21no—
38C2×C11×M16—21no—
39C2×C11×M16—21no—
40C2×C11×M16—21no—
41C2×C11×M16—21no—
42C2×C11×M16—21no—
43C2×C11×M16—21no—
44C2×C11×M16—21no—
45C2×C11×M16—21no—
46C2×C11×M16D412yes—
47C2×C11×M16D412yes—
48C2×C11×M16D412yes—
49C22×C8×C11—21no—
50C22×C8×C11—21no—
51C22×C8×C11—21no—
52C22×C8×C11Q812yes—
53C11×#117—21no—
54C11×#117—21no—
55C11×#117—21no—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117D412yes—
64C11×#117Q812yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C22⋊C4C2×C412yes—
69C2×C11×C22⋊C4C2×C412yes—
70C2×C11×C22⋊C4C2×C412yes—
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11—21no—
74C11×C4⋊C8—28no—
75#11280C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C22×C411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×Q811yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C11×M16—22no—
95C11×M16—22no—
96C11×M16—22no—
97C11×M16—22no—
98C11×M16—22no—
99C11×M16—22no—
100C11×M16—41no—
101C11×M16—41no—
102C11×M16—41no—
103C11×M16—41no—
104C11×M16—41no—
105C11×M16—41no—
106C11×M16—41no—
107C11×M16—41no—
108C11×M16—41no—
109C11×M16—41no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—22no—
130C11×C22⋊C4—22no—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4C4⋊C414yes—
134C42×C11—22no—
135C42×C11—22no—
136C42×C11—41no—
137C42×C11—41no—
138C42×C11—41no—
139C42×C11—41no—
140#2905C2×C1111yescharacteristic
141C2×#344C2×C1111yescharacteristic
142C2×#344C2×C1111yescharacteristic
143C2×#344C2×C1111yescharacteristic
144C2×#344C2×C1111yescharacteristic
145#1742C2×C1111yescharacteristic
146#1740C2×C1111yescharacteristic
147C23×C11—81no—
148C23×C11C2×C4⋊C411yescharacteristic
149C23×C11#11711yescharacteristic
150C23×C11#11711yescharacteristic
151C23×C11C4×D411yescharacteristic
152C23×C11C4×D411yescharacteristic
153C23×C11C4×D411yescharacteristic
154C23×C11C4×Q811yescharacteristic
155C2×C4×C11—24no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11—82no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11C22⋊Q811yescharacteristic
166C2×C4×C11C22⋊Q811yescharacteristic
167C2×C4×C11C22⋊Q811yescharacteristic
168C2×C4×C11C22⋊Q811yescharacteristic
169C2×C4×C11C22⋊Q811yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C2×C4×C11#12311yescharacteristic
172C2×C4×C11#12311yescharacteristic
173C2×C4×C11#12311yescharacteristic
174C2×C4×C11#12311yescharacteristic
175C2×C4×C11#12411yescharacteristic
176C2×C4×C11#12411yescharacteristic
177C2×C4×C11#12411yescharacteristic
178C2×C4×C11#12411yescharacteristic
179C2×C4×C11#12511yescharacteristic
180C2×C4×C11#12511yescharacteristic
181C2×C4×C11#12511yescharacteristic
182C2×C4×C11#12511yescharacteristic
183C2×C4×C11#12511yescharacteristic
184C2×C4×C11#12611yescharacteristic
185C2×C4×C11#12611yescharacteristic
186C2×C4×C11#12611yescharacteristic
187C2×C4×C11#12611yescharacteristic
188C2×C4×C11C4⋊Q811yescharacteristic
189C8×C11—42no—
190C8×C11—42no—
191C8×C11—42no—
192C8×C11—42no—
193C22×M16C22×C1111yescharacteristic
194C22×M16C22×C1111yescharacteristic
195C22×M16C22×C1111yescharacteristic
196C22×M16C22×C1111yescharacteristic
197C2×#117C22×C1111yescharacteristic
198C2×#117C22×C1111yescharacteristic
199C2×#117C22×C1111yescharacteristic
200#424—22no—
201#424—22no—
202#423—22no—
203#344—22no—
204#344—22no—
205#344—22no—
206#344—22no—
207#343—22no—
208#342C4×C1114yes—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11#38211yescharacteristic
217C22×C11#38511yescharacteristic
218C22×C11#38711yescharacteristic
219C22×C11#38711yescharacteristic
220C22×C11#38811yescharacteristic
221C22×C11#38811yescharacteristic
222C22×C11#38911yescharacteristic
223C4×C11—44no—
224C4×C11—82no—
225C4×C11—82no—
226C4×C11#39311yescharacteristic
227C4×C11#39411yescharacteristic
228C4×C11#39711yescharacteristic
229C4×C11#39811yescharacteristic
230C4×C11#39811yescharacteristic
231C4×C11#40011yescharacteristic
232C4×C11#40011yescharacteristic
233C4×C11#40011yescharacteristic
234C23×C4C23×C1111yescharacteristic
235C2×M16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16D4×C1112yes—
257C2×M16D4×C1112yes—
258C2×M16D4×C1112yes—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8Q8×C1112yes—
263#117—21no—
264#117—21no—
265#117—21no—
266#117—21no—
267#117—21no—
268#117—21no—
269#117—21no—
270#117—21no—
271#117—21no—
272#117—21no—
273#117D4×C1112yes—
274#117Q8×C1112yes—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C22⋊C4C2×C4×C1112yes—
279C2×C22⋊C4C2×C4×C1112yes—
280C2×C22⋊C4C2×C4×C1112yes—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C4⋊C8—28no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11#144211yescharacteristic
293C24C22×C4×C1111yescharacteristic
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4C2×D4×C1111yescharacteristic
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C2×D4×C1111yescharacteristic
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C2×Q8×C1111yescharacteristic
302C22×C4C2×Q8×C1111yescharacteristic
303C22×C4C11×#4111yescharacteristic
304C22×C4C11×#4111yescharacteristic
305C22×C4C11×#4111yescharacteristic
306C22×C4C11×#4111yescharacteristic
307C22×C4C11×#4111yescharacteristic
308C22×C4C11×#4111yescharacteristic
309C22×C4C11×#4111yescharacteristic
310C22×C4C11×#4111yescharacteristic
311M16—22no—
312M16—22no—
313M16—22no—
314M16—22no—
315M16—22no—
316M16—22no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16—41no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4C11×C4⋊C414yes—
351C42—22no—
352C42—22no—
353C42—41no—
354C42—41no—
355C42—41no—
356C42—41no—
357C11#1128011yescharacteristic, direct product factor, Sylow
358C23—81no—
359C23C2×C11×C4⋊C411yescharacteristic
360C23C11×#11711yescharacteristic
361C23C11×#11711yescharacteristic
362C23C4×D4×C1111yescharacteristic
363C23C4×D4×C1111yescharacteristic
364C23C4×D4×C1111yescharacteristic
365C23C4×Q8×C1111yescharacteristic
366C2×C4—24no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4C11×#12011yescharacteristic
373C2×C4C11×#12111yescharacteristic
374C2×C4C11×#12111yescharacteristic
375C2×C4C11×#12111yescharacteristic
376C2×C4C11×C22⋊Q811yescharacteristic
377C2×C4C11×C22⋊Q811yescharacteristic
378C2×C4C11×C22⋊Q811yescharacteristic
379C2×C4C11×C22⋊Q811yescharacteristic
380C2×C4C11×C22⋊Q811yescharacteristic
381C2×C4C11×#12311yescharacteristic
382C2×C4C11×#12311yescharacteristic
383C2×C4C11×#12311yescharacteristic
384C2×C4C11×#12311yescharacteristic
385C2×C4C11×#12311yescharacteristic
386C2×C4C11×#12411yescharacteristic
387C2×C4C11×#12411yescharacteristic
388C2×C4C11×#12411yescharacteristic
389C2×C4C11×#12411yescharacteristic
390C2×C4C11×#12511yescharacteristic
391C2×C4C11×#12511yescharacteristic
392C2×C4C11×#12511yescharacteristic
393C2×C4C11×#12511yescharacteristic
394C2×C4C11×#12511yescharacteristic
395C2×C4C11×#12611yescharacteristic
396C2×C4C11×#12611yescharacteristic
397C2×C4C11×#12611yescharacteristic
398C2×C4C11×#12611yescharacteristic
399C2×C4C11×C4⋊Q811yescharacteristic
400C8—42no—
401C8—42no—
402C8—42no—
403C8—42no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22C11×#38211yescharacteristic
412C22C11×#38511yescharacteristic
413C22C11×#38711yescharacteristic
414C22C11×#38711yescharacteristic
415C22C11×#38811yescharacteristic
416C22C11×#38811yescharacteristic
417C22C11×#38911yescharacteristic
418C4—44no—
419C4—82no—
420C4—82no—
421C4C11×#39311yescharacteristic
422C4C11×#39411yescharacteristic
423C4C11×#39711yescharacteristic
424C4C11×#39811yescharacteristic
425C4C11×#39811yescharacteristic
426C4C11×#40011yescharacteristic
427C4C11×#40011yescharacteristic
428C4C11×#40011yescharacteristic
429C2—21no—
430C2—21no—
431C2—21no—
432C2—21no—
433C2—21no—
434C2—21no—
435C2—21no—
436C2C11×#144211yescharacteristic
subgroupG/H
centerC4×C11#393
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC2×C11#1442
prime radicalC24×C11C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
75. #11280C11direct (N × H)
357. C11#11280direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29052
C2×C11×#3442
C11×#17422
C11×#17402
#1128011