Finite Group Databasebeta

← C11×#11363 #14588556

Subgroups — C11×#11363 #14588556

Order 2816.

560 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic
2C2×C11×#344C211yesmaximal, characteristic
3C2×C11×#344C211yesmaximal, characteristic
4C11×#1742C211yesmaximal, characteristic
5C11×#1738C211yesmaximal, characteristic
6C11×#1738C211yesmaximal, characteristic
7C2×C11×#338C211yesmaximal, characteristic
8C22×C11×M16C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#430—22no—
16C11×#430C414yescomplemented
17C2×C11×#108—22no—
18C11×#344—22no—
19C11×#344—22no—
20C11×#343—22no—
21C11×#341—22no—
22C11×#341—22no—
23C11×#338—22no—
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×M16—21no—
47C2×C11×M16—21no—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16C2×C412yes—
55C2×C11×M16C2×C412yes—
56C2×C11×M16C2×C412yes—
57C2×C11×M16D412yes—
58C2×C11×M16D412yes—
59C2×C11×M16D412yes—
60C2×C11×M16Q812yes—
61C22×C8×C11—21no—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C22×C8×C11D412yes—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C22⋊C4Q812yes—
73C2×C42×C11—21no—
74C11×#108—28no—
75#11363C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C2×Q811yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×Q811yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C11×M16—22no—
93C11×M16—22no—
94C11×M16—22no—
95C11×M16—22no—
96C11×M16—22no—
97C11×M16—22no—
98C11×M16—22no—
99C11×M16—22no—
100C11×M16—22no—
101C11×M16—22no—
102C11×M16—22no—
103C11×M16—22no—
104C11×M16—22no—
105C11×M16—22no—
106C11×M16—41no—
107C11×M16—41no—
108C11×M16—41no—
109C11×M16—41no—
110C11×M16—41no—
111C11×M16—41no—
112C11×M16—41no—
113C11×M16—41no—
114C11×M16—41no—
115C11×M16—41no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—41no—
124C2×C8×C11—41no—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C2×C8×C11—41no—
132C2×C8×C11—41no—
133C2×C8×C11C22⋊C414yes—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—22no—
137C11×C22⋊C4—22no—
138C42×C11—41no—
139C42×C11—41no—
140C2×#430C2×C1111yescharacteristic
141C2×#344C2×C1111yescharacteristic
142C2×#344C2×C1111yescharacteristic
143#1742C2×C1111yescharacteristic
144#1738C2×C1111yescharacteristic
145#1738C2×C1111yescharacteristic
146C2×#338C2×C1111yescharacteristic
147C23×C11—81no—
148C23×C11C4×Q811yescharacteristic
149C23×C11C22⋊Q811yescharacteristic
150C23×C11C22⋊Q811yescharacteristic
151C23×C11C22⋊Q811yescharacteristic
152C23×C11#12511yescharacteristic
153C23×C11#12511yescharacteristic
154C23×C11C4⋊Q811yescharacteristic
155C2×C4×C11—42no—
156C2×C4×C11—82no—
157C2×C4×C11C2×C22⋊C411yescharacteristic
158C2×C4×C11#11711yescharacteristic
159C2×C4×C11#11711yescharacteristic
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C4×Q811yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11C22⋊Q811yescharacteristic
166C2×C4×C11C22⋊Q811yescharacteristic
167C2×C4×C11C22⋊Q811yescharacteristic
168C2×C4×C11#12311yescharacteristic
169C2×C4×C11#12311yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C2×C4×C11#12311yescharacteristic
172C2×C4×C11#12311yescharacteristic
173C2×C4×C11#12311yescharacteristic
174C2×C4×C11#12311yescharacteristic
175C2×C4×C11#12311yescharacteristic
176C2×C4×C11#12411yescharacteristic
177C2×C4×C11#12411yescharacteristic
178C2×C4×C11#12511yescharacteristic
179C2×C4×C11#12511yescharacteristic
180C2×C4×C11#12611yescharacteristic
181C2×C4×C11#12611yescharacteristic
182C2×C4×C11#12611yescharacteristic
183C2×C4×C11#12611yescharacteristic
184C2×C4×C11#12711yescharacteristic
185C8×C11—24no—
186C8×C11—42no—
187C8×C11—42no—
188C8×C11—42no—
189C8×C11—42no—
190C8×C11—42no—
191C22×M16C22×C1111yescharacteristic
192C22×M16C22×C1111yescharacteristic
193C22×M16C22×C1111yescharacteristic
194C22×M16C22×C1111yescharacteristic
195C22×M16C22×C1111yescharacteristic
196C22×M16C22×C1111yescharacteristic
197C2×#117C22×C1111yescharacteristic
198#430—22no—
199#430C4×C1114yescomplemented
200C2×#108—22no—
201#344—22no—
202#344—22no—
203#343—22no—
204#341—22no—
205#341—22no—
206#338—22no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11#38711yescharacteristic
215C22×C11#38711yescharacteristic
216C22×C11#39111yescharacteristic
217C22×C11#39811yescharacteristic
218C22×C11#39811yescharacteristic
219C22×C11#39911yescharacteristic
220C22×C11#40011yescharacteristic
221C4×C11—82no—
222C4×C11#38111yescharacteristic
223C4×C11#38711yescharacteristic
224C4×C11#38711yescharacteristic
225C4×C11#39011yescharacteristic
226C4×C11#39711yescharacteristic
227C4×C11#39711yescharacteristic
228C4×C11#39911yescharacteristic
229C4×C11#40011yescharacteristic
230C23×C4C23×C1111yescharacteristic
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
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×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16C2×C4×C1112yes—
261C2×M16C2×C4×C1112yes—
262C2×M16C2×C4×C1112yes—
263C2×M16D4×C1112yes—
264C2×M16D4×C1112yes—
265C2×M16D4×C1112yes—
266C2×M16Q8×C1112yes—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8D4×C1112yes—
273#117—21no—
274#117—21no—
275#117—21no—
276#117—21no—
277C2×C4⋊C4—21no—
278C2×C22⋊C4Q8×C1112yes—
279C2×C42—21no—
280#108—28no—
281C2×C11—21no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11#144511yescharacteristic
289C24C2×Q8×C1111yescharacteristic
290C22×C4—22no—
291C22×C4C22×C4×C1111yescharacteristic
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C2×D4×C1111yescharacteristic
295C22×C4C2×D4×C1111yescharacteristic
296C22×C4C2×Q8×C1111yescharacteristic
297C22×C4C11×#4111yescharacteristic
298C22×C4C11×#4111yescharacteristic
299C22×C4C11×#4111yescharacteristic
300C22×C4C11×#4111yescharacteristic
301C22×C4C11×#4111yescharacteristic
302C22×C4C11×#4111yescharacteristic
303C22×C4C11×#4111yescharacteristic
304C22×C4C11×#4111yescharacteristic
305M16—22no—
306M16—22no—
307M16—22no—
308M16—22no—
309M16—22no—
310M16—22no—
311M16—22no—
312M16—22no—
313M16—22no—
314M16—22no—
315M16—22no—
316M16—22no—
317M16—22no—
318M16—22no—
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16—41no—
327M16—41no—
328M16—41no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8C11×C22⋊C414yes—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C42—41no—
352C42—41no—
353C11#1136311yescharacteristic, direct product factor, Sylow
354C23—81no—
355C23C4×Q8×C1111yescharacteristic
356C23C11×C22⋊Q811yescharacteristic
357C23C11×C22⋊Q811yescharacteristic
358C23C11×C22⋊Q811yescharacteristic
359C23C11×#12511yescharacteristic
360C23C11×#12511yescharacteristic
361C23C11×C4⋊Q811yescharacteristic
362C2×C4—42no—
363C2×C4—82no—
364C2×C4C2×C11×C22⋊C411yescharacteristic
365C2×C4C11×#11711yescharacteristic
366C2×C4C11×#11711yescharacteristic
367C2×C4C4×D4×C1111yescharacteristic
368C2×C4C4×D4×C1111yescharacteristic
369C2×C4C4×Q8×C1111yescharacteristic
370C2×C4C11×#12111yescharacteristic
371C2×C4C11×#12111yescharacteristic
372C2×C4C11×C22⋊Q811yescharacteristic
373C2×C4C11×C22⋊Q811yescharacteristic
374C2×C4C11×C22⋊Q811yescharacteristic
375C2×C4C11×#12311yescharacteristic
376C2×C4C11×#12311yescharacteristic
377C2×C4C11×#12311yescharacteristic
378C2×C4C11×#12311yescharacteristic
379C2×C4C11×#12311yescharacteristic
380C2×C4C11×#12311yescharacteristic
381C2×C4C11×#12311yescharacteristic
382C2×C4C11×#12311yescharacteristic
383C2×C4C11×#12411yescharacteristic
384C2×C4C11×#12411yescharacteristic
385C2×C4C11×#12511yescharacteristic
386C2×C4C11×#12511yescharacteristic
387C2×C4C11×#12611yescharacteristic
388C2×C4C11×#12611yescharacteristic
389C2×C4C11×#12611yescharacteristic
390C2×C4C11×#12611yescharacteristic
391C2×C4C11×#12711yescharacteristic
392C8—24no—
393C8—42no—
394C8—42no—
395C8—42no—
396C8—42no—
397C8—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22C11×#38711yescharacteristic
406C22C11×#38711yescharacteristic
407C22C11×#39111yescharacteristic
408C22C11×#39811yescharacteristic
409C22C11×#39811yescharacteristic
410C22C11×#39911yescharacteristic
411C22C11×#40011yescharacteristic
412C4—82no—
413C4C11×#38111yescharacteristic
414C4C11×#38711yescharacteristic
415C4C11×#38711yescharacteristic
416C4C11×#39011yescharacteristic
417C4C11×#39711yescharacteristic
418C4C11×#39711yescharacteristic
419C4C11×#39911yescharacteristic
420C4C11×#40011yescharacteristic
421C2—21no—
422C2—21no—
423C2—21no—
424C2—21no—
425C2—21no—
426C2—21no—
427C2—21no—
428C2C11×#144511yescharacteristic
subgroupG/H
centerC4×C11#397
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC2×C11#1445
prime radicalC24×C11C2×Q8
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
16. C11×#430C4semidirect
75. #11363C11direct (N × H)
199. #430C4×C11semidirect
353. C11#11363direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4302
C2×C11×#3442
C11×#17422
C11×#17382
C2×C11×#3382
#1136311