Finite Group Databasebeta

← C2×C11×#1930 #14598266

Subgroups — C2×C11×#1930 #14598266

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic
2C2×C11×#419C211yesmaximal, characteristic
3C22×C11×#103C211yesmaximal, characteristic
4C22×C11×#101C211yesmaximal, characteristic
5C2×C11×#405C211yesmaximal, characteristic
6C11×#1930C218yesmaximal, direct product factor
7C2×C11×#343C211yesmaximal, characteristic
8C2×C11×#341C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C11×#428—22no—
17C11×#428C2214yes—
18C2×C11×#107—21no—
19C2×C11×#106—21no—
20C11×#419—22no—
21C11×#419C2214yes—
22C2×C11×#103—21no—
23C2×C11×#103—21no—
24C2×C11×#103—22no—
25C2×C11×#103—21no—
26C2×C11×#103—21no—
27C2×C11×#103C2214yes—
28C2×C11×#101C418yescomplemented
29C2×C11×#101C2214yes—
30C11×#405—22no—
31C11×#405C2214yes—
32C2×C11×#97—21no—
33C2×C4×C8×C11—21no—
34C11×#343C2214yes—
35C11×#341C2214yes—
36C22×Q8×C11—22no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11C2×C414yes—
45C22×Q8×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—21no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C2×C11×M16C2×C414yes—
57C2×C11×M16C2×C414yes—
58C2×C11×M16C2312yes—
59C2×C11×M16C2312yes—
60C2×C11×M16C2312yes—
61C22×C8×C11—21no—
62C22×C8×C11—21no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—21no—
66C22×C8×C11D411yescharacteristic
67C22×C8×C11D411yescharacteristic
68C22×C8×C11D412yes—
69C22×C8×C11C2312yes—
70C11×#117—21no—
71C11×#117—21no—
72C11×#117D412yes—
73C11×#117C2312yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C11×#107—24no—
85C11×#106—24no—
86C11×#103—24no—
87C11×#103—24no—
88C11×#103—24no—
89C11×#103—24no—
90C11×#101C2×C4116yescomplemented
91C11×#97—24no—
92C4×C8×C11—24no—
93C2×#1930C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11#4111yescharacteristic
95C2×Q8×C11—24no—
96C2×Q8×C11—22no—
97C2×Q8×C11—24no—
98C2×Q8×C11—24no—
99C2×Q8×C11—24no—
100C2×Q8×C11—24no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—41no—
106C2×Q8×C11—41no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C2×Q8×C11C22×C414yes—
113C22×C4×C11—24no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11—42no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—82no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C11×M16—24no—
135C11×M16—24no—
136C11×M16—22no—
137C11×M16—22no—
138C11×M16—22no—
139C11×M16—22no—
140C11×M16—42no—
141C11×M16C22×C414yes—
142C11×M16C22×C414yes—
143C2×C8×C11—24no—
144C2×C8×C11—24no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—24no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—42no—
154C2×C8×C11C2×D412yes—
155C2×C8×C11C2×D412yes—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C42×C11—22no—
167C42×C11—22no—
168C2×#428C2×C1111yescharacteristic
169C2×#419C2×C1111yescharacteristic
170C22×#103C2×C1111yescharacteristic
171C22×#101C2×C1111yescharacteristic
172C2×#405C2×C1111yescharacteristic
173#1930C2×C1118yesdirect product factor
174C2×#343C2×C1111yescharacteristic
175C2×#341C2×C1111yescharacteristic
176C23×C11—22no—
177C23×C11—22no—
178C23×C11#11712yes—
179C23×C11#12111yescharacteristic
180C23×C11#12111yescharacteristic
181C23×C11#12612yes—
182C23×C11C2×#4111yescharacteristic
183Q8×C11—24no—
184Q8×C11—24no—
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—44no—
188Q8×C11—44no—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—44no—
195C2×C4×C11—44no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—82no—
200C2×C4×C11—82no—
201C2×C4×C11—82no—
202C2×C4×C11#11712yes—
203C2×C4×C11C4×D412yes—
204C2×C4×C11C4×D412yes—
205C2×C4×C11C4×D412yes—
206C2×C4×C11C4×D412yes—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12312yes—
210C2×C4×C11#12312yes—
211C2×C4×C11#12412yes—
212C2×C4×C11#12412yes—
213C2×C4×C11#12612yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C8×C11—24no—
221C8×C11—24no—
222C8×C11—22no—
223C8×C11—22no—
224C8×C11—42no—
225C23×Q8C22×C1111yescharacteristic
226C22×M16C22×C1111yescharacteristic
227C22×M16C22×C1111yescharacteristic
228C22×M16C22×C1111yescharacteristic
229C23×C8C22×C1111yescharacteristic
230C2×#117C22×C1111yescharacteristic
231C22×C4⋊C4C22×C1111yescharacteristic
232#428—22no—
233#428C22×C1114yes—
234C2×#107—21no—
235C2×#106—21no—
236#419—22no—
237#419C22×C1114yes—
238C2×#103—21no—
239C2×#103—21no—
240C2×#103—22no—
241C2×#103—21no—
242C2×#103—21no—
243C2×#103C22×C1114yes—
244C2×#101C4×C1118yescomplemented
245C2×#101C22×C1114yes—
246#405—22no—
247#405C22×C1114yes—
248C2×#97—21no—
249C2×C4×C8—21no—
250#343C22×C1114yes—
251#341C22×C1114yes—
252C22×C11—24no—
253C22×C11—24no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11#38812yes—
259C22×C11#38812yes—
260C22×C11#47112yes—
261C22×C11#47312yes—
262C22×C11C2×#11711yescharacteristic
263C22×C11C2×#12111yescharacteristic
264C22×C11C2×#12611yescharacteristic
265C4×C11—44no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—82no—
269C4×C11#38812yes—
270C4×C11#38812yes—
271C4×C11C2×C4×D411yescharacteristic
272C4×C11C2×C4×D411yescharacteristic
273C4×C11C2×#12311yescharacteristic
274C4×C11C2×#12411yescharacteristic
275C22×Q8—22no—
276C22×Q8—21no—
277C22×Q8—21no—
278C22×Q8—21no—
279C22×Q8—21no—
280C22×Q8—21no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8C2×C4×C1114yes—
284C22×Q8C23×C1112yes—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4C23×C1111yescharacteristic
288C2×M16—21no—
289C2×M16—21no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—21no—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16C2×C4×C1114yes—
296C2×M16C2×C4×C1114yes—
297C2×M16C23×C1112yes—
298C2×M16C23×C1112yes—
299C2×M16C23×C1112yes—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—21no—
305C22×C8D4×C1111yescharacteristic
306C22×C8D4×C1111yescharacteristic
307C22×C8D4×C1112yes—
308C22×C8C23×C1112yes—
309#117—21no—
310#117—21no—
311#117D4×C1112yes—
312#117C23×C1112yes—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4D4×C1111yescharacteristic
319C2×C4⋊C4D4×C1111yescharacteristic
320C2×C4⋊C4C23×C1112yes—
321C2×C22⋊C4—21no—
322C2×C42—21no—
323#107—24no—
324#106—24no—
325#103—24no—
326#103—24no—
327#103—24no—
328#103—24no—
329#101C2×C4×C11116yescomplemented
330#97—24no—
331C4×C8—24no—
332C2×C11—21no—
333C2×C11—21no—
334C2×C11—22no—
335C2×C11#193014yesdirect product factor
336C2×C11C2×#38811yescharacteristic
337C2×C11C2×#47111yescharacteristic
338C2×C11C2×#47311yescharacteristic
339C24C11×#4111yescharacteristic
340C2×Q8—24no—
341C2×Q8—22no—
342C2×Q8—24no—
343C2×Q8—24no—
344C2×Q8—24no—
345C2×Q8—24no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—42no—
353C2×Q8—42no—
354C2×Q8—42no—
355C2×Q8—42no—
356C2×Q8—42no—
357C2×Q8C22×C4×C1114yes—
358C22×C4—24no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—42no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—82no—
369C22×C4C22×C4×C1112yes—
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1111yescharacteristic
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C11×#4111yescharacteristic
375C22×C4C11×#4112yes—
376C22×C4C11×#4112yes—
377C22×C4C11×#4112yes—
378C22×C4C24×C1111yescharacteristic
379M16—24no—
380M16—24no—
381M16—22no—
382M16—22no—
383M16—22no—
384M16—22no—
385M16—42no—
386M16C22×C4×C1114yes—
387M16C22×C4×C1114yes—
388C2×C8—24no—
389C2×C8—24no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—24no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—42no—
399C2×C8C2×D4×C1112yes—
400C2×C8C2×D4×C1112yes—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4C2×D4×C1112yes—
408C4⋊C4C2×D4×C1112yes—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C42—22no—
412C42—22no—
413C11C2×#193011yescharacteristic, direct product factor, Sylow
414C23—22no—
415C23—22no—
416C23C11×#11712yes—
417C23C11×#12111yescharacteristic
418C23C11×#12111yescharacteristic
419C23C11×#12612yes—
420C23C2×C11×#4111yescharacteristic
421Q8—24no—
422Q8—24no—
423Q8—42no—
424Q8—44no—
425Q8—44no—
426Q8—42no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4C11×#11712yes—
441C2×C4C4×D4×C1112yes—
442C2×C4C4×D4×C1112yes—
443C2×C4C4×D4×C1112yes—
444C2×C4C4×D4×C1112yes—
445C2×C4C11×#12111yescharacteristic
446C2×C4C11×#12111yescharacteristic
447C2×C4C11×#12312yes—
448C2×C4C11×#12312yes—
449C2×C4C11×#12412yes—
450C2×C4C11×#12412yes—
451C2×C4C11×#12612yes—
452C2×C4C23×C4×C1111yescharacteristic
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C22×D4×C1111yescharacteristic
455C2×C4C2×C11×#4111yescharacteristic
456C2×C4C2×C11×#4111yescharacteristic
457C2×C4C2×C11×#4111yescharacteristic
458C8—24no—
459C8—24no—
460C8—22no—
461C8—22no—
462C8—42no—
463C22—24no—
464C22—24no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22C11×#38812yes—
470C22C11×#38812yes—
471C22C11×#47112yes—
472C22C11×#47312yes—
473C22C2×C11×#11711yescharacteristic
474C22C2×C11×#12111yescharacteristic
475C22C2×C11×#12611yescharacteristic
476C4—44no—
477C4—42no—
478C4—42no—
479C4—82no—
480C4C11×#38812yes—
481C4C11×#38812yes—
482C4C2×C4×D4×C1111yescharacteristic
483C4C2×C4×D4×C1111yescharacteristic
484C4C2×C11×#12311yescharacteristic
485C4C2×C11×#12411yescharacteristic
486C2—21no—
487C2—22no—
488C2—21no—
489C2C11×#193014yesdirect product factor
490C2C2×C11×#38811yescharacteristic
491C2C2×C11×#47111yescharacteristic
492C2C2×C11×#47311yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11#41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
6. C11×#1930C2direct (N × H)
28. C2×C11×#101C4semidirect
90. C11×#101C2×C4semidirect
93. C2×#1930C11direct (N × H)
173. #1930C2×C11direct (N × H)
244. C2×#101C4×C11semidirect
329. #101C2×C4×C11semidirect
335. C2×C11#1930direct (N × H)
413. C11C2×#1930direct (N × H)
489. C2C11×#1930direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#4192
C22×C11×#1032
C22×C11×#1012
C2×C11×#4052
C11×#19302
C2×C11×#3432
C2×C11×#3412
C2×#193011